diff options
| -rw-r--r-- | include/libdecnumber/dconfig.h | 52 | ||||
| -rw-r--r-- | include/libdecnumber/decContext.h | 258 | ||||
| -rw-r--r-- | include/libdecnumber/decDPD.h | 1215 | ||||
| -rw-r--r-- | include/libdecnumber/decNumber.h | 200 | ||||
| -rw-r--r-- | include/libdecnumber/decNumberLocal.h | 667 | ||||
| -rw-r--r-- | include/libdecnumber/dpd/decimal128.h | 101 | ||||
| -rw-r--r-- | include/libdecnumber/dpd/decimal128Local.h | 47 | ||||
| -rw-r--r-- | include/libdecnumber/dpd/decimal32.h | 99 | ||||
| -rw-r--r-- | include/libdecnumber/dpd/decimal64.h | 101 | ||||
| -rw-r--r-- | libdecnumber/decContext.c | 431 | ||||
| -rw-r--r-- | libdecnumber/decNumber.c | 8122 | ||||
| -rw-r--r-- | libdecnumber/dpd/decimal128.c | 566 | ||||
| -rw-r--r-- | libdecnumber/dpd/decimal128Local.h | 42 | ||||
| -rw-r--r-- | libdecnumber/dpd/decimal32.c | 491 | ||||
| -rw-r--r-- | libdecnumber/dpd/decimal64.c | 852 |
15 files changed, 13244 insertions, 0 deletions
diff --git a/include/libdecnumber/dconfig.h b/include/libdecnumber/dconfig.h new file mode 100644 index 0000000000..ffbad255ce --- /dev/null +++ b/include/libdecnumber/dconfig.h @@ -0,0 +1,52 @@ +/* Configure decNumber for either host or target. + Copyright (C) 2008 Free Software Foundation, Inc. + + This file is part of GCC. + + GCC is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation; either version 2, or (at your option) any later + version. + + In addition to the permissions in the GNU General Public License, + the Free Software Foundation gives you unlimited permission to link + the compiled version of this file into combinations with other + programs, and to distribute those combinations without any + restriction coming from the use of this file. (The General Public + License restrictions do apply in other respects; for example, they + cover modification of the file, and distribution when not linked + into a combine executable.) + + GCC is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or + FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License + along with GCC; see the file COPYING. If not, write to the Free + Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA + 02110-1301, USA. */ + +#ifdef IN_LIBGCC2 + +#include "tconfig.h" +#include "coretypes.h" +#include "tm.h" + +#ifndef LIBGCC2_WORDS_BIG_ENDIAN +#define LIBGCC2_WORDS_BIG_ENDIAN WORDS_BIG_ENDIAN +#endif + +#ifndef LIBGCC2_FLOAT_WORDS_BIG_ENDIAN +#define LIBGCC2_FLOAT_WORDS_BIG_ENDIAN LIBGCC2_WORDS_BIG_ENDIAN +#endif + +#if LIBGCC2_FLOAT_WORDS_BIG_ENDIAN +#define WORDS_BIGENDIAN 1 +#endif + +#else + +#include "config.h" + +#endif diff --git a/include/libdecnumber/decContext.h b/include/libdecnumber/decContext.h new file mode 100644 index 0000000000..f80d03c50c --- /dev/null +++ b/include/libdecnumber/decContext.h @@ -0,0 +1,258 @@ +/* Decimal context header module for the decNumber C Library. + Copyright (C) 2005, 2007 Free Software Foundation, Inc. + Contributed by IBM Corporation. Author Mike Cowlishaw. + + This file is part of GCC. + + GCC is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation; either version 2, or (at your option) any later + version. + + In addition to the permissions in the GNU General Public License, + the Free Software Foundation gives you unlimited permission to link + the compiled version of this file into combinations with other + programs, and to distribute those combinations without any + restriction coming from the use of this file. (The General Public + License restrictions do apply in other respects; for example, they + cover modification of the file, and distribution when not linked + into a combine executable.) + + GCC is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or + FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License + along with GCC; see the file COPYING. If not, write to the Free + Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA + 02110-1301, USA. */ + +/* ------------------------------------------------------------------ */ +/* Decimal Context module header */ +/* ------------------------------------------------------------------ */ +/* */ +/* Context variables must always have valid values: */ +/* */ +/* status -- [any bits may be cleared, but not set, by user] */ +/* round -- must be one of the enumerated rounding modes */ +/* */ +/* The following variables are implied for fixed size formats (i.e., */ +/* they are ignored) but should still be set correctly in case used */ +/* with decNumber functions: */ +/* */ +/* clamp -- must be either 0 or 1 */ +/* digits -- must be in the range 1 through 999999999 */ +/* emax -- must be in the range 0 through 999999999 */ +/* emin -- must be in the range 0 through -999999999 */ +/* extended -- must be either 0 or 1 [present only if DECSUBSET] */ +/* traps -- only defined bits may be set */ +/* */ +/* ------------------------------------------------------------------ */ + +#if !defined(DECCONTEXT) + #define DECCONTEXT + #define DECCNAME "decContext" /* Short name */ + #define DECCFULLNAME "Decimal Context Descriptor" /* Verbose name */ + #define DECCAUTHOR "Mike Cowlishaw" /* Who to blame */ + + #include "gstdint.h" /* C99 standard integers */ + #include <stdio.h> /* for printf, etc. */ + #include <signal.h> /* for traps */ + + /* Extended flags setting -- set this to 0 to use only IEEE flags */ + #define DECEXTFLAG 1 /* 1=enable extended flags */ + + /* Conditional code flag -- set this to 0 for best performance */ + #define DECSUBSET 0 /* 1=enable subset arithmetic */ + + /* Context for operations, with associated constants */ + enum rounding { + DEC_ROUND_CEILING, /* round towards +infinity */ + DEC_ROUND_UP, /* round away from 0 */ + DEC_ROUND_HALF_UP, /* 0.5 rounds up */ + DEC_ROUND_HALF_EVEN, /* 0.5 rounds to nearest even */ + DEC_ROUND_HALF_DOWN, /* 0.5 rounds down */ + DEC_ROUND_DOWN, /* round towards 0 (truncate) */ + DEC_ROUND_FLOOR, /* round towards -infinity */ + DEC_ROUND_05UP, /* round for reround */ + DEC_ROUND_MAX /* enum must be less than this */ + }; + #define DEC_ROUND_DEFAULT DEC_ROUND_HALF_EVEN; + + typedef struct { + int32_t digits; /* working precision */ + int32_t emax; /* maximum positive exponent */ + int32_t emin; /* minimum negative exponent */ + enum rounding round; /* rounding mode */ + uint32_t traps; /* trap-enabler flags */ + uint32_t status; /* status flags */ + uint8_t clamp; /* flag: apply IEEE exponent clamp */ + #if DECSUBSET + uint8_t extended; /* flag: special-values allowed */ + #endif + } decContext; + + /* Maxima and Minima for context settings */ + #define DEC_MAX_DIGITS 999999999 + #define DEC_MIN_DIGITS 1 + #define DEC_MAX_EMAX 999999999 + #define DEC_MIN_EMAX 0 + #define DEC_MAX_EMIN 0 + #define DEC_MIN_EMIN -999999999 + #define DEC_MAX_MATH 999999 /* max emax, etc., for math funcs. */ + + /* Classifications for decimal numbers, aligned with 754r (note */ + /* that 'normal' and 'subnormal' are meaningful only with a */ + /* decContext or a fixed size format). */ + enum decClass { + DEC_CLASS_SNAN, + DEC_CLASS_QNAN, + DEC_CLASS_NEG_INF, + DEC_CLASS_NEG_NORMAL, + DEC_CLASS_NEG_SUBNORMAL, + DEC_CLASS_NEG_ZERO, + DEC_CLASS_POS_ZERO, + DEC_CLASS_POS_SUBNORMAL, + DEC_CLASS_POS_NORMAL, + DEC_CLASS_POS_INF + }; + /* Strings for the decClasses */ + #define DEC_ClassString_SN "sNaN" + #define DEC_ClassString_QN "NaN" + #define DEC_ClassString_NI "-Infinity" + #define DEC_ClassString_NN "-Normal" + #define DEC_ClassString_NS "-Subnormal" + #define DEC_ClassString_NZ "-Zero" + #define DEC_ClassString_PZ "+Zero" + #define DEC_ClassString_PS "+Subnormal" + #define DEC_ClassString_PN "+Normal" + #define DEC_ClassString_PI "+Infinity" + #define DEC_ClassString_UN "Invalid" + + /* Trap-enabler and Status flags (exceptional conditions), and */ + /* their names. The top byte is reserved for internal use */ + #if DECEXTFLAG + /* Extended flags */ + #define DEC_Conversion_syntax 0x00000001 + #define DEC_Division_by_zero 0x00000002 + #define DEC_Division_impossible 0x00000004 + #define DEC_Division_undefined 0x00000008 + #define DEC_Insufficient_storage 0x00000010 /* [when malloc fails] */ + #define DEC_Inexact 0x00000020 + #define DEC_Invalid_context 0x00000040 + #define DEC_Invalid_operation 0x00000080 + #if DECSUBSET + #define DEC_Lost_digits 0x00000100 + #endif + #define DEC_Overflow 0x00000200 + #define DEC_Clamped 0x00000400 + #define DEC_Rounded 0x00000800 + #define DEC_Subnormal 0x00001000 + #define DEC_Underflow 0x00002000 + #else + /* IEEE flags only */ + #define DEC_Conversion_syntax 0x00000010 + #define DEC_Division_by_zero 0x00000002 + #define DEC_Division_impossible 0x00000010 + #define DEC_Division_undefined 0x00000010 + #define DEC_Insufficient_storage 0x00000010 /* [when malloc fails] */ + #define DEC_Inexact 0x00000001 + #define DEC_Invalid_context 0x00000010 + #define DEC_Invalid_operation 0x00000010 + #if DECSUBSET + #define DEC_Lost_digits 0x00000000 + #endif + #define DEC_Overflow 0x00000008 + #define DEC_Clamped 0x00000000 + #define DEC_Rounded 0x00000000 + #define DEC_Subnormal 0x00000000 + #define DEC_Underflow 0x00000004 + #endif + + /* IEEE 854 groupings for the flags */ + /* [DEC_Clamped, DEC_Lost_digits, DEC_Rounded, and DEC_Subnormal */ + /* are not in IEEE 854] */ + #define DEC_IEEE_854_Division_by_zero (DEC_Division_by_zero) + #if DECSUBSET + #define DEC_IEEE_854_Inexact (DEC_Inexact | DEC_Lost_digits) + #else + #define DEC_IEEE_854_Inexact (DEC_Inexact) + #endif + #define DEC_IEEE_854_Invalid_operation (DEC_Conversion_syntax | \ + DEC_Division_impossible | \ + DEC_Division_undefined | \ + DEC_Insufficient_storage | \ + DEC_Invalid_context | \ + DEC_Invalid_operation) + #define DEC_IEEE_854_Overflow (DEC_Overflow) + #define DEC_IEEE_854_Underflow (DEC_Underflow) + + /* flags which are normally errors (result is qNaN, infinite, or 0) */ + #define DEC_Errors (DEC_IEEE_854_Division_by_zero | \ + DEC_IEEE_854_Invalid_operation | \ + DEC_IEEE_854_Overflow | DEC_IEEE_854_Underflow) + /* flags which cause a result to become qNaN */ + #define DEC_NaNs DEC_IEEE_854_Invalid_operation + + /* flags which are normally for information only (finite results) */ + #if DECSUBSET + #define DEC_Information (DEC_Clamped | DEC_Rounded | DEC_Inexact \ + | DEC_Lost_digits) + #else + #define DEC_Information (DEC_Clamped | DEC_Rounded | DEC_Inexact) + #endif + + /* Name strings for the exceptional conditions */ + #define DEC_Condition_CS "Conversion syntax" + #define DEC_Condition_DZ "Division by zero" + #define DEC_Condition_DI "Division impossible" + #define DEC_Condition_DU "Division undefined" + #define DEC_Condition_IE "Inexact" + #define DEC_Condition_IS "Insufficient storage" + #define DEC_Condition_IC "Invalid context" + #define DEC_Condition_IO "Invalid operation" + #if DECSUBSET + #define DEC_Condition_LD "Lost digits" + #endif + #define DEC_Condition_OV "Overflow" + #define DEC_Condition_PA "Clamped" + #define DEC_Condition_RO "Rounded" + #define DEC_Condition_SU "Subnormal" + #define DEC_Condition_UN "Underflow" + #define DEC_Condition_ZE "No status" + #define DEC_Condition_MU "Multiple status" + #define DEC_Condition_Length 21 /* length of the longest string, */ + /* including terminator */ + + /* Initialization descriptors, used by decContextDefault */ + #define DEC_INIT_BASE 0 + #define DEC_INIT_DECIMAL32 32 + #define DEC_INIT_DECIMAL64 64 + #define DEC_INIT_DECIMAL128 128 + /* Synonyms */ + #define DEC_INIT_DECSINGLE DEC_INIT_DECIMAL32 + #define DEC_INIT_DECDOUBLE DEC_INIT_DECIMAL64 + #define DEC_INIT_DECQUAD DEC_INIT_DECIMAL128 + + /* decContext routines */ + + #include "decContextSymbols.h" + + extern decContext * decContextClearStatus(decContext *, uint32_t); + extern decContext * decContextDefault(decContext *, int32_t); + extern enum rounding decContextGetRounding(decContext *); + extern uint32_t decContextGetStatus(decContext *); + extern decContext * decContextRestoreStatus(decContext *, uint32_t, uint32_t); + extern uint32_t decContextSaveStatus(decContext *, uint32_t); + extern decContext * decContextSetRounding(decContext *, enum rounding); + extern decContext * decContextSetStatus(decContext *, uint32_t); + extern decContext * decContextSetStatusFromString(decContext *, const char *); + extern decContext * decContextSetStatusFromStringQuiet(decContext *, const char *); + extern decContext * decContextSetStatusQuiet(decContext *, uint32_t); + extern const char * decContextStatusToString(const decContext *); + extern uint32_t decContextTestSavedStatus(uint32_t, uint32_t); + extern uint32_t decContextTestStatus(decContext *, uint32_t); + extern decContext * decContextZeroStatus(decContext *); + +#endif diff --git a/include/libdecnumber/decDPD.h b/include/libdecnumber/decDPD.h new file mode 100644 index 0000000000..3cc1d63413 --- /dev/null +++ b/include/libdecnumber/decDPD.h @@ -0,0 +1,1215 @@ +/* Conversion lookup tables for the decNumber C Library. + Copyright (C) 2007 Free Software Foundation, Inc. + Contributed by IBM Corporation. Author Mike Cowlishaw. + + This file is part of GCC. + + GCC is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation; either version 2, or (at your option) any later + version. + + In addition to the permissions in the GNU General Public License, + the Free Software Foundation gives you unlimited permission to link + the compiled version of this file into combinations with other + programs, and to distribute those combinations without any + restriction coming from the use of this file. (The General Public + License restrictions do apply in other respects; for example, they + cover modification of the file, and distribution when not linked + into a combine executable.) + + GCC is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or + FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License + along with GCC; see the file COPYING. If not, write to the Free + Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA + 02110-1301, USA. */ + +/* ------------------------------------------------------------------------ */ +/* Binary Coded Decimal and Densely Packed Decimal conversion lookup tables */ +/* [Automatically generated -- do not edit. 2007.05.05] */ +/* ------------------------------------------------------------------------ */ +/* ------------------------------------------------------------------------ */ +/* For details, see: http://www2.hursley.ibm.com/decimal/DPDecimal.html */ + +#include "decDPDSymbols.h" + +/* This include file defines several DPD and BCD conversion tables: */ +/* */ +/* uint16_t BCD2DPD[2458]; -- BCD -> DPD (0x999 => 2457) */ +/* uint16_t BIN2DPD[1000]; -- Bin -> DPD (999 => 2457) */ +/* uint8_t BIN2CHAR[4001]; -- Bin -> CHAR (999 => '\3' '9' '9' '9') */ +/* uint8_t BIN2BCD8[4000]; -- Bin -> bytes (999 => 9 9 9 3) */ +/* uint16_t DPD2BCD[1024]; -- DPD -> BCD (0x3FF => 0x999) */ +/* uint16_t DPD2BIN[1024]; -- DPD -> BIN (0x3FF => 999) */ +/* uint32_t DPD2BINK[1024]; -- DPD -> BIN * 1000 (0x3FF => 999000) */ +/* uint32_t DPD2BINM[1024]; -- DPD -> BIN * 1E+6 (0x3FF => 999000000) */ +/* uint8_t DPD2BCD8[4096]; -- DPD -> bytes (x3FF => 9 9 9 3) */ +/* */ +/* In all cases the result (10 bits or 12 bits, or binary) is right-aligned */ +/* in the table entry. BIN2CHAR entries are a single byte length (0 for */ +/* value 0) followed by three digit characters; a trailing terminator is */ +/* included to allow 4-char moves always. BIN2BCD8 and DPD2BCD8 entries */ +/* are similar with the three BCD8 digits followed by a one-byte length */ +/* (again, length=0 for value 0). */ +/* */ +/* To use a table, its name, prefixed with DEC_, must be defined with a */ +/* value of 1 before this header file is included. For example: */ +/* #define DEC_BCD2DPD 1 */ +/* This mechanism allows software to only include tables that are needed. */ +/* ------------------------------------------------------------------------ */ + +#if defined(DEC_BCD2DPD) && DEC_BCD2DPD==1 && !defined(DECBCD2DPD) +#define DECBCD2DPD + +const uint16_t BCD2DPD[2458]={ 0, 1, 2, 3, 4, 5, 6, 7, + 8, 9, 0, 0, 0, 0, 0, 0, 16, 17, 18, 19, 20, + 21, 22, 23, 24, 25, 0, 0, 0, 0, 0, 0, 32, 33, + 34, 35, 36, 37, 38, 39, 40, 41, 0, 0, 0, 0, 0, + 0, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 0, 0, + 0, 0, 0, 0, 64, 65, 66, 67, 68, 69, 70, 71, 72, + 73, 0, 0, 0, 0, 0, 0, 80, 81, 82, 83, 84, 85, + 86, 87, 88, 89, 0, 0, 0, 0, 0, 0, 96, 97, 98, + 99, 100, 101, 102, 103, 104, 105, 0, 0, 0, 0, 0, 0, + 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 0, 0, 0, + 0, 0, 0, 10, 11, 42, 43, 74, 75, 106, 107, 78, 79, + 0, 0, 0, 0, 0, 0, 26, 27, 58, 59, 90, 91, 122, + 123, 94, 95, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 0, 0, + 0, 0, 0, 0, 144, 145, 146, 147, 148, 149, 150, 151, 152, + 153, 0, 0, 0, 0, 0, 0, 160, 161, 162, 163, 164, 165, + 166, 167, 168, 169, 0, 0, 0, 0, 0, 0, 176, 177, 178, + 179, 180, 181, 182, 183, 184, 185, 0, 0, 0, 0, 0, 0, + 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 0, 0, 0, + 0, 0, 0, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, + 0, 0, 0, 0, 0, 0, 224, 225, 226, 227, 228, 229, 230, + 231, 232, 233, 0, 0, 0, 0, 0, 0, 240, 241, 242, 243, + 244, 245, 246, 247, 248, 249, 0, 0, 0, 0, 0, 0, 138, + 139, 170, 171, 202, 203, 234, 235, 206, 207, 0, 0, 0, 0, + 0, 0, 154, 155, 186, 187, 218, 219, 250, 251, 222, 223, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 256, 257, 258, + 259, 260, 261, 262, 263, 264, 265, 0, 0, 0, 0, 0, 0, + 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 0, 0, 0, + 0, 0, 0, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, + 0, 0, 0, 0, 0, 0, 304, 305, 306, 307, 308, 309, 310, + 311, 312, 313, 0, 0, 0, 0, 0, 0, 320, 321, 322, 323, + 324, 325, 326, 327, 328, 329, 0, 0, 0, 0, 0, 0, 336, + 337, 338, 339, 340, 341, 342, 343, 344, 345, 0, 0, 0, 0, + 0, 0, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 0, + 0, 0, 0, 0, 0, 368, 369, 370, 371, 372, 373, 374, 375, + 376, 377, 0, 0, 0, 0, 0, 0, 266, 267, 298, 299, 330, + 331, 362, 363, 334, 335, 0, 0, 0, 0, 0, 0, 282, 283, + 314, 315, 346, 347, 378, 379, 350, 351, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 384, 385, 386, 387, 388, 389, 390, + 391, 392, 393, 0, 0, 0, 0, 0, 0, 400, 401, 402, 403, + 404, 405, 406, 407, 408, 409, 0, 0, 0, 0, 0, 0, 416, + 417, 418, 419, 420, 421, 422, 423, 424, 425, 0, 0, 0, 0, + 0, 0, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 0, + 0, 0, 0, 0, 0, 448, 449, 450, 451, 452, 453, 454, 455, + 456, 457, 0, 0, 0, 0, 0, 0, 464, 465, 466, 467, 468, + 469, 470, 471, 472, 473, 0, 0, 0, 0, 0, 0, 480, 481, + 482, 483, 484, 485, 486, 487, 488, 489, 0, 0, 0, 0, 0, + 0, 496, 497, 498, 499, 500, 501, 502, 503, 504, 505, 0, 0, + 0, 0, 0, 0, 394, 395, 426, 427, 458, 459, 490, 491, 462, + 463, 0, 0, 0, 0, 0, 0, 410, 411, 442, 443, 474, 475, + 506, 507, 478, 479, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 512, 513, 514, 515, 516, 517, 518, 519, 520, 521, 0, + 0, 0, 0, 0, 0, 528, 529, 530, 531, 532, 533, 534, 535, + 536, 537, 0, 0, 0, 0, 0, 0, 544, 545, 546, 547, 548, + 549, 550, 551, 552, 553, 0, 0, 0, 0, 0, 0, 560, 561, + 562, 563, 564, 565, 566, 567, 568, 569, 0, 0, 0, 0, 0, + 0, 576, 577, 578, 579, 580, 581, 582, 583, 584, 585, 0, 0, + 0, 0, 0, 0, 592, 593, 594, 595, 596, 597, 598, 599, 600, + 601, 0, 0, 0, 0, 0, 0, 608, 609, 610, 611, 612, 613, + 614, 615, 616, 617, 0, 0, 0, 0, 0, 0, 624, 625, 626, + 627, 628, 629, 630, 631, 632, 633, 0, 0, 0, 0, 0, 0, + 522, 523, 554, 555, 586, 587, 618, 619, 590, 591, 0, 0, 0, + 0, 0, 0, 538, 539, 570, 571, 602, 603, 634, 635, 606, 607, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 640, 641, + 642, 643, 644, 645, 646, 647, 648, 649, 0, 0, 0, 0, 0, + 0, 656, 657, 658, 659, 660, 661, 662, 663, 664, 665, 0, 0, + 0, 0, 0, 0, 672, 673, 674, 675, 676, 677, 678, 679, 680, + 681, 0, 0, 0, 0, 0, 0, 688, 689, 690, 691, 692, 693, + 694, 695, 696, 697, 0, 0, 0, 0, 0, 0, 704, 705, 706, + 707, 708, 709, 710, 711, 712, 713, 0, 0, 0, 0, 0, 0, + 720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 0, 0, 0, + 0, 0, 0, 736, 737, 738, 739, 740, 741, 742, 743, 744, 745, + 0, 0, 0, 0, 0, 0, 752, 753, 754, 755, 756, 757, 758, + 759, 760, 761, 0, 0, 0, 0, 0, 0, 650, 651, 682, 683, + 714, 715, 746, 747, 718, 719, 0, 0, 0, 0, 0, 0, 666, + 667, 698, 699, 730, 731, 762, 763, 734, 735, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 768, 769, 770, 771, 772, 773, + 774, 775, 776, 777, 0, 0, 0, 0, 0, 0, 784, 785, 786, + 787, 788, 789, 790, 791, 792, 793, 0, 0, 0, 0, 0, 0, + 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 0, 0, 0, + 0, 0, 0, 816, 817, 818, 819, 820, 821, 822, 823, 824, 825, + 0, 0, 0, 0, 0, 0, 832, 833, 834, 835, 836, 837, 838, + 839, 840, 841, 0, 0, 0, 0, 0, 0, 848, 849, 850, 851, + 852, 853, 854, 855, 856, 857, 0, 0, 0, 0, 0, 0, 864, + 865, 866, 867, 868, 869, 870, 871, 872, 873, 0, 0, 0, 0, + 0, 0, 880, 881, 882, 883, 884, 885, 886, 887, 888, 889, 0, + 0, 0, 0, 0, 0, 778, 779, 810, 811, 842, 843, 874, 875, + 846, 847, 0, 0, 0, 0, 0, 0, 794, 795, 826, 827, 858, + 859, 890, 891, 862, 863, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 896, 897, 898, 899, 900, 901, 902, 903, 904, 905, + 0, 0, 0, 0, 0, 0, 912, 913, 914, 915, 916, 917, 918, + 919, 920, 921, 0, 0, 0, 0, 0, 0, 928, 929, 930, 931, + 932, 933, 934, 935, 936, 937, 0, 0, 0, 0, 0, 0, 944, + 945, 946, 947, 948, 949, 950, 951, 952, 953, 0, 0, 0, 0, + 0, 0, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 0, + 0, 0, 0, 0, 0, 976, 977, 978, 979, 980, 981, 982, 983, + 984, 985, 0, 0, 0, 0, 0, 0, 992, 993, 994, 995, 996, + 997, 998, 999, 1000, 1001, 0, 0, 0, 0, 0, 0, 1008, 1009, + 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 0, 0, 0, 0, 0, + 0, 906, 907, 938, 939, 970, 971, 1002, 1003, 974, 975, 0, 0, + 0, 0, 0, 0, 922, 923, 954, 955, 986, 987, 1018, 1019, 990, + 991, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, + 13, 268, 269, 524, 525, 780, 781, 46, 47, 0, 0, 0, 0, + 0, 0, 28, 29, 284, 285, 540, 541, 796, 797, 62, 63, 0, + 0, 0, 0, 0, 0, 44, 45, 300, 301, 556, 557, 812, 813, + 302, 303, 0, 0, 0, 0, 0, 0, 60, 61, 316, 317, 572, + 573, 828, 829, 318, 319, 0, 0, 0, 0, 0, 0, 76, 77, + 332, 333, 588, 589, 844, 845, 558, 559, 0, 0, 0, 0, 0, + 0, 92, 93, 348, 349, 604, 605, 860, 861, 574, 575, 0, 0, + 0, 0, 0, 0, 108, 109, 364, 365, 620, 621, 876, 877, 814, + 815, 0, 0, 0, 0, 0, 0, 124, 125, 380, 381, 636, 637, + 892, 893, 830, 831, 0, 0, 0, 0, 0, 0, 14, 15, 270, + 271, 526, 527, 782, 783, 110, 111, 0, 0, 0, 0, 0, 0, + 30, 31, 286, 287, 542, 543, 798, 799, 126, 127, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 0, 0, 0, 0, 0, 0, 140, 141, 396, 397, 652, + 653, 908, 909, 174, 175, 0, 0, 0, 0, 0, 0, 156, 157, + 412, 413, 668, 669, 924, 925, 190, 191, 0, 0, 0, 0, 0, + 0, 172, 173, 428, 429, 684, 685, 940, 941, 430, 431, 0, 0, + 0, 0, 0, 0, 188, 189, 444, 445, 700, 701, 956, 957, 446, + 447, 0, 0, 0, 0, 0, 0, 204, 205, 460, 461, 716, 717, + 972, 973, 686, 687, 0, 0, 0, 0, 0, 0, 220, 221, 476, + 477, 732, 733, 988, 989, 702, 703, 0, 0, 0, 0, 0, 0, + 236, 237, 492, 493, 748, 749, 1004, 1005, 942, 943, 0, 0, 0, + 0, 0, 0, 252, 253, 508, 509, 764, 765, 1020, 1021, 958, 959, + 0, 0, 0, 0, 0, 0, 142, 143, 398, 399, 654, 655, 910, + 911, 238, 239, 0, 0, 0, 0, 0, 0, 158, 159, 414, 415, + 670, 671, 926, 927, 254, 255}; +#endif + +#if defined(DEC_DPD2BCD) && DEC_DPD2BCD==1 && !defined(DECDPD2BCD) +#define DECDPD2BCD + +const uint16_t DPD2BCD[1024]={ 0, 1, 2, 3, 4, 5, 6, 7, + 8, 9, 128, 129, 2048, 2049, 2176, 2177, 16, 17, 18, 19, 20, + 21, 22, 23, 24, 25, 144, 145, 2064, 2065, 2192, 2193, 32, 33, + 34, 35, 36, 37, 38, 39, 40, 41, 130, 131, 2080, 2081, 2056, + 2057, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 146, 147, + 2096, 2097, 2072, 2073, 64, 65, 66, 67, 68, 69, 70, 71, 72, + 73, 132, 133, 2112, 2113, 136, 137, 80, 81, 82, 83, 84, 85, + 86, 87, 88, 89, 148, 149, 2128, 2129, 152, 153, 96, 97, 98, + 99, 100, 101, 102, 103, 104, 105, 134, 135, 2144, 2145, 2184, 2185, + 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 150, 151, 2160, + 2161, 2200, 2201, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, + 384, 385, 2304, 2305, 2432, 2433, 272, 273, 274, 275, 276, 277, 278, + 279, 280, 281, 400, 401, 2320, 2321, 2448, 2449, 288, 289, 290, 291, + 292, 293, 294, 295, 296, 297, 386, 387, 2336, 2337, 2312, 2313, 304, + 305, 306, 307, 308, 309, 310, 311, 312, 313, 402, 403, 2352, 2353, + 2328, 2329, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 388, + 389, 2368, 2369, 392, 393, 336, 337, 338, 339, 340, 341, 342, 343, + 344, 345, 404, 405, 2384, 2385, 408, 409, 352, 353, 354, 355, 356, + 357, 358, 359, 360, 361, 390, 391, 2400, 2401, 2440, 2441, 368, 369, + 370, 371, 372, 373, 374, 375, 376, 377, 406, 407, 2416, 2417, 2456, + 2457, 512, 513, 514, 515, 516, 517, 518, 519, 520, 521, 640, 641, + 2050, 2051, 2178, 2179, 528, 529, 530, 531, 532, 533, 534, 535, 536, + 537, 656, 657, 2066, 2067, 2194, 2195, 544, 545, 546, 547, 548, 549, + 550, 551, 552, 553, 642, 643, 2082, 2083, 2088, 2089, 560, 561, 562, + 563, 564, 565, 566, 567, 568, 569, 658, 659, 2098, 2099, 2104, 2105, + 576, 577, 578, 579, 580, 581, 582, 583, 584, 585, 644, 645, 2114, + 2115, 648, 649, 592, 593, 594, 595, 596, 597, 598, 599, 600, 601, + 660, 661, 2130, 2131, 664, 665, 608, 609, 610, 611, 612, 613, 614, + 615, 616, 617, 646, 647, 2146, 2147, 2184, 2185, 624, 625, 626, 627, + 628, 629, 630, 631, 632, 633, 662, 663, 2162, 2163, 2200, 2201, 768, + 769, 770, 771, 772, 773, 774, 775, 776, 777, 896, 897, 2306, 2307, + 2434, 2435, 784, 785, 786, 787, 788, 789, 790, 791, 792, 793, 912, + 913, 2322, 2323, 2450, 2451, 800, 801, 802, 803, 804, 805, 806, 807, + 808, 809, 898, 899, 2338, 2339, 2344, 2345, 816, 817, 818, 819, 820, + 821, 822, 823, 824, 825, 914, 915, 2354, 2355, 2360, 2361, 832, 833, + 834, 835, 836, 837, 838, 839, 840, 841, 900, 901, 2370, 2371, 904, + 905, 848, 849, 850, 851, 852, 853, 854, 855, 856, 857, 916, 917, + 2386, 2387, 920, 921, 864, 865, 866, 867, 868, 869, 870, 871, 872, + 873, 902, 903, 2402, 2403, 2440, 2441, 880, 881, 882, 883, 884, 885, + 886, 887, 888, 889, 918, 919, 2418, 2419, 2456, 2457, 1024, 1025, 1026, + 1027, 1028, 1029, 1030, 1031, 1032, 1033, 1152, 1153, 2052, 2053, 2180, 2181, + 1040, 1041, 1042, 1043, 1044, 1045, 1046, 1047, 1048, 1049, 1168, 1169, 2068, + 2069, 2196, 2197, 1056, 1057, 1058, 1059, 1060, 1061, 1062, 1063, 1064, 1065, + 1154, 1155, 2084, 2085, 2120, 2121, 1072, 1073, 1074, 1075, 1076, 1077, 1078, + 1079, 1080, 1081, 1170, 1171, 2100, 2101, 2136, 2137, 1088, 1089, 1090, 1091, + 1092, 1093, 1094, 1095, 1096, 1097, 1156, 1157, 2116, 2117, 1160, 1161, 1104, + 1105, 1106, 1107, 1108, 1109, 1110, 1111, 1112, 1113, 1172, 1173, 2132, 2133, + 1176, 1177, 1120, 1121, 1122, 1123, 1124, 1125, 1126, 1127, 1128, 1129, 1158, + 1159, 2148, 2149, 2184, 2185, 1136, 1137, 1138, 1139, 1140, 1141, 1142, 1143, + 1144, 1145, 1174, 1175, 2164, 2165, 2200, 2201, 1280, 1281, 1282, 1283, 1284, + 1285, 1286, 1287, 1288, 1289, 1408, 1409, 2308, 2309, 2436, 2437, 1296, 1297, + 1298, 1299, 1300, 1301, 1302, 1303, 1304, 1305, 1424, 1425, 2324, 2325, 2452, + 2453, 1312, 1313, 1314, 1315, 1316, 1317, 1318, 1319, 1320, 1321, 1410, 1411, + 2340, 2341, 2376, 2377, 1328, 1329, 1330, 1331, 1332, 1333, 1334, 1335, 1336, + 1337, 1426, 1427, 2356, 2357, 2392, 2393, 1344, 1345, 1346, 1347, 1348, 1349, + 1350, 1351, 1352, 1353, 1412, 1413, 2372, 2373, 1416, 1417, 1360, 1361, 1362, + 1363, 1364, 1365, 1366, 1367, 1368, 1369, 1428, 1429, 2388, 2389, 1432, 1433, + 1376, 1377, 1378, 1379, 1380, 1381, 1382, 1383, 1384, 1385, 1414, 1415, 2404, + 2405, 2440, 2441, 1392, 1393, 1394, 1395, 1396, 1397, 1398, 1399, 1400, 1401, + 1430, 1431, 2420, 2421, 2456, 2457, 1536, 1537, 1538, 1539, 1540, 1541, 1542, + 1543, 1544, 1545, 1664, 1665, 2054, 2055, 2182, 2183, 1552, 1553, 1554, 1555, + 1556, 1557, 1558, 1559, 1560, 1561, 1680, 1681, 2070, 2071, 2198, 2199, 1568, + 1569, 1570, 1571, 1572, 1573, 1574, 1575, 1576, 1577, 1666, 1667, 2086, 2087, + 2152, 2153, 1584, 1585, 1586, 1587, 1588, 1589, 1590, 1591, 1592, 1593, 1682, + 1683, 2102, 2103, 2168, 2169, 1600, 1601, 1602, 1603, 1604, 1605, 1606, 1607, + 1608, 1609, 1668, 1669, 2118, 2119, 1672, 1673, 1616, 1617, 1618, 1619, 1620, + 1621, 1622, 1623, 1624, 1625, 1684, 1685, 2134, 2135, 1688, 1689, 1632, 1633, + 1634, 1635, 1636, 1637, 1638, 1639, 1640, 1641, 1670, 1671, 2150, 2151, 2184, + 2185, 1648, 1649, 1650, 1651, 1652, 1653, 1654, 1655, 1656, 1657, 1686, 1687, + 2166, 2167, 2200, 2201, 1792, 1793, 1794, 1795, 1796, 1797, 1798, 1799, 1800, + 1801, 1920, 1921, 2310, 2311, 2438, 2439, 1808, 1809, 1810, 1811, 1812, 1813, + 1814, 1815, 1816, 1817, 1936, 1937, 2326, 2327, 2454, 2455, 1824, 1825, 1826, + 1827, 1828, 1829, 1830, 1831, 1832, 1833, 1922, 1923, 2342, 2343, 2408, 2409, + 1840, 1841, 1842, 1843, 1844, 1845, 1846, 1847, 1848, 1849, 1938, 1939, 2358, + 2359, 2424, 2425, 1856, 1857, 1858, 1859, 1860, 1861, 1862, 1863, 1864, 1865, + 1924, 1925, 2374, 2375, 1928, 1929, 1872, 1873, 1874, 1875, 1876, 1877, 1878, + 1879, 1880, 1881, 1940, 1941, 2390, 2391, 1944, 1945, 1888, 1889, 1890, 1891, + 1892, 1893, 1894, 1895, 1896, 1897, 1926, 1927, 2406, 2407, 2440, 2441, 1904, + 1905, 1906, 1907, 1908, 1909, 1910, 1911, 1912, 1913, 1942, 1943, 2422, 2423, + 2456, 2457}; +#endif + +#if defined(DEC_BIN2DPD) && DEC_BIN2DPD==1 && !defined(DECBIN2DPD) +#define DECBIN2DPD + +const uint16_t BIN2DPD[1000]={ 0, 1, 2, 3, 4, 5, 6, 7, + 8, 9, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 32, + 33, 34, 35, 36, 37, 38, 39, 40, 41, 48, 49, 50, 51, + 52, 53, 54, 55, 56, 57, 64, 65, 66, 67, 68, 69, 70, + 71, 72, 73, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, + 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 112, 113, 114, + 115, 116, 117, 118, 119, 120, 121, 10, 11, 42, 43, 74, 75, + 106, 107, 78, 79, 26, 27, 58, 59, 90, 91, 122, 123, 94, + 95, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 144, 145, + 146, 147, 148, 149, 150, 151, 152, 153, 160, 161, 162, 163, 164, + 165, 166, 167, 168, 169, 176, 177, 178, 179, 180, 181, 182, 183, + 184, 185, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 208, + 209, 210, 211, 212, 213, 214, 215, 216, 217, 224, 225, 226, 227, + 228, 229, 230, 231, 232, 233, 240, 241, 242, 243, 244, 245, 246, + 247, 248, 249, 138, 139, 170, 171, 202, 203, 234, 235, 206, 207, + 154, 155, 186, 187, 218, 219, 250, 251, 222, 223, 256, 257, 258, + 259, 260, 261, 262, 263, 264, 265, 272, 273, 274, 275, 276, 277, + 278, 279, 280, 281, 288, 289, 290, 291, 292, 293, 294, 295, 296, + 297, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 320, 321, + 322, 323, 324, 325, 326, 327, 328, 329, 336, 337, 338, 339, 340, + 341, 342, 343, 344, 345, 352, 353, 354, 355, 356, 357, 358, 359, + 360, 361, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 266, + 267, 298, 299, 330, 331, 362, 363, 334, 335, 282, 283, 314, 315, + 346, 347, 378, 379, 350, 351, 384, 385, 386, 387, 388, 389, 390, + 391, 392, 393, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, + 416, 417, 418, 419, 420, 421, 422, 423, 424, 425, 432, 433, 434, + 435, 436, 437, 438, 439, 440, 441, 448, 449, 450, 451, 452, 453, + 454, 455, 456, 457, 464, 465, 466, 467, 468, 469, 470, 471, 472, + 473, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 496, 497, + 498, 499, 500, 501, 502, 503, 504, 505, 394, 395, 426, 427, 458, + 459, 490, 491, 462, 463, 410, 411, 442, 443, 474, 475, 506, 507, + 478, 479, 512, 513, 514, 515, 516, 517, 518, 519, 520, 521, 528, + 529, 530, 531, 532, 533, 534, 535, 536, 537, 544, 545, 546, 547, + 548, 549, 550, 551, 552, 553, 560, 561, 562, 563, 564, 565, 566, + 567, 568, 569, 576, 577, 578, 579, 580, 581, 582, 583, 584, 585, + 592, 593, 594, 595, 596, 597, 598, 599, 600, 601, 608, 609, 610, + 611, 612, 613, 614, 615, 616, 617, 624, 625, 626, 627, 628, 629, + 630, 631, 632, 633, 522, 523, 554, 555, 586, 587, 618, 619, 590, + 591, 538, 539, 570, 571, 602, 603, 634, 635, 606, 607, 640, 641, + 642, 643, 644, 645, 646, 647, 648, 649, 656, 657, 658, 659, 660, + 661, 662, 663, 664, 665, 672, 673, 674, 675, 676, 677, 678, 679, + 680, 681, 688, 689, 690, 691, 692, 693, 694, 695, 696, 697, 704, + 705, 706, 707, 708, 709, 710, 711, 712, 713, 720, 721, 722, 723, + 724, 725, 726, 727, 728, 729, 736, 737, 738, 739, 740, 741, 742, + 743, 744, 745, 752, 753, 754, 755, 756, 757, 758, 759, 760, 761, + 650, 651, 682, 683, 714, 715, 746, 747, 718, 719, 666, 667, 698, + 699, 730, 731, 762, 763, 734, 735, 768, 769, 770, 771, 772, 773, + 774, 775, 776, 777, 784, 785, 786, 787, 788, 789, 790, 791, 792, + 793, 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 816, 817, + 818, 819, 820, 821, 822, 823, 824, 825, 832, 833, 834, 835, 836, + 837, 838, 839, 840, 841, 848, 849, 850, 851, 852, 853, 854, 855, + 856, 857, 864, 865, 866, 867, 868, 869, 870, 871, 872, 873, 880, + 881, 882, 883, 884, 885, 886, 887, 888, 889, 778, 779, 810, 811, + 842, 843, 874, 875, 846, 847, 794, 795, 826, 827, 858, 859, 890, + 891, 862, 863, 896, 897, 898, 899, 900, 901, 902, 903, 904, 905, + 912, 913, 914, 915, 916, 917, 918, 919, 920, 921, 928, 929, 930, + 931, 932, 933, 934, 935, 936, 937, 944, 945, 946, 947, 948, 949, + 950, 951, 952, 953, 960, 961, 962, 963, 964, 965, 966, 967, 968, + 969, 976, 977, 978, 979, 980, 981, 982, 983, 984, 985, 992, 993, + 994, 995, 996, 997, 998, 999, 1000, 1001, 1008, 1009, 1010, 1011, 1012, + 1013, 1014, 1015, 1016, 1017, 906, 907, 938, 939, 970, 971, 1002, 1003, + 974, 975, 922, 923, 954, 955, 986, 987, 1018, 1019, 990, 991, 12, + 13, 268, 269, 524, 525, 780, 781, 46, 47, 28, 29, 284, 285, + 540, 541, 796, 797, 62, 63, 44, 45, 300, 301, 556, 557, 812, + 813, 302, 303, 60, 61, 316, 317, 572, 573, 828, 829, 318, 319, + 76, 77, 332, 333, 588, 589, 844, 845, 558, 559, 92, 93, 348, + 349, 604, 605, 860, 861, 574, 575, 108, 109, 364, 365, 620, 621, + 876, 877, 814, 815, 124, 125, 380, 381, 636, 637, 892, 893, 830, + 831, 14, 15, 270, 271, 526, 527, 782, 783, 110, 111, 30, 31, + 286, 287, 542, 543, 798, 799, 126, 127, 140, 141, 396, 397, 652, + 653, 908, 909, 174, 175, 156, 157, 412, 413, 668, 669, 924, 925, + 190, 191, 172, 173, 428, 429, 684, 685, 940, 941, 430, 431, 188, + 189, 444, 445, 700, 701, 956, 957, 446, 447, 204, 205, 460, 461, + 716, 717, 972, 973, 686, 687, 220, 221, 476, 477, 732, 733, 988, + 989, 702, 703, 236, 237, 492, 493, 748, 749, 1004, 1005, 942, 943, + 252, 253, 508, 509, 764, 765, 1020, 1021, 958, 959, 142, 143, 398, + 399, 654, 655, 910, 911, 238, 239, 158, 159, 414, 415, 670, 671, + 926, 927, 254, 255}; +#endif + +#if defined(DEC_DPD2BIN) && DEC_DPD2BIN==1 && !defined(DECDPD2BIN) +#define DECDPD2BIN + +const uint16_t DPD2BIN[1024]={ 0, 1, 2, 3, 4, 5, 6, 7, + 8, 9, 80, 81, 800, 801, 880, 881, 10, 11, 12, 13, 14, + 15, 16, 17, 18, 19, 90, 91, 810, 811, 890, 891, 20, 21, + 22, 23, 24, 25, 26, 27, 28, 29, 82, 83, 820, 821, 808, + 809, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 92, 93, + 830, 831, 818, 819, 40, 41, 42, 43, 44, 45, 46, 47, 48, + 49, 84, 85, 840, 841, 88, 89, 50, 51, 52, 53, 54, 55, + 56, 57, 58, 59, 94, 95, 850, 851, 98, 99, 60, 61, 62, + 63, 64, 65, 66, 67, 68, 69, 86, 87, 860, 861, 888, 889, + 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 96, 97, 870, + 871, 898, 899, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, + 180, 181, 900, 901, 980, 981, 110, 111, 112, 113, 114, 115, 116, + 117, 118, 119, 190, 191, 910, 911, 990, 991, 120, 121, 122, 123, + 124, 125, 126, 127, 128, 129, 182, 183, 920, 921, 908, 909, 130, + 131, 132, 133, 134, 135, 136, 137, 138, 139, 192, 193, 930, 931, + 918, 919, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 184, + 185, 940, 941, 188, 189, 150, 151, 152, 153, 154, 155, 156, 157, + 158, 159, 194, 195, 950, 951, 198, 199, 160, 161, 162, 163, 164, + 165, 166, 167, 168, 169, 186, 187, 960, 961, 988, 989, 170, 171, + 172, 173, 174, 175, 176, 177, 178, 179, 196, 197, 970, 971, 998, + 999, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 280, 281, + 802, 803, 882, 883, 210, 211, 212, 213, 214, 215, 216, 217, 218, + 219, 290, 291, 812, 813, 892, 893, 220, 221, 222, 223, 224, 225, + 226, 227, 228, 229, 282, 283, 822, 823, 828, 829, 230, 231, 232, + 233, 234, 235, 236, 237, 238, 239, 292, 293, 832, 833, 838, 839, + 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 284, 285, 842, + 843, 288, 289, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, + 294, 295, 852, 853, 298, 299, 260, 261, 262, 263, 264, 265, 266, + 267, 268, 269, 286, 287, 862, 863, 888, 889, 270, 271, 272, 273, + 274, 275, 276, 277, 278, 279, 296, 297, 872, 873, 898, 899, 300, + 301, 302, 303, 304, 305, 306, 307, 308, 309, 380, 381, 902, 903, + 982, 983, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 390, + 391, 912, 913, 992, 993, 320, 321, 322, 323, 324, 325, 326, 327, + 328, 329, 382, 383, 922, 923, 928, 929, 330, 331, 332, 333, 334, + 335, 336, 337, 338, 339, 392, 393, 932, 933, 938, 939, 340, 341, + 342, 343, 344, 345, 346, 347, 348, 349, 384, 385, 942, 943, 388, + 389, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 394, 395, + 952, 953, 398, 399, 360, 361, 362, 363, 364, 365, 366, 367, 368, + 369, 386, 387, 962, 963, 988, 989, 370, 371, 372, 373, 374, 375, + 376, 377, 378, 379, 396, 397, 972, 973, 998, 999, 400, 401, 402, + 403, 404, 405, 406, 407, 408, 409, 480, 481, 804, 805, 884, 885, + 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 490, 491, 814, + 815, 894, 895, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, + 482, 483, 824, 825, 848, 849, 430, 431, 432, 433, 434, 435, 436, + 437, 438, 439, 492, 493, 834, 835, 858, 859, 440, 441, 442, 443, + 444, 445, 446, 447, 448, 449, 484, 485, 844, 845, 488, 489, 450, + 451, 452, 453, 454, 455, 456, 457, 458, 459, 494, 495, 854, 855, + 498, 499, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 486, + 487, 864, 865, 888, 889, 470, 471, 472, 473, 474, 475, 476, 477, + 478, 479, 496, 497, 874, 875, 898, 899, 500, 501, 502, 503, 504, + 505, 506, 507, 508, 509, 580, 581, 904, 905, 984, 985, 510, 511, + 512, 513, 514, 515, 516, 517, 518, 519, 590, 591, 914, 915, 994, + 995, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 582, 583, + 924, 925, 948, 949, 530, 531, 532, 533, 534, 535, 536, 537, 538, + 539, 592, 593, 934, 935, 958, 959, 540, 541, 542, 543, 544, 545, + 546, 547, 548, 549, 584, 585, 944, 945, 588, 589, 550, 551, 552, + 553, 554, 555, 556, 557, 558, 559, 594, 595, 954, 955, 598, 599, + 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 586, 587, 964, + 965, 988, 989, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, + 596, 597, 974, 975, 998, 999, 600, 601, 602, 603, 604, 605, 606, + 607, 608, 609, 680, 681, 806, 807, 886, 887, 610, 611, 612, 613, + 614, 615, 616, 617, 618, 619, 690, 691, 816, 817, 896, 897, 620, + 621, 622, 623, 624, 625, 626, 627, 628, 629, 682, 683, 826, 827, + 868, 869, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 692, + 693, 836, 837, 878, 879, 640, 641, 642, 643, 644, 645, 646, 647, + 648, 649, 684, 685, 846, 847, 688, 689, 650, 651, 652, 653, 654, + 655, 656, 657, 658, 659, 694, 695, 856, 857, 698, 699, 660, 661, + 662, 663, 664, 665, 666, 667, 668, 669, 686, 687, 866, 867, 888, + 889, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 696, 697, + 876, 877, 898, 899, 700, 701, 702, 703, 704, 705, 706, 707, 708, + 709, 780, 781, 906, 907, 986, 987, 710, 711, 712, 713, 714, 715, + 716, 717, 718, 719, 790, 791, 916, 917, 996, 997, 720, 721, 722, + 723, 724, 725, 726, 727, 728, 729, 782, 783, 926, 927, 968, 969, + 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 792, 793, 936, + 937, 978, 979, 740, 741, 742, 743, 744, 745, 746, 747, 748, 749, + 784, 785, 946, 947, 788, 789, 750, 751, 752, 753, 754, 755, 756, + 757, 758, 759, 794, 795, 956, 957, 798, 799, 760, 761, 762, 763, + 764, 765, 766, 767, 768, 769, 786, 787, 966, 967, 988, 989, 770, + 771, 772, 773, 774, 775, 776, 777, 778, 779, 796, 797, 976, 977, + 998, 999}; +#endif + +#if defined(DEC_DPD2BINK) && DEC_DPD2BINK==1 && !defined(DECDPD2BINK) +#define DECDPD2BINK + +const uint32_t DPD2BINK[1024]={ 0, 1000, 2000, 3000, 4000, 5000, + 6000, 7000, 8000, 9000, 80000, 81000, 800000, 801000, 880000, 881000, + 10000, 11000, 12000, 13000, 14000, 15000, 16000, 17000, 18000, 19000, + 90000, 91000, 810000, 811000, 890000, 891000, 20000, 21000, 22000, 23000, + 24000, 25000, 26000, 27000, 28000, 29000, 82000, 83000, 820000, 821000, + 808000, 809000, 30000, 31000, 32000, 33000, 34000, 35000, 36000, 37000, + 38000, 39000, 92000, 93000, 830000, 831000, 818000, 819000, 40000, 41000, + 42000, 43000, 44000, 45000, 46000, 47000, 48000, 49000, 84000, 85000, + 840000, 841000, 88000, 89000, 50000, 51000, 52000, 53000, 54000, 55000, + 56000, 57000, 58000, 59000, 94000, 95000, 850000, 851000, 98000, 99000, + 60000, 61000, 62000, 63000, 64000, 65000, 66000, 67000, 68000, 69000, + 86000, 87000, 860000, 861000, 888000, 889000, 70000, 71000, 72000, 73000, + 74000, 75000, 76000, 77000, 78000, 79000, 96000, 97000, 870000, 871000, + 898000, 899000, 100000, 101000, 102000, 103000, 104000, 105000, 106000, 107000, + 108000, 109000, 180000, 181000, 900000, 901000, 980000, 981000, 110000, 111000, + 112000, 113000, 114000, 115000, 116000, 117000, 118000, 119000, 190000, 191000, + 910000, 911000, 990000, 991000, 120000, 121000, 122000, 123000, 124000, 125000, + 126000, 127000, 128000, 129000, 182000, 183000, 920000, 921000, 908000, 909000, + 130000, 131000, 132000, 133000, 134000, 135000, 136000, 137000, 138000, 139000, + 192000, 193000, 930000, 931000, 918000, 919000, 140000, 141000, 142000, 143000, + 144000, 145000, 146000, 147000, 148000, 149000, 184000, 185000, 940000, 941000, + 188000, 189000, 150000, 151000, 152000, 153000, 154000, 155000, 156000, 157000, + 158000, 159000, 194000, 195000, 950000, 951000, 198000, 199000, 160000, 161000, + 162000, 163000, 164000, 165000, 166000, 167000, 168000, 169000, 186000, 187000, + 960000, 961000, 988000, 989000, 170000, 171000, 172000, 173000, 174000, 175000, + 176000, 177000, 178000, 179000, 196000, 197000, 970000, 971000, 998000, 999000, + 200000, 201000, 202000, 203000, 204000, 205000, 206000, 207000, 208000, 209000, + 280000, 281000, 802000, 803000, 882000, 883000, 210000, 211000, 212000, 213000, + 214000, 215000, 216000, 217000, 218000, 219000, 290000, 291000, 812000, 813000, + 892000, 893000, 220000, 221000, 222000, 223000, 224000, 225000, 226000, 227000, + 228000, 229000, 282000, 283000, 822000, 823000, 828000, 829000, 230000, 231000, + 232000, 233000, 234000, 235000, 236000, 237000, 238000, 239000, 292000, 293000, + 832000, 833000, 838000, 839000, 240000, 241000, 242000, 243000, 244000, 245000, + 246000, 247000, 248000, 249000, 284000, 285000, 842000, 843000, 288000, 289000, + 250000, 251000, 252000, 253000, 254000, 255000, 256000, 257000, 258000, 259000, + 294000, 295000, 852000, 853000, 298000, 299000, 260000, 261000, 262000, 263000, + 264000, 265000, 266000, 267000, 268000, 269000, 286000, 287000, 862000, 863000, + 888000, 889000, 270000, 271000, 272000, 273000, 274000, 275000, 276000, 277000, + 278000, 279000, 296000, 297000, 872000, 873000, 898000, 899000, 300000, 301000, + 302000, 303000, 304000, 305000, 306000, 307000, 308000, 309000, 380000, 381000, + 902000, 903000, 982000, 983000, 310000, 311000, 312000, 313000, 314000, 315000, + 316000, 317000, 318000, 319000, 390000, 391000, 912000, 913000, 992000, 993000, + 320000, 321000, 322000, 323000, 324000, 325000, 326000, 327000, 328000, 329000, + 382000, 383000, 922000, 923000, 928000, 929000, 330000, 331000, 332000, 333000, + 334000, 335000, 336000, 337000, 338000, 339000, 392000, 393000, 932000, 933000, + 938000, 939000, 340000, 341000, 342000, 343000, 344000, 345000, 346000, 347000, + 348000, 349000, 384000, 385000, 942000, 943000, 388000, 389000, 350000, 351000, + 352000, 353000, 354000, 355000, 356000, 357000, 358000, 359000, 394000, 395000, + 952000, 953000, 398000, 399000, 360000, 361000, 362000, 363000, 364000, 365000, + 366000, 367000, 368000, 369000, 386000, 387000, 962000, 963000, 988000, 989000, + 370000, 371000, 372000, 373000, 374000, 375000, 376000, 377000, 378000, 379000, + 396000, 397000, 972000, 973000, 998000, 999000, 400000, 401000, 402000, 403000, + 404000, 405000, 406000, 407000, 408000, 409000, 480000, 481000, 804000, 805000, + 884000, 885000, 410000, 411000, 412000, 413000, 414000, 415000, 416000, 417000, + 418000, 419000, 490000, 491000, 814000, 815000, 894000, 895000, 420000, 421000, + 422000, 423000, 424000, 425000, 426000, 427000, 428000, 429000, 482000, 483000, + 824000, 825000, 848000, 849000, 430000, 431000, 432000, 433000, 434000, 435000, + 436000, 437000, 438000, 439000, 492000, 493000, 834000, 835000, 858000, 859000, + 440000, 441000, 442000, 443000, 444000, 445000, 446000, 447000, 448000, 449000, + 484000, 485000, 844000, 845000, 488000, 489000, 450000, 451000, 452000, 453000, + 454000, 455000, 456000, 457000, 458000, 459000, 494000, 495000, 854000, 855000, + 498000, 499000, 460000, 461000, 462000, 463000, 464000, 465000, 466000, 467000, + 468000, 469000, 486000, 487000, 864000, 865000, 888000, 889000, 470000, 471000, + 472000, 473000, 474000, 475000, 476000, 477000, 478000, 479000, 496000, 497000, + 874000, 875000, 898000, 899000, 500000, 501000, 502000, 503000, 504000, 505000, + 506000, 507000, 508000, 509000, 580000, 581000, 904000, 905000, 984000, 985000, + 510000, 511000, 512000, 513000, 514000, 515000, 516000, 517000, 518000, 519000, + 590000, 591000, 914000, 915000, 994000, 995000, 520000, 521000, 522000, 523000, + 524000, 525000, 526000, 527000, 528000, 529000, 582000, 583000, 924000, 925000, + 948000, 949000, 530000, 531000, 532000, 533000, 534000, 535000, 536000, 537000, + 538000, 539000, 592000, 593000, 934000, 935000, 958000, 959000, 540000, 541000, + 542000, 543000, 544000, 545000, 546000, 547000, 548000, 549000, 584000, 585000, + 944000, 945000, 588000, 589000, 550000, 551000, 552000, 553000, 554000, 555000, + 556000, 557000, 558000, 559000, 594000, 595000, 954000, 955000, 598000, 599000, + 560000, 561000, 562000, 563000, 564000, 565000, 566000, 567000, 568000, 569000, + 586000, 587000, 964000, 965000, 988000, 989000, 570000, 571000, 572000, 573000, + 574000, 575000, 576000, 577000, 578000, 579000, 596000, 597000, 974000, 975000, + 998000, 999000, 600000, 601000, 602000, 603000, 604000, 605000, 606000, 607000, + 608000, 609000, 680000, 681000, 806000, 807000, 886000, 887000, 610000, 611000, + 612000, 613000, 614000, 615000, 616000, 617000, 618000, 619000, 690000, 691000, + 816000, 817000, 896000, 897000, 620000, 621000, 622000, 623000, 624000, 625000, + 626000, 627000, 628000, 629000, 682000, 683000, 826000, 827000, 868000, 869000, + 630000, 631000, 632000, 633000, 634000, 635000, 636000, 637000, 638000, 639000, + 692000, 693000, 836000, 837000, 878000, 879000, 640000, 641000, 642000, 643000, + 644000, 645000, 646000, 647000, 648000, 649000, 684000, 685000, 846000, 847000, + 688000, 689000, 650000, 651000, 652000, 653000, 654000, 655000, 656000, 657000, + 658000, 659000, 694000, 695000, 856000, 857000, 698000, 699000, 660000, 661000, + 662000, 663000, 664000, 665000, 666000, 667000, 668000, 669000, 686000, 687000, + 866000, 867000, 888000, 889000, 670000, 671000, 672000, 673000, 674000, 675000, + 676000, 677000, 678000, 679000, 696000, 697000, 876000, 877000, 898000, 899000, + 700000, 701000, 702000, 703000, 704000, 705000, 706000, 707000, 708000, 709000, + 780000, 781000, 906000, 907000, 986000, 987000, 710000, 711000, 712000, 713000, + 714000, 715000, 716000, 717000, 718000, 719000, 790000, 791000, 916000, 917000, + 996000, 997000, 720000, 721000, 722000, 723000, 724000, 725000, 726000, 727000, + 728000, 729000, 782000, 783000, 926000, 927000, 968000, 969000, 730000, 731000, + 732000, 733000, 734000, 735000, 736000, 737000, 738000, 739000, 792000, 793000, + 936000, 937000, 978000, 979000, 740000, 741000, 742000, 743000, 744000, 745000, + 746000, 747000, 748000, 749000, 784000, 785000, 946000, 947000, 788000, 789000, + 750000, 751000, 752000, 753000, 754000, 755000, 756000, 757000, 758000, 759000, + 794000, 795000, 956000, 957000, 798000, 799000, 760000, 761000, 762000, 763000, + 764000, 765000, 766000, 767000, 768000, 769000, 786000, 787000, 966000, 967000, + 988000, 989000, 770000, 771000, 772000, 773000, 774000, 775000, 776000, 777000, + 778000, 779000, 796000, 797000, 976000, 977000, 998000, 999000}; +#endif + +#if defined(DEC_DPD2BINM) && DEC_DPD2BINM==1 && !defined(DECDPD2BINM) +#define DECDPD2BINM + +const uint32_t DPD2BINM[1024]={0, 1000000, 2000000, 3000000, 4000000, + 5000000, 6000000, 7000000, 8000000, 9000000, 80000000, 81000000, + 800000000, 801000000, 880000000, 881000000, 10000000, 11000000, 12000000, + 13000000, 14000000, 15000000, 16000000, 17000000, 18000000, 19000000, + 90000000, 91000000, 810000000, 811000000, 890000000, 891000000, 20000000, + 21000000, 22000000, 23000000, 24000000, 25000000, 26000000, 27000000, + 28000000, 29000000, 82000000, 83000000, 820000000, 821000000, 808000000, + 809000000, 30000000, 31000000, 32000000, 33000000, 34000000, 35000000, + 36000000, 37000000, 38000000, 39000000, 92000000, 93000000, 830000000, + 831000000, 818000000, 819000000, 40000000, 41000000, 42000000, 43000000, + 44000000, 45000000, 46000000, 47000000, 48000000, 49000000, 84000000, + 85000000, 840000000, 841000000, 88000000, 89000000, 50000000, 51000000, + 52000000, 53000000, 54000000, 55000000, 56000000, 57000000, 58000000, + 59000000, 94000000, 95000000, 850000000, 851000000, 98000000, 99000000, + 60000000, 61000000, 62000000, 63000000, 64000000, 65000000, 66000000, + 67000000, 68000000, 69000000, 86000000, 87000000, 860000000, 861000000, + 888000000, 889000000, 70000000, 71000000, 72000000, 73000000, 74000000, + 75000000, 76000000, 77000000, 78000000, 79000000, 96000000, 97000000, + 870000000, 871000000, 898000000, 899000000, 100000000, 101000000, 102000000, + 103000000, 104000000, 105000000, 106000000, 107000000, 108000000, 109000000, + 180000000, 181000000, 900000000, 901000000, 980000000, 981000000, 110000000, + 111000000, 112000000, 113000000, 114000000, 115000000, 116000000, 117000000, + 118000000, 119000000, 190000000, 191000000, 910000000, 911000000, 990000000, + 991000000, 120000000, 121000000, 122000000, 123000000, 124000000, 125000000, + 126000000, 127000000, 128000000, 129000000, 182000000, 183000000, 920000000, + 921000000, 908000000, 909000000, 130000000, 131000000, 132000000, 133000000, + 134000000, 135000000, 136000000, 137000000, 138000000, 139000000, 192000000, + 193000000, 930000000, 931000000, 918000000, 919000000, 140000000, 141000000, + 142000000, 143000000, 144000000, 145000000, 146000000, 147000000, 148000000, + 149000000, 184000000, 185000000, 940000000, 941000000, 188000000, 189000000, + 150000000, 151000000, 152000000, 153000000, 154000000, 155000000, 156000000, + 157000000, 158000000, 159000000, 194000000, 195000000, 950000000, 951000000, + 198000000, 199000000, 160000000, 161000000, 162000000, 163000000, 164000000, + 165000000, 166000000, 167000000, 168000000, 169000000, 186000000, 187000000, + 960000000, 961000000, 988000000, 989000000, 170000000, 171000000, 172000000, + 173000000, 174000000, 175000000, 176000000, 177000000, 178000000, 179000000, + 196000000, 197000000, 970000000, 971000000, 998000000, 999000000, 200000000, + 201000000, 202000000, 203000000, 204000000, 205000000, 206000000, 207000000, + 208000000, 209000000, 280000000, 281000000, 802000000, 803000000, 882000000, + 883000000, 210000000, 211000000, 212000000, 213000000, 214000000, 215000000, + 216000000, 217000000, 218000000, 219000000, 290000000, 291000000, 812000000, + 813000000, 892000000, 893000000, 220000000, 221000000, 222000000, 223000000, + 224000000, 225000000, 226000000, 227000000, 228000000, 229000000, 282000000, + 283000000, 822000000, 823000000, 828000000, 829000000, 230000000, 231000000, + 232000000, 233000000, 234000000, 235000000, 236000000, 237000000, 238000000, + 239000000, 292000000, 293000000, 832000000, 833000000, 838000000, 839000000, + 240000000, 241000000, 242000000, 243000000, 244000000, 245000000, 246000000, + 247000000, 248000000, 249000000, 284000000, 285000000, 842000000, 843000000, + 288000000, 289000000, 250000000, 251000000, 252000000, 253000000, 254000000, + 255000000, 256000000, 257000000, 258000000, 259000000, 294000000, 295000000, + 852000000, 853000000, 298000000, 299000000, 260000000, 261000000, 262000000, + 263000000, 264000000, 265000000, 266000000, 267000000, 268000000, 269000000, + 286000000, 287000000, 862000000, 863000000, 888000000, 889000000, 270000000, + 271000000, 272000000, 273000000, 274000000, 275000000, 276000000, 277000000, + 278000000, 279000000, 296000000, 297000000, 872000000, 873000000, 898000000, + 899000000, 300000000, 301000000, 302000000, 303000000, 304000000, 305000000, + 306000000, 307000000, 308000000, 309000000, 380000000, 381000000, 902000000, + 903000000, 982000000, 983000000, 310000000, 311000000, 312000000, 313000000, + 314000000, 315000000, 316000000, 317000000, 318000000, 319000000, 390000000, + 391000000, 912000000, 913000000, 992000000, 993000000, 320000000, 321000000, + 322000000, 323000000, 324000000, 325000000, 326000000, 327000000, 328000000, + 329000000, 382000000, 383000000, 922000000, 923000000, 928000000, 929000000, + 330000000, 331000000, 332000000, 333000000, 334000000, 335000000, 336000000, + 337000000, 338000000, 339000000, 392000000, 393000000, 932000000, 933000000, + 938000000, 939000000, 340000000, 341000000, 342000000, 343000000, 344000000, + 345000000, 346000000, 347000000, 348000000, 349000000, 384000000, 385000000, + 942000000, 943000000, 388000000, 389000000, 350000000, 351000000, 352000000, + 353000000, 354000000, 355000000, 356000000, 357000000, 358000000, 359000000, + 394000000, 395000000, 952000000, 953000000, 398000000, 399000000, 360000000, + 361000000, 362000000, 363000000, 364000000, 365000000, 366000000, 367000000, + 368000000, 369000000, 386000000, 387000000, 962000000, 963000000, 988000000, + 989000000, 370000000, 371000000, 372000000, 373000000, 374000000, 375000000, + 376000000, 377000000, 378000000, 379000000, 396000000, 397000000, 972000000, + 973000000, 998000000, 999000000, 400000000, 401000000, 402000000, 403000000, + 404000000, 405000000, 406000000, 407000000, 408000000, 409000000, 480000000, + 481000000, 804000000, 805000000, 884000000, 885000000, 410000000, 411000000, + 412000000, 413000000, 414000000, 415000000, 416000000, 417000000, 418000000, + 419000000, 490000000, 491000000, 814000000, 815000000, 894000000, 895000000, + 420000000, 421000000, 422000000, 423000000, 424000000, 425000000, 426000000, + 427000000, 428000000, 429000000, 482000000, 483000000, 824000000, 825000000, + 848000000, 849000000, 430000000, 431000000, 432000000, 433000000, 434000000, + 435000000, 436000000, 437000000, 438000000, 439000000, 492000000, 493000000, + 834000000, 835000000, 858000000, 859000000, 440000000, 441000000, 442000000, + 443000000, 444000000, 445000000, 446000000, 447000000, 448000000, 449000000, + 484000000, 485000000, 844000000, 845000000, 488000000, 489000000, 450000000, + 451000000, 452000000, 453000000, 454000000, 455000000, 456000000, 457000000, + 458000000, 459000000, 494000000, 495000000, 854000000, 855000000, 498000000, + 499000000, 460000000, 461000000, 462000000, 463000000, 464000000, 465000000, + 466000000, 467000000, 468000000, 469000000, 486000000, 487000000, 864000000, + 865000000, 888000000, 889000000, 470000000, 471000000, 472000000, 473000000, + 474000000, 475000000, 476000000, 477000000, 478000000, 479000000, 496000000, + 497000000, 874000000, 875000000, 898000000, 899000000, 500000000, 501000000, + 502000000, 503000000, 504000000, 505000000, 506000000, 507000000, 508000000, + 509000000, 580000000, 581000000, 904000000, 905000000, 984000000, 985000000, + 510000000, 511000000, 512000000, 513000000, 514000000, 515000000, 516000000, + 517000000, 518000000, 519000000, 590000000, 591000000, 914000000, 915000000, + 994000000, 995000000, 520000000, 521000000, 522000000, 523000000, 524000000, + 525000000, 526000000, 527000000, 528000000, 529000000, 582000000, 583000000, + 924000000, 925000000, 948000000, 949000000, 530000000, 531000000, 532000000, + 533000000, 534000000, 535000000, 536000000, 537000000, 538000000, 539000000, + 592000000, 593000000, 934000000, 935000000, 958000000, 959000000, 540000000, + 541000000, 542000000, 543000000, 544000000, 545000000, 546000000, 547000000, + 548000000, 549000000, 584000000, 585000000, 944000000, 945000000, 588000000, + 589000000, 550000000, 551000000, 552000000, 553000000, 554000000, 555000000, + 556000000, 557000000, 558000000, 559000000, 594000000, 595000000, 954000000, + 955000000, 598000000, 599000000, 560000000, 561000000, 562000000, 563000000, + 564000000, 565000000, 566000000, 567000000, 568000000, 569000000, 586000000, + 587000000, 964000000, 965000000, 988000000, 989000000, 570000000, 571000000, + 572000000, 573000000, 574000000, 575000000, 576000000, 577000000, 578000000, + 579000000, 596000000, 597000000, 974000000, 975000000, 998000000, 999000000, + 600000000, 601000000, 602000000, 603000000, 604000000, 605000000, 606000000, + 607000000, 608000000, 609000000, 680000000, 681000000, 806000000, 807000000, + 886000000, 887000000, 610000000, 611000000, 612000000, 613000000, 614000000, + 615000000, 616000000, 617000000, 618000000, 619000000, 690000000, 691000000, + 816000000, 817000000, 896000000, 897000000, 620000000, 621000000, 622000000, + 623000000, 624000000, 625000000, 626000000, 627000000, 628000000, 629000000, + 682000000, 683000000, 826000000, 827000000, 868000000, 869000000, 630000000, + 631000000, 632000000, 633000000, 634000000, 635000000, 636000000, 637000000, + 638000000, 639000000, 692000000, 693000000, 836000000, 837000000, 878000000, + 879000000, 640000000, 641000000, 642000000, 643000000, 644000000, 645000000, + 646000000, 647000000, 648000000, 649000000, 684000000, 685000000, 846000000, + 847000000, 688000000, 689000000, 650000000, 651000000, 652000000, 653000000, + 654000000, 655000000, 656000000, 657000000, 658000000, 659000000, 694000000, + 695000000, 856000000, 857000000, 698000000, 699000000, 660000000, 661000000, + 662000000, 663000000, 664000000, 665000000, 666000000, 667000000, 668000000, + 669000000, 686000000, 687000000, 866000000, 867000000, 888000000, 889000000, + 670000000, 671000000, 672000000, 673000000, 674000000, 675000000, 676000000, + 677000000, 678000000, 679000000, 696000000, 697000000, 876000000, 877000000, + 898000000, 899000000, 700000000, 701000000, 702000000, 703000000, 704000000, + 705000000, 706000000, 707000000, 708000000, 709000000, 780000000, 781000000, + 906000000, 907000000, 986000000, 987000000, 710000000, 711000000, 712000000, + 713000000, 714000000, 715000000, 716000000, 717000000, 718000000, 719000000, + 790000000, 791000000, 916000000, 917000000, 996000000, 997000000, 720000000, + 721000000, 722000000, 723000000, 724000000, 725000000, 726000000, 727000000, + 728000000, 729000000, 782000000, 783000000, 926000000, 927000000, 968000000, + 969000000, 730000000, 731000000, 732000000, 733000000, 734000000, 735000000, + 736000000, 737000000, 738000000, 739000000, 792000000, 793000000, 936000000, + 937000000, 978000000, 979000000, 740000000, 741000000, 742000000, 743000000, + 744000000, 745000000, 746000000, 747000000, 748000000, 749000000, 784000000, + 785000000, 946000000, 947000000, 788000000, 789000000, 750000000, 751000000, + 752000000, 753000000, 754000000, 755000000, 756000000, 757000000, 758000000, + 759000000, 794000000, 795000000, 956000000, 957000000, 798000000, 799000000, + 760000000, 761000000, 762000000, 763000000, 764000000, 765000000, 766000000, + 767000000, 768000000, 769000000, 786000000, 787000000, 966000000, 967000000, + 988000000, 989000000, 770000000, 771000000, 772000000, 773000000, 774000000, + 775000000, 776000000, 777000000, 778000000, 779000000, 796000000, 797000000, + 976000000, 977000000, 998000000, 999000000}; +#endif + +#if defined(DEC_BIN2CHAR) && DEC_BIN2CHAR==1 && !defined(DECBIN2CHAR) +#define DECBIN2CHAR + +const uint8_t BIN2CHAR[4001]={ + '\0','0','0','0', '\1','0','0','1', '\1','0','0','2', '\1','0','0','3', '\1','0','0','4', + '\1','0','0','5', '\1','0','0','6', '\1','0','0','7', '\1','0','0','8', '\1','0','0','9', + '\2','0','1','0', '\2','0','1','1', '\2','0','1','2', '\2','0','1','3', '\2','0','1','4', + '\2','0','1','5', '\2','0','1','6', '\2','0','1','7', '\2','0','1','8', '\2','0','1','9', + '\2','0','2','0', '\2','0','2','1', '\2','0','2','2', '\2','0','2','3', '\2','0','2','4', + '\2','0','2','5', '\2','0','2','6', '\2','0','2','7', '\2','0','2','8', '\2','0','2','9', + '\2','0','3','0', '\2','0','3','1', '\2','0','3','2', '\2','0','3','3', '\2','0','3','4', + '\2','0','3','5', '\2','0','3','6', '\2','0','3','7', '\2','0','3','8', '\2','0','3','9', + '\2','0','4','0', '\2','0','4','1', '\2','0','4','2', '\2','0','4','3', '\2','0','4','4', + '\2','0','4','5', '\2','0','4','6', '\2','0','4','7', '\2','0','4','8', '\2','0','4','9', + '\2','0','5','0', '\2','0','5','1', '\2','0','5','2', '\2','0','5','3', '\2','0','5','4', + '\2','0','5','5', '\2','0','5','6', '\2','0','5','7', '\2','0','5','8', '\2','0','5','9', + '\2','0','6','0', '\2','0','6','1', '\2','0','6','2', '\2','0','6','3', '\2','0','6','4', + '\2','0','6','5', '\2','0','6','6', '\2','0','6','7', '\2','0','6','8', '\2','0','6','9', + '\2','0','7','0', '\2','0','7','1', '\2','0','7','2', '\2','0','7','3', '\2','0','7','4', + '\2','0','7','5', '\2','0','7','6', '\2','0','7','7', '\2','0','7','8', '\2','0','7','9', + '\2','0','8','0', '\2','0','8','1', '\2','0','8','2', '\2','0','8','3', '\2','0','8','4', + '\2','0','8','5', '\2','0','8','6', '\2','0','8','7', '\2','0','8','8', '\2','0','8','9', + '\2','0','9','0', '\2','0','9','1', '\2','0','9','2', '\2','0','9','3', '\2','0','9','4', + '\2','0','9','5', '\2','0','9','6', '\2','0','9','7', '\2','0','9','8', '\2','0','9','9', + '\3','1','0','0', '\3','1','0','1', '\3','1','0','2', '\3','1','0','3', '\3','1','0','4', + '\3','1','0','5', '\3','1','0','6', '\3','1','0','7', '\3','1','0','8', '\3','1','0','9', + '\3','1','1','0', '\3','1','1','1', '\3','1','1','2', '\3','1','1','3', '\3','1','1','4', + '\3','1','1','5', '\3','1','1','6', '\3','1','1','7', '\3','1','1','8', '\3','1','1','9', + '\3','1','2','0', '\3','1','2','1', '\3','1','2','2', '\3','1','2','3', '\3','1','2','4', + '\3','1','2','5', '\3','1','2','6', '\3','1','2','7', '\3','1','2','8', '\3','1','2','9', + '\3','1','3','0', '\3','1','3','1', '\3','1','3','2', '\3','1','3','3', '\3','1','3','4', + '\3','1','3','5', '\3','1','3','6', '\3','1','3','7', '\3','1','3','8', '\3','1','3','9', + '\3','1','4','0', '\3','1','4','1', '\3','1','4','2', '\3','1','4','3', '\3','1','4','4', + '\3','1','4','5', '\3','1','4','6', '\3','1','4','7', '\3','1','4','8', '\3','1','4','9', + '\3','1','5','0', '\3','1','5','1', '\3','1','5','2', '\3','1','5','3', '\3','1','5','4', + '\3','1','5','5', '\3','1','5','6', '\3','1','5','7', '\3','1','5','8', '\3','1','5','9', + '\3','1','6','0', '\3','1','6','1', '\3','1','6','2', '\3','1','6','3', '\3','1','6','4', + '\3','1','6','5', '\3','1','6','6', '\3','1','6','7', '\3','1','6','8', '\3','1','6','9', + '\3','1','7','0', '\3','1','7','1', '\3','1','7','2', '\3','1','7','3', '\3','1','7','4', + '\3','1','7','5', '\3','1','7','6', '\3','1','7','7', '\3','1','7','8', 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'\3','9','8','9', + '\3','9','9','0', '\3','9','9','1', '\3','9','9','2', '\3','9','9','3', '\3','9','9','4', + '\3','9','9','5', '\3','9','9','6', '\3','9','9','7', '\3','9','9','8', '\3','9','9','9', '\0'}; +#endif + +#if defined(DEC_DPD2BCD8) && DEC_DPD2BCD8==1 && !defined(DECDPD2BCD8) +#define DECDPD2BCD8 + +const uint8_t DPD2BCD8[4096]={ + 0,0,0,0, 0,0,1,1, 0,0,2,1, 0,0,3,1, 0,0,4,1, 0,0,5,1, 0,0,6,1, 0,0,7,1, 0,0,8,1, + 0,0,9,1, 0,8,0,2, 0,8,1,2, 8,0,0,3, 8,0,1,3, 8,8,0,3, 8,8,1,3, 0,1,0,2, 0,1,1,2, + 0,1,2,2, 0,1,3,2, 0,1,4,2, 0,1,5,2, 0,1,6,2, 0,1,7,2, 0,1,8,2, 0,1,9,2, 0,9,0,2, + 0,9,1,2, 8,1,0,3, 8,1,1,3, 8,9,0,3, 8,9,1,3, 0,2,0,2, 0,2,1,2, 0,2,2,2, 0,2,3,2, + 0,2,4,2, 0,2,5,2, 0,2,6,2, 0,2,7,2, 0,2,8,2, 0,2,9,2, 0,8,2,2, 0,8,3,2, 8,2,0,3, + 8,2,1,3, 8,0,8,3, 8,0,9,3, 0,3,0,2, 0,3,1,2, 0,3,2,2, 0,3,3,2, 0,3,4,2, 0,3,5,2, + 0,3,6,2, 0,3,7,2, 0,3,8,2, 0,3,9,2, 0,9,2,2, 0,9,3,2, 8,3,0,3, 8,3,1,3, 8,1,8,3, + 8,1,9,3, 0,4,0,2, 0,4,1,2, 0,4,2,2, 0,4,3,2, 0,4,4,2, 0,4,5,2, 0,4,6,2, 0,4,7,2, + 0,4,8,2, 0,4,9,2, 0,8,4,2, 0,8,5,2, 8,4,0,3, 8,4,1,3, 0,8,8,2, 0,8,9,2, 0,5,0,2, + 0,5,1,2, 0,5,2,2, 0,5,3,2, 0,5,4,2, 0,5,5,2, 0,5,6,2, 0,5,7,2, 0,5,8,2, 0,5,9,2, + 0,9,4,2, 0,9,5,2, 8,5,0,3, 8,5,1,3, 0,9,8,2, 0,9,9,2, 0,6,0,2, 0,6,1,2, 0,6,2,2, + 0,6,3,2, 0,6,4,2, 0,6,5,2, 0,6,6,2, 0,6,7,2, 0,6,8,2, 0,6,9,2, 0,8,6,2, 0,8,7,2, + 8,6,0,3, 8,6,1,3, 8,8,8,3, 8,8,9,3, 0,7,0,2, 0,7,1,2, 0,7,2,2, 0,7,3,2, 0,7,4,2, + 0,7,5,2, 0,7,6,2, 0,7,7,2, 0,7,8,2, 0,7,9,2, 0,9,6,2, 0,9,7,2, 8,7,0,3, 8,7,1,3, + 8,9,8,3, 8,9,9,3, 1,0,0,3, 1,0,1,3, 1,0,2,3, 1,0,3,3, 1,0,4,3, 1,0,5,3, 1,0,6,3, + 1,0,7,3, 1,0,8,3, 1,0,9,3, 1,8,0,3, 1,8,1,3, 9,0,0,3, 9,0,1,3, 9,8,0,3, 9,8,1,3, + 1,1,0,3, 1,1,1,3, 1,1,2,3, 1,1,3,3, 1,1,4,3, 1,1,5,3, 1,1,6,3, 1,1,7,3, 1,1,8,3, + 1,1,9,3, 1,9,0,3, 1,9,1,3, 9,1,0,3, 9,1,1,3, 9,9,0,3, 9,9,1,3, 1,2,0,3, 1,2,1,3, + 1,2,2,3, 1,2,3,3, 1,2,4,3, 1,2,5,3, 1,2,6,3, 1,2,7,3, 1,2,8,3, 1,2,9,3, 1,8,2,3, + 1,8,3,3, 9,2,0,3, 9,2,1,3, 9,0,8,3, 9,0,9,3, 1,3,0,3, 1,3,1,3, 1,3,2,3, 1,3,3,3, + 1,3,4,3, 1,3,5,3, 1,3,6,3, 1,3,7,3, 1,3,8,3, 1,3,9,3, 1,9,2,3, 1,9,3,3, 9,3,0,3, + 9,3,1,3, 9,1,8,3, 9,1,9,3, 1,4,0,3, 1,4,1,3, 1,4,2,3, 1,4,3,3, 1,4,4,3, 1,4,5,3, + 1,4,6,3, 1,4,7,3, 1,4,8,3, 1,4,9,3, 1,8,4,3, 1,8,5,3, 9,4,0,3, 9,4,1,3, 1,8,8,3, + 1,8,9,3, 1,5,0,3, 1,5,1,3, 1,5,2,3, 1,5,3,3, 1,5,4,3, 1,5,5,3, 1,5,6,3, 1,5,7,3, + 1,5,8,3, 1,5,9,3, 1,9,4,3, 1,9,5,3, 9,5,0,3, 9,5,1,3, 1,9,8,3, 1,9,9,3, 1,6,0,3, + 1,6,1,3, 1,6,2,3, 1,6,3,3, 1,6,4,3, 1,6,5,3, 1,6,6,3, 1,6,7,3, 1,6,8,3, 1,6,9,3, + 1,8,6,3, 1,8,7,3, 9,6,0,3, 9,6,1,3, 9,8,8,3, 9,8,9,3, 1,7,0,3, 1,7,1,3, 1,7,2,3, + 1,7,3,3, 1,7,4,3, 1,7,5,3, 1,7,6,3, 1,7,7,3, 1,7,8,3, 1,7,9,3, 1,9,6,3, 1,9,7,3, + 9,7,0,3, 9,7,1,3, 9,9,8,3, 9,9,9,3, 2,0,0,3, 2,0,1,3, 2,0,2,3, 2,0,3,3, 2,0,4,3, + 2,0,5,3, 2,0,6,3, 2,0,7,3, 2,0,8,3, 2,0,9,3, 2,8,0,3, 2,8,1,3, 8,0,2,3, 8,0,3,3, + 8,8,2,3, 8,8,3,3, 2,1,0,3, 2,1,1,3, 2,1,2,3, 2,1,3,3, 2,1,4,3, 2,1,5,3, 2,1,6,3, + 2,1,7,3, 2,1,8,3, 2,1,9,3, 2,9,0,3, 2,9,1,3, 8,1,2,3, 8,1,3,3, 8,9,2,3, 8,9,3,3, + 2,2,0,3, 2,2,1,3, 2,2,2,3, 2,2,3,3, 2,2,4,3, 2,2,5,3, 2,2,6,3, 2,2,7,3, 2,2,8,3, + 2,2,9,3, 2,8,2,3, 2,8,3,3, 8,2,2,3, 8,2,3,3, 8,2,8,3, 8,2,9,3, 2,3,0,3, 2,3,1,3, + 2,3,2,3, 2,3,3,3, 2,3,4,3, 2,3,5,3, 2,3,6,3, 2,3,7,3, 2,3,8,3, 2,3,9,3, 2,9,2,3, + 2,9,3,3, 8,3,2,3, 8,3,3,3, 8,3,8,3, 8,3,9,3, 2,4,0,3, 2,4,1,3, 2,4,2,3, 2,4,3,3, + 2,4,4,3, 2,4,5,3, 2,4,6,3, 2,4,7,3, 2,4,8,3, 2,4,9,3, 2,8,4,3, 2,8,5,3, 8,4,2,3, + 8,4,3,3, 2,8,8,3, 2,8,9,3, 2,5,0,3, 2,5,1,3, 2,5,2,3, 2,5,3,3, 2,5,4,3, 2,5,5,3, + 2,5,6,3, 2,5,7,3, 2,5,8,3, 2,5,9,3, 2,9,4,3, 2,9,5,3, 8,5,2,3, 8,5,3,3, 2,9,8,3, + 2,9,9,3, 2,6,0,3, 2,6,1,3, 2,6,2,3, 2,6,3,3, 2,6,4,3, 2,6,5,3, 2,6,6,3, 2,6,7,3, + 2,6,8,3, 2,6,9,3, 2,8,6,3, 2,8,7,3, 8,6,2,3, 8,6,3,3, 8,8,8,3, 8,8,9,3, 2,7,0,3, + 2,7,1,3, 2,7,2,3, 2,7,3,3, 2,7,4,3, 2,7,5,3, 2,7,6,3, 2,7,7,3, 2,7,8,3, 2,7,9,3, + 2,9,6,3, 2,9,7,3, 8,7,2,3, 8,7,3,3, 8,9,8,3, 8,9,9,3, 3,0,0,3, 3,0,1,3, 3,0,2,3, + 3,0,3,3, 3,0,4,3, 3,0,5,3, 3,0,6,3, 3,0,7,3, 3,0,8,3, 3,0,9,3, 3,8,0,3, 3,8,1,3, + 9,0,2,3, 9,0,3,3, 9,8,2,3, 9,8,3,3, 3,1,0,3, 3,1,1,3, 3,1,2,3, 3,1,3,3, 3,1,4,3, + 3,1,5,3, 3,1,6,3, 3,1,7,3, 3,1,8,3, 3,1,9,3, 3,9,0,3, 3,9,1,3, 9,1,2,3, 9,1,3,3, + 9,9,2,3, 9,9,3,3, 3,2,0,3, 3,2,1,3, 3,2,2,3, 3,2,3,3, 3,2,4,3, 3,2,5,3, 3,2,6,3, + 3,2,7,3, 3,2,8,3, 3,2,9,3, 3,8,2,3, 3,8,3,3, 9,2,2,3, 9,2,3,3, 9,2,8,3, 9,2,9,3, + 3,3,0,3, 3,3,1,3, 3,3,2,3, 3,3,3,3, 3,3,4,3, 3,3,5,3, 3,3,6,3, 3,3,7,3, 3,3,8,3, + 3,3,9,3, 3,9,2,3, 3,9,3,3, 9,3,2,3, 9,3,3,3, 9,3,8,3, 9,3,9,3, 3,4,0,3, 3,4,1,3, + 3,4,2,3, 3,4,3,3, 3,4,4,3, 3,4,5,3, 3,4,6,3, 3,4,7,3, 3,4,8,3, 3,4,9,3, 3,8,4,3, + 3,8,5,3, 9,4,2,3, 9,4,3,3, 3,8,8,3, 3,8,9,3, 3,5,0,3, 3,5,1,3, 3,5,2,3, 3,5,3,3, + 3,5,4,3, 3,5,5,3, 3,5,6,3, 3,5,7,3, 3,5,8,3, 3,5,9,3, 3,9,4,3, 3,9,5,3, 9,5,2,3, + 9,5,3,3, 3,9,8,3, 3,9,9,3, 3,6,0,3, 3,6,1,3, 3,6,2,3, 3,6,3,3, 3,6,4,3, 3,6,5,3, + 3,6,6,3, 3,6,7,3, 3,6,8,3, 3,6,9,3, 3,8,6,3, 3,8,7,3, 9,6,2,3, 9,6,3,3, 9,8,8,3, + 9,8,9,3, 3,7,0,3, 3,7,1,3, 3,7,2,3, 3,7,3,3, 3,7,4,3, 3,7,5,3, 3,7,6,3, 3,7,7,3, + 3,7,8,3, 3,7,9,3, 3,9,6,3, 3,9,7,3, 9,7,2,3, 9,7,3,3, 9,9,8,3, 9,9,9,3, 4,0,0,3, + 4,0,1,3, 4,0,2,3, 4,0,3,3, 4,0,4,3, 4,0,5,3, 4,0,6,3, 4,0,7,3, 4,0,8,3, 4,0,9,3, + 4,8,0,3, 4,8,1,3, 8,0,4,3, 8,0,5,3, 8,8,4,3, 8,8,5,3, 4,1,0,3, 4,1,1,3, 4,1,2,3, + 4,1,3,3, 4,1,4,3, 4,1,5,3, 4,1,6,3, 4,1,7,3, 4,1,8,3, 4,1,9,3, 4,9,0,3, 4,9,1,3, + 8,1,4,3, 8,1,5,3, 8,9,4,3, 8,9,5,3, 4,2,0,3, 4,2,1,3, 4,2,2,3, 4,2,3,3, 4,2,4,3, + 4,2,5,3, 4,2,6,3, 4,2,7,3, 4,2,8,3, 4,2,9,3, 4,8,2,3, 4,8,3,3, 8,2,4,3, 8,2,5,3, + 8,4,8,3, 8,4,9,3, 4,3,0,3, 4,3,1,3, 4,3,2,3, 4,3,3,3, 4,3,4,3, 4,3,5,3, 4,3,6,3, + 4,3,7,3, 4,3,8,3, 4,3,9,3, 4,9,2,3, 4,9,3,3, 8,3,4,3, 8,3,5,3, 8,5,8,3, 8,5,9,3, + 4,4,0,3, 4,4,1,3, 4,4,2,3, 4,4,3,3, 4,4,4,3, 4,4,5,3, 4,4,6,3, 4,4,7,3, 4,4,8,3, + 4,4,9,3, 4,8,4,3, 4,8,5,3, 8,4,4,3, 8,4,5,3, 4,8,8,3, 4,8,9,3, 4,5,0,3, 4,5,1,3, + 4,5,2,3, 4,5,3,3, 4,5,4,3, 4,5,5,3, 4,5,6,3, 4,5,7,3, 4,5,8,3, 4,5,9,3, 4,9,4,3, + 4,9,5,3, 8,5,4,3, 8,5,5,3, 4,9,8,3, 4,9,9,3, 4,6,0,3, 4,6,1,3, 4,6,2,3, 4,6,3,3, + 4,6,4,3, 4,6,5,3, 4,6,6,3, 4,6,7,3, 4,6,8,3, 4,6,9,3, 4,8,6,3, 4,8,7,3, 8,6,4,3, + 8,6,5,3, 8,8,8,3, 8,8,9,3, 4,7,0,3, 4,7,1,3, 4,7,2,3, 4,7,3,3, 4,7,4,3, 4,7,5,3, + 4,7,6,3, 4,7,7,3, 4,7,8,3, 4,7,9,3, 4,9,6,3, 4,9,7,3, 8,7,4,3, 8,7,5,3, 8,9,8,3, + 8,9,9,3, 5,0,0,3, 5,0,1,3, 5,0,2,3, 5,0,3,3, 5,0,4,3, 5,0,5,3, 5,0,6,3, 5,0,7,3, + 5,0,8,3, 5,0,9,3, 5,8,0,3, 5,8,1,3, 9,0,4,3, 9,0,5,3, 9,8,4,3, 9,8,5,3, 5,1,0,3, + 5,1,1,3, 5,1,2,3, 5,1,3,3, 5,1,4,3, 5,1,5,3, 5,1,6,3, 5,1,7,3, 5,1,8,3, 5,1,9,3, + 5,9,0,3, 5,9,1,3, 9,1,4,3, 9,1,5,3, 9,9,4,3, 9,9,5,3, 5,2,0,3, 5,2,1,3, 5,2,2,3, + 5,2,3,3, 5,2,4,3, 5,2,5,3, 5,2,6,3, 5,2,7,3, 5,2,8,3, 5,2,9,3, 5,8,2,3, 5,8,3,3, + 9,2,4,3, 9,2,5,3, 9,4,8,3, 9,4,9,3, 5,3,0,3, 5,3,1,3, 5,3,2,3, 5,3,3,3, 5,3,4,3, + 5,3,5,3, 5,3,6,3, 5,3,7,3, 5,3,8,3, 5,3,9,3, 5,9,2,3, 5,9,3,3, 9,3,4,3, 9,3,5,3, + 9,5,8,3, 9,5,9,3, 5,4,0,3, 5,4,1,3, 5,4,2,3, 5,4,3,3, 5,4,4,3, 5,4,5,3, 5,4,6,3, + 5,4,7,3, 5,4,8,3, 5,4,9,3, 5,8,4,3, 5,8,5,3, 9,4,4,3, 9,4,5,3, 5,8,8,3, 5,8,9,3, + 5,5,0,3, 5,5,1,3, 5,5,2,3, 5,5,3,3, 5,5,4,3, 5,5,5,3, 5,5,6,3, 5,5,7,3, 5,5,8,3, + 5,5,9,3, 5,9,4,3, 5,9,5,3, 9,5,4,3, 9,5,5,3, 5,9,8,3, 5,9,9,3, 5,6,0,3, 5,6,1,3, + 5,6,2,3, 5,6,3,3, 5,6,4,3, 5,6,5,3, 5,6,6,3, 5,6,7,3, 5,6,8,3, 5,6,9,3, 5,8,6,3, + 5,8,7,3, 9,6,4,3, 9,6,5,3, 9,8,8,3, 9,8,9,3, 5,7,0,3, 5,7,1,3, 5,7,2,3, 5,7,3,3, + 5,7,4,3, 5,7,5,3, 5,7,6,3, 5,7,7,3, 5,7,8,3, 5,7,9,3, 5,9,6,3, 5,9,7,3, 9,7,4,3, + 9,7,5,3, 9,9,8,3, 9,9,9,3, 6,0,0,3, 6,0,1,3, 6,0,2,3, 6,0,3,3, 6,0,4,3, 6,0,5,3, + 6,0,6,3, 6,0,7,3, 6,0,8,3, 6,0,9,3, 6,8,0,3, 6,8,1,3, 8,0,6,3, 8,0,7,3, 8,8,6,3, + 8,8,7,3, 6,1,0,3, 6,1,1,3, 6,1,2,3, 6,1,3,3, 6,1,4,3, 6,1,5,3, 6,1,6,3, 6,1,7,3, + 6,1,8,3, 6,1,9,3, 6,9,0,3, 6,9,1,3, 8,1,6,3, 8,1,7,3, 8,9,6,3, 8,9,7,3, 6,2,0,3, + 6,2,1,3, 6,2,2,3, 6,2,3,3, 6,2,4,3, 6,2,5,3, 6,2,6,3, 6,2,7,3, 6,2,8,3, 6,2,9,3, + 6,8,2,3, 6,8,3,3, 8,2,6,3, 8,2,7,3, 8,6,8,3, 8,6,9,3, 6,3,0,3, 6,3,1,3, 6,3,2,3, + 6,3,3,3, 6,3,4,3, 6,3,5,3, 6,3,6,3, 6,3,7,3, 6,3,8,3, 6,3,9,3, 6,9,2,3, 6,9,3,3, + 8,3,6,3, 8,3,7,3, 8,7,8,3, 8,7,9,3, 6,4,0,3, 6,4,1,3, 6,4,2,3, 6,4,3,3, 6,4,4,3, + 6,4,5,3, 6,4,6,3, 6,4,7,3, 6,4,8,3, 6,4,9,3, 6,8,4,3, 6,8,5,3, 8,4,6,3, 8,4,7,3, + 6,8,8,3, 6,8,9,3, 6,5,0,3, 6,5,1,3, 6,5,2,3, 6,5,3,3, 6,5,4,3, 6,5,5,3, 6,5,6,3, + 6,5,7,3, 6,5,8,3, 6,5,9,3, 6,9,4,3, 6,9,5,3, 8,5,6,3, 8,5,7,3, 6,9,8,3, 6,9,9,3, + 6,6,0,3, 6,6,1,3, 6,6,2,3, 6,6,3,3, 6,6,4,3, 6,6,5,3, 6,6,6,3, 6,6,7,3, 6,6,8,3, + 6,6,9,3, 6,8,6,3, 6,8,7,3, 8,6,6,3, 8,6,7,3, 8,8,8,3, 8,8,9,3, 6,7,0,3, 6,7,1,3, + 6,7,2,3, 6,7,3,3, 6,7,4,3, 6,7,5,3, 6,7,6,3, 6,7,7,3, 6,7,8,3, 6,7,9,3, 6,9,6,3, + 6,9,7,3, 8,7,6,3, 8,7,7,3, 8,9,8,3, 8,9,9,3, 7,0,0,3, 7,0,1,3, 7,0,2,3, 7,0,3,3, + 7,0,4,3, 7,0,5,3, 7,0,6,3, 7,0,7,3, 7,0,8,3, 7,0,9,3, 7,8,0,3, 7,8,1,3, 9,0,6,3, + 9,0,7,3, 9,8,6,3, 9,8,7,3, 7,1,0,3, 7,1,1,3, 7,1,2,3, 7,1,3,3, 7,1,4,3, 7,1,5,3, + 7,1,6,3, 7,1,7,3, 7,1,8,3, 7,1,9,3, 7,9,0,3, 7,9,1,3, 9,1,6,3, 9,1,7,3, 9,9,6,3, + 9,9,7,3, 7,2,0,3, 7,2,1,3, 7,2,2,3, 7,2,3,3, 7,2,4,3, 7,2,5,3, 7,2,6,3, 7,2,7,3, + 7,2,8,3, 7,2,9,3, 7,8,2,3, 7,8,3,3, 9,2,6,3, 9,2,7,3, 9,6,8,3, 9,6,9,3, 7,3,0,3, + 7,3,1,3, 7,3,2,3, 7,3,3,3, 7,3,4,3, 7,3,5,3, 7,3,6,3, 7,3,7,3, 7,3,8,3, 7,3,9,3, + 7,9,2,3, 7,9,3,3, 9,3,6,3, 9,3,7,3, 9,7,8,3, 9,7,9,3, 7,4,0,3, 7,4,1,3, 7,4,2,3, + 7,4,3,3, 7,4,4,3, 7,4,5,3, 7,4,6,3, 7,4,7,3, 7,4,8,3, 7,4,9,3, 7,8,4,3, 7,8,5,3, + 9,4,6,3, 9,4,7,3, 7,8,8,3, 7,8,9,3, 7,5,0,3, 7,5,1,3, 7,5,2,3, 7,5,3,3, 7,5,4,3, + 7,5,5,3, 7,5,6,3, 7,5,7,3, 7,5,8,3, 7,5,9,3, 7,9,4,3, 7,9,5,3, 9,5,6,3, 9,5,7,3, + 7,9,8,3, 7,9,9,3, 7,6,0,3, 7,6,1,3, 7,6,2,3, 7,6,3,3, 7,6,4,3, 7,6,5,3, 7,6,6,3, + 7,6,7,3, 7,6,8,3, 7,6,9,3, 7,8,6,3, 7,8,7,3, 9,6,6,3, 9,6,7,3, 9,8,8,3, 9,8,9,3, + 7,7,0,3, 7,7,1,3, 7,7,2,3, 7,7,3,3, 7,7,4,3, 7,7,5,3, 7,7,6,3, 7,7,7,3, 7,7,8,3, + 7,7,9,3, 7,9,6,3, 7,9,7,3, 9,7,6,3, 9,7,7,3, 9,9,8,3, 9,9,9,3}; +#endif + +#if defined(DEC_BIN2BCD8) && DEC_BIN2BCD8==1 && !defined(DECBIN2BCD8) +#define DECBIN2BCD8 + +const uint8_t BIN2BCD8[4000]={ + 0,0,0,0, 0,0,1,1, 0,0,2,1, 0,0,3,1, 0,0,4,1, 0,0,5,1, 0,0,6,1, 0,0,7,1, 0,0,8,1, + 0,0,9,1, 0,1,0,2, 0,1,1,2, 0,1,2,2, 0,1,3,2, 0,1,4,2, 0,1,5,2, 0,1,6,2, 0,1,7,2, + 0,1,8,2, 0,1,9,2, 0,2,0,2, 0,2,1,2, 0,2,2,2, 0,2,3,2, 0,2,4,2, 0,2,5,2, 0,2,6,2, + 0,2,7,2, 0,2,8,2, 0,2,9,2, 0,3,0,2, 0,3,1,2, 0,3,2,2, 0,3,3,2, 0,3,4,2, 0,3,5,2, + 0,3,6,2, 0,3,7,2, 0,3,8,2, 0,3,9,2, 0,4,0,2, 0,4,1,2, 0,4,2,2, 0,4,3,2, 0,4,4,2, + 0,4,5,2, 0,4,6,2, 0,4,7,2, 0,4,8,2, 0,4,9,2, 0,5,0,2, 0,5,1,2, 0,5,2,2, 0,5,3,2, + 0,5,4,2, 0,5,5,2, 0,5,6,2, 0,5,7,2, 0,5,8,2, 0,5,9,2, 0,6,0,2, 0,6,1,2, 0,6,2,2, + 0,6,3,2, 0,6,4,2, 0,6,5,2, 0,6,6,2, 0,6,7,2, 0,6,8,2, 0,6,9,2, 0,7,0,2, 0,7,1,2, + 0,7,2,2, 0,7,3,2, 0,7,4,2, 0,7,5,2, 0,7,6,2, 0,7,7,2, 0,7,8,2, 0,7,9,2, 0,8,0,2, + 0,8,1,2, 0,8,2,2, 0,8,3,2, 0,8,4,2, 0,8,5,2, 0,8,6,2, 0,8,7,2, 0,8,8,2, 0,8,9,2, + 0,9,0,2, 0,9,1,2, 0,9,2,2, 0,9,3,2, 0,9,4,2, 0,9,5,2, 0,9,6,2, 0,9,7,2, 0,9,8,2, + 0,9,9,2, 1,0,0,3, 1,0,1,3, 1,0,2,3, 1,0,3,3, 1,0,4,3, 1,0,5,3, 1,0,6,3, 1,0,7,3, + 1,0,8,3, 1,0,9,3, 1,1,0,3, 1,1,1,3, 1,1,2,3, 1,1,3,3, 1,1,4,3, 1,1,5,3, 1,1,6,3, + 1,1,7,3, 1,1,8,3, 1,1,9,3, 1,2,0,3, 1,2,1,3, 1,2,2,3, 1,2,3,3, 1,2,4,3, 1,2,5,3, + 1,2,6,3, 1,2,7,3, 1,2,8,3, 1,2,9,3, 1,3,0,3, 1,3,1,3, 1,3,2,3, 1,3,3,3, 1,3,4,3, + 1,3,5,3, 1,3,6,3, 1,3,7,3, 1,3,8,3, 1,3,9,3, 1,4,0,3, 1,4,1,3, 1,4,2,3, 1,4,3,3, + 1,4,4,3, 1,4,5,3, 1,4,6,3, 1,4,7,3, 1,4,8,3, 1,4,9,3, 1,5,0,3, 1,5,1,3, 1,5,2,3, + 1,5,3,3, 1,5,4,3, 1,5,5,3, 1,5,6,3, 1,5,7,3, 1,5,8,3, 1,5,9,3, 1,6,0,3, 1,6,1,3, + 1,6,2,3, 1,6,3,3, 1,6,4,3, 1,6,5,3, 1,6,6,3, 1,6,7,3, 1,6,8,3, 1,6,9,3, 1,7,0,3, + 1,7,1,3, 1,7,2,3, 1,7,3,3, 1,7,4,3, 1,7,5,3, 1,7,6,3, 1,7,7,3, 1,7,8,3, 1,7,9,3, + 1,8,0,3, 1,8,1,3, 1,8,2,3, 1,8,3,3, 1,8,4,3, 1,8,5,3, 1,8,6,3, 1,8,7,3, 1,8,8,3, + 1,8,9,3, 1,9,0,3, 1,9,1,3, 1,9,2,3, 1,9,3,3, 1,9,4,3, 1,9,5,3, 1,9,6,3, 1,9,7,3, + 1,9,8,3, 1,9,9,3, 2,0,0,3, 2,0,1,3, 2,0,2,3, 2,0,3,3, 2,0,4,3, 2,0,5,3, 2,0,6,3, + 2,0,7,3, 2,0,8,3, 2,0,9,3, 2,1,0,3, 2,1,1,3, 2,1,2,3, 2,1,3,3, 2,1,4,3, 2,1,5,3, + 2,1,6,3, 2,1,7,3, 2,1,8,3, 2,1,9,3, 2,2,0,3, 2,2,1,3, 2,2,2,3, 2,2,3,3, 2,2,4,3, + 2,2,5,3, 2,2,6,3, 2,2,7,3, 2,2,8,3, 2,2,9,3, 2,3,0,3, 2,3,1,3, 2,3,2,3, 2,3,3,3, + 2,3,4,3, 2,3,5,3, 2,3,6,3, 2,3,7,3, 2,3,8,3, 2,3,9,3, 2,4,0,3, 2,4,1,3, 2,4,2,3, + 2,4,3,3, 2,4,4,3, 2,4,5,3, 2,4,6,3, 2,4,7,3, 2,4,8,3, 2,4,9,3, 2,5,0,3, 2,5,1,3, + 2,5,2,3, 2,5,3,3, 2,5,4,3, 2,5,5,3, 2,5,6,3, 2,5,7,3, 2,5,8,3, 2,5,9,3, 2,6,0,3, + 2,6,1,3, 2,6,2,3, 2,6,3,3, 2,6,4,3, 2,6,5,3, 2,6,6,3, 2,6,7,3, 2,6,8,3, 2,6,9,3, + 2,7,0,3, 2,7,1,3, 2,7,2,3, 2,7,3,3, 2,7,4,3, 2,7,5,3, 2,7,6,3, 2,7,7,3, 2,7,8,3, + 2,7,9,3, 2,8,0,3, 2,8,1,3, 2,8,2,3, 2,8,3,3, 2,8,4,3, 2,8,5,3, 2,8,6,3, 2,8,7,3, + 2,8,8,3, 2,8,9,3, 2,9,0,3, 2,9,1,3, 2,9,2,3, 2,9,3,3, 2,9,4,3, 2,9,5,3, 2,9,6,3, + 2,9,7,3, 2,9,8,3, 2,9,9,3, 3,0,0,3, 3,0,1,3, 3,0,2,3, 3,0,3,3, 3,0,4,3, 3,0,5,3, + 3,0,6,3, 3,0,7,3, 3,0,8,3, 3,0,9,3, 3,1,0,3, 3,1,1,3, 3,1,2,3, 3,1,3,3, 3,1,4,3, + 3,1,5,3, 3,1,6,3, 3,1,7,3, 3,1,8,3, 3,1,9,3, 3,2,0,3, 3,2,1,3, 3,2,2,3, 3,2,3,3, + 3,2,4,3, 3,2,5,3, 3,2,6,3, 3,2,7,3, 3,2,8,3, 3,2,9,3, 3,3,0,3, 3,3,1,3, 3,3,2,3, + 3,3,3,3, 3,3,4,3, 3,3,5,3, 3,3,6,3, 3,3,7,3, 3,3,8,3, 3,3,9,3, 3,4,0,3, 3,4,1,3, + 3,4,2,3, 3,4,3,3, 3,4,4,3, 3,4,5,3, 3,4,6,3, 3,4,7,3, 3,4,8,3, 3,4,9,3, 3,5,0,3, + 3,5,1,3, 3,5,2,3, 3,5,3,3, 3,5,4,3, 3,5,5,3, 3,5,6,3, 3,5,7,3, 3,5,8,3, 3,5,9,3, + 3,6,0,3, 3,6,1,3, 3,6,2,3, 3,6,3,3, 3,6,4,3, 3,6,5,3, 3,6,6,3, 3,6,7,3, 3,6,8,3, + 3,6,9,3, 3,7,0,3, 3,7,1,3, 3,7,2,3, 3,7,3,3, 3,7,4,3, 3,7,5,3, 3,7,6,3, 3,7,7,3, + 3,7,8,3, 3,7,9,3, 3,8,0,3, 3,8,1,3, 3,8,2,3, 3,8,3,3, 3,8,4,3, 3,8,5,3, 3,8,6,3, + 3,8,7,3, 3,8,8,3, 3,8,9,3, 3,9,0,3, 3,9,1,3, 3,9,2,3, 3,9,3,3, 3,9,4,3, 3,9,5,3, + 3,9,6,3, 3,9,7,3, 3,9,8,3, 3,9,9,3, 4,0,0,3, 4,0,1,3, 4,0,2,3, 4,0,3,3, 4,0,4,3, + 4,0,5,3, 4,0,6,3, 4,0,7,3, 4,0,8,3, 4,0,9,3, 4,1,0,3, 4,1,1,3, 4,1,2,3, 4,1,3,3, + 4,1,4,3, 4,1,5,3, 4,1,6,3, 4,1,7,3, 4,1,8,3, 4,1,9,3, 4,2,0,3, 4,2,1,3, 4,2,2,3, + 4,2,3,3, 4,2,4,3, 4,2,5,3, 4,2,6,3, 4,2,7,3, 4,2,8,3, 4,2,9,3, 4,3,0,3, 4,3,1,3, + 4,3,2,3, 4,3,3,3, 4,3,4,3, 4,3,5,3, 4,3,6,3, 4,3,7,3, 4,3,8,3, 4,3,9,3, 4,4,0,3, + 4,4,1,3, 4,4,2,3, 4,4,3,3, 4,4,4,3, 4,4,5,3, 4,4,6,3, 4,4,7,3, 4,4,8,3, 4,4,9,3, + 4,5,0,3, 4,5,1,3, 4,5,2,3, 4,5,3,3, 4,5,4,3, 4,5,5,3, 4,5,6,3, 4,5,7,3, 4,5,8,3, + 4,5,9,3, 4,6,0,3, 4,6,1,3, 4,6,2,3, 4,6,3,3, 4,6,4,3, 4,6,5,3, 4,6,6,3, 4,6,7,3, + 4,6,8,3, 4,6,9,3, 4,7,0,3, 4,7,1,3, 4,7,2,3, 4,7,3,3, 4,7,4,3, 4,7,5,3, 4,7,6,3, + 4,7,7,3, 4,7,8,3, 4,7,9,3, 4,8,0,3, 4,8,1,3, 4,8,2,3, 4,8,3,3, 4,8,4,3, 4,8,5,3, + 4,8,6,3, 4,8,7,3, 4,8,8,3, 4,8,9,3, 4,9,0,3, 4,9,1,3, 4,9,2,3, 4,9,3,3, 4,9,4,3, + 4,9,5,3, 4,9,6,3, 4,9,7,3, 4,9,8,3, 4,9,9,3, 5,0,0,3, 5,0,1,3, 5,0,2,3, 5,0,3,3, + 5,0,4,3, 5,0,5,3, 5,0,6,3, 5,0,7,3, 5,0,8,3, 5,0,9,3, 5,1,0,3, 5,1,1,3, 5,1,2,3, + 5,1,3,3, 5,1,4,3, 5,1,5,3, 5,1,6,3, 5,1,7,3, 5,1,8,3, 5,1,9,3, 5,2,0,3, 5,2,1,3, + 5,2,2,3, 5,2,3,3, 5,2,4,3, 5,2,5,3, 5,2,6,3, 5,2,7,3, 5,2,8,3, 5,2,9,3, 5,3,0,3, + 5,3,1,3, 5,3,2,3, 5,3,3,3, 5,3,4,3, 5,3,5,3, 5,3,6,3, 5,3,7,3, 5,3,8,3, 5,3,9,3, + 5,4,0,3, 5,4,1,3, 5,4,2,3, 5,4,3,3, 5,4,4,3, 5,4,5,3, 5,4,6,3, 5,4,7,3, 5,4,8,3, + 5,4,9,3, 5,5,0,3, 5,5,1,3, 5,5,2,3, 5,5,3,3, 5,5,4,3, 5,5,5,3, 5,5,6,3, 5,5,7,3, + 5,5,8,3, 5,5,9,3, 5,6,0,3, 5,6,1,3, 5,6,2,3, 5,6,3,3, 5,6,4,3, 5,6,5,3, 5,6,6,3, + 5,6,7,3, 5,6,8,3, 5,6,9,3, 5,7,0,3, 5,7,1,3, 5,7,2,3, 5,7,3,3, 5,7,4,3, 5,7,5,3, + 5,7,6,3, 5,7,7,3, 5,7,8,3, 5,7,9,3, 5,8,0,3, 5,8,1,3, 5,8,2,3, 5,8,3,3, 5,8,4,3, + 5,8,5,3, 5,8,6,3, 5,8,7,3, 5,8,8,3, 5,8,9,3, 5,9,0,3, 5,9,1,3, 5,9,2,3, 5,9,3,3, + 5,9,4,3, 5,9,5,3, 5,9,6,3, 5,9,7,3, 5,9,8,3, 5,9,9,3, 6,0,0,3, 6,0,1,3, 6,0,2,3, + 6,0,3,3, 6,0,4,3, 6,0,5,3, 6,0,6,3, 6,0,7,3, 6,0,8,3, 6,0,9,3, 6,1,0,3, 6,1,1,3, + 6,1,2,3, 6,1,3,3, 6,1,4,3, 6,1,5,3, 6,1,6,3, 6,1,7,3, 6,1,8,3, 6,1,9,3, 6,2,0,3, + 6,2,1,3, 6,2,2,3, 6,2,3,3, 6,2,4,3, 6,2,5,3, 6,2,6,3, 6,2,7,3, 6,2,8,3, 6,2,9,3, + 6,3,0,3, 6,3,1,3, 6,3,2,3, 6,3,3,3, 6,3,4,3, 6,3,5,3, 6,3,6,3, 6,3,7,3, 6,3,8,3, + 6,3,9,3, 6,4,0,3, 6,4,1,3, 6,4,2,3, 6,4,3,3, 6,4,4,3, 6,4,5,3, 6,4,6,3, 6,4,7,3, + 6,4,8,3, 6,4,9,3, 6,5,0,3, 6,5,1,3, 6,5,2,3, 6,5,3,3, 6,5,4,3, 6,5,5,3, 6,5,6,3, + 6,5,7,3, 6,5,8,3, 6,5,9,3, 6,6,0,3, 6,6,1,3, 6,6,2,3, 6,6,3,3, 6,6,4,3, 6,6,5,3, + 6,6,6,3, 6,6,7,3, 6,6,8,3, 6,6,9,3, 6,7,0,3, 6,7,1,3, 6,7,2,3, 6,7,3,3, 6,7,4,3, + 6,7,5,3, 6,7,6,3, 6,7,7,3, 6,7,8,3, 6,7,9,3, 6,8,0,3, 6,8,1,3, 6,8,2,3, 6,8,3,3, + 6,8,4,3, 6,8,5,3, 6,8,6,3, 6,8,7,3, 6,8,8,3, 6,8,9,3, 6,9,0,3, 6,9,1,3, 6,9,2,3, + 6,9,3,3, 6,9,4,3, 6,9,5,3, 6,9,6,3, 6,9,7,3, 6,9,8,3, 6,9,9,3, 7,0,0,3, 7,0,1,3, + 7,0,2,3, 7,0,3,3, 7,0,4,3, 7,0,5,3, 7,0,6,3, 7,0,7,3, 7,0,8,3, 7,0,9,3, 7,1,0,3, + 7,1,1,3, 7,1,2,3, 7,1,3,3, 7,1,4,3, 7,1,5,3, 7,1,6,3, 7,1,7,3, 7,1,8,3, 7,1,9,3, + 7,2,0,3, 7,2,1,3, 7,2,2,3, 7,2,3,3, 7,2,4,3, 7,2,5,3, 7,2,6,3, 7,2,7,3, 7,2,8,3, + 7,2,9,3, 7,3,0,3, 7,3,1,3, 7,3,2,3, 7,3,3,3, 7,3,4,3, 7,3,5,3, 7,3,6,3, 7,3,7,3, + 7,3,8,3, 7,3,9,3, 7,4,0,3, 7,4,1,3, 7,4,2,3, 7,4,3,3, 7,4,4,3, 7,4,5,3, 7,4,6,3, + 7,4,7,3, 7,4,8,3, 7,4,9,3, 7,5,0,3, 7,5,1,3, 7,5,2,3, 7,5,3,3, 7,5,4,3, 7,5,5,3, + 7,5,6,3, 7,5,7,3, 7,5,8,3, 7,5,9,3, 7,6,0,3, 7,6,1,3, 7,6,2,3, 7,6,3,3, 7,6,4,3, + 7,6,5,3, 7,6,6,3, 7,6,7,3, 7,6,8,3, 7,6,9,3, 7,7,0,3, 7,7,1,3, 7,7,2,3, 7,7,3,3, + 7,7,4,3, 7,7,5,3, 7,7,6,3, 7,7,7,3, 7,7,8,3, 7,7,9,3, 7,8,0,3, 7,8,1,3, 7,8,2,3, + 7,8,3,3, 7,8,4,3, 7,8,5,3, 7,8,6,3, 7,8,7,3, 7,8,8,3, 7,8,9,3, 7,9,0,3, 7,9,1,3, + 7,9,2,3, 7,9,3,3, 7,9,4,3, 7,9,5,3, 7,9,6,3, 7,9,7,3, 7,9,8,3, 7,9,9,3, 8,0,0,3, + 8,0,1,3, 8,0,2,3, 8,0,3,3, 8,0,4,3, 8,0,5,3, 8,0,6,3, 8,0,7,3, 8,0,8,3, 8,0,9,3, + 8,1,0,3, 8,1,1,3, 8,1,2,3, 8,1,3,3, 8,1,4,3, 8,1,5,3, 8,1,6,3, 8,1,7,3, 8,1,8,3, + 8,1,9,3, 8,2,0,3, 8,2,1,3, 8,2,2,3, 8,2,3,3, 8,2,4,3, 8,2,5,3, 8,2,6,3, 8,2,7,3, + 8,2,8,3, 8,2,9,3, 8,3,0,3, 8,3,1,3, 8,3,2,3, 8,3,3,3, 8,3,4,3, 8,3,5,3, 8,3,6,3, + 8,3,7,3, 8,3,8,3, 8,3,9,3, 8,4,0,3, 8,4,1,3, 8,4,2,3, 8,4,3,3, 8,4,4,3, 8,4,5,3, + 8,4,6,3, 8,4,7,3, 8,4,8,3, 8,4,9,3, 8,5,0,3, 8,5,1,3, 8,5,2,3, 8,5,3,3, 8,5,4,3, + 8,5,5,3, 8,5,6,3, 8,5,7,3, 8,5,8,3, 8,5,9,3, 8,6,0,3, 8,6,1,3, 8,6,2,3, 8,6,3,3, + 8,6,4,3, 8,6,5,3, 8,6,6,3, 8,6,7,3, 8,6,8,3, 8,6,9,3, 8,7,0,3, 8,7,1,3, 8,7,2,3, + 8,7,3,3, 8,7,4,3, 8,7,5,3, 8,7,6,3, 8,7,7,3, 8,7,8,3, 8,7,9,3, 8,8,0,3, 8,8,1,3, + 8,8,2,3, 8,8,3,3, 8,8,4,3, 8,8,5,3, 8,8,6,3, 8,8,7,3, 8,8,8,3, 8,8,9,3, 8,9,0,3, + 8,9,1,3, 8,9,2,3, 8,9,3,3, 8,9,4,3, 8,9,5,3, 8,9,6,3, 8,9,7,3, 8,9,8,3, 8,9,9,3, + 9,0,0,3, 9,0,1,3, 9,0,2,3, 9,0,3,3, 9,0,4,3, 9,0,5,3, 9,0,6,3, 9,0,7,3, 9,0,8,3, + 9,0,9,3, 9,1,0,3, 9,1,1,3, 9,1,2,3, 9,1,3,3, 9,1,4,3, 9,1,5,3, 9,1,6,3, 9,1,7,3, + 9,1,8,3, 9,1,9,3, 9,2,0,3, 9,2,1,3, 9,2,2,3, 9,2,3,3, 9,2,4,3, 9,2,5,3, 9,2,6,3, + 9,2,7,3, 9,2,8,3, 9,2,9,3, 9,3,0,3, 9,3,1,3, 9,3,2,3, 9,3,3,3, 9,3,4,3, 9,3,5,3, + 9,3,6,3, 9,3,7,3, 9,3,8,3, 9,3,9,3, 9,4,0,3, 9,4,1,3, 9,4,2,3, 9,4,3,3, 9,4,4,3, + 9,4,5,3, 9,4,6,3, 9,4,7,3, 9,4,8,3, 9,4,9,3, 9,5,0,3, 9,5,1,3, 9,5,2,3, 9,5,3,3, + 9,5,4,3, 9,5,5,3, 9,5,6,3, 9,5,7,3, 9,5,8,3, 9,5,9,3, 9,6,0,3, 9,6,1,3, 9,6,2,3, + 9,6,3,3, 9,6,4,3, 9,6,5,3, 9,6,6,3, 9,6,7,3, 9,6,8,3, 9,6,9,3, 9,7,0,3, 9,7,1,3, + 9,7,2,3, 9,7,3,3, 9,7,4,3, 9,7,5,3, 9,7,6,3, 9,7,7,3, 9,7,8,3, 9,7,9,3, 9,8,0,3, + 9,8,1,3, 9,8,2,3, 9,8,3,3, 9,8,4,3, 9,8,5,3, 9,8,6,3, 9,8,7,3, 9,8,8,3, 9,8,9,3, + 9,9,0,3, 9,9,1,3, 9,9,2,3, 9,9,3,3, 9,9,4,3, 9,9,5,3, 9,9,6,3, 9,9,7,3, 9,9,8,3, + 9,9,9,3}; +#endif diff --git a/include/libdecnumber/decNumber.h b/include/libdecnumber/decNumber.h new file mode 100644 index 0000000000..0a9fdced8b --- /dev/null +++ b/include/libdecnumber/decNumber.h @@ -0,0 +1,200 @@ +/* Decimal number arithmetic module header for the decNumber C Library. + Copyright (C) 2005, 2007 Free Software Foundation, Inc. + Contributed by IBM Corporation. Author Mike Cowlishaw. + + This file is part of GCC. + + GCC is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation; either version 2, or (at your option) any later + version. + + In addition to the permissions in the GNU General Public License, + the Free Software Foundation gives you unlimited permission to link + the compiled version of this file into combinations with other + programs, and to distribute those combinations without any + restriction coming from the use of this file. (The General Public + License restrictions do apply in other respects; for example, they + cover modification of the file, and distribution when not linked + into a combine executable.) + + GCC is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or + FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License + along with GCC; see the file COPYING. If not, write to the Free + Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA + 02110-1301, USA. */ + +/* ------------------------------------------------------------------ */ +/* Decimal Number arithmetic module header */ +/* ------------------------------------------------------------------ */ + +#if !defined(DECNUMBER) + #define DECNUMBER + #define DECNAME "decNumber" /* Short name */ + #define DECFULLNAME "Decimal Number Module" /* Verbose name */ + #define DECAUTHOR "Mike Cowlishaw" /* Who to blame */ + + #if !defined(DECCONTEXT) + #include "decContext.h" + #endif + + /* Bit settings for decNumber.bits */ + #define DECNEG 0x80 /* Sign; 1=negative, 0=positive or zero */ + #define DECINF 0x40 /* 1=Infinity */ + #define DECNAN 0x20 /* 1=NaN */ + #define DECSNAN 0x10 /* 1=sNaN */ + /* The remaining bits are reserved; they must be 0 */ + #define DECSPECIAL (DECINF|DECNAN|DECSNAN) /* any special value */ + + /* Define the decNumber data structure. The size and shape of the */ + /* units array in the structure is determined by the following */ + /* constant. This must not be changed without recompiling the */ + /* decNumber library modules. */ + + #define DECDPUN 3 /* DECimal Digits Per UNit [must be >0 */ + /* and <10; 3 or powers of 2 are best]. */ + + /* DECNUMDIGITS is the default number of digits that can be held in */ + /* the structure. If undefined, 1 is assumed and it is assumed */ + /* that the structure will be immediately followed by extra space, */ + /* as required. DECNUMDIGITS is always >0. */ + #if !defined(DECNUMDIGITS) + #define DECNUMDIGITS 1 + #endif + + /* The size (integer data type) of each unit is determined by the */ + /* number of digits it will hold. */ + #if DECDPUN<=2 + #define decNumberUnit uint8_t + #elif DECDPUN<=4 + #define decNumberUnit uint16_t + #else + #define decNumberUnit uint32_t + #endif + /* The number of units needed is ceil(DECNUMDIGITS/DECDPUN) */ + #define DECNUMUNITS ((DECNUMDIGITS+DECDPUN-1)/DECDPUN) + + /* The data structure... */ + typedef struct { + int32_t digits; /* Count of digits in the coefficient; >0 */ + int32_t exponent; /* Unadjusted exponent, unbiased, in */ + /* range: -1999999997 through 999999999 */ + uint8_t bits; /* Indicator bits (see above) */ + /* Coefficient, from least significant unit */ + decNumberUnit lsu[DECNUMUNITS]; + } decNumber; + + /* Notes: */ + /* 1. If digits is > DECDPUN then there will one or more */ + /* decNumberUnits immediately following the first element of lsu.*/ + /* These contain the remaining (more significant) digits of the */ + /* number, and may be in the lsu array, or may be guaranteed by */ + /* some other mechanism (such as being contained in another */ + /* structure, or being overlaid on dynamically allocated */ + /* storage). */ + /* */ + /* Each integer of the coefficient (except potentially the last) */ + /* contains DECDPUN digits (e.g., a value in the range 0 through */ + /* 99999999 if DECDPUN is 8, or 0 through 999 if DECDPUN is 3). */ + /* */ + /* 2. A decNumber converted to a string may need up to digits+14 */ + /* characters. The worst cases (non-exponential and exponential */ + /* formats) are -0.00000{9...}# and -9.{9...}E+999999999# */ + /* (where # is '\0') */ + + + /* ---------------------------------------------------------------- */ + /* decNumber public functions and macros */ + /* ---------------------------------------------------------------- */ + + #include "decNumberSymbols.h" + + /* Conversions */ + decNumber * decNumberFromInt32(decNumber *, int32_t); + decNumber * decNumberFromUInt32(decNumber *, uint32_t); + decNumber * decNumberFromString(decNumber *, const char *, decContext *); + char * decNumberToString(const decNumber *, char *); + char * decNumberToEngString(const decNumber *, char *); + uint32_t decNumberToUInt32(const decNumber *, decContext *); + int32_t decNumberToInt32(const decNumber *, decContext *); + uint8_t * decNumberGetBCD(const decNumber *, uint8_t *); + decNumber * decNumberSetBCD(decNumber *, const uint8_t *, uint32_t); + + /* Operators and elementary functions */ + decNumber * decNumberAbs(decNumber *, const decNumber *, decContext *); + decNumber * decNumberAdd(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberAnd(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberCompare(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberCompareSignal(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberCompareTotal(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberCompareTotalMag(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberDivide(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberDivideInteger(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberExp(decNumber *, const decNumber *, decContext *); + decNumber * decNumberFMA(decNumber *, const decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberInvert(decNumber *, const decNumber *, decContext *); + decNumber * decNumberLn(decNumber *, const decNumber *, decContext *); + decNumber * decNumberLogB(decNumber *, const decNumber *, decContext *); + decNumber * decNumberLog10(decNumber *, const decNumber *, decContext *); + decNumber * decNumberMax(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberMaxMag(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberMin(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberMinMag(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberMinus(decNumber *, const decNumber *, decContext *); + decNumber * decNumberMultiply(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberNormalize(decNumber *, const decNumber *, decContext *); + decNumber * decNumberOr(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberPlus(decNumber *, const decNumber *, decContext *); + decNumber * decNumberPower(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberQuantize(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberReduce(decNumber *, const decNumber *, decContext *); + decNumber * decNumberRemainder(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberRemainderNear(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberRescale(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberRotate(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberSameQuantum(decNumber *, const decNumber *, const decNumber *); + decNumber * decNumberScaleB(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberShift(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberSquareRoot(decNumber *, const decNumber *, decContext *); + decNumber * decNumberSubtract(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberToIntegralExact(decNumber *, const decNumber *, decContext *); + decNumber * decNumberToIntegralValue(decNumber *, const decNumber *, decContext *); + decNumber * decNumberXor(decNumber *, const decNumber *, const decNumber *, decContext *); + + /* Utilities */ + enum decClass decNumberClass(const decNumber *, decContext *); + const char * decNumberClassToString(enum decClass); + decNumber * decNumberCopy(decNumber *, const decNumber *); + decNumber * decNumberCopyAbs(decNumber *, const decNumber *); + decNumber * decNumberCopyNegate(decNumber *, const decNumber *); + decNumber * decNumberCopySign(decNumber *, const decNumber *, const decNumber *); + decNumber * decNumberNextMinus(decNumber *, const decNumber *, decContext *); + decNumber * decNumberNextPlus(decNumber *, const decNumber *, decContext *); + decNumber * decNumberNextToward(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberTrim(decNumber *); + const char * decNumberVersion(void); + decNumber * decNumberZero(decNumber *); + + /* Functions for testing decNumbers (normality depends on context) */ + int32_t decNumberIsNormal(const decNumber *, decContext *); + int32_t decNumberIsSubnormal(const decNumber *, decContext *); + + /* Macros for testing decNumber *dn */ + #define decNumberIsCanonical(dn) (1) /* All decNumbers are saintly */ + #define decNumberIsFinite(dn) (((dn)->bits&DECSPECIAL)==0) + #define decNumberIsInfinite(dn) (((dn)->bits&DECINF)!=0) + #define decNumberIsNaN(dn) (((dn)->bits&(DECNAN|DECSNAN))!=0) + #define decNumberIsNegative(dn) (((dn)->bits&DECNEG)!=0) + #define decNumberIsQNaN(dn) (((dn)->bits&(DECNAN))!=0) + #define decNumberIsSNaN(dn) (((dn)->bits&(DECSNAN))!=0) + #define decNumberIsSpecial(dn) (((dn)->bits&DECSPECIAL)!=0) + #define decNumberIsZero(dn) (*(dn)->lsu==0 \ + && (dn)->digits==1 \ + && (((dn)->bits&DECSPECIAL)==0)) + #define decNumberRadix(dn) (10) + +#endif diff --git a/include/libdecnumber/decNumberLocal.h b/include/libdecnumber/decNumberLocal.h new file mode 100644 index 0000000000..f1568f725e --- /dev/null +++ b/include/libdecnumber/decNumberLocal.h @@ -0,0 +1,667 @@ +/* Local definitions for the decNumber C Library. + Copyright (C) 2007 Free Software Foundation, Inc. + Contributed by IBM Corporation. Author Mike Cowlishaw. + + This file is part of GCC. + + GCC is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation; either version 2, or (at your option) any later + version. + + In addition to the permissions in the GNU General Public License, + the Free Software Foundation gives you unlimited permission to link + the compiled version of this file into combinations with other + programs, and to distribute those combinations without any + restriction coming from the use of this file. (The General Public + License restrictions do apply in other respects; for example, they + cover modification of the file, and distribution when not linked + into a combine executable.) + + GCC is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or + FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License + along with GCC; see the file COPYING. If not, write to the Free + Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA + 02110-1301, USA. */ + +/* ------------------------------------------------------------------ */ +/* decNumber package local type, tuning, and macro definitions */ +/* ------------------------------------------------------------------ */ +/* This header file is included by all modules in the decNumber */ +/* library, and contains local type definitions, tuning parameters, */ +/* etc. It should not need to be used by application programs. */ +/* decNumber.h or one of decDouble (etc.) must be included first. */ +/* ------------------------------------------------------------------ */ + +#if !defined(DECNUMBERLOC) + #define DECNUMBERLOC + #define DECVERSION "decNumber 3.53" /* Package Version [16 max.] */ + #define DECNLAUTHOR "Mike Cowlishaw" /* Who to blame */ + + #include <stdlib.h> /* for abs */ + #include <string.h> /* for memset, strcpy */ + #include "dconfig.h" /* for WORDS_BIGENDIAN */ + + /* Conditional code flag -- set this to match hardware platform */ + /* 1=little-endian, 0=big-endian */ + #if WORDS_BIGENDIAN + #define DECLITEND 0 + #else + #define DECLITEND 1 + #endif + + /* Conditional code flag -- set this to 1 for best performance */ + #define DECUSE64 1 /* 1=use int64s, 0=int32 & smaller only */ + + /* Conditional check flags -- set these to 0 for best performance */ + #define DECCHECK 0 /* 1 to enable robust checking */ + #define DECALLOC 0 /* 1 to enable memory accounting */ + #define DECTRACE 0 /* 1 to trace certain internals, etc. */ + + /* Tuning parameter for decNumber (arbitrary precision) module */ + #define DECBUFFER 36 /* Size basis for local buffers. This */ + /* should be a common maximum precision */ + /* rounded up to a multiple of 4; must */ + /* be zero or positive. */ + + /* ---------------------------------------------------------------- */ + /* Definitions for all modules (general-purpose) */ + /* ---------------------------------------------------------------- */ + + /* Local names for common types -- for safety, decNumber modules do */ + /* not use int or long directly. */ + #define Flag uint8_t + #define Byte int8_t + #define uByte uint8_t + #define Short int16_t + #define uShort uint16_t + #define Int int32_t + #define uInt uint32_t + #define Unit decNumberUnit + #if DECUSE64 + #define Long int64_t + #define uLong uint64_t + #endif + + /* Development-use definitions */ + typedef long int LI; /* for printf arguments only */ + #define DECNOINT 0 /* 1 to check no internal use of 'int' */ + #if DECNOINT + /* if these interfere with your C includes, do not set DECNOINT */ + #define int ? /* enable to ensure that plain C 'int' */ + #define long ?? /* .. or 'long' types are not used */ + #endif + + /* Shared lookup tables */ + extern const uByte DECSTICKYTAB[10]; /* re-round digits if sticky */ + extern const uInt DECPOWERS[10]; /* powers of ten table */ + /* The following are included from decDPD.h */ +#include "decDPDSymbols.h" + extern const uShort DPD2BIN[1024]; /* DPD -> 0-999 */ + extern const uShort BIN2DPD[1000]; /* 0-999 -> DPD */ + extern const uInt DPD2BINK[1024]; /* DPD -> 0-999000 */ + extern const uInt DPD2BINM[1024]; /* DPD -> 0-999000000 */ + extern const uByte DPD2BCD8[4096]; /* DPD -> ddd + len */ + extern const uByte BIN2BCD8[4000]; /* 0-999 -> ddd + len */ + extern const uShort BCD2DPD[2458]; /* 0-0x999 -> DPD (0x999=2457)*/ + + /* LONGMUL32HI -- set w=(u*v)>>32, where w, u, and v are uInts */ + /* (that is, sets w to be the high-order word of the 64-bit result; */ + /* the low-order word is simply u*v.) */ + /* This version is derived from Knuth via Hacker's Delight; */ + /* it seems to optimize better than some others tried */ + #define LONGMUL32HI(w, u, v) { \ + uInt u0, u1, v0, v1, w0, w1, w2, t; \ + u0=u & 0xffff; u1=u>>16; \ + v0=v & 0xffff; v1=v>>16; \ + w0=u0*v0; \ + t=u1*v0 + (w0>>16); \ + w1=t & 0xffff; w2=t>>16; \ + w1=u0*v1 + w1; \ + (w)=u1*v1 + w2 + (w1>>16);} + + /* ROUNDUP -- round an integer up to a multiple of n */ + #define ROUNDUP(i, n) ((((i)+(n)-1)/n)*n) + + /* ROUNDDOWN -- round an integer down to a multiple of n */ + #define ROUNDDOWN(i, n) (((i)/n)*n) + #define ROUNDDOWN4(i) ((i)&~3) /* special for n=4 */ + + /* References to multi-byte sequences under different sizes */ + /* Refer to a uInt from four bytes starting at a char* or uByte*, */ + /* etc. */ + #define UINTAT(b) (*((uInt *)(b))) + #define USHORTAT(b) (*((uShort *)(b))) + #define UBYTEAT(b) (*((uByte *)(b))) + + /* X10 and X100 -- multiply integer i by 10 or 100 */ + /* [shifts are usually faster than multiply; could be conditional] */ + #define X10(i) (((i)<<1)+((i)<<3)) + #define X100(i) (((i)<<2)+((i)<<5)+((i)<<6)) + + /* MAXI and MINI -- general max & min (not in ANSI) for integers */ + #define MAXI(x,y) ((x)<(y)?(y):(x)) + #define MINI(x,y) ((x)>(y)?(y):(x)) + + /* Useful constants */ + #define BILLION 1000000000 /* 10**9 */ + /* CHARMASK: 0x30303030 for ASCII/UTF8; 0xF0F0F0F0 for EBCDIC */ + #define CHARMASK ((((((((uInt)'0')<<8)+'0')<<8)+'0')<<8)+'0') + + + /* ---------------------------------------------------------------- */ + /* Definitions for arbitary-precision modules (only valid after */ + /* decNumber.h has been included) */ + /* ---------------------------------------------------------------- */ + + /* Limits and constants */ + #define DECNUMMAXP 999999999 /* maximum precision code can handle */ + #define DECNUMMAXE 999999999 /* maximum adjusted exponent ditto */ + #define DECNUMMINE -999999999 /* minimum adjusted exponent ditto */ + #if (DECNUMMAXP != DEC_MAX_DIGITS) + #error Maximum digits mismatch + #endif + #if (DECNUMMAXE != DEC_MAX_EMAX) + #error Maximum exponent mismatch + #endif + #if (DECNUMMINE != DEC_MIN_EMIN) + #error Minimum exponent mismatch + #endif + + /* Set DECDPUNMAX -- the maximum integer that fits in DECDPUN */ + /* digits, and D2UTABLE -- the initializer for the D2U table */ + #if DECDPUN==1 + #define DECDPUNMAX 9 + #define D2UTABLE {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17, \ + 18,19,20,21,22,23,24,25,26,27,28,29,30,31,32, \ + 33,34,35,36,37,38,39,40,41,42,43,44,45,46,47, \ + 48,49} + #elif DECDPUN==2 + #define DECDPUNMAX 99 + #define D2UTABLE {0,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10, \ + 11,11,12,12,13,13,14,14,15,15,16,16,17,17,18, \ + 18,19,19,20,20,21,21,22,22,23,23,24,24,25} + #elif DECDPUN==3 + #define DECDPUNMAX 999 + #define D2UTABLE {0,1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,7,7, \ + 8,8,8,9,9,9,10,10,10,11,11,11,12,12,12,13,13, \ + 13,14,14,14,15,15,15,16,16,16,17} + #elif DECDPUN==4 + #define DECDPUNMAX 9999 + #define D2UTABLE {0,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,6, \ + 6,6,6,7,7,7,7,8,8,8,8,9,9,9,9,10,10,10,10,11, \ + 11,11,11,12,12,12,12,13} + #elif DECDPUN==5 + #define DECDPUNMAX 99999 + #define D2UTABLE {0,1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,5, \ + 5,5,5,5,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,9,9,9, \ + 9,9,10,10,10,10} + #elif DECDPUN==6 + #define DECDPUNMAX 999999 + #define D2UTABLE {0,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4, \ + 4,4,4,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8, \ + 8,8,8,8,8,9} + #elif DECDPUN==7 + #define DECDPUNMAX 9999999 + #define D2UTABLE {0,1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,3, \ + 4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,6,7, \ + 7,7,7,7,7,7} + #elif DECDPUN==8 + #define DECDPUNMAX 99999999 + #define D2UTABLE {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3, \ + 3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6, \ + 6,6,6,6,6,7} + #elif DECDPUN==9 + #define DECDPUNMAX 999999999 + #define D2UTABLE {0,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,3, \ + 3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5, \ + 5,5,6,6,6,6} + #elif defined(DECDPUN) + #error DECDPUN must be in the range 1-9 + #endif + + /* ----- Shared data (in decNumber.c) ----- */ + /* Public lookup table used by the D2U macro (see below) */ + #define DECMAXD2U 49 + extern const uByte d2utable[DECMAXD2U+1]; + + /* ----- Macros ----- */ + /* ISZERO -- return true if decNumber dn is a zero */ + /* [performance-critical in some situations] */ + #define ISZERO(dn) decNumberIsZero(dn) /* now just a local name */ + + /* D2U -- return the number of Units needed to hold d digits */ + /* (runtime version, with table lookaside for small d) */ + #if DECDPUN==8 + #define D2U(d) ((unsigned)((d)<=DECMAXD2U?d2utable[d]:((d)+7)>>3)) + #elif DECDPUN==4 + #define D2U(d) ((unsigned)((d)<=DECMAXD2U?d2utable[d]:((d)+3)>>2)) + #else + #define D2U(d) ((d)<=DECMAXD2U?d2utable[d]:((d)+DECDPUN-1)/DECDPUN) + #endif + /* SD2U -- static D2U macro (for compile-time calculation) */ + #define SD2U(d) (((d)+DECDPUN-1)/DECDPUN) + + /* MSUDIGITS -- returns digits in msu, from digits, calculated */ + /* using D2U */ + #define MSUDIGITS(d) ((d)-(D2U(d)-1)*DECDPUN) + + /* D2N -- return the number of decNumber structs that would be */ + /* needed to contain that number of digits (and the initial */ + /* decNumber struct) safely. Note that one Unit is included in the */ + /* initial structure. Used for allocating space that is aligned on */ + /* a decNumber struct boundary. */ + #define D2N(d) \ + ((((SD2U(d)-1)*sizeof(Unit))+sizeof(decNumber)*2-1)/sizeof(decNumber)) + + /* TODIGIT -- macro to remove the leading digit from the unsigned */ + /* integer u at column cut (counting from the right, LSD=0) and */ + /* place it as an ASCII character into the character pointed to by */ + /* c. Note that cut must be <= 9, and the maximum value for u is */ + /* 2,000,000,000 (as is needed for negative exponents of */ + /* subnormals). The unsigned integer pow is used as a temporary */ + /* variable. */ + #define TODIGIT(u, cut, c, pow) { \ + *(c)='0'; \ + pow=DECPOWERS[cut]*2; \ + if ((u)>pow) { \ + pow*=4; \ + if ((u)>=pow) {(u)-=pow; *(c)+=8;} \ + pow/=2; \ + if ((u)>=pow) {(u)-=pow; *(c)+=4;} \ + pow/=2; \ + } \ + if ((u)>=pow) {(u)-=pow; *(c)+=2;} \ + pow/=2; \ + if ((u)>=pow) {(u)-=pow; *(c)+=1;} \ + } + + /* ---------------------------------------------------------------- */ + /* Definitions for fixed-precision modules (only valid after */ + /* decSingle.h, decDouble.h, or decQuad.h has been included) */ + /* ---------------------------------------------------------------- */ + + /* bcdnum -- a structure describing a format-independent finite */ + /* number, whose coefficient is a string of bcd8 uBytes */ + typedef struct { + uByte *msd; /* -> most significant digit */ + uByte *lsd; /* -> least ditto */ + uInt sign; /* 0=positive, DECFLOAT_Sign=negative */ + Int exponent; /* Unadjusted signed exponent (q), or */ + /* DECFLOAT_NaN etc. for a special */ + } bcdnum; + + /* Test if exponent or bcdnum exponent must be a special, etc. */ + #define EXPISSPECIAL(exp) ((exp)>=DECFLOAT_MinSp) + #define EXPISINF(exp) (exp==DECFLOAT_Inf) + #define EXPISNAN(exp) (exp==DECFLOAT_qNaN || exp==DECFLOAT_sNaN) + #define NUMISSPECIAL(num) (EXPISSPECIAL((num)->exponent)) + + /* Refer to a 32-bit word or byte in a decFloat (df) by big-endian */ + /* (array) notation (the 0 word or byte contains the sign bit), */ + /* automatically adjusting for endianness; similarly address a word */ + /* in the next-wider format (decFloatWider, or dfw) */ + #define DECWORDS (DECBYTES/4) + #define DECWWORDS (DECWBYTES/4) + #if DECLITEND + #define DFWORD(df, off) ((df)->words[DECWORDS-1-(off)]) + #define DFBYTE(df, off) ((df)->bytes[DECBYTES-1-(off)]) + #define DFWWORD(dfw, off) ((dfw)->words[DECWWORDS-1-(off)]) + #else + #define DFWORD(df, off) ((df)->words[off]) + #define DFBYTE(df, off) ((df)->bytes[off]) + #define DFWWORD(dfw, off) ((dfw)->words[off]) + #endif + + /* Tests for sign or specials, directly on DECFLOATs */ + #define DFISSIGNED(df) (DFWORD(df, 0)&0x80000000) + #define DFISSPECIAL(df) ((DFWORD(df, 0)&0x78000000)==0x78000000) + #define DFISINF(df) ((DFWORD(df, 0)&0x7c000000)==0x78000000) + #define DFISNAN(df) ((DFWORD(df, 0)&0x7c000000)==0x7c000000) + #define DFISQNAN(df) ((DFWORD(df, 0)&0x7e000000)==0x7c000000) + #define DFISSNAN(df) ((DFWORD(df, 0)&0x7e000000)==0x7e000000) + + /* Shared lookup tables */ +#include "decCommonSymbols.h" + extern const uInt DECCOMBMSD[64]; /* Combination field -> MSD */ + extern const uInt DECCOMBFROM[48]; /* exp+msd -> Combination */ + + /* Private generic (utility) routine */ + #if DECCHECK || DECTRACE + extern void decShowNum(const bcdnum *, const char *); + #endif + + /* Format-dependent macros and constants */ + #if defined(DECPMAX) + + /* Useful constants */ + #define DECPMAX9 (ROUNDUP(DECPMAX, 9)/9) /* 'Pmax' in 10**9s */ + /* Top words for a zero */ + #define SINGLEZERO 0x22500000 + #define DOUBLEZERO 0x22380000 + #define QUADZERO 0x22080000 + /* [ZEROWORD is defined to be one of these in the DFISZERO macro] */ + + /* Format-dependent common tests: */ + /* DFISZERO -- test for (any) zero */ + /* DFISCCZERO -- test for coefficient continuation being zero */ + /* DFISCC01 -- test for coefficient contains only 0s and 1s */ + /* DFISINT -- test for finite and exponent q=0 */ + /* DFISUINT01 -- test for sign=0, finite, exponent q=0, and */ + /* MSD=0 or 1 */ + /* ZEROWORD is also defined here. */ + /* In DFISZERO the first test checks the least-significant word */ + /* (most likely to be non-zero); the penultimate tests MSD and */ + /* DPDs in the signword, and the final test excludes specials and */ + /* MSD>7. DFISINT similarly has to allow for the two forms of */ + /* MSD codes. DFISUINT01 only has to allow for one form of MSD */ + /* code. */ + #if DECPMAX==7 + #define ZEROWORD SINGLEZERO + /* [test macros not needed except for Zero] */ + #define DFISZERO(df) ((DFWORD(df, 0)&0x1c0fffff)==0 \ + && (DFWORD(df, 0)&0x60000000)!=0x60000000) + #elif DECPMAX==16 + #define ZEROWORD DOUBLEZERO + #define DFISZERO(df) ((DFWORD(df, 1)==0 \ + && (DFWORD(df, 0)&0x1c03ffff)==0 \ + && (DFWORD(df, 0)&0x60000000)!=0x60000000)) + #define DFISINT(df) ((DFWORD(df, 0)&0x63fc0000)==0x22380000 \ + ||(DFWORD(df, 0)&0x7bfc0000)==0x6a380000) + #define DFISUINT01(df) ((DFWORD(df, 0)&0xfbfc0000)==0x22380000) + #define DFISCCZERO(df) (DFWORD(df, 1)==0 \ + && (DFWORD(df, 0)&0x0003ffff)==0) + #define DFISCC01(df) ((DFWORD(df, 0)&~0xfffc9124)==0 \ + && (DFWORD(df, 1)&~0x49124491)==0) + #elif DECPMAX==34 + #define ZEROWORD QUADZERO + #define DFISZERO(df) ((DFWORD(df, 3)==0 \ + && DFWORD(df, 2)==0 \ + && DFWORD(df, 1)==0 \ + && (DFWORD(df, 0)&0x1c003fff)==0 \ + && (DFWORD(df, 0)&0x60000000)!=0x60000000)) + #define DFISINT(df) ((DFWORD(df, 0)&0x63ffc000)==0x22080000 \ + ||(DFWORD(df, 0)&0x7bffc000)==0x6a080000) + #define DFISUINT01(df) ((DFWORD(df, 0)&0xfbffc000)==0x22080000) + #define DFISCCZERO(df) (DFWORD(df, 3)==0 \ + && DFWORD(df, 2)==0 \ + && DFWORD(df, 1)==0 \ + && (DFWORD(df, 0)&0x00003fff)==0) + + #define DFISCC01(df) ((DFWORD(df, 0)&~0xffffc912)==0 \ + && (DFWORD(df, 1)&~0x44912449)==0 \ + && (DFWORD(df, 2)&~0x12449124)==0 \ + && (DFWORD(df, 3)&~0x49124491)==0) + #endif + + /* Macros to test if a certain 10 bits of a uInt or pair of uInts */ + /* are a canonical declet [higher or lower bits are ignored]. */ + /* declet is at offset 0 (from the right) in a uInt: */ + #define CANONDPD(dpd) (((dpd)&0x300)==0 || ((dpd)&0x6e)!=0x6e) + /* declet is at offset k (a multiple of 2) in a uInt: */ + #define CANONDPDOFF(dpd, k) (((dpd)&(0x300<<(k)))==0 \ + || ((dpd)&(((uInt)0x6e)<<(k)))!=(((uInt)0x6e)<<(k))) + /* declet is at offset k (a multiple of 2) in a pair of uInts: */ + /* [the top 2 bits will always be in the more-significant uInt] */ + #define CANONDPDTWO(hi, lo, k) (((hi)&(0x300>>(32-(k))))==0 \ + || ((hi)&(0x6e>>(32-(k))))!=(0x6e>>(32-(k))) \ + || ((lo)&(((uInt)0x6e)<<(k)))!=(((uInt)0x6e)<<(k))) + + /* Macro to test whether a full-length (length DECPMAX) BCD8 */ + /* coefficient is zero */ + /* test just the LSWord first, then the remainder */ + #if DECPMAX==7 + #define ISCOEFFZERO(u) (UINTAT((u)+DECPMAX-4)==0 \ + && UINTAT((u)+DECPMAX-7)==0) + #elif DECPMAX==16 + #define ISCOEFFZERO(u) (UINTAT((u)+DECPMAX-4)==0 \ + && (UINTAT((u)+DECPMAX-8)+UINTAT((u)+DECPMAX-12) \ + +UINTAT((u)+DECPMAX-16))==0) + #elif DECPMAX==34 + #define ISCOEFFZERO(u) (UINTAT((u)+DECPMAX-4)==0 \ + && (UINTAT((u)+DECPMAX-8) +UINTAT((u)+DECPMAX-12) \ + +UINTAT((u)+DECPMAX-16)+UINTAT((u)+DECPMAX-20) \ + +UINTAT((u)+DECPMAX-24)+UINTAT((u)+DECPMAX-28) \ + +UINTAT((u)+DECPMAX-32)+USHORTAT((u)+DECPMAX-34))==0) + #endif + + /* Macros and masks for the exponent continuation field and MSD */ + /* Get the exponent continuation from a decFloat *df as an Int */ + #define GETECON(df) ((Int)((DFWORD((df), 0)&0x03ffffff)>>(32-6-DECECONL))) + /* Ditto, from the next-wider format */ + #define GETWECON(df) ((Int)((DFWWORD((df), 0)&0x03ffffff)>>(32-6-DECWECONL))) + /* Get the biased exponent similarly */ + #define GETEXP(df) ((Int)(DECCOMBEXP[DFWORD((df), 0)>>26]+GETECON(df))) + /* Get the unbiased exponent similarly */ + #define GETEXPUN(df) ((Int)GETEXP(df)-DECBIAS) + /* Get the MSD similarly (as uInt) */ + #define GETMSD(df) (DECCOMBMSD[DFWORD((df), 0)>>26]) + + /* Compile-time computes of the exponent continuation field masks */ + /* full exponent continuation field: */ + #define ECONMASK ((0x03ffffff>>(32-6-DECECONL))<<(32-6-DECECONL)) + /* same, not including its first digit (the qNaN/sNaN selector): */ + #define ECONNANMASK ((0x01ffffff>>(32-6-DECECONL))<<(32-6-DECECONL)) + + /* Macros to decode the coefficient in a finite decFloat *df into */ + /* a BCD string (uByte *bcdin) of length DECPMAX uBytes */ + + /* In-line sequence to convert 10 bits at right end of uInt dpd */ + /* to three BCD8 digits starting at uByte u. Note that an extra */ + /* byte is written to the right of the three digits because this */ + /* moves four at a time for speed; the alternative macro moves */ + /* exactly three bytes */ + #define dpd2bcd8(u, dpd) { \ + UINTAT(u)=UINTAT(&DPD2BCD8[((dpd)&0x3ff)*4]);} + + #define dpd2bcd83(u, dpd) { \ + *(u)=DPD2BCD8[((dpd)&0x3ff)*4]; \ + *(u+1)=DPD2BCD8[((dpd)&0x3ff)*4+1]; \ + *(u+2)=DPD2BCD8[((dpd)&0x3ff)*4+2];} + + /* Decode the declets. After extracting each one, it is decoded */ + /* to BCD8 using a table lookup (also used for variable-length */ + /* decode). Each DPD decode is 3 bytes BCD8 plus a one-byte */ + /* length which is not used, here). Fixed-length 4-byte moves */ + /* are fast, however, almost everywhere, and so are used except */ + /* for the final three bytes (to avoid overrun). The code below */ + /* is 36 instructions for Doubles and about 70 for Quads, even */ + /* on IA32. */ + + /* Two macros are defined for each format: */ + /* GETCOEFF extracts the coefficient of the current format */ + /* GETWCOEFF extracts the coefficient of the next-wider format. */ + /* The latter is a copy of the next-wider GETCOEFF using DFWWORD. */ + + #if DECPMAX==7 + #define GETCOEFF(df, bcd) { \ + uInt sourhi=DFWORD(df, 0); \ + *(bcd)=(uByte)DECCOMBMSD[sourhi>>26]; \ + dpd2bcd8(bcd+1, sourhi>>10); \ + dpd2bcd83(bcd+4, sourhi);} + #define GETWCOEFF(df, bcd) { \ + uInt sourhi=DFWWORD(df, 0); \ + uInt sourlo=DFWWORD(df, 1); \ + *(bcd)=(uByte)DECCOMBMSD[sourhi>>26]; \ + dpd2bcd8(bcd+1, sourhi>>8); \ + dpd2bcd8(bcd+4, (sourhi<<2) | (sourlo>>30)); \ + dpd2bcd8(bcd+7, sourlo>>20); \ + dpd2bcd8(bcd+10, sourlo>>10); \ + dpd2bcd83(bcd+13, sourlo);} + + #elif DECPMAX==16 + #define GETCOEFF(df, bcd) { \ + uInt sourhi=DFWORD(df, 0); \ + uInt sourlo=DFWORD(df, 1); \ + *(bcd)=(uByte)DECCOMBMSD[sourhi>>26]; \ + dpd2bcd8(bcd+1, sourhi>>8); \ + dpd2bcd8(bcd+4, (sourhi<<2) | (sourlo>>30)); \ + dpd2bcd8(bcd+7, sourlo>>20); \ + dpd2bcd8(bcd+10, sourlo>>10); \ + dpd2bcd83(bcd+13, sourlo);} + #define GETWCOEFF(df, bcd) { \ + uInt sourhi=DFWWORD(df, 0); \ + uInt sourmh=DFWWORD(df, 1); \ + uInt sourml=DFWWORD(df, 2); \ + uInt sourlo=DFWWORD(df, 3); \ + *(bcd)=(uByte)DECCOMBMSD[sourhi>>26]; \ + dpd2bcd8(bcd+1, sourhi>>4); \ + dpd2bcd8(bcd+4, ((sourhi)<<6) | (sourmh>>26)); \ + dpd2bcd8(bcd+7, sourmh>>16); \ + dpd2bcd8(bcd+10, sourmh>>6); \ + dpd2bcd8(bcd+13, ((sourmh)<<4) | (sourml>>28)); \ + dpd2bcd8(bcd+16, sourml>>18); \ + dpd2bcd8(bcd+19, sourml>>8); \ + dpd2bcd8(bcd+22, ((sourml)<<2) | (sourlo>>30)); \ + dpd2bcd8(bcd+25, sourlo>>20); \ + dpd2bcd8(bcd+28, sourlo>>10); \ + dpd2bcd83(bcd+31, sourlo);} + + #elif DECPMAX==34 + #define GETCOEFF(df, bcd) { \ + uInt sourhi=DFWORD(df, 0); \ + uInt sourmh=DFWORD(df, 1); \ + uInt sourml=DFWORD(df, 2); \ + uInt sourlo=DFWORD(df, 3); \ + *(bcd)=(uByte)DECCOMBMSD[sourhi>>26]; \ + dpd2bcd8(bcd+1, sourhi>>4); \ + dpd2bcd8(bcd+4, ((sourhi)<<6) | (sourmh>>26)); \ + dpd2bcd8(bcd+7, sourmh>>16); \ + dpd2bcd8(bcd+10, sourmh>>6); \ + dpd2bcd8(bcd+13, ((sourmh)<<4) | (sourml>>28)); \ + dpd2bcd8(bcd+16, sourml>>18); \ + dpd2bcd8(bcd+19, sourml>>8); \ + dpd2bcd8(bcd+22, ((sourml)<<2) | (sourlo>>30)); \ + dpd2bcd8(bcd+25, sourlo>>20); \ + dpd2bcd8(bcd+28, sourlo>>10); \ + dpd2bcd83(bcd+31, sourlo);} + + #define GETWCOEFF(df, bcd) {??} /* [should never be used] */ + #endif + + /* Macros to decode the coefficient in a finite decFloat *df into */ + /* a base-billion uInt array, with the least-significant */ + /* 0-999999999 'digit' at offset 0. */ + + /* Decode the declets. After extracting each one, it is decoded */ + /* to binary using a table lookup. Three tables are used; one */ + /* the usual DPD to binary, the other two pre-multiplied by 1000 */ + /* and 1000000 to avoid multiplication during decode. These */ + /* tables can also be used for multiplying up the MSD as the DPD */ + /* code for 0 through 9 is the identity. */ + #define DPD2BIN0 DPD2BIN /* for prettier code */ + + #if DECPMAX==7 + #define GETCOEFFBILL(df, buf) { \ + uInt sourhi=DFWORD(df, 0); \ + (buf)[0]=DPD2BIN0[sourhi&0x3ff] \ + +DPD2BINK[(sourhi>>10)&0x3ff] \ + +DPD2BINM[DECCOMBMSD[sourhi>>26]];} + + #elif DECPMAX==16 + #define GETCOEFFBILL(df, buf) { \ + uInt sourhi, sourlo; \ + sourlo=DFWORD(df, 1); \ + (buf)[0]=DPD2BIN0[sourlo&0x3ff] \ + +DPD2BINK[(sourlo>>10)&0x3ff] \ + +DPD2BINM[(sourlo>>20)&0x3ff]; \ + sourhi=DFWORD(df, 0); \ + (buf)[1]=DPD2BIN0[((sourhi<<2) | (sourlo>>30))&0x3ff] \ + +DPD2BINK[(sourhi>>8)&0x3ff] \ + +DPD2BINM[DECCOMBMSD[sourhi>>26]];} + + #elif DECPMAX==34 + #define GETCOEFFBILL(df, buf) { \ + uInt sourhi, sourmh, sourml, sourlo; \ + sourlo=DFWORD(df, 3); \ + (buf)[0]=DPD2BIN0[sourlo&0x3ff] \ + +DPD2BINK[(sourlo>>10)&0x3ff] \ + +DPD2BINM[(sourlo>>20)&0x3ff]; \ + sourml=DFWORD(df, 2); \ + (buf)[1]=DPD2BIN0[((sourml<<2) | (sourlo>>30))&0x3ff] \ + +DPD2BINK[(sourml>>8)&0x3ff] \ + +DPD2BINM[(sourml>>18)&0x3ff]; \ + sourmh=DFWORD(df, 1); \ + (buf)[2]=DPD2BIN0[((sourmh<<4) | (sourml>>28))&0x3ff] \ + +DPD2BINK[(sourmh>>6)&0x3ff] \ + +DPD2BINM[(sourmh>>16)&0x3ff]; \ + sourhi=DFWORD(df, 0); \ + (buf)[3]=DPD2BIN0[((sourhi<<6) | (sourmh>>26))&0x3ff] \ + +DPD2BINK[(sourhi>>4)&0x3ff] \ + +DPD2BINM[DECCOMBMSD[sourhi>>26]];} + + #endif + + /* Macros to decode the coefficient in a finite decFloat *df into */ + /* a base-thousand uInt array, with the least-significant 0-999 */ + /* 'digit' at offset 0. */ + + /* Decode the declets. After extracting each one, it is decoded */ + /* to binary using a table lookup. */ + #if DECPMAX==7 + #define GETCOEFFTHOU(df, buf) { \ + uInt sourhi=DFWORD(df, 0); \ + (buf)[0]=DPD2BIN[sourhi&0x3ff]; \ + (buf)[1]=DPD2BIN[(sourhi>>10)&0x3ff]; \ + (buf)[2]=DECCOMBMSD[sourhi>>26];} + + #elif DECPMAX==16 + #define GETCOEFFTHOU(df, buf) { \ + uInt sourhi, sourlo; \ + sourlo=DFWORD(df, 1); \ + (buf)[0]=DPD2BIN[sourlo&0x3ff]; \ + (buf)[1]=DPD2BIN[(sourlo>>10)&0x3ff]; \ + (buf)[2]=DPD2BIN[(sourlo>>20)&0x3ff]; \ + sourhi=DFWORD(df, 0); \ + (buf)[3]=DPD2BIN[((sourhi<<2) | (sourlo>>30))&0x3ff]; \ + (buf)[4]=DPD2BIN[(sourhi>>8)&0x3ff]; \ + (buf)[5]=DECCOMBMSD[sourhi>>26];} + + #elif DECPMAX==34 + #define GETCOEFFTHOU(df, buf) { \ + uInt sourhi, sourmh, sourml, sourlo; \ + sourlo=DFWORD(df, 3); \ + (buf)[0]=DPD2BIN[sourlo&0x3ff]; \ + (buf)[1]=DPD2BIN[(sourlo>>10)&0x3ff]; \ + (buf)[2]=DPD2BIN[(sourlo>>20)&0x3ff]; \ + sourml=DFWORD(df, 2); \ + (buf)[3]=DPD2BIN[((sourml<<2) | (sourlo>>30))&0x3ff]; \ + (buf)[4]=DPD2BIN[(sourml>>8)&0x3ff]; \ + (buf)[5]=DPD2BIN[(sourml>>18)&0x3ff]; \ + sourmh=DFWORD(df, 1); \ + (buf)[6]=DPD2BIN[((sourmh<<4) | (sourml>>28))&0x3ff]; \ + (buf)[7]=DPD2BIN[(sourmh>>6)&0x3ff]; \ + (buf)[8]=DPD2BIN[(sourmh>>16)&0x3ff]; \ + sourhi=DFWORD(df, 0); \ + (buf)[9]=DPD2BIN[((sourhi<<6) | (sourmh>>26))&0x3ff]; \ + (buf)[10]=DPD2BIN[(sourhi>>4)&0x3ff]; \ + (buf)[11]=DECCOMBMSD[sourhi>>26];} + + #endif + + /* Set a decFloat to the maximum positive finite number (Nmax) */ + #if DECPMAX==7 + #define DFSETNMAX(df) \ + {DFWORD(df, 0)=0x77f3fcff;} + #elif DECPMAX==16 + #define DFSETNMAX(df) \ + {DFWORD(df, 0)=0x77fcff3f; \ + DFWORD(df, 1)=0xcff3fcff;} + #elif DECPMAX==34 + #define DFSETNMAX(df) \ + {DFWORD(df, 0)=0x77ffcff3; \ + DFWORD(df, 1)=0xfcff3fcf; \ + DFWORD(df, 2)=0xf3fcff3f; \ + DFWORD(df, 3)=0xcff3fcff;} + #endif + + /* [end of format-dependent macros and constants] */ + #endif + +#else + #error decNumberLocal included more than once +#endif diff --git a/include/libdecnumber/dpd/decimal128.h b/include/libdecnumber/dpd/decimal128.h new file mode 100644 index 0000000000..f8f5b5a8ff --- /dev/null +++ b/include/libdecnumber/dpd/decimal128.h @@ -0,0 +1,101 @@ +/* Decimal 128-bit format module header for the decNumber C Library. + Copyright (C) 2005, 2007 Free Software Foundation, Inc. + Contributed by IBM Corporation. Author Mike Cowlishaw. + + This file is part of GCC. + + GCC is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation; either version 2, or (at your option) any later + version. + + In addition to the permissions in the GNU General Public License, + the Free Software Foundation gives you unlimited permission to link + the compiled version of this file into combinations with other + programs, and to distribute those combinations without any + restriction coming from the use of this file. (The General Public + License restrictions do apply in other respects; for example, they + cover modification of the file, and distribution when not linked + into a combine executable.) + + GCC is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or + FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License + along with GCC; see the file COPYING. If not, write to the Free + Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA + 02110-1301, USA. */ + +/* ------------------------------------------------------------------ */ +/* Decimal 128-bit format module header */ +/* ------------------------------------------------------------------ */ + +#if !defined(DECIMAL128) + #define DECIMAL128 + #define DEC128NAME "decimal128" /* Short name */ + #define DEC128FULLNAME "Decimal 128-bit Number" /* Verbose name */ + #define DEC128AUTHOR "Mike Cowlishaw" /* Who to blame */ + + /* parameters for decimal128s */ + #define DECIMAL128_Bytes 16 /* length */ + #define DECIMAL128_Pmax 34 /* maximum precision (digits) */ + #define DECIMAL128_Emax 6144 /* maximum adjusted exponent */ + #define DECIMAL128_Emin -6143 /* minimum adjusted exponent */ + #define DECIMAL128_Bias 6176 /* bias for the exponent */ + #define DECIMAL128_String 43 /* maximum string length, +1 */ + #define DECIMAL128_EconL 12 /* exp. continuation length */ + /* highest biased exponent (Elimit-1) */ + #define DECIMAL128_Ehigh (DECIMAL128_Emax+DECIMAL128_Bias-DECIMAL128_Pmax+1) + + /* check enough digits, if pre-defined */ + #if defined(DECNUMDIGITS) + #if (DECNUMDIGITS<DECIMAL128_Pmax) + #error decimal128.h needs pre-defined DECNUMDIGITS>=34 for safe use + #endif + #endif + + #ifndef DECNUMDIGITS + #define DECNUMDIGITS DECIMAL128_Pmax /* size if not already defined*/ + #endif + #ifndef DECNUMBER + #include "decNumber.h" /* context and number library */ + #endif + + /* Decimal 128-bit type, accessible by bytes */ + typedef struct { + uint8_t bytes[DECIMAL128_Bytes]; /* decimal128: 1, 5, 12, 110 bits*/ + } decimal128; + + /* special values [top byte excluding sign bit; last two bits are */ + /* don't-care for Infinity on input, last bit don't-care for NaN] */ + #if !defined(DECIMAL_NaN) + #define DECIMAL_NaN 0x7c /* 0 11111 00 NaN */ + #define DECIMAL_sNaN 0x7e /* 0 11111 10 sNaN */ + #define DECIMAL_Inf 0x78 /* 0 11110 00 Infinity */ + #endif + + #include "decimal128Local.h" + + /* ---------------------------------------------------------------- */ + /* Routines */ + /* ---------------------------------------------------------------- */ + + #include "decimal128Symbols.h" + + /* String conversions */ + decimal128 * decimal128FromString(decimal128 *, const char *, decContext *); + char * decimal128ToString(const decimal128 *, char *); + char * decimal128ToEngString(const decimal128 *, char *); + + /* decNumber conversions */ + decimal128 * decimal128FromNumber(decimal128 *, const decNumber *, + decContext *); + decNumber * decimal128ToNumber(const decimal128 *, decNumber *); + + /* Format-dependent utilities */ + uint32_t decimal128IsCanonical(const decimal128 *); + decimal128 * decimal128Canonical(decimal128 *, const decimal128 *); + +#endif diff --git a/include/libdecnumber/dpd/decimal128Local.h b/include/libdecnumber/dpd/decimal128Local.h new file mode 100644 index 0000000000..9765427719 --- /dev/null +++ b/include/libdecnumber/dpd/decimal128Local.h @@ -0,0 +1,47 @@ +/* Local definitions for use with the decNumber C Library. + Copyright (C) 2007 Free Software Foundation, Inc. + + This file is part of GCC. + + GCC is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation; either version 2, or (at your option) any later + version. + + In addition to the permissions in the GNU General Public License, + the Free Software Foundation gives you unlimited permission to link + the compiled version of this file into combinations with other + programs, and to distribute those combinations without any + restriction coming from the use of this file. (The General Public + License restrictions do apply in other respects; for example, they + cover modification of the file, and distribution when not linked + into a combine executable.) + + GCC is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or + FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License + along with GCC; see the file COPYING. If not, write to the Free + Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA + 02110-1301, USA. */ + +#if !defined(DECIMAL128LOCAL) + +/* The compiler needs sign manipulation functions for decimal128 which + are not part of the decNumber package. */ + +/* Set sign; this assumes the sign was previously zero. */ +#define decimal128SetSign(d,b) \ + { (d)->bytes[WORDS_BIGENDIAN ? 0 : 15] |= ((unsigned) (b) << 7); } + +/* Clear sign. */ +#define decimal128ClearSign(d) \ + { (d)->bytes[WORDS_BIGENDIAN ? 0 : 15] &= ~0x80; } + +/* Flip sign. */ +#define decimal128FlipSign(d) \ + { (d)->bytes[WORDS_BIGENDIAN ? 0 : 15] ^= 0x80; } + +#endif diff --git a/include/libdecnumber/dpd/decimal32.h b/include/libdecnumber/dpd/decimal32.h new file mode 100644 index 0000000000..0d53046417 --- /dev/null +++ b/include/libdecnumber/dpd/decimal32.h @@ -0,0 +1,99 @@ +/* Decimal 32-bit format module header for the decNumber C Library. + Copyright (C) 2005, 2007 Free Software Foundation, Inc. + Contributed by IBM Corporation. Author Mike Cowlishaw. + + This file is part of GCC. + + GCC is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation; either version 2, or (at your option) any later + version. + + In addition to the permissions in the GNU General Public License, + the Free Software Foundation gives you unlimited permission to link + the compiled version of this file into combinations with other + programs, and to distribute those combinations without any + restriction coming from the use of this file. (The General Public + License restrictions do apply in other respects; for example, they + cover modification of the file, and distribution when not linked + into a combine executable.) + + GCC is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or + FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License + along with GCC; see the file COPYING. If not, write to the Free + Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA + 02110-1301, USA. */ + +/* ------------------------------------------------------------------ */ +/* Decimal 32-bit format module header */ +/* ------------------------------------------------------------------ */ + +#if !defined(DECIMAL32) + #define DECIMAL32 + #define DEC32NAME "decimal32" /* Short name */ + #define DEC32FULLNAME "Decimal 32-bit Number" /* Verbose name */ + #define DEC32AUTHOR "Mike Cowlishaw" /* Who to blame */ + + /* parameters for decimal32s */ + #define DECIMAL32_Bytes 4 /* length */ + #define DECIMAL32_Pmax 7 /* maximum precision (digits) */ + #define DECIMAL32_Emax 96 /* maximum adjusted exponent */ + #define DECIMAL32_Emin -95 /* minimum adjusted exponent */ + #define DECIMAL32_Bias 101 /* bias for the exponent */ + #define DECIMAL32_String 15 /* maximum string length, +1 */ + #define DECIMAL32_EconL 6 /* exp. continuation length */ + /* highest biased exponent (Elimit-1) */ + #define DECIMAL32_Ehigh (DECIMAL32_Emax+DECIMAL32_Bias-DECIMAL32_Pmax+1) + + /* check enough digits, if pre-defined */ + #if defined(DECNUMDIGITS) + #if (DECNUMDIGITS<DECIMAL32_Pmax) + #error decimal32.h needs pre-defined DECNUMDIGITS>=7 for safe use + #endif + #endif + + #ifndef DECNUMDIGITS + #define DECNUMDIGITS DECIMAL32_Pmax /* size if not already defined*/ + #endif + #ifndef DECNUMBER + #include "decNumber.h" /* context and number library */ + #endif + + /* Decimal 32-bit type, accessible by bytes */ + typedef struct { + uint8_t bytes[DECIMAL32_Bytes]; /* decimal32: 1, 5, 6, 20 bits*/ + } decimal32; + + /* special values [top byte excluding sign bit; last two bits are */ + /* don't-care for Infinity on input, last bit don't-care for NaN] */ + #if !defined(DECIMAL_NaN) + #define DECIMAL_NaN 0x7c /* 0 11111 00 NaN */ + #define DECIMAL_sNaN 0x7e /* 0 11111 10 sNaN */ + #define DECIMAL_Inf 0x78 /* 0 11110 00 Infinity */ + #endif + + /* ---------------------------------------------------------------- */ + /* Routines */ + /* ---------------------------------------------------------------- */ + + #include "decimal32Symbols.h" + + /* String conversions */ + decimal32 * decimal32FromString(decimal32 *, const char *, decContext *); + char * decimal32ToString(const decimal32 *, char *); + char * decimal32ToEngString(const decimal32 *, char *); + + /* decNumber conversions */ + decimal32 * decimal32FromNumber(decimal32 *, const decNumber *, + decContext *); + decNumber * decimal32ToNumber(const decimal32 *, decNumber *); + + /* Format-dependent utilities */ + uint32_t decimal32IsCanonical(const decimal32 *); + decimal32 * decimal32Canonical(decimal32 *, const decimal32 *); + +#endif diff --git a/include/libdecnumber/dpd/decimal64.h b/include/libdecnumber/dpd/decimal64.h new file mode 100644 index 0000000000..549b626536 --- /dev/null +++ b/include/libdecnumber/dpd/decimal64.h @@ -0,0 +1,101 @@ +/* Decimal 64-bit format module header for the decNumber C Library. + Copyright (C) 2005, 2007 Free Software Foundation, Inc. + Contributed by IBM Corporation. Author Mike Cowlishaw. + + This file is part of GCC. + + GCC is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation; either version 2, or (at your option) any later + version. + + In addition to the permissions in the GNU General Public License, + the Free Software Foundation gives you unlimited permission to link + the compiled version of this file into combinations with other + programs, and to distribute those combinations without any + restriction coming from the use of this file. (The General Public + License restrictions do apply in other respects; for example, they + cover modification of the file, and distribution when not linked + into a combine executable.) + + GCC is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or + FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License + along with GCC; see the file COPYING. If not, write to the Free + Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA + 02110-1301, USA. */ + +/* ------------------------------------------------------------------ */ +/* Decimal 64-bit format module header */ +/* ------------------------------------------------------------------ */ + +#if !defined(DECIMAL64) + #define DECIMAL64 + #define DEC64NAME "decimal64" /* Short name */ + #define DEC64FULLNAME "Decimal 64-bit Number" /* Verbose name */ + #define DEC64AUTHOR "Mike Cowlishaw" /* Who to blame */ + + + /* parameters for decimal64s */ + #define DECIMAL64_Bytes 8 /* length */ + #define DECIMAL64_Pmax 16 /* maximum precision (digits) */ + #define DECIMAL64_Emax 384 /* maximum adjusted exponent */ + #define DECIMAL64_Emin -383 /* minimum adjusted exponent */ + #define DECIMAL64_Bias 398 /* bias for the exponent */ + #define DECIMAL64_String 24 /* maximum string length, +1 */ + #define DECIMAL64_EconL 8 /* exp. continuation length */ + /* highest biased exponent (Elimit-1) */ + #define DECIMAL64_Ehigh (DECIMAL64_Emax+DECIMAL64_Bias-DECIMAL64_Pmax+1) + + /* check enough digits, if pre-defined */ + #if defined(DECNUMDIGITS) + #if (DECNUMDIGITS<DECIMAL64_Pmax) + #error decimal64.h needs pre-defined DECNUMDIGITS>=16 for safe use + #endif + #endif + + + #ifndef DECNUMDIGITS + #define DECNUMDIGITS DECIMAL64_Pmax /* size if not already defined*/ + #endif + #ifndef DECNUMBER + #include "decNumber.h" /* context and number library */ + #endif + + /* Decimal 64-bit type, accessible by bytes */ + typedef struct { + uint8_t bytes[DECIMAL64_Bytes]; /* decimal64: 1, 5, 8, 50 bits*/ + } decimal64; + + /* special values [top byte excluding sign bit; last two bits are */ + /* don't-care for Infinity on input, last bit don't-care for NaN] */ + #if !defined(DECIMAL_NaN) + #define DECIMAL_NaN 0x7c /* 0 11111 00 NaN */ + #define DECIMAL_sNaN 0x7e /* 0 11111 10 sNaN */ + #define DECIMAL_Inf 0x78 /* 0 11110 00 Infinity */ + #endif + + /* ---------------------------------------------------------------- */ + /* Routines */ + /* ---------------------------------------------------------------- */ + + #include "decimal64Symbols.h" + + /* String conversions */ + decimal64 * decimal64FromString(decimal64 *, const char *, decContext *); + char * decimal64ToString(const decimal64 *, char *); + char * decimal64ToEngString(const decimal64 *, char *); + + /* decNumber conversions */ + decimal64 * decimal64FromNumber(decimal64 *, const decNumber *, + decContext *); + decNumber * decimal64ToNumber(const decimal64 *, decNumber *); + + /* Format-dependent utilities */ + uint32_t decimal64IsCanonical(const decimal64 *); + decimal64 * decimal64Canonical(decimal64 *, const decimal64 *); + +#endif diff --git a/libdecnumber/decContext.c b/libdecnumber/decContext.c new file mode 100644 index 0000000000..8d577f48ad --- /dev/null +++ b/libdecnumber/decContext.c @@ -0,0 +1,431 @@ +/* Decimal context module for the decNumber C Library. + Copyright (C) 2005, 2007 Free Software Foundation, Inc. + Contributed by IBM Corporation. Author Mike Cowlishaw. + + This file is part of GCC. + + GCC is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation; either version 2, or (at your option) any later + version. + + In addition to the permissions in the GNU General Public License, + the Free Software Foundation gives you unlimited permission to link + the compiled version of this file into combinations with other + programs, and to distribute those combinations without any + restriction coming from the use of this file. (The General Public + License restrictions do apply in other respects; for example, they + cover modification of the file, and distribution when not linked + into a combine executable.) + + GCC is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or + FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License + along with GCC; see the file COPYING. If not, write to the Free + Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA + 02110-1301, USA. */ + +/* ------------------------------------------------------------------ */ +/* Decimal Context module */ +/* ------------------------------------------------------------------ */ +/* This module comprises the routines for handling arithmetic */ +/* context structures. */ +/* ------------------------------------------------------------------ */ + +#include <string.h> /* for strcmp */ +#include <stdio.h> /* for printf if DECCHECK */ +#include "dconfig.h" /* for GCC definitions */ +#include "decContext.h" /* context and base types */ +#include "decNumberLocal.h" /* decNumber local types, etc. */ + +#if DECCHECK +/* compile-time endian tester [assumes sizeof(Int)>1] */ +static const Int mfcone=1; /* constant 1 */ +static const Flag *mfctop=(Flag *)&mfcone; /* -> top byte */ +#define LITEND *mfctop /* named flag; 1=little-endian */ +#endif + +/* ------------------------------------------------------------------ */ +/* round-for-reround digits */ +/* ------------------------------------------------------------------ */ +const uByte DECSTICKYTAB[10]={1,1,2,3,4,6,6,7,8,9}; /* used if sticky */ + +/* ------------------------------------------------------------------ */ +/* Powers of ten (powers[n]==10**n, 0<=n<=9) */ +/* ------------------------------------------------------------------ */ +const uInt DECPOWERS[10]={1, 10, 100, 1000, 10000, 100000, 1000000, + 10000000, 100000000, 1000000000}; + +/* ------------------------------------------------------------------ */ +/* decContextClearStatus -- clear bits in current status */ +/* */ +/* context is the context structure to be queried */ +/* mask indicates the bits to be cleared (the status bit that */ +/* corresponds to each 1 bit in the mask is cleared) */ +/* returns context */ +/* */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +decContext *decContextClearStatus(decContext *context, uInt mask) { + context->status&=~mask; + return context; + } /* decContextClearStatus */ + +/* ------------------------------------------------------------------ */ +/* decContextDefault -- initialize a context structure */ +/* */ +/* context is the structure to be initialized */ +/* kind selects the required set of default values, one of: */ +/* DEC_INIT_BASE -- select ANSI X3-274 defaults */ +/* DEC_INIT_DECIMAL32 -- select IEEE 754r defaults, 32-bit */ +/* DEC_INIT_DECIMAL64 -- select IEEE 754r defaults, 64-bit */ +/* DEC_INIT_DECIMAL128 -- select IEEE 754r defaults, 128-bit */ +/* For any other value a valid context is returned, but with */ +/* Invalid_operation set in the status field. */ +/* returns a context structure with the appropriate initial values. */ +/* ------------------------------------------------------------------ */ +decContext * decContextDefault(decContext *context, Int kind) { + /* set defaults... */ + context->digits=9; /* 9 digits */ + context->emax=DEC_MAX_EMAX; /* 9-digit exponents */ + context->emin=DEC_MIN_EMIN; /* .. balanced */ + context->round=DEC_ROUND_HALF_UP; /* 0.5 rises */ + context->traps=DEC_Errors; /* all but informational */ + context->status=0; /* cleared */ + context->clamp=0; /* no clamping */ + #if DECSUBSET + context->extended=0; /* cleared */ + #endif + switch (kind) { + case DEC_INIT_BASE: + /* [use defaults] */ + break; + case DEC_INIT_DECIMAL32: + context->digits=7; /* digits */ + context->emax=96; /* Emax */ + context->emin=-95; /* Emin */ + context->round=DEC_ROUND_HALF_EVEN; /* 0.5 to nearest even */ + context->traps=0; /* no traps set */ + context->clamp=1; /* clamp exponents */ + #if DECSUBSET + context->extended=1; /* set */ + #endif + break; + case DEC_INIT_DECIMAL64: + context->digits=16; /* digits */ + context->emax=384; /* Emax */ + context->emin=-383; /* Emin */ + context->round=DEC_ROUND_HALF_EVEN; /* 0.5 to nearest even */ + context->traps=0; /* no traps set */ + context->clamp=1; /* clamp exponents */ + #if DECSUBSET + context->extended=1; /* set */ + #endif + break; + case DEC_INIT_DECIMAL128: + context->digits=34; /* digits */ + context->emax=6144; /* Emax */ + context->emin=-6143; /* Emin */ + context->round=DEC_ROUND_HALF_EVEN; /* 0.5 to nearest even */ + context->traps=0; /* no traps set */ + context->clamp=1; /* clamp exponents */ + #if DECSUBSET + context->extended=1; /* set */ + #endif + break; + + default: /* invalid Kind */ + /* use defaults, and .. */ + decContextSetStatus(context, DEC_Invalid_operation); /* trap */ + } + + #if DECCHECK + if (LITEND!=DECLITEND) { + const char *adj; + if (LITEND) adj="little"; + else adj="big"; + printf("Warning: DECLITEND is set to %d, but this computer appears to be %s-endian\n", + DECLITEND, adj); + } + #endif + return context;} /* decContextDefault */ + +/* ------------------------------------------------------------------ */ +/* decContextGetRounding -- return current rounding mode */ +/* */ +/* context is the context structure to be queried */ +/* returns the rounding mode */ +/* */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +enum rounding decContextGetRounding(decContext *context) { + return context->round; + } /* decContextGetRounding */ + +/* ------------------------------------------------------------------ */ +/* decContextGetStatus -- return current status */ +/* */ +/* context is the context structure to be queried */ +/* returns status */ +/* */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +uInt decContextGetStatus(decContext *context) { + return context->status; + } /* decContextGetStatus */ + +/* ------------------------------------------------------------------ */ +/* decContextRestoreStatus -- restore bits in current status */ +/* */ +/* context is the context structure to be updated */ +/* newstatus is the source for the bits to be restored */ +/* mask indicates the bits to be restored (the status bit that */ +/* corresponds to each 1 bit in the mask is set to the value of */ +/* the correspnding bit in newstatus) */ +/* returns context */ +/* */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +decContext *decContextRestoreStatus(decContext *context, + uInt newstatus, uInt mask) { + context->status&=~mask; /* clear the selected bits */ + context->status|=(mask&newstatus); /* or in the new bits */ + return context; + } /* decContextRestoreStatus */ + +/* ------------------------------------------------------------------ */ +/* decContextSaveStatus -- save bits in current status */ +/* */ +/* context is the context structure to be queried */ +/* mask indicates the bits to be saved (the status bits that */ +/* correspond to each 1 bit in the mask are saved) */ +/* returns the AND of the mask and the current status */ +/* */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +uInt decContextSaveStatus(decContext *context, uInt mask) { + return context->status&mask; + } /* decContextSaveStatus */ + +/* ------------------------------------------------------------------ */ +/* decContextSetRounding -- set current rounding mode */ +/* */ +/* context is the context structure to be updated */ +/* newround is the value which will replace the current mode */ +/* returns context */ +/* */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +decContext *decContextSetRounding(decContext *context, + enum rounding newround) { + context->round=newround; + return context; + } /* decContextSetRounding */ + +/* ------------------------------------------------------------------ */ +/* decContextSetStatus -- set status and raise trap if appropriate */ +/* */ +/* context is the context structure to be updated */ +/* status is the DEC_ exception code */ +/* returns the context structure */ +/* */ +/* Control may never return from this routine, if there is a signal */ +/* handler and it takes a long jump. */ +/* ------------------------------------------------------------------ */ +decContext * decContextSetStatus(decContext *context, uInt status) { + context->status|=status; + if (status & context->traps) raise(SIGFPE); + return context;} /* decContextSetStatus */ + +/* ------------------------------------------------------------------ */ +/* decContextSetStatusFromString -- set status from a string + trap */ +/* */ +/* context is the context structure to be updated */ +/* string is a string exactly equal to one that might be returned */ +/* by decContextStatusToString */ +/* */ +/* The status bit corresponding to the string is set, and a trap */ +/* is raised if appropriate. */ +/* */ +/* returns the context structure, unless the string is equal to */ +/* DEC_Condition_MU or is not recognized. In these cases NULL is */ +/* returned. */ +/* ------------------------------------------------------------------ */ +decContext * decContextSetStatusFromString(decContext *context, + const char *string) { + if (strcmp(string, DEC_Condition_CS)==0) + return decContextSetStatus(context, DEC_Conversion_syntax); + if (strcmp(string, DEC_Condition_DZ)==0) + return decContextSetStatus(context, DEC_Division_by_zero); + if (strcmp(string, DEC_Condition_DI)==0) + return decContextSetStatus(context, DEC_Division_impossible); + if (strcmp(string, DEC_Condition_DU)==0) + return decContextSetStatus(context, DEC_Division_undefined); + if (strcmp(string, DEC_Condition_IE)==0) + return decContextSetStatus(context, DEC_Inexact); + if (strcmp(string, DEC_Condition_IS)==0) + return decContextSetStatus(context, DEC_Insufficient_storage); + if (strcmp(string, DEC_Condition_IC)==0) + return decContextSetStatus(context, DEC_Invalid_context); + if (strcmp(string, DEC_Condition_IO)==0) + return decContextSetStatus(context, DEC_Invalid_operation); + #if DECSUBSET + if (strcmp(string, DEC_Condition_LD)==0) + return decContextSetStatus(context, DEC_Lost_digits); + #endif + if (strcmp(string, DEC_Condition_OV)==0) + return decContextSetStatus(context, DEC_Overflow); + if (strcmp(string, DEC_Condition_PA)==0) + return decContextSetStatus(context, DEC_Clamped); + if (strcmp(string, DEC_Condition_RO)==0) + return decContextSetStatus(context, DEC_Rounded); + if (strcmp(string, DEC_Condition_SU)==0) + return decContextSetStatus(context, DEC_Subnormal); + if (strcmp(string, DEC_Condition_UN)==0) + return decContextSetStatus(context, DEC_Underflow); + if (strcmp(string, DEC_Condition_ZE)==0) + return context; + return NULL; /* Multiple status, or unknown */ + } /* decContextSetStatusFromString */ + +/* ------------------------------------------------------------------ */ +/* decContextSetStatusFromStringQuiet -- set status from a string */ +/* */ +/* context is the context structure to be updated */ +/* string is a string exactly equal to one that might be returned */ +/* by decContextStatusToString */ +/* */ +/* The status bit corresponding to the string is set; no trap is */ +/* raised. */ +/* */ +/* returns the context structure, unless the string is equal to */ +/* DEC_Condition_MU or is not recognized. In these cases NULL is */ +/* returned. */ +/* ------------------------------------------------------------------ */ +decContext * decContextSetStatusFromStringQuiet(decContext *context, + const char *string) { + if (strcmp(string, DEC_Condition_CS)==0) + return decContextSetStatusQuiet(context, DEC_Conversion_syntax); + if (strcmp(string, DEC_Condition_DZ)==0) + return decContextSetStatusQuiet(context, DEC_Division_by_zero); + if (strcmp(string, DEC_Condition_DI)==0) + return decContextSetStatusQuiet(context, DEC_Division_impossible); + if (strcmp(string, DEC_Condition_DU)==0) + return decContextSetStatusQuiet(context, DEC_Division_undefined); + if (strcmp(string, DEC_Condition_IE)==0) + return decContextSetStatusQuiet(context, DEC_Inexact); + if (strcmp(string, DEC_Condition_IS)==0) + return decContextSetStatusQuiet(context, DEC_Insufficient_storage); + if (strcmp(string, DEC_Condition_IC)==0) + return decContextSetStatusQuiet(context, DEC_Invalid_context); + if (strcmp(string, DEC_Condition_IO)==0) + return decContextSetStatusQuiet(context, DEC_Invalid_operation); + #if DECSUBSET + if (strcmp(string, DEC_Condition_LD)==0) + return decContextSetStatusQuiet(context, DEC_Lost_digits); + #endif + if (strcmp(string, DEC_Condition_OV)==0) + return decContextSetStatusQuiet(context, DEC_Overflow); + if (strcmp(string, DEC_Condition_PA)==0) + return decContextSetStatusQuiet(context, DEC_Clamped); + if (strcmp(string, DEC_Condition_RO)==0) + return decContextSetStatusQuiet(context, DEC_Rounded); + if (strcmp(string, DEC_Condition_SU)==0) + return decContextSetStatusQuiet(context, DEC_Subnormal); + if (strcmp(string, DEC_Condition_UN)==0) + return decContextSetStatusQuiet(context, DEC_Underflow); + if (strcmp(string, DEC_Condition_ZE)==0) + return context; + return NULL; /* Multiple status, or unknown */ + } /* decContextSetStatusFromStringQuiet */ + +/* ------------------------------------------------------------------ */ +/* decContextSetStatusQuiet -- set status without trap */ +/* */ +/* context is the context structure to be updated */ +/* status is the DEC_ exception code */ +/* returns the context structure */ +/* */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +decContext * decContextSetStatusQuiet(decContext *context, uInt status) { + context->status|=status; + return context;} /* decContextSetStatusQuiet */ + +/* ------------------------------------------------------------------ */ +/* decContextStatusToString -- convert status flags to a string */ +/* */ +/* context is a context with valid status field */ +/* */ +/* returns a constant string describing the condition. If multiple */ +/* (or no) flags are set, a generic constant message is returned. */ +/* ------------------------------------------------------------------ */ +const char *decContextStatusToString(const decContext *context) { + Int status=context->status; + + /* test the five IEEE first, as some of the others are ambiguous when */ + /* DECEXTFLAG=0 */ + if (status==DEC_Invalid_operation ) return DEC_Condition_IO; + if (status==DEC_Division_by_zero ) return DEC_Condition_DZ; + if (status==DEC_Overflow ) return DEC_Condition_OV; + if (status==DEC_Underflow ) return DEC_Condition_UN; + if (status==DEC_Inexact ) return DEC_Condition_IE; + + if (status==DEC_Division_impossible ) return DEC_Condition_DI; + if (status==DEC_Division_undefined ) return DEC_Condition_DU; + if (status==DEC_Rounded ) return DEC_Condition_RO; + if (status==DEC_Clamped ) return DEC_Condition_PA; + if (status==DEC_Subnormal ) return DEC_Condition_SU; + if (status==DEC_Conversion_syntax ) return DEC_Condition_CS; + if (status==DEC_Insufficient_storage ) return DEC_Condition_IS; + if (status==DEC_Invalid_context ) return DEC_Condition_IC; + #if DECSUBSET + if (status==DEC_Lost_digits ) return DEC_Condition_LD; + #endif + if (status==0 ) return DEC_Condition_ZE; + return DEC_Condition_MU; /* Multiple errors */ + } /* decContextStatusToString */ + +/* ------------------------------------------------------------------ */ +/* decContextTestSavedStatus -- test bits in saved status */ +/* */ +/* oldstatus is the status word to be tested */ +/* mask indicates the bits to be tested (the oldstatus bits that */ +/* correspond to each 1 bit in the mask are tested) */ +/* returns 1 if any of the tested bits are 1, or 0 otherwise */ +/* */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +uInt decContextTestSavedStatus(uInt oldstatus, uInt mask) { + return (oldstatus&mask)!=0; + } /* decContextTestSavedStatus */ + +/* ------------------------------------------------------------------ */ +/* decContextTestStatus -- test bits in current status */ +/* */ +/* context is the context structure to be updated */ +/* mask indicates the bits to be tested (the status bits that */ +/* correspond to each 1 bit in the mask are tested) */ +/* returns 1 if any of the tested bits are 1, or 0 otherwise */ +/* */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +uInt decContextTestStatus(decContext *context, uInt mask) { + return (context->status&mask)!=0; + } /* decContextTestStatus */ + +/* ------------------------------------------------------------------ */ +/* decContextZeroStatus -- clear all status bits */ +/* */ +/* context is the context structure to be updated */ +/* returns context */ +/* */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +decContext *decContextZeroStatus(decContext *context) { + context->status=0; + return context; + } /* decContextZeroStatus */ diff --git a/libdecnumber/decNumber.c b/libdecnumber/decNumber.c new file mode 100644 index 0000000000..f9a624a1af --- /dev/null +++ b/libdecnumber/decNumber.c @@ -0,0 +1,8122 @@ +/* Decimal number arithmetic module for the decNumber C Library. + Copyright (C) 2005, 2007 Free Software Foundation, Inc. + Contributed by IBM Corporation. Author Mike Cowlishaw. + + This file is part of GCC. + + GCC is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation; either version 2, or (at your option) any later + version. + + In addition to the permissions in the GNU General Public License, + the Free Software Foundation gives you unlimited permission to link + the compiled version of this file into combinations with other + programs, and to distribute those combinations without any + restriction coming from the use of this file. (The General Public + License restrictions do apply in other respects; for example, they + cover modification of the file, and distribution when not linked + into a combine executable.) + + GCC is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or + FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License + along with GCC; see the file COPYING. If not, write to the Free + Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA + 02110-1301, USA. */ + +/* ------------------------------------------------------------------ */ +/* Decimal Number arithmetic module */ +/* ------------------------------------------------------------------ */ +/* This module comprises the routines for General Decimal Arithmetic */ +/* as defined in the specification which may be found on the */ +/* http://www2.hursley.ibm.com/decimal web pages. It implements both */ +/* the full ('extended') arithmetic and the simpler ('subset') */ +/* arithmetic. */ +/* */ +/* Usage notes: */ +/* */ +/* 1. This code is ANSI C89 except: */ +/* */ +/* If DECDPUN>4 or DECUSE64=1, the C99 64-bit int64_t and */ +/* uint64_t types may be used. To avoid these, set DECUSE64=0 */ +/* and DECDPUN<=4 (see documentation). */ +/* */ +/* 2. The decNumber format which this library uses is optimized for */ +/* efficient processing of relatively short numbers; in particular */ +/* it allows the use of fixed sized structures and minimizes copy */ +/* and move operations. It does, however, support arbitrary */ +/* precision (up to 999,999,999 digits) and arbitrary exponent */ +/* range (Emax in the range 0 through 999,999,999 and Emin in the */ +/* range -999,999,999 through 0). Mathematical functions (for */ +/* example decNumberExp) as identified below are restricted more */ +/* tightly: digits, emax, and -emin in the context must be <= */ +/* DEC_MAX_MATH (999999), and their operand(s) must be within */ +/* these bounds. */ +/* */ +/* 3. Logical functions are further restricted; their operands must */ +/* be finite, positive, have an exponent of zero, and all digits */ +/* must be either 0 or 1. The result will only contain digits */ +/* which are 0 or 1 (and will have exponent=0 and a sign of 0). */ +/* */ +/* 4. Operands to operator functions are never modified unless they */ +/* are also specified to be the result number (which is always */ +/* permitted). Other than that case, operands must not overlap. */ +/* */ +/* 5. Error handling: the type of the error is ORed into the status */ +/* flags in the current context (decContext structure). The */ +/* SIGFPE signal is then raised if the corresponding trap-enabler */ +/* flag in the decContext is set (is 1). */ +/* */ +/* It is the responsibility of the caller to clear the status */ +/* flags as required. */ +/* */ +/* The result of any routine which returns a number will always */ +/* be a valid number (which may be a special value, such as an */ +/* Infinity or NaN). */ +/* */ +/* 6. The decNumber format is not an exchangeable concrete */ +/* representation as it comprises fields which may be machine- */ +/* dependent (packed or unpacked, or special length, for example). */ +/* Canonical conversions to and from strings are provided; other */ +/* conversions are available in separate modules. */ +/* */ +/* 7. Normally, input operands are assumed to be valid. Set DECCHECK */ +/* to 1 for extended operand checking (including NULL operands). */ +/* Results are undefined if a badly-formed structure (or a NULL */ +/* pointer to a structure) is provided, though with DECCHECK */ +/* enabled the operator routines are protected against exceptions. */ +/* (Except if the result pointer is NULL, which is unrecoverable.) */ +/* */ +/* However, the routines will never cause exceptions if they are */ +/* given well-formed operands, even if the value of the operands */ +/* is inappropriate for the operation and DECCHECK is not set. */ +/* (Except for SIGFPE, as and where documented.) */ +/* */ +/* 8. Subset arithmetic is available only if DECSUBSET is set to 1. */ +/* ------------------------------------------------------------------ */ +/* Implementation notes for maintenance of this module: */ +/* */ +/* 1. Storage leak protection: Routines which use malloc are not */ +/* permitted to use return for fastpath or error exits (i.e., */ +/* they follow strict structured programming conventions). */ +/* Instead they have a do{}while(0); construct surrounding the */ +/* code which is protected -- break may be used to exit this. */ +/* Other routines can safely use the return statement inline. */ +/* */ +/* Storage leak accounting can be enabled using DECALLOC. */ +/* */ +/* 2. All loops use the for(;;) construct. Any do construct does */ +/* not loop; it is for allocation protection as just described. */ +/* */ +/* 3. Setting status in the context must always be the very last */ +/* action in a routine, as non-0 status may raise a trap and hence */ +/* the call to set status may not return (if the handler uses long */ +/* jump). Therefore all cleanup must be done first. In general, */ +/* to achieve this status is accumulated and is only applied just */ +/* before return by calling decContextSetStatus (via decStatus). */ +/* */ +/* Routines which allocate storage cannot, in general, use the */ +/* 'top level' routines which could cause a non-returning */ +/* transfer of control. The decXxxxOp routines are safe (do not */ +/* call decStatus even if traps are set in the context) and should */ +/* be used instead (they are also a little faster). */ +/* */ +/* 4. Exponent checking is minimized by allowing the exponent to */ +/* grow outside its limits during calculations, provided that */ +/* the decFinalize function is called later. Multiplication and */ +/* division, and intermediate calculations in exponentiation, */ +/* require more careful checks because of the risk of 31-bit */ +/* overflow (the most negative valid exponent is -1999999997, for */ +/* a 999999999-digit number with adjusted exponent of -999999999). */ +/* */ +/* 5. Rounding is deferred until finalization of results, with any */ +/* 'off to the right' data being represented as a single digit */ +/* residue (in the range -1 through 9). This avoids any double- */ +/* rounding when more than one shortening takes place (for */ +/* example, when a result is subnormal). */ +/* */ +/* 6. The digits count is allowed to rise to a multiple of DECDPUN */ +/* during many operations, so whole Units are handled and exact */ +/* accounting of digits is not needed. The correct digits value */ +/* is found by decGetDigits, which accounts for leading zeros. */ +/* This must be called before any rounding if the number of digits */ +/* is not known exactly. */ +/* */ +/* 7. The multiply-by-reciprocal 'trick' is used for partitioning */ +/* numbers up to four digits, using appropriate constants. This */ +/* is not useful for longer numbers because overflow of 32 bits */ +/* would lead to 4 multiplies, which is almost as expensive as */ +/* a divide (unless a floating-point or 64-bit multiply is */ +/* assumed to be available). */ +/* */ +/* 8. Unusual abbreviations that may be used in the commentary: */ +/* lhs -- left hand side (operand, of an operation) */ +/* lsd -- least significant digit (of coefficient) */ +/* lsu -- least significant Unit (of coefficient) */ +/* msd -- most significant digit (of coefficient) */ +/* msi -- most significant item (in an array) */ +/* msu -- most significant Unit (of coefficient) */ +/* rhs -- right hand side (operand, of an operation) */ +/* +ve -- positive */ +/* -ve -- negative */ +/* ** -- raise to the power */ +/* ------------------------------------------------------------------ */ + +#include <stdlib.h> /* for malloc, free, etc. */ +#include <stdio.h> /* for printf [if needed] */ +#include <string.h> /* for strcpy */ +#include <ctype.h> /* for lower */ +#include "dconfig.h" /* for GCC definitions */ +#include "decNumber.h" /* base number library */ +#include "decNumberLocal.h" /* decNumber local types, etc. */ + +/* Constants */ +/* Public lookup table used by the D2U macro */ +const uByte d2utable[DECMAXD2U+1]=D2UTABLE; + +#define DECVERB 1 /* set to 1 for verbose DECCHECK */ +#define powers DECPOWERS /* old internal name */ + +/* Local constants */ +#define DIVIDE 0x80 /* Divide operators */ +#define REMAINDER 0x40 /* .. */ +#define DIVIDEINT 0x20 /* .. */ +#define REMNEAR 0x10 /* .. */ +#define COMPARE 0x01 /* Compare operators */ +#define COMPMAX 0x02 /* .. */ +#define COMPMIN 0x03 /* .. */ +#define COMPTOTAL 0x04 /* .. */ +#define COMPNAN 0x05 /* .. [NaN processing] */ +#define COMPSIG 0x06 /* .. [signaling COMPARE] */ +#define COMPMAXMAG 0x07 /* .. */ +#define COMPMINMAG 0x08 /* .. */ + +#define DEC_sNaN 0x40000000 /* local status: sNaN signal */ +#define BADINT (Int)0x80000000 /* most-negative Int; error indicator */ +/* Next two indicate an integer >= 10**6, and its parity (bottom bit) */ +#define BIGEVEN (Int)0x80000002 +#define BIGODD (Int)0x80000003 + +static Unit uarrone[1]={1}; /* Unit array of 1, used for incrementing */ + +/* Granularity-dependent code */ +#if DECDPUN<=4 + #define eInt Int /* extended integer */ + #define ueInt uInt /* unsigned extended integer */ + /* Constant multipliers for divide-by-power-of five using reciprocal */ + /* multiply, after removing powers of 2 by shifting, and final shift */ + /* of 17 [we only need up to **4] */ + static const uInt multies[]={131073, 26215, 5243, 1049, 210}; + /* QUOT10 -- macro to return the quotient of unit u divided by 10**n */ + #define QUOT10(u, n) ((((uInt)(u)>>(n))*multies[n])>>17) +#else + /* For DECDPUN>4 non-ANSI-89 64-bit types are needed. */ + #if !DECUSE64 + #error decNumber.c: DECUSE64 must be 1 when DECDPUN>4 + #endif + #define eInt Long /* extended integer */ + #define ueInt uLong /* unsigned extended integer */ +#endif + +/* Local routines */ +static decNumber * decAddOp(decNumber *, const decNumber *, const decNumber *, + decContext *, uByte, uInt *); +static Flag decBiStr(const char *, const char *, const char *); +static uInt decCheckMath(const decNumber *, decContext *, uInt *); +static void decApplyRound(decNumber *, decContext *, Int, uInt *); +static Int decCompare(const decNumber *lhs, const decNumber *rhs, Flag); +static decNumber * decCompareOp(decNumber *, const decNumber *, + const decNumber *, decContext *, + Flag, uInt *); +static void decCopyFit(decNumber *, const decNumber *, decContext *, + Int *, uInt *); +static decNumber * decDecap(decNumber *, Int); +static decNumber * decDivideOp(decNumber *, const decNumber *, + const decNumber *, decContext *, Flag, uInt *); +static decNumber * decExpOp(decNumber *, const decNumber *, + decContext *, uInt *); +static void decFinalize(decNumber *, decContext *, Int *, uInt *); +static Int decGetDigits(Unit *, Int); +static Int decGetInt(const decNumber *); +static decNumber * decLnOp(decNumber *, const decNumber *, + decContext *, uInt *); +static decNumber * decMultiplyOp(decNumber *, const decNumber *, + const decNumber *, decContext *, + uInt *); +static decNumber * decNaNs(decNumber *, const decNumber *, + const decNumber *, decContext *, uInt *); +static decNumber * decQuantizeOp(decNumber *, const decNumber *, + const decNumber *, decContext *, Flag, + uInt *); +static void decReverse(Unit *, Unit *); +static void decSetCoeff(decNumber *, decContext *, const Unit *, + Int, Int *, uInt *); +static void decSetMaxValue(decNumber *, decContext *); +static void decSetOverflow(decNumber *, decContext *, uInt *); +static void decSetSubnormal(decNumber *, decContext *, Int *, uInt *); +static Int decShiftToLeast(Unit *, Int, Int); +static Int decShiftToMost(Unit *, Int, Int); +static void decStatus(decNumber *, uInt, decContext *); +static void decToString(const decNumber *, char[], Flag); +static decNumber * decTrim(decNumber *, decContext *, Flag, Int *); +static Int decUnitAddSub(const Unit *, Int, const Unit *, Int, Int, + Unit *, Int); +static Int decUnitCompare(const Unit *, Int, const Unit *, Int, Int); + +#if !DECSUBSET +/* decFinish == decFinalize when no subset arithmetic needed */ +#define decFinish(a,b,c,d) decFinalize(a,b,c,d) +#else +static void decFinish(decNumber *, decContext *, Int *, uInt *); +static decNumber * decRoundOperand(const decNumber *, decContext *, uInt *); +#endif + +/* Local macros */ +/* masked special-values bits */ +#define SPECIALARG (rhs->bits & DECSPECIAL) +#define SPECIALARGS ((lhs->bits | rhs->bits) & DECSPECIAL) + +/* Diagnostic macros, etc. */ +#if DECALLOC +/* Handle malloc/free accounting. If enabled, our accountable routines */ +/* are used; otherwise the code just goes straight to the system malloc */ +/* and free routines. */ +#define malloc(a) decMalloc(a) +#define free(a) decFree(a) +#define DECFENCE 0x5a /* corruption detector */ +/* 'Our' malloc and free: */ +static void *decMalloc(size_t); +static void decFree(void *); +uInt decAllocBytes=0; /* count of bytes allocated */ +/* Note that DECALLOC code only checks for storage buffer overflow. */ +/* To check for memory leaks, the decAllocBytes variable must be */ +/* checked to be 0 at appropriate times (e.g., after the test */ +/* harness completes a set of tests). This checking may be unreliable */ +/* if the testing is done in a multi-thread environment. */ +#endif + +#if DECCHECK +/* Optional checking routines. Enabling these means that decNumber */ +/* and decContext operands to operator routines are checked for */ +/* correctness. This roughly doubles the execution time of the */ +/* fastest routines (and adds 600+ bytes), so should not normally be */ +/* used in 'production'. */ +/* decCheckInexact is used to check that inexact results have a full */ +/* complement of digits (where appropriate -- this is not the case */ +/* for Quantize, for example) */ +#define DECUNRESU ((decNumber *)(void *)0xffffffff) +#define DECUNUSED ((const decNumber *)(void *)0xffffffff) +#define DECUNCONT ((decContext *)(void *)(0xffffffff)) +static Flag decCheckOperands(decNumber *, const decNumber *, + const decNumber *, decContext *); +static Flag decCheckNumber(const decNumber *); +static void decCheckInexact(const decNumber *, decContext *); +#endif + +#if DECTRACE || DECCHECK +/* Optional trace/debugging routines (may or may not be used) */ +void decNumberShow(const decNumber *); /* displays the components of a number */ +static void decDumpAr(char, const Unit *, Int); +#endif + +/* ================================================================== */ +/* Conversions */ +/* ================================================================== */ + +/* ------------------------------------------------------------------ */ +/* from-int32 -- conversion from Int or uInt */ +/* */ +/* dn is the decNumber to receive the integer */ +/* in or uin is the integer to be converted */ +/* returns dn */ +/* */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberFromInt32(decNumber *dn, Int in) { + uInt unsig; + if (in>=0) unsig=in; + else { /* negative (possibly BADINT) */ + if (in==BADINT) unsig=(uInt)1073741824*2; /* special case */ + else unsig=-in; /* invert */ + } + /* in is now positive */ + decNumberFromUInt32(dn, unsig); + if (in<0) dn->bits=DECNEG; /* sign needed */ + return dn; + } /* decNumberFromInt32 */ + +decNumber * decNumberFromUInt32(decNumber *dn, uInt uin) { + Unit *up; /* work pointer */ + decNumberZero(dn); /* clean */ + if (uin==0) return dn; /* [or decGetDigits bad call] */ + for (up=dn->lsu; uin>0; up++) { + *up=(Unit)(uin%(DECDPUNMAX+1)); + uin=uin/(DECDPUNMAX+1); + } + dn->digits=decGetDigits(dn->lsu, up-dn->lsu); + return dn; + } /* decNumberFromUInt32 */ + +/* ------------------------------------------------------------------ */ +/* to-int32 -- conversion to Int or uInt */ +/* */ +/* dn is the decNumber to convert */ +/* set is the context for reporting errors */ +/* returns the converted decNumber, or 0 if Invalid is set */ +/* */ +/* Invalid is set if the decNumber does not have exponent==0 or if */ +/* it is a NaN, Infinite, or out-of-range. */ +/* ------------------------------------------------------------------ */ +Int decNumberToInt32(const decNumber *dn, decContext *set) { + #if DECCHECK + if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; + #endif + + /* special or too many digits, or bad exponent */ + if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0) ; /* bad */ + else { /* is a finite integer with 10 or fewer digits */ + Int d; /* work */ + const Unit *up; /* .. */ + uInt hi=0, lo; /* .. */ + up=dn->lsu; /* -> lsu */ + lo=*up; /* get 1 to 9 digits */ + #if DECDPUN>1 /* split to higher */ + hi=lo/10; + lo=lo%10; + #endif + up++; + /* collect remaining Units, if any, into hi */ + for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1]; + /* now low has the lsd, hi the remainder */ + if (hi>214748364 || (hi==214748364 && lo>7)) { /* out of range? */ + /* most-negative is a reprieve */ + if (dn->bits&DECNEG && hi==214748364 && lo==8) return 0x80000000; + /* bad -- drop through */ + } + else { /* in-range always */ + Int i=X10(hi)+lo; + if (dn->bits&DECNEG) return -i; + return i; + } + } /* integer */ + decContextSetStatus(set, DEC_Invalid_operation); /* [may not return] */ + return 0; + } /* decNumberToInt32 */ + +uInt decNumberToUInt32(const decNumber *dn, decContext *set) { + #if DECCHECK + if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; + #endif + /* special or too many digits, or bad exponent, or negative (<0) */ + if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0 + || (dn->bits&DECNEG && !ISZERO(dn))); /* bad */ + else { /* is a finite integer with 10 or fewer digits */ + Int d; /* work */ + const Unit *up; /* .. */ + uInt hi=0, lo; /* .. */ + up=dn->lsu; /* -> lsu */ + lo=*up; /* get 1 to 9 digits */ + #if DECDPUN>1 /* split to higher */ + hi=lo/10; + lo=lo%10; + #endif + up++; + /* collect remaining Units, if any, into hi */ + for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1]; + + /* now low has the lsd, hi the remainder */ + if (hi>429496729 || (hi==429496729 && lo>5)) ; /* no reprieve possible */ + else return X10(hi)+lo; + } /* integer */ + decContextSetStatus(set, DEC_Invalid_operation); /* [may not return] */ + return 0; + } /* decNumberToUInt32 */ + +/* ------------------------------------------------------------------ */ +/* to-scientific-string -- conversion to numeric string */ +/* to-engineering-string -- conversion to numeric string */ +/* */ +/* decNumberToString(dn, string); */ +/* decNumberToEngString(dn, string); */ +/* */ +/* dn is the decNumber to convert */ +/* string is the string where the result will be laid out */ +/* */ +/* string must be at least dn->digits+14 characters long */ +/* */ +/* No error is possible, and no status can be set. */ +/* ------------------------------------------------------------------ */ +char * decNumberToString(const decNumber *dn, char *string){ + decToString(dn, string, 0); + return string; + } /* DecNumberToString */ + +char * decNumberToEngString(const decNumber *dn, char *string){ + decToString(dn, string, 1); + return string; + } /* DecNumberToEngString */ + +/* ------------------------------------------------------------------ */ +/* to-number -- conversion from numeric string */ +/* */ +/* decNumberFromString -- convert string to decNumber */ +/* dn -- the number structure to fill */ +/* chars[] -- the string to convert ('\0' terminated) */ +/* set -- the context used for processing any error, */ +/* determining the maximum precision available */ +/* (set.digits), determining the maximum and minimum */ +/* exponent (set.emax and set.emin), determining if */ +/* extended values are allowed, and checking the */ +/* rounding mode if overflow occurs or rounding is */ +/* needed. */ +/* */ +/* The length of the coefficient and the size of the exponent are */ +/* checked by this routine, so the correct error (Underflow or */ +/* Overflow) can be reported or rounding applied, as necessary. */ +/* */ +/* If bad syntax is detected, the result will be a quiet NaN. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberFromString(decNumber *dn, const char chars[], + decContext *set) { + Int exponent=0; /* working exponent [assume 0] */ + uByte bits=0; /* working flags [assume +ve] */ + Unit *res; /* where result will be built */ + Unit resbuff[SD2U(DECBUFFER+9)];/* local buffer in case need temporary */ + /* [+9 allows for ln() constants] */ + Unit *allocres=NULL; /* -> allocated result, iff allocated */ + Int d=0; /* count of digits found in decimal part */ + const char *dotchar=NULL; /* where dot was found */ + const char *cfirst=chars; /* -> first character of decimal part */ + const char *last=NULL; /* -> last digit of decimal part */ + const char *c; /* work */ + Unit *up; /* .. */ + #if DECDPUN>1 + Int cut, out; /* .. */ + #endif + Int residue; /* rounding residue */ + uInt status=0; /* error code */ + + #if DECCHECK + if (decCheckOperands(DECUNRESU, DECUNUSED, DECUNUSED, set)) + return decNumberZero(dn); + #endif + + do { /* status & malloc protection */ + for (c=chars;; c++) { /* -> input character */ + if (*c>='0' && *c<='9') { /* test for Arabic digit */ + last=c; + d++; /* count of real digits */ + continue; /* still in decimal part */ + } + if (*c=='.' && dotchar==NULL) { /* first '.' */ + dotchar=c; /* record offset into decimal part */ + if (c==cfirst) cfirst++; /* first digit must follow */ + continue;} + if (c==chars) { /* first in string... */ + if (*c=='-') { /* valid - sign */ + cfirst++; + bits=DECNEG; + continue;} + if (*c=='+') { /* valid + sign */ + cfirst++; + continue;} + } + /* *c is not a digit, or a valid +, -, or '.' */ + break; + } /* c */ + + if (last==NULL) { /* no digits yet */ + status=DEC_Conversion_syntax;/* assume the worst */ + if (*c=='\0') break; /* and no more to come... */ + #if DECSUBSET + /* if subset then infinities and NaNs are not allowed */ + if (!set->extended) break; /* hopeless */ + #endif + /* Infinities and NaNs are possible, here */ + if (dotchar!=NULL) break; /* .. unless had a dot */ + decNumberZero(dn); /* be optimistic */ + if (decBiStr(c, "infinity", "INFINITY") + || decBiStr(c, "inf", "INF")) { + dn->bits=bits | DECINF; + status=0; /* is OK */ + break; /* all done */ + } + /* a NaN expected */ + /* 2003.09.10 NaNs are now permitted to have a sign */ + dn->bits=bits | DECNAN; /* assume simple NaN */ + if (*c=='s' || *c=='S') { /* looks like an sNaN */ + c++; + dn->bits=bits | DECSNAN; + } + if (*c!='n' && *c!='N') break; /* check caseless "NaN" */ + c++; + if (*c!='a' && *c!='A') break; /* .. */ + c++; + if (*c!='n' && *c!='N') break; /* .. */ + c++; + /* now either nothing, or nnnn payload, expected */ + /* -> start of integer and skip leading 0s [including plain 0] */ + for (cfirst=c; *cfirst=='0';) cfirst++; + if (*cfirst=='\0') { /* "NaN" or "sNaN", maybe with all 0s */ + status=0; /* it's good */ + break; /* .. */ + } + /* something other than 0s; setup last and d as usual [no dots] */ + for (c=cfirst;; c++, d++) { + if (*c<'0' || *c>'9') break; /* test for Arabic digit */ + last=c; + } + if (*c!='\0') break; /* not all digits */ + if (d>set->digits-1) { + /* [NB: payload in a decNumber can be full length unless */ + /* clamped, in which case can only be digits-1] */ + if (set->clamp) break; + if (d>set->digits) break; + } /* too many digits? */ + /* good; drop through to convert the integer to coefficient */ + status=0; /* syntax is OK */ + bits=dn->bits; /* for copy-back */ + } /* last==NULL */ + + else if (*c!='\0') { /* more to process... */ + /* had some digits; exponent is only valid sequence now */ + Flag nege; /* 1=negative exponent */ + const char *firstexp; /* -> first significant exponent digit */ + status=DEC_Conversion_syntax;/* assume the worst */ + if (*c!='e' && *c!='E') break; + /* Found 'e' or 'E' -- now process explicit exponent */ + /* 1998.07.11: sign no longer required */ + nege=0; + c++; /* to (possible) sign */ + if (*c=='-') {nege=1; c++;} + else if (*c=='+') c++; + if (*c=='\0') break; + + for (; *c=='0' && *(c+1)!='\0';) c++; /* strip insignificant zeros */ + firstexp=c; /* save exponent digit place */ + for (; ;c++) { + if (*c<'0' || *c>'9') break; /* not a digit */ + exponent=X10(exponent)+(Int)*c-(Int)'0'; + } /* c */ + /* if not now on a '\0', *c must not be a digit */ + if (*c!='\0') break; + + /* (this next test must be after the syntax checks) */ + /* if it was too long the exponent may have wrapped, so check */ + /* carefully and set it to a certain overflow if wrap possible */ + if (c>=firstexp+9+1) { + if (c>firstexp+9+1 || *firstexp>'1') exponent=DECNUMMAXE*2; + /* [up to 1999999999 is OK, for example 1E-1000000998] */ + } + if (nege) exponent=-exponent; /* was negative */ + status=0; /* is OK */ + } /* stuff after digits */ + + /* Here when whole string has been inspected; syntax is good */ + /* cfirst->first digit (never dot), last->last digit (ditto) */ + + /* strip leading zeros/dot [leave final 0 if all 0's] */ + if (*cfirst=='0') { /* [cfirst has stepped over .] */ + for (c=cfirst; c<last; c++, cfirst++) { + if (*c=='.') continue; /* ignore dots */ + if (*c!='0') break; /* non-zero found */ + d--; /* 0 stripped */ + } /* c */ + #if DECSUBSET + /* make a rapid exit for easy zeros if !extended */ + if (*cfirst=='0' && !set->extended) { + decNumberZero(dn); /* clean result */ + break; /* [could be return] */ + } + #endif + } /* at least one leading 0 */ + + /* Handle decimal point... */ + if (dotchar!=NULL && dotchar<last) /* non-trailing '.' found? */ + exponent-=(last-dotchar); /* adjust exponent */ + /* [we can now ignore the .] */ + + /* OK, the digits string is good. Assemble in the decNumber, or in */ + /* a temporary units array if rounding is needed */ + if (d<=set->digits) res=dn->lsu; /* fits into supplied decNumber */ + else { /* rounding needed */ + Int needbytes=D2U(d)*sizeof(Unit);/* bytes needed */ + res=resbuff; /* assume use local buffer */ + if (needbytes>(Int)sizeof(resbuff)) { /* too big for local */ + allocres=(Unit *)malloc(needbytes); + if (allocres==NULL) {status|=DEC_Insufficient_storage; break;} + res=allocres; + } + } + /* res now -> number lsu, buffer, or allocated storage for Unit array */ + + /* Place the coefficient into the selected Unit array */ + /* [this is often 70% of the cost of this function when DECDPUN>1] */ + #if DECDPUN>1 + out=0; /* accumulator */ + up=res+D2U(d)-1; /* -> msu */ + cut=d-(up-res)*DECDPUN; /* digits in top unit */ + for (c=cfirst;; c++) { /* along the digits */ + if (*c=='.') continue; /* ignore '.' [don't decrement cut] */ + out=X10(out)+(Int)*c-(Int)'0'; + if (c==last) break; /* done [never get to trailing '.'] */ + cut--; + if (cut>0) continue; /* more for this unit */ + *up=(Unit)out; /* write unit */ + up--; /* prepare for unit below.. */ + cut=DECDPUN; /* .. */ + out=0; /* .. */ + } /* c */ + *up=(Unit)out; /* write lsu */ + + #else + /* DECDPUN==1 */ + up=res; /* -> lsu */ + for (c=last; c>=cfirst; c--) { /* over each character, from least */ + if (*c=='.') continue; /* ignore . [don't step up] */ + *up=(Unit)((Int)*c-(Int)'0'); + up++; + } /* c */ + #endif + + dn->bits=bits; + dn->exponent=exponent; + dn->digits=d; + + /* if not in number (too long) shorten into the number */ + if (d>set->digits) { + residue=0; + decSetCoeff(dn, set, res, d, &residue, &status); + /* always check for overflow or subnormal and round as needed */ + decFinalize(dn, set, &residue, &status); + } + else { /* no rounding, but may still have overflow or subnormal */ + /* [these tests are just for performance; finalize repeats them] */ + if ((dn->exponent-1<set->emin-dn->digits) + || (dn->exponent-1>set->emax-set->digits)) { + residue=0; + decFinalize(dn, set, &residue, &status); + } + } + /* decNumberShow(dn); */ + } while(0); /* [for break] */ + + if (allocres!=NULL) free(allocres); /* drop any storage used */ + if (status!=0) decStatus(dn, status, set); + return dn; + } /* decNumberFromString */ + +/* ================================================================== */ +/* Operators */ +/* ================================================================== */ + +/* ------------------------------------------------------------------ */ +/* decNumberAbs -- absolute value operator */ +/* */ +/* This computes C = abs(A) */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context */ +/* */ +/* See also decNumberCopyAbs for a quiet bitwise version of this. */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +/* This has the same effect as decNumberPlus unless A is negative, */ +/* in which case it has the same effect as decNumberMinus. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberAbs(decNumber *res, const decNumber *rhs, + decContext *set) { + decNumber dzero; /* for 0 */ + uInt status=0; /* accumulator */ + + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + decNumberZero(&dzero); /* set 0 */ + dzero.exponent=rhs->exponent; /* [no coefficient expansion] */ + decAddOp(res, &dzero, rhs, set, (uByte)(rhs->bits & DECNEG), &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } /* decNumberAbs */ + +/* ------------------------------------------------------------------ */ +/* decNumberAdd -- add two Numbers */ +/* */ +/* This computes C = A + B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X+X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +/* This just calls the routine shared with Subtract */ +decNumber * decNumberAdd(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; /* accumulator */ + decAddOp(res, lhs, rhs, set, 0, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } /* decNumberAdd */ + +/* ------------------------------------------------------------------ */ +/* decNumberAnd -- AND two Numbers, digitwise */ +/* */ +/* This computes C = A & B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X&X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context (used for result length and error report) */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Logical function restrictions apply (see above); a NaN is */ +/* returned with Invalid_operation if a restriction is violated. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberAnd(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + const Unit *ua, *ub; /* -> operands */ + const Unit *msua, *msub; /* -> operand msus */ + Unit *uc, *msuc; /* -> result and its msu */ + Int msudigs; /* digits in res msu */ + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs) + || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { + decStatus(res, DEC_Invalid_operation, set); + return res; + } + + /* operands are valid */ + ua=lhs->lsu; /* bottom-up */ + ub=rhs->lsu; /* .. */ + uc=res->lsu; /* .. */ + msua=ua+D2U(lhs->digits)-1; /* -> msu of lhs */ + msub=ub+D2U(rhs->digits)-1; /* -> msu of rhs */ + msuc=uc+D2U(set->digits)-1; /* -> msu of result */ + msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */ + for (; uc<=msuc; ua++, ub++, uc++) { /* Unit loop */ + Unit a, b; /* extract units */ + if (ua>msua) a=0; + else a=*ua; + if (ub>msub) b=0; + else b=*ub; + *uc=0; /* can now write back */ + if (a|b) { /* maybe 1 bits to examine */ + Int i, j; + *uc=0; /* can now write back */ + /* This loop could be unrolled and/or use BIN2BCD tables */ + for (i=0; i<DECDPUN; i++) { + if (a&b&1) *uc=*uc+(Unit)powers[i]; /* effect AND */ + j=a%10; + a=a/10; + j|=b%10; + b=b/10; + if (j>1) { + decStatus(res, DEC_Invalid_operation, set); + return res; + } + if (uc==msuc && i==msudigs-1) break; /* just did final digit */ + } /* each digit */ + } /* both OK */ + } /* each unit */ + /* [here uc-1 is the msu of the result] */ + res->digits=decGetDigits(res->lsu, uc-res->lsu); + res->exponent=0; /* integer */ + res->bits=0; /* sign=0 */ + return res; /* [no status to set] */ + } /* decNumberAnd */ + +/* ------------------------------------------------------------------ */ +/* decNumberCompare -- compare two Numbers */ +/* */ +/* This computes C = A ? B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for one digit (or NaN). */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberCompare(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; /* accumulator */ + decCompareOp(res, lhs, rhs, set, COMPARE, &status); + if (status!=0) decStatus(res, status, set); + return res; + } /* decNumberCompare */ + +/* ------------------------------------------------------------------ */ +/* decNumberCompareSignal -- compare, signalling on all NaNs */ +/* */ +/* This computes C = A ? B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for one digit (or NaN). */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberCompareSignal(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; /* accumulator */ + decCompareOp(res, lhs, rhs, set, COMPSIG, &status); + if (status!=0) decStatus(res, status, set); + return res; + } /* decNumberCompareSignal */ + +/* ------------------------------------------------------------------ */ +/* decNumberCompareTotal -- compare two Numbers, using total ordering */ +/* */ +/* This computes C = A ? B, under total ordering */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for one digit; the result will always be one of */ +/* -1, 0, or 1. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberCompareTotal(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; /* accumulator */ + decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status); + if (status!=0) decStatus(res, status, set); + return res; + } /* decNumberCompareTotal */ + +/* ------------------------------------------------------------------ */ +/* decNumberCompareTotalMag -- compare, total ordering of magnitudes */ +/* */ +/* This computes C = |A| ? |B|, under total ordering */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for one digit; the result will always be one of */ +/* -1, 0, or 1. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberCompareTotalMag(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; /* accumulator */ + uInt needbytes; /* for space calculations */ + decNumber bufa[D2N(DECBUFFER+1)];/* +1 in case DECBUFFER=0 */ + decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ + decNumber bufb[D2N(DECBUFFER+1)]; + decNumber *allocbufb=NULL; /* -> allocated bufb, iff allocated */ + decNumber *a, *b; /* temporary pointers */ + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + do { /* protect allocated storage */ + /* if either is negative, take a copy and absolute */ + if (decNumberIsNegative(lhs)) { /* lhs<0 */ + a=bufa; + needbytes=sizeof(decNumber)+(D2U(lhs->digits)-1)*sizeof(Unit); + if (needbytes>sizeof(bufa)) { /* need malloc space */ + allocbufa=(decNumber *)malloc(needbytes); + if (allocbufa==NULL) { /* hopeless -- abandon */ + status|=DEC_Insufficient_storage; + break;} + a=allocbufa; /* use the allocated space */ + } + decNumberCopy(a, lhs); /* copy content */ + a->bits&=~DECNEG; /* .. and clear the sign */ + lhs=a; /* use copy from here on */ + } + if (decNumberIsNegative(rhs)) { /* rhs<0 */ + b=bufb; + needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit); + if (needbytes>sizeof(bufb)) { /* need malloc space */ + allocbufb=(decNumber *)malloc(needbytes); + if (allocbufb==NULL) { /* hopeless -- abandon */ + status|=DEC_Insufficient_storage; + break;} + b=allocbufb; /* use the allocated space */ + } + decNumberCopy(b, rhs); /* copy content */ + b->bits&=~DECNEG; /* .. and clear the sign */ + rhs=b; /* use copy from here on */ + } + decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status); + } while(0); /* end protected */ + + if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */ + if (allocbufb!=NULL) free(allocbufb); /* .. */ + if (status!=0) decStatus(res, status, set); + return res; + } /* decNumberCompareTotalMag */ + +/* ------------------------------------------------------------------ */ +/* decNumberDivide -- divide one number by another */ +/* */ +/* This computes C = A / B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X/X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberDivide(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; /* accumulator */ + decDivideOp(res, lhs, rhs, set, DIVIDE, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } /* decNumberDivide */ + +/* ------------------------------------------------------------------ */ +/* decNumberDivideInteger -- divide and return integer quotient */ +/* */ +/* This computes C = A # B, where # is the integer divide operator */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X#X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberDivideInteger(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; /* accumulator */ + decDivideOp(res, lhs, rhs, set, DIVIDEINT, &status); + if (status!=0) decStatus(res, status, set); + return res; + } /* decNumberDivideInteger */ + +/* ------------------------------------------------------------------ */ +/* decNumberExp -- exponentiation */ +/* */ +/* This computes C = exp(A) */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context; note that rounding mode has no effect */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Mathematical function restrictions apply (see above); a NaN is */ +/* returned with Invalid_operation if a restriction is violated. */ +/* */ +/* Finite results will always be full precision and Inexact, except */ +/* when A is a zero or -Infinity (giving 1 or 0 respectively). */ +/* */ +/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */ +/* almost always be correctly rounded, but may be up to 1 ulp in */ +/* error in rare cases. */ +/* ------------------------------------------------------------------ */ +/* This is a wrapper for decExpOp which can handle the slightly wider */ +/* (double) range needed by Ln (which has to be able to calculate */ +/* exp(-a) where a can be the tiniest number (Ntiny). */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberExp(decNumber *res, const decNumber *rhs, + decContext *set) { + uInt status=0; /* accumulator */ + #if DECSUBSET + decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ + #endif + + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + /* Check restrictions; these restrictions ensure that if h=8 (see */ + /* decExpOp) then the result will either overflow or underflow to 0. */ + /* Other math functions restrict the input range, too, for inverses. */ + /* If not violated then carry out the operation. */ + if (!decCheckMath(rhs, set, &status)) do { /* protect allocation */ + #if DECSUBSET + if (!set->extended) { + /* reduce operand and set lostDigits status, as needed */ + if (rhs->digits>set->digits) { + allocrhs=decRoundOperand(rhs, set, &status); + if (allocrhs==NULL) break; + rhs=allocrhs; + } + } + #endif + decExpOp(res, rhs, set, &status); + } while(0); /* end protected */ + + #if DECSUBSET + if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */ + #endif + /* apply significant status */ + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } /* decNumberExp */ + +/* ------------------------------------------------------------------ */ +/* decNumberFMA -- fused multiply add */ +/* */ +/* This computes D = (A * B) + C with only one rounding */ +/* */ +/* res is D, the result. D may be A or B or C (e.g., X=FMA(X,X,X)) */ +/* lhs is A */ +/* rhs is B */ +/* fhs is C [far hand side] */ +/* set is the context */ +/* */ +/* Mathematical function restrictions apply (see above); a NaN is */ +/* returned with Invalid_operation if a restriction is violated. */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberFMA(decNumber *res, const decNumber *lhs, + const decNumber *rhs, const decNumber *fhs, + decContext *set) { + uInt status=0; /* accumulator */ + decContext dcmul; /* context for the multiplication */ + uInt needbytes; /* for space calculations */ + decNumber bufa[D2N(DECBUFFER*2+1)]; + decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ + decNumber *acc; /* accumulator pointer */ + decNumber dzero; /* work */ + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + if (decCheckOperands(res, fhs, DECUNUSED, set)) return res; + #endif + + do { /* protect allocated storage */ + #if DECSUBSET + if (!set->extended) { /* [undefined if subset] */ + status|=DEC_Invalid_operation; + break;} + #endif + /* Check math restrictions [these ensure no overflow or underflow] */ + if ((!decNumberIsSpecial(lhs) && decCheckMath(lhs, set, &status)) + || (!decNumberIsSpecial(rhs) && decCheckMath(rhs, set, &status)) + || (!decNumberIsSpecial(fhs) && decCheckMath(fhs, set, &status))) break; + /* set up context for multiply */ + dcmul=*set; + dcmul.digits=lhs->digits+rhs->digits; /* just enough */ + /* [The above may be an over-estimate for subset arithmetic, but that's OK] */ + dcmul.emax=DEC_MAX_EMAX; /* effectively unbounded .. */ + dcmul.emin=DEC_MIN_EMIN; /* [thanks to Math restrictions] */ + /* set up decNumber space to receive the result of the multiply */ + acc=bufa; /* may fit */ + needbytes=sizeof(decNumber)+(D2U(dcmul.digits)-1)*sizeof(Unit); + if (needbytes>sizeof(bufa)) { /* need malloc space */ + allocbufa=(decNumber *)malloc(needbytes); + if (allocbufa==NULL) { /* hopeless -- abandon */ + status|=DEC_Insufficient_storage; + break;} + acc=allocbufa; /* use the allocated space */ + } + /* multiply with extended range and necessary precision */ + /*printf("emin=%ld\n", dcmul.emin); */ + decMultiplyOp(acc, lhs, rhs, &dcmul, &status); + /* Only Invalid operation (from sNaN or Inf * 0) is possible in */ + /* status; if either is seen than ignore fhs (in case it is */ + /* another sNaN) and set acc to NaN unless we had an sNaN */ + /* [decMultiplyOp leaves that to caller] */ + /* Note sNaN has to go through addOp to shorten payload if */ + /* necessary */ + if ((status&DEC_Invalid_operation)!=0) { + if (!(status&DEC_sNaN)) { /* but be true invalid */ + decNumberZero(res); /* acc not yet set */ + res->bits=DECNAN; + break; + } + decNumberZero(&dzero); /* make 0 (any non-NaN would do) */ + fhs=&dzero; /* use that */ + } + #if DECCHECK + else { /* multiply was OK */ + if (status!=0) printf("Status=%08lx after FMA multiply\n", status); + } + #endif + /* add the third operand and result -> res, and all is done */ + decAddOp(res, acc, fhs, set, 0, &status); + } while(0); /* end protected */ + + if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */ + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } /* decNumberFMA */ + +/* ------------------------------------------------------------------ */ +/* decNumberInvert -- invert a Number, digitwise */ +/* */ +/* This computes C = ~A */ +/* */ +/* res is C, the result. C may be A (e.g., X=~X) */ +/* rhs is A */ +/* set is the context (used for result length and error report) */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Logical function restrictions apply (see above); a NaN is */ +/* returned with Invalid_operation if a restriction is violated. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberInvert(decNumber *res, const decNumber *rhs, + decContext *set) { + const Unit *ua, *msua; /* -> operand and its msu */ + Unit *uc, *msuc; /* -> result and its msu */ + Int msudigs; /* digits in res msu */ + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + if (rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { + decStatus(res, DEC_Invalid_operation, set); + return res; + } + /* operand is valid */ + ua=rhs->lsu; /* bottom-up */ + uc=res->lsu; /* .. */ + msua=ua+D2U(rhs->digits)-1; /* -> msu of rhs */ + msuc=uc+D2U(set->digits)-1; /* -> msu of result */ + msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */ + for (; uc<=msuc; ua++, uc++) { /* Unit loop */ + Unit a; /* extract unit */ + Int i, j; /* work */ + if (ua>msua) a=0; + else a=*ua; + *uc=0; /* can now write back */ + /* always need to examine all bits in rhs */ + /* This loop could be unrolled and/or use BIN2BCD tables */ + for (i=0; i<DECDPUN; i++) { + if ((~a)&1) *uc=*uc+(Unit)powers[i]; /* effect INVERT */ + j=a%10; + a=a/10; + if (j>1) { + decStatus(res, DEC_Invalid_operation, set); + return res; + } + if (uc==msuc && i==msudigs-1) break; /* just did final digit */ + } /* each digit */ + } /* each unit */ + /* [here uc-1 is the msu of the result] */ + res->digits=decGetDigits(res->lsu, uc-res->lsu); + res->exponent=0; /* integer */ + res->bits=0; /* sign=0 */ + return res; /* [no status to set] */ + } /* decNumberInvert */ + +/* ------------------------------------------------------------------ */ +/* decNumberLn -- natural logarithm */ +/* */ +/* This computes C = ln(A) */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context; note that rounding mode has no effect */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Notable cases: */ +/* A<0 -> Invalid */ +/* A=0 -> -Infinity (Exact) */ +/* A=+Infinity -> +Infinity (Exact) */ +/* A=1 exactly -> 0 (Exact) */ +/* */ +/* Mathematical function restrictions apply (see above); a NaN is */ +/* returned with Invalid_operation if a restriction is violated. */ +/* */ +/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */ +/* almost always be correctly rounded, but may be up to 1 ulp in */ +/* error in rare cases. */ +/* ------------------------------------------------------------------ */ +/* This is a wrapper for decLnOp which can handle the slightly wider */ +/* (+11) range needed by Ln, Log10, etc. (which may have to be able */ +/* to calculate at p+e+2). */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberLn(decNumber *res, const decNumber *rhs, + decContext *set) { + uInt status=0; /* accumulator */ + #if DECSUBSET + decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ + #endif + + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + /* Check restrictions; this is a math function; if not violated */ + /* then carry out the operation. */ + if (!decCheckMath(rhs, set, &status)) do { /* protect allocation */ + #if DECSUBSET + if (!set->extended) { + /* reduce operand and set lostDigits status, as needed */ + if (rhs->digits>set->digits) { + allocrhs=decRoundOperand(rhs, set, &status); + if (allocrhs==NULL) break; + rhs=allocrhs; + } + /* special check in subset for rhs=0 */ + if (ISZERO(rhs)) { /* +/- zeros -> error */ + status|=DEC_Invalid_operation; + break;} + } /* extended=0 */ + #endif + decLnOp(res, rhs, set, &status); + } while(0); /* end protected */ + + #if DECSUBSET + if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */ + #endif + /* apply significant status */ + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } /* decNumberLn */ + +/* ------------------------------------------------------------------ */ +/* decNumberLogB - get adjusted exponent, by 754r rules */ +/* */ +/* This computes C = adjustedexponent(A) */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context, used only for digits and status */ +/* */ +/* C must have space for 10 digits (A might have 10**9 digits and */ +/* an exponent of +999999999, or one digit and an exponent of */ +/* -1999999999). */ +/* */ +/* This returns the adjusted exponent of A after (in theory) padding */ +/* with zeros on the right to set->digits digits while keeping the */ +/* same value. The exponent is not limited by emin/emax. */ +/* */ +/* Notable cases: */ +/* A<0 -> Use |A| */ +/* A=0 -> -Infinity (Division by zero) */ +/* A=Infinite -> +Infinity (Exact) */ +/* A=1 exactly -> 0 (Exact) */ +/* NaNs are propagated as usual */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberLogB(decNumber *res, const decNumber *rhs, + decContext *set) { + uInt status=0; /* accumulator */ + + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + /* NaNs as usual; Infinities return +Infinity; 0->oops */ + if (decNumberIsNaN(rhs)) decNaNs(res, rhs, NULL, set, &status); + else if (decNumberIsInfinite(rhs)) decNumberCopyAbs(res, rhs); + else if (decNumberIsZero(rhs)) { + decNumberZero(res); /* prepare for Infinity */ + res->bits=DECNEG|DECINF; /* -Infinity */ + status|=DEC_Division_by_zero; /* as per 754r */ + } + else { /* finite non-zero */ + Int ae=rhs->exponent+rhs->digits-1; /* adjusted exponent */ + decNumberFromInt32(res, ae); /* lay it out */ + } + + if (status!=0) decStatus(res, status, set); + return res; + } /* decNumberLogB */ + +/* ------------------------------------------------------------------ */ +/* decNumberLog10 -- logarithm in base 10 */ +/* */ +/* This computes C = log10(A) */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context; note that rounding mode has no effect */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Notable cases: */ +/* A<0 -> Invalid */ +/* A=0 -> -Infinity (Exact) */ +/* A=+Infinity -> +Infinity (Exact) */ +/* A=10**n (if n is an integer) -> n (Exact) */ +/* */ +/* Mathematical function restrictions apply (see above); a NaN is */ +/* returned with Invalid_operation if a restriction is violated. */ +/* */ +/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */ +/* almost always be correctly rounded, but may be up to 1 ulp in */ +/* error in rare cases. */ +/* ------------------------------------------------------------------ */ +/* This calculates ln(A)/ln(10) using appropriate precision. For */ +/* ln(A) this is the max(p, rhs->digits + t) + 3, where p is the */ +/* requested digits and t is the number of digits in the exponent */ +/* (maximum 6). For ln(10) it is p + 3; this is often handled by the */ +/* fastpath in decLnOp. The final division is done to the requested */ +/* precision. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberLog10(decNumber *res, const decNumber *rhs, + decContext *set) { + uInt status=0, ignore=0; /* status accumulators */ + uInt needbytes; /* for space calculations */ + Int p; /* working precision */ + Int t; /* digits in exponent of A */ + + /* buffers for a and b working decimals */ + /* (adjustment calculator, same size) */ + decNumber bufa[D2N(DECBUFFER+2)]; + decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ + decNumber *a=bufa; /* temporary a */ + decNumber bufb[D2N(DECBUFFER+2)]; + decNumber *allocbufb=NULL; /* -> allocated bufb, iff allocated */ + decNumber *b=bufb; /* temporary b */ + decNumber bufw[D2N(10)]; /* working 2-10 digit number */ + decNumber *w=bufw; /* .. */ + #if DECSUBSET + decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ + #endif + + decContext aset; /* working context */ + + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + /* Check restrictions; this is a math function; if not violated */ + /* then carry out the operation. */ + if (!decCheckMath(rhs, set, &status)) do { /* protect malloc */ + #if DECSUBSET + if (!set->extended) { + /* reduce operand and set lostDigits status, as needed */ + if (rhs->digits>set->digits) { + allocrhs=decRoundOperand(rhs, set, &status); + if (allocrhs==NULL) break; + rhs=allocrhs; + } + /* special check in subset for rhs=0 */ + if (ISZERO(rhs)) { /* +/- zeros -> error */ + status|=DEC_Invalid_operation; + break;} + } /* extended=0 */ + #endif + + decContextDefault(&aset, DEC_INIT_DECIMAL64); /* clean context */ + + /* handle exact powers of 10; only check if +ve finite */ + if (!(rhs->bits&(DECNEG|DECSPECIAL)) && !ISZERO(rhs)) { + Int residue=0; /* (no residue) */ + uInt copystat=0; /* clean status */ + + /* round to a single digit... */ + aset.digits=1; + decCopyFit(w, rhs, &aset, &residue, ©stat); /* copy & shorten */ + /* if exact and the digit is 1, rhs is a power of 10 */ + if (!(copystat&DEC_Inexact) && w->lsu[0]==1) { + /* the exponent, conveniently, is the power of 10; making */ + /* this the result needs a little care as it might not fit, */ + /* so first convert it into the working number, and then move */ + /* to res */ + decNumberFromInt32(w, w->exponent); + residue=0; + decCopyFit(res, w, set, &residue, &status); /* copy & round */ + decFinish(res, set, &residue, &status); /* cleanup/set flags */ + break; + } /* not a power of 10 */ + } /* not a candidate for exact */ + + /* simplify the information-content calculation to use 'total */ + /* number of digits in a, including exponent' as compared to the */ + /* requested digits, as increasing this will only rarely cost an */ + /* iteration in ln(a) anyway */ + t=6; /* it can never be >6 */ + + /* allocate space when needed... */ + p=(rhs->digits+t>set->digits?rhs->digits+t:set->digits)+3; + needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit); + if (needbytes>sizeof(bufa)) { /* need malloc space */ + allocbufa=(decNumber *)malloc(needbytes); + if (allocbufa==NULL) { /* hopeless -- abandon */ + status|=DEC_Insufficient_storage; + break;} + a=allocbufa; /* use the allocated space */ + } + aset.digits=p; /* as calculated */ + aset.emax=DEC_MAX_MATH; /* usual bounds */ + aset.emin=-DEC_MAX_MATH; /* .. */ + aset.clamp=0; /* and no concrete format */ + decLnOp(a, rhs, &aset, &status); /* a=ln(rhs) */ + + /* skip the division if the result so far is infinite, NaN, or */ + /* zero, or there was an error; note NaN from sNaN needs copy */ + if (status&DEC_NaNs && !(status&DEC_sNaN)) break; + if (a->bits&DECSPECIAL || ISZERO(a)) { + decNumberCopy(res, a); /* [will fit] */ + break;} + + /* for ln(10) an extra 3 digits of precision are needed */ + p=set->digits+3; + needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit); + if (needbytes>sizeof(bufb)) { /* need malloc space */ + allocbufb=(decNumber *)malloc(needbytes); + if (allocbufb==NULL) { /* hopeless -- abandon */ + status|=DEC_Insufficient_storage; + break;} + b=allocbufb; /* use the allocated space */ + } + decNumberZero(w); /* set up 10... */ + #if DECDPUN==1 + w->lsu[1]=1; w->lsu[0]=0; /* .. */ + #else + w->lsu[0]=10; /* .. */ + #endif + w->digits=2; /* .. */ + + aset.digits=p; + decLnOp(b, w, &aset, &ignore); /* b=ln(10) */ + + aset.digits=set->digits; /* for final divide */ + decDivideOp(res, a, b, &aset, DIVIDE, &status); /* into result */ + } while(0); /* [for break] */ + + if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */ + if (allocbufb!=NULL) free(allocbufb); /* .. */ + #if DECSUBSET + if (allocrhs !=NULL) free(allocrhs); /* .. */ + #endif + /* apply significant status */ + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } /* decNumberLog10 */ + +/* ------------------------------------------------------------------ */ +/* decNumberMax -- compare two Numbers and return the maximum */ +/* */ +/* This computes C = A ? B, returning the maximum by 754R rules */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberMax(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; /* accumulator */ + decCompareOp(res, lhs, rhs, set, COMPMAX, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } /* decNumberMax */ + +/* ------------------------------------------------------------------ */ +/* decNumberMaxMag -- compare and return the maximum by magnitude */ +/* */ +/* This computes C = A ? B, returning the maximum by 754R rules */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberMaxMag(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; /* accumulator */ + decCompareOp(res, lhs, rhs, set, COMPMAXMAG, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } /* decNumberMaxMag */ + +/* ------------------------------------------------------------------ */ +/* decNumberMin -- compare two Numbers and return the minimum */ +/* */ +/* This computes C = A ? B, returning the minimum by 754R rules */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberMin(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; /* accumulator */ + decCompareOp(res, lhs, rhs, set, COMPMIN, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } /* decNumberMin */ + +/* ------------------------------------------------------------------ */ +/* decNumberMinMag -- compare and return the minimum by magnitude */ +/* */ +/* This computes C = A ? B, returning the minimum by 754R rules */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberMinMag(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; /* accumulator */ + decCompareOp(res, lhs, rhs, set, COMPMINMAG, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } /* decNumberMinMag */ + +/* ------------------------------------------------------------------ */ +/* decNumberMinus -- prefix minus operator */ +/* */ +/* This computes C = 0 - A */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context */ +/* */ +/* See also decNumberCopyNegate for a quiet bitwise version of this. */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +/* Simply use AddOp for the subtract, which will do the necessary. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberMinus(decNumber *res, const decNumber *rhs, + decContext *set) { + decNumber dzero; + uInt status=0; /* accumulator */ + + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + decNumberZero(&dzero); /* make 0 */ + dzero.exponent=rhs->exponent; /* [no coefficient expansion] */ + decAddOp(res, &dzero, rhs, set, DECNEG, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } /* decNumberMinus */ + +/* ------------------------------------------------------------------ */ +/* decNumberNextMinus -- next towards -Infinity */ +/* */ +/* This computes C = A - infinitesimal, rounded towards -Infinity */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context */ +/* */ +/* This is a generalization of 754r NextDown. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberNextMinus(decNumber *res, const decNumber *rhs, + decContext *set) { + decNumber dtiny; /* constant */ + decContext workset=*set; /* work */ + uInt status=0; /* accumulator */ + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + /* +Infinity is the special case */ + if ((rhs->bits&(DECINF|DECNEG))==DECINF) { + decSetMaxValue(res, set); /* is +ve */ + /* there is no status to set */ + return res; + } + decNumberZero(&dtiny); /* start with 0 */ + dtiny.lsu[0]=1; /* make number that is .. */ + dtiny.exponent=DEC_MIN_EMIN-1; /* .. smaller than tiniest */ + workset.round=DEC_ROUND_FLOOR; + decAddOp(res, rhs, &dtiny, &workset, DECNEG, &status); + status&=DEC_Invalid_operation|DEC_sNaN; /* only sNaN Invalid please */ + if (status!=0) decStatus(res, status, set); + return res; + } /* decNumberNextMinus */ + +/* ------------------------------------------------------------------ */ +/* decNumberNextPlus -- next towards +Infinity */ +/* */ +/* This computes C = A + infinitesimal, rounded towards +Infinity */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context */ +/* */ +/* This is a generalization of 754r NextUp. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberNextPlus(decNumber *res, const decNumber *rhs, + decContext *set) { + decNumber dtiny; /* constant */ + decContext workset=*set; /* work */ + uInt status=0; /* accumulator */ + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + /* -Infinity is the special case */ + if ((rhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) { + decSetMaxValue(res, set); + res->bits=DECNEG; /* negative */ + /* there is no status to set */ + return res; + } + decNumberZero(&dtiny); /* start with 0 */ + dtiny.lsu[0]=1; /* make number that is .. */ + dtiny.exponent=DEC_MIN_EMIN-1; /* .. smaller than tiniest */ + workset.round=DEC_ROUND_CEILING; + decAddOp(res, rhs, &dtiny, &workset, 0, &status); + status&=DEC_Invalid_operation|DEC_sNaN; /* only sNaN Invalid please */ + if (status!=0) decStatus(res, status, set); + return res; + } /* decNumberNextPlus */ + +/* ------------------------------------------------------------------ */ +/* decNumberNextToward -- next towards rhs */ +/* */ +/* This computes C = A +/- infinitesimal, rounded towards */ +/* +/-Infinity in the direction of B, as per 754r nextafter rules */ +/* */ +/* res is C, the result. C may be A or B. */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* This is a generalization of 754r NextAfter. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberNextToward(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + decNumber dtiny; /* constant */ + decContext workset=*set; /* work */ + Int result; /* .. */ + uInt status=0; /* accumulator */ + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) { + decNaNs(res, lhs, rhs, set, &status); + } + else { /* Is numeric, so no chance of sNaN Invalid, etc. */ + result=decCompare(lhs, rhs, 0); /* sign matters */ + if (result==BADINT) status|=DEC_Insufficient_storage; /* rare */ + else { /* valid compare */ + if (result==0) decNumberCopySign(res, lhs, rhs); /* easy */ + else { /* differ: need NextPlus or NextMinus */ + uByte sub; /* add or subtract */ + if (result<0) { /* lhs<rhs, do nextplus */ + /* -Infinity is the special case */ + if ((lhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) { + decSetMaxValue(res, set); + res->bits=DECNEG; /* negative */ + return res; /* there is no status to set */ + } + workset.round=DEC_ROUND_CEILING; + sub=0; /* add, please */ + } /* plus */ + else { /* lhs>rhs, do nextminus */ + /* +Infinity is the special case */ + if ((lhs->bits&(DECINF|DECNEG))==DECINF) { + decSetMaxValue(res, set); + return res; /* there is no status to set */ + } + workset.round=DEC_ROUND_FLOOR; + sub=DECNEG; /* subtract, please */ + } /* minus */ + decNumberZero(&dtiny); /* start with 0 */ + dtiny.lsu[0]=1; /* make number that is .. */ + dtiny.exponent=DEC_MIN_EMIN-1; /* .. smaller than tiniest */ + decAddOp(res, lhs, &dtiny, &workset, sub, &status); /* + or - */ + /* turn off exceptions if the result is a normal number */ + /* (including Nmin), otherwise let all status through */ + if (decNumberIsNormal(res, set)) status=0; + } /* unequal */ + } /* compare OK */ + } /* numeric */ + if (status!=0) decStatus(res, status, set); + return res; + } /* decNumberNextToward */ + +/* ------------------------------------------------------------------ */ +/* decNumberOr -- OR two Numbers, digitwise */ +/* */ +/* This computes C = A | B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X|X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context (used for result length and error report) */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Logical function restrictions apply (see above); a NaN is */ +/* returned with Invalid_operation if a restriction is violated. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberOr(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + const Unit *ua, *ub; /* -> operands */ + const Unit *msua, *msub; /* -> operand msus */ + Unit *uc, *msuc; /* -> result and its msu */ + Int msudigs; /* digits in res msu */ + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs) + || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { + decStatus(res, DEC_Invalid_operation, set); + return res; + } + /* operands are valid */ + ua=lhs->lsu; /* bottom-up */ + ub=rhs->lsu; /* .. */ + uc=res->lsu; /* .. */ + msua=ua+D2U(lhs->digits)-1; /* -> msu of lhs */ + msub=ub+D2U(rhs->digits)-1; /* -> msu of rhs */ + msuc=uc+D2U(set->digits)-1; /* -> msu of result */ + msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */ + for (; uc<=msuc; ua++, ub++, uc++) { /* Unit loop */ + Unit a, b; /* extract units */ + if (ua>msua) a=0; + else a=*ua; + if (ub>msub) b=0; + else b=*ub; + *uc=0; /* can now write back */ + if (a|b) { /* maybe 1 bits to examine */ + Int i, j; + /* This loop could be unrolled and/or use BIN2BCD tables */ + for (i=0; i<DECDPUN; i++) { + if ((a|b)&1) *uc=*uc+(Unit)powers[i]; /* effect OR */ + j=a%10; + a=a/10; + j|=b%10; + b=b/10; + if (j>1) { + decStatus(res, DEC_Invalid_operation, set); + return res; + } + if (uc==msuc && i==msudigs-1) break; /* just did final digit */ + } /* each digit */ + } /* non-zero */ + } /* each unit */ + /* [here uc-1 is the msu of the result] */ + res->digits=decGetDigits(res->lsu, uc-res->lsu); + res->exponent=0; /* integer */ + res->bits=0; /* sign=0 */ + return res; /* [no status to set] */ + } /* decNumberOr */ + +/* ------------------------------------------------------------------ */ +/* decNumberPlus -- prefix plus operator */ +/* */ +/* This computes C = 0 + A */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context */ +/* */ +/* See also decNumberCopy for a quiet bitwise version of this. */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +/* This simply uses AddOp; Add will take fast path after preparing A. */ +/* Performance is a concern here, as this routine is often used to */ +/* check operands and apply rounding and overflow/underflow testing. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberPlus(decNumber *res, const decNumber *rhs, + decContext *set) { + decNumber dzero; + uInt status=0; /* accumulator */ + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + decNumberZero(&dzero); /* make 0 */ + dzero.exponent=rhs->exponent; /* [no coefficient expansion] */ + decAddOp(res, &dzero, rhs, set, 0, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } /* decNumberPlus */ + +/* ------------------------------------------------------------------ */ +/* decNumberMultiply -- multiply two Numbers */ +/* */ +/* This computes C = A x B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X+X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberMultiply(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; /* accumulator */ + decMultiplyOp(res, lhs, rhs, set, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } /* decNumberMultiply */ + +/* ------------------------------------------------------------------ */ +/* decNumberPower -- raise a number to a power */ +/* */ +/* This computes C = A ** B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X**X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Mathematical function restrictions apply (see above); a NaN is */ +/* returned with Invalid_operation if a restriction is violated. */ +/* */ +/* However, if 1999999997<=B<=999999999 and B is an integer then the */ +/* restrictions on A and the context are relaxed to the usual bounds, */ +/* for compatibility with the earlier (integer power only) version */ +/* of this function. */ +/* */ +/* When B is an integer, the result may be exact, even if rounded. */ +/* */ +/* The final result is rounded according to the context; it will */ +/* almost always be correctly rounded, but may be up to 1 ulp in */ +/* error in rare cases. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberPower(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + #if DECSUBSET + decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */ + decNumber *allocrhs=NULL; /* .., rhs */ + #endif + decNumber *allocdac=NULL; /* -> allocated acc buffer, iff used */ + decNumber *allocinv=NULL; /* -> allocated 1/x buffer, iff used */ + Int reqdigits=set->digits; /* requested DIGITS */ + Int n; /* rhs in binary */ + Flag rhsint=0; /* 1 if rhs is an integer */ + Flag useint=0; /* 1 if can use integer calculation */ + Flag isoddint=0; /* 1 if rhs is an integer and odd */ + Int i; /* work */ + #if DECSUBSET + Int dropped; /* .. */ + #endif + uInt needbytes; /* buffer size needed */ + Flag seenbit; /* seen a bit while powering */ + Int residue=0; /* rounding residue */ + uInt status=0; /* accumulators */ + uByte bits=0; /* result sign if errors */ + decContext aset; /* working context */ + decNumber dnOne; /* work value 1... */ + /* local accumulator buffer [a decNumber, with digits+elength+1 digits] */ + decNumber dacbuff[D2N(DECBUFFER+9)]; + decNumber *dac=dacbuff; /* -> result accumulator */ + /* same again for possible 1/lhs calculation */ + decNumber invbuff[D2N(DECBUFFER+9)]; + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + do { /* protect allocated storage */ + #if DECSUBSET + if (!set->extended) { /* reduce operands and set status, as needed */ + if (lhs->digits>reqdigits) { + alloclhs=decRoundOperand(lhs, set, &status); + if (alloclhs==NULL) break; + lhs=alloclhs; + } + if (rhs->digits>reqdigits) { + allocrhs=decRoundOperand(rhs, set, &status); + if (allocrhs==NULL) break; + rhs=allocrhs; + } + } + #endif + /* [following code does not require input rounding] */ + + /* handle NaNs and rhs Infinity (lhs infinity is harder) */ + if (SPECIALARGS) { + if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) { /* NaNs */ + decNaNs(res, lhs, rhs, set, &status); + break;} + if (decNumberIsInfinite(rhs)) { /* rhs Infinity */ + Flag rhsneg=rhs->bits&DECNEG; /* save rhs sign */ + if (decNumberIsNegative(lhs) /* lhs<0 */ + && !decNumberIsZero(lhs)) /* .. */ + status|=DEC_Invalid_operation; + else { /* lhs >=0 */ + decNumberZero(&dnOne); /* set up 1 */ + dnOne.lsu[0]=1; + decNumberCompare(dac, lhs, &dnOne, set); /* lhs ? 1 */ + decNumberZero(res); /* prepare for 0/1/Infinity */ + if (decNumberIsNegative(dac)) { /* lhs<1 */ + if (rhsneg) res->bits|=DECINF; /* +Infinity [else is +0] */ + } + else if (dac->lsu[0]==0) { /* lhs=1 */ + /* 1**Infinity is inexact, so return fully-padded 1.0000 */ + Int shift=set->digits-1; + *res->lsu=1; /* was 0, make int 1 */ + res->digits=decShiftToMost(res->lsu, 1, shift); + res->exponent=-shift; /* make 1.0000... */ + status|=DEC_Inexact|DEC_Rounded; /* deemed inexact */ + } + else { /* lhs>1 */ + if (!rhsneg) res->bits|=DECINF; /* +Infinity [else is +0] */ + } + } /* lhs>=0 */ + break;} + /* [lhs infinity drops through] */ + } /* specials */ + + /* Original rhs may be an integer that fits and is in range */ + n=decGetInt(rhs); + if (n!=BADINT) { /* it is an integer */ + rhsint=1; /* record the fact for 1**n */ + isoddint=(Flag)n&1; /* [works even if big] */ + if (n!=BIGEVEN && n!=BIGODD) /* can use integer path? */ + useint=1; /* looks good */ + } + + if (decNumberIsNegative(lhs) /* -x .. */ + && isoddint) bits=DECNEG; /* .. to an odd power */ + + /* handle LHS infinity */ + if (decNumberIsInfinite(lhs)) { /* [NaNs already handled] */ + uByte rbits=rhs->bits; /* save */ + decNumberZero(res); /* prepare */ + if (n==0) *res->lsu=1; /* [-]Inf**0 => 1 */ + else { + /* -Inf**nonint -> error */ + if (!rhsint && decNumberIsNegative(lhs)) { + status|=DEC_Invalid_operation; /* -Inf**nonint is error */ + break;} + if (!(rbits & DECNEG)) bits|=DECINF; /* was not a **-n */ + /* [otherwise will be 0 or -0] */ + res->bits=bits; + } + break;} + + /* similarly handle LHS zero */ + if (decNumberIsZero(lhs)) { + if (n==0) { /* 0**0 => Error */ + #if DECSUBSET + if (!set->extended) { /* [unless subset] */ + decNumberZero(res); + *res->lsu=1; /* return 1 */ + break;} + #endif + status|=DEC_Invalid_operation; + } + else { /* 0**x */ + uByte rbits=rhs->bits; /* save */ + if (rbits & DECNEG) { /* was a 0**(-n) */ + #if DECSUBSET + if (!set->extended) { /* [bad if subset] */ + status|=DEC_Invalid_operation; + break;} + #endif + bits|=DECINF; + } + decNumberZero(res); /* prepare */ + /* [otherwise will be 0 or -0] */ + res->bits=bits; + } + break;} + + /* here both lhs and rhs are finite; rhs==0 is handled in the */ + /* integer path. Next handle the non-integer cases */ + if (!useint) { /* non-integral rhs */ + /* any -ve lhs is bad, as is either operand or context out of */ + /* bounds */ + if (decNumberIsNegative(lhs)) { + status|=DEC_Invalid_operation; + break;} + if (decCheckMath(lhs, set, &status) + || decCheckMath(rhs, set, &status)) break; /* variable status */ + + decContextDefault(&aset, DEC_INIT_DECIMAL64); /* clean context */ + aset.emax=DEC_MAX_MATH; /* usual bounds */ + aset.emin=-DEC_MAX_MATH; /* .. */ + aset.clamp=0; /* and no concrete format */ + + /* calculate the result using exp(ln(lhs)*rhs), which can */ + /* all be done into the accumulator, dac. The precision needed */ + /* is enough to contain the full information in the lhs (which */ + /* is the total digits, including exponent), or the requested */ + /* precision, if larger, + 4; 6 is used for the exponent */ + /* maximum length, and this is also used when it is shorter */ + /* than the requested digits as it greatly reduces the >0.5 ulp */ + /* cases at little cost (because Ln doubles digits each */ + /* iteration so a few extra digits rarely causes an extra */ + /* iteration) */ + aset.digits=MAXI(lhs->digits, set->digits)+6+4; + } /* non-integer rhs */ + + else { /* rhs is in-range integer */ + if (n==0) { /* x**0 = 1 */ + /* (0**0 was handled above) */ + decNumberZero(res); /* result=1 */ + *res->lsu=1; /* .. */ + break;} + /* rhs is a non-zero integer */ + if (n<0) n=-n; /* use abs(n) */ + + aset=*set; /* clone the context */ + aset.round=DEC_ROUND_HALF_EVEN; /* internally use balanced */ + /* calculate the working DIGITS */ + aset.digits=reqdigits+(rhs->digits+rhs->exponent)+2; + #if DECSUBSET + if (!set->extended) aset.digits--; /* use classic precision */ + #endif + /* it's an error if this is more than can be handled */ + if (aset.digits>DECNUMMAXP) {status|=DEC_Invalid_operation; break;} + } /* integer path */ + + /* aset.digits is the count of digits for the accumulator needed */ + /* if accumulator is too long for local storage, then allocate */ + needbytes=sizeof(decNumber)+(D2U(aset.digits)-1)*sizeof(Unit); + /* [needbytes also used below if 1/lhs needed] */ + if (needbytes>sizeof(dacbuff)) { + allocdac=(decNumber *)malloc(needbytes); + if (allocdac==NULL) { /* hopeless -- abandon */ + status|=DEC_Insufficient_storage; + break;} + dac=allocdac; /* use the allocated space */ + } + /* here, aset is set up and accumulator is ready for use */ + + if (!useint) { /* non-integral rhs */ + /* x ** y; special-case x=1 here as it will otherwise always */ + /* reduce to integer 1; decLnOp has a fastpath which detects */ + /* the case of x=1 */ + decLnOp(dac, lhs, &aset, &status); /* dac=ln(lhs) */ + /* [no error possible, as lhs 0 already handled] */ + if (ISZERO(dac)) { /* x==1, 1.0, etc. */ + /* need to return fully-padded 1.0000 etc., but rhsint->1 */ + *dac->lsu=1; /* was 0, make int 1 */ + if (!rhsint) { /* add padding */ + Int shift=set->digits-1; + dac->digits=decShiftToMost(dac->lsu, 1, shift); + dac->exponent=-shift; /* make 1.0000... */ + status|=DEC_Inexact|DEC_Rounded; /* deemed inexact */ + } + } + else { + decMultiplyOp(dac, dac, rhs, &aset, &status); /* dac=dac*rhs */ + decExpOp(dac, dac, &aset, &status); /* dac=exp(dac) */ + } + /* and drop through for final rounding */ + } /* non-integer rhs */ + + else { /* carry on with integer */ + decNumberZero(dac); /* acc=1 */ + *dac->lsu=1; /* .. */ + + /* if a negative power the constant 1 is needed, and if not subset */ + /* invert the lhs now rather than inverting the result later */ + if (decNumberIsNegative(rhs)) { /* was a **-n [hence digits>0] */ + decNumber *inv=invbuff; /* asssume use fixed buffer */ + decNumberCopy(&dnOne, dac); /* dnOne=1; [needed now or later] */ + #if DECSUBSET + if (set->extended) { /* need to calculate 1/lhs */ + #endif + /* divide lhs into 1, putting result in dac [dac=1/dac] */ + decDivideOp(dac, &dnOne, lhs, &aset, DIVIDE, &status); + /* now locate or allocate space for the inverted lhs */ + if (needbytes>sizeof(invbuff)) { + allocinv=(decNumber *)malloc(needbytes); + if (allocinv==NULL) { /* hopeless -- abandon */ + status|=DEC_Insufficient_storage; + break;} + inv=allocinv; /* use the allocated space */ + } + /* [inv now points to big-enough buffer or allocated storage] */ + decNumberCopy(inv, dac); /* copy the 1/lhs */ + decNumberCopy(dac, &dnOne); /* restore acc=1 */ + lhs=inv; /* .. and go forward with new lhs */ + #if DECSUBSET + } + #endif + } + + /* Raise-to-the-power loop... */ + seenbit=0; /* set once a 1-bit is encountered */ + for (i=1;;i++){ /* for each bit [top bit ignored] */ + /* abandon if had overflow or terminal underflow */ + if (status & (DEC_Overflow|DEC_Underflow)) { /* interesting? */ + if (status&DEC_Overflow || ISZERO(dac)) break; + } + /* [the following two lines revealed an optimizer bug in a C++ */ + /* compiler, with symptom: 5**3 -> 25, when n=n+n was used] */ + n=n<<1; /* move next bit to testable position */ + if (n<0) { /* top bit is set */ + seenbit=1; /* OK, significant bit seen */ + decMultiplyOp(dac, dac, lhs, &aset, &status); /* dac=dac*x */ + } + if (i==31) break; /* that was the last bit */ + if (!seenbit) continue; /* no need to square 1 */ + decMultiplyOp(dac, dac, dac, &aset, &status); /* dac=dac*dac [square] */ + } /*i*/ /* 32 bits */ + + /* complete internal overflow or underflow processing */ + if (status & (DEC_Overflow|DEC_Underflow)) { + #if DECSUBSET + /* If subset, and power was negative, reverse the kind of -erflow */ + /* [1/x not yet done] */ + if (!set->extended && decNumberIsNegative(rhs)) { + if (status & DEC_Overflow) + status^=DEC_Overflow | DEC_Underflow | DEC_Subnormal; + else { /* trickier -- Underflow may or may not be set */ + status&=~(DEC_Underflow | DEC_Subnormal); /* [one or both] */ + status|=DEC_Overflow; + } + } + #endif + dac->bits=(dac->bits & ~DECNEG) | bits; /* force correct sign */ + /* round subnormals [to set.digits rather than aset.digits] */ + /* or set overflow result similarly as required */ + decFinalize(dac, set, &residue, &status); + decNumberCopy(res, dac); /* copy to result (is now OK length) */ + break; + } + + #if DECSUBSET + if (!set->extended && /* subset math */ + decNumberIsNegative(rhs)) { /* was a **-n [hence digits>0] */ + /* so divide result into 1 [dac=1/dac] */ + decDivideOp(dac, &dnOne, dac, &aset, DIVIDE, &status); + } + #endif + } /* rhs integer path */ + + /* reduce result to the requested length and copy to result */ + decCopyFit(res, dac, set, &residue, &status); + decFinish(res, set, &residue, &status); /* final cleanup */ + #if DECSUBSET + if (!set->extended) decTrim(res, set, 0, &dropped); /* trailing zeros */ + #endif + } while(0); /* end protected */ + + if (allocdac!=NULL) free(allocdac); /* drop any storage used */ + if (allocinv!=NULL) free(allocinv); /* .. */ + #if DECSUBSET + if (alloclhs!=NULL) free(alloclhs); /* .. */ + if (allocrhs!=NULL) free(allocrhs); /* .. */ + #endif + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } /* decNumberPower */ + +/* ------------------------------------------------------------------ */ +/* decNumberQuantize -- force exponent to requested value */ +/* */ +/* This computes C = op(A, B), where op adjusts the coefficient */ +/* of C (by rounding or shifting) such that the exponent (-scale) */ +/* of C has exponent of B. The numerical value of C will equal A, */ +/* except for the effects of any rounding that occurred. */ +/* */ +/* res is C, the result. C may be A or B */ +/* lhs is A, the number to adjust */ +/* rhs is B, the number with exponent to match */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Unless there is an error or the result is infinite, the exponent */ +/* after the operation is guaranteed to be equal to that of B. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberQuantize(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; /* accumulator */ + decQuantizeOp(res, lhs, rhs, set, 1, &status); + if (status!=0) decStatus(res, status, set); + return res; + } /* decNumberQuantize */ + +/* ------------------------------------------------------------------ */ +/* decNumberReduce -- remove trailing zeros */ +/* */ +/* This computes C = 0 + A, and normalizes the result */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +/* Previously known as Normalize */ +decNumber * decNumberNormalize(decNumber *res, const decNumber *rhs, + decContext *set) { + return decNumberReduce(res, rhs, set); + } /* decNumberNormalize */ + +decNumber * decNumberReduce(decNumber *res, const decNumber *rhs, + decContext *set) { + #if DECSUBSET + decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ + #endif + uInt status=0; /* as usual */ + Int residue=0; /* as usual */ + Int dropped; /* work */ + + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + do { /* protect allocated storage */ + #if DECSUBSET + if (!set->extended) { + /* reduce operand and set lostDigits status, as needed */ + if (rhs->digits>set->digits) { + allocrhs=decRoundOperand(rhs, set, &status); + if (allocrhs==NULL) break; + rhs=allocrhs; + } + } + #endif + /* [following code does not require input rounding] */ + + /* Infinities copy through; NaNs need usual treatment */ + if (decNumberIsNaN(rhs)) { + decNaNs(res, rhs, NULL, set, &status); + break; + } + + /* reduce result to the requested length and copy to result */ + decCopyFit(res, rhs, set, &residue, &status); /* copy & round */ + decFinish(res, set, &residue, &status); /* cleanup/set flags */ + decTrim(res, set, 1, &dropped); /* normalize in place */ + } while(0); /* end protected */ + + #if DECSUBSET + if (allocrhs !=NULL) free(allocrhs); /* .. */ + #endif + if (status!=0) decStatus(res, status, set);/* then report status */ + return res; + } /* decNumberReduce */ + +/* ------------------------------------------------------------------ */ +/* decNumberRescale -- force exponent to requested value */ +/* */ +/* This computes C = op(A, B), where op adjusts the coefficient */ +/* of C (by rounding or shifting) such that the exponent (-scale) */ +/* of C has the value B. The numerical value of C will equal A, */ +/* except for the effects of any rounding that occurred. */ +/* */ +/* res is C, the result. C may be A or B */ +/* lhs is A, the number to adjust */ +/* rhs is B, the requested exponent */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Unless there is an error or the result is infinite, the exponent */ +/* after the operation is guaranteed to be equal to B. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberRescale(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; /* accumulator */ + decQuantizeOp(res, lhs, rhs, set, 0, &status); + if (status!=0) decStatus(res, status, set); + return res; + } /* decNumberRescale */ + +/* ------------------------------------------------------------------ */ +/* decNumberRemainder -- divide and return remainder */ +/* */ +/* This computes C = A % B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X%X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberRemainder(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; /* accumulator */ + decDivideOp(res, lhs, rhs, set, REMAINDER, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } /* decNumberRemainder */ + +/* ------------------------------------------------------------------ */ +/* decNumberRemainderNear -- divide and return remainder from nearest */ +/* */ +/* This computes C = A % B, where % is the IEEE remainder operator */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X%X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberRemainderNear(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; /* accumulator */ + decDivideOp(res, lhs, rhs, set, REMNEAR, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } /* decNumberRemainderNear */ + +/* ------------------------------------------------------------------ */ +/* decNumberRotate -- rotate the coefficient of a Number left/right */ +/* */ +/* This computes C = A rot B (in base ten and rotating set->digits */ +/* digits). */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=XrotX) */ +/* lhs is A */ +/* rhs is B, the number of digits to rotate (-ve to right) */ +/* set is the context */ +/* */ +/* The digits of the coefficient of A are rotated to the left (if B */ +/* is positive) or to the right (if B is negative) without adjusting */ +/* the exponent or the sign of A. If lhs->digits is less than */ +/* set->digits the coefficient is padded with zeros on the left */ +/* before the rotate. Any leading zeros in the result are removed */ +/* as usual. */ +/* */ +/* B must be an integer (q=0) and in the range -set->digits through */ +/* +set->digits. */ +/* C must have space for set->digits digits. */ +/* NaNs are propagated as usual. Infinities are unaffected (but */ +/* B must be valid). No status is set unless B is invalid or an */ +/* operand is an sNaN. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberRotate(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; /* accumulator */ + Int rotate; /* rhs as an Int */ + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + /* NaNs propagate as normal */ + if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) + decNaNs(res, lhs, rhs, set, &status); + /* rhs must be an integer */ + else if (decNumberIsInfinite(rhs) || rhs->exponent!=0) + status=DEC_Invalid_operation; + else { /* both numeric, rhs is an integer */ + rotate=decGetInt(rhs); /* [cannot fail] */ + if (rotate==BADINT /* something bad .. */ + || rotate==BIGODD || rotate==BIGEVEN /* .. very big .. */ + || abs(rotate)>set->digits) /* .. or out of range */ + status=DEC_Invalid_operation; + else { /* rhs is OK */ + decNumberCopy(res, lhs); + /* convert -ve rotate to equivalent positive rotation */ + if (rotate<0) rotate=set->digits+rotate; + if (rotate!=0 && rotate!=set->digits /* zero or full rotation */ + && !decNumberIsInfinite(res)) { /* lhs was infinite */ + /* left-rotate to do; 0 < rotate < set->digits */ + uInt units, shift; /* work */ + uInt msudigits; /* digits in result msu */ + Unit *msu=res->lsu+D2U(res->digits)-1; /* current msu */ + Unit *msumax=res->lsu+D2U(set->digits)-1; /* rotation msu */ + for (msu++; msu<=msumax; msu++) *msu=0; /* ensure high units=0 */ + res->digits=set->digits; /* now full-length */ + msudigits=MSUDIGITS(res->digits); /* actual digits in msu */ + + /* rotation here is done in-place, in three steps */ + /* 1. shift all to least up to one unit to unit-align final */ + /* lsd [any digits shifted out are rotated to the left, */ + /* abutted to the original msd (which may require split)] */ + /* */ + /* [if there are no whole units left to rotate, the */ + /* rotation is now complete] */ + /* */ + /* 2. shift to least, from below the split point only, so that */ + /* the final msd is in the right place in its Unit [any */ + /* digits shifted out will fit exactly in the current msu, */ + /* left aligned, no split required] */ + /* */ + /* 3. rotate all the units by reversing left part, right */ + /* part, and then whole */ + /* */ + /* example: rotate right 8 digits (2 units + 2), DECDPUN=3. */ + /* */ + /* start: 00a bcd efg hij klm npq */ + /* */ + /* 1a 000 0ab cde fgh|ijk lmn [pq saved] */ + /* 1b 00p qab cde fgh|ijk lmn */ + /* */ + /* 2a 00p qab cde fgh|00i jkl [mn saved] */ + /* 2b mnp qab cde fgh|00i jkl */ + /* */ + /* 3a fgh cde qab mnp|00i jkl */ + /* 3b fgh cde qab mnp|jkl 00i */ + /* 3c 00i jkl mnp qab cde fgh */ + + /* Step 1: amount to shift is the partial right-rotate count */ + rotate=set->digits-rotate; /* make it right-rotate */ + units=rotate/DECDPUN; /* whole units to rotate */ + shift=rotate%DECDPUN; /* left-over digits count */ + if (shift>0) { /* not an exact number of units */ + uInt save=res->lsu[0]%powers[shift]; /* save low digit(s) */ + decShiftToLeast(res->lsu, D2U(res->digits), shift); + if (shift>msudigits) { /* msumax-1 needs >0 digits */ + uInt rem=save%powers[shift-msudigits];/* split save */ + *msumax=(Unit)(save/powers[shift-msudigits]); /* and insert */ + *(msumax-1)=*(msumax-1) + +(Unit)(rem*powers[DECDPUN-(shift-msudigits)]); /* .. */ + } + else { /* all fits in msumax */ + *msumax=*msumax+(Unit)(save*powers[msudigits-shift]); /* [maybe *1] */ + } + } /* digits shift needed */ + + /* If whole units to rotate... */ + if (units>0) { /* some to do */ + /* Step 2: the units to touch are the whole ones in rotate, */ + /* if any, and the shift is DECDPUN-msudigits (which may be */ + /* 0, again) */ + shift=DECDPUN-msudigits; + if (shift>0) { /* not an exact number of units */ + uInt save=res->lsu[0]%powers[shift]; /* save low digit(s) */ + decShiftToLeast(res->lsu, units, shift); + *msumax=*msumax+(Unit)(save*powers[msudigits]); + } /* partial shift needed */ + + /* Step 3: rotate the units array using triple reverse */ + /* (reversing is easy and fast) */ + decReverse(res->lsu+units, msumax); /* left part */ + decReverse(res->lsu, res->lsu+units-1); /* right part */ + decReverse(res->lsu, msumax); /* whole */ + } /* whole units to rotate */ + /* the rotation may have left an undetermined number of zeros */ + /* on the left, so true length needs to be calculated */ + res->digits=decGetDigits(res->lsu, msumax-res->lsu+1); + } /* rotate needed */ + } /* rhs OK */ + } /* numerics */ + if (status!=0) decStatus(res, status, set); + return res; + } /* decNumberRotate */ + +/* ------------------------------------------------------------------ */ +/* decNumberSameQuantum -- test for equal exponents */ +/* */ +/* res is the result number, which will contain either 0 or 1 */ +/* lhs is a number to test */ +/* rhs is the second (usually a pattern) */ +/* */ +/* No errors are possible and no context is needed. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberSameQuantum(decNumber *res, const decNumber *lhs, + const decNumber *rhs) { + Unit ret=0; /* return value */ + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, DECUNCONT)) return res; + #endif + + if (SPECIALARGS) { + if (decNumberIsNaN(lhs) && decNumberIsNaN(rhs)) ret=1; + else if (decNumberIsInfinite(lhs) && decNumberIsInfinite(rhs)) ret=1; + /* [anything else with a special gives 0] */ + } + else if (lhs->exponent==rhs->exponent) ret=1; + + decNumberZero(res); /* OK to overwrite an operand now */ + *res->lsu=ret; + return res; + } /* decNumberSameQuantum */ + +/* ------------------------------------------------------------------ */ +/* decNumberScaleB -- multiply by a power of 10 */ +/* */ +/* This computes C = A x 10**B where B is an integer (q=0) with */ +/* maximum magnitude 2*(emax+digits) */ +/* */ +/* res is C, the result. C may be A or B */ +/* lhs is A, the number to adjust */ +/* rhs is B, the requested power of ten to use */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* The result may underflow or overflow. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberScaleB(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + Int reqexp; /* requested exponent change [B] */ + uInt status=0; /* accumulator */ + Int residue; /* work */ + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + /* Handle special values except lhs infinite */ + if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) + decNaNs(res, lhs, rhs, set, &status); + /* rhs must be an integer */ + else if (decNumberIsInfinite(rhs) || rhs->exponent!=0) + status=DEC_Invalid_operation; + else { + /* lhs is a number; rhs is a finite with q==0 */ + reqexp=decGetInt(rhs); /* [cannot fail] */ + if (reqexp==BADINT /* something bad .. */ + || reqexp==BIGODD || reqexp==BIGEVEN /* .. very big .. */ + || abs(reqexp)>(2*(set->digits+set->emax))) /* .. or out of range */ + status=DEC_Invalid_operation; + else { /* rhs is OK */ + decNumberCopy(res, lhs); /* all done if infinite lhs */ + if (!decNumberIsInfinite(res)) { /* prepare to scale */ + res->exponent+=reqexp; /* adjust the exponent */ + residue=0; + decFinalize(res, set, &residue, &status); /* .. and check */ + } /* finite LHS */ + } /* rhs OK */ + } /* rhs finite */ + if (status!=0) decStatus(res, status, set); + return res; + } /* decNumberScaleB */ + +/* ------------------------------------------------------------------ */ +/* decNumberShift -- shift the coefficient of a Number left or right */ +/* */ +/* This computes C = A << B or C = A >> -B (in base ten). */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X<<X) */ +/* lhs is A */ +/* rhs is B, the number of digits to shift (-ve to right) */ +/* set is the context */ +/* */ +/* The digits of the coefficient of A are shifted to the left (if B */ +/* is positive) or to the right (if B is negative) without adjusting */ +/* the exponent or the sign of A. */ +/* */ +/* B must be an integer (q=0) and in the range -set->digits through */ +/* +set->digits. */ +/* C must have space for set->digits digits. */ +/* NaNs are propagated as usual. Infinities are unaffected (but */ +/* B must be valid). No status is set unless B is invalid or an */ +/* operand is an sNaN. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberShift(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; /* accumulator */ + Int shift; /* rhs as an Int */ + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + /* NaNs propagate as normal */ + if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) + decNaNs(res, lhs, rhs, set, &status); + /* rhs must be an integer */ + else if (decNumberIsInfinite(rhs) || rhs->exponent!=0) + status=DEC_Invalid_operation; + else { /* both numeric, rhs is an integer */ + shift=decGetInt(rhs); /* [cannot fail] */ + if (shift==BADINT /* something bad .. */ + || shift==BIGODD || shift==BIGEVEN /* .. very big .. */ + || abs(shift)>set->digits) /* .. or out of range */ + status=DEC_Invalid_operation; + else { /* rhs is OK */ + decNumberCopy(res, lhs); + if (shift!=0 && !decNumberIsInfinite(res)) { /* something to do */ + if (shift>0) { /* to left */ + if (shift==set->digits) { /* removing all */ + *res->lsu=0; /* so place 0 */ + res->digits=1; /* .. */ + } + else { /* */ + /* first remove leading digits if necessary */ + if (res->digits+shift>set->digits) { + decDecap(res, res->digits+shift-set->digits); + /* that updated res->digits; may have gone to 1 (for a */ + /* single digit or for zero */ + } + if (res->digits>1 || *res->lsu) /* if non-zero.. */ + res->digits=decShiftToMost(res->lsu, res->digits, shift); + } /* partial left */ + } /* left */ + else { /* to right */ + if (-shift>=res->digits) { /* discarding all */ + *res->lsu=0; /* so place 0 */ + res->digits=1; /* .. */ + } + else { + decShiftToLeast(res->lsu, D2U(res->digits), -shift); + res->digits-=(-shift); + } + } /* to right */ + } /* non-0 non-Inf shift */ + } /* rhs OK */ + } /* numerics */ + if (status!=0) decStatus(res, status, set); + return res; + } /* decNumberShift */ + +/* ------------------------------------------------------------------ */ +/* decNumberSquareRoot -- square root operator */ +/* */ +/* This computes C = squareroot(A) */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context; note that rounding mode has no effect */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +/* This uses the following varying-precision algorithm in: */ +/* */ +/* Properly Rounded Variable Precision Square Root, T. E. Hull and */ +/* A. Abrham, ACM Transactions on Mathematical Software, Vol 11 #3, */ +/* pp229-237, ACM, September 1985. */ +/* */ +/* The square-root is calculated using Newton's method, after which */ +/* a check is made to ensure the result is correctly rounded. */ +/* */ +/* % [Reformatted original Numerical Turing source code follows.] */ +/* function sqrt(x : real) : real */ +/* % sqrt(x) returns the properly rounded approximation to the square */ +/* % root of x, in the precision of the calling environment, or it */ +/* % fails if x < 0. */ +/* % t e hull and a abrham, august, 1984 */ +/* if x <= 0 then */ +/* if x < 0 then */ +/* assert false */ +/* else */ +/* result 0 */ +/* end if */ +/* end if */ +/* var f := setexp(x, 0) % fraction part of x [0.1 <= x < 1] */ +/* var e := getexp(x) % exponent part of x */ +/* var approx : real */ +/* if e mod 2 = 0 then */ +/* approx := .259 + .819 * f % approx to root of f */ +/* else */ +/* f := f/l0 % adjustments */ +/* e := e + 1 % for odd */ +/* approx := .0819 + 2.59 * f % exponent */ +/* end if */ +/* */ +/* var p:= 3 */ +/* const maxp := currentprecision + 2 */ +/* loop */ +/* p := min(2*p - 2, maxp) % p = 4,6,10, . . . , maxp */ +/* precision p */ +/* approx := .5 * (approx + f/approx) */ +/* exit when p = maxp */ +/* end loop */ +/* */ +/* % approx is now within 1 ulp of the properly rounded square root */ +/* % of f; to ensure proper rounding, compare squares of (approx - */ +/* % l/2 ulp) and (approx + l/2 ulp) with f. */ +/* p := currentprecision */ +/* begin */ +/* precision p + 2 */ +/* const approxsubhalf := approx - setexp(.5, -p) */ +/* if mulru(approxsubhalf, approxsubhalf) > f then */ +/* approx := approx - setexp(.l, -p + 1) */ +/* else */ +/* const approxaddhalf := approx + setexp(.5, -p) */ +/* if mulrd(approxaddhalf, approxaddhalf) < f then */ +/* approx := approx + setexp(.l, -p + 1) */ +/* end if */ +/* end if */ +/* end */ +/* result setexp(approx, e div 2) % fix exponent */ +/* end sqrt */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberSquareRoot(decNumber *res, const decNumber *rhs, + decContext *set) { + decContext workset, approxset; /* work contexts */ + decNumber dzero; /* used for constant zero */ + Int maxp; /* largest working precision */ + Int workp; /* working precision */ + Int residue=0; /* rounding residue */ + uInt status=0, ignore=0; /* status accumulators */ + uInt rstatus; /* .. */ + Int exp; /* working exponent */ + Int ideal; /* ideal (preferred) exponent */ + Int needbytes; /* work */ + Int dropped; /* .. */ + + #if DECSUBSET + decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */ + #endif + /* buffer for f [needs +1 in case DECBUFFER 0] */ + decNumber buff[D2N(DECBUFFER+1)]; + /* buffer for a [needs +2 to match likely maxp] */ + decNumber bufa[D2N(DECBUFFER+2)]; + /* buffer for temporary, b [must be same size as a] */ + decNumber bufb[D2N(DECBUFFER+2)]; + decNumber *allocbuff=NULL; /* -> allocated buff, iff allocated */ + decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ + decNumber *allocbufb=NULL; /* -> allocated bufb, iff allocated */ + decNumber *f=buff; /* reduced fraction */ + decNumber *a=bufa; /* approximation to result */ + decNumber *b=bufb; /* intermediate result */ + /* buffer for temporary variable, up to 3 digits */ + decNumber buft[D2N(3)]; + decNumber *t=buft; /* up-to-3-digit constant or work */ + + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + do { /* protect allocated storage */ + #if DECSUBSET + if (!set->extended) { + /* reduce operand and set lostDigits status, as needed */ + if (rhs->digits>set->digits) { + allocrhs=decRoundOperand(rhs, set, &status); + if (allocrhs==NULL) break; + /* [Note: 'f' allocation below could reuse this buffer if */ + /* used, but as this is rare they are kept separate for clarity.] */ + rhs=allocrhs; + } + } + #endif + /* [following code does not require input rounding] */ + + /* handle infinities and NaNs */ + if (SPECIALARG) { + if (decNumberIsInfinite(rhs)) { /* an infinity */ + if (decNumberIsNegative(rhs)) status|=DEC_Invalid_operation; + else decNumberCopy(res, rhs); /* +Infinity */ + } + else decNaNs(res, rhs, NULL, set, &status); /* a NaN */ + break; + } + + /* calculate the ideal (preferred) exponent [floor(exp/2)] */ + /* [We would like to write: ideal=rhs->exponent>>1, but this */ + /* generates a compiler warning. Generated code is the same.] */ + ideal=(rhs->exponent&~1)/2; /* target */ + + /* handle zeros */ + if (ISZERO(rhs)) { + decNumberCopy(res, rhs); /* could be 0 or -0 */ + res->exponent=ideal; /* use the ideal [safe] */ + /* use decFinish to clamp any out-of-range exponent, etc. */ + decFinish(res, set, &residue, &status); + break; + } + + /* any other -x is an oops */ + if (decNumberIsNegative(rhs)) { + status|=DEC_Invalid_operation; + break; + } + + /* space is needed for three working variables */ + /* f -- the same precision as the RHS, reduced to 0.01->0.99... */ + /* a -- Hull's approximation -- precision, when assigned, is */ + /* currentprecision+1 or the input argument precision, */ + /* whichever is larger (+2 for use as temporary) */ + /* b -- intermediate temporary result (same size as a) */ + /* if any is too long for local storage, then allocate */ + workp=MAXI(set->digits+1, rhs->digits); /* actual rounding precision */ + maxp=workp+2; /* largest working precision */ + + needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit); + if (needbytes>(Int)sizeof(buff)) { + allocbuff=(decNumber *)malloc(needbytes); + if (allocbuff==NULL) { /* hopeless -- abandon */ + status|=DEC_Insufficient_storage; + break;} + f=allocbuff; /* use the allocated space */ + } + /* a and b both need to be able to hold a maxp-length number */ + needbytes=sizeof(decNumber)+(D2U(maxp)-1)*sizeof(Unit); + if (needbytes>(Int)sizeof(bufa)) { /* [same applies to b] */ + allocbufa=(decNumber *)malloc(needbytes); + allocbufb=(decNumber *)malloc(needbytes); + if (allocbufa==NULL || allocbufb==NULL) { /* hopeless */ + status|=DEC_Insufficient_storage; + break;} + a=allocbufa; /* use the allocated spaces */ + b=allocbufb; /* .. */ + } + + /* copy rhs -> f, save exponent, and reduce so 0.1 <= f < 1 */ + decNumberCopy(f, rhs); + exp=f->exponent+f->digits; /* adjusted to Hull rules */ + f->exponent=-(f->digits); /* to range */ + + /* set up working context */ + decContextDefault(&workset, DEC_INIT_DECIMAL64); + + /* [Until further notice, no error is possible and status bits */ + /* (Rounded, etc.) should be ignored, not accumulated.] */ + + /* Calculate initial approximation, and allow for odd exponent */ + workset.digits=workp; /* p for initial calculation */ + t->bits=0; t->digits=3; + a->bits=0; a->digits=3; + if ((exp & 1)==0) { /* even exponent */ + /* Set t=0.259, a=0.819 */ + t->exponent=-3; + a->exponent=-3; + #if DECDPUN>=3 + t->lsu[0]=259; + a->lsu[0]=819; + #elif DECDPUN==2 + t->lsu[0]=59; t->lsu[1]=2; + a->lsu[0]=19; a->lsu[1]=8; + #else + t->lsu[0]=9; t->lsu[1]=5; t->lsu[2]=2; + a->lsu[0]=9; a->lsu[1]=1; a->lsu[2]=8; + #endif + } + else { /* odd exponent */ + /* Set t=0.0819, a=2.59 */ + f->exponent--; /* f=f/10 */ + exp++; /* e=e+1 */ + t->exponent=-4; + a->exponent=-2; + #if DECDPUN>=3 + t->lsu[0]=819; + a->lsu[0]=259; + #elif DECDPUN==2 + t->lsu[0]=19; t->lsu[1]=8; + a->lsu[0]=59; a->lsu[1]=2; + #else + t->lsu[0]=9; t->lsu[1]=1; t->lsu[2]=8; + a->lsu[0]=9; a->lsu[1]=5; a->lsu[2]=2; + #endif + } + decMultiplyOp(a, a, f, &workset, &ignore); /* a=a*f */ + decAddOp(a, a, t, &workset, 0, &ignore); /* ..+t */ + /* [a is now the initial approximation for sqrt(f), calculated with */ + /* currentprecision, which is also a's precision.] */ + + /* the main calculation loop */ + decNumberZero(&dzero); /* make 0 */ + decNumberZero(t); /* set t = 0.5 */ + t->lsu[0]=5; /* .. */ + t->exponent=-1; /* .. */ + workset.digits=3; /* initial p */ + for (;;) { + /* set p to min(2*p - 2, maxp) [hence 3; or: 4, 6, 10, ... , maxp] */ + workset.digits=workset.digits*2-2; + if (workset.digits>maxp) workset.digits=maxp; + /* a = 0.5 * (a + f/a) */ + /* [calculated at p then rounded to currentprecision] */ + decDivideOp(b, f, a, &workset, DIVIDE, &ignore); /* b=f/a */ + decAddOp(b, b, a, &workset, 0, &ignore); /* b=b+a */ + decMultiplyOp(a, b, t, &workset, &ignore); /* a=b*0.5 */ + if (a->digits==maxp) break; /* have required digits */ + } /* loop */ + + /* Here, 0.1 <= a < 1 [Hull], and a has maxp digits */ + /* now reduce to length, etc.; this needs to be done with a */ + /* having the correct exponent so as to handle subnormals */ + /* correctly */ + approxset=*set; /* get emin, emax, etc. */ + approxset.round=DEC_ROUND_HALF_EVEN; + a->exponent+=exp/2; /* set correct exponent */ + + rstatus=0; /* clear status */ + residue=0; /* .. and accumulator */ + decCopyFit(a, a, &approxset, &residue, &rstatus); /* reduce (if needed) */ + decFinish(a, &approxset, &residue, &rstatus); /* clean and finalize */ + + /* Overflow was possible if the input exponent was out-of-range, */ + /* in which case quit */ + if (rstatus&DEC_Overflow) { + status=rstatus; /* use the status as-is */ + decNumberCopy(res, a); /* copy to result */ + break; + } + + /* Preserve status except Inexact/Rounded */ + status|=(rstatus & ~(DEC_Rounded|DEC_Inexact)); + + /* Carry out the Hull correction */ + a->exponent-=exp/2; /* back to 0.1->1 */ + + /* a is now at final precision and within 1 ulp of the properly */ + /* rounded square root of f; to ensure proper rounding, compare */ + /* squares of (a - l/2 ulp) and (a + l/2 ulp) with f. */ + /* Here workset.digits=maxp and t=0.5, and a->digits determines */ + /* the ulp */ + workset.digits--; /* maxp-1 is OK now */ + t->exponent=-a->digits-1; /* make 0.5 ulp */ + decAddOp(b, a, t, &workset, DECNEG, &ignore); /* b = a - 0.5 ulp */ + workset.round=DEC_ROUND_UP; + decMultiplyOp(b, b, b, &workset, &ignore); /* b = mulru(b, b) */ + decCompareOp(b, f, b, &workset, COMPARE, &ignore); /* b ? f, reversed */ + if (decNumberIsNegative(b)) { /* f < b [i.e., b > f] */ + /* this is the more common adjustment, though both are rare */ + t->exponent++; /* make 1.0 ulp */ + t->lsu[0]=1; /* .. */ + decAddOp(a, a, t, &workset, DECNEG, &ignore); /* a = a - 1 ulp */ + /* assign to approx [round to length] */ + approxset.emin-=exp/2; /* adjust to match a */ + approxset.emax-=exp/2; + decAddOp(a, &dzero, a, &approxset, 0, &ignore); + } + else { + decAddOp(b, a, t, &workset, 0, &ignore); /* b = a + 0.5 ulp */ + workset.round=DEC_ROUND_DOWN; + decMultiplyOp(b, b, b, &workset, &ignore); /* b = mulrd(b, b) */ + decCompareOp(b, b, f, &workset, COMPARE, &ignore); /* b ? f */ + if (decNumberIsNegative(b)) { /* b < f */ + t->exponent++; /* make 1.0 ulp */ + t->lsu[0]=1; /* .. */ + decAddOp(a, a, t, &workset, 0, &ignore); /* a = a + 1 ulp */ + /* assign to approx [round to length] */ + approxset.emin-=exp/2; /* adjust to match a */ + approxset.emax-=exp/2; + decAddOp(a, &dzero, a, &approxset, 0, &ignore); + } + } + /* [no errors are possible in the above, and rounding/inexact during */ + /* estimation are irrelevant, so status was not accumulated] */ + + /* Here, 0.1 <= a < 1 (still), so adjust back */ + a->exponent+=exp/2; /* set correct exponent */ + + /* count droppable zeros [after any subnormal rounding] by */ + /* trimming a copy */ + decNumberCopy(b, a); + decTrim(b, set, 1, &dropped); /* [drops trailing zeros] */ + + /* Set Inexact and Rounded. The answer can only be exact if */ + /* it is short enough so that squaring it could fit in workp digits, */ + /* and it cannot have trailing zeros due to clamping, so these are */ + /* the only (relatively rare) conditions a careful check is needed */ + if (b->digits*2-1 > workp && !set->clamp) { /* cannot fit */ + status|=DEC_Inexact|DEC_Rounded; + } + else { /* could be exact/unrounded */ + uInt mstatus=0; /* local status */ + decMultiplyOp(b, b, b, &workset, &mstatus); /* try the multiply */ + if (mstatus&DEC_Overflow) { /* result just won't fit */ + status|=DEC_Inexact|DEC_Rounded; + } + else { /* plausible */ + decCompareOp(t, b, rhs, &workset, COMPARE, &mstatus); /* b ? rhs */ + if (!ISZERO(t)) status|=DEC_Inexact|DEC_Rounded; /* not equal */ + else { /* is Exact */ + /* here, dropped is the count of trailing zeros in 'a' */ + /* use closest exponent to ideal... */ + Int todrop=ideal-a->exponent; /* most that can be dropped */ + if (todrop<0) status|=DEC_Rounded; /* ideally would add 0s */ + else { /* unrounded */ + if (dropped<todrop) { /* clamp to those available */ + todrop=dropped; + status|=DEC_Clamped; + } + if (todrop>0) { /* have some to drop */ + decShiftToLeast(a->lsu, D2U(a->digits), todrop); + a->exponent+=todrop; /* maintain numerical value */ + a->digits-=todrop; /* new length */ + } + } + } + } + } + + /* double-check Underflow, as perhaps the result could not have */ + /* been subnormal (initial argument too big), or it is now Exact */ + if (status&DEC_Underflow) { + Int ae=rhs->exponent+rhs->digits-1; /* adjusted exponent */ + /* check if truly subnormal */ + #if DECEXTFLAG /* DEC_Subnormal too */ + if (ae>=set->emin*2) status&=~(DEC_Subnormal|DEC_Underflow); + #else + if (ae>=set->emin*2) status&=~DEC_Underflow; + #endif + /* check if truly inexact */ + if (!(status&DEC_Inexact)) status&=~DEC_Underflow; + } + + decNumberCopy(res, a); /* a is now the result */ + } while(0); /* end protected */ + + if (allocbuff!=NULL) free(allocbuff); /* drop any storage used */ + if (allocbufa!=NULL) free(allocbufa); /* .. */ + if (allocbufb!=NULL) free(allocbufb); /* .. */ + #if DECSUBSET + if (allocrhs !=NULL) free(allocrhs); /* .. */ + #endif + if (status!=0) decStatus(res, status, set);/* then report status */ + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } /* decNumberSquareRoot */ + +/* ------------------------------------------------------------------ */ +/* decNumberSubtract -- subtract two Numbers */ +/* */ +/* This computes C = A - B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X-X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberSubtract(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; /* accumulator */ + + decAddOp(res, lhs, rhs, set, DECNEG, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } /* decNumberSubtract */ + +/* ------------------------------------------------------------------ */ +/* decNumberToIntegralExact -- round-to-integral-value with InExact */ +/* decNumberToIntegralValue -- round-to-integral-value */ +/* */ +/* res is the result */ +/* rhs is input number */ +/* set is the context */ +/* */ +/* res must have space for any value of rhs. */ +/* */ +/* This implements the IEEE special operators and therefore treats */ +/* special values as valid. For finite numbers it returns */ +/* rescale(rhs, 0) if rhs->exponent is <0. */ +/* Otherwise the result is rhs (so no error is possible, except for */ +/* sNaN). */ +/* */ +/* The context is used for rounding mode and status after sNaN, but */ +/* the digits setting is ignored. The Exact version will signal */ +/* Inexact if the result differs numerically from rhs; the other */ +/* never signals Inexact. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberToIntegralExact(decNumber *res, const decNumber *rhs, + decContext *set) { + decNumber dn; + decContext workset; /* working context */ + uInt status=0; /* accumulator */ + + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + /* handle infinities and NaNs */ + if (SPECIALARG) { + if (decNumberIsInfinite(rhs)) decNumberCopy(res, rhs); /* an Infinity */ + else decNaNs(res, rhs, NULL, set, &status); /* a NaN */ + } + else { /* finite */ + /* have a finite number; no error possible (res must be big enough) */ + if (rhs->exponent>=0) return decNumberCopy(res, rhs); + /* that was easy, but if negative exponent there is work to do... */ + workset=*set; /* clone rounding, etc. */ + workset.digits=rhs->digits; /* no length rounding */ + workset.traps=0; /* no traps */ + decNumberZero(&dn); /* make a number with exponent 0 */ + decNumberQuantize(res, rhs, &dn, &workset); + status|=workset.status; + } + if (status!=0) decStatus(res, status, set); + return res; + } /* decNumberToIntegralExact */ + +decNumber * decNumberToIntegralValue(decNumber *res, const decNumber *rhs, + decContext *set) { + decContext workset=*set; /* working context */ + workset.traps=0; /* no traps */ + decNumberToIntegralExact(res, rhs, &workset); + /* this never affects set, except for sNaNs; NaN will have been set */ + /* or propagated already, so no need to call decStatus */ + set->status|=workset.status&DEC_Invalid_operation; + return res; + } /* decNumberToIntegralValue */ + +/* ------------------------------------------------------------------ */ +/* decNumberXor -- XOR two Numbers, digitwise */ +/* */ +/* This computes C = A ^ B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X^X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context (used for result length and error report) */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Logical function restrictions apply (see above); a NaN is */ +/* returned with Invalid_operation if a restriction is violated. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberXor(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + const Unit *ua, *ub; /* -> operands */ + const Unit *msua, *msub; /* -> operand msus */ + Unit *uc, *msuc; /* -> result and its msu */ + Int msudigs; /* digits in res msu */ + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs) + || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { + decStatus(res, DEC_Invalid_operation, set); + return res; + } + /* operands are valid */ + ua=lhs->lsu; /* bottom-up */ + ub=rhs->lsu; /* .. */ + uc=res->lsu; /* .. */ + msua=ua+D2U(lhs->digits)-1; /* -> msu of lhs */ + msub=ub+D2U(rhs->digits)-1; /* -> msu of rhs */ + msuc=uc+D2U(set->digits)-1; /* -> msu of result */ + msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */ + for (; uc<=msuc; ua++, ub++, uc++) { /* Unit loop */ + Unit a, b; /* extract units */ + if (ua>msua) a=0; + else a=*ua; + if (ub>msub) b=0; + else b=*ub; + *uc=0; /* can now write back */ + if (a|b) { /* maybe 1 bits to examine */ + Int i, j; + /* This loop could be unrolled and/or use BIN2BCD tables */ + for (i=0; i<DECDPUN; i++) { + if ((a^b)&1) *uc=*uc+(Unit)powers[i]; /* effect XOR */ + j=a%10; + a=a/10; + j|=b%10; + b=b/10; + if (j>1) { + decStatus(res, DEC_Invalid_operation, set); + return res; + } + if (uc==msuc && i==msudigs-1) break; /* just did final digit */ + } /* each digit */ + } /* non-zero */ + } /* each unit */ + /* [here uc-1 is the msu of the result] */ + res->digits=decGetDigits(res->lsu, uc-res->lsu); + res->exponent=0; /* integer */ + res->bits=0; /* sign=0 */ + return res; /* [no status to set] */ + } /* decNumberXor */ + + +/* ================================================================== */ +/* Utility routines */ +/* ================================================================== */ + +/* ------------------------------------------------------------------ */ +/* decNumberClass -- return the decClass of a decNumber */ +/* dn -- the decNumber to test */ +/* set -- the context to use for Emin */ +/* returns the decClass enum */ +/* ------------------------------------------------------------------ */ +enum decClass decNumberClass(const decNumber *dn, decContext *set) { + if (decNumberIsSpecial(dn)) { + if (decNumberIsQNaN(dn)) return DEC_CLASS_QNAN; + if (decNumberIsSNaN(dn)) return DEC_CLASS_SNAN; + /* must be an infinity */ + if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_INF; + return DEC_CLASS_POS_INF; + } + /* is finite */ + if (decNumberIsNormal(dn, set)) { /* most common */ + if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_NORMAL; + return DEC_CLASS_POS_NORMAL; + } + /* is subnormal or zero */ + if (decNumberIsZero(dn)) { /* most common */ + if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_ZERO; + return DEC_CLASS_POS_ZERO; + } + if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_SUBNORMAL; + return DEC_CLASS_POS_SUBNORMAL; + } /* decNumberClass */ + +/* ------------------------------------------------------------------ */ +/* decNumberClassToString -- convert decClass to a string */ +/* */ +/* eclass is a valid decClass */ +/* returns a constant string describing the class (max 13+1 chars) */ +/* ------------------------------------------------------------------ */ +const char *decNumberClassToString(enum decClass eclass) { + if (eclass==DEC_CLASS_POS_NORMAL) return DEC_ClassString_PN; + if (eclass==DEC_CLASS_NEG_NORMAL) return DEC_ClassString_NN; + if (eclass==DEC_CLASS_POS_ZERO) return DEC_ClassString_PZ; + if (eclass==DEC_CLASS_NEG_ZERO) return DEC_ClassString_NZ; + if (eclass==DEC_CLASS_POS_SUBNORMAL) return DEC_ClassString_PS; + if (eclass==DEC_CLASS_NEG_SUBNORMAL) return DEC_ClassString_NS; + if (eclass==DEC_CLASS_POS_INF) return DEC_ClassString_PI; + if (eclass==DEC_CLASS_NEG_INF) return DEC_ClassString_NI; + if (eclass==DEC_CLASS_QNAN) return DEC_ClassString_QN; + if (eclass==DEC_CLASS_SNAN) return DEC_ClassString_SN; + return DEC_ClassString_UN; /* Unknown */ + } /* decNumberClassToString */ + +/* ------------------------------------------------------------------ */ +/* decNumberCopy -- copy a number */ +/* */ +/* dest is the target decNumber */ +/* src is the source decNumber */ +/* returns dest */ +/* */ +/* (dest==src is allowed and is a no-op) */ +/* All fields are updated as required. This is a utility operation, */ +/* so special values are unchanged and no error is possible. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberCopy(decNumber *dest, const decNumber *src) { + + #if DECCHECK + if (src==NULL) return decNumberZero(dest); + #endif + + if (dest==src) return dest; /* no copy required */ + + /* Use explicit assignments here as structure assignment could copy */ + /* more than just the lsu (for small DECDPUN). This would not affect */ + /* the value of the results, but could disturb test harness spill */ + /* checking. */ + dest->bits=src->bits; + dest->exponent=src->exponent; + dest->digits=src->digits; + dest->lsu[0]=src->lsu[0]; + if (src->digits>DECDPUN) { /* more Units to come */ + const Unit *smsup, *s; /* work */ + Unit *d; /* .. */ + /* memcpy for the remaining Units would be safe as they cannot */ + /* overlap. However, this explicit loop is faster in short cases. */ + d=dest->lsu+1; /* -> first destination */ + smsup=src->lsu+D2U(src->digits); /* -> source msu+1 */ + for (s=src->lsu+1; s<smsup; s++, d++) *d=*s; + } + return dest; + } /* decNumberCopy */ + +/* ------------------------------------------------------------------ */ +/* decNumberCopyAbs -- quiet absolute value operator */ +/* */ +/* This sets C = abs(A) */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* */ +/* C must have space for set->digits digits. */ +/* No exception or error can occur; this is a quiet bitwise operation.*/ +/* See also decNumberAbs for a checking version of this. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberCopyAbs(decNumber *res, const decNumber *rhs) { + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res; + #endif + decNumberCopy(res, rhs); + res->bits&=~DECNEG; /* turn off sign */ + return res; + } /* decNumberCopyAbs */ + +/* ------------------------------------------------------------------ */ +/* decNumberCopyNegate -- quiet negate value operator */ +/* */ +/* This sets C = negate(A) */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* */ +/* C must have space for set->digits digits. */ +/* No exception or error can occur; this is a quiet bitwise operation.*/ +/* See also decNumberMinus for a checking version of this. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberCopyNegate(decNumber *res, const decNumber *rhs) { + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res; + #endif + decNumberCopy(res, rhs); + res->bits^=DECNEG; /* invert the sign */ + return res; + } /* decNumberCopyNegate */ + +/* ------------------------------------------------------------------ */ +/* decNumberCopySign -- quiet copy and set sign operator */ +/* */ +/* This sets C = A with the sign of B */ +/* */ +/* res is C, the result. C may be A */ +/* lhs is A */ +/* rhs is B */ +/* */ +/* C must have space for set->digits digits. */ +/* No exception or error can occur; this is a quiet bitwise operation.*/ +/* ------------------------------------------------------------------ */ +decNumber * decNumberCopySign(decNumber *res, const decNumber *lhs, + const decNumber *rhs) { + uByte sign; /* rhs sign */ + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res; + #endif + sign=rhs->bits & DECNEG; /* save sign bit */ + decNumberCopy(res, lhs); + res->bits&=~DECNEG; /* clear the sign */ + res->bits|=sign; /* set from rhs */ + return res; + } /* decNumberCopySign */ + +/* ------------------------------------------------------------------ */ +/* decNumberGetBCD -- get the coefficient in BCD8 */ +/* dn is the source decNumber */ +/* bcd is the uInt array that will receive dn->digits BCD bytes, */ +/* most-significant at offset 0 */ +/* returns bcd */ +/* */ +/* bcd must have at least dn->digits bytes. No error is possible; if */ +/* dn is a NaN or Infinite, digits must be 1 and the coefficient 0. */ +/* ------------------------------------------------------------------ */ +uByte * decNumberGetBCD(const decNumber *dn, uint8_t *bcd) { + uByte *ub=bcd+dn->digits-1; /* -> lsd */ + const Unit *up=dn->lsu; /* Unit pointer, -> lsu */ + + #if DECDPUN==1 /* trivial simple copy */ + for (; ub>=bcd; ub--, up++) *ub=*up; + #else /* chopping needed */ + uInt u=*up; /* work */ + uInt cut=DECDPUN; /* downcounter through unit */ + for (; ub>=bcd; ub--) { + *ub=(uByte)(u%10); /* [*6554 trick inhibits, here] */ + u=u/10; + cut--; + if (cut>0) continue; /* more in this unit */ + up++; + u=*up; + cut=DECDPUN; + } + #endif + return bcd; + } /* decNumberGetBCD */ + +/* ------------------------------------------------------------------ */ +/* decNumberSetBCD -- set (replace) the coefficient from BCD8 */ +/* dn is the target decNumber */ +/* bcd is the uInt array that will source n BCD bytes, most- */ +/* significant at offset 0 */ +/* n is the number of digits in the source BCD array (bcd) */ +/* returns dn */ +/* */ +/* dn must have space for at least n digits. No error is possible; */ +/* if dn is a NaN, or Infinite, or is to become a zero, n must be 1 */ +/* and bcd[0] zero. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberSetBCD(decNumber *dn, const uByte *bcd, uInt n) { + Unit *up=dn->lsu+D2U(dn->digits)-1; /* -> msu [target pointer] */ + const uByte *ub=bcd; /* -> source msd */ + + #if DECDPUN==1 /* trivial simple copy */ + for (; ub<bcd+n; ub++, up--) *up=*ub; + #else /* some assembly needed */ + /* calculate how many digits in msu, and hence first cut */ + Int cut=MSUDIGITS(n); /* [faster than remainder] */ + for (;up>=dn->lsu; up--) { /* each Unit from msu */ + *up=0; /* will take <=DECDPUN digits */ + for (; cut>0; ub++, cut--) *up=X10(*up)+*ub; + cut=DECDPUN; /* next Unit has all digits */ + } + #endif + dn->digits=n; /* set digit count */ + return dn; + } /* decNumberSetBCD */ + +/* ------------------------------------------------------------------ */ +/* decNumberIsNormal -- test normality of a decNumber */ +/* dn is the decNumber to test */ +/* set is the context to use for Emin */ +/* returns 1 if |dn| is finite and >=Nmin, 0 otherwise */ +/* ------------------------------------------------------------------ */ +Int decNumberIsNormal(const decNumber *dn, decContext *set) { + Int ae; /* adjusted exponent */ + #if DECCHECK + if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; + #endif + + if (decNumberIsSpecial(dn)) return 0; /* not finite */ + if (decNumberIsZero(dn)) return 0; /* not non-zero */ + + ae=dn->exponent+dn->digits-1; /* adjusted exponent */ + if (ae<set->emin) return 0; /* is subnormal */ + return 1; + } /* decNumberIsNormal */ + +/* ------------------------------------------------------------------ */ +/* decNumberIsSubnormal -- test subnormality of a decNumber */ +/* dn is the decNumber to test */ +/* set is the context to use for Emin */ +/* returns 1 if |dn| is finite, non-zero, and <Nmin, 0 otherwise */ +/* ------------------------------------------------------------------ */ +Int decNumberIsSubnormal(const decNumber *dn, decContext *set) { + Int ae; /* adjusted exponent */ + #if DECCHECK + if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; + #endif + + if (decNumberIsSpecial(dn)) return 0; /* not finite */ + if (decNumberIsZero(dn)) return 0; /* not non-zero */ + + ae=dn->exponent+dn->digits-1; /* adjusted exponent */ + if (ae<set->emin) return 1; /* is subnormal */ + return 0; + } /* decNumberIsSubnormal */ + +/* ------------------------------------------------------------------ */ +/* decNumberTrim -- remove insignificant zeros */ +/* */ +/* dn is the number to trim */ +/* returns dn */ +/* */ +/* All fields are updated as required. This is a utility operation, */ +/* so special values are unchanged and no error is possible. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberTrim(decNumber *dn) { + Int dropped; /* work */ + decContext set; /* .. */ + #if DECCHECK + if (decCheckOperands(DECUNRESU, DECUNUSED, dn, DECUNCONT)) return dn; + #endif + decContextDefault(&set, DEC_INIT_BASE); /* clamp=0 */ + return decTrim(dn, &set, 0, &dropped); + } /* decNumberTrim */ + +/* ------------------------------------------------------------------ */ +/* decNumberVersion -- return the name and version of this module */ +/* */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +const char * decNumberVersion(void) { + return DECVERSION; + } /* decNumberVersion */ + +/* ------------------------------------------------------------------ */ +/* decNumberZero -- set a number to 0 */ +/* */ +/* dn is the number to set, with space for one digit */ +/* returns dn */ +/* */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +/* Memset is not used as it is much slower in some environments. */ +decNumber * decNumberZero(decNumber *dn) { + + #if DECCHECK + if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn; + #endif + + dn->bits=0; + dn->exponent=0; + dn->digits=1; + dn->lsu[0]=0; + return dn; + } /* decNumberZero */ + +/* ================================================================== */ +/* Local routines */ +/* ================================================================== */ + +/* ------------------------------------------------------------------ */ +/* decToString -- lay out a number into a string */ +/* */ +/* dn is the number to lay out */ +/* string is where to lay out the number */ +/* eng is 1 if Engineering, 0 if Scientific */ +/* */ +/* string must be at least dn->digits+14 characters long */ +/* No error is possible. */ +/* */ +/* Note that this routine can generate a -0 or 0.000. These are */ +/* never generated in subset to-number or arithmetic, but can occur */ +/* in non-subset arithmetic (e.g., -1*0 or 1.234-1.234). */ +/* ------------------------------------------------------------------ */ +/* If DECCHECK is enabled the string "?" is returned if a number is */ +/* invalid. */ +static void decToString(const decNumber *dn, char *string, Flag eng) { + Int exp=dn->exponent; /* local copy */ + Int e; /* E-part value */ + Int pre; /* digits before the '.' */ + Int cut; /* for counting digits in a Unit */ + char *c=string; /* work [output pointer] */ + const Unit *up=dn->lsu+D2U(dn->digits)-1; /* -> msu [input pointer] */ + uInt u, pow; /* work */ + + #if DECCHECK + if (decCheckOperands(DECUNRESU, dn, DECUNUSED, DECUNCONT)) { + strcpy(string, "?"); + return;} + #endif + + if (decNumberIsNegative(dn)) { /* Negatives get a minus */ + *c='-'; + c++; + } + if (dn->bits&DECSPECIAL) { /* Is a special value */ + if (decNumberIsInfinite(dn)) { + strcpy(c, "Inf"); + strcpy(c+3, "inity"); + return;} + /* a NaN */ + if (dn->bits&DECSNAN) { /* signalling NaN */ + *c='s'; + c++; + } + strcpy(c, "NaN"); + c+=3; /* step past */ + /* if not a clean non-zero coefficient, that's all there is in a */ + /* NaN string */ + if (exp!=0 || (*dn->lsu==0 && dn->digits==1)) return; + /* [drop through to add integer] */ + } + + /* calculate how many digits in msu, and hence first cut */ + cut=MSUDIGITS(dn->digits); /* [faster than remainder] */ + cut--; /* power of ten for digit */ + + if (exp==0) { /* simple integer [common fastpath] */ + for (;up>=dn->lsu; up--) { /* each Unit from msu */ + u=*up; /* contains DECDPUN digits to lay out */ + for (; cut>=0; c++, cut--) TODIGIT(u, cut, c, pow); + cut=DECDPUN-1; /* next Unit has all digits */ + } + *c='\0'; /* terminate the string */ + return;} + + /* non-0 exponent -- assume plain form */ + pre=dn->digits+exp; /* digits before '.' */ + e=0; /* no E */ + if ((exp>0) || (pre<-5)) { /* need exponential form */ + e=exp+dn->digits-1; /* calculate E value */ + pre=1; /* assume one digit before '.' */ + if (eng && (e!=0)) { /* engineering: may need to adjust */ + Int adj; /* adjustment */ + /* The C remainder operator is undefined for negative numbers, so */ + /* a positive remainder calculation must be used here */ + if (e<0) { + adj=(-e)%3; + if (adj!=0) adj=3-adj; + } + else { /* e>0 */ + adj=e%3; + } + e=e-adj; + /* if dealing with zero still produce an exponent which is a */ + /* multiple of three, as expected, but there will only be the */ + /* one zero before the E, still. Otherwise note the padding. */ + if (!ISZERO(dn)) pre+=adj; + else { /* is zero */ + if (adj!=0) { /* 0.00Esnn needed */ + e=e+3; + pre=-(2-adj); + } + } /* zero */ + } /* eng */ + } /* need exponent */ + + /* lay out the digits of the coefficient, adding 0s and . as needed */ + u=*up; + if (pre>0) { /* xxx.xxx or xx00 (engineering) form */ + Int n=pre; + for (; pre>0; pre--, c++, cut--) { + if (cut<0) { /* need new Unit */ + if (up==dn->lsu) break; /* out of input digits (pre>digits) */ + up--; + cut=DECDPUN-1; + u=*up; + } + TODIGIT(u, cut, c, pow); + } + if (n<dn->digits) { /* more to come, after '.' */ + *c='.'; c++; + for (;; c++, cut--) { + if (cut<0) { /* need new Unit */ + if (up==dn->lsu) break; /* out of input digits */ + up--; + cut=DECDPUN-1; + u=*up; + } + TODIGIT(u, cut, c, pow); + } + } + else for (; pre>0; pre--, c++) *c='0'; /* 0 padding (for engineering) needed */ + } + else { /* 0.xxx or 0.000xxx form */ + *c='0'; c++; + *c='.'; c++; + for (; pre<0; pre++, c++) *c='0'; /* add any 0's after '.' */ + for (; ; c++, cut--) { + if (cut<0) { /* need new Unit */ + if (up==dn->lsu) break; /* out of input digits */ + up--; + cut=DECDPUN-1; + u=*up; + } + TODIGIT(u, cut, c, pow); + } + } + + /* Finally add the E-part, if needed. It will never be 0, has a + base maximum and minimum of +999999999 through -999999999, but + could range down to -1999999998 for anormal numbers */ + if (e!=0) { + Flag had=0; /* 1=had non-zero */ + *c='E'; c++; + *c='+'; c++; /* assume positive */ + u=e; /* .. */ + if (e<0) { + *(c-1)='-'; /* oops, need - */ + u=-e; /* uInt, please */ + } + /* lay out the exponent [_itoa or equivalent is not ANSI C] */ + for (cut=9; cut>=0; cut--) { + TODIGIT(u, cut, c, pow); + if (*c=='0' && !had) continue; /* skip leading zeros */ + had=1; /* had non-0 */ + c++; /* step for next */ + } /* cut */ + } + *c='\0'; /* terminate the string (all paths) */ + return; + } /* decToString */ + +/* ------------------------------------------------------------------ */ +/* decAddOp -- add/subtract operation */ +/* */ +/* This computes C = A + B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X+X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* negate is DECNEG if rhs should be negated, or 0 otherwise */ +/* status accumulates status for the caller */ +/* */ +/* C must have space for set->digits digits. */ +/* Inexact in status must be 0 for correct Exact zero sign in result */ +/* ------------------------------------------------------------------ */ +/* If possible, the coefficient is calculated directly into C. */ +/* However, if: */ +/* -- a digits+1 calculation is needed because the numbers are */ +/* unaligned and span more than set->digits digits */ +/* -- a carry to digits+1 digits looks possible */ +/* -- C is the same as A or B, and the result would destructively */ +/* overlap the A or B coefficient */ +/* then the result must be calculated into a temporary buffer. In */ +/* this case a local (stack) buffer is used if possible, and only if */ +/* too long for that does malloc become the final resort. */ +/* */ +/* Misalignment is handled as follows: */ +/* Apad: (AExp>BExp) Swap operands and proceed as for BExp>AExp. */ +/* BPad: Apply the padding by a combination of shifting (whole */ +/* units) and multiplication (part units). */ +/* */ +/* Addition, especially x=x+1, is speed-critical. */ +/* The static buffer is larger than might be expected to allow for */ +/* calls from higher-level funtions (notable exp). */ +/* ------------------------------------------------------------------ */ +static decNumber * decAddOp(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set, + uByte negate, uInt *status) { + #if DECSUBSET + decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */ + decNumber *allocrhs=NULL; /* .., rhs */ + #endif + Int rhsshift; /* working shift (in Units) */ + Int maxdigits; /* longest logical length */ + Int mult; /* multiplier */ + Int residue; /* rounding accumulator */ + uByte bits; /* result bits */ + Flag diffsign; /* non-0 if arguments have different sign */ + Unit *acc; /* accumulator for result */ + Unit accbuff[SD2U(DECBUFFER*2+20)]; /* local buffer [*2+20 reduces many */ + /* allocations when called from */ + /* other operations, notable exp] */ + Unit *allocacc=NULL; /* -> allocated acc buffer, iff allocated */ + Int reqdigits=set->digits; /* local copy; requested DIGITS */ + Int padding; /* work */ + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + do { /* protect allocated storage */ + #if DECSUBSET + if (!set->extended) { + /* reduce operands and set lostDigits status, as needed */ + if (lhs->digits>reqdigits) { + alloclhs=decRoundOperand(lhs, set, status); + if (alloclhs==NULL) break; + lhs=alloclhs; + } + if (rhs->digits>reqdigits) { + allocrhs=decRoundOperand(rhs, set, status); + if (allocrhs==NULL) break; + rhs=allocrhs; + } + } + #endif + /* [following code does not require input rounding] */ + + /* note whether signs differ [used all paths] */ + diffsign=(Flag)((lhs->bits^rhs->bits^negate)&DECNEG); + + /* handle infinities and NaNs */ + if (SPECIALARGS) { /* a special bit set */ + if (SPECIALARGS & (DECSNAN | DECNAN)) /* a NaN */ + decNaNs(res, lhs, rhs, set, status); + else { /* one or two infinities */ + if (decNumberIsInfinite(lhs)) { /* LHS is infinity */ + /* two infinities with different signs is invalid */ + if (decNumberIsInfinite(rhs) && diffsign) { + *status|=DEC_Invalid_operation; + break; + } + bits=lhs->bits & DECNEG; /* get sign from LHS */ + } + else bits=(rhs->bits^negate) & DECNEG;/* RHS must be Infinity */ + bits|=DECINF; + decNumberZero(res); + res->bits=bits; /* set +/- infinity */ + } /* an infinity */ + break; + } + + /* Quick exit for add 0s; return the non-0, modified as need be */ + if (ISZERO(lhs)) { + Int adjust; /* work */ + Int lexp=lhs->exponent; /* save in case LHS==RES */ + bits=lhs->bits; /* .. */ + residue=0; /* clear accumulator */ + decCopyFit(res, rhs, set, &residue, status); /* copy (as needed) */ + res->bits^=negate; /* flip if rhs was negated */ + #if DECSUBSET + if (set->extended) { /* exponents on zeros count */ + #endif + /* exponent will be the lower of the two */ + adjust=lexp-res->exponent; /* adjustment needed [if -ve] */ + if (ISZERO(res)) { /* both 0: special IEEE 854 rules */ + if (adjust<0) res->exponent=lexp; /* set exponent */ + /* 0-0 gives +0 unless rounding to -infinity, and -0-0 gives -0 */ + if (diffsign) { + if (set->round!=DEC_ROUND_FLOOR) res->bits=0; + else res->bits=DECNEG; /* preserve 0 sign */ + } + } + else { /* non-0 res */ + if (adjust<0) { /* 0-padding needed */ + if ((res->digits-adjust)>set->digits) { + adjust=res->digits-set->digits; /* to fit exactly */ + *status|=DEC_Rounded; /* [but exact] */ + } + res->digits=decShiftToMost(res->lsu, res->digits, -adjust); + res->exponent+=adjust; /* set the exponent. */ + } + } /* non-0 res */ + #if DECSUBSET + } /* extended */ + #endif + decFinish(res, set, &residue, status); /* clean and finalize */ + break;} + + if (ISZERO(rhs)) { /* [lhs is non-zero] */ + Int adjust; /* work */ + Int rexp=rhs->exponent; /* save in case RHS==RES */ + bits=rhs->bits; /* be clean */ + residue=0; /* clear accumulator */ + decCopyFit(res, lhs, set, &residue, status); /* copy (as needed) */ + #if DECSUBSET + if (set->extended) { /* exponents on zeros count */ + #endif + /* exponent will be the lower of the two */ + /* [0-0 case handled above] */ + adjust=rexp-res->exponent; /* adjustment needed [if -ve] */ + if (adjust<0) { /* 0-padding needed */ + if ((res->digits-adjust)>set->digits) { + adjust=res->digits-set->digits; /* to fit exactly */ + *status|=DEC_Rounded; /* [but exact] */ + } + res->digits=decShiftToMost(res->lsu, res->digits, -adjust); + res->exponent+=adjust; /* set the exponent. */ + } + #if DECSUBSET + } /* extended */ + #endif + decFinish(res, set, &residue, status); /* clean and finalize */ + break;} + + /* [NB: both fastpath and mainpath code below assume these cases */ + /* (notably 0-0) have already been handled] */ + + /* calculate the padding needed to align the operands */ + padding=rhs->exponent-lhs->exponent; + + /* Fastpath cases where the numbers are aligned and normal, the RHS */ + /* is all in one unit, no operand rounding is needed, and no carry, */ + /* lengthening, or borrow is needed */ + if (padding==0 + && rhs->digits<=DECDPUN + && rhs->exponent>=set->emin /* [some normals drop through] */ + && rhs->exponent<=set->emax-set->digits+1 /* [could clamp] */ + && rhs->digits<=reqdigits + && lhs->digits<=reqdigits) { + Int partial=*lhs->lsu; + if (!diffsign) { /* adding */ + partial+=*rhs->lsu; + if ((partial<=DECDPUNMAX) /* result fits in unit */ + && (lhs->digits>=DECDPUN || /* .. and no digits-count change */ + partial<(Int)powers[lhs->digits])) { /* .. */ + if (res!=lhs) decNumberCopy(res, lhs); /* not in place */ + *res->lsu=(Unit)partial; /* [copy could have overwritten RHS] */ + break; + } + /* else drop out for careful add */ + } + else { /* signs differ */ + partial-=*rhs->lsu; + if (partial>0) { /* no borrow needed, and non-0 result */ + if (res!=lhs) decNumberCopy(res, lhs); /* not in place */ + *res->lsu=(Unit)partial; + /* this could have reduced digits [but result>0] */ + res->digits=decGetDigits(res->lsu, D2U(res->digits)); + break; + } + /* else drop out for careful subtract */ + } + } + + /* Now align (pad) the lhs or rhs so they can be added or */ + /* subtracted, as necessary. If one number is much larger than */ + /* the other (that is, if in plain form there is a least one */ + /* digit between the lowest digit of one and the highest of the */ + /* other) padding with up to DIGITS-1 trailing zeros may be */ + /* needed; then apply rounding (as exotic rounding modes may be */ + /* affected by the residue). */ + rhsshift=0; /* rhs shift to left (padding) in Units */ + bits=lhs->bits; /* assume sign is that of LHS */ + mult=1; /* likely multiplier */ + + /* [if padding==0 the operands are aligned; no padding is needed] */ + if (padding!=0) { + /* some padding needed; always pad the RHS, as any required */ + /* padding can then be effected by a simple combination of */ + /* shifts and a multiply */ + Flag swapped=0; + if (padding<0) { /* LHS needs the padding */ + const decNumber *t; + padding=-padding; /* will be +ve */ + bits=(uByte)(rhs->bits^negate); /* assumed sign is now that of RHS */ + t=lhs; lhs=rhs; rhs=t; + swapped=1; + } + + /* If, after pad, rhs would be longer than lhs by digits+1 or */ + /* more then lhs cannot affect the answer, except as a residue, */ + /* so only need to pad up to a length of DIGITS+1. */ + if (rhs->digits+padding > lhs->digits+reqdigits+1) { + /* The RHS is sufficient */ + /* for residue use the relative sign indication... */ + Int shift=reqdigits-rhs->digits; /* left shift needed */ + residue=1; /* residue for rounding */ + if (diffsign) residue=-residue; /* signs differ */ + /* copy, shortening if necessary */ + decCopyFit(res, rhs, set, &residue, status); + /* if it was already shorter, then need to pad with zeros */ + if (shift>0) { + res->digits=decShiftToMost(res->lsu, res->digits, shift); + res->exponent-=shift; /* adjust the exponent. */ + } + /* flip the result sign if unswapped and rhs was negated */ + if (!swapped) res->bits^=negate; + decFinish(res, set, &residue, status); /* done */ + break;} + + /* LHS digits may affect result */ + rhsshift=D2U(padding+1)-1; /* this much by Unit shift .. */ + mult=powers[padding-(rhsshift*DECDPUN)]; /* .. this by multiplication */ + } /* padding needed */ + + if (diffsign) mult=-mult; /* signs differ */ + + /* determine the longer operand */ + maxdigits=rhs->digits+padding; /* virtual length of RHS */ + if (lhs->digits>maxdigits) maxdigits=lhs->digits; + + /* Decide on the result buffer to use; if possible place directly */ + /* into result. */ + acc=res->lsu; /* assume add direct to result */ + /* If destructive overlap, or the number is too long, or a carry or */ + /* borrow to DIGITS+1 might be possible, a buffer must be used. */ + /* [Might be worth more sophisticated tests when maxdigits==reqdigits] */ + if ((maxdigits>=reqdigits) /* is, or could be, too large */ + || (res==rhs && rhsshift>0)) { /* destructive overlap */ + /* buffer needed, choose it; units for maxdigits digits will be */ + /* needed, +1 Unit for carry or borrow */ + Int need=D2U(maxdigits)+1; + acc=accbuff; /* assume use local buffer */ + if (need*sizeof(Unit)>sizeof(accbuff)) { + /* printf("malloc add %ld %ld\n", need, sizeof(accbuff)); */ + allocacc=(Unit *)malloc(need*sizeof(Unit)); + if (allocacc==NULL) { /* hopeless -- abandon */ + *status|=DEC_Insufficient_storage; + break;} + acc=allocacc; + } + } + + res->bits=(uByte)(bits&DECNEG); /* it's now safe to overwrite.. */ + res->exponent=lhs->exponent; /* .. operands (even if aliased) */ + + #if DECTRACE + decDumpAr('A', lhs->lsu, D2U(lhs->digits)); + decDumpAr('B', rhs->lsu, D2U(rhs->digits)); + printf(" :h: %ld %ld\n", rhsshift, mult); + #endif + + /* add [A+B*m] or subtract [A+B*(-m)] */ + res->digits=decUnitAddSub(lhs->lsu, D2U(lhs->digits), + rhs->lsu, D2U(rhs->digits), + rhsshift, acc, mult) + *DECDPUN; /* [units -> digits] */ + if (res->digits<0) { /* borrowed... */ + res->digits=-res->digits; + res->bits^=DECNEG; /* flip the sign */ + } + #if DECTRACE + decDumpAr('+', acc, D2U(res->digits)); + #endif + + /* If a buffer was used the result must be copied back, possibly */ + /* shortening. (If no buffer was used then the result must have */ + /* fit, so can't need rounding and residue must be 0.) */ + residue=0; /* clear accumulator */ + if (acc!=res->lsu) { + #if DECSUBSET + if (set->extended) { /* round from first significant digit */ + #endif + /* remove leading zeros that were added due to rounding up to */ + /* integral Units -- before the test for rounding. */ + if (res->digits>reqdigits) + res->digits=decGetDigits(acc, D2U(res->digits)); + decSetCoeff(res, set, acc, res->digits, &residue, status); + #if DECSUBSET + } + else { /* subset arithmetic rounds from original significant digit */ + /* May have an underestimate. This only occurs when both */ + /* numbers fit in DECDPUN digits and are padding with a */ + /* negative multiple (-10, -100...) and the top digit(s) become */ + /* 0. (This only matters when using X3.274 rules where the */ + /* leading zero could be included in the rounding.) */ + if (res->digits<maxdigits) { + *(acc+D2U(res->digits))=0; /* ensure leading 0 is there */ + res->digits=maxdigits; + } + else { + /* remove leading zeros that added due to rounding up to */ + /* integral Units (but only those in excess of the original */ + /* maxdigits length, unless extended) before test for rounding. */ + if (res->digits>reqdigits) { + res->digits=decGetDigits(acc, D2U(res->digits)); + if (res->digits<maxdigits) res->digits=maxdigits; + } + } + decSetCoeff(res, set, acc, res->digits, &residue, status); + /* Now apply rounding if needed before removing leading zeros. */ + /* This is safe because subnormals are not a possibility */ + if (residue!=0) { + decApplyRound(res, set, residue, status); + residue=0; /* did what needed to be done */ + } + } /* subset */ + #endif + } /* used buffer */ + + /* strip leading zeros [these were left on in case of subset subtract] */ + res->digits=decGetDigits(res->lsu, D2U(res->digits)); + + /* apply checks and rounding */ + decFinish(res, set, &residue, status); + + /* "When the sum of two operands with opposite signs is exactly */ + /* zero, the sign of that sum shall be '+' in all rounding modes */ + /* except round toward -Infinity, in which mode that sign shall be */ + /* '-'." [Subset zeros also never have '-', set by decFinish.] */ + if (ISZERO(res) && diffsign + #if DECSUBSET + && set->extended + #endif + && (*status&DEC_Inexact)==0) { + if (set->round==DEC_ROUND_FLOOR) res->bits|=DECNEG; /* sign - */ + else res->bits&=~DECNEG; /* sign + */ + } + } while(0); /* end protected */ + + if (allocacc!=NULL) free(allocacc); /* drop any storage used */ + #if DECSUBSET + if (allocrhs!=NULL) free(allocrhs); /* .. */ + if (alloclhs!=NULL) free(alloclhs); /* .. */ + #endif + return res; + } /* decAddOp */ + +/* ------------------------------------------------------------------ */ +/* decDivideOp -- division operation */ +/* */ +/* This routine performs the calculations for all four division */ +/* operators (divide, divideInteger, remainder, remainderNear). */ +/* */ +/* C=A op B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X/X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* op is DIVIDE, DIVIDEINT, REMAINDER, or REMNEAR respectively. */ +/* status is the usual accumulator */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* ------------------------------------------------------------------ */ +/* The underlying algorithm of this routine is the same as in the */ +/* 1981 S/370 implementation, that is, non-restoring long division */ +/* with bi-unit (rather than bi-digit) estimation for each unit */ +/* multiplier. In this pseudocode overview, complications for the */ +/* Remainder operators and division residues for exact rounding are */ +/* omitted for clarity. */ +/* */ +/* Prepare operands and handle special values */ +/* Test for x/0 and then 0/x */ +/* Exp =Exp1 - Exp2 */ +/* Exp =Exp +len(var1) -len(var2) */ +/* Sign=Sign1 * Sign2 */ +/* Pad accumulator (Var1) to double-length with 0's (pad1) */ +/* Pad Var2 to same length as Var1 */ +/* msu2pair/plus=1st 2 or 1 units of var2, +1 to allow for round */ +/* have=0 */ +/* Do until (have=digits+1 OR residue=0) */ +/* if exp<0 then if integer divide/residue then leave */ +/* this_unit=0 */ +/* Do forever */ +/* compare numbers */ +/* if <0 then leave inner_loop */ +/* if =0 then (* quick exit without subtract *) do */ +/* this_unit=this_unit+1; output this_unit */ +/* leave outer_loop; end */ +/* Compare lengths of numbers (mantissae): */ +/* If same then tops2=msu2pair -- {units 1&2 of var2} */ +/* else tops2=msu2plus -- {0, unit 1 of var2} */ +/* tops1=first_unit_of_Var1*10**DECDPUN +second_unit_of_var1 */ +/* mult=tops1/tops2 -- Good and safe guess at divisor */ +/* if mult=0 then mult=1 */ +/* this_unit=this_unit+mult */ +/* subtract */ +/* end inner_loop */ +/* if have\=0 | this_unit\=0 then do */ +/* output this_unit */ +/* have=have+1; end */ +/* var2=var2/10 */ +/* exp=exp-1 */ +/* end outer_loop */ +/* exp=exp+1 -- set the proper exponent */ +/* if have=0 then generate answer=0 */ +/* Return (Result is defined by Var1) */ +/* */ +/* ------------------------------------------------------------------ */ +/* Two working buffers are needed during the division; one (digits+ */ +/* 1) to accumulate the result, and the other (up to 2*digits+1) for */ +/* long subtractions. These are acc and var1 respectively. */ +/* var1 is a copy of the lhs coefficient, var2 is the rhs coefficient.*/ +/* The static buffers may be larger than might be expected to allow */ +/* for calls from higher-level funtions (notable exp). */ +/* ------------------------------------------------------------------ */ +static decNumber * decDivideOp(decNumber *res, + const decNumber *lhs, const decNumber *rhs, + decContext *set, Flag op, uInt *status) { + #if DECSUBSET + decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */ + decNumber *allocrhs=NULL; /* .., rhs */ + #endif + Unit accbuff[SD2U(DECBUFFER+DECDPUN+10)]; /* local buffer */ + Unit *acc=accbuff; /* -> accumulator array for result */ + Unit *allocacc=NULL; /* -> allocated buffer, iff allocated */ + Unit *accnext; /* -> where next digit will go */ + Int acclength; /* length of acc needed [Units] */ + Int accunits; /* count of units accumulated */ + Int accdigits; /* count of digits accumulated */ + + Unit varbuff[SD2U(DECBUFFER*2+DECDPUN)*sizeof(Unit)]; /* buffer for var1 */ + Unit *var1=varbuff; /* -> var1 array for long subtraction */ + Unit *varalloc=NULL; /* -> allocated buffer, iff used */ + Unit *msu1; /* -> msu of var1 */ + + const Unit *var2; /* -> var2 array */ + const Unit *msu2; /* -> msu of var2 */ + Int msu2plus; /* msu2 plus one [does not vary] */ + eInt msu2pair; /* msu2 pair plus one [does not vary] */ + + Int var1units, var2units; /* actual lengths */ + Int var2ulen; /* logical length (units) */ + Int var1initpad=0; /* var1 initial padding (digits) */ + Int maxdigits; /* longest LHS or required acc length */ + Int mult; /* multiplier for subtraction */ + Unit thisunit; /* current unit being accumulated */ + Int residue; /* for rounding */ + Int reqdigits=set->digits; /* requested DIGITS */ + Int exponent; /* working exponent */ + Int maxexponent=0; /* DIVIDE maximum exponent if unrounded */ + uByte bits; /* working sign */ + Unit *target; /* work */ + const Unit *source; /* .. */ + uInt const *pow; /* .. */ + Int shift, cut; /* .. */ + #if DECSUBSET + Int dropped; /* work */ + #endif + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + do { /* protect allocated storage */ + #if DECSUBSET + if (!set->extended) { + /* reduce operands and set lostDigits status, as needed */ + if (lhs->digits>reqdigits) { + alloclhs=decRoundOperand(lhs, set, status); + if (alloclhs==NULL) break; + lhs=alloclhs; + } + if (rhs->digits>reqdigits) { + allocrhs=decRoundOperand(rhs, set, status); + if (allocrhs==NULL) break; + rhs=allocrhs; + } + } + #endif + /* [following code does not require input rounding] */ + + bits=(lhs->bits^rhs->bits)&DECNEG; /* assumed sign for divisions */ + + /* handle infinities and NaNs */ + if (SPECIALARGS) { /* a special bit set */ + if (SPECIALARGS & (DECSNAN | DECNAN)) { /* one or two NaNs */ + decNaNs(res, lhs, rhs, set, status); + break; + } + /* one or two infinities */ + if (decNumberIsInfinite(lhs)) { /* LHS (dividend) is infinite */ + if (decNumberIsInfinite(rhs) || /* two infinities are invalid .. */ + op & (REMAINDER | REMNEAR)) { /* as is remainder of infinity */ + *status|=DEC_Invalid_operation; + break; + } + /* [Note that infinity/0 raises no exceptions] */ + decNumberZero(res); + res->bits=bits|DECINF; /* set +/- infinity */ + break; + } + else { /* RHS (divisor) is infinite */ + residue=0; + if (op&(REMAINDER|REMNEAR)) { + /* result is [finished clone of] lhs */ + decCopyFit(res, lhs, set, &residue, status); + } + else { /* a division */ + decNumberZero(res); + res->bits=bits; /* set +/- zero */ + /* for DIVIDEINT the exponent is always 0. For DIVIDE, result */ + /* is a 0 with infinitely negative exponent, clamped to minimum */ + if (op&DIVIDE) { + res->exponent=set->emin-set->digits+1; + *status|=DEC_Clamped; + } + } + decFinish(res, set, &residue, status); + break; + } + } + + /* handle 0 rhs (x/0) */ + if (ISZERO(rhs)) { /* x/0 is always exceptional */ + if (ISZERO(lhs)) { + decNumberZero(res); /* [after lhs test] */ + *status|=DEC_Division_undefined;/* 0/0 will become NaN */ + } + else { + decNumberZero(res); + if (op&(REMAINDER|REMNEAR)) *status|=DEC_Invalid_operation; + else { + *status|=DEC_Division_by_zero; /* x/0 */ + res->bits=bits|DECINF; /* .. is +/- Infinity */ + } + } + break;} + + /* handle 0 lhs (0/x) */ + if (ISZERO(lhs)) { /* 0/x [x!=0] */ + #if DECSUBSET + if (!set->extended) decNumberZero(res); + else { + #endif + if (op&DIVIDE) { + residue=0; + exponent=lhs->exponent-rhs->exponent; /* ideal exponent */ + decNumberCopy(res, lhs); /* [zeros always fit] */ + res->bits=bits; /* sign as computed */ + res->exponent=exponent; /* exponent, too */ + decFinalize(res, set, &residue, status); /* check exponent */ + } + else if (op&DIVIDEINT) { + decNumberZero(res); /* integer 0 */ + res->bits=bits; /* sign as computed */ + } + else { /* a remainder */ + exponent=rhs->exponent; /* [save in case overwrite] */ + decNumberCopy(res, lhs); /* [zeros always fit] */ + if (exponent<res->exponent) res->exponent=exponent; /* use lower */ + } + #if DECSUBSET + } + #endif + break;} + + /* Precalculate exponent. This starts off adjusted (and hence fits */ + /* in 31 bits) and becomes the usual unadjusted exponent as the */ + /* division proceeds. The order of evaluation is important, here, */ + /* to avoid wrap. */ + exponent=(lhs->exponent+lhs->digits)-(rhs->exponent+rhs->digits); + + /* If the working exponent is -ve, then some quick exits are */ + /* possible because the quotient is known to be <1 */ + /* [for REMNEAR, it needs to be < -1, as -0.5 could need work] */ + if (exponent<0 && !(op==DIVIDE)) { + if (op&DIVIDEINT) { + decNumberZero(res); /* integer part is 0 */ + #if DECSUBSET + if (set->extended) + #endif + res->bits=bits; /* set +/- zero */ + break;} + /* fastpath remainders so long as the lhs has the smaller */ + /* (or equal) exponent */ + if (lhs->exponent<=rhs->exponent) { + if (op&REMAINDER || exponent<-1) { + /* It is REMAINDER or safe REMNEAR; result is [finished */ + /* clone of] lhs (r = x - 0*y) */ + residue=0; + decCopyFit(res, lhs, set, &residue, status); + decFinish(res, set, &residue, status); + break; + } + /* [unsafe REMNEAR drops through] */ + } + } /* fastpaths */ + + /* Long (slow) division is needed; roll up the sleeves... */ + + /* The accumulator will hold the quotient of the division. */ + /* If it needs to be too long for stack storage, then allocate. */ + acclength=D2U(reqdigits+DECDPUN); /* in Units */ + if (acclength*sizeof(Unit)>sizeof(accbuff)) { + /* printf("malloc dvacc %ld units\n", acclength); */ + allocacc=(Unit *)malloc(acclength*sizeof(Unit)); + if (allocacc==NULL) { /* hopeless -- abandon */ + *status|=DEC_Insufficient_storage; + break;} + acc=allocacc; /* use the allocated space */ + } + + /* var1 is the padded LHS ready for subtractions. */ + /* If it needs to be too long for stack storage, then allocate. */ + /* The maximum units needed for var1 (long subtraction) is: */ + /* Enough for */ + /* (rhs->digits+reqdigits-1) -- to allow full slide to right */ + /* or (lhs->digits) -- to allow for long lhs */ + /* whichever is larger */ + /* +1 -- for rounding of slide to right */ + /* +1 -- for leading 0s */ + /* +1 -- for pre-adjust if a remainder or DIVIDEINT */ + /* [Note: unused units do not participate in decUnitAddSub data] */ + maxdigits=rhs->digits+reqdigits-1; + if (lhs->digits>maxdigits) maxdigits=lhs->digits; + var1units=D2U(maxdigits)+2; + /* allocate a guard unit above msu1 for REMAINDERNEAR */ + if (!(op&DIVIDE)) var1units++; + if ((var1units+1)*sizeof(Unit)>sizeof(varbuff)) { + /* printf("malloc dvvar %ld units\n", var1units+1); */ + varalloc=(Unit *)malloc((var1units+1)*sizeof(Unit)); + if (varalloc==NULL) { /* hopeless -- abandon */ + *status|=DEC_Insufficient_storage; + break;} + var1=varalloc; /* use the allocated space */ + } + + /* Extend the lhs and rhs to full long subtraction length. The lhs */ + /* is truly extended into the var1 buffer, with 0 padding, so a */ + /* subtract in place is always possible. The rhs (var2) has */ + /* virtual padding (implemented by decUnitAddSub). */ + /* One guard unit was allocated above msu1 for rem=rem+rem in */ + /* REMAINDERNEAR. */ + msu1=var1+var1units-1; /* msu of var1 */ + source=lhs->lsu+D2U(lhs->digits)-1; /* msu of input array */ + for (target=msu1; source>=lhs->lsu; source--, target--) *target=*source; + for (; target>=var1; target--) *target=0; + + /* rhs (var2) is left-aligned with var1 at the start */ + var2ulen=var1units; /* rhs logical length (units) */ + var2units=D2U(rhs->digits); /* rhs actual length (units) */ + var2=rhs->lsu; /* -> rhs array */ + msu2=var2+var2units-1; /* -> msu of var2 [never changes] */ + /* now set up the variables which will be used for estimating the */ + /* multiplication factor. If these variables are not exact, add */ + /* 1 to make sure that the multiplier is never overestimated. */ + msu2plus=*msu2; /* it's value .. */ + if (var2units>1) msu2plus++; /* .. +1 if any more */ + msu2pair=(eInt)*msu2*(DECDPUNMAX+1);/* top two pair .. */ + if (var2units>1) { /* .. [else treat 2nd as 0] */ + msu2pair+=*(msu2-1); /* .. */ + if (var2units>2) msu2pair++; /* .. +1 if any more */ + } + + /* The calculation is working in units, which may have leading zeros, */ + /* but the exponent was calculated on the assumption that they are */ + /* both left-aligned. Adjust the exponent to compensate: add the */ + /* number of leading zeros in var1 msu and subtract those in var2 msu. */ + /* [This is actually done by counting the digits and negating, as */ + /* lead1=DECDPUN-digits1, and similarly for lead2.] */ + for (pow=&powers[1]; *msu1>=*pow; pow++) exponent--; + for (pow=&powers[1]; *msu2>=*pow; pow++) exponent++; + + /* Now, if doing an integer divide or remainder, ensure that */ + /* the result will be Unit-aligned. To do this, shift the var1 */ + /* accumulator towards least if need be. (It's much easier to */ + /* do this now than to reassemble the residue afterwards, if */ + /* doing a remainder.) Also ensure the exponent is not negative. */ + if (!(op&DIVIDE)) { + Unit *u; /* work */ + /* save the initial 'false' padding of var1, in digits */ + var1initpad=(var1units-D2U(lhs->digits))*DECDPUN; + /* Determine the shift to do. */ + if (exponent<0) cut=-exponent; + else cut=DECDPUN-exponent%DECDPUN; + decShiftToLeast(var1, var1units, cut); + exponent+=cut; /* maintain numerical value */ + var1initpad-=cut; /* .. and reduce padding */ + /* clean any most-significant units which were just emptied */ + for (u=msu1; cut>=DECDPUN; cut-=DECDPUN, u--) *u=0; + } /* align */ + else { /* is DIVIDE */ + maxexponent=lhs->exponent-rhs->exponent; /* save */ + /* optimization: if the first iteration will just produce 0, */ + /* preadjust to skip it [valid for DIVIDE only] */ + if (*msu1<*msu2) { + var2ulen--; /* shift down */ + exponent-=DECDPUN; /* update the exponent */ + } + } + + /* ---- start the long-division loops ------------------------------ */ + accunits=0; /* no units accumulated yet */ + accdigits=0; /* .. or digits */ + accnext=acc+acclength-1; /* -> msu of acc [NB: allows digits+1] */ + for (;;) { /* outer forever loop */ + thisunit=0; /* current unit assumed 0 */ + /* find the next unit */ + for (;;) { /* inner forever loop */ + /* strip leading zero units [from either pre-adjust or from */ + /* subtract last time around]. Leave at least one unit. */ + for (; *msu1==0 && msu1>var1; msu1--) var1units--; + + if (var1units<var2ulen) break; /* var1 too low for subtract */ + if (var1units==var2ulen) { /* unit-by-unit compare needed */ + /* compare the two numbers, from msu */ + const Unit *pv1, *pv2; + Unit v2; /* units to compare */ + pv2=msu2; /* -> msu */ + for (pv1=msu1; ; pv1--, pv2--) { + /* v1=*pv1 -- always OK */ + v2=0; /* assume in padding */ + if (pv2>=var2) v2=*pv2; /* in range */ + if (*pv1!=v2) break; /* no longer the same */ + if (pv1==var1) break; /* done; leave pv1 as is */ + } + /* here when all inspected or a difference seen */ + if (*pv1<v2) break; /* var1 too low to subtract */ + if (*pv1==v2) { /* var1 == var2 */ + /* reach here if var1 and var2 are identical; subtraction */ + /* would increase digit by one, and the residue will be 0 so */ + /* the calculation is done; leave the loop with residue=0. */ + thisunit++; /* as though subtracted */ + *var1=0; /* set var1 to 0 */ + var1units=1; /* .. */ + break; /* from inner */ + } /* var1 == var2 */ + /* *pv1>v2. Prepare for real subtraction; the lengths are equal */ + /* Estimate the multiplier (there's always a msu1-1)... */ + /* Bring in two units of var2 to provide a good estimate. */ + mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2pair); + } /* lengths the same */ + else { /* var1units > var2ulen, so subtraction is safe */ + /* The var2 msu is one unit towards the lsu of the var1 msu, */ + /* so only one unit for var2 can be used. */ + mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2plus); + } + if (mult==0) mult=1; /* must always be at least 1 */ + /* subtraction needed; var1 is > var2 */ + thisunit=(Unit)(thisunit+mult); /* accumulate */ + /* subtract var1-var2, into var1; only the overlap needs */ + /* processing, as this is an in-place calculation */ + shift=var2ulen-var2units; + #if DECTRACE + decDumpAr('1', &var1[shift], var1units-shift); + decDumpAr('2', var2, var2units); + printf("m=%ld\n", -mult); + #endif + decUnitAddSub(&var1[shift], var1units-shift, + var2, var2units, 0, + &var1[shift], -mult); + #if DECTRACE + decDumpAr('#', &var1[shift], var1units-shift); + #endif + /* var1 now probably has leading zeros; these are removed at the */ + /* top of the inner loop. */ + } /* inner loop */ + + /* The next unit has been calculated in full; unless it's a */ + /* leading zero, add to acc */ + if (accunits!=0 || thisunit!=0) { /* is first or non-zero */ + *accnext=thisunit; /* store in accumulator */ + /* account exactly for the new digits */ + if (accunits==0) { + accdigits++; /* at least one */ + for (pow=&powers[1]; thisunit>=*pow; pow++) accdigits++; + } + else accdigits+=DECDPUN; + accunits++; /* update count */ + accnext--; /* ready for next */ + if (accdigits>reqdigits) break; /* have enough digits */ + } + + /* if the residue is zero, the operation is done (unless divide */ + /* or divideInteger and still not enough digits yet) */ + if (*var1==0 && var1units==1) { /* residue is 0 */ + if (op&(REMAINDER|REMNEAR)) break; + if ((op&DIVIDE) && (exponent<=maxexponent)) break; + /* [drop through if divideInteger] */ + } + /* also done enough if calculating remainder or integer */ + /* divide and just did the last ('units') unit */ + if (exponent==0 && !(op&DIVIDE)) break; + + /* to get here, var1 is less than var2, so divide var2 by the per- */ + /* Unit power of ten and go for the next digit */ + var2ulen--; /* shift down */ + exponent-=DECDPUN; /* update the exponent */ + } /* outer loop */ + + /* ---- division is complete --------------------------------------- */ + /* here: acc has at least reqdigits+1 of good results (or fewer */ + /* if early stop), starting at accnext+1 (its lsu) */ + /* var1 has any residue at the stopping point */ + /* accunits is the number of digits collected in acc */ + if (accunits==0) { /* acc is 0 */ + accunits=1; /* show have a unit .. */ + accdigits=1; /* .. */ + *accnext=0; /* .. whose value is 0 */ + } + else accnext++; /* back to last placed */ + /* accnext now -> lowest unit of result */ + + residue=0; /* assume no residue */ + if (op&DIVIDE) { + /* record the presence of any residue, for rounding */ + if (*var1!=0 || var1units>1) residue=1; + else { /* no residue */ + /* Had an exact division; clean up spurious trailing 0s. */ + /* There will be at most DECDPUN-1, from the final multiply, */ + /* and then only if the result is non-0 (and even) and the */ + /* exponent is 'loose'. */ + #if DECDPUN>1 + Unit lsu=*accnext; + if (!(lsu&0x01) && (lsu!=0)) { + /* count the trailing zeros */ + Int drop=0; + for (;; drop++) { /* [will terminate because lsu!=0] */ + if (exponent>=maxexponent) break; /* don't chop real 0s */ + #if DECDPUN<=4 + if ((lsu-QUOT10(lsu, drop+1) + *powers[drop+1])!=0) break; /* found non-0 digit */ + #else + if (lsu%powers[drop+1]!=0) break; /* found non-0 digit */ + #endif + exponent++; + } + if (drop>0) { + accunits=decShiftToLeast(accnext, accunits, drop); + accdigits=decGetDigits(accnext, accunits); + accunits=D2U(accdigits); + /* [exponent was adjusted in the loop] */ + } + } /* neither odd nor 0 */ + #endif + } /* exact divide */ + } /* divide */ + else /* op!=DIVIDE */ { + /* check for coefficient overflow */ + if (accdigits+exponent>reqdigits) { + *status|=DEC_Division_impossible; + break; + } + if (op & (REMAINDER|REMNEAR)) { + /* [Here, the exponent will be 0, because var1 was adjusted */ + /* appropriately.] */ + Int postshift; /* work */ + Flag wasodd=0; /* integer was odd */ + Unit *quotlsu; /* for save */ + Int quotdigits; /* .. */ + + bits=lhs->bits; /* remainder sign is always as lhs */ + + /* Fastpath when residue is truly 0 is worthwhile [and */ + /* simplifies the code below] */ + if (*var1==0 && var1units==1) { /* residue is 0 */ + Int exp=lhs->exponent; /* save min(exponents) */ + if (rhs->exponent<exp) exp=rhs->exponent; + decNumberZero(res); /* 0 coefficient */ + #if DECSUBSET + if (set->extended) + #endif + res->exponent=exp; /* .. with proper exponent */ + res->bits=(uByte)(bits&DECNEG); /* [cleaned] */ + decFinish(res, set, &residue, status); /* might clamp */ + break; + } + /* note if the quotient was odd */ + if (*accnext & 0x01) wasodd=1; /* acc is odd */ + quotlsu=accnext; /* save in case need to reinspect */ + quotdigits=accdigits; /* .. */ + + /* treat the residue, in var1, as the value to return, via acc */ + /* calculate the unused zero digits. This is the smaller of: */ + /* var1 initial padding (saved above) */ + /* var2 residual padding, which happens to be given by: */ + postshift=var1initpad+exponent-lhs->exponent+rhs->exponent; + /* [the 'exponent' term accounts for the shifts during divide] */ + if (var1initpad<postshift) postshift=var1initpad; + + /* shift var1 the requested amount, and adjust its digits */ + var1units=decShiftToLeast(var1, var1units, postshift); + accnext=var1; + accdigits=decGetDigits(var1, var1units); + accunits=D2U(accdigits); + + exponent=lhs->exponent; /* exponent is smaller of lhs & rhs */ + if (rhs->exponent<exponent) exponent=rhs->exponent; + + /* Now correct the result if doing remainderNear; if it */ + /* (looking just at coefficients) is > rhs/2, or == rhs/2 and */ + /* the integer was odd then the result should be rem-rhs. */ + if (op&REMNEAR) { + Int compare, tarunits; /* work */ + Unit *up; /* .. */ + /* calculate remainder*2 into the var1 buffer (which has */ + /* 'headroom' of an extra unit and hence enough space) */ + /* [a dedicated 'double' loop would be faster, here] */ + tarunits=decUnitAddSub(accnext, accunits, accnext, accunits, + 0, accnext, 1); + /* decDumpAr('r', accnext, tarunits); */ + + /* Here, accnext (var1) holds tarunits Units with twice the */ + /* remainder's coefficient, which must now be compared to the */ + /* RHS. The remainder's exponent may be smaller than the RHS's. */ + compare=decUnitCompare(accnext, tarunits, rhs->lsu, D2U(rhs->digits), + rhs->exponent-exponent); + if (compare==BADINT) { /* deep trouble */ + *status|=DEC_Insufficient_storage; + break;} + + /* now restore the remainder by dividing by two; the lsu */ + /* is known to be even. */ + for (up=accnext; up<accnext+tarunits; up++) { + Int half; /* half to add to lower unit */ + half=*up & 0x01; + *up/=2; /* [shift] */ + if (!half) continue; + *(up-1)+=(DECDPUNMAX+1)/2; + } + /* [accunits still describes the original remainder length] */ + + if (compare>0 || (compare==0 && wasodd)) { /* adjustment needed */ + Int exp, expunits, exprem; /* work */ + /* This is effectively causing round-up of the quotient, */ + /* so if it was the rare case where it was full and all */ + /* nines, it would overflow and hence division-impossible */ + /* should be raised */ + Flag allnines=0; /* 1 if quotient all nines */ + if (quotdigits==reqdigits) { /* could be borderline */ + for (up=quotlsu; ; up++) { + if (quotdigits>DECDPUN) { + if (*up!=DECDPUNMAX) break;/* non-nines */ + } + else { /* this is the last Unit */ + if (*up==powers[quotdigits]-1) allnines=1; + break; + } + quotdigits-=DECDPUN; /* checked those digits */ + } /* up */ + } /* borderline check */ + if (allnines) { + *status|=DEC_Division_impossible; + break;} + + /* rem-rhs is needed; the sign will invert. Again, var1 */ + /* can safely be used for the working Units array. */ + exp=rhs->exponent-exponent; /* RHS padding needed */ + /* Calculate units and remainder from exponent. */ + expunits=exp/DECDPUN; + exprem=exp%DECDPUN; + /* subtract [A+B*(-m)]; the result will always be negative */ + accunits=-decUnitAddSub(accnext, accunits, + rhs->lsu, D2U(rhs->digits), + expunits, accnext, -(Int)powers[exprem]); + accdigits=decGetDigits(accnext, accunits); /* count digits exactly */ + accunits=D2U(accdigits); /* and recalculate the units for copy */ + /* [exponent is as for original remainder] */ + bits^=DECNEG; /* flip the sign */ + } + } /* REMNEAR */ + } /* REMAINDER or REMNEAR */ + } /* not DIVIDE */ + + /* Set exponent and bits */ + res->exponent=exponent; + res->bits=(uByte)(bits&DECNEG); /* [cleaned] */ + + /* Now the coefficient. */ + decSetCoeff(res, set, accnext, accdigits, &residue, status); + + decFinish(res, set, &residue, status); /* final cleanup */ + + #if DECSUBSET + /* If a divide then strip trailing zeros if subset [after round] */ + if (!set->extended && (op==DIVIDE)) decTrim(res, set, 0, &dropped); + #endif + } while(0); /* end protected */ + + if (varalloc!=NULL) free(varalloc); /* drop any storage used */ + if (allocacc!=NULL) free(allocacc); /* .. */ + #if DECSUBSET + if (allocrhs!=NULL) free(allocrhs); /* .. */ + if (alloclhs!=NULL) free(alloclhs); /* .. */ + #endif + return res; + } /* decDivideOp */ + +/* ------------------------------------------------------------------ */ +/* decMultiplyOp -- multiplication operation */ +/* */ +/* This routine performs the multiplication C=A x B. */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X*X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* status is the usual accumulator */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* ------------------------------------------------------------------ */ +/* 'Classic' multiplication is used rather than Karatsuba, as the */ +/* latter would give only a minor improvement for the short numbers */ +/* expected to be handled most (and uses much more memory). */ +/* */ +/* There are two major paths here: the general-purpose ('old code') */ +/* path which handles all DECDPUN values, and a fastpath version */ +/* which is used if 64-bit ints are available, DECDPUN<=4, and more */ +/* than two calls to decUnitAddSub would be made. */ +/* */ +/* The fastpath version lumps units together into 8-digit or 9-digit */ +/* chunks, and also uses a lazy carry strategy to minimise expensive */ +/* 64-bit divisions. The chunks are then broken apart again into */ +/* units for continuing processing. Despite this overhead, the */ +/* fastpath can speed up some 16-digit operations by 10x (and much */ +/* more for higher-precision calculations). */ +/* */ +/* A buffer always has to be used for the accumulator; in the */ +/* fastpath, buffers are also always needed for the chunked copies of */ +/* of the operand coefficients. */ +/* Static buffers are larger than needed just for multiply, to allow */ +/* for calls from other operations (notably exp). */ +/* ------------------------------------------------------------------ */ +#define FASTMUL (DECUSE64 && DECDPUN<5) +static decNumber * decMultiplyOp(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set, + uInt *status) { + Int accunits; /* Units of accumulator in use */ + Int exponent; /* work */ + Int residue=0; /* rounding residue */ + uByte bits; /* result sign */ + Unit *acc; /* -> accumulator Unit array */ + Int needbytes; /* size calculator */ + void *allocacc=NULL; /* -> allocated accumulator, iff allocated */ + Unit accbuff[SD2U(DECBUFFER*4+1)]; /* buffer (+1 for DECBUFFER==0, */ + /* *4 for calls from other operations) */ + const Unit *mer, *mermsup; /* work */ + Int madlength; /* Units in multiplicand */ + Int shift; /* Units to shift multiplicand by */ + + #if FASTMUL + /* if DECDPUN is 1 or 3 work in base 10**9, otherwise */ + /* (DECDPUN is 2 or 4) then work in base 10**8 */ + #if DECDPUN & 1 /* odd */ + #define FASTBASE 1000000000 /* base */ + #define FASTDIGS 9 /* digits in base */ + #define FASTLAZY 18 /* carry resolution point [1->18] */ + #else + #define FASTBASE 100000000 + #define FASTDIGS 8 + #define FASTLAZY 1844 /* carry resolution point [1->1844] */ + #endif + /* three buffers are used, two for chunked copies of the operands */ + /* (base 10**8 or base 10**9) and one base 2**64 accumulator with */ + /* lazy carry evaluation */ + uInt zlhibuff[(DECBUFFER*2+1)/8+1]; /* buffer (+1 for DECBUFFER==0) */ + uInt *zlhi=zlhibuff; /* -> lhs array */ + uInt *alloclhi=NULL; /* -> allocated buffer, iff allocated */ + uInt zrhibuff[(DECBUFFER*2+1)/8+1]; /* buffer (+1 for DECBUFFER==0) */ + uInt *zrhi=zrhibuff; /* -> rhs array */ + uInt *allocrhi=NULL; /* -> allocated buffer, iff allocated */ + uLong zaccbuff[(DECBUFFER*2+1)/4+2]; /* buffer (+1 for DECBUFFER==0) */ + /* [allocacc is shared for both paths, as only one will run] */ + uLong *zacc=zaccbuff; /* -> accumulator array for exact result */ + #if DECDPUN==1 + Int zoff; /* accumulator offset */ + #endif + uInt *lip, *rip; /* item pointers */ + uInt *lmsi, *rmsi; /* most significant items */ + Int ilhs, irhs, iacc; /* item counts in the arrays */ + Int lazy; /* lazy carry counter */ + uLong lcarry; /* uLong carry */ + uInt carry; /* carry (NB not uLong) */ + Int count; /* work */ + const Unit *cup; /* .. */ + Unit *up; /* .. */ + uLong *lp; /* .. */ + Int p; /* .. */ + #endif + + #if DECSUBSET + decNumber *alloclhs=NULL; /* -> allocated buffer, iff allocated */ + decNumber *allocrhs=NULL; /* -> allocated buffer, iff allocated */ + #endif + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + /* precalculate result sign */ + bits=(uByte)((lhs->bits^rhs->bits)&DECNEG); + + /* handle infinities and NaNs */ + if (SPECIALARGS) { /* a special bit set */ + if (SPECIALARGS & (DECSNAN | DECNAN)) { /* one or two NaNs */ + decNaNs(res, lhs, rhs, set, status); + return res;} + /* one or two infinities; Infinity * 0 is invalid */ + if (((lhs->bits & DECINF)==0 && ISZERO(lhs)) + ||((rhs->bits & DECINF)==0 && ISZERO(rhs))) { + *status|=DEC_Invalid_operation; + return res;} + decNumberZero(res); + res->bits=bits|DECINF; /* infinity */ + return res;} + + /* For best speed, as in DMSRCN [the original Rexx numerics */ + /* module], use the shorter number as the multiplier (rhs) and */ + /* the longer as the multiplicand (lhs) to minimise the number of */ + /* adds (partial products) */ + if (lhs->digits<rhs->digits) { /* swap... */ + const decNumber *hold=lhs; + lhs=rhs; + rhs=hold; + } + + do { /* protect allocated storage */ + #if DECSUBSET + if (!set->extended) { + /* reduce operands and set lostDigits status, as needed */ + if (lhs->digits>set->digits) { + alloclhs=decRoundOperand(lhs, set, status); + if (alloclhs==NULL) break; + lhs=alloclhs; + } + if (rhs->digits>set->digits) { + allocrhs=decRoundOperand(rhs, set, status); + if (allocrhs==NULL) break; + rhs=allocrhs; + } + } + #endif + /* [following code does not require input rounding] */ + + #if FASTMUL /* fastpath can be used */ + /* use the fast path if there are enough digits in the shorter */ + /* operand to make the setup and takedown worthwhile */ + #define NEEDTWO (DECDPUN*2) /* within two decUnitAddSub calls */ + if (rhs->digits>NEEDTWO) { /* use fastpath... */ + /* calculate the number of elements in each array */ + ilhs=(lhs->digits+FASTDIGS-1)/FASTDIGS; /* [ceiling] */ + irhs=(rhs->digits+FASTDIGS-1)/FASTDIGS; /* .. */ + iacc=ilhs+irhs; + + /* allocate buffers if required, as usual */ + needbytes=ilhs*sizeof(uInt); + if (needbytes>(Int)sizeof(zlhibuff)) { + alloclhi=(uInt *)malloc(needbytes); + zlhi=alloclhi;} + needbytes=irhs*sizeof(uInt); + if (needbytes>(Int)sizeof(zrhibuff)) { + allocrhi=(uInt *)malloc(needbytes); + zrhi=allocrhi;} + + /* Allocating the accumulator space needs a special case when */ + /* DECDPUN=1 because when converting the accumulator to Units */ + /* after the multiplication each 8-byte item becomes 9 1-byte */ + /* units. Therefore iacc extra bytes are needed at the front */ + /* (rounded up to a multiple of 8 bytes), and the uLong */ + /* accumulator starts offset the appropriate number of units */ + /* to the right to avoid overwrite during the unchunking. */ + needbytes=iacc*sizeof(uLong); + #if DECDPUN==1 + zoff=(iacc+7)/8; /* items to offset by */ + needbytes+=zoff*8; + #endif + if (needbytes>(Int)sizeof(zaccbuff)) { + allocacc=(uLong *)malloc(needbytes); + zacc=(uLong *)allocacc;} + if (zlhi==NULL||zrhi==NULL||zacc==NULL) { + *status|=DEC_Insufficient_storage; + break;} + + acc=(Unit *)zacc; /* -> target Unit array */ + #if DECDPUN==1 + zacc+=zoff; /* start uLong accumulator to right */ + #endif + + /* assemble the chunked copies of the left and right sides */ + for (count=lhs->digits, cup=lhs->lsu, lip=zlhi; count>0; lip++) + for (p=0, *lip=0; p<FASTDIGS && count>0; + p+=DECDPUN, cup++, count-=DECDPUN) + *lip+=*cup*powers[p]; + lmsi=lip-1; /* save -> msi */ + for (count=rhs->digits, cup=rhs->lsu, rip=zrhi; count>0; rip++) + for (p=0, *rip=0; p<FASTDIGS && count>0; + p+=DECDPUN, cup++, count-=DECDPUN) + *rip+=*cup*powers[p]; + rmsi=rip-1; /* save -> msi */ + + /* zero the accumulator */ + for (lp=zacc; lp<zacc+iacc; lp++) *lp=0; + + /* Start the multiplication */ + /* Resolving carries can dominate the cost of accumulating the */ + /* partial products, so this is only done when necessary. */ + /* Each uLong item in the accumulator can hold values up to */ + /* 2**64-1, and each partial product can be as large as */ + /* (10**FASTDIGS-1)**2. When FASTDIGS=9, this can be added to */ + /* itself 18.4 times in a uLong without overflowing, so during */ + /* the main calculation resolution is carried out every 18th */ + /* add -- every 162 digits. Similarly, when FASTDIGS=8, the */ + /* partial products can be added to themselves 1844.6 times in */ + /* a uLong without overflowing, so intermediate carry */ + /* resolution occurs only every 14752 digits. Hence for common */ + /* short numbers usually only the one final carry resolution */ + /* occurs. */ + /* (The count is set via FASTLAZY to simplify experiments to */ + /* measure the value of this approach: a 35% improvement on a */ + /* [34x34] multiply.) */ + lazy=FASTLAZY; /* carry delay count */ + for (rip=zrhi; rip<=rmsi; rip++) { /* over each item in rhs */ + lp=zacc+(rip-zrhi); /* where to add the lhs */ + for (lip=zlhi; lip<=lmsi; lip++, lp++) { /* over each item in lhs */ + *lp+=(uLong)(*lip)*(*rip); /* [this should in-line] */ + } /* lip loop */ + lazy--; + if (lazy>0 && rip!=rmsi) continue; + lazy=FASTLAZY; /* reset delay count */ + /* spin up the accumulator resolving overflows */ + for (lp=zacc; lp<zacc+iacc; lp++) { + if (*lp<FASTBASE) continue; /* it fits */ + lcarry=*lp/FASTBASE; /* top part [slow divide] */ + /* lcarry can exceed 2**32-1, so check again; this check */ + /* and occasional extra divide (slow) is well worth it, as */ + /* it allows FASTLAZY to be increased to 18 rather than 4 */ + /* in the FASTDIGS=9 case */ + if (lcarry<FASTBASE) carry=(uInt)lcarry; /* [usual] */ + else { /* two-place carry [fairly rare] */ + uInt carry2=(uInt)(lcarry/FASTBASE); /* top top part */ + *(lp+2)+=carry2; /* add to item+2 */ + *lp-=((uLong)FASTBASE*FASTBASE*carry2); /* [slow] */ + carry=(uInt)(lcarry-((uLong)FASTBASE*carry2)); /* [inline] */ + } + *(lp+1)+=carry; /* add to item above [inline] */ + *lp-=((uLong)FASTBASE*carry); /* [inline] */ + } /* carry resolution */ + } /* rip loop */ + + /* The multiplication is complete; time to convert back into */ + /* units. This can be done in-place in the accumulator and in */ + /* 32-bit operations, because carries were resolved after the */ + /* final add. This needs N-1 divides and multiplies for */ + /* each item in the accumulator (which will become up to N */ + /* units, where 2<=N<=9). */ + for (lp=zacc, up=acc; lp<zacc+iacc; lp++) { + uInt item=(uInt)*lp; /* decapitate to uInt */ + for (p=0; p<FASTDIGS-DECDPUN; p+=DECDPUN, up++) { + uInt part=item/(DECDPUNMAX+1); + *up=(Unit)(item-(part*(DECDPUNMAX+1))); + item=part; + } /* p */ + *up=(Unit)item; up++; /* [final needs no division] */ + } /* lp */ + accunits=up-acc; /* count of units */ + } + else { /* here to use units directly, without chunking ['old code'] */ + #endif + + /* if accumulator will be too long for local storage, then allocate */ + acc=accbuff; /* -> assume buffer for accumulator */ + needbytes=(D2U(lhs->digits)+D2U(rhs->digits))*sizeof(Unit); + if (needbytes>(Int)sizeof(accbuff)) { + allocacc=(Unit *)malloc(needbytes); + if (allocacc==NULL) {*status|=DEC_Insufficient_storage; break;} + acc=(Unit *)allocacc; /* use the allocated space */ + } + + /* Now the main long multiplication loop */ + /* Unlike the equivalent in the IBM Java implementation, there */ + /* is no advantage in calculating from msu to lsu. So, do it */ + /* by the book, as it were. */ + /* Each iteration calculates ACC=ACC+MULTAND*MULT */ + accunits=1; /* accumulator starts at '0' */ + *acc=0; /* .. (lsu=0) */ + shift=0; /* no multiplicand shift at first */ + madlength=D2U(lhs->digits); /* this won't change */ + mermsup=rhs->lsu+D2U(rhs->digits); /* -> msu+1 of multiplier */ + + for (mer=rhs->lsu; mer<mermsup; mer++) { + /* Here, *mer is the next Unit in the multiplier to use */ + /* If non-zero [optimization] add it... */ + if (*mer!=0) accunits=decUnitAddSub(&acc[shift], accunits-shift, + lhs->lsu, madlength, 0, + &acc[shift], *mer) + + shift; + else { /* extend acc with a 0; it will be used shortly */ + *(acc+accunits)=0; /* [this avoids length of <=0 later] */ + accunits++; + } + /* multiply multiplicand by 10**DECDPUN for next Unit to left */ + shift++; /* add this for 'logical length' */ + } /* n */ + #if FASTMUL + } /* unchunked units */ + #endif + /* common end-path */ + #if DECTRACE + decDumpAr('*', acc, accunits); /* Show exact result */ + #endif + + /* acc now contains the exact result of the multiplication, */ + /* possibly with a leading zero unit; build the decNumber from */ + /* it, noting if any residue */ + res->bits=bits; /* set sign */ + res->digits=decGetDigits(acc, accunits); /* count digits exactly */ + + /* There can be a 31-bit wrap in calculating the exponent. */ + /* This can only happen if both input exponents are negative and */ + /* both their magnitudes are large. If there was a wrap, set a */ + /* safe very negative exponent, from which decFinalize() will */ + /* raise a hard underflow shortly. */ + exponent=lhs->exponent+rhs->exponent; /* calculate exponent */ + if (lhs->exponent<0 && rhs->exponent<0 && exponent>0) + exponent=-2*DECNUMMAXE; /* force underflow */ + res->exponent=exponent; /* OK to overwrite now */ + + + /* Set the coefficient. If any rounding, residue records */ + decSetCoeff(res, set, acc, res->digits, &residue, status); + decFinish(res, set, &residue, status); /* final cleanup */ + } while(0); /* end protected */ + + if (allocacc!=NULL) free(allocacc); /* drop any storage used */ + #if DECSUBSET + if (allocrhs!=NULL) free(allocrhs); /* .. */ + if (alloclhs!=NULL) free(alloclhs); /* .. */ + #endif + #if FASTMUL + if (allocrhi!=NULL) free(allocrhi); /* .. */ + if (alloclhi!=NULL) free(alloclhi); /* .. */ + #endif + return res; + } /* decMultiplyOp */ + +/* ------------------------------------------------------------------ */ +/* decExpOp -- effect exponentiation */ +/* */ +/* This computes C = exp(A) */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context; note that rounding mode has no effect */ +/* */ +/* C must have space for set->digits digits. status is updated but */ +/* not set. */ +/* */ +/* Restrictions: */ +/* */ +/* digits, emax, and -emin in the context must be less than */ +/* 2*DEC_MAX_MATH (1999998), and the rhs must be within these */ +/* bounds or a zero. This is an internal routine, so these */ +/* restrictions are contractual and not enforced. */ +/* */ +/* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */ +/* almost always be correctly rounded, but may be up to 1 ulp in */ +/* error in rare cases. */ +/* */ +/* Finite results will always be full precision and Inexact, except */ +/* when A is a zero or -Infinity (giving 1 or 0 respectively). */ +/* ------------------------------------------------------------------ */ +/* This approach used here is similar to the algorithm described in */ +/* */ +/* Variable Precision Exponential Function, T. E. Hull and */ +/* A. Abrham, ACM Transactions on Mathematical Software, Vol 12 #2, */ +/* pp79-91, ACM, June 1986. */ +/* */ +/* with the main difference being that the iterations in the series */ +/* evaluation are terminated dynamically (which does not require the */ +/* extra variable-precision variables which are expensive in this */ +/* context). */ +/* */ +/* The error analysis in Hull & Abrham's paper applies except for the */ +/* round-off error accumulation during the series evaluation. This */ +/* code does not precalculate the number of iterations and so cannot */ +/* use Horner's scheme. Instead, the accumulation is done at double- */ +/* precision, which ensures that the additions of the terms are exact */ +/* and do not accumulate round-off (and any round-off errors in the */ +/* terms themselves move 'to the right' faster than they can */ +/* accumulate). This code also extends the calculation by allowing, */ +/* in the spirit of other decNumber operators, the input to be more */ +/* precise than the result (the precision used is based on the more */ +/* precise of the input or requested result). */ +/* */ +/* Implementation notes: */ +/* */ +/* 1. This is separated out as decExpOp so it can be called from */ +/* other Mathematical functions (notably Ln) with a wider range */ +/* than normal. In particular, it can handle the slightly wider */ +/* (double) range needed by Ln (which has to be able to calculate */ +/* exp(-x) where x can be the tiniest number (Ntiny). */ +/* */ +/* 2. Normalizing x to be <=0.1 (instead of <=1) reduces loop */ +/* iterations by appoximately a third with additional (although */ +/* diminishing) returns as the range is reduced to even smaller */ +/* fractions. However, h (the power of 10 used to correct the */ +/* result at the end, see below) must be kept <=8 as otherwise */ +/* the final result cannot be computed. Hence the leverage is a */ +/* sliding value (8-h), where potentially the range is reduced */ +/* more for smaller values. */ +/* */ +/* The leverage that can be applied in this way is severely */ +/* limited by the cost of the raise-to-the power at the end, */ +/* which dominates when the number of iterations is small (less */ +/* than ten) or when rhs is short. As an example, the adjustment */ +/* x**10,000,000 needs 31 multiplications, all but one full-width. */ +/* */ +/* 3. The restrictions (especially precision) could be raised with */ +/* care, but the full decNumber range seems very hard within the */ +/* 32-bit limits. */ +/* */ +/* 4. The working precisions for the static buffers are twice the */ +/* obvious size to allow for calls from decNumberPower. */ +/* ------------------------------------------------------------------ */ +decNumber * decExpOp(decNumber *res, const decNumber *rhs, + decContext *set, uInt *status) { + uInt ignore=0; /* working status */ + Int h; /* adjusted exponent for 0.xxxx */ + Int p; /* working precision */ + Int residue; /* rounding residue */ + uInt needbytes; /* for space calculations */ + const decNumber *x=rhs; /* (may point to safe copy later) */ + decContext aset, tset, dset; /* working contexts */ + Int comp; /* work */ + + /* the argument is often copied to normalize it, so (unusually) it */ + /* is treated like other buffers, using DECBUFFER, +1 in case */ + /* DECBUFFER is 0 */ + decNumber bufr[D2N(DECBUFFER*2+1)]; + decNumber *allocrhs=NULL; /* non-NULL if rhs buffer allocated */ + + /* the working precision will be no more than set->digits+8+1 */ + /* so for on-stack buffers DECBUFFER+9 is used, +1 in case DECBUFFER */ + /* is 0 (and twice that for the accumulator) */ + + /* buffer for t, term (working precision plus) */ + decNumber buft[D2N(DECBUFFER*2+9+1)]; + decNumber *allocbuft=NULL; /* -> allocated buft, iff allocated */ + decNumber *t=buft; /* term */ + /* buffer for a, accumulator (working precision * 2), at least 9 */ + decNumber bufa[D2N(DECBUFFER*4+18+1)]; + decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ + decNumber *a=bufa; /* accumulator */ + /* decNumber for the divisor term; this needs at most 9 digits */ + /* and so can be fixed size [16 so can use standard context] */ + decNumber bufd[D2N(16)]; + decNumber *d=bufd; /* divisor */ + decNumber numone; /* constant 1 */ + + #if DECCHECK + Int iterations=0; /* for later sanity check */ + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + do { /* protect allocated storage */ + if (SPECIALARG) { /* handle infinities and NaNs */ + if (decNumberIsInfinite(rhs)) { /* an infinity */ + if (decNumberIsNegative(rhs)) /* -Infinity -> +0 */ + decNumberZero(res); + else decNumberCopy(res, rhs); /* +Infinity -> self */ + } + else decNaNs(res, rhs, NULL, set, status); /* a NaN */ + break;} + + if (ISZERO(rhs)) { /* zeros -> exact 1 */ + decNumberZero(res); /* make clean 1 */ + *res->lsu=1; /* .. */ + break;} /* [no status to set] */ + + /* e**x when 0 < x < 0.66 is < 1+3x/2, hence can fast-path */ + /* positive and negative tiny cases which will result in inexact */ + /* 1. This also allows the later add-accumulate to always be */ + /* exact (because its length will never be more than twice the */ + /* working precision). */ + /* The comparator (tiny) needs just one digit, so use the */ + /* decNumber d for it (reused as the divisor, etc., below); its */ + /* exponent is such that if x is positive it will have */ + /* set->digits-1 zeros between the decimal point and the digit, */ + /* which is 4, and if x is negative one more zero there as the */ + /* more precise result will be of the form 0.9999999 rather than */ + /* 1.0000001. Hence, tiny will be 0.0000004 if digits=7 and x>0 */ + /* or 0.00000004 if digits=7 and x<0. If RHS not larger than */ + /* this then the result will be 1.000000 */ + decNumberZero(d); /* clean */ + *d->lsu=4; /* set 4 .. */ + d->exponent=-set->digits; /* * 10**(-d) */ + if (decNumberIsNegative(rhs)) d->exponent--; /* negative case */ + comp=decCompare(d, rhs, 1); /* signless compare */ + if (comp==BADINT) { + *status|=DEC_Insufficient_storage; + break;} + if (comp>=0) { /* rhs < d */ + Int shift=set->digits-1; + decNumberZero(res); /* set 1 */ + *res->lsu=1; /* .. */ + res->digits=decShiftToMost(res->lsu, 1, shift); + res->exponent=-shift; /* make 1.0000... */ + *status|=DEC_Inexact | DEC_Rounded; /* .. inexactly */ + break;} /* tiny */ + + /* set up the context to be used for calculating a, as this is */ + /* used on both paths below */ + decContextDefault(&aset, DEC_INIT_DECIMAL64); + /* accumulator bounds are as requested (could underflow) */ + aset.emax=set->emax; /* usual bounds */ + aset.emin=set->emin; /* .. */ + aset.clamp=0; /* and no concrete format */ + + /* calculate the adjusted (Hull & Abrham) exponent (where the */ + /* decimal point is just to the left of the coefficient msd) */ + h=rhs->exponent+rhs->digits; + /* if h>8 then 10**h cannot be calculated safely; however, when */ + /* h=8 then exp(|rhs|) will be at least exp(1E+7) which is at */ + /* least 6.59E+4342944, so (due to the restriction on Emax/Emin) */ + /* overflow (or underflow to 0) is guaranteed -- so this case can */ + /* be handled by simply forcing the appropriate excess */ + if (h>8) { /* overflow/underflow */ + /* set up here so Power call below will over or underflow to */ + /* zero; set accumulator to either 2 or 0.02 */ + /* [stack buffer for a is always big enough for this] */ + decNumberZero(a); + *a->lsu=2; /* not 1 but < exp(1) */ + if (decNumberIsNegative(rhs)) a->exponent=-2; /* make 0.02 */ + h=8; /* clamp so 10**h computable */ + p=9; /* set a working precision */ + } + else { /* h<=8 */ + Int maxlever=(rhs->digits>8?1:0); + /* [could/should increase this for precisions >40 or so, too] */ + + /* if h is 8, cannot normalize to a lower upper limit because */ + /* the final result will not be computable (see notes above), */ + /* but leverage can be applied whenever h is less than 8. */ + /* Apply as much as possible, up to a MAXLEVER digits, which */ + /* sets the tradeoff against the cost of the later a**(10**h). */ + /* As h is increased, the working precision below also */ + /* increases to compensate for the "constant digits at the */ + /* front" effect. */ + Int lever=MINI(8-h, maxlever); /* leverage attainable */ + Int use=-rhs->digits-lever; /* exponent to use for RHS */ + h+=lever; /* apply leverage selected */ + if (h<0) { /* clamp */ + use+=h; /* [may end up subnormal] */ + h=0; + } + /* Take a copy of RHS if it needs normalization (true whenever x>=1) */ + if (rhs->exponent!=use) { + decNumber *newrhs=bufr; /* assume will fit on stack */ + needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit); + if (needbytes>sizeof(bufr)) { /* need malloc space */ + allocrhs=(decNumber *)malloc(needbytes); + if (allocrhs==NULL) { /* hopeless -- abandon */ + *status|=DEC_Insufficient_storage; + break;} + newrhs=allocrhs; /* use the allocated space */ + } + decNumberCopy(newrhs, rhs); /* copy to safe space */ + newrhs->exponent=use; /* normalize; now <1 */ + x=newrhs; /* ready for use */ + /* decNumberShow(x); */ + } + + /* Now use the usual power series to evaluate exp(x). The */ + /* series starts as 1 + x + x^2/2 ... so prime ready for the */ + /* third term by setting the term variable t=x, the accumulator */ + /* a=1, and the divisor d=2. */ + + /* First determine the working precision. From Hull & Abrham */ + /* this is set->digits+h+2. However, if x is 'over-precise' we */ + /* need to allow for all its digits to potentially participate */ + /* (consider an x where all the excess digits are 9s) so in */ + /* this case use x->digits+h+2 */ + p=MAXI(x->digits, set->digits)+h+2; /* [h<=8] */ + + /* a and t are variable precision, and depend on p, so space */ + /* must be allocated for them if necessary */ + + /* the accumulator needs to be able to hold 2p digits so that */ + /* the additions on the second and subsequent iterations are */ + /* sufficiently exact. */ + needbytes=sizeof(decNumber)+(D2U(p*2)-1)*sizeof(Unit); + if (needbytes>sizeof(bufa)) { /* need malloc space */ + allocbufa=(decNumber *)malloc(needbytes); + if (allocbufa==NULL) { /* hopeless -- abandon */ + *status|=DEC_Insufficient_storage; + break;} + a=allocbufa; /* use the allocated space */ + } + /* the term needs to be able to hold p digits (which is */ + /* guaranteed to be larger than x->digits, so the initial copy */ + /* is safe); it may also be used for the raise-to-power */ + /* calculation below, which needs an extra two digits */ + needbytes=sizeof(decNumber)+(D2U(p+2)-1)*sizeof(Unit); + if (needbytes>sizeof(buft)) { /* need malloc space */ + allocbuft=(decNumber *)malloc(needbytes); + if (allocbuft==NULL) { /* hopeless -- abandon */ + *status|=DEC_Insufficient_storage; + break;} + t=allocbuft; /* use the allocated space */ + } + + decNumberCopy(t, x); /* term=x */ + decNumberZero(a); *a->lsu=1; /* accumulator=1 */ + decNumberZero(d); *d->lsu=2; /* divisor=2 */ + decNumberZero(&numone); *numone.lsu=1; /* constant 1 for increment */ + + /* set up the contexts for calculating a, t, and d */ + decContextDefault(&tset, DEC_INIT_DECIMAL64); + dset=tset; + /* accumulator bounds are set above, set precision now */ + aset.digits=p*2; /* double */ + /* term bounds avoid any underflow or overflow */ + tset.digits=p; + tset.emin=DEC_MIN_EMIN; /* [emax is plenty] */ + /* [dset.digits=16, etc., are sufficient] */ + + /* finally ready to roll */ + for (;;) { + #if DECCHECK + iterations++; + #endif + /* only the status from the accumulation is interesting */ + /* [but it should remain unchanged after first add] */ + decAddOp(a, a, t, &aset, 0, status); /* a=a+t */ + decMultiplyOp(t, t, x, &tset, &ignore); /* t=t*x */ + decDivideOp(t, t, d, &tset, DIVIDE, &ignore); /* t=t/d */ + /* the iteration ends when the term cannot affect the result, */ + /* if rounded to p digits, which is when its value is smaller */ + /* than the accumulator by p+1 digits. There must also be */ + /* full precision in a. */ + if (((a->digits+a->exponent)>=(t->digits+t->exponent+p+1)) + && (a->digits>=p)) break; + decAddOp(d, d, &numone, &dset, 0, &ignore); /* d=d+1 */ + } /* iterate */ + + #if DECCHECK + /* just a sanity check; comment out test to show always */ + if (iterations>p+3) + printf("Exp iterations=%ld, status=%08lx, p=%ld, d=%ld\n", + iterations, *status, p, x->digits); + #endif + } /* h<=8 */ + + /* apply postconditioning: a=a**(10**h) -- this is calculated */ + /* at a slightly higher precision than Hull & Abrham suggest */ + if (h>0) { + Int seenbit=0; /* set once a 1-bit is seen */ + Int i; /* counter */ + Int n=powers[h]; /* always positive */ + aset.digits=p+2; /* sufficient precision */ + /* avoid the overhead and many extra digits of decNumberPower */ + /* as all that is needed is the short 'multipliers' loop; here */ + /* accumulate the answer into t */ + decNumberZero(t); *t->lsu=1; /* acc=1 */ + for (i=1;;i++){ /* for each bit [top bit ignored] */ + /* abandon if have had overflow or terminal underflow */ + if (*status & (DEC_Overflow|DEC_Underflow)) { /* interesting? */ + if (*status&DEC_Overflow || ISZERO(t)) break;} + n=n<<1; /* move next bit to testable position */ + if (n<0) { /* top bit is set */ + seenbit=1; /* OK, have a significant bit */ + decMultiplyOp(t, t, a, &aset, status); /* acc=acc*x */ + } + if (i==31) break; /* that was the last bit */ + if (!seenbit) continue; /* no need to square 1 */ + decMultiplyOp(t, t, t, &aset, status); /* acc=acc*acc [square] */ + } /*i*/ /* 32 bits */ + /* decNumberShow(t); */ + a=t; /* and carry on using t instead of a */ + } + + /* Copy and round the result to res */ + residue=1; /* indicate dirt to right .. */ + if (ISZERO(a)) residue=0; /* .. unless underflowed to 0 */ + aset.digits=set->digits; /* [use default rounding] */ + decCopyFit(res, a, &aset, &residue, status); /* copy & shorten */ + decFinish(res, set, &residue, status); /* cleanup/set flags */ + } while(0); /* end protected */ + + if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */ + if (allocbufa!=NULL) free(allocbufa); /* .. */ + if (allocbuft!=NULL) free(allocbuft); /* .. */ + /* [status is handled by caller] */ + return res; + } /* decExpOp */ + +/* ------------------------------------------------------------------ */ +/* Initial-estimate natural logarithm table */ +/* */ +/* LNnn -- 90-entry 16-bit table for values from .10 through .99. */ +/* The result is a 4-digit encode of the coefficient (c=the */ +/* top 14 bits encoding 0-9999) and a 2-digit encode of the */ +/* exponent (e=the bottom 2 bits encoding 0-3) */ +/* */ +/* The resulting value is given by: */ +/* */ +/* v = -c * 10**(-e-3) */ +/* */ +/* where e and c are extracted from entry k = LNnn[x-10] */ +/* where x is truncated (NB) into the range 10 through 99, */ +/* and then c = k>>2 and e = k&3. */ +/* ------------------------------------------------------------------ */ +const uShort LNnn[90]={9016, 8652, 8316, 8008, 7724, 7456, 7208, + 6972, 6748, 6540, 6340, 6148, 5968, 5792, 5628, 5464, 5312, + 5164, 5020, 4884, 4748, 4620, 4496, 4376, 4256, 4144, 4032, + 39233, 38181, 37157, 36157, 35181, 34229, 33297, 32389, 31501, 30629, + 29777, 28945, 28129, 27329, 26545, 25777, 25021, 24281, 23553, 22837, + 22137, 21445, 20769, 20101, 19445, 18801, 18165, 17541, 16925, 16321, + 15721, 15133, 14553, 13985, 13421, 12865, 12317, 11777, 11241, 10717, + 10197, 9685, 9177, 8677, 8185, 7697, 7213, 6737, 6269, 5801, + 5341, 4889, 4437, 39930, 35534, 31186, 26886, 22630, 18418, 14254, + 10130, 6046, 20055}; + +/* ------------------------------------------------------------------ */ +/* decLnOp -- effect natural logarithm */ +/* */ +/* This computes C = ln(A) */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context; note that rounding mode has no effect */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Notable cases: */ +/* A<0 -> Invalid */ +/* A=0 -> -Infinity (Exact) */ +/* A=+Infinity -> +Infinity (Exact) */ +/* A=1 exactly -> 0 (Exact) */ +/* */ +/* Restrictions (as for Exp): */ +/* */ +/* digits, emax, and -emin in the context must be less than */ +/* DEC_MAX_MATH+11 (1000010), and the rhs must be within these */ +/* bounds or a zero. This is an internal routine, so these */ +/* restrictions are contractual and not enforced. */ +/* */ +/* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */ +/* almost always be correctly rounded, but may be up to 1 ulp in */ +/* error in rare cases. */ +/* ------------------------------------------------------------------ */ +/* The result is calculated using Newton's method, with each */ +/* iteration calculating a' = a + x * exp(-a) - 1. See, for example, */ +/* Epperson 1989. */ +/* */ +/* The iteration ends when the adjustment x*exp(-a)-1 is tiny enough. */ +/* This has to be calculated at the sum of the precision of x and the */ +/* working precision. */ +/* */ +/* Implementation notes: */ +/* */ +/* 1. This is separated out as decLnOp so it can be called from */ +/* other Mathematical functions (e.g., Log 10) with a wider range */ +/* than normal. In particular, it can handle the slightly wider */ +/* (+9+2) range needed by a power function. */ +/* */ +/* 2. The speed of this function is about 10x slower than exp, as */ +/* it typically needs 4-6 iterations for short numbers, and the */ +/* extra precision needed adds a squaring effect, twice. */ +/* */ +/* 3. Fastpaths are included for ln(10) and ln(2), up to length 40, */ +/* as these are common requests. ln(10) is used by log10(x). */ +/* */ +/* 4. An iteration might be saved by widening the LNnn table, and */ +/* would certainly save at least one if it were made ten times */ +/* bigger, too (for truncated fractions 0.100 through 0.999). */ +/* However, for most practical evaluations, at least four or five */ +/* iterations will be neede -- so this would only speed up by */ +/* 20-25% and that probably does not justify increasing the table */ +/* size. */ +/* */ +/* 5. The static buffers are larger than might be expected to allow */ +/* for calls from decNumberPower. */ +/* ------------------------------------------------------------------ */ +decNumber * decLnOp(decNumber *res, const decNumber *rhs, + decContext *set, uInt *status) { + uInt ignore=0; /* working status accumulator */ + uInt needbytes; /* for space calculations */ + Int residue; /* rounding residue */ + Int r; /* rhs=f*10**r [see below] */ + Int p; /* working precision */ + Int pp; /* precision for iteration */ + Int t; /* work */ + + /* buffers for a (accumulator, typically precision+2) and b */ + /* (adjustment calculator, same size) */ + decNumber bufa[D2N(DECBUFFER+12)]; + decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */ + decNumber *a=bufa; /* accumulator/work */ + decNumber bufb[D2N(DECBUFFER*2+2)]; + decNumber *allocbufb=NULL; /* -> allocated bufa, iff allocated */ + decNumber *b=bufb; /* adjustment/work */ + + decNumber numone; /* constant 1 */ + decNumber cmp; /* work */ + decContext aset, bset; /* working contexts */ + + #if DECCHECK + Int iterations=0; /* for later sanity check */ + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + do { /* protect allocated storage */ + if (SPECIALARG) { /* handle infinities and NaNs */ + if (decNumberIsInfinite(rhs)) { /* an infinity */ + if (decNumberIsNegative(rhs)) /* -Infinity -> error */ + *status|=DEC_Invalid_operation; + else decNumberCopy(res, rhs); /* +Infinity -> self */ + } + else decNaNs(res, rhs, NULL, set, status); /* a NaN */ + break;} + + if (ISZERO(rhs)) { /* +/- zeros -> -Infinity */ + decNumberZero(res); /* make clean */ + res->bits=DECINF|DECNEG; /* set - infinity */ + break;} /* [no status to set] */ + + /* Non-zero negatives are bad... */ + if (decNumberIsNegative(rhs)) { /* -x -> error */ + *status|=DEC_Invalid_operation; + break;} + + /* Here, rhs is positive, finite, and in range */ + + /* lookaside fastpath code for ln(2) and ln(10) at common lengths */ + if (rhs->exponent==0 && set->digits<=40) { + #if DECDPUN==1 + if (rhs->lsu[0]==0 && rhs->lsu[1]==1 && rhs->digits==2) { /* ln(10) */ + #else + if (rhs->lsu[0]==10 && rhs->digits==2) { /* ln(10) */ + #endif + aset=*set; aset.round=DEC_ROUND_HALF_EVEN; + #define LN10 "2.302585092994045684017991454684364207601" + decNumberFromString(res, LN10, &aset); + *status|=(DEC_Inexact | DEC_Rounded); /* is inexact */ + break;} + if (rhs->lsu[0]==2 && rhs->digits==1) { /* ln(2) */ + aset=*set; aset.round=DEC_ROUND_HALF_EVEN; + #define LN2 "0.6931471805599453094172321214581765680755" + decNumberFromString(res, LN2, &aset); + *status|=(DEC_Inexact | DEC_Rounded); + break;} + } /* integer and short */ + + /* Determine the working precision. This is normally the */ + /* requested precision + 2, with a minimum of 9. However, if */ + /* the rhs is 'over-precise' then allow for all its digits to */ + /* potentially participate (consider an rhs where all the excess */ + /* digits are 9s) so in this case use rhs->digits+2. */ + p=MAXI(rhs->digits, MAXI(set->digits, 7))+2; + + /* Allocate space for the accumulator and the high-precision */ + /* adjustment calculator, if necessary. The accumulator must */ + /* be able to hold p digits, and the adjustment up to */ + /* rhs->digits+p digits. They are also made big enough for 16 */ + /* digits so that they can be used for calculating the initial */ + /* estimate. */ + needbytes=sizeof(decNumber)+(D2U(MAXI(p,16))-1)*sizeof(Unit); + if (needbytes>sizeof(bufa)) { /* need malloc space */ + allocbufa=(decNumber *)malloc(needbytes); + if (allocbufa==NULL) { /* hopeless -- abandon */ + *status|=DEC_Insufficient_storage; + break;} + a=allocbufa; /* use the allocated space */ + } + pp=p+rhs->digits; + needbytes=sizeof(decNumber)+(D2U(MAXI(pp,16))-1)*sizeof(Unit); + if (needbytes>sizeof(bufb)) { /* need malloc space */ + allocbufb=(decNumber *)malloc(needbytes); + if (allocbufb==NULL) { /* hopeless -- abandon */ + *status|=DEC_Insufficient_storage; + break;} + b=allocbufb; /* use the allocated space */ + } + + /* Prepare an initial estimate in acc. Calculate this by */ + /* considering the coefficient of x to be a normalized fraction, */ + /* f, with the decimal point at far left and multiplied by */ + /* 10**r. Then, rhs=f*10**r and 0.1<=f<1, and */ + /* ln(x) = ln(f) + ln(10)*r */ + /* Get the initial estimate for ln(f) from a small lookup */ + /* table (see above) indexed by the first two digits of f, */ + /* truncated. */ + + decContextDefault(&aset, DEC_INIT_DECIMAL64); /* 16-digit extended */ + r=rhs->exponent+rhs->digits; /* 'normalised' exponent */ + decNumberFromInt32(a, r); /* a=r */ + decNumberFromInt32(b, 2302585); /* b=ln(10) (2.302585) */ + b->exponent=-6; /* .. */ + decMultiplyOp(a, a, b, &aset, &ignore); /* a=a*b */ + /* now get top two digits of rhs into b by simple truncate and */ + /* force to integer */ + residue=0; /* (no residue) */ + aset.digits=2; aset.round=DEC_ROUND_DOWN; + decCopyFit(b, rhs, &aset, &residue, &ignore); /* copy & shorten */ + b->exponent=0; /* make integer */ + t=decGetInt(b); /* [cannot fail] */ + if (t<10) t=X10(t); /* adjust single-digit b */ + t=LNnn[t-10]; /* look up ln(b) */ + decNumberFromInt32(b, t>>2); /* b=ln(b) coefficient */ + b->exponent=-(t&3)-3; /* set exponent */ + b->bits=DECNEG; /* ln(0.10)->ln(0.99) always -ve */ + aset.digits=16; aset.round=DEC_ROUND_HALF_EVEN; /* restore */ + decAddOp(a, a, b, &aset, 0, &ignore); /* acc=a+b */ + /* the initial estimate is now in a, with up to 4 digits correct. */ + /* When rhs is at or near Nmax the estimate will be low, so we */ + /* will approach it from below, avoiding overflow when calling exp. */ + + decNumberZero(&numone); *numone.lsu=1; /* constant 1 for adjustment */ + + /* accumulator bounds are as requested (could underflow, but */ + /* cannot overflow) */ + aset.emax=set->emax; + aset.emin=set->emin; + aset.clamp=0; /* no concrete format */ + /* set up a context to be used for the multiply and subtract */ + bset=aset; + bset.emax=DEC_MAX_MATH*2; /* use double bounds for the */ + bset.emin=-DEC_MAX_MATH*2; /* adjustment calculation */ + /* [see decExpOp call below] */ + /* for each iteration double the number of digits to calculate, */ + /* up to a maximum of p */ + pp=9; /* initial precision */ + /* [initially 9 as then the sequence starts 7+2, 16+2, and */ + /* 34+2, which is ideal for standard-sized numbers] */ + aset.digits=pp; /* working context */ + bset.digits=pp+rhs->digits; /* wider context */ + for (;;) { /* iterate */ + #if DECCHECK + iterations++; + if (iterations>24) break; /* consider 9 * 2**24 */ + #endif + /* calculate the adjustment (exp(-a)*x-1) into b. This is a */ + /* catastrophic subtraction but it really is the difference */ + /* from 1 that is of interest. */ + /* Use the internal entry point to Exp as it allows the double */ + /* range for calculating exp(-a) when a is the tiniest subnormal. */ + a->bits^=DECNEG; /* make -a */ + decExpOp(b, a, &bset, &ignore); /* b=exp(-a) */ + a->bits^=DECNEG; /* restore sign of a */ + /* now multiply by rhs and subtract 1, at the wider precision */ + decMultiplyOp(b, b, rhs, &bset, &ignore); /* b=b*rhs */ + decAddOp(b, b, &numone, &bset, DECNEG, &ignore); /* b=b-1 */ + + /* the iteration ends when the adjustment cannot affect the */ + /* result by >=0.5 ulp (at the requested digits), which */ + /* is when its value is smaller than the accumulator by */ + /* set->digits+1 digits (or it is zero) -- this is a looser */ + /* requirement than for Exp because all that happens to the */ + /* accumulator after this is the final rounding (but note that */ + /* there must also be full precision in a, or a=0). */ + + if (decNumberIsZero(b) || + (a->digits+a->exponent)>=(b->digits+b->exponent+set->digits+1)) { + if (a->digits==p) break; + if (decNumberIsZero(a)) { + decCompareOp(&cmp, rhs, &numone, &aset, COMPARE, &ignore); /* rhs=1 ? */ + if (cmp.lsu[0]==0) a->exponent=0; /* yes, exact 0 */ + else *status|=(DEC_Inexact | DEC_Rounded); /* no, inexact */ + break; + } + /* force padding if adjustment has gone to 0 before full length */ + if (decNumberIsZero(b)) b->exponent=a->exponent-p; + } + + /* not done yet ... */ + decAddOp(a, a, b, &aset, 0, &ignore); /* a=a+b for next estimate */ + if (pp==p) continue; /* precision is at maximum */ + /* lengthen the next calculation */ + pp=pp*2; /* double precision */ + if (pp>p) pp=p; /* clamp to maximum */ + aset.digits=pp; /* working context */ + bset.digits=pp+rhs->digits; /* wider context */ + } /* Newton's iteration */ + + #if DECCHECK + /* just a sanity check; remove the test to show always */ + if (iterations>24) + printf("Ln iterations=%ld, status=%08lx, p=%ld, d=%ld\n", + iterations, *status, p, rhs->digits); + #endif + + /* Copy and round the result to res */ + residue=1; /* indicate dirt to right */ + if (ISZERO(a)) residue=0; /* .. unless underflowed to 0 */ + aset.digits=set->digits; /* [use default rounding] */ + decCopyFit(res, a, &aset, &residue, status); /* copy & shorten */ + decFinish(res, set, &residue, status); /* cleanup/set flags */ + } while(0); /* end protected */ + + if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */ + if (allocbufb!=NULL) free(allocbufb); /* .. */ + /* [status is handled by caller] */ + return res; + } /* decLnOp */ + +/* ------------------------------------------------------------------ */ +/* decQuantizeOp -- force exponent to requested value */ +/* */ +/* This computes C = op(A, B), where op adjusts the coefficient */ +/* of C (by rounding or shifting) such that the exponent (-scale) */ +/* of C has the value B or matches the exponent of B. */ +/* The numerical value of C will equal A, except for the effects of */ +/* any rounding that occurred. */ +/* */ +/* res is C, the result. C may be A or B */ +/* lhs is A, the number to adjust */ +/* rhs is B, the requested exponent */ +/* set is the context */ +/* quant is 1 for quantize or 0 for rescale */ +/* status is the status accumulator (this can be called without */ +/* risk of control loss) */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Unless there is an error or the result is infinite, the exponent */ +/* after the operation is guaranteed to be that requested. */ +/* ------------------------------------------------------------------ */ +static decNumber * decQuantizeOp(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set, + Flag quant, uInt *status) { + #if DECSUBSET + decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */ + decNumber *allocrhs=NULL; /* .., rhs */ + #endif + const decNumber *inrhs=rhs; /* save original rhs */ + Int reqdigits=set->digits; /* requested DIGITS */ + Int reqexp; /* requested exponent [-scale] */ + Int residue=0; /* rounding residue */ + Int etiny=set->emin-(reqdigits-1); + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + do { /* protect allocated storage */ + #if DECSUBSET + if (!set->extended) { + /* reduce operands and set lostDigits status, as needed */ + if (lhs->digits>reqdigits) { + alloclhs=decRoundOperand(lhs, set, status); + if (alloclhs==NULL) break; + lhs=alloclhs; + } + if (rhs->digits>reqdigits) { /* [this only checks lostDigits] */ + allocrhs=decRoundOperand(rhs, set, status); + if (allocrhs==NULL) break; + rhs=allocrhs; + } + } + #endif + /* [following code does not require input rounding] */ + + /* Handle special values */ + if (SPECIALARGS) { + /* NaNs get usual processing */ + if (SPECIALARGS & (DECSNAN | DECNAN)) + decNaNs(res, lhs, rhs, set, status); + /* one infinity but not both is bad */ + else if ((lhs->bits ^ rhs->bits) & DECINF) + *status|=DEC_Invalid_operation; + /* both infinity: return lhs */ + else decNumberCopy(res, lhs); /* [nop if in place] */ + break; + } + + /* set requested exponent */ + if (quant) reqexp=inrhs->exponent; /* quantize -- match exponents */ + else { /* rescale -- use value of rhs */ + /* Original rhs must be an integer that fits and is in range, */ + /* which could be from -1999999997 to +999999999, thanks to */ + /* subnormals */ + reqexp=decGetInt(inrhs); /* [cannot fail] */ + } + + #if DECSUBSET + if (!set->extended) etiny=set->emin; /* no subnormals */ + #endif + + if (reqexp==BADINT /* bad (rescale only) or .. */ + || reqexp==BIGODD || reqexp==BIGEVEN /* very big (ditto) or .. */ + || (reqexp<etiny) /* < lowest */ + || (reqexp>set->emax)) { /* > emax */ + *status|=DEC_Invalid_operation; + break;} + + /* the RHS has been processed, so it can be overwritten now if necessary */ + if (ISZERO(lhs)) { /* zero coefficient unchanged */ + decNumberCopy(res, lhs); /* [nop if in place] */ + res->exponent=reqexp; /* .. just set exponent */ + #if DECSUBSET + if (!set->extended) res->bits=0; /* subset specification; no -0 */ + #endif + } + else { /* non-zero lhs */ + Int adjust=reqexp-lhs->exponent; /* digit adjustment needed */ + /* if adjusted coefficient will definitely not fit, give up now */ + if ((lhs->digits-adjust)>reqdigits) { + *status|=DEC_Invalid_operation; + break; + } + + if (adjust>0) { /* increasing exponent */ + /* this will decrease the length of the coefficient by adjust */ + /* digits, and must round as it does so */ + decContext workset; /* work */ + workset=*set; /* clone rounding, etc. */ + workset.digits=lhs->digits-adjust; /* set requested length */ + /* [note that the latter can be <1, here] */ + decCopyFit(res, lhs, &workset, &residue, status); /* fit to result */ + decApplyRound(res, &workset, residue, status); /* .. and round */ + residue=0; /* [used] */ + /* If just rounded a 999s case, exponent will be off by one; */ + /* adjust back (after checking space), if so. */ + if (res->exponent>reqexp) { + /* re-check needed, e.g., for quantize(0.9999, 0.001) under */ + /* set->digits==3 */ + if (res->digits==reqdigits) { /* cannot shift by 1 */ + *status&=~(DEC_Inexact | DEC_Rounded); /* [clean these] */ + *status|=DEC_Invalid_operation; + break; + } + res->digits=decShiftToMost(res->lsu, res->digits, 1); /* shift */ + res->exponent--; /* (re)adjust the exponent. */ + } + #if DECSUBSET + if (ISZERO(res) && !set->extended) res->bits=0; /* subset; no -0 */ + #endif + } /* increase */ + else /* adjust<=0 */ { /* decreasing or = exponent */ + /* this will increase the length of the coefficient by -adjust */ + /* digits, by adding zero or more trailing zeros; this is */ + /* already checked for fit, above */ + decNumberCopy(res, lhs); /* [it will fit] */ + /* if padding needed (adjust<0), add it now... */ + if (adjust<0) { + res->digits=decShiftToMost(res->lsu, res->digits, -adjust); + res->exponent+=adjust; /* adjust the exponent */ + } + } /* decrease */ + } /* non-zero */ + + /* Check for overflow [do not use Finalize in this case, as an */ + /* overflow here is a "don't fit" situation] */ + if (res->exponent>set->emax-res->digits+1) { /* too big */ + *status|=DEC_Invalid_operation; + break; + } + else { + decFinalize(res, set, &residue, status); /* set subnormal flags */ + *status&=~DEC_Underflow; /* suppress Underflow [754r] */ + } + } while(0); /* end protected */ + + #if DECSUBSET + if (allocrhs!=NULL) free(allocrhs); /* drop any storage used */ + if (alloclhs!=NULL) free(alloclhs); /* .. */ + #endif + return res; + } /* decQuantizeOp */ + +/* ------------------------------------------------------------------ */ +/* decCompareOp -- compare, min, or max two Numbers */ +/* */ +/* This computes C = A ? B and carries out one of four operations: */ +/* COMPARE -- returns the signum (as a number) giving the */ +/* result of a comparison unless one or both */ +/* operands is a NaN (in which case a NaN results) */ +/* COMPSIG -- as COMPARE except that a quiet NaN raises */ +/* Invalid operation. */ +/* COMPMAX -- returns the larger of the operands, using the */ +/* 754r maxnum operation */ +/* COMPMAXMAG -- ditto, comparing absolute values */ +/* COMPMIN -- the 754r minnum operation */ +/* COMPMINMAG -- ditto, comparing absolute values */ +/* COMTOTAL -- returns the signum (as a number) giving the */ +/* result of a comparison using 754r total ordering */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* op is the operation flag */ +/* status is the usual accumulator */ +/* */ +/* C must have space for one digit for COMPARE or set->digits for */ +/* COMPMAX, COMPMIN, COMPMAXMAG, or COMPMINMAG. */ +/* ------------------------------------------------------------------ */ +/* The emphasis here is on speed for common cases, and avoiding */ +/* coefficient comparison if possible. */ +/* ------------------------------------------------------------------ */ +decNumber * decCompareOp(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set, + Flag op, uInt *status) { + #if DECSUBSET + decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */ + decNumber *allocrhs=NULL; /* .., rhs */ + #endif + Int result=0; /* default result value */ + uByte merged; /* work */ + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + do { /* protect allocated storage */ + #if DECSUBSET + if (!set->extended) { + /* reduce operands and set lostDigits status, as needed */ + if (lhs->digits>set->digits) { + alloclhs=decRoundOperand(lhs, set, status); + if (alloclhs==NULL) {result=BADINT; break;} + lhs=alloclhs; + } + if (rhs->digits>set->digits) { + allocrhs=decRoundOperand(rhs, set, status); + if (allocrhs==NULL) {result=BADINT; break;} + rhs=allocrhs; + } + } + #endif + /* [following code does not require input rounding] */ + + /* If total ordering then handle differing signs 'up front' */ + if (op==COMPTOTAL) { /* total ordering */ + if (decNumberIsNegative(lhs) & !decNumberIsNegative(rhs)) { + result=-1; + break; + } + if (!decNumberIsNegative(lhs) & decNumberIsNegative(rhs)) { + result=+1; + break; + } + } + + /* handle NaNs specially; let infinities drop through */ + /* This assumes sNaN (even just one) leads to NaN. */ + merged=(lhs->bits | rhs->bits) & (DECSNAN | DECNAN); + if (merged) { /* a NaN bit set */ + if (op==COMPARE); /* result will be NaN */ + else if (op==COMPSIG) /* treat qNaN as sNaN */ + *status|=DEC_Invalid_operation | DEC_sNaN; + else if (op==COMPTOTAL) { /* total ordering, always finite */ + /* signs are known to be the same; compute the ordering here */ + /* as if the signs are both positive, then invert for negatives */ + if (!decNumberIsNaN(lhs)) result=-1; + else if (!decNumberIsNaN(rhs)) result=+1; + /* here if both NaNs */ + else if (decNumberIsSNaN(lhs) && decNumberIsQNaN(rhs)) result=-1; + else if (decNumberIsQNaN(lhs) && decNumberIsSNaN(rhs)) result=+1; + else { /* both NaN or both sNaN */ + /* now it just depends on the payload */ + result=decUnitCompare(lhs->lsu, D2U(lhs->digits), + rhs->lsu, D2U(rhs->digits), 0); + /* [Error not possible, as these are 'aligned'] */ + } /* both same NaNs */ + if (decNumberIsNegative(lhs)) result=-result; + break; + } /* total order */ + + else if (merged & DECSNAN); /* sNaN -> qNaN */ + else { /* here if MIN or MAX and one or two quiet NaNs */ + /* min or max -- 754r rules ignore single NaN */ + if (!decNumberIsNaN(lhs) || !decNumberIsNaN(rhs)) { + /* just one NaN; force choice to be the non-NaN operand */ + op=COMPMAX; + if (lhs->bits & DECNAN) result=-1; /* pick rhs */ + else result=+1; /* pick lhs */ + break; + } + } /* max or min */ + op=COMPNAN; /* use special path */ + decNaNs(res, lhs, rhs, set, status); /* propagate NaN */ + break; + } + /* have numbers */ + if (op==COMPMAXMAG || op==COMPMINMAG) result=decCompare(lhs, rhs, 1); + else result=decCompare(lhs, rhs, 0); /* sign matters */ + } while(0); /* end protected */ + + if (result==BADINT) *status|=DEC_Insufficient_storage; /* rare */ + else { + if (op==COMPARE || op==COMPSIG ||op==COMPTOTAL) { /* returning signum */ + if (op==COMPTOTAL && result==0) { + /* operands are numerically equal or same NaN (and same sign, */ + /* tested first); if identical, leave result 0 */ + if (lhs->exponent!=rhs->exponent) { + if (lhs->exponent<rhs->exponent) result=-1; + else result=+1; + if (decNumberIsNegative(lhs)) result=-result; + } /* lexp!=rexp */ + } /* total-order by exponent */ + decNumberZero(res); /* [always a valid result] */ + if (result!=0) { /* must be -1 or +1 */ + *res->lsu=1; + if (result<0) res->bits=DECNEG; + } + } + else if (op==COMPNAN); /* special, drop through */ + else { /* MAX or MIN, non-NaN result */ + Int residue=0; /* rounding accumulator */ + /* choose the operand for the result */ + const decNumber *choice; + if (result==0) { /* operands are numerically equal */ + /* choose according to sign then exponent (see 754r) */ + uByte slhs=(lhs->bits & DECNEG); + uByte srhs=(rhs->bits & DECNEG); + #if DECSUBSET + if (!set->extended) { /* subset: force left-hand */ + op=COMPMAX; + result=+1; + } + else + #endif + if (slhs!=srhs) { /* signs differ */ + if (slhs) result=-1; /* rhs is max */ + else result=+1; /* lhs is max */ + } + else if (slhs && srhs) { /* both negative */ + if (lhs->exponent<rhs->exponent) result=+1; + else result=-1; + /* [if equal, use lhs, technically identical] */ + } + else { /* both positive */ + if (lhs->exponent>rhs->exponent) result=+1; + else result=-1; + /* [ditto] */ + } + } /* numerically equal */ + /* here result will be non-0; reverse if looking for MIN */ + if (op==COMPMIN || op==COMPMINMAG) result=-result; + choice=(result>0 ? lhs : rhs); /* choose */ + /* copy chosen to result, rounding if need be */ + decCopyFit(res, choice, set, &residue, status); + decFinish(res, set, &residue, status); + } + } + #if DECSUBSET + if (allocrhs!=NULL) free(allocrhs); /* free any storage used */ + if (alloclhs!=NULL) free(alloclhs); /* .. */ + #endif + return res; + } /* decCompareOp */ + +/* ------------------------------------------------------------------ */ +/* decCompare -- compare two decNumbers by numerical value */ +/* */ +/* This routine compares A ? B without altering them. */ +/* */ +/* Arg1 is A, a decNumber which is not a NaN */ +/* Arg2 is B, a decNumber which is not a NaN */ +/* Arg3 is 1 for a sign-independent compare, 0 otherwise */ +/* */ +/* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */ +/* (the only possible failure is an allocation error) */ +/* ------------------------------------------------------------------ */ +static Int decCompare(const decNumber *lhs, const decNumber *rhs, + Flag abs) { + Int result; /* result value */ + Int sigr; /* rhs signum */ + Int compare; /* work */ + + result=1; /* assume signum(lhs) */ + if (ISZERO(lhs)) result=0; + if (abs) { + if (ISZERO(rhs)) return result; /* LHS wins or both 0 */ + /* RHS is non-zero */ + if (result==0) return -1; /* LHS is 0; RHS wins */ + /* [here, both non-zero, result=1] */ + } + else { /* signs matter */ + if (result && decNumberIsNegative(lhs)) result=-1; + sigr=1; /* compute signum(rhs) */ + if (ISZERO(rhs)) sigr=0; + else if (decNumberIsNegative(rhs)) sigr=-1; + if (result > sigr) return +1; /* L > R, return 1 */ + if (result < sigr) return -1; /* L < R, return -1 */ + if (result==0) return 0; /* both 0 */ + } + + /* signums are the same; both are non-zero */ + if ((lhs->bits | rhs->bits) & DECINF) { /* one or more infinities */ + if (decNumberIsInfinite(rhs)) { + if (decNumberIsInfinite(lhs)) result=0;/* both infinite */ + else result=-result; /* only rhs infinite */ + } + return result; + } + /* must compare the coefficients, allowing for exponents */ + if (lhs->exponent>rhs->exponent) { /* LHS exponent larger */ + /* swap sides, and sign */ + const decNumber *temp=lhs; + lhs=rhs; + rhs=temp; + result=-result; + } + compare=decUnitCompare(lhs->lsu, D2U(lhs->digits), + rhs->lsu, D2U(rhs->digits), + rhs->exponent-lhs->exponent); + if (compare!=BADINT) compare*=result; /* comparison succeeded */ + return compare; + } /* decCompare */ + +/* ------------------------------------------------------------------ */ +/* decUnitCompare -- compare two >=0 integers in Unit arrays */ +/* */ +/* This routine compares A ? B*10**E where A and B are unit arrays */ +/* A is a plain integer */ +/* B has an exponent of E (which must be non-negative) */ +/* */ +/* Arg1 is A first Unit (lsu) */ +/* Arg2 is A length in Units */ +/* Arg3 is B first Unit (lsu) */ +/* Arg4 is B length in Units */ +/* Arg5 is E (0 if the units are aligned) */ +/* */ +/* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */ +/* (the only possible failure is an allocation error, which can */ +/* only occur if E!=0) */ +/* ------------------------------------------------------------------ */ +static Int decUnitCompare(const Unit *a, Int alength, + const Unit *b, Int blength, Int exp) { + Unit *acc; /* accumulator for result */ + Unit accbuff[SD2U(DECBUFFER*2+1)]; /* local buffer */ + Unit *allocacc=NULL; /* -> allocated acc buffer, iff allocated */ + Int accunits, need; /* units in use or needed for acc */ + const Unit *l, *r, *u; /* work */ + Int expunits, exprem, result; /* .. */ + + if (exp==0) { /* aligned; fastpath */ + if (alength>blength) return 1; + if (alength<blength) return -1; + /* same number of units in both -- need unit-by-unit compare */ + l=a+alength-1; + r=b+alength-1; + for (;l>=a; l--, r--) { + if (*l>*r) return 1; + if (*l<*r) return -1; + } + return 0; /* all units match */ + } /* aligned */ + + /* Unaligned. If one is >1 unit longer than the other, padded */ + /* approximately, then can return easily */ + if (alength>blength+(Int)D2U(exp)) return 1; + if (alength+1<blength+(Int)D2U(exp)) return -1; + + /* Need to do a real subtract. For this, a result buffer is needed */ + /* even though only the sign is of interest. Its length needs */ + /* to be the larger of alength and padded blength, +2 */ + need=blength+D2U(exp); /* maximum real length of B */ + if (need<alength) need=alength; + need+=2; + acc=accbuff; /* assume use local buffer */ + if (need*sizeof(Unit)>sizeof(accbuff)) { + allocacc=(Unit *)malloc(need*sizeof(Unit)); + if (allocacc==NULL) return BADINT; /* hopeless -- abandon */ + acc=allocacc; + } + /* Calculate units and remainder from exponent. */ + expunits=exp/DECDPUN; + exprem=exp%DECDPUN; + /* subtract [A+B*(-m)] */ + accunits=decUnitAddSub(a, alength, b, blength, expunits, acc, + -(Int)powers[exprem]); + /* [UnitAddSub result may have leading zeros, even on zero] */ + if (accunits<0) result=-1; /* negative result */ + else { /* non-negative result */ + /* check units of the result before freeing any storage */ + for (u=acc; u<acc+accunits-1 && *u==0;) u++; + result=(*u==0 ? 0 : +1); + } + /* clean up and return the result */ + if (allocacc!=NULL) free(allocacc); /* drop any storage used */ + return result; + } /* decUnitCompare */ + +/* ------------------------------------------------------------------ */ +/* decUnitAddSub -- add or subtract two >=0 integers in Unit arrays */ +/* */ +/* This routine performs the calculation: */ +/* */ +/* C=A+(B*M) */ +/* */ +/* Where M is in the range -DECDPUNMAX through +DECDPUNMAX. */ +/* */ +/* A may be shorter or longer than B. */ +/* */ +/* Leading zeros are not removed after a calculation. The result is */ +/* either the same length as the longer of A and B (adding any */ +/* shift), or one Unit longer than that (if a Unit carry occurred). */ +/* */ +/* A and B content are not altered unless C is also A or B. */ +/* C may be the same array as A or B, but only if no zero padding is */ +/* requested (that is, C may be B only if bshift==0). */ +/* C is filled from the lsu; only those units necessary to complete */ +/* the calculation are referenced. */ +/* */ +/* Arg1 is A first Unit (lsu) */ +/* Arg2 is A length in Units */ +/* Arg3 is B first Unit (lsu) */ +/* Arg4 is B length in Units */ +/* Arg5 is B shift in Units (>=0; pads with 0 units if positive) */ +/* Arg6 is C first Unit (lsu) */ +/* Arg7 is M, the multiplier */ +/* */ +/* returns the count of Units written to C, which will be non-zero */ +/* and negated if the result is negative. That is, the sign of the */ +/* returned Int is the sign of the result (positive for zero) and */ +/* the absolute value of the Int is the count of Units. */ +/* */ +/* It is the caller's responsibility to make sure that C size is */ +/* safe, allowing space if necessary for a one-Unit carry. */ +/* */ +/* This routine is severely performance-critical; *any* change here */ +/* must be measured (timed) to assure no performance degradation. */ +/* In particular, trickery here tends to be counter-productive, as */ +/* increased complexity of code hurts register optimizations on */ +/* register-poor architectures. Avoiding divisions is nearly */ +/* always a Good Idea, however. */ +/* */ +/* Special thanks to Rick McGuire (IBM Cambridge, MA) and Dave Clark */ +/* (IBM Warwick, UK) for some of the ideas used in this routine. */ +/* ------------------------------------------------------------------ */ +static Int decUnitAddSub(const Unit *a, Int alength, + const Unit *b, Int blength, Int bshift, + Unit *c, Int m) { + const Unit *alsu=a; /* A lsu [need to remember it] */ + Unit *clsu=c; /* C ditto */ + Unit *minC; /* low water mark for C */ + Unit *maxC; /* high water mark for C */ + eInt carry=0; /* carry integer (could be Long) */ + Int add; /* work */ + #if DECDPUN<=4 /* myriadal, millenary, etc. */ + Int est; /* estimated quotient */ + #endif + + #if DECTRACE + if (alength<1 || blength<1) + printf("decUnitAddSub: alen blen m %ld %ld [%ld]\n", alength, blength, m); + #endif + + maxC=c+alength; /* A is usually the longer */ + minC=c+blength; /* .. and B the shorter */ + if (bshift!=0) { /* B is shifted; low As copy across */ + minC+=bshift; + /* if in place [common], skip copy unless there's a gap [rare] */ + if (a==c && bshift<=alength) { + c+=bshift; + a+=bshift; + } + else for (; c<clsu+bshift; a++, c++) { /* copy needed */ + if (a<alsu+alength) *c=*a; + else *c=0; + } + } + if (minC>maxC) { /* swap */ + Unit *hold=minC; + minC=maxC; + maxC=hold; + } + + /* For speed, do the addition as two loops; the first where both A */ + /* and B contribute, and the second (if necessary) where only one or */ + /* other of the numbers contribute. */ + /* Carry handling is the same (i.e., duplicated) in each case. */ + for (; c<minC; c++) { + carry+=*a; + a++; + carry+=((eInt)*b)*m; /* [special-casing m=1/-1 */ + b++; /* here is not a win] */ + /* here carry is new Unit of digits; it could be +ve or -ve */ + if ((ueInt)carry<=DECDPUNMAX) { /* fastpath 0-DECDPUNMAX */ + *c=(Unit)carry; + carry=0; + continue; + } + #if DECDPUN==4 /* use divide-by-multiply */ + if (carry>=0) { + est=(((ueInt)carry>>11)*53687)>>18; + *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ + carry=est; /* likely quotient [89%] */ + if (*c<DECDPUNMAX+1) continue; /* estimate was correct */ + carry++; + *c-=DECDPUNMAX+1; + continue; + } + /* negative case */ + carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ + est=(((ueInt)carry>>11)*53687)>>18; + *c=(Unit)(carry-est*(DECDPUNMAX+1)); + carry=est-(DECDPUNMAX+1); /* correctly negative */ + if (*c<DECDPUNMAX+1) continue; /* was OK */ + carry++; + *c-=DECDPUNMAX+1; + #elif DECDPUN==3 + if (carry>=0) { + est=(((ueInt)carry>>3)*16777)>>21; + *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ + carry=est; /* likely quotient [99%] */ + if (*c<DECDPUNMAX+1) continue; /* estimate was correct */ + carry++; + *c-=DECDPUNMAX+1; + continue; + } + /* negative case */ + carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ + est=(((ueInt)carry>>3)*16777)>>21; + *c=(Unit)(carry-est*(DECDPUNMAX+1)); + carry=est-(DECDPUNMAX+1); /* correctly negative */ + if (*c<DECDPUNMAX+1) continue; /* was OK */ + carry++; + *c-=DECDPUNMAX+1; + #elif DECDPUN<=2 + /* Can use QUOT10 as carry <= 4 digits */ + if (carry>=0) { + est=QUOT10(carry, DECDPUN); + *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ + carry=est; /* quotient */ + continue; + } + /* negative case */ + carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ + est=QUOT10(carry, DECDPUN); + *c=(Unit)(carry-est*(DECDPUNMAX+1)); + carry=est-(DECDPUNMAX+1); /* correctly negative */ + #else + /* remainder operator is undefined if negative, so must test */ + if ((ueInt)carry<(DECDPUNMAX+1)*2) { /* fastpath carry +1 */ + *c=(Unit)(carry-(DECDPUNMAX+1)); /* [helps additions] */ + carry=1; + continue; + } + if (carry>=0) { + *c=(Unit)(carry%(DECDPUNMAX+1)); + carry=carry/(DECDPUNMAX+1); + continue; + } + /* negative case */ + carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ + *c=(Unit)(carry%(DECDPUNMAX+1)); + carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1); + #endif + } /* c */ + + /* now may have one or other to complete */ + /* [pretest to avoid loop setup/shutdown] */ + if (c<maxC) for (; c<maxC; c++) { + if (a<alsu+alength) { /* still in A */ + carry+=*a; + a++; + } + else { /* inside B */ + carry+=((eInt)*b)*m; + b++; + } + /* here carry is new Unit of digits; it could be +ve or -ve and */ + /* magnitude up to DECDPUNMAX squared */ + if ((ueInt)carry<=DECDPUNMAX) { /* fastpath 0-DECDPUNMAX */ + *c=(Unit)carry; + carry=0; + continue; + } + /* result for this unit is negative or >DECDPUNMAX */ + #if DECDPUN==4 /* use divide-by-multiply */ + if (carry>=0) { + est=(((ueInt)carry>>11)*53687)>>18; + *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ + carry=est; /* likely quotient [79.7%] */ + if (*c<DECDPUNMAX+1) continue; /* estimate was correct */ + carry++; + *c-=DECDPUNMAX+1; + continue; + } + /* negative case */ + carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ + est=(((ueInt)carry>>11)*53687)>>18; + *c=(Unit)(carry-est*(DECDPUNMAX+1)); + carry=est-(DECDPUNMAX+1); /* correctly negative */ + if (*c<DECDPUNMAX+1) continue; /* was OK */ + carry++; + *c-=DECDPUNMAX+1; + #elif DECDPUN==3 + if (carry>=0) { + est=(((ueInt)carry>>3)*16777)>>21; + *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ + carry=est; /* likely quotient [99%] */ + if (*c<DECDPUNMAX+1) continue; /* estimate was correct */ + carry++; + *c-=DECDPUNMAX+1; + continue; + } + /* negative case */ + carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ + est=(((ueInt)carry>>3)*16777)>>21; + *c=(Unit)(carry-est*(DECDPUNMAX+1)); + carry=est-(DECDPUNMAX+1); /* correctly negative */ + if (*c<DECDPUNMAX+1) continue; /* was OK */ + carry++; + *c-=DECDPUNMAX+1; + #elif DECDPUN<=2 + if (carry>=0) { + est=QUOT10(carry, DECDPUN); + *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */ + carry=est; /* quotient */ + continue; + } + /* negative case */ + carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ + est=QUOT10(carry, DECDPUN); + *c=(Unit)(carry-est*(DECDPUNMAX+1)); + carry=est-(DECDPUNMAX+1); /* correctly negative */ + #else + if ((ueInt)carry<(DECDPUNMAX+1)*2){ /* fastpath carry 1 */ + *c=(Unit)(carry-(DECDPUNMAX+1)); + carry=1; + continue; + } + /* remainder operator is undefined if negative, so must test */ + if (carry>=0) { + *c=(Unit)(carry%(DECDPUNMAX+1)); + carry=carry/(DECDPUNMAX+1); + continue; + } + /* negative case */ + carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */ + *c=(Unit)(carry%(DECDPUNMAX+1)); + carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1); + #endif + } /* c */ + + /* OK, all A and B processed; might still have carry or borrow */ + /* return number of Units in the result, negated if a borrow */ + if (carry==0) return c-clsu; /* no carry, so no more to do */ + if (carry>0) { /* positive carry */ + *c=(Unit)carry; /* place as new unit */ + c++; /* .. */ + return c-clsu; + } + /* -ve carry: it's a borrow; complement needed */ + add=1; /* temporary carry... */ + for (c=clsu; c<maxC; c++) { + add=DECDPUNMAX+add-*c; + if (add<=DECDPUNMAX) { + *c=(Unit)add; + add=0; + } + else { + *c=0; + add=1; + } + } + /* add an extra unit iff it would be non-zero */ + #if DECTRACE + printf("UAS borrow: add %ld, carry %ld\n", add, carry); + #endif + if ((add-carry-1)!=0) { + *c=(Unit)(add-carry-1); + c++; /* interesting, include it */ + } + return clsu-c; /* -ve result indicates borrowed */ + } /* decUnitAddSub */ + +/* ------------------------------------------------------------------ */ +/* decTrim -- trim trailing zeros or normalize */ +/* */ +/* dn is the number to trim or normalize */ +/* set is the context to use to check for clamp */ +/* all is 1 to remove all trailing zeros, 0 for just fraction ones */ +/* dropped returns the number of discarded trailing zeros */ +/* returns dn */ +/* */ +/* If clamp is set in the context then the number of zeros trimmed */ +/* may be limited if the exponent is high. */ +/* All fields are updated as required. This is a utility operation, */ +/* so special values are unchanged and no error is possible. */ +/* ------------------------------------------------------------------ */ +static decNumber * decTrim(decNumber *dn, decContext *set, Flag all, + Int *dropped) { + Int d, exp; /* work */ + uInt cut; /* .. */ + Unit *up; /* -> current Unit */ + + #if DECCHECK + if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn; + #endif + + *dropped=0; /* assume no zeros dropped */ + if ((dn->bits & DECSPECIAL) /* fast exit if special .. */ + || (*dn->lsu & 0x01)) return dn; /* .. or odd */ + if (ISZERO(dn)) { /* .. or 0 */ + dn->exponent=0; /* (sign is preserved) */ + return dn; + } + + /* have a finite number which is even */ + exp=dn->exponent; + cut=1; /* digit (1-DECDPUN) in Unit */ + up=dn->lsu; /* -> current Unit */ + for (d=0; d<dn->digits-1; d++) { /* [don't strip the final digit] */ + /* slice by powers */ + #if DECDPUN<=4 + uInt quot=QUOT10(*up, cut); + if ((*up-quot*powers[cut])!=0) break; /* found non-0 digit */ + #else + if (*up%powers[cut]!=0) break; /* found non-0 digit */ + #endif + /* have a trailing 0 */ + if (!all) { /* trimming */ + /* [if exp>0 then all trailing 0s are significant for trim] */ + if (exp<=0) { /* if digit might be significant */ + if (exp==0) break; /* then quit */ + exp++; /* next digit might be significant */ + } + } + cut++; /* next power */ + if (cut>DECDPUN) { /* need new Unit */ + up++; + cut=1; + } + } /* d */ + if (d==0) return dn; /* none to drop */ + + /* may need to limit drop if clamping */ + if (set->clamp) { + Int maxd=set->emax-set->digits+1-dn->exponent; + if (maxd<=0) return dn; /* nothing possible */ + if (d>maxd) d=maxd; + } + + /* effect the drop */ + decShiftToLeast(dn->lsu, D2U(dn->digits), d); + dn->exponent+=d; /* maintain numerical value */ + dn->digits-=d; /* new length */ + *dropped=d; /* report the count */ + return dn; + } /* decTrim */ + +/* ------------------------------------------------------------------ */ +/* decReverse -- reverse a Unit array in place */ +/* */ +/* ulo is the start of the array */ +/* uhi is the end of the array (highest Unit to include) */ +/* */ +/* The units ulo through uhi are reversed in place (if the number */ +/* of units is odd, the middle one is untouched). Note that the */ +/* digit(s) in each unit are unaffected. */ +/* ------------------------------------------------------------------ */ +static void decReverse(Unit *ulo, Unit *uhi) { + Unit temp; + for (; ulo<uhi; ulo++, uhi--) { + temp=*ulo; + *ulo=*uhi; + *uhi=temp; + } + return; + } /* decReverse */ + +/* ------------------------------------------------------------------ */ +/* decShiftToMost -- shift digits in array towards most significant */ +/* */ +/* uar is the array */ +/* digits is the count of digits in use in the array */ +/* shift is the number of zeros to pad with (least significant); */ +/* it must be zero or positive */ +/* */ +/* returns the new length of the integer in the array, in digits */ +/* */ +/* No overflow is permitted (that is, the uar array must be known to */ +/* be large enough to hold the result, after shifting). */ +/* ------------------------------------------------------------------ */ +static Int decShiftToMost(Unit *uar, Int digits, Int shift) { + Unit *target, *source, *first; /* work */ + Int cut; /* odd 0's to add */ + uInt next; /* work */ + + if (shift==0) return digits; /* [fastpath] nothing to do */ + if ((digits+shift)<=DECDPUN) { /* [fastpath] single-unit case */ + *uar=(Unit)(*uar*powers[shift]); + return digits+shift; + } + + next=0; /* all paths */ + source=uar+D2U(digits)-1; /* where msu comes from */ + target=source+D2U(shift); /* where upper part of first cut goes */ + cut=DECDPUN-MSUDIGITS(shift); /* where to slice */ + if (cut==0) { /* unit-boundary case */ + for (; source>=uar; source--, target--) *target=*source; + } + else { + first=uar+D2U(digits+shift)-1; /* where msu of source will end up */ + for (; source>=uar; source--, target--) { + /* split the source Unit and accumulate remainder for next */ + #if DECDPUN<=4 + uInt quot=QUOT10(*source, cut); + uInt rem=*source-quot*powers[cut]; + next+=quot; + #else + uInt rem=*source%powers[cut]; + next+=*source/powers[cut]; + #endif + if (target<=first) *target=(Unit)next; /* write to target iff valid */ + next=rem*powers[DECDPUN-cut]; /* save remainder for next Unit */ + } + } /* shift-move */ + + /* propagate any partial unit to one below and clear the rest */ + for (; target>=uar; target--) { + *target=(Unit)next; + next=0; + } + return digits+shift; + } /* decShiftToMost */ + +/* ------------------------------------------------------------------ */ +/* decShiftToLeast -- shift digits in array towards least significant */ +/* */ +/* uar is the array */ +/* units is length of the array, in units */ +/* shift is the number of digits to remove from the lsu end; it */ +/* must be zero or positive and <= than units*DECDPUN. */ +/* */ +/* returns the new length of the integer in the array, in units */ +/* */ +/* Removed digits are discarded (lost). Units not required to hold */ +/* the final result are unchanged. */ +/* ------------------------------------------------------------------ */ +static Int decShiftToLeast(Unit *uar, Int units, Int shift) { + Unit *target, *up; /* work */ + Int cut, count; /* work */ + Int quot, rem; /* for division */ + + if (shift==0) return units; /* [fastpath] nothing to do */ + if (shift==units*DECDPUN) { /* [fastpath] little to do */ + *uar=0; /* all digits cleared gives zero */ + return 1; /* leaves just the one */ + } + + target=uar; /* both paths */ + cut=MSUDIGITS(shift); + if (cut==DECDPUN) { /* unit-boundary case; easy */ + up=uar+D2U(shift); + for (; up<uar+units; target++, up++) *target=*up; + return target-uar; + } + + /* messier */ + up=uar+D2U(shift-cut); /* source; correct to whole Units */ + count=units*DECDPUN-shift; /* the maximum new length */ + #if DECDPUN<=4 + quot=QUOT10(*up, cut); + #else + quot=*up/powers[cut]; + #endif + for (; ; target++) { + *target=(Unit)quot; + count-=(DECDPUN-cut); + if (count<=0) break; + up++; + quot=*up; + #if DECDPUN<=4 + quot=QUOT10(quot, cut); + rem=*up-quot*powers[cut]; + #else + rem=quot%powers[cut]; + quot=quot/powers[cut]; + #endif + *target=(Unit)(*target+rem*powers[DECDPUN-cut]); + count-=cut; + if (count<=0) break; + } + return target-uar+1; + } /* decShiftToLeast */ + +#if DECSUBSET +/* ------------------------------------------------------------------ */ +/* decRoundOperand -- round an operand [used for subset only] */ +/* */ +/* dn is the number to round (dn->digits is > set->digits) */ +/* set is the relevant context */ +/* status is the status accumulator */ +/* */ +/* returns an allocated decNumber with the rounded result. */ +/* */ +/* lostDigits and other status may be set by this. */ +/* */ +/* Since the input is an operand, it must not be modified. */ +/* Instead, return an allocated decNumber, rounded as required. */ +/* It is the caller's responsibility to free the allocated storage. */ +/* */ +/* If no storage is available then the result cannot be used, so NULL */ +/* is returned. */ +/* ------------------------------------------------------------------ */ +static decNumber *decRoundOperand(const decNumber *dn, decContext *set, + uInt *status) { + decNumber *res; /* result structure */ + uInt newstatus=0; /* status from round */ + Int residue=0; /* rounding accumulator */ + + /* Allocate storage for the returned decNumber, big enough for the */ + /* length specified by the context */ + res=(decNumber *)malloc(sizeof(decNumber) + +(D2U(set->digits)-1)*sizeof(Unit)); + if (res==NULL) { + *status|=DEC_Insufficient_storage; + return NULL; + } + decCopyFit(res, dn, set, &residue, &newstatus); + decApplyRound(res, set, residue, &newstatus); + + /* If that set Inexact then "lost digits" is raised... */ + if (newstatus & DEC_Inexact) newstatus|=DEC_Lost_digits; + *status|=newstatus; + return res; + } /* decRoundOperand */ +#endif + +/* ------------------------------------------------------------------ */ +/* decCopyFit -- copy a number, truncating the coefficient if needed */ +/* */ +/* dest is the target decNumber */ +/* src is the source decNumber */ +/* set is the context [used for length (digits) and rounding mode] */ +/* residue is the residue accumulator */ +/* status contains the current status to be updated */ +/* */ +/* (dest==src is allowed and will be a no-op if fits) */ +/* All fields are updated as required. */ +/* ------------------------------------------------------------------ */ +static void decCopyFit(decNumber *dest, const decNumber *src, + decContext *set, Int *residue, uInt *status) { + dest->bits=src->bits; + dest->exponent=src->exponent; + decSetCoeff(dest, set, src->lsu, src->digits, residue, status); + } /* decCopyFit */ + +/* ------------------------------------------------------------------ */ +/* decSetCoeff -- set the coefficient of a number */ +/* */ +/* dn is the number whose coefficient array is to be set. */ +/* It must have space for set->digits digits */ +/* set is the context [for size] */ +/* lsu -> lsu of the source coefficient [may be dn->lsu] */ +/* len is digits in the source coefficient [may be dn->digits] */ +/* residue is the residue accumulator. This has values as in */ +/* decApplyRound, and will be unchanged unless the */ +/* target size is less than len. In this case, the */ +/* coefficient is truncated and the residue is updated to */ +/* reflect the previous residue and the dropped digits. */ +/* status is the status accumulator, as usual */ +/* */ +/* The coefficient may already be in the number, or it can be an */ +/* external intermediate array. If it is in the number, lsu must == */ +/* dn->lsu and len must == dn->digits. */ +/* */ +/* Note that the coefficient length (len) may be < set->digits, and */ +/* in this case this merely copies the coefficient (or is a no-op */ +/* if dn->lsu==lsu). */ +/* */ +/* Note also that (only internally, from decQuantizeOp and */ +/* decSetSubnormal) the value of set->digits may be less than one, */ +/* indicating a round to left. This routine handles that case */ +/* correctly; caller ensures space. */ +/* */ +/* dn->digits, dn->lsu (and as required), and dn->exponent are */ +/* updated as necessary. dn->bits (sign) is unchanged. */ +/* */ +/* DEC_Rounded status is set if any digits are discarded. */ +/* DEC_Inexact status is set if any non-zero digits are discarded, or */ +/* incoming residue was non-0 (implies rounded) */ +/* ------------------------------------------------------------------ */ +/* mapping array: maps 0-9 to canonical residues, so that a residue */ +/* can be adjusted in the range [-1, +1] and achieve correct rounding */ +/* 0 1 2 3 4 5 6 7 8 9 */ +static const uByte resmap[10]={0, 3, 3, 3, 3, 5, 7, 7, 7, 7}; +static void decSetCoeff(decNumber *dn, decContext *set, const Unit *lsu, + Int len, Int *residue, uInt *status) { + Int discard; /* number of digits to discard */ + uInt cut; /* cut point in Unit */ + const Unit *up; /* work */ + Unit *target; /* .. */ + Int count; /* .. */ + #if DECDPUN<=4 + uInt temp; /* .. */ + #endif + + discard=len-set->digits; /* digits to discard */ + if (discard<=0) { /* no digits are being discarded */ + if (dn->lsu!=lsu) { /* copy needed */ + /* copy the coefficient array to the result number; no shift needed */ + count=len; /* avoids D2U */ + up=lsu; + for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN) + *target=*up; + dn->digits=len; /* set the new length */ + } + /* dn->exponent and residue are unchanged, record any inexactitude */ + if (*residue!=0) *status|=(DEC_Inexact | DEC_Rounded); + return; + } + + /* some digits must be discarded ... */ + dn->exponent+=discard; /* maintain numerical value */ + *status|=DEC_Rounded; /* accumulate Rounded status */ + if (*residue>1) *residue=1; /* previous residue now to right, so reduce */ + + if (discard>len) { /* everything, +1, is being discarded */ + /* guard digit is 0 */ + /* residue is all the number [NB could be all 0s] */ + if (*residue<=0) { /* not already positive */ + count=len; /* avoids D2U */ + for (up=lsu; count>0; up++, count-=DECDPUN) if (*up!=0) { /* found non-0 */ + *residue=1; + break; /* no need to check any others */ + } + } + if (*residue!=0) *status|=DEC_Inexact; /* record inexactitude */ + *dn->lsu=0; /* coefficient will now be 0 */ + dn->digits=1; /* .. */ + return; + } /* total discard */ + + /* partial discard [most common case] */ + /* here, at least the first (most significant) discarded digit exists */ + + /* spin up the number, noting residue during the spin, until get to */ + /* the Unit with the first discarded digit. When reach it, extract */ + /* it and remember its position */ + count=0; + for (up=lsu;; up++) { + count+=DECDPUN; + if (count>=discard) break; /* full ones all checked */ + if (*up!=0) *residue=1; + } /* up */ + + /* here up -> Unit with first discarded digit */ + cut=discard-(count-DECDPUN)-1; + if (cut==DECDPUN-1) { /* unit-boundary case (fast) */ + Unit half=(Unit)powers[DECDPUN]>>1; + /* set residue directly */ + if (*up>=half) { + if (*up>half) *residue=7; + else *residue+=5; /* add sticky bit */ + } + else { /* <half */ + if (*up!=0) *residue=3; /* [else is 0, leave as sticky bit] */ + } + if (set->digits<=0) { /* special for Quantize/Subnormal :-( */ + *dn->lsu=0; /* .. result is 0 */ + dn->digits=1; /* .. */ + } + else { /* shift to least */ + count=set->digits; /* now digits to end up with */ + dn->digits=count; /* set the new length */ + up++; /* move to next */ + /* on unit boundary, so shift-down copy loop is simple */ + for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN) + *target=*up; + } + } /* unit-boundary case */ + + else { /* discard digit is in low digit(s), and not top digit */ + uInt discard1; /* first discarded digit */ + uInt quot, rem; /* for divisions */ + if (cut==0) quot=*up; /* is at bottom of unit */ + else /* cut>0 */ { /* it's not at bottom of unit */ + #if DECDPUN<=4 + quot=QUOT10(*up, cut); + rem=*up-quot*powers[cut]; + #else + rem=*up%powers[cut]; + quot=*up/powers[cut]; + #endif + if (rem!=0) *residue=1; + } + /* discard digit is now at bottom of quot */ + #if DECDPUN<=4 + temp=(quot*6554)>>16; /* fast /10 */ + /* Vowels algorithm here not a win (9 instructions) */ + discard1=quot-X10(temp); + quot=temp; + #else + discard1=quot%10; + quot=quot/10; + #endif + /* here, discard1 is the guard digit, and residue is everything */ + /* else [use mapping array to accumulate residue safely] */ + *residue+=resmap[discard1]; + cut++; /* update cut */ + /* here: up -> Unit of the array with bottom digit */ + /* cut is the division point for each Unit */ + /* quot holds the uncut high-order digits for the current unit */ + if (set->digits<=0) { /* special for Quantize/Subnormal :-( */ + *dn->lsu=0; /* .. result is 0 */ + dn->digits=1; /* .. */ + } + else { /* shift to least needed */ + count=set->digits; /* now digits to end up with */ + dn->digits=count; /* set the new length */ + /* shift-copy the coefficient array to the result number */ + for (target=dn->lsu; ; target++) { + *target=(Unit)quot; + count-=(DECDPUN-cut); + if (count<=0) break; + up++; + quot=*up; + #if DECDPUN<=4 + quot=QUOT10(quot, cut); + rem=*up-quot*powers[cut]; + #else + rem=quot%powers[cut]; + quot=quot/powers[cut]; + #endif + *target=(Unit)(*target+rem*powers[DECDPUN-cut]); + count-=cut; + if (count<=0) break; + } /* shift-copy loop */ + } /* shift to least */ + } /* not unit boundary */ + + if (*residue!=0) *status|=DEC_Inexact; /* record inexactitude */ + return; + } /* decSetCoeff */ + +/* ------------------------------------------------------------------ */ +/* decApplyRound -- apply pending rounding to a number */ +/* */ +/* dn is the number, with space for set->digits digits */ +/* set is the context [for size and rounding mode] */ +/* residue indicates pending rounding, being any accumulated */ +/* guard and sticky information. It may be: */ +/* 6-9: rounding digit is >5 */ +/* 5: rounding digit is exactly half-way */ +/* 1-4: rounding digit is <5 and >0 */ +/* 0: the coefficient is exact */ +/* -1: as 1, but the hidden digits are subtractive, that */ +/* is, of the opposite sign to dn. In this case the */ +/* coefficient must be non-0. This case occurs when */ +/* subtracting a small number (which can be reduced to */ +/* a sticky bit); see decAddOp. */ +/* status is the status accumulator, as usual */ +/* */ +/* This routine applies rounding while keeping the length of the */ +/* coefficient constant. The exponent and status are unchanged */ +/* except if: */ +/* */ +/* -- the coefficient was increased and is all nines (in which */ +/* case Overflow could occur, and is handled directly here so */ +/* the caller does not need to re-test for overflow) */ +/* */ +/* -- the coefficient was decreased and becomes all nines (in which */ +/* case Underflow could occur, and is also handled directly). */ +/* */ +/* All fields in dn are updated as required. */ +/* */ +/* ------------------------------------------------------------------ */ +static void decApplyRound(decNumber *dn, decContext *set, Int residue, + uInt *status) { + Int bump; /* 1 if coefficient needs to be incremented */ + /* -1 if coefficient needs to be decremented */ + + if (residue==0) return; /* nothing to apply */ + + bump=0; /* assume a smooth ride */ + + /* now decide whether, and how, to round, depending on mode */ + switch (set->round) { + case DEC_ROUND_05UP: { /* round zero or five up (for reround) */ + /* This is the same as DEC_ROUND_DOWN unless there is a */ + /* positive residue and the lsd of dn is 0 or 5, in which case */ + /* it is bumped; when residue is <0, the number is therefore */ + /* bumped down unless the final digit was 1 or 6 (in which */ + /* case it is bumped down and then up -- a no-op) */ + Int lsd5=*dn->lsu%5; /* get lsd and quintate */ + if (residue<0 && lsd5!=1) bump=-1; + else if (residue>0 && lsd5==0) bump=1; + /* [bump==1 could be applied directly; use common path for clarity] */ + break;} /* r-05 */ + + case DEC_ROUND_DOWN: { + /* no change, except if negative residue */ + if (residue<0) bump=-1; + break;} /* r-d */ + + case DEC_ROUND_HALF_DOWN: { + if (residue>5) bump=1; + break;} /* r-h-d */ + + case DEC_ROUND_HALF_EVEN: { + if (residue>5) bump=1; /* >0.5 goes up */ + else if (residue==5) { /* exactly 0.5000... */ + /* 0.5 goes up iff [new] lsd is odd */ + if (*dn->lsu & 0x01) bump=1; + } + break;} /* r-h-e */ + + case DEC_ROUND_HALF_UP: { + if (residue>=5) bump=1; + break;} /* r-h-u */ + + case DEC_ROUND_UP: { + if (residue>0) bump=1; + break;} /* r-u */ + + case DEC_ROUND_CEILING: { + /* same as _UP for positive numbers, and as _DOWN for negatives */ + /* [negative residue cannot occur on 0] */ + if (decNumberIsNegative(dn)) { + if (residue<0) bump=-1; + } + else { + if (residue>0) bump=1; + } + break;} /* r-c */ + + case DEC_ROUND_FLOOR: { + /* same as _UP for negative numbers, and as _DOWN for positive */ + /* [negative residue cannot occur on 0] */ + if (!decNumberIsNegative(dn)) { + if (residue<0) bump=-1; + } + else { + if (residue>0) bump=1; + } + break;} /* r-f */ + + default: { /* e.g., DEC_ROUND_MAX */ + *status|=DEC_Invalid_context; + #if DECTRACE || (DECCHECK && DECVERB) + printf("Unknown rounding mode: %d\n", set->round); + #endif + break;} + } /* switch */ + + /* now bump the number, up or down, if need be */ + if (bump==0) return; /* no action required */ + + /* Simply use decUnitAddSub unless bumping up and the number is */ + /* all nines. In this special case set to 100... explicitly */ + /* and adjust the exponent by one (as otherwise could overflow */ + /* the array) */ + /* Similarly handle all-nines result if bumping down. */ + if (bump>0) { + Unit *up; /* work */ + uInt count=dn->digits; /* digits to be checked */ + for (up=dn->lsu; ; up++) { + if (count<=DECDPUN) { + /* this is the last Unit (the msu) */ + if (*up!=powers[count]-1) break; /* not still 9s */ + /* here if it, too, is all nines */ + *up=(Unit)powers[count-1]; /* here 999 -> 100 etc. */ + for (up=up-1; up>=dn->lsu; up--) *up=0; /* others all to 0 */ + dn->exponent++; /* and bump exponent */ + /* [which, very rarely, could cause Overflow...] */ + if ((dn->exponent+dn->digits)>set->emax+1) { + decSetOverflow(dn, set, status); + } + return; /* done */ + } + /* a full unit to check, with more to come */ + if (*up!=DECDPUNMAX) break; /* not still 9s */ + count-=DECDPUN; + } /* up */ + } /* bump>0 */ + else { /* -1 */ + /* here checking for a pre-bump of 1000... (leading 1, all */ + /* other digits zero) */ + Unit *up, *sup; /* work */ + uInt count=dn->digits; /* digits to be checked */ + for (up=dn->lsu; ; up++) { + if (count<=DECDPUN) { + /* this is the last Unit (the msu) */ + if (*up!=powers[count-1]) break; /* not 100.. */ + /* here if have the 1000... case */ + sup=up; /* save msu pointer */ + *up=(Unit)powers[count]-1; /* here 100 in msu -> 999 */ + /* others all to all-nines, too */ + for (up=up-1; up>=dn->lsu; up--) *up=(Unit)powers[DECDPUN]-1; + dn->exponent--; /* and bump exponent */ + + /* iff the number was at the subnormal boundary (exponent=etiny) */ + /* then the exponent is now out of range, so it will in fact get */ + /* clamped to etiny and the final 9 dropped. */ + /* printf(">> emin=%d exp=%d sdig=%d\n", set->emin, */ + /* dn->exponent, set->digits); */ + if (dn->exponent+1==set->emin-set->digits+1) { + if (count==1 && dn->digits==1) *sup=0; /* here 9 -> 0[.9] */ + else { + *sup=(Unit)powers[count-1]-1; /* here 999.. in msu -> 99.. */ + dn->digits--; + } + dn->exponent++; + *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded; + } + return; /* done */ + } + + /* a full unit to check, with more to come */ + if (*up!=0) break; /* not still 0s */ + count-=DECDPUN; + } /* up */ + + } /* bump<0 */ + + /* Actual bump needed. Do it. */ + decUnitAddSub(dn->lsu, D2U(dn->digits), uarrone, 1, 0, dn->lsu, bump); + } /* decApplyRound */ + +#if DECSUBSET +/* ------------------------------------------------------------------ */ +/* decFinish -- finish processing a number */ +/* */ +/* dn is the number */ +/* set is the context */ +/* residue is the rounding accumulator (as in decApplyRound) */ +/* status is the accumulator */ +/* */ +/* This finishes off the current number by: */ +/* 1. If not extended: */ +/* a. Converting a zero result to clean '0' */ +/* b. Reducing positive exponents to 0, if would fit in digits */ +/* 2. Checking for overflow and subnormals (always) */ +/* Note this is just Finalize when no subset arithmetic. */ +/* All fields are updated as required. */ +/* ------------------------------------------------------------------ */ +static void decFinish(decNumber *dn, decContext *set, Int *residue, + uInt *status) { + if (!set->extended) { + if ISZERO(dn) { /* value is zero */ + dn->exponent=0; /* clean exponent .. */ + dn->bits=0; /* .. and sign */ + return; /* no error possible */ + } + if (dn->exponent>=0) { /* non-negative exponent */ + /* >0; reduce to integer if possible */ + if (set->digits >= (dn->exponent+dn->digits)) { + dn->digits=decShiftToMost(dn->lsu, dn->digits, dn->exponent); + dn->exponent=0; + } + } + } /* !extended */ + + decFinalize(dn, set, residue, status); + } /* decFinish */ +#endif + +/* ------------------------------------------------------------------ */ +/* decFinalize -- final check, clamp, and round of a number */ +/* */ +/* dn is the number */ +/* set is the context */ +/* residue is the rounding accumulator (as in decApplyRound) */ +/* status is the status accumulator */ +/* */ +/* This finishes off the current number by checking for subnormal */ +/* results, applying any pending rounding, checking for overflow, */ +/* and applying any clamping. */ +/* Underflow and overflow conditions are raised as appropriate. */ +/* All fields are updated as required. */ +/* ------------------------------------------------------------------ */ +static void decFinalize(decNumber *dn, decContext *set, Int *residue, + uInt *status) { + Int shift; /* shift needed if clamping */ + Int tinyexp=set->emin-dn->digits+1; /* precalculate subnormal boundary */ + + /* Must be careful, here, when checking the exponent as the */ + /* adjusted exponent could overflow 31 bits [because it may already */ + /* be up to twice the expected]. */ + + /* First test for subnormal. This must be done before any final */ + /* round as the result could be rounded to Nmin or 0. */ + if (dn->exponent<=tinyexp) { /* prefilter */ + Int comp; + decNumber nmin; + /* A very nasty case here is dn == Nmin and residue<0 */ + if (dn->exponent<tinyexp) { + /* Go handle subnormals; this will apply round if needed. */ + decSetSubnormal(dn, set, residue, status); + return; + } + /* Equals case: only subnormal if dn=Nmin and negative residue */ + decNumberZero(&nmin); + nmin.lsu[0]=1; + nmin.exponent=set->emin; + comp=decCompare(dn, &nmin, 1); /* (signless compare) */ + if (comp==BADINT) { /* oops */ + *status|=DEC_Insufficient_storage; /* abandon... */ + return; + } + if (*residue<0 && comp==0) { /* neg residue and dn==Nmin */ + decApplyRound(dn, set, *residue, status); /* might force down */ + decSetSubnormal(dn, set, residue, status); + return; + } + } + + /* now apply any pending round (this could raise overflow). */ + if (*residue!=0) decApplyRound(dn, set, *residue, status); + + /* Check for overflow [redundant in the 'rare' case] or clamp */ + if (dn->exponent<=set->emax-set->digits+1) return; /* neither needed */ + + + /* here when might have an overflow or clamp to do */ + if (dn->exponent>set->emax-dn->digits+1) { /* too big */ + decSetOverflow(dn, set, status); + return; + } + /* here when the result is normal but in clamp range */ + if (!set->clamp) return; + + /* here when need to apply the IEEE exponent clamp (fold-down) */ + shift=dn->exponent-(set->emax-set->digits+1); + + /* shift coefficient (if non-zero) */ + if (!ISZERO(dn)) { + dn->digits=decShiftToMost(dn->lsu, dn->digits, shift); + } + dn->exponent-=shift; /* adjust the exponent to match */ + *status|=DEC_Clamped; /* and record the dirty deed */ + return; + } /* decFinalize */ + +/* ------------------------------------------------------------------ */ +/* decSetOverflow -- set number to proper overflow value */ +/* */ +/* dn is the number (used for sign [only] and result) */ +/* set is the context [used for the rounding mode, etc.] */ +/* status contains the current status to be updated */ +/* */ +/* This sets the sign of a number and sets its value to either */ +/* Infinity or the maximum finite value, depending on the sign of */ +/* dn and the rounding mode, following IEEE 854 rules. */ +/* ------------------------------------------------------------------ */ +static void decSetOverflow(decNumber *dn, decContext *set, uInt *status) { + Flag needmax=0; /* result is maximum finite value */ + uByte sign=dn->bits&DECNEG; /* clean and save sign bit */ + + if (ISZERO(dn)) { /* zero does not overflow magnitude */ + Int emax=set->emax; /* limit value */ + if (set->clamp) emax-=set->digits-1; /* lower if clamping */ + if (dn->exponent>emax) { /* clamp required */ + dn->exponent=emax; + *status|=DEC_Clamped; + } + return; + } + + decNumberZero(dn); + switch (set->round) { + case DEC_ROUND_DOWN: { + needmax=1; /* never Infinity */ + break;} /* r-d */ + case DEC_ROUND_05UP: { + needmax=1; /* never Infinity */ + break;} /* r-05 */ + case DEC_ROUND_CEILING: { + if (sign) needmax=1; /* Infinity if non-negative */ + break;} /* r-c */ + case DEC_ROUND_FLOOR: { + if (!sign) needmax=1; /* Infinity if negative */ + break;} /* r-f */ + default: break; /* Infinity in all other cases */ + } + if (needmax) { + decSetMaxValue(dn, set); + dn->bits=sign; /* set sign */ + } + else dn->bits=sign|DECINF; /* Value is +/-Infinity */ + *status|=DEC_Overflow | DEC_Inexact | DEC_Rounded; + } /* decSetOverflow */ + +/* ------------------------------------------------------------------ */ +/* decSetMaxValue -- set number to +Nmax (maximum normal value) */ +/* */ +/* dn is the number to set */ +/* set is the context [used for digits and emax] */ +/* */ +/* This sets the number to the maximum positive value. */ +/* ------------------------------------------------------------------ */ +static void decSetMaxValue(decNumber *dn, decContext *set) { + Unit *up; /* work */ + Int count=set->digits; /* nines to add */ + dn->digits=count; + /* fill in all nines to set maximum value */ + for (up=dn->lsu; ; up++) { + if (count>DECDPUN) *up=DECDPUNMAX; /* unit full o'nines */ + else { /* this is the msu */ + *up=(Unit)(powers[count]-1); + break; + } + count-=DECDPUN; /* filled those digits */ + } /* up */ + dn->bits=0; /* + sign */ + dn->exponent=set->emax-set->digits+1; + } /* decSetMaxValue */ + +/* ------------------------------------------------------------------ */ +/* decSetSubnormal -- process value whose exponent is <Emin */ +/* */ +/* dn is the number (used as input as well as output; it may have */ +/* an allowed subnormal value, which may need to be rounded) */ +/* set is the context [used for the rounding mode] */ +/* residue is any pending residue */ +/* status contains the current status to be updated */ +/* */ +/* If subset mode, set result to zero and set Underflow flags. */ +/* */ +/* Value may be zero with a low exponent; this does not set Subnormal */ +/* but the exponent will be clamped to Etiny. */ +/* */ +/* Otherwise ensure exponent is not out of range, and round as */ +/* necessary. Underflow is set if the result is Inexact. */ +/* ------------------------------------------------------------------ */ +static void decSetSubnormal(decNumber *dn, decContext *set, Int *residue, + uInt *status) { + Int dnexp; /* saves original exponent */ + decContext workset; /* work */ + Int etiny, adjust; /* .. */ + + #if DECSUBSET + /* simple set to zero and 'hard underflow' for subset */ + if (!set->extended) { + decNumberZero(dn); + /* always full overflow */ + *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded; + return; + } + #endif + + /* Full arithmetic -- allow subnormals, rounded to minimum exponent */ + /* (Etiny) if needed */ + etiny=set->emin-(set->digits-1); /* smallest allowed exponent */ + + if ISZERO(dn) { /* value is zero */ + /* residue can never be non-zero here */ + #if DECCHECK + if (*residue!=0) { + printf("++ Subnormal 0 residue %ld\n", (LI)*residue); + *status|=DEC_Invalid_operation; + } + #endif + if (dn->exponent<etiny) { /* clamp required */ + dn->exponent=etiny; + *status|=DEC_Clamped; + } + return; + } + + *status|=DEC_Subnormal; /* have a non-zero subnormal */ + adjust=etiny-dn->exponent; /* calculate digits to remove */ + if (adjust<=0) { /* not out of range; unrounded */ + /* residue can never be non-zero here, except in the Nmin-residue */ + /* case (which is a subnormal result), so can take fast-path here */ + /* it may already be inexact (from setting the coefficient) */ + if (*status&DEC_Inexact) *status|=DEC_Underflow; + return; + } + + /* adjust>0, so need to rescale the result so exponent becomes Etiny */ + /* [this code is similar to that in rescale] */ + dnexp=dn->exponent; /* save exponent */ + workset=*set; /* clone rounding, etc. */ + workset.digits=dn->digits-adjust; /* set requested length */ + workset.emin-=adjust; /* and adjust emin to match */ + /* [note that the latter can be <1, here, similar to Rescale case] */ + decSetCoeff(dn, &workset, dn->lsu, dn->digits, residue, status); + decApplyRound(dn, &workset, *residue, status); + + /* Use 754R/854 default rule: Underflow is set iff Inexact */ + /* [independent of whether trapped] */ + if (*status&DEC_Inexact) *status|=DEC_Underflow; + + /* if rounded up a 999s case, exponent will be off by one; adjust */ + /* back if so [it will fit, because it was shortened earlier] */ + if (dn->exponent>etiny) { + dn->digits=decShiftToMost(dn->lsu, dn->digits, 1); + dn->exponent--; /* (re)adjust the exponent. */ + } + + /* if rounded to zero, it is by definition clamped... */ + if (ISZERO(dn)) *status|=DEC_Clamped; + } /* decSetSubnormal */ + +/* ------------------------------------------------------------------ */ +/* decCheckMath - check entry conditions for a math function */ +/* */ +/* This checks the context and the operand */ +/* */ +/* rhs is the operand to check */ +/* set is the context to check */ +/* status is unchanged if both are good */ +/* */ +/* returns non-zero if status is changed, 0 otherwise */ +/* */ +/* Restrictions enforced: */ +/* */ +/* digits, emax, and -emin in the context must be less than */ +/* DEC_MAX_MATH (999999), and A must be within these bounds if */ +/* non-zero. Invalid_operation is set in the status if a */ +/* restriction is violated. */ +/* ------------------------------------------------------------------ */ +static uInt decCheckMath(const decNumber *rhs, decContext *set, + uInt *status) { + uInt save=*status; /* record */ + if (set->digits>DEC_MAX_MATH + || set->emax>DEC_MAX_MATH + || -set->emin>DEC_MAX_MATH) *status|=DEC_Invalid_context; + else if ((rhs->digits>DEC_MAX_MATH + || rhs->exponent+rhs->digits>DEC_MAX_MATH+1 + || rhs->exponent+rhs->digits<2*(1-DEC_MAX_MATH)) + && !ISZERO(rhs)) *status|=DEC_Invalid_operation; + return (*status!=save); + } /* decCheckMath */ + +/* ------------------------------------------------------------------ */ +/* decGetInt -- get integer from a number */ +/* */ +/* dn is the number [which will not be altered] */ +/* */ +/* returns one of: */ +/* BADINT if there is a non-zero fraction */ +/* the converted integer */ +/* BIGEVEN if the integer is even and magnitude > 2*10**9 */ +/* BIGODD if the integer is odd and magnitude > 2*10**9 */ +/* */ +/* This checks and gets a whole number from the input decNumber. */ +/* The sign can be determined from dn by the caller when BIGEVEN or */ +/* BIGODD is returned. */ +/* ------------------------------------------------------------------ */ +static Int decGetInt(const decNumber *dn) { + Int theInt; /* result accumulator */ + const Unit *up; /* work */ + Int got; /* digits (real or not) processed */ + Int ilength=dn->digits+dn->exponent; /* integral length */ + Flag neg=decNumberIsNegative(dn); /* 1 if -ve */ + + /* The number must be an integer that fits in 10 digits */ + /* Assert, here, that 10 is enough for any rescale Etiny */ + #if DEC_MAX_EMAX > 999999999 + #error GetInt may need updating [for Emax] + #endif + #if DEC_MIN_EMIN < -999999999 + #error GetInt may need updating [for Emin] + #endif + if (ISZERO(dn)) return 0; /* zeros are OK, with any exponent */ + + up=dn->lsu; /* ready for lsu */ + theInt=0; /* ready to accumulate */ + if (dn->exponent>=0) { /* relatively easy */ + /* no fractional part [usual]; allow for positive exponent */ + got=dn->exponent; + } + else { /* -ve exponent; some fractional part to check and discard */ + Int count=-dn->exponent; /* digits to discard */ + /* spin up whole units until reach the Unit with the unit digit */ + for (; count>=DECDPUN; up++) { + if (*up!=0) return BADINT; /* non-zero Unit to discard */ + count-=DECDPUN; + } + if (count==0) got=0; /* [a multiple of DECDPUN] */ + else { /* [not multiple of DECDPUN] */ + Int rem; /* work */ + /* slice off fraction digits and check for non-zero */ + #if DECDPUN<=4 + theInt=QUOT10(*up, count); + rem=*up-theInt*powers[count]; + #else + rem=*up%powers[count]; /* slice off discards */ + theInt=*up/powers[count]; + #endif + if (rem!=0) return BADINT; /* non-zero fraction */ + /* it looks good */ + got=DECDPUN-count; /* number of digits so far */ + up++; /* ready for next */ + } + } + /* now it's known there's no fractional part */ + + /* tricky code now, to accumulate up to 9.3 digits */ + if (got==0) {theInt=*up; got+=DECDPUN; up++;} /* ensure lsu is there */ + + if (ilength<11) { + Int save=theInt; + /* collect any remaining unit(s) */ + for (; got<ilength; up++) { + theInt+=*up*powers[got]; + got+=DECDPUN; + } + if (ilength==10) { /* need to check for wrap */ + if (theInt/(Int)powers[got-DECDPUN]!=(Int)*(up-1)) ilength=11; + /* [that test also disallows the BADINT result case] */ + else if (neg && theInt>1999999997) ilength=11; + else if (!neg && theInt>999999999) ilength=11; + if (ilength==11) theInt=save; /* restore correct low bit */ + } + } + + if (ilength>10) { /* too big */ + if (theInt&1) return BIGODD; /* bottom bit 1 */ + return BIGEVEN; /* bottom bit 0 */ + } + + if (neg) theInt=-theInt; /* apply sign */ + return theInt; + } /* decGetInt */ + +/* ------------------------------------------------------------------ */ +/* decDecap -- decapitate the coefficient of a number */ +/* */ +/* dn is the number to be decapitated */ +/* drop is the number of digits to be removed from the left of dn; */ +/* this must be <= dn->digits (if equal, the coefficient is */ +/* set to 0) */ +/* */ +/* Returns dn; dn->digits will be <= the initial digits less drop */ +/* (after removing drop digits there may be leading zero digits */ +/* which will also be removed). Only dn->lsu and dn->digits change. */ +/* ------------------------------------------------------------------ */ +static decNumber *decDecap(decNumber *dn, Int drop) { + Unit *msu; /* -> target cut point */ + Int cut; /* work */ + if (drop>=dn->digits) { /* losing the whole thing */ + #if DECCHECK + if (drop>dn->digits) + printf("decDecap called with drop>digits [%ld>%ld]\n", + (LI)drop, (LI)dn->digits); + #endif + dn->lsu[0]=0; + dn->digits=1; + return dn; + } + msu=dn->lsu+D2U(dn->digits-drop)-1; /* -> likely msu */ + cut=MSUDIGITS(dn->digits-drop); /* digits to be in use in msu */ + if (cut!=DECDPUN) *msu%=powers[cut]; /* clear left digits */ + /* that may have left leading zero digits, so do a proper count... */ + dn->digits=decGetDigits(dn->lsu, msu-dn->lsu+1); + return dn; + } /* decDecap */ + +/* ------------------------------------------------------------------ */ +/* decBiStr -- compare string with pairwise options */ +/* */ +/* targ is the string to compare */ +/* str1 is one of the strings to compare against (length may be 0) */ +/* str2 is the other; it must be the same length as str1 */ +/* */ +/* returns 1 if strings compare equal, (that is, it is the same */ +/* length as str1 and str2, and each character of targ is in either */ +/* str1 or str2 in the corresponding position), or 0 otherwise */ +/* */ +/* This is used for generic caseless compare, including the awkward */ +/* case of the Turkish dotted and dotless Is. Use as (for example): */ +/* if (decBiStr(test, "mike", "MIKE")) ... */ +/* ------------------------------------------------------------------ */ +static Flag decBiStr(const char *targ, const char *str1, const char *str2) { + for (;;targ++, str1++, str2++) { + if (*targ!=*str1 && *targ!=*str2) return 0; + /* *targ has a match in one (or both, if terminator) */ + if (*targ=='\0') break; + } /* forever */ + return 1; + } /* decBiStr */ + +/* ------------------------------------------------------------------ */ +/* decNaNs -- handle NaN operand or operands */ +/* */ +/* res is the result number */ +/* lhs is the first operand */ +/* rhs is the second operand, or NULL if none */ +/* context is used to limit payload length */ +/* status contains the current status */ +/* returns res in case convenient */ +/* */ +/* Called when one or both operands is a NaN, and propagates the */ +/* appropriate result to res. When an sNaN is found, it is changed */ +/* to a qNaN and Invalid operation is set. */ +/* ------------------------------------------------------------------ */ +static decNumber * decNaNs(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set, + uInt *status) { + /* This decision tree ends up with LHS being the source pointer, */ + /* and status updated if need be */ + if (lhs->bits & DECSNAN) + *status|=DEC_Invalid_operation | DEC_sNaN; + else if (rhs==NULL); + else if (rhs->bits & DECSNAN) { + lhs=rhs; + *status|=DEC_Invalid_operation | DEC_sNaN; + } + else if (lhs->bits & DECNAN); + else lhs=rhs; + + /* propagate the payload */ + if (lhs->digits<=set->digits) decNumberCopy(res, lhs); /* easy */ + else { /* too long */ + const Unit *ul; + Unit *ur, *uresp1; + /* copy safe number of units, then decapitate */ + res->bits=lhs->bits; /* need sign etc. */ + uresp1=res->lsu+D2U(set->digits); + for (ur=res->lsu, ul=lhs->lsu; ur<uresp1; ur++, ul++) *ur=*ul; + res->digits=D2U(set->digits)*DECDPUN; + /* maybe still too long */ + if (res->digits>set->digits) decDecap(res, res->digits-set->digits); + } + + res->bits&=~DECSNAN; /* convert any sNaN to NaN, while */ + res->bits|=DECNAN; /* .. preserving sign */ + res->exponent=0; /* clean exponent */ + /* [coefficient was copied/decapitated] */ + return res; + } /* decNaNs */ + +/* ------------------------------------------------------------------ */ +/* decStatus -- apply non-zero status */ +/* */ +/* dn is the number to set if error */ +/* status contains the current status (not yet in context) */ +/* set is the context */ +/* */ +/* If the status is an error status, the number is set to a NaN, */ +/* unless the error was an overflow, divide-by-zero, or underflow, */ +/* in which case the number will have already been set. */ +/* */ +/* The context status is then updated with the new status. Note that */ +/* this may raise a signal, so control may never return from this */ +/* routine (hence resources must be recovered before it is called). */ +/* ------------------------------------------------------------------ */ +static void decStatus(decNumber *dn, uInt status, decContext *set) { + if (status & DEC_NaNs) { /* error status -> NaN */ + /* if cause was an sNaN, clear and propagate [NaN is already set up] */ + if (status & DEC_sNaN) status&=~DEC_sNaN; + else { + decNumberZero(dn); /* other error: clean throughout */ + dn->bits=DECNAN; /* and make a quiet NaN */ + } + } + decContextSetStatus(set, status); /* [may not return] */ + return; + } /* decStatus */ + +/* ------------------------------------------------------------------ */ +/* decGetDigits -- count digits in a Units array */ +/* */ +/* uar is the Unit array holding the number (this is often an */ +/* accumulator of some sort) */ +/* len is the length of the array in units [>=1] */ +/* */ +/* returns the number of (significant) digits in the array */ +/* */ +/* All leading zeros are excluded, except the last if the array has */ +/* only zero Units. */ +/* ------------------------------------------------------------------ */ +/* This may be called twice during some operations. */ +static Int decGetDigits(Unit *uar, Int len) { + Unit *up=uar+(len-1); /* -> msu */ + Int digits=(len-1)*DECDPUN+1; /* possible digits excluding msu */ + #if DECDPUN>4 + uInt const *pow; /* work */ + #endif + /* (at least 1 in final msu) */ + #if DECCHECK + if (len<1) printf("decGetDigits called with len<1 [%ld]\n", (LI)len); + #endif + + for (; up>=uar; up--) { + if (*up==0) { /* unit is all 0s */ + if (digits==1) break; /* a zero has one digit */ + digits-=DECDPUN; /* adjust for 0 unit */ + continue;} + /* found the first (most significant) non-zero Unit */ + #if DECDPUN>1 /* not done yet */ + if (*up<10) break; /* is 1-9 */ + digits++; + #if DECDPUN>2 /* not done yet */ + if (*up<100) break; /* is 10-99 */ + digits++; + #if DECDPUN>3 /* not done yet */ + if (*up<1000) break; /* is 100-999 */ + digits++; + #if DECDPUN>4 /* count the rest ... */ + for (pow=&powers[4]; *up>=*pow; pow++) digits++; + #endif + #endif + #endif + #endif + break; + } /* up */ + return digits; + } /* decGetDigits */ + +#if DECTRACE | DECCHECK +/* ------------------------------------------------------------------ */ +/* decNumberShow -- display a number [debug aid] */ +/* dn is the number to show */ +/* */ +/* Shows: sign, exponent, coefficient (msu first), digits */ +/* or: sign, special-value */ +/* ------------------------------------------------------------------ */ +/* this is public so other modules can use it */ +void decNumberShow(const decNumber *dn) { + const Unit *up; /* work */ + uInt u, d; /* .. */ + Int cut; /* .. */ + char isign='+'; /* main sign */ + if (dn==NULL) { + printf("NULL\n"); + return;} + if (decNumberIsNegative(dn)) isign='-'; + printf(" >> %c ", isign); + if (dn->bits&DECSPECIAL) { /* Is a special value */ + if (decNumberIsInfinite(dn)) printf("Infinity"); + else { /* a NaN */ + if (dn->bits&DECSNAN) printf("sNaN"); /* signalling NaN */ + else printf("NaN"); + } + /* if coefficient and exponent are 0, no more to do */ + if (dn->exponent==0 && dn->digits==1 && *dn->lsu==0) { + printf("\n"); + return;} + /* drop through to report other information */ + printf(" "); + } + + /* now carefully display the coefficient */ + up=dn->lsu+D2U(dn->digits)-1; /* msu */ + printf("%ld", (LI)*up); + for (up=up-1; up>=dn->lsu; up--) { + u=*up; + printf(":"); + for (cut=DECDPUN-1; cut>=0; cut--) { + d=u/powers[cut]; + u-=d*powers[cut]; + printf("%ld", (LI)d); + } /* cut */ + } /* up */ + if (dn->exponent!=0) { + char esign='+'; + if (dn->exponent<0) esign='-'; + printf(" E%c%ld", esign, (LI)abs(dn->exponent)); + } + printf(" [%ld]\n", (LI)dn->digits); + } /* decNumberShow */ +#endif + +#if DECTRACE || DECCHECK +/* ------------------------------------------------------------------ */ +/* decDumpAr -- display a unit array [debug/check aid] */ +/* name is a single-character tag name */ +/* ar is the array to display */ +/* len is the length of the array in Units */ +/* ------------------------------------------------------------------ */ +static void decDumpAr(char name, const Unit *ar, Int len) { + Int i; + const char *spec; + #if DECDPUN==9 + spec="%09d "; + #elif DECDPUN==8 + spec="%08d "; + #elif DECDPUN==7 + spec="%07d "; + #elif DECDPUN==6 + spec="%06d "; + #elif DECDPUN==5 + spec="%05d "; + #elif DECDPUN==4 + spec="%04d "; + #elif DECDPUN==3 + spec="%03d "; + #elif DECDPUN==2 + spec="%02d "; + #else + spec="%d "; + #endif + printf(" :%c: ", name); + for (i=len-1; i>=0; i--) { + if (i==len-1) printf("%ld ", (LI)ar[i]); + else printf(spec, ar[i]); + } + printf("\n"); + return;} +#endif + +#if DECCHECK +/* ------------------------------------------------------------------ */ +/* decCheckOperands -- check operand(s) to a routine */ +/* res is the result structure (not checked; it will be set to */ +/* quiet NaN if error found (and it is not NULL)) */ +/* lhs is the first operand (may be DECUNRESU) */ +/* rhs is the second (may be DECUNUSED) */ +/* set is the context (may be DECUNCONT) */ +/* returns 0 if both operands, and the context are clean, or 1 */ +/* otherwise (in which case the context will show an error, */ +/* unless NULL). Note that res is not cleaned; caller should */ +/* handle this so res=NULL case is safe. */ +/* The caller is expected to abandon immediately if 1 is returned. */ +/* ------------------------------------------------------------------ */ +static Flag decCheckOperands(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + Flag bad=0; + if (set==NULL) { /* oops; hopeless */ + #if DECTRACE || DECVERB + printf("Reference to context is NULL.\n"); + #endif + bad=1; + return 1;} + else if (set!=DECUNCONT + && (set->digits<1 || set->round>=DEC_ROUND_MAX)) { + bad=1; + #if DECTRACE || DECVERB + printf("Bad context [digits=%ld round=%ld].\n", + (LI)set->digits, (LI)set->round); + #endif + } + else { + if (res==NULL) { + bad=1; + #if DECTRACE + /* this one not DECVERB as standard tests include NULL */ + printf("Reference to result is NULL.\n"); + #endif + } + if (!bad && lhs!=DECUNUSED) bad=(decCheckNumber(lhs)); + if (!bad && rhs!=DECUNUSED) bad=(decCheckNumber(rhs)); + } + if (bad) { + if (set!=DECUNCONT) decContextSetStatus(set, DEC_Invalid_operation); + if (res!=DECUNRESU && res!=NULL) { + decNumberZero(res); + res->bits=DECNAN; /* qNaN */ + } + } + return bad; + } /* decCheckOperands */ + +/* ------------------------------------------------------------------ */ +/* decCheckNumber -- check a number */ +/* dn is the number to check */ +/* returns 0 if the number is clean, or 1 otherwise */ +/* */ +/* The number is considered valid if it could be a result from some */ +/* operation in some valid context. */ +/* ------------------------------------------------------------------ */ +static Flag decCheckNumber(const decNumber *dn) { + const Unit *up; /* work */ + uInt maxuint; /* .. */ + Int ae, d, digits; /* .. */ + Int emin, emax; /* .. */ + + if (dn==NULL) { /* hopeless */ + #if DECTRACE + /* this one not DECVERB as standard tests include NULL */ + printf("Reference to decNumber is NULL.\n"); + #endif + return 1;} + + /* check special values */ + if (dn->bits & DECSPECIAL) { + if (dn->exponent!=0) { + #if DECTRACE || DECVERB + printf("Exponent %ld (not 0) for a special value [%02x].\n", + (LI)dn->exponent, dn->bits); + #endif + return 1;} + + /* 2003.09.08: NaNs may now have coefficients, so next tests Inf only */ + if (decNumberIsInfinite(dn)) { + if (dn->digits!=1) { + #if DECTRACE || DECVERB + printf("Digits %ld (not 1) for an infinity.\n", (LI)dn->digits); + #endif + return 1;} + if (*dn->lsu!=0) { + #if DECTRACE || DECVERB + printf("LSU %ld (not 0) for an infinity.\n", (LI)*dn->lsu); + #endif + decDumpAr('I', dn->lsu, D2U(dn->digits)); + return 1;} + } /* Inf */ + /* 2002.12.26: negative NaNs can now appear through proposed IEEE */ + /* concrete formats (decimal64, etc.). */ + return 0; + } + + /* check the coefficient */ + if (dn->digits<1 || dn->digits>DECNUMMAXP) { + #if DECTRACE || DECVERB + printf("Digits %ld in number.\n", (LI)dn->digits); + #endif + return 1;} + + d=dn->digits; + + for (up=dn->lsu; d>0; up++) { + if (d>DECDPUN) maxuint=DECDPUNMAX; + else { /* reached the msu */ + maxuint=powers[d]-1; + if (dn->digits>1 && *up<powers[d-1]) { + #if DECTRACE || DECVERB + printf("Leading 0 in number.\n"); + decNumberShow(dn); + #endif + return 1;} + } + if (*up>maxuint) { + #if DECTRACE || DECVERB + printf("Bad Unit [%08lx] in %ld-digit number at offset %ld [maxuint %ld].\n", + (LI)*up, (LI)dn->digits, (LI)(up-dn->lsu), (LI)maxuint); + #endif + return 1;} + d-=DECDPUN; + } + + /* check the exponent. Note that input operands can have exponents */ + /* which are out of the set->emin/set->emax and set->digits range */ + /* (just as they can have more digits than set->digits). */ + ae=dn->exponent+dn->digits-1; /* adjusted exponent */ + emax=DECNUMMAXE; + emin=DECNUMMINE; + digits=DECNUMMAXP; + if (ae<emin-(digits-1)) { + #if DECTRACE || DECVERB + printf("Adjusted exponent underflow [%ld].\n", (LI)ae); + decNumberShow(dn); + #endif + return 1;} + if (ae>+emax) { + #if DECTRACE || DECVERB + printf("Adjusted exponent overflow [%ld].\n", (LI)ae); + decNumberShow(dn); + #endif + return 1;} + + return 0; /* it's OK */ + } /* decCheckNumber */ + +/* ------------------------------------------------------------------ */ +/* decCheckInexact -- check a normal finite inexact result has digits */ +/* dn is the number to check */ +/* set is the context (for status and precision) */ +/* sets Invalid operation, etc., if some digits are missing */ +/* [this check is not made for DECSUBSET compilation or when */ +/* subnormal is not set] */ +/* ------------------------------------------------------------------ */ +static void decCheckInexact(const decNumber *dn, decContext *set) { + #if !DECSUBSET && DECEXTFLAG + if ((set->status & (DEC_Inexact|DEC_Subnormal))==DEC_Inexact + && (set->digits!=dn->digits) && !(dn->bits & DECSPECIAL)) { + #if DECTRACE || DECVERB + printf("Insufficient digits [%ld] on normal Inexact result.\n", + (LI)dn->digits); + decNumberShow(dn); + #endif + decContextSetStatus(set, DEC_Invalid_operation); + } + #else + /* next is a noop for quiet compiler */ + if (dn!=NULL && dn->digits==0) set->status|=DEC_Invalid_operation; + #endif + return; + } /* decCheckInexact */ +#endif + +#if DECALLOC +#undef malloc +#undef free +/* ------------------------------------------------------------------ */ +/* decMalloc -- accountable allocation routine */ +/* n is the number of bytes to allocate */ +/* */ +/* Semantics is the same as the stdlib malloc routine, but bytes */ +/* allocated are accounted for globally, and corruption fences are */ +/* added before and after the 'actual' storage. */ +/* ------------------------------------------------------------------ */ +/* This routine allocates storage with an extra twelve bytes; 8 are */ +/* at the start and hold: */ +/* 0-3 the original length requested */ +/* 4-7 buffer corruption detection fence (DECFENCE, x4) */ +/* The 4 bytes at the end also hold a corruption fence (DECFENCE, x4) */ +/* ------------------------------------------------------------------ */ +static void *decMalloc(size_t n) { + uInt size=n+12; /* true size */ + void *alloc; /* -> allocated storage */ + uInt *j; /* work */ + uByte *b, *b0; /* .. */ + + alloc=malloc(size); /* -> allocated storage */ + if (alloc==NULL) return NULL; /* out of strorage */ + b0=(uByte *)alloc; /* as bytes */ + decAllocBytes+=n; /* account for storage */ + j=(uInt *)alloc; /* -> first four bytes */ + *j=n; /* save n */ + /* printf(" alloc ++ dAB: %ld (%d)\n", decAllocBytes, n); */ + for (b=b0+4; b<b0+8; b++) *b=DECFENCE; + for (b=b0+n+8; b<b0+n+12; b++) *b=DECFENCE; + return b0+8; /* -> play area */ + } /* decMalloc */ + +/* ------------------------------------------------------------------ */ +/* decFree -- accountable free routine */ +/* alloc is the storage to free */ +/* */ +/* Semantics is the same as the stdlib malloc routine, except that */ +/* the global storage accounting is updated and the fences are */ +/* checked to ensure that no routine has written 'out of bounds'. */ +/* ------------------------------------------------------------------ */ +/* This routine first checks that the fences have not been corrupted. */ +/* It then frees the storage using the 'truw' storage address (that */ +/* is, offset by 8). */ +/* ------------------------------------------------------------------ */ +static void decFree(void *alloc) { + uInt *j, n; /* pointer, original length */ + uByte *b, *b0; /* work */ + + if (alloc==NULL) return; /* allowed; it's a nop */ + b0=(uByte *)alloc; /* as bytes */ + b0-=8; /* -> true start of storage */ + j=(uInt *)b0; /* -> first four bytes */ + n=*j; /* lift */ + for (b=b0+4; b<b0+8; b++) if (*b!=DECFENCE) + printf("=== Corrupt byte [%02x] at offset %d from %ld ===\n", *b, + b-b0-8, (Int)b0); + for (b=b0+n+8; b<b0+n+12; b++) if (*b!=DECFENCE) + printf("=== Corrupt byte [%02x] at offset +%d from %ld, n=%ld ===\n", *b, + b-b0-8, (Int)b0, n); + free(b0); /* drop the storage */ + decAllocBytes-=n; /* account for storage */ + /* printf(" free -- dAB: %d (%d)\n", decAllocBytes, -n); */ + } /* decFree */ +#define malloc(a) decMalloc(a) +#define free(a) decFree(a) +#endif diff --git a/libdecnumber/dpd/decimal128.c b/libdecnumber/dpd/decimal128.c new file mode 100644 index 0000000000..54191aab5c --- /dev/null +++ b/libdecnumber/dpd/decimal128.c @@ -0,0 +1,566 @@ +/* Decimal 128-bit format module for the decNumber C Library. + Copyright (C) 2005, 2007 Free Software Foundation, Inc. + Contributed by IBM Corporation. Author Mike Cowlishaw. + + This file is part of GCC. + + GCC is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation; either version 2, or (at your option) any later + version. + + In addition to the permissions in the GNU General Public License, + the Free Software Foundation gives you unlimited permission to link + the compiled version of this file into combinations with other + programs, and to distribute those combinations without any + restriction coming from the use of this file. (The General Public + License restrictions do apply in other respects; for example, they + cover modification of the file, and distribution when not linked + into a combine executable.) + + GCC is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or + FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License + along with GCC; see the file COPYING. If not, write to the Free + Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA + 02110-1301, USA. */ + +/* ------------------------------------------------------------------ */ +/* Decimal 128-bit format module */ +/* ------------------------------------------------------------------ */ +/* This module comprises the routines for decimal128 format numbers. */ +/* Conversions are supplied to and from decNumber and String. */ +/* */ +/* This is used when decNumber provides operations, either for all */ +/* operations or as a proxy between decNumber and decSingle. */ +/* */ +/* Error handling is the same as decNumber (qv.). */ +/* ------------------------------------------------------------------ */ +#include <string.h> /* [for memset/memcpy] */ +#include <stdio.h> /* [for printf] */ + +#include "dconfig.h" /* GCC definitions */ +#define DECNUMDIGITS 34 /* make decNumbers with space for 34 */ +#include "decNumber.h" /* base number library */ +#include "decNumberLocal.h" /* decNumber local types, etc. */ +#include "decimal128.h" /* our primary include */ + +/* Utility routines and tables [in decimal64.c] */ +extern const uInt COMBEXP[32], COMBMSD[32]; +extern const uShort DPD2BIN[1024]; +extern const uShort BIN2DPD[1000]; /* [not used] */ +extern const uByte BIN2CHAR[4001]; + +extern void decDigitsFromDPD(decNumber *, const uInt *, Int); +extern void decDigitsToDPD(const decNumber *, uInt *, Int); + +#if DECTRACE || DECCHECK +void decimal128Show(const decimal128 *); /* for debug */ +extern void decNumberShow(const decNumber *); /* .. */ +#endif + +/* Useful macro */ +/* Clear a structure (e.g., a decNumber) */ +#define DEC_clear(d) memset(d, 0, sizeof(*d)) + +/* ------------------------------------------------------------------ */ +/* decimal128FromNumber -- convert decNumber to decimal128 */ +/* */ +/* ds is the target decimal128 */ +/* dn is the source number (assumed valid) */ +/* set is the context, used only for reporting errors */ +/* */ +/* The set argument is used only for status reporting and for the */ +/* rounding mode (used if the coefficient is more than DECIMAL128_Pmax*/ +/* digits or an overflow is detected). If the exponent is out of the */ +/* valid range then Overflow or Underflow will be raised. */ +/* After Underflow a subnormal result is possible. */ +/* */ +/* DEC_Clamped is set if the number has to be 'folded down' to fit, */ +/* by reducing its exponent and multiplying the coefficient by a */ +/* power of ten, or if the exponent on a zero had to be clamped. */ +/* ------------------------------------------------------------------ */ +decimal128 * decimal128FromNumber(decimal128 *d128, const decNumber *dn, + decContext *set) { + uInt status=0; /* status accumulator */ + Int ae; /* adjusted exponent */ + decNumber dw; /* work */ + decContext dc; /* .. */ + uInt *pu; /* .. */ + uInt comb, exp; /* .. */ + uInt targar[4]={0,0,0,0}; /* target 128-bit */ + #define targhi targar[3] /* name the word with the sign */ + #define targmh targar[2] /* name the words */ + #define targml targar[1] /* .. */ + #define targlo targar[0] /* .. */ + + /* If the number has too many digits, or the exponent could be */ + /* out of range then reduce the number under the appropriate */ + /* constraints. This could push the number to Infinity or zero, */ + /* so this check and rounding must be done before generating the */ + /* decimal128] */ + ae=dn->exponent+dn->digits-1; /* [0 if special] */ + if (dn->digits>DECIMAL128_Pmax /* too many digits */ + || ae>DECIMAL128_Emax /* likely overflow */ + || ae<DECIMAL128_Emin) { /* likely underflow */ + decContextDefault(&dc, DEC_INIT_DECIMAL128); /* [no traps] */ + dc.round=set->round; /* use supplied rounding */ + decNumberPlus(&dw, dn, &dc); /* (round and check) */ + /* [this changes -0 to 0, so enforce the sign...] */ + dw.bits|=dn->bits&DECNEG; + status=dc.status; /* save status */ + dn=&dw; /* use the work number */ + } /* maybe out of range */ + + if (dn->bits&DECSPECIAL) { /* a special value */ + if (dn->bits&DECINF) targhi=DECIMAL_Inf<<24; + else { /* sNaN or qNaN */ + if ((*dn->lsu!=0 || dn->digits>1) /* non-zero coefficient */ + && (dn->digits<DECIMAL128_Pmax)) { /* coefficient fits */ + decDigitsToDPD(dn, targar, 0); + } + if (dn->bits&DECNAN) targhi|=DECIMAL_NaN<<24; + else targhi|=DECIMAL_sNaN<<24; + } /* a NaN */ + } /* special */ + + else { /* is finite */ + if (decNumberIsZero(dn)) { /* is a zero */ + /* set and clamp exponent */ + if (dn->exponent<-DECIMAL128_Bias) { + exp=0; /* low clamp */ + status|=DEC_Clamped; + } + else { + exp=dn->exponent+DECIMAL128_Bias; /* bias exponent */ + if (exp>DECIMAL128_Ehigh) { /* top clamp */ + exp=DECIMAL128_Ehigh; + status|=DEC_Clamped; + } + } + comb=(exp>>9) & 0x18; /* msd=0, exp top 2 bits .. */ + } + else { /* non-zero finite number */ + uInt msd; /* work */ + Int pad=0; /* coefficient pad digits */ + + /* the dn is known to fit, but it may need to be padded */ + exp=(uInt)(dn->exponent+DECIMAL128_Bias); /* bias exponent */ + if (exp>DECIMAL128_Ehigh) { /* fold-down case */ + pad=exp-DECIMAL128_Ehigh; + exp=DECIMAL128_Ehigh; /* [to maximum] */ + status|=DEC_Clamped; + } + + /* [fastpath for common case is not a win, here] */ + decDigitsToDPD(dn, targar, pad); + /* save and clear the top digit */ + msd=targhi>>14; + targhi&=0x00003fff; + + /* create the combination field */ + if (msd>=8) comb=0x18 | ((exp>>11) & 0x06) | (msd & 0x01); + else comb=((exp>>9) & 0x18) | msd; + } + targhi|=comb<<26; /* add combination field .. */ + targhi|=(exp&0xfff)<<14; /* .. and exponent continuation */ + } /* finite */ + + if (dn->bits&DECNEG) targhi|=0x80000000; /* add sign bit */ + + /* now write to storage; this is endian */ + pu=(uInt *)d128->bytes; /* overlay */ + if (DECLITEND) { + pu[0]=targlo; /* directly store the low int */ + pu[1]=targml; /* then the mid-low */ + pu[2]=targmh; /* then the mid-high */ + pu[3]=targhi; /* then the high int */ + } + else { + pu[0]=targhi; /* directly store the high int */ + pu[1]=targmh; /* then the mid-high */ + pu[2]=targml; /* then the mid-low */ + pu[3]=targlo; /* then the low int */ + } + + if (status!=0) decContextSetStatus(set, status); /* pass on status */ + /* decimal128Show(d128); */ + return d128; + } /* decimal128FromNumber */ + +/* ------------------------------------------------------------------ */ +/* decimal128ToNumber -- convert decimal128 to decNumber */ +/* d128 is the source decimal128 */ +/* dn is the target number, with appropriate space */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +decNumber * decimal128ToNumber(const decimal128 *d128, decNumber *dn) { + uInt msd; /* coefficient MSD */ + uInt exp; /* exponent top two bits */ + uInt comb; /* combination field */ + const uInt *pu; /* work */ + Int need; /* .. */ + uInt sourar[4]; /* source 128-bit */ + #define sourhi sourar[3] /* name the word with the sign */ + #define sourmh sourar[2] /* and the mid-high word */ + #define sourml sourar[1] /* and the mod-low word */ + #define sourlo sourar[0] /* and the lowest word */ + + /* load source from storage; this is endian */ + pu=(const uInt *)d128->bytes; /* overlay */ + if (DECLITEND) { + sourlo=pu[0]; /* directly load the low int */ + sourml=pu[1]; /* then the mid-low */ + sourmh=pu[2]; /* then the mid-high */ + sourhi=pu[3]; /* then the high int */ + } + else { + sourhi=pu[0]; /* directly load the high int */ + sourmh=pu[1]; /* then the mid-high */ + sourml=pu[2]; /* then the mid-low */ + sourlo=pu[3]; /* then the low int */ + } + + comb=(sourhi>>26)&0x1f; /* combination field */ + + decNumberZero(dn); /* clean number */ + if (sourhi&0x80000000) dn->bits=DECNEG; /* set sign if negative */ + + msd=COMBMSD[comb]; /* decode the combination field */ + exp=COMBEXP[comb]; /* .. */ + + if (exp==3) { /* is a special */ + if (msd==0) { + dn->bits|=DECINF; + return dn; /* no coefficient needed */ + } + else if (sourhi&0x02000000) dn->bits|=DECSNAN; + else dn->bits|=DECNAN; + msd=0; /* no top digit */ + } + else { /* is a finite number */ + dn->exponent=(exp<<12)+((sourhi>>14)&0xfff)-DECIMAL128_Bias; /* unbiased */ + } + + /* get the coefficient */ + sourhi&=0x00003fff; /* clean coefficient continuation */ + if (msd) { /* non-zero msd */ + sourhi|=msd<<14; /* prefix to coefficient */ + need=12; /* process 12 declets */ + } + else { /* msd=0 */ + if (sourhi) need=11; /* declets to process */ + else if (sourmh) need=10; + else if (sourml) need=7; + else if (sourlo) need=4; + else return dn; /* easy: coefficient is 0 */ + } /*msd=0 */ + + decDigitsFromDPD(dn, sourar, need); /* process declets */ + /* decNumberShow(dn); */ + return dn; + } /* decimal128ToNumber */ + +/* ------------------------------------------------------------------ */ +/* to-scientific-string -- conversion to numeric string */ +/* to-engineering-string -- conversion to numeric string */ +/* */ +/* decimal128ToString(d128, string); */ +/* decimal128ToEngString(d128, string); */ +/* */ +/* d128 is the decimal128 format number to convert */ +/* string is the string where the result will be laid out */ +/* */ +/* string must be at least 24 characters */ +/* */ +/* No error is possible, and no status can be set. */ +/* ------------------------------------------------------------------ */ +char * decimal128ToEngString(const decimal128 *d128, char *string){ + decNumber dn; /* work */ + decimal128ToNumber(d128, &dn); + decNumberToEngString(&dn, string); + return string; + } /* decimal128ToEngString */ + +char * decimal128ToString(const decimal128 *d128, char *string){ + uInt msd; /* coefficient MSD */ + Int exp; /* exponent top two bits or full */ + uInt comb; /* combination field */ + char *cstart; /* coefficient start */ + char *c; /* output pointer in string */ + const uInt *pu; /* work */ + char *s, *t; /* .. (source, target) */ + Int dpd; /* .. */ + Int pre, e; /* .. */ + const uByte *u; /* .. */ + + uInt sourar[4]; /* source 128-bit */ + #define sourhi sourar[3] /* name the word with the sign */ + #define sourmh sourar[2] /* and the mid-high word */ + #define sourml sourar[1] /* and the mod-low word */ + #define sourlo sourar[0] /* and the lowest word */ + + /* load source from storage; this is endian */ + pu=(const uInt *)d128->bytes; /* overlay */ + if (DECLITEND) { + sourlo=pu[0]; /* directly load the low int */ + sourml=pu[1]; /* then the mid-low */ + sourmh=pu[2]; /* then the mid-high */ + sourhi=pu[3]; /* then the high int */ + } + else { + sourhi=pu[0]; /* directly load the high int */ + sourmh=pu[1]; /* then the mid-high */ + sourml=pu[2]; /* then the mid-low */ + sourlo=pu[3]; /* then the low int */ + } + + c=string; /* where result will go */ + if (((Int)sourhi)<0) *c++='-'; /* handle sign */ + + comb=(sourhi>>26)&0x1f; /* combination field */ + msd=COMBMSD[comb]; /* decode the combination field */ + exp=COMBEXP[comb]; /* .. */ + + if (exp==3) { + if (msd==0) { /* infinity */ + strcpy(c, "Inf"); + strcpy(c+3, "inity"); + return string; /* easy */ + } + if (sourhi&0x02000000) *c++='s'; /* sNaN */ + strcpy(c, "NaN"); /* complete word */ + c+=3; /* step past */ + if (sourlo==0 && sourml==0 && sourmh==0 + && (sourhi&0x0003ffff)==0) return string; /* zero payload */ + /* otherwise drop through to add integer; set correct exp */ + exp=0; msd=0; /* setup for following code */ + } + else exp=(exp<<12)+((sourhi>>14)&0xfff)-DECIMAL128_Bias; /* unbiased */ + + /* convert 34 digits of significand to characters */ + cstart=c; /* save start of coefficient */ + if (msd) *c++='0'+(char)msd; /* non-zero most significant digit */ + + /* Now decode the declets. After extracting each one, it is */ + /* decoded to binary and then to a 4-char sequence by table lookup; */ + /* the 4-chars are a 1-char length (significant digits, except 000 */ + /* has length 0). This allows us to left-align the first declet */ + /* with non-zero content, then remaining ones are full 3-char */ + /* length. We use fixed-length memcpys because variable-length */ + /* causes a subroutine call in GCC. (These are length 4 for speed */ + /* and are safe because the array has an extra terminator byte.) */ + #define dpd2char u=&BIN2CHAR[DPD2BIN[dpd]*4]; \ + if (c!=cstart) {memcpy(c, u+1, 4); c+=3;} \ + else if (*u) {memcpy(c, u+4-*u, 4); c+=*u;} + dpd=(sourhi>>4)&0x3ff; /* declet 1 */ + dpd2char; + dpd=((sourhi&0xf)<<6) | (sourmh>>26); /* declet 2 */ + dpd2char; + dpd=(sourmh>>16)&0x3ff; /* declet 3 */ + dpd2char; + dpd=(sourmh>>6)&0x3ff; /* declet 4 */ + dpd2char; + dpd=((sourmh&0x3f)<<4) | (sourml>>28); /* declet 5 */ + dpd2char; + dpd=(sourml>>18)&0x3ff; /* declet 6 */ + dpd2char; + dpd=(sourml>>8)&0x3ff; /* declet 7 */ + dpd2char; + dpd=((sourml&0xff)<<2) | (sourlo>>30); /* declet 8 */ + dpd2char; + dpd=(sourlo>>20)&0x3ff; /* declet 9 */ + dpd2char; + dpd=(sourlo>>10)&0x3ff; /* declet 10 */ + dpd2char; + dpd=(sourlo)&0x3ff; /* declet 11 */ + dpd2char; + + if (c==cstart) *c++='0'; /* all zeros -- make 0 */ + + if (exp==0) { /* integer or NaN case -- easy */ + *c='\0'; /* terminate */ + return string; + } + + /* non-0 exponent */ + e=0; /* assume no E */ + pre=c-cstart+exp; + /* [here, pre-exp is the digits count (==1 for zero)] */ + if (exp>0 || pre<-5) { /* need exponential form */ + e=pre-1; /* calculate E value */ + pre=1; /* assume one digit before '.' */ + } /* exponential form */ + + /* modify the coefficient, adding 0s, '.', and E+nn as needed */ + s=c-1; /* source (LSD) */ + if (pre>0) { /* ddd.ddd (plain), perhaps with E */ + char *dotat=cstart+pre; + if (dotat<c) { /* if embedded dot needed... */ + t=c; /* target */ + for (; s>=dotat; s--, t--) *t=*s; /* open the gap; leave t at gap */ + *t='.'; /* insert the dot */ + c++; /* length increased by one */ + } + + /* finally add the E-part, if needed; it will never be 0, and has */ + /* a maximum length of 4 digits */ + if (e!=0) { + *c++='E'; /* starts with E */ + *c++='+'; /* assume positive */ + if (e<0) { + *(c-1)='-'; /* oops, need '-' */ + e=-e; /* uInt, please */ + } + if (e<1000) { /* 3 (or fewer) digits case */ + u=&BIN2CHAR[e*4]; /* -> length byte */ + memcpy(c, u+4-*u, 4); /* copy fixed 4 characters [is safe] */ + c+=*u; /* bump pointer appropriately */ + } + else { /* 4-digits */ + Int thou=((e>>3)*1049)>>17; /* e/1000 */ + Int rem=e-(1000*thou); /* e%1000 */ + *c++='0'+(char)thou; + u=&BIN2CHAR[rem*4]; /* -> length byte */ + memcpy(c, u+1, 4); /* copy fixed 3+1 characters [is safe] */ + c+=3; /* bump pointer, always 3 digits */ + } + } + *c='\0'; /* add terminator */ + /*printf("res %s\n", string); */ + return string; + } /* pre>0 */ + + /* -5<=pre<=0: here for plain 0.ddd or 0.000ddd forms (can never have E) */ + t=c+1-pre; + *(t+1)='\0'; /* can add terminator now */ + for (; s>=cstart; s--, t--) *t=*s; /* shift whole coefficient right */ + c=cstart; + *c++='0'; /* always starts with 0. */ + *c++='.'; + for (; pre<0; pre++) *c++='0'; /* add any 0's after '.' */ + /*printf("res %s\n", string); */ + return string; + } /* decimal128ToString */ + +/* ------------------------------------------------------------------ */ +/* to-number -- conversion from numeric string */ +/* */ +/* decimal128FromString(result, string, set); */ +/* */ +/* result is the decimal128 format number which gets the result of */ +/* the conversion */ +/* *string is the character string which should contain a valid */ +/* number (which may be a special value) */ +/* set is the context */ +/* */ +/* The context is supplied to this routine is used for error handling */ +/* (setting of status and traps) and for the rounding mode, only. */ +/* If an error occurs, the result will be a valid decimal128 NaN. */ +/* ------------------------------------------------------------------ */ +decimal128 * decimal128FromString(decimal128 *result, const char *string, + decContext *set) { + decContext dc; /* work */ + decNumber dn; /* .. */ + + decContextDefault(&dc, DEC_INIT_DECIMAL128); /* no traps, please */ + dc.round=set->round; /* use supplied rounding */ + + decNumberFromString(&dn, string, &dc); /* will round if needed */ + decimal128FromNumber(result, &dn, &dc); + if (dc.status!=0) { /* something happened */ + decContextSetStatus(set, dc.status); /* .. pass it on */ + } + return result; + } /* decimal128FromString */ + +/* ------------------------------------------------------------------ */ +/* decimal128IsCanonical -- test whether encoding is canonical */ +/* d128 is the source decimal128 */ +/* returns 1 if the encoding of d128 is canonical, 0 otherwise */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +uint32_t decimal128IsCanonical(const decimal128 *d128) { + decNumber dn; /* work */ + decimal128 canon; /* .. */ + decContext dc; /* .. */ + decContextDefault(&dc, DEC_INIT_DECIMAL128); + decimal128ToNumber(d128, &dn); + decimal128FromNumber(&canon, &dn, &dc);/* canon will now be canonical */ + return memcmp(d128, &canon, DECIMAL128_Bytes)==0; + } /* decimal128IsCanonical */ + +/* ------------------------------------------------------------------ */ +/* decimal128Canonical -- copy an encoding, ensuring it is canonical */ +/* d128 is the source decimal128 */ +/* result is the target (may be the same decimal128) */ +/* returns result */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +decimal128 * decimal128Canonical(decimal128 *result, const decimal128 *d128) { + decNumber dn; /* work */ + decContext dc; /* .. */ + decContextDefault(&dc, DEC_INIT_DECIMAL128); + decimal128ToNumber(d128, &dn); + decimal128FromNumber(result, &dn, &dc);/* result will now be canonical */ + return result; + } /* decimal128Canonical */ + +#if DECTRACE || DECCHECK +/* Macros for accessing decimal128 fields. These assume the argument + is a reference (pointer) to the decimal128 structure, and the + decimal128 is in network byte order (big-endian) */ +/* Get sign */ +#define decimal128Sign(d) ((unsigned)(d)->bytes[0]>>7) + +/* Get combination field */ +#define decimal128Comb(d) (((d)->bytes[0] & 0x7c)>>2) + +/* Get exponent continuation [does not remove bias] */ +#define decimal128ExpCon(d) ((((d)->bytes[0] & 0x03)<<10) \ + | ((unsigned)(d)->bytes[1]<<2) \ + | ((unsigned)(d)->bytes[2]>>6)) + +/* Set sign [this assumes sign previously 0] */ +#define decimal128SetSign(d, b) { \ + (d)->bytes[0]|=((unsigned)(b)<<7);} + +/* Set exponent continuation [does not apply bias] */ +/* This assumes range has been checked and exponent previously 0; */ +/* type of exponent must be unsigned */ +#define decimal128SetExpCon(d, e) { \ + (d)->bytes[0]|=(uint8_t)((e)>>10); \ + (d)->bytes[1] =(uint8_t)(((e)&0x3fc)>>2); \ + (d)->bytes[2]|=(uint8_t)(((e)&0x03)<<6);} + +/* ------------------------------------------------------------------ */ +/* decimal128Show -- display a decimal128 in hexadecimal [debug aid] */ +/* d128 -- the number to show */ +/* ------------------------------------------------------------------ */ +/* Also shows sign/cob/expconfields extracted */ +void decimal128Show(const decimal128 *d128) { + char buf[DECIMAL128_Bytes*2+1]; + Int i, j=0; + + if (DECLITEND) { + for (i=0; i<DECIMAL128_Bytes; i++, j+=2) { + sprintf(&buf[j], "%02x", d128->bytes[15-i]); + } + printf(" D128> %s [S:%d Cb:%02x Ec:%02x] LittleEndian\n", buf, + d128->bytes[15]>>7, (d128->bytes[15]>>2)&0x1f, + ((d128->bytes[15]&0x3)<<10)|(d128->bytes[14]<<2)| + (d128->bytes[13]>>6)); + } + else { + for (i=0; i<DECIMAL128_Bytes; i++, j+=2) { + sprintf(&buf[j], "%02x", d128->bytes[i]); + } + printf(" D128> %s [S:%d Cb:%02x Ec:%02x] BigEndian\n", buf, + decimal128Sign(d128), decimal128Comb(d128), + decimal128ExpCon(d128)); + } + } /* decimal128Show */ +#endif diff --git a/libdecnumber/dpd/decimal128Local.h b/libdecnumber/dpd/decimal128Local.h new file mode 100644 index 0000000000..1963678cdd --- /dev/null +++ b/libdecnumber/dpd/decimal128Local.h @@ -0,0 +1,42 @@ +/* Local definitions for use with the decNumber C Library. + Copyright (C) 2007, 2009 Free Software Foundation, Inc. + + This file is part of GCC. + + GCC is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation; either version 3, or (at your option) any later + version. + + GCC is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or + FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + +Under Section 7 of GPL version 3, you are granted additional +permissions described in the GCC Runtime Library Exception, version +3.1, as published by the Free Software Foundation. + +You should have received a copy of the GNU General Public License and +a copy of the GCC Runtime Library Exception along with this program; +see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +<http://www.gnu.org/licenses/>. */ + +#if !defined(DECIMAL128LOCAL) + +/* The compiler needs sign manipulation functions for decimal128 which + are not part of the decNumber package. */ + +/* Set sign; this assumes the sign was previously zero. */ +#define decimal128SetSign(d,b) \ + { (d)->bytes[WORDS_BIGENDIAN ? 0 : 15] |= ((unsigned) (b) << 7); } + +/* Clear sign. */ +#define decimal128ClearSign(d) \ + { (d)->bytes[WORDS_BIGENDIAN ? 0 : 15] &= ~0x80; } + +/* Flip sign. */ +#define decimal128FlipSign(d) \ + { (d)->bytes[WORDS_BIGENDIAN ? 0 : 15] ^= 0x80; } + +#endif diff --git a/libdecnumber/dpd/decimal32.c b/libdecnumber/dpd/decimal32.c new file mode 100644 index 0000000000..d8e3f59781 --- /dev/null +++ b/libdecnumber/dpd/decimal32.c @@ -0,0 +1,491 @@ +/* Decimal 32-bit format module for the decNumber C Library. + Copyright (C) 2005, 2007 Free Software Foundation, Inc. + Contributed by IBM Corporation. Author Mike Cowlishaw. + + This file is part of GCC. + + GCC is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation; either version 2, or (at your option) any later + version. + + In addition to the permissions in the GNU General Public License, + the Free Software Foundation gives you unlimited permission to link + the compiled version of this file into combinations with other + programs, and to distribute those combinations without any + restriction coming from the use of this file. (The General Public + License restrictions do apply in other respects; for example, they + cover modification of the file, and distribution when not linked + into a combine executable.) + + GCC is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or + FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License + along with GCC; see the file COPYING. If not, write to the Free + Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA + 02110-1301, USA. */ + +/* ------------------------------------------------------------------ */ +/* Decimal 32-bit format module */ +/* ------------------------------------------------------------------ */ +/* This module comprises the routines for decimal32 format numbers. */ +/* Conversions are supplied to and from decNumber and String. */ +/* */ +/* This is used when decNumber provides operations, either for all */ +/* operations or as a proxy between decNumber and decSingle. */ +/* */ +/* Error handling is the same as decNumber (qv.). */ +/* ------------------------------------------------------------------ */ +#include <string.h> /* [for memset/memcpy] */ +#include <stdio.h> /* [for printf] */ + +#include "dconfig.h" /* GCC definitions */ +#define DECNUMDIGITS 7 /* make decNumbers with space for 7 */ +#include "decNumber.h" /* base number library */ +#include "decNumberLocal.h" /* decNumber local types, etc. */ +#include "decimal32.h" /* our primary include */ + +/* Utility tables and routines [in decimal64.c] */ +extern const uInt COMBEXP[32], COMBMSD[32]; +extern const uShort DPD2BIN[1024]; +extern const uShort BIN2DPD[1000]; +extern const uByte BIN2CHAR[4001]; + +extern void decDigitsToDPD(const decNumber *, uInt *, Int); +extern void decDigitsFromDPD(decNumber *, const uInt *, Int); + +#if DECTRACE || DECCHECK +void decimal32Show(const decimal32 *); /* for debug */ +extern void decNumberShow(const decNumber *); /* .. */ +#endif + +/* Useful macro */ +/* Clear a structure (e.g., a decNumber) */ +#define DEC_clear(d) memset(d, 0, sizeof(*d)) + +/* ------------------------------------------------------------------ */ +/* decimal32FromNumber -- convert decNumber to decimal32 */ +/* */ +/* ds is the target decimal32 */ +/* dn is the source number (assumed valid) */ +/* set is the context, used only for reporting errors */ +/* */ +/* The set argument is used only for status reporting and for the */ +/* rounding mode (used if the coefficient is more than DECIMAL32_Pmax */ +/* digits or an overflow is detected). If the exponent is out of the */ +/* valid range then Overflow or Underflow will be raised. */ +/* After Underflow a subnormal result is possible. */ +/* */ +/* DEC_Clamped is set if the number has to be 'folded down' to fit, */ +/* by reducing its exponent and multiplying the coefficient by a */ +/* power of ten, or if the exponent on a zero had to be clamped. */ +/* ------------------------------------------------------------------ */ +decimal32 * decimal32FromNumber(decimal32 *d32, const decNumber *dn, + decContext *set) { + uInt status=0; /* status accumulator */ + Int ae; /* adjusted exponent */ + decNumber dw; /* work */ + decContext dc; /* .. */ + uInt *pu; /* .. */ + uInt comb, exp; /* .. */ + uInt targ=0; /* target 32-bit */ + + /* If the number has too many digits, or the exponent could be */ + /* out of range then reduce the number under the appropriate */ + /* constraints. This could push the number to Infinity or zero, */ + /* so this check and rounding must be done before generating the */ + /* decimal32] */ + ae=dn->exponent+dn->digits-1; /* [0 if special] */ + if (dn->digits>DECIMAL32_Pmax /* too many digits */ + || ae>DECIMAL32_Emax /* likely overflow */ + || ae<DECIMAL32_Emin) { /* likely underflow */ + decContextDefault(&dc, DEC_INIT_DECIMAL32); /* [no traps] */ + dc.round=set->round; /* use supplied rounding */ + decNumberPlus(&dw, dn, &dc); /* (round and check) */ + /* [this changes -0 to 0, so enforce the sign...] */ + dw.bits|=dn->bits&DECNEG; + status=dc.status; /* save status */ + dn=&dw; /* use the work number */ + } /* maybe out of range */ + + if (dn->bits&DECSPECIAL) { /* a special value */ + if (dn->bits&DECINF) targ=DECIMAL_Inf<<24; + else { /* sNaN or qNaN */ + if ((*dn->lsu!=0 || dn->digits>1) /* non-zero coefficient */ + && (dn->digits<DECIMAL32_Pmax)) { /* coefficient fits */ + decDigitsToDPD(dn, &targ, 0); + } + if (dn->bits&DECNAN) targ|=DECIMAL_NaN<<24; + else targ|=DECIMAL_sNaN<<24; + } /* a NaN */ + } /* special */ + + else { /* is finite */ + if (decNumberIsZero(dn)) { /* is a zero */ + /* set and clamp exponent */ + if (dn->exponent<-DECIMAL32_Bias) { + exp=0; /* low clamp */ + status|=DEC_Clamped; + } + else { + exp=dn->exponent+DECIMAL32_Bias; /* bias exponent */ + if (exp>DECIMAL32_Ehigh) { /* top clamp */ + exp=DECIMAL32_Ehigh; + status|=DEC_Clamped; + } + } + comb=(exp>>3) & 0x18; /* msd=0, exp top 2 bits .. */ + } + else { /* non-zero finite number */ + uInt msd; /* work */ + Int pad=0; /* coefficient pad digits */ + + /* the dn is known to fit, but it may need to be padded */ + exp=(uInt)(dn->exponent+DECIMAL32_Bias); /* bias exponent */ + if (exp>DECIMAL32_Ehigh) { /* fold-down case */ + pad=exp-DECIMAL32_Ehigh; + exp=DECIMAL32_Ehigh; /* [to maximum] */ + status|=DEC_Clamped; + } + + /* fastpath common case */ + if (DECDPUN==3 && pad==0) { + targ=BIN2DPD[dn->lsu[0]]; + if (dn->digits>3) targ|=(uInt)(BIN2DPD[dn->lsu[1]])<<10; + msd=(dn->digits==7 ? dn->lsu[2] : 0); + } + else { /* general case */ + decDigitsToDPD(dn, &targ, pad); + /* save and clear the top digit */ + msd=targ>>20; + targ&=0x000fffff; + } + + /* create the combination field */ + if (msd>=8) comb=0x18 | ((exp>>5) & 0x06) | (msd & 0x01); + else comb=((exp>>3) & 0x18) | msd; + } + targ|=comb<<26; /* add combination field .. */ + targ|=(exp&0x3f)<<20; /* .. and exponent continuation */ + } /* finite */ + + if (dn->bits&DECNEG) targ|=0x80000000; /* add sign bit */ + + /* now write to storage; this is endian */ + pu=(uInt *)d32->bytes; /* overlay */ + *pu=targ; /* directly store the int */ + + if (status!=0) decContextSetStatus(set, status); /* pass on status */ + /* decimal32Show(d32); */ + return d32; + } /* decimal32FromNumber */ + +/* ------------------------------------------------------------------ */ +/* decimal32ToNumber -- convert decimal32 to decNumber */ +/* d32 is the source decimal32 */ +/* dn is the target number, with appropriate space */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +decNumber * decimal32ToNumber(const decimal32 *d32, decNumber *dn) { + uInt msd; /* coefficient MSD */ + uInt exp; /* exponent top two bits */ + uInt comb; /* combination field */ + uInt sour; /* source 32-bit */ + const uInt *pu; /* work */ + + /* load source from storage; this is endian */ + pu=(const uInt *)d32->bytes; /* overlay */ + sour=*pu; /* directly load the int */ + + comb=(sour>>26)&0x1f; /* combination field */ + + decNumberZero(dn); /* clean number */ + if (sour&0x80000000) dn->bits=DECNEG; /* set sign if negative */ + + msd=COMBMSD[comb]; /* decode the combination field */ + exp=COMBEXP[comb]; /* .. */ + + if (exp==3) { /* is a special */ + if (msd==0) { + dn->bits|=DECINF; + return dn; /* no coefficient needed */ + } + else if (sour&0x02000000) dn->bits|=DECSNAN; + else dn->bits|=DECNAN; + msd=0; /* no top digit */ + } + else { /* is a finite number */ + dn->exponent=(exp<<6)+((sour>>20)&0x3f)-DECIMAL32_Bias; /* unbiased */ + } + + /* get the coefficient */ + sour&=0x000fffff; /* clean coefficient continuation */ + if (msd) { /* non-zero msd */ + sour|=msd<<20; /* prefix to coefficient */ + decDigitsFromDPD(dn, &sour, 3); /* process 3 declets */ + return dn; + } + /* msd=0 */ + if (!sour) return dn; /* easy: coefficient is 0 */ + if (sour&0x000ffc00) /* need 2 declets? */ + decDigitsFromDPD(dn, &sour, 2); /* process 2 declets */ + else + decDigitsFromDPD(dn, &sour, 1); /* process 1 declet */ + return dn; + } /* decimal32ToNumber */ + +/* ------------------------------------------------------------------ */ +/* to-scientific-string -- conversion to numeric string */ +/* to-engineering-string -- conversion to numeric string */ +/* */ +/* decimal32ToString(d32, string); */ +/* decimal32ToEngString(d32, string); */ +/* */ +/* d32 is the decimal32 format number to convert */ +/* string is the string where the result will be laid out */ +/* */ +/* string must be at least 24 characters */ +/* */ +/* No error is possible, and no status can be set. */ +/* ------------------------------------------------------------------ */ +char * decimal32ToEngString(const decimal32 *d32, char *string){ + decNumber dn; /* work */ + decimal32ToNumber(d32, &dn); + decNumberToEngString(&dn, string); + return string; + } /* decimal32ToEngString */ + +char * decimal32ToString(const decimal32 *d32, char *string){ + uInt msd; /* coefficient MSD */ + Int exp; /* exponent top two bits or full */ + uInt comb; /* combination field */ + char *cstart; /* coefficient start */ + char *c; /* output pointer in string */ + const uInt *pu; /* work */ + const uByte *u; /* .. */ + char *s, *t; /* .. (source, target) */ + Int dpd; /* .. */ + Int pre, e; /* .. */ + uInt sour; /* source 32-bit */ + + /* load source from storage; this is endian */ + pu=(const uInt *)d32->bytes; /* overlay */ + sour=*pu; /* directly load the int */ + + c=string; /* where result will go */ + if (((Int)sour)<0) *c++='-'; /* handle sign */ + + comb=(sour>>26)&0x1f; /* combination field */ + msd=COMBMSD[comb]; /* decode the combination field */ + exp=COMBEXP[comb]; /* .. */ + + if (exp==3) { + if (msd==0) { /* infinity */ + strcpy(c, "Inf"); + strcpy(c+3, "inity"); + return string; /* easy */ + } + if (sour&0x02000000) *c++='s'; /* sNaN */ + strcpy(c, "NaN"); /* complete word */ + c+=3; /* step past */ + if ((sour&0x000fffff)==0) return string; /* zero payload */ + /* otherwise drop through to add integer; set correct exp */ + exp=0; msd=0; /* setup for following code */ + } + else exp=(exp<<6)+((sour>>20)&0x3f)-DECIMAL32_Bias; /* unbiased */ + + /* convert 7 digits of significand to characters */ + cstart=c; /* save start of coefficient */ + if (msd) *c++='0'+(char)msd; /* non-zero most significant digit */ + + /* Now decode the declets. After extracting each one, it is */ + /* decoded to binary and then to a 4-char sequence by table lookup; */ + /* the 4-chars are a 1-char length (significant digits, except 000 */ + /* has length 0). This allows us to left-align the first declet */ + /* with non-zero content, then remaining ones are full 3-char */ + /* length. We use fixed-length memcpys because variable-length */ + /* causes a subroutine call in GCC. (These are length 4 for speed */ + /* and are safe because the array has an extra terminator byte.) */ + #define dpd2char u=&BIN2CHAR[DPD2BIN[dpd]*4]; \ + if (c!=cstart) {memcpy(c, u+1, 4); c+=3;} \ + else if (*u) {memcpy(c, u+4-*u, 4); c+=*u;} + + dpd=(sour>>10)&0x3ff; /* declet 1 */ + dpd2char; + dpd=(sour)&0x3ff; /* declet 2 */ + dpd2char; + + if (c==cstart) *c++='0'; /* all zeros -- make 0 */ + + if (exp==0) { /* integer or NaN case -- easy */ + *c='\0'; /* terminate */ + return string; + } + + /* non-0 exponent */ + e=0; /* assume no E */ + pre=c-cstart+exp; + /* [here, pre-exp is the digits count (==1 for zero)] */ + if (exp>0 || pre<-5) { /* need exponential form */ + e=pre-1; /* calculate E value */ + pre=1; /* assume one digit before '.' */ + } /* exponential form */ + + /* modify the coefficient, adding 0s, '.', and E+nn as needed */ + s=c-1; /* source (LSD) */ + if (pre>0) { /* ddd.ddd (plain), perhaps with E */ + char *dotat=cstart+pre; + if (dotat<c) { /* if embedded dot needed... */ + t=c; /* target */ + for (; s>=dotat; s--, t--) *t=*s; /* open the gap; leave t at gap */ + *t='.'; /* insert the dot */ + c++; /* length increased by one */ + } + + /* finally add the E-part, if needed; it will never be 0, and has */ + /* a maximum length of 3 digits (E-101 case) */ + if (e!=0) { + *c++='E'; /* starts with E */ + *c++='+'; /* assume positive */ + if (e<0) { + *(c-1)='-'; /* oops, need '-' */ + e=-e; /* uInt, please */ + } + u=&BIN2CHAR[e*4]; /* -> length byte */ + memcpy(c, u+4-*u, 4); /* copy fixed 4 characters [is safe] */ + c+=*u; /* bump pointer appropriately */ + } + *c='\0'; /* add terminator */ + /*printf("res %s\n", string); */ + return string; + } /* pre>0 */ + + /* -5<=pre<=0: here for plain 0.ddd or 0.000ddd forms (can never have E) */ + t=c+1-pre; + *(t+1)='\0'; /* can add terminator now */ + for (; s>=cstart; s--, t--) *t=*s; /* shift whole coefficient right */ + c=cstart; + *c++='0'; /* always starts with 0. */ + *c++='.'; + for (; pre<0; pre++) *c++='0'; /* add any 0's after '.' */ + /*printf("res %s\n", string); */ + return string; + } /* decimal32ToString */ + +/* ------------------------------------------------------------------ */ +/* to-number -- conversion from numeric string */ +/* */ +/* decimal32FromString(result, string, set); */ +/* */ +/* result is the decimal32 format number which gets the result of */ +/* the conversion */ +/* *string is the character string which should contain a valid */ +/* number (which may be a special value) */ +/* set is the context */ +/* */ +/* The context is supplied to this routine is used for error handling */ +/* (setting of status and traps) and for the rounding mode, only. */ +/* If an error occurs, the result will be a valid decimal32 NaN. */ +/* ------------------------------------------------------------------ */ +decimal32 * decimal32FromString(decimal32 *result, const char *string, + decContext *set) { + decContext dc; /* work */ + decNumber dn; /* .. */ + + decContextDefault(&dc, DEC_INIT_DECIMAL32); /* no traps, please */ + dc.round=set->round; /* use supplied rounding */ + + decNumberFromString(&dn, string, &dc); /* will round if needed */ + decimal32FromNumber(result, &dn, &dc); + if (dc.status!=0) { /* something happened */ + decContextSetStatus(set, dc.status); /* .. pass it on */ + } + return result; + } /* decimal32FromString */ + +/* ------------------------------------------------------------------ */ +/* decimal32IsCanonical -- test whether encoding is canonical */ +/* d32 is the source decimal32 */ +/* returns 1 if the encoding of d32 is canonical, 0 otherwise */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +uint32_t decimal32IsCanonical(const decimal32 *d32) { + decNumber dn; /* work */ + decimal32 canon; /* .. */ + decContext dc; /* .. */ + decContextDefault(&dc, DEC_INIT_DECIMAL32); + decimal32ToNumber(d32, &dn); + decimal32FromNumber(&canon, &dn, &dc);/* canon will now be canonical */ + return memcmp(d32, &canon, DECIMAL32_Bytes)==0; + } /* decimal32IsCanonical */ + +/* ------------------------------------------------------------------ */ +/* decimal32Canonical -- copy an encoding, ensuring it is canonical */ +/* d32 is the source decimal32 */ +/* result is the target (may be the same decimal32) */ +/* returns result */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +decimal32 * decimal32Canonical(decimal32 *result, const decimal32 *d32) { + decNumber dn; /* work */ + decContext dc; /* .. */ + decContextDefault(&dc, DEC_INIT_DECIMAL32); + decimal32ToNumber(d32, &dn); + decimal32FromNumber(result, &dn, &dc);/* result will now be canonical */ + return result; + } /* decimal32Canonical */ + +#if DECTRACE || DECCHECK +/* Macros for accessing decimal32 fields. These assume the argument + is a reference (pointer) to the decimal32 structure, and the + decimal32 is in network byte order (big-endian) */ +/* Get sign */ +#define decimal32Sign(d) ((unsigned)(d)->bytes[0]>>7) + +/* Get combination field */ +#define decimal32Comb(d) (((d)->bytes[0] & 0x7c)>>2) + +/* Get exponent continuation [does not remove bias] */ +#define decimal32ExpCon(d) ((((d)->bytes[0] & 0x03)<<4) \ + | ((unsigned)(d)->bytes[1]>>4)) + +/* Set sign [this assumes sign previously 0] */ +#define decimal32SetSign(d, b) { \ + (d)->bytes[0]|=((unsigned)(b)<<7);} + +/* Set exponent continuation [does not apply bias] */ +/* This assumes range has been checked and exponent previously 0; */ +/* type of exponent must be unsigned */ +#define decimal32SetExpCon(d, e) { \ + (d)->bytes[0]|=(uint8_t)((e)>>4); \ + (d)->bytes[1]|=(uint8_t)(((e)&0x0F)<<4);} + +/* ------------------------------------------------------------------ */ +/* decimal32Show -- display a decimal32 in hexadecimal [debug aid] */ +/* d32 -- the number to show */ +/* ------------------------------------------------------------------ */ +/* Also shows sign/cob/expconfields extracted - valid bigendian only */ +void decimal32Show(const decimal32 *d32) { + char buf[DECIMAL32_Bytes*2+1]; + Int i, j=0; + + if (DECLITEND) { + for (i=0; i<DECIMAL32_Bytes; i++, j+=2) { + sprintf(&buf[j], "%02x", d32->bytes[3-i]); + } + printf(" D32> %s [S:%d Cb:%02x Ec:%02x] LittleEndian\n", buf, + d32->bytes[3]>>7, (d32->bytes[3]>>2)&0x1f, + ((d32->bytes[3]&0x3)<<4)| (d32->bytes[2]>>4)); + } + else { + for (i=0; i<DECIMAL32_Bytes; i++, j+=2) { + sprintf(&buf[j], "%02x", d32->bytes[i]); + } + printf(" D32> %s [S:%d Cb:%02x Ec:%02x] BigEndian\n", buf, + decimal32Sign(d32), decimal32Comb(d32), decimal32ExpCon(d32)); + } + } /* decimal32Show */ +#endif diff --git a/libdecnumber/dpd/decimal64.c b/libdecnumber/dpd/decimal64.c new file mode 100644 index 0000000000..474eb7cf8a --- /dev/null +++ b/libdecnumber/dpd/decimal64.c @@ -0,0 +1,852 @@ +/* Decimal 64-bit format module for the decNumber C Library. + Copyright (C) 2005, 2007 Free Software Foundation, Inc. + Contributed by IBM Corporation. Author Mike Cowlishaw. + + This file is part of GCC. + + GCC is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation; either version 2, or (at your option) any later + version. + + In addition to the permissions in the GNU General Public License, + the Free Software Foundation gives you unlimited permission to link + the compiled version of this file into combinations with other + programs, and to distribute those combinations without any + restriction coming from the use of this file. (The General Public + License restrictions do apply in other respects; for example, they + cover modification of the file, and distribution when not linked + into a combine executable.) + + GCC is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or + FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License + along with GCC; see the file COPYING. If not, write to the Free + Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA + 02110-1301, USA. */ + +/* ------------------------------------------------------------------ */ +/* Decimal 64-bit format module */ +/* ------------------------------------------------------------------ */ +/* This module comprises the routines for decimal64 format numbers. */ +/* Conversions are supplied to and from decNumber and String. */ +/* */ +/* This is used when decNumber provides operations, either for all */ +/* operations or as a proxy between decNumber and decSingle. */ +/* */ +/* Error handling is the same as decNumber (qv.). */ +/* ------------------------------------------------------------------ */ +#include <string.h> /* [for memset/memcpy] */ +#include <stdio.h> /* [for printf] */ + +#include "dconfig.h" /* GCC definitions */ +#define DECNUMDIGITS 16 /* make decNumbers with space for 16 */ +#include "decNumber.h" /* base number library */ +#include "decNumberLocal.h" /* decNumber local types, etc. */ +#include "decimal64.h" /* our primary include */ + +/* Utility routines and tables [in decimal64.c]; externs for C++ */ +extern const uInt COMBEXP[32], COMBMSD[32]; +extern const uShort DPD2BIN[1024]; +extern const uShort BIN2DPD[1000]; +extern const uByte BIN2CHAR[4001]; + +extern void decDigitsFromDPD(decNumber *, const uInt *, Int); +extern void decDigitsToDPD(const decNumber *, uInt *, Int); + +#if DECTRACE || DECCHECK +void decimal64Show(const decimal64 *); /* for debug */ +extern void decNumberShow(const decNumber *); /* .. */ +#endif + +/* Useful macro */ +/* Clear a structure (e.g., a decNumber) */ +#define DEC_clear(d) memset(d, 0, sizeof(*d)) + +/* define and include the tables to use for conversions */ +#define DEC_BIN2CHAR 1 +#define DEC_DPD2BIN 1 +#define DEC_BIN2DPD 1 /* used for all sizes */ +#include "decDPD.h" /* lookup tables */ + +/* ------------------------------------------------------------------ */ +/* decimal64FromNumber -- convert decNumber to decimal64 */ +/* */ +/* ds is the target decimal64 */ +/* dn is the source number (assumed valid) */ +/* set is the context, used only for reporting errors */ +/* */ +/* The set argument is used only for status reporting and for the */ +/* rounding mode (used if the coefficient is more than DECIMAL64_Pmax */ +/* digits or an overflow is detected). If the exponent is out of the */ +/* valid range then Overflow or Underflow will be raised. */ +/* After Underflow a subnormal result is possible. */ +/* */ +/* DEC_Clamped is set if the number has to be 'folded down' to fit, */ +/* by reducing its exponent and multiplying the coefficient by a */ +/* power of ten, or if the exponent on a zero had to be clamped. */ +/* ------------------------------------------------------------------ */ +decimal64 * decimal64FromNumber(decimal64 *d64, const decNumber *dn, + decContext *set) { + uInt status=0; /* status accumulator */ + Int ae; /* adjusted exponent */ + decNumber dw; /* work */ + decContext dc; /* .. */ + uInt *pu; /* .. */ + uInt comb, exp; /* .. */ + uInt targar[2]={0, 0}; /* target 64-bit */ + #define targhi targar[1] /* name the word with the sign */ + #define targlo targar[0] /* and the other */ + + /* If the number has too many digits, or the exponent could be */ + /* out of range then reduce the number under the appropriate */ + /* constraints. This could push the number to Infinity or zero, */ + /* so this check and rounding must be done before generating the */ + /* decimal64] */ + ae=dn->exponent+dn->digits-1; /* [0 if special] */ + if (dn->digits>DECIMAL64_Pmax /* too many digits */ + || ae>DECIMAL64_Emax /* likely overflow */ + || ae<DECIMAL64_Emin) { /* likely underflow */ + decContextDefault(&dc, DEC_INIT_DECIMAL64); /* [no traps] */ + dc.round=set->round; /* use supplied rounding */ + decNumberPlus(&dw, dn, &dc); /* (round and check) */ + /* [this changes -0 to 0, so enforce the sign...] */ + dw.bits|=dn->bits&DECNEG; + status=dc.status; /* save status */ + dn=&dw; /* use the work number */ + } /* maybe out of range */ + + if (dn->bits&DECSPECIAL) { /* a special value */ + if (dn->bits&DECINF) targhi=DECIMAL_Inf<<24; + else { /* sNaN or qNaN */ + if ((*dn->lsu!=0 || dn->digits>1) /* non-zero coefficient */ + && (dn->digits<DECIMAL64_Pmax)) { /* coefficient fits */ + decDigitsToDPD(dn, targar, 0); + } + if (dn->bits&DECNAN) targhi|=DECIMAL_NaN<<24; + else targhi|=DECIMAL_sNaN<<24; + } /* a NaN */ + } /* special */ + + else { /* is finite */ + if (decNumberIsZero(dn)) { /* is a zero */ + /* set and clamp exponent */ + if (dn->exponent<-DECIMAL64_Bias) { + exp=0; /* low clamp */ + status|=DEC_Clamped; + } + else { + exp=dn->exponent+DECIMAL64_Bias; /* bias exponent */ + if (exp>DECIMAL64_Ehigh) { /* top clamp */ + exp=DECIMAL64_Ehigh; + status|=DEC_Clamped; + } + } + comb=(exp>>5) & 0x18; /* msd=0, exp top 2 bits .. */ + } + else { /* non-zero finite number */ + uInt msd; /* work */ + Int pad=0; /* coefficient pad digits */ + + /* the dn is known to fit, but it may need to be padded */ + exp=(uInt)(dn->exponent+DECIMAL64_Bias); /* bias exponent */ + if (exp>DECIMAL64_Ehigh) { /* fold-down case */ + pad=exp-DECIMAL64_Ehigh; + exp=DECIMAL64_Ehigh; /* [to maximum] */ + status|=DEC_Clamped; + } + + /* fastpath common case */ + if (DECDPUN==3 && pad==0) { + uInt dpd[6]={0,0,0,0,0,0}; + uInt i; + Int d=dn->digits; + for (i=0; d>0; i++, d-=3) dpd[i]=BIN2DPD[dn->lsu[i]]; + targlo =dpd[0]; + targlo|=dpd[1]<<10; + targlo|=dpd[2]<<20; + if (dn->digits>6) { + targlo|=dpd[3]<<30; + targhi =dpd[3]>>2; + targhi|=dpd[4]<<8; + } + msd=dpd[5]; /* [did not really need conversion] */ + } + else { /* general case */ + decDigitsToDPD(dn, targar, pad); + /* save and clear the top digit */ + msd=targhi>>18; + targhi&=0x0003ffff; + } + + /* create the combination field */ + if (msd>=8) comb=0x18 | ((exp>>7) & 0x06) | (msd & 0x01); + else comb=((exp>>5) & 0x18) | msd; + } + targhi|=comb<<26; /* add combination field .. */ + targhi|=(exp&0xff)<<18; /* .. and exponent continuation */ + } /* finite */ + + if (dn->bits&DECNEG) targhi|=0x80000000; /* add sign bit */ + + /* now write to storage; this is now always endian */ + pu=(uInt *)d64->bytes; /* overlay */ + if (DECLITEND) { + pu[0]=targar[0]; /* directly store the low int */ + pu[1]=targar[1]; /* then the high int */ + } + else { + pu[0]=targar[1]; /* directly store the high int */ + pu[1]=targar[0]; /* then the low int */ + } + + if (status!=0) decContextSetStatus(set, status); /* pass on status */ + /* decimal64Show(d64); */ + return d64; + } /* decimal64FromNumber */ + +/* ------------------------------------------------------------------ */ +/* decimal64ToNumber -- convert decimal64 to decNumber */ +/* d64 is the source decimal64 */ +/* dn is the target number, with appropriate space */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +decNumber * decimal64ToNumber(const decimal64 *d64, decNumber *dn) { + uInt msd; /* coefficient MSD */ + uInt exp; /* exponent top two bits */ + uInt comb; /* combination field */ + const uInt *pu; /* work */ + Int need; /* .. */ + uInt sourar[2]; /* source 64-bit */ + #define sourhi sourar[1] /* name the word with the sign */ + #define sourlo sourar[0] /* and the lower word */ + + /* load source from storage; this is endian */ + pu=(const uInt *)d64->bytes; /* overlay */ + if (DECLITEND) { + sourlo=pu[0]; /* directly load the low int */ + sourhi=pu[1]; /* then the high int */ + } + else { + sourhi=pu[0]; /* directly load the high int */ + sourlo=pu[1]; /* then the low int */ + } + + comb=(sourhi>>26)&0x1f; /* combination field */ + + decNumberZero(dn); /* clean number */ + if (sourhi&0x80000000) dn->bits=DECNEG; /* set sign if negative */ + + msd=COMBMSD[comb]; /* decode the combination field */ + exp=COMBEXP[comb]; /* .. */ + + if (exp==3) { /* is a special */ + if (msd==0) { + dn->bits|=DECINF; + return dn; /* no coefficient needed */ + } + else if (sourhi&0x02000000) dn->bits|=DECSNAN; + else dn->bits|=DECNAN; + msd=0; /* no top digit */ + } + else { /* is a finite number */ + dn->exponent=(exp<<8)+((sourhi>>18)&0xff)-DECIMAL64_Bias; /* unbiased */ + } + + /* get the coefficient */ + sourhi&=0x0003ffff; /* clean coefficient continuation */ + if (msd) { /* non-zero msd */ + sourhi|=msd<<18; /* prefix to coefficient */ + need=6; /* process 6 declets */ + } + else { /* msd=0 */ + if (!sourhi) { /* top word 0 */ + if (!sourlo) return dn; /* easy: coefficient is 0 */ + need=3; /* process at least 3 declets */ + if (sourlo&0xc0000000) need++; /* process 4 declets */ + /* [could reduce some more, here] */ + } + else { /* some bits in top word, msd=0 */ + need=4; /* process at least 4 declets */ + if (sourhi&0x0003ff00) need++; /* top declet!=0, process 5 */ + } + } /*msd=0 */ + + decDigitsFromDPD(dn, sourar, need); /* process declets */ + return dn; + } /* decimal64ToNumber */ + + +/* ------------------------------------------------------------------ */ +/* to-scientific-string -- conversion to numeric string */ +/* to-engineering-string -- conversion to numeric string */ +/* */ +/* decimal64ToString(d64, string); */ +/* decimal64ToEngString(d64, string); */ +/* */ +/* d64 is the decimal64 format number to convert */ +/* string is the string where the result will be laid out */ +/* */ +/* string must be at least 24 characters */ +/* */ +/* No error is possible, and no status can be set. */ +/* ------------------------------------------------------------------ */ +char * decimal64ToEngString(const decimal64 *d64, char *string){ + decNumber dn; /* work */ + decimal64ToNumber(d64, &dn); + decNumberToEngString(&dn, string); + return string; + } /* decimal64ToEngString */ + +char * decimal64ToString(const decimal64 *d64, char *string){ + uInt msd; /* coefficient MSD */ + Int exp; /* exponent top two bits or full */ + uInt comb; /* combination field */ + char *cstart; /* coefficient start */ + char *c; /* output pointer in string */ + const uInt *pu; /* work */ + char *s, *t; /* .. (source, target) */ + Int dpd; /* .. */ + Int pre, e; /* .. */ + const uByte *u; /* .. */ + + uInt sourar[2]; /* source 64-bit */ + #define sourhi sourar[1] /* name the word with the sign */ + #define sourlo sourar[0] /* and the lower word */ + + /* load source from storage; this is endian */ + pu=(const uInt *)d64->bytes; /* overlay */ + if (DECLITEND) { + sourlo=pu[0]; /* directly load the low int */ + sourhi=pu[1]; /* then the high int */ + } + else { + sourhi=pu[0]; /* directly load the high int */ + sourlo=pu[1]; /* then the low int */ + } + + c=string; /* where result will go */ + if (((Int)sourhi)<0) *c++='-'; /* handle sign */ + + comb=(sourhi>>26)&0x1f; /* combination field */ + msd=COMBMSD[comb]; /* decode the combination field */ + exp=COMBEXP[comb]; /* .. */ + + if (exp==3) { + if (msd==0) { /* infinity */ + strcpy(c, "Inf"); + strcpy(c+3, "inity"); + return string; /* easy */ + } + if (sourhi&0x02000000) *c++='s'; /* sNaN */ + strcpy(c, "NaN"); /* complete word */ + c+=3; /* step past */ + if (sourlo==0 && (sourhi&0x0003ffff)==0) return string; /* zero payload */ + /* otherwise drop through to add integer; set correct exp */ + exp=0; msd=0; /* setup for following code */ + } + else exp=(exp<<8)+((sourhi>>18)&0xff)-DECIMAL64_Bias; + + /* convert 16 digits of significand to characters */ + cstart=c; /* save start of coefficient */ + if (msd) *c++='0'+(char)msd; /* non-zero most significant digit */ + + /* Now decode the declets. After extracting each one, it is */ + /* decoded to binary and then to a 4-char sequence by table lookup; */ + /* the 4-chars are a 1-char length (significant digits, except 000 */ + /* has length 0). This allows us to left-align the first declet */ + /* with non-zero content, then remaining ones are full 3-char */ + /* length. We use fixed-length memcpys because variable-length */ + /* causes a subroutine call in GCC. (These are length 4 for speed */ + /* and are safe because the array has an extra terminator byte.) */ + #define dpd2char u=&BIN2CHAR[DPD2BIN[dpd]*4]; \ + if (c!=cstart) {memcpy(c, u+1, 4); c+=3;} \ + else if (*u) {memcpy(c, u+4-*u, 4); c+=*u;} + + dpd=(sourhi>>8)&0x3ff; /* declet 1 */ + dpd2char; + dpd=((sourhi&0xff)<<2) | (sourlo>>30); /* declet 2 */ + dpd2char; + dpd=(sourlo>>20)&0x3ff; /* declet 3 */ + dpd2char; + dpd=(sourlo>>10)&0x3ff; /* declet 4 */ + dpd2char; + dpd=(sourlo)&0x3ff; /* declet 5 */ + dpd2char; + + if (c==cstart) *c++='0'; /* all zeros -- make 0 */ + + if (exp==0) { /* integer or NaN case -- easy */ + *c='\0'; /* terminate */ + return string; + } + + /* non-0 exponent */ + e=0; /* assume no E */ + pre=c-cstart+exp; + /* [here, pre-exp is the digits count (==1 for zero)] */ + if (exp>0 || pre<-5) { /* need exponential form */ + e=pre-1; /* calculate E value */ + pre=1; /* assume one digit before '.' */ + } /* exponential form */ + + /* modify the coefficient, adding 0s, '.', and E+nn as needed */ + s=c-1; /* source (LSD) */ + if (pre>0) { /* ddd.ddd (plain), perhaps with E */ + char *dotat=cstart+pre; + if (dotat<c) { /* if embedded dot needed... */ + t=c; /* target */ + for (; s>=dotat; s--, t--) *t=*s; /* open the gap; leave t at gap */ + *t='.'; /* insert the dot */ + c++; /* length increased by one */ + } + + /* finally add the E-part, if needed; it will never be 0, and has */ + /* a maximum length of 3 digits */ + if (e!=0) { + *c++='E'; /* starts with E */ + *c++='+'; /* assume positive */ + if (e<0) { + *(c-1)='-'; /* oops, need '-' */ + e=-e; /* uInt, please */ + } + u=&BIN2CHAR[e*4]; /* -> length byte */ + memcpy(c, u+4-*u, 4); /* copy fixed 4 characters [is safe] */ + c+=*u; /* bump pointer appropriately */ + } + *c='\0'; /* add terminator */ + /*printf("res %s\n", string); */ + return string; + } /* pre>0 */ + + /* -5<=pre<=0: here for plain 0.ddd or 0.000ddd forms (can never have E) */ + t=c+1-pre; + *(t+1)='\0'; /* can add terminator now */ + for (; s>=cstart; s--, t--) *t=*s; /* shift whole coefficient right */ + c=cstart; + *c++='0'; /* always starts with 0. */ + *c++='.'; + for (; pre<0; pre++) *c++='0'; /* add any 0's after '.' */ + /*printf("res %s\n", string); */ + return string; + } /* decimal64ToString */ + +/* ------------------------------------------------------------------ */ +/* to-number -- conversion from numeric string */ +/* */ +/* decimal64FromString(result, string, set); */ +/* */ +/* result is the decimal64 format number which gets the result of */ +/* the conversion */ +/* *string is the character string which should contain a valid */ +/* number (which may be a special value) */ +/* set is the context */ +/* */ +/* The context is supplied to this routine is used for error handling */ +/* (setting of status and traps) and for the rounding mode, only. */ +/* If an error occurs, the result will be a valid decimal64 NaN. */ +/* ------------------------------------------------------------------ */ +decimal64 * decimal64FromString(decimal64 *result, const char *string, + decContext *set) { + decContext dc; /* work */ + decNumber dn; /* .. */ + + decContextDefault(&dc, DEC_INIT_DECIMAL64); /* no traps, please */ + dc.round=set->round; /* use supplied rounding */ + + decNumberFromString(&dn, string, &dc); /* will round if needed */ + + decimal64FromNumber(result, &dn, &dc); + if (dc.status!=0) { /* something happened */ + decContextSetStatus(set, dc.status); /* .. pass it on */ + } + return result; + } /* decimal64FromString */ + +/* ------------------------------------------------------------------ */ +/* decimal64IsCanonical -- test whether encoding is canonical */ +/* d64 is the source decimal64 */ +/* returns 1 if the encoding of d64 is canonical, 0 otherwise */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +uint32_t decimal64IsCanonical(const decimal64 *d64) { + decNumber dn; /* work */ + decimal64 canon; /* .. */ + decContext dc; /* .. */ + decContextDefault(&dc, DEC_INIT_DECIMAL64); + decimal64ToNumber(d64, &dn); + decimal64FromNumber(&canon, &dn, &dc);/* canon will now be canonical */ + return memcmp(d64, &canon, DECIMAL64_Bytes)==0; + } /* decimal64IsCanonical */ + +/* ------------------------------------------------------------------ */ +/* decimal64Canonical -- copy an encoding, ensuring it is canonical */ +/* d64 is the source decimal64 */ +/* result is the target (may be the same decimal64) */ +/* returns result */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +decimal64 * decimal64Canonical(decimal64 *result, const decimal64 *d64) { + decNumber dn; /* work */ + decContext dc; /* .. */ + decContextDefault(&dc, DEC_INIT_DECIMAL64); + decimal64ToNumber(d64, &dn); + decimal64FromNumber(result, &dn, &dc);/* result will now be canonical */ + return result; + } /* decimal64Canonical */ + +#if DECTRACE || DECCHECK +/* Macros for accessing decimal64 fields. These assume the + argument is a reference (pointer) to the decimal64 structure, + and the decimal64 is in network byte order (big-endian) */ +/* Get sign */ +#define decimal64Sign(d) ((unsigned)(d)->bytes[0]>>7) + +/* Get combination field */ +#define decimal64Comb(d) (((d)->bytes[0] & 0x7c)>>2) + +/* Get exponent continuation [does not remove bias] */ +#define decimal64ExpCon(d) ((((d)->bytes[0] & 0x03)<<6) \ + | ((unsigned)(d)->bytes[1]>>2)) + +/* Set sign [this assumes sign previously 0] */ +#define decimal64SetSign(d, b) { \ + (d)->bytes[0]|=((unsigned)(b)<<7);} + +/* Set exponent continuation [does not apply bias] */ +/* This assumes range has been checked and exponent previously 0; */ +/* type of exponent must be unsigned */ +#define decimal64SetExpCon(d, e) { \ + (d)->bytes[0]|=(uint8_t)((e)>>6); \ + (d)->bytes[1]|=(uint8_t)(((e)&0x3F)<<2);} + +/* ------------------------------------------------------------------ */ +/* decimal64Show -- display a decimal64 in hexadecimal [debug aid] */ +/* d64 -- the number to show */ +/* ------------------------------------------------------------------ */ +/* Also shows sign/cob/expconfields extracted */ +void decimal64Show(const decimal64 *d64) { + char buf[DECIMAL64_Bytes*2+1]; + Int i, j=0; + + if (DECLITEND) { + for (i=0; i<DECIMAL64_Bytes; i++, j+=2) { + sprintf(&buf[j], "%02x", d64->bytes[7-i]); + } + printf(" D64> %s [S:%d Cb:%02x Ec:%02x] LittleEndian\n", buf, + d64->bytes[7]>>7, (d64->bytes[7]>>2)&0x1f, + ((d64->bytes[7]&0x3)<<6)| (d64->bytes[6]>>2)); + } + else { /* big-endian */ + for (i=0; i<DECIMAL64_Bytes; i++, j+=2) { + sprintf(&buf[j], "%02x", d64->bytes[i]); + } + printf(" D64> %s [S:%d Cb:%02x Ec:%02x] BigEndian\n", buf, + decimal64Sign(d64), decimal64Comb(d64), decimal64ExpCon(d64)); + } + } /* decimal64Show */ +#endif + +/* ================================================================== */ +/* Shared utility routines and tables */ +/* ================================================================== */ +/* define and include the conversion tables to use for shared code */ +#if DECDPUN==3 + #define DEC_DPD2BIN 1 +#else + #define DEC_DPD2BCD 1 +#endif +#include "decDPD.h" /* lookup tables */ + +/* The maximum number of decNumberUnits needed for a working copy of */ +/* the units array is the ceiling of digits/DECDPUN, where digits is */ +/* the maximum number of digits in any of the formats for which this */ +/* is used. decimal128.h must not be included in this module, so, as */ +/* a very special case, that number is defined as a literal here. */ +#define DECMAX754 34 +#define DECMAXUNITS ((DECMAX754+DECDPUN-1)/DECDPUN) + +/* ------------------------------------------------------------------ */ +/* Combination field lookup tables (uInts to save measurable work) */ +/* */ +/* COMBEXP - 2-bit most-significant-bits of exponent */ +/* [11 if an Infinity or NaN] */ +/* COMBMSD - 4-bit most-significant-digit */ +/* [0=Infinity, 1=NaN if COMBEXP=11] */ +/* */ +/* Both are indexed by the 5-bit combination field (0-31) */ +/* ------------------------------------------------------------------ */ +const uInt COMBEXP[32]={0, 0, 0, 0, 0, 0, 0, 0, + 1, 1, 1, 1, 1, 1, 1, 1, + 2, 2, 2, 2, 2, 2, 2, 2, + 0, 0, 1, 1, 2, 2, 3, 3}; +const uInt COMBMSD[32]={0, 1, 2, 3, 4, 5, 6, 7, + 0, 1, 2, 3, 4, 5, 6, 7, + 0, 1, 2, 3, 4, 5, 6, 7, + 8, 9, 8, 9, 8, 9, 0, 1}; + +/* ------------------------------------------------------------------ */ +/* decDigitsToDPD -- pack coefficient into DPD form */ +/* */ +/* dn is the source number (assumed valid, max DECMAX754 digits) */ +/* targ is 1, 2, or 4-element uInt array, which the caller must */ +/* have cleared to zeros */ +/* shift is the number of 0 digits to add on the right (normally 0) */ +/* */ +/* The coefficient must be known small enough to fit. The full */ +/* coefficient is copied, including the leading 'odd' digit. This */ +/* digit is retrieved and packed into the combination field by the */ +/* caller. */ +/* */ +/* The target uInts are altered only as necessary to receive the */ +/* digits of the decNumber. When more than one uInt is needed, they */ +/* are filled from left to right (that is, the uInt at offset 0 will */ +/* end up with the least-significant digits). */ +/* */ +/* shift is used for 'fold-down' padding. */ +/* */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +#if DECDPUN<=4 +/* Constant multipliers for divide-by-power-of five using reciprocal */ +/* multiply, after removing powers of 2 by shifting, and final shift */ +/* of 17 [we only need up to **4] */ +static const uInt multies[]={131073, 26215, 5243, 1049, 210}; +/* QUOT10 -- macro to return the quotient of unit u divided by 10**n */ +#define QUOT10(u, n) ((((uInt)(u)>>(n))*multies[n])>>17) +#endif +void decDigitsToDPD(const decNumber *dn, uInt *targ, Int shift) { + Int cut; /* work */ + Int n; /* output bunch counter */ + Int digits=dn->digits; /* digit countdown */ + uInt dpd; /* densely packed decimal value */ + uInt bin; /* binary value 0-999 */ + uInt *uout=targ; /* -> current output uInt */ + uInt uoff=0; /* -> current output offset [from right] */ + const Unit *inu=dn->lsu; /* -> current input unit */ + Unit uar[DECMAXUNITS]; /* working copy of units, iff shifted */ + #if DECDPUN!=3 /* not fast path */ + Unit in; /* current unit */ + #endif + + if (shift!=0) { /* shift towards most significant required */ + /* shift the units array to the left by pad digits and copy */ + /* [this code is a special case of decShiftToMost, which could */ + /* be used instead if exposed and the array were copied first] */ + const Unit *source; /* .. */ + Unit *target, *first; /* .. */ + uInt next=0; /* work */ + + source=dn->lsu+D2U(digits)-1; /* where msu comes from */ + target=uar+D2U(digits)-1+D2U(shift);/* where upper part of first cut goes */ + cut=DECDPUN-MSUDIGITS(shift); /* where to slice */ + if (cut==0) { /* unit-boundary case */ + for (; source>=dn->lsu; source--, target--) *target=*source; + } + else { + first=uar+D2U(digits+shift)-1; /* where msu will end up */ + for (; source>=dn->lsu; source--, target--) { + /* split the source Unit and accumulate remainder for next */ + #if DECDPUN<=4 + uInt quot=QUOT10(*source, cut); + uInt rem=*source-quot*DECPOWERS[cut]; + next+=quot; + #else + uInt rem=*source%DECPOWERS[cut]; + next+=*source/DECPOWERS[cut]; + #endif + if (target<=first) *target=(Unit)next; /* write to target iff valid */ + next=rem*DECPOWERS[DECDPUN-cut]; /* save remainder for next Unit */ + } + } /* shift-move */ + /* propagate remainder to one below and clear the rest */ + for (; target>=uar; target--) { + *target=(Unit)next; + next=0; + } + digits+=shift; /* add count (shift) of zeros added */ + inu=uar; /* use units in working array */ + } + + /* now densely pack the coefficient into DPD declets */ + + #if DECDPUN!=3 /* not fast path */ + in=*inu; /* current unit */ + cut=0; /* at lowest digit */ + bin=0; /* [keep compiler quiet] */ + #endif + + for(n=0; digits>0; n++) { /* each output bunch */ + #if DECDPUN==3 /* fast path, 3-at-a-time */ + bin=*inu; /* 3 digits ready for convert */ + digits-=3; /* [may go negative] */ + inu++; /* may need another */ + + #else /* must collect digit-by-digit */ + Unit dig; /* current digit */ + Int j; /* digit-in-declet count */ + for (j=0; j<3; j++) { + #if DECDPUN<=4 + Unit temp=(Unit)((uInt)(in*6554)>>16); + dig=(Unit)(in-X10(temp)); + in=temp; + #else + dig=in%10; + in=in/10; + #endif + if (j==0) bin=dig; + else if (j==1) bin+=X10(dig); + else /* j==2 */ bin+=X100(dig); + digits--; + if (digits==0) break; /* [also protects *inu below] */ + cut++; + if (cut==DECDPUN) {inu++; in=*inu; cut=0;} + } + #endif + /* here there are 3 digits in bin, or have used all input digits */ + + dpd=BIN2DPD[bin]; + + /* write declet to uInt array */ + *uout|=dpd<<uoff; + uoff+=10; + if (uoff<32) continue; /* no uInt boundary cross */ + uout++; + uoff-=32; + *uout|=dpd>>(10-uoff); /* collect top bits */ + } /* n declets */ + return; + } /* decDigitsToDPD */ + +/* ------------------------------------------------------------------ */ +/* decDigitsFromDPD -- unpack a format's coefficient */ +/* */ +/* dn is the target number, with 7, 16, or 34-digit space. */ +/* sour is a 1, 2, or 4-element uInt array containing only declets */ +/* declets is the number of (right-aligned) declets in sour to */ +/* be processed. This may be 1 more than the obvious number in */ +/* a format, as any top digit is prefixed to the coefficient */ +/* continuation field. It also may be as small as 1, as the */ +/* caller may pre-process leading zero declets. */ +/* */ +/* When doing the 'extra declet' case care is taken to avoid writing */ +/* extra digits when there are leading zeros, as these could overflow */ +/* the units array when DECDPUN is not 3. */ +/* */ +/* The target uInts are used only as necessary to process declets */ +/* declets into the decNumber. When more than one uInt is needed, */ +/* they are used from left to right (that is, the uInt at offset 0 */ +/* provides the least-significant digits). */ +/* */ +/* dn->digits is set, but not the sign or exponent. */ +/* No error is possible [the redundant 888 codes are allowed]. */ +/* ------------------------------------------------------------------ */ +void decDigitsFromDPD(decNumber *dn, const uInt *sour, Int declets) { + + uInt dpd; /* collector for 10 bits */ + Int n; /* counter */ + Unit *uout=dn->lsu; /* -> current output unit */ + Unit *last=uout; /* will be unit containing msd */ + const uInt *uin=sour; /* -> current input uInt */ + uInt uoff=0; /* -> current input offset [from right] */ + + #if DECDPUN!=3 + uInt bcd; /* BCD result */ + uInt nibble; /* work */ + Unit out=0; /* accumulator */ + Int cut=0; /* power of ten in current unit */ + #endif + #if DECDPUN>4 + uInt const *pow; /* work */ + #endif + + /* Expand the densely-packed integer, right to left */ + for (n=declets-1; n>=0; n--) { /* count down declets of 10 bits */ + dpd=*uin>>uoff; + uoff+=10; + if (uoff>32) { /* crossed uInt boundary */ + uin++; + uoff-=32; + dpd|=*uin<<(10-uoff); /* get waiting bits */ + } + dpd&=0x3ff; /* clear uninteresting bits */ + + #if DECDPUN==3 + if (dpd==0) *uout=0; + else { + *uout=DPD2BIN[dpd]; /* convert 10 bits to binary 0-999 */ + last=uout; /* record most significant unit */ + } + uout++; + } /* n */ + + #else /* DECDPUN!=3 */ + if (dpd==0) { /* fastpath [e.g., leading zeros] */ + /* write out three 0 digits (nibbles); out may have digit(s) */ + cut++; + if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;} + if (n==0) break; /* [as below, works even if MSD=0] */ + cut++; + if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;} + cut++; + if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;} + continue; + } + + bcd=DPD2BCD[dpd]; /* convert 10 bits to 12 bits BCD */ + + /* now accumulate the 3 BCD nibbles into units */ + nibble=bcd & 0x00f; + if (nibble) out=(Unit)(out+nibble*DECPOWERS[cut]); + cut++; + if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;} + bcd>>=4; + + /* if this is the last declet and the remaining nibbles in bcd */ + /* are 00 then process no more nibbles, because this could be */ + /* the 'odd' MSD declet and writing any more Units would then */ + /* overflow the unit array */ + if (n==0 && !bcd) break; + + nibble=bcd & 0x00f; + if (nibble) out=(Unit)(out+nibble*DECPOWERS[cut]); + cut++; + if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;} + bcd>>=4; + + nibble=bcd & 0x00f; + if (nibble) out=(Unit)(out+nibble*DECPOWERS[cut]); + cut++; + if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;} + } /* n */ + if (cut!=0) { /* some more left over */ + *uout=out; /* write out final unit */ + if (out) last=uout; /* and note if non-zero */ + } + #endif + + /* here, last points to the most significant unit with digits; */ + /* inspect it to get the final digits count -- this is essentially */ + /* the same code as decGetDigits in decNumber.c */ + dn->digits=(last-dn->lsu)*DECDPUN+1; /* floor of digits, plus */ + /* must be at least 1 digit */ + #if DECDPUN>1 + if (*last<10) return; /* common odd digit or 0 */ + dn->digits++; /* must be 2 at least */ + #if DECDPUN>2 + if (*last<100) return; /* 10-99 */ + dn->digits++; /* must be 3 at least */ + #if DECDPUN>3 + if (*last<1000) return; /* 100-999 */ + dn->digits++; /* must be 4 at least */ + #if DECDPUN>4 + for (pow=&DECPOWERS[4]; *last>=*pow; pow++) dn->digits++; + #endif + #endif + #endif + #endif + return; + } /*decDigitsFromDPD */ |