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Diffstat (limited to 'fpu/softfloat-macros.h')
| -rw-r--r-- | fpu/softfloat-macros.h | 841 |
1 files changed, 0 insertions, 841 deletions
diff --git a/fpu/softfloat-macros.h b/fpu/softfloat-macros.h deleted file mode 100644 index c45a23193e..0000000000 --- a/fpu/softfloat-macros.h +++ /dev/null @@ -1,841 +0,0 @@ -/* - * QEMU float support macros - * - * The code in this source file is derived from release 2a of the SoftFloat - * IEC/IEEE Floating-point Arithmetic Package. Those parts of the code (and - * some later contributions) are provided under that license, as detailed below. - * It has subsequently been modified by contributors to the QEMU Project, - * so some portions are provided under: - * the SoftFloat-2a license - * the BSD license - * GPL-v2-or-later - * - * Any future contributions to this file after December 1st 2014 will be - * taken to be licensed under the Softfloat-2a license unless specifically - * indicated otherwise. - */ - -/* -=============================================================================== -This C source fragment is part of the SoftFloat IEC/IEEE Floating-point -Arithmetic Package, Release 2a. - -Written by John R. Hauser. This work was made possible in part by the -International Computer Science Institute, located at Suite 600, 1947 Center -Street, Berkeley, California 94704. Funding was partially provided by the -National Science Foundation under grant MIP-9311980. The original version -of this code was written as part of a project to build a fixed-point vector -processor in collaboration with the University of California at Berkeley, -overseen by Profs. Nelson Morgan and John Wawrzynek. More information -is available through the Web page `http://HTTP.CS.Berkeley.EDU/~jhauser/ -arithmetic/SoftFloat.html'. - -THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort -has been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT -TIMES RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO -PERSONS AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ANY -AND ALL LOSSES, COSTS, OR OTHER PROBLEMS ARISING FROM ITS USE. - -Derivative works are acceptable, even for commercial purposes, so long as -(1) they include prominent notice that the work is derivative, and (2) they -include prominent notice akin to these four paragraphs for those parts of -this code that are retained. - -=============================================================================== -*/ - -/* BSD licensing: - * Copyright (c) 2006, Fabrice Bellard - * All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions are met: - * - * 1. Redistributions of source code must retain the above copyright notice, - * this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright notice, - * this list of conditions and the following disclaimer in the documentation - * and/or other materials provided with the distribution. - * - * 3. Neither the name of the copyright holder nor the names of its contributors - * may be used to endorse or promote products derived from this software without - * specific prior written permission. - * - * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" - * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE - * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR - * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF - * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS - * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN - * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) - * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF - * THE POSSIBILITY OF SUCH DAMAGE. - */ - -/* Portions of this work are licensed under the terms of the GNU GPL, - * version 2 or later. See the COPYING file in the top-level directory. - */ - -/*---------------------------------------------------------------------------- -| This macro tests for minimum version of the GNU C compiler. -*----------------------------------------------------------------------------*/ -#if defined(__GNUC__) && defined(__GNUC_MINOR__) -# define SOFTFLOAT_GNUC_PREREQ(maj, min) \ - ((__GNUC__ << 16) + __GNUC_MINOR__ >= ((maj) << 16) + (min)) -#else -# define SOFTFLOAT_GNUC_PREREQ(maj, min) 0 -#endif - - -/*---------------------------------------------------------------------------- -| Shifts `a' right by the number of bits given in `count'. If any nonzero -| bits are shifted off, they are ``jammed'' into the least significant bit of -| the result by setting the least significant bit to 1. The value of `count' -| can be arbitrarily large; in particular, if `count' is greater than 32, the -| result will be either 0 or 1, depending on whether `a' is zero or nonzero. -| The result is stored in the location pointed to by `zPtr'. -*----------------------------------------------------------------------------*/ - -static inline void shift32RightJamming(uint32_t a, int count, uint32_t *zPtr) -{ - uint32_t z; - - if ( count == 0 ) { - z = a; - } - else if ( count < 32 ) { - z = ( a>>count ) | ( ( a<<( ( - count ) & 31 ) ) != 0 ); - } - else { - z = ( a != 0 ); - } - *zPtr = z; - -} - -/*---------------------------------------------------------------------------- -| Shifts `a' right by the number of bits given in `count'. If any nonzero -| bits are shifted off, they are ``jammed'' into the least significant bit of -| the result by setting the least significant bit to 1. The value of `count' -| can be arbitrarily large; in particular, if `count' is greater than 64, the -| result will be either 0 or 1, depending on whether `a' is zero or nonzero. -| The result is stored in the location pointed to by `zPtr'. -*----------------------------------------------------------------------------*/ - -static inline void shift64RightJamming(uint64_t a, int count, uint64_t *zPtr) -{ - uint64_t z; - - if ( count == 0 ) { - z = a; - } - else if ( count < 64 ) { - z = ( a>>count ) | ( ( a<<( ( - count ) & 63 ) ) != 0 ); - } - else { - z = ( a != 0 ); - } - *zPtr = z; - -} - -/*---------------------------------------------------------------------------- -| Shifts the 128-bit value formed by concatenating `a0' and `a1' right by 64 -| _plus_ the number of bits given in `count'. The shifted result is at most -| 64 nonzero bits; this is stored at the location pointed to by `z0Ptr'. The -| bits shifted off form a second 64-bit result as follows: The _last_ bit -| shifted off is the most-significant bit of the extra result, and the other -| 63 bits of the extra result are all zero if and only if _all_but_the_last_ -| bits shifted off were all zero. This extra result is stored in the location -| pointed to by `z1Ptr'. The value of `count' can be arbitrarily large. -| (This routine makes more sense if `a0' and `a1' are considered to form a -| fixed-point value with binary point between `a0' and `a1'. This fixed-point -| value is shifted right by the number of bits given in `count', and the -| integer part of the result is returned at the location pointed to by -| `z0Ptr'. The fractional part of the result may be slightly corrupted as -| described above, and is returned at the location pointed to by `z1Ptr'.) -*----------------------------------------------------------------------------*/ - -static inline void - shift64ExtraRightJamming( - uint64_t a0, uint64_t a1, int count, uint64_t *z0Ptr, uint64_t *z1Ptr) -{ - uint64_t z0, z1; - int8_t negCount = ( - count ) & 63; - - if ( count == 0 ) { - z1 = a1; - z0 = a0; - } - else if ( count < 64 ) { - z1 = ( a0<<negCount ) | ( a1 != 0 ); - z0 = a0>>count; - } - else { - if ( count == 64 ) { - z1 = a0 | ( a1 != 0 ); - } - else { - z1 = ( ( a0 | a1 ) != 0 ); - } - z0 = 0; - } - *z1Ptr = z1; - *z0Ptr = z0; - -} - -/*---------------------------------------------------------------------------- -| Shifts the 128-bit value formed by concatenating `a0' and `a1' right by the -| number of bits given in `count'. Any bits shifted off are lost. The value -| of `count' can be arbitrarily large; in particular, if `count' is greater -| than 128, the result will be 0. The result is broken into two 64-bit pieces -| which are stored at the locations pointed to by `z0Ptr' and `z1Ptr'. -*----------------------------------------------------------------------------*/ - -static inline void - shift128Right( - uint64_t a0, uint64_t a1, int count, uint64_t *z0Ptr, uint64_t *z1Ptr) -{ - uint64_t z0, z1; - int8_t negCount = ( - count ) & 63; - - if ( count == 0 ) { - z1 = a1; - z0 = a0; - } - else if ( count < 64 ) { - z1 = ( a0<<negCount ) | ( a1>>count ); - z0 = a0>>count; - } - else { - z1 = (count < 128) ? (a0 >> (count & 63)) : 0; - z0 = 0; - } - *z1Ptr = z1; - *z0Ptr = z0; - -} - -/*---------------------------------------------------------------------------- -| Shifts the 128-bit value formed by concatenating `a0' and `a1' right by the -| number of bits given in `count'. If any nonzero bits are shifted off, they -| are ``jammed'' into the least significant bit of the result by setting the -| least significant bit to 1. The value of `count' can be arbitrarily large; -| in particular, if `count' is greater than 128, the result will be either -| 0 or 1, depending on whether the concatenation of `a0' and `a1' is zero or -| nonzero. The result is broken into two 64-bit pieces which are stored at -| the locations pointed to by `z0Ptr' and `z1Ptr'. -*----------------------------------------------------------------------------*/ - -static inline void - shift128RightJamming( - uint64_t a0, uint64_t a1, int count, uint64_t *z0Ptr, uint64_t *z1Ptr) -{ - uint64_t z0, z1; - int8_t negCount = ( - count ) & 63; - - if ( count == 0 ) { - z1 = a1; - z0 = a0; - } - else if ( count < 64 ) { - z1 = ( a0<<negCount ) | ( a1>>count ) | ( ( a1<<negCount ) != 0 ); - z0 = a0>>count; - } - else { - if ( count == 64 ) { - z1 = a0 | ( a1 != 0 ); - } - else if ( count < 128 ) { - z1 = ( a0>>( count & 63 ) ) | ( ( ( a0<<negCount ) | a1 ) != 0 ); - } - else { - z1 = ( ( a0 | a1 ) != 0 ); - } - z0 = 0; - } - *z1Ptr = z1; - *z0Ptr = z0; - -} - -/*---------------------------------------------------------------------------- -| Shifts the 192-bit value formed by concatenating `a0', `a1', and `a2' right -| by 64 _plus_ the number of bits given in `count'. The shifted result is -| at most 128 nonzero bits; these are broken into two 64-bit pieces which are -| stored at the locations pointed to by `z0Ptr' and `z1Ptr'. The bits shifted -| off form a third 64-bit result as follows: The _last_ bit shifted off is -| the most-significant bit of the extra result, and the other 63 bits of the -| extra result are all zero if and only if _all_but_the_last_ bits shifted off -| were all zero. This extra result is stored in the location pointed to by -| `z2Ptr'. The value of `count' can be arbitrarily large. -| (This routine makes more sense if `a0', `a1', and `a2' are considered -| to form a fixed-point value with binary point between `a1' and `a2'. This -| fixed-point value is shifted right by the number of bits given in `count', -| and the integer part of the result is returned at the locations pointed to -| by `z0Ptr' and `z1Ptr'. The fractional part of the result may be slightly -| corrupted as described above, and is returned at the location pointed to by -| `z2Ptr'.) -*----------------------------------------------------------------------------*/ - -static inline void - shift128ExtraRightJamming( - uint64_t a0, - uint64_t a1, - uint64_t a2, - int count, - uint64_t *z0Ptr, - uint64_t *z1Ptr, - uint64_t *z2Ptr - ) -{ - uint64_t z0, z1, z2; - int8_t negCount = ( - count ) & 63; - - if ( count == 0 ) { - z2 = a2; - z1 = a1; - z0 = a0; - } - else { - if ( count < 64 ) { - z2 = a1<<negCount; - z1 = ( a0<<negCount ) | ( a1>>count ); - z0 = a0>>count; - } - else { - if ( count == 64 ) { - z2 = a1; - z1 = a0; - } - else { - a2 |= a1; - if ( count < 128 ) { - z2 = a0<<negCount; - z1 = a0>>( count & 63 ); - } - else { - z2 = ( count == 128 ) ? a0 : ( a0 != 0 ); - z1 = 0; - } - } - z0 = 0; - } - z2 |= ( a2 != 0 ); - } - *z2Ptr = z2; - *z1Ptr = z1; - *z0Ptr = z0; - -} - -/*---------------------------------------------------------------------------- -| Shifts the 128-bit value formed by concatenating `a0' and `a1' left by the -| number of bits given in `count'. Any bits shifted off are lost. The value -| of `count' must be less than 64. The result is broken into two 64-bit -| pieces which are stored at the locations pointed to by `z0Ptr' and `z1Ptr'. -*----------------------------------------------------------------------------*/ - -static inline void - shortShift128Left( - uint64_t a0, uint64_t a1, int count, uint64_t *z0Ptr, uint64_t *z1Ptr) -{ - - *z1Ptr = a1<<count; - *z0Ptr = - ( count == 0 ) ? a0 : ( a0<<count ) | ( a1>>( ( - count ) & 63 ) ); - -} - -/*---------------------------------------------------------------------------- -| Shifts the 192-bit value formed by concatenating `a0', `a1', and `a2' left -| by the number of bits given in `count'. Any bits shifted off are lost. -| The value of `count' must be less than 64. The result is broken into three -| 64-bit pieces which are stored at the locations pointed to by `z0Ptr', -| `z1Ptr', and `z2Ptr'. -*----------------------------------------------------------------------------*/ - -static inline void - shortShift192Left( - uint64_t a0, - uint64_t a1, - uint64_t a2, - int count, - uint64_t *z0Ptr, - uint64_t *z1Ptr, - uint64_t *z2Ptr - ) -{ - uint64_t z0, z1, z2; - int8_t negCount; - - z2 = a2<<count; - z1 = a1<<count; - z0 = a0<<count; - if ( 0 < count ) { - negCount = ( ( - count ) & 63 ); - z1 |= a2>>negCount; - z0 |= a1>>negCount; - } - *z2Ptr = z2; - *z1Ptr = z1; - *z0Ptr = z0; - -} - -/*---------------------------------------------------------------------------- -| Adds the 128-bit value formed by concatenating `a0' and `a1' to the 128-bit -| value formed by concatenating `b0' and `b1'. Addition is modulo 2^128, so -| any carry out is lost. The result is broken into two 64-bit pieces which -| are stored at the locations pointed to by `z0Ptr' and `z1Ptr'. -*----------------------------------------------------------------------------*/ - -static inline void - add128( - uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1, uint64_t *z0Ptr, uint64_t *z1Ptr ) -{ - uint64_t z1; - - z1 = a1 + b1; - *z1Ptr = z1; - *z0Ptr = a0 + b0 + ( z1 < a1 ); - -} - -/*---------------------------------------------------------------------------- -| Adds the 192-bit value formed by concatenating `a0', `a1', and `a2' to the -| 192-bit value formed by concatenating `b0', `b1', and `b2'. Addition is -| modulo 2^192, so any carry out is lost. The result is broken into three -| 64-bit pieces which are stored at the locations pointed to by `z0Ptr', -| `z1Ptr', and `z2Ptr'. -*----------------------------------------------------------------------------*/ - -static inline void - add192( - uint64_t a0, - uint64_t a1, - uint64_t a2, - uint64_t b0, - uint64_t b1, - uint64_t b2, - uint64_t *z0Ptr, - uint64_t *z1Ptr, - uint64_t *z2Ptr - ) -{ - uint64_t z0, z1, z2; - int8_t carry0, carry1; - - z2 = a2 + b2; - carry1 = ( z2 < a2 ); - z1 = a1 + b1; - carry0 = ( z1 < a1 ); - z0 = a0 + b0; - z1 += carry1; - z0 += ( z1 < carry1 ); - z0 += carry0; - *z2Ptr = z2; - *z1Ptr = z1; - *z0Ptr = z0; - -} - -/*---------------------------------------------------------------------------- -| Subtracts the 128-bit value formed by concatenating `b0' and `b1' from the -| 128-bit value formed by concatenating `a0' and `a1'. Subtraction is modulo -| 2^128, so any borrow out (carry out) is lost. The result is broken into two -| 64-bit pieces which are stored at the locations pointed to by `z0Ptr' and -| `z1Ptr'. -*----------------------------------------------------------------------------*/ - -static inline void - sub128( - uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1, uint64_t *z0Ptr, uint64_t *z1Ptr ) -{ - - *z1Ptr = a1 - b1; - *z0Ptr = a0 - b0 - ( a1 < b1 ); - -} - -/*---------------------------------------------------------------------------- -| Subtracts the 192-bit value formed by concatenating `b0', `b1', and `b2' -| from the 192-bit value formed by concatenating `a0', `a1', and `a2'. -| Subtraction is modulo 2^192, so any borrow out (carry out) is lost. The -| result is broken into three 64-bit pieces which are stored at the locations -| pointed to by `z0Ptr', `z1Ptr', and `z2Ptr'. -*----------------------------------------------------------------------------*/ - -static inline void - sub192( - uint64_t a0, - uint64_t a1, - uint64_t a2, - uint64_t b0, - uint64_t b1, - uint64_t b2, - uint64_t *z0Ptr, - uint64_t *z1Ptr, - uint64_t *z2Ptr - ) -{ - uint64_t z0, z1, z2; - int8_t borrow0, borrow1; - - z2 = a2 - b2; - borrow1 = ( a2 < b2 ); - z1 = a1 - b1; - borrow0 = ( a1 < b1 ); - z0 = a0 - b0; - z0 -= ( z1 < borrow1 ); - z1 -= borrow1; - z0 -= borrow0; - *z2Ptr = z2; - *z1Ptr = z1; - *z0Ptr = z0; - -} - -/*---------------------------------------------------------------------------- -| Multiplies `a' by `b' to obtain a 128-bit product. The product is broken -| into two 64-bit pieces which are stored at the locations pointed to by -| `z0Ptr' and `z1Ptr'. -*----------------------------------------------------------------------------*/ - -static inline void mul64To128( uint64_t a, uint64_t b, uint64_t *z0Ptr, uint64_t *z1Ptr ) -{ - uint32_t aHigh, aLow, bHigh, bLow; - uint64_t z0, zMiddleA, zMiddleB, z1; - - aLow = a; - aHigh = a>>32; - bLow = b; - bHigh = b>>32; - z1 = ( (uint64_t) aLow ) * bLow; - zMiddleA = ( (uint64_t) aLow ) * bHigh; - zMiddleB = ( (uint64_t) aHigh ) * bLow; - z0 = ( (uint64_t) aHigh ) * bHigh; - zMiddleA += zMiddleB; - z0 += ( ( (uint64_t) ( zMiddleA < zMiddleB ) )<<32 ) + ( zMiddleA>>32 ); - zMiddleA <<= 32; - z1 += zMiddleA; - z0 += ( z1 < zMiddleA ); - *z1Ptr = z1; - *z0Ptr = z0; - -} - -/*---------------------------------------------------------------------------- -| Multiplies the 128-bit value formed by concatenating `a0' and `a1' by -| `b' to obtain a 192-bit product. The product is broken into three 64-bit -| pieces which are stored at the locations pointed to by `z0Ptr', `z1Ptr', and -| `z2Ptr'. -*----------------------------------------------------------------------------*/ - -static inline void - mul128By64To192( - uint64_t a0, - uint64_t a1, - uint64_t b, - uint64_t *z0Ptr, - uint64_t *z1Ptr, - uint64_t *z2Ptr - ) -{ - uint64_t z0, z1, z2, more1; - - mul64To128( a1, b, &z1, &z2 ); - mul64To128( a0, b, &z0, &more1 ); - add128( z0, more1, 0, z1, &z0, &z1 ); - *z2Ptr = z2; - *z1Ptr = z1; - *z0Ptr = z0; - -} - -/*---------------------------------------------------------------------------- -| Multiplies the 128-bit value formed by concatenating `a0' and `a1' to the -| 128-bit value formed by concatenating `b0' and `b1' to obtain a 256-bit -| product. The product is broken into four 64-bit pieces which are stored at -| the locations pointed to by `z0Ptr', `z1Ptr', `z2Ptr', and `z3Ptr'. -*----------------------------------------------------------------------------*/ - -static inline void - mul128To256( - uint64_t a0, - uint64_t a1, - uint64_t b0, - uint64_t b1, - uint64_t *z0Ptr, - uint64_t *z1Ptr, - uint64_t *z2Ptr, - uint64_t *z3Ptr - ) -{ - uint64_t z0, z1, z2, z3; - uint64_t more1, more2; - - mul64To128( a1, b1, &z2, &z3 ); - mul64To128( a1, b0, &z1, &more2 ); - add128( z1, more2, 0, z2, &z1, &z2 ); - mul64To128( a0, b0, &z0, &more1 ); - add128( z0, more1, 0, z1, &z0, &z1 ); - mul64To128( a0, b1, &more1, &more2 ); - add128( more1, more2, 0, z2, &more1, &z2 ); - add128( z0, z1, 0, more1, &z0, &z1 ); - *z3Ptr = z3; - *z2Ptr = z2; - *z1Ptr = z1; - *z0Ptr = z0; - -} - -/*---------------------------------------------------------------------------- -| Returns an approximation to the 64-bit integer quotient obtained by dividing -| `b' into the 128-bit value formed by concatenating `a0' and `a1'. The -| divisor `b' must be at least 2^63. If q is the exact quotient truncated -| toward zero, the approximation returned lies between q and q + 2 inclusive. -| If the exact quotient q is larger than 64 bits, the maximum positive 64-bit -| unsigned integer is returned. -*----------------------------------------------------------------------------*/ - -static uint64_t estimateDiv128To64( uint64_t a0, uint64_t a1, uint64_t b ) -{ - uint64_t b0, b1; - uint64_t rem0, rem1, term0, term1; - uint64_t z; - - if ( b <= a0 ) return LIT64( 0xFFFFFFFFFFFFFFFF ); - b0 = b>>32; - z = ( b0<<32 <= a0 ) ? LIT64( 0xFFFFFFFF00000000 ) : ( a0 / b0 )<<32; - mul64To128( b, z, &term0, &term1 ); - sub128( a0, a1, term0, term1, &rem0, &rem1 ); - while ( ( (int64_t) rem0 ) < 0 ) { - z -= LIT64( 0x100000000 ); - b1 = b<<32; - add128( rem0, rem1, b0, b1, &rem0, &rem1 ); - } - rem0 = ( rem0<<32 ) | ( rem1>>32 ); - z |= ( b0<<32 <= rem0 ) ? 0xFFFFFFFF : rem0 / b0; - return z; - -} - -/* From the GNU Multi Precision Library - longlong.h __udiv_qrnnd - * (https://gmplib.org/repo/gmp/file/tip/longlong.h) - * - * Licensed under the GPLv2/LGPLv3 - */ -static uint64_t div128To64(uint64_t n0, uint64_t n1, uint64_t d) -{ - uint64_t d0, d1, q0, q1, r1, r0, m; - - d0 = (uint32_t)d; - d1 = d >> 32; - - r1 = n1 % d1; - q1 = n1 / d1; - m = q1 * d0; - r1 = (r1 << 32) | (n0 >> 32); - if (r1 < m) { - q1 -= 1; - r1 += d; - if (r1 >= d) { - if (r1 < m) { - q1 -= 1; - r1 += d; - } - } - } - r1 -= m; - - r0 = r1 % d1; - q0 = r1 / d1; - m = q0 * d0; - r0 = (r0 << 32) | (uint32_t)n0; - if (r0 < m) { - q0 -= 1; - r0 += d; - if (r0 >= d) { - if (r0 < m) { - q0 -= 1; - r0 += d; - } - } - } - r0 -= m; - - /* Return remainder in LSB */ - return (q1 << 32) | q0 | (r0 != 0); -} - -/*---------------------------------------------------------------------------- -| Returns an approximation to the square root of the 32-bit significand given -| by `a'. Considered as an integer, `a' must be at least 2^31. If bit 0 of -| `aExp' (the least significant bit) is 1, the integer returned approximates -| 2^31*sqrt(`a'/2^31), where `a' is considered an integer. If bit 0 of `aExp' -| is 0, the integer returned approximates 2^31*sqrt(`a'/2^30). In either -| case, the approximation returned lies strictly within +/-2 of the exact -| value. -*----------------------------------------------------------------------------*/ - -static uint32_t estimateSqrt32(int aExp, uint32_t a) -{ - static const uint16_t sqrtOddAdjustments[] = { - 0x0004, 0x0022, 0x005D, 0x00B1, 0x011D, 0x019F, 0x0236, 0x02E0, - 0x039C, 0x0468, 0x0545, 0x0631, 0x072B, 0x0832, 0x0946, 0x0A67 - }; - static const uint16_t sqrtEvenAdjustments[] = { - 0x0A2D, 0x08AF, 0x075A, 0x0629, 0x051A, 0x0429, 0x0356, 0x029E, - 0x0200, 0x0179, 0x0109, 0x00AF, 0x0068, 0x0034, 0x0012, 0x0002 - }; - int8_t index; - uint32_t z; - - index = ( a>>27 ) & 15; - if ( aExp & 1 ) { - z = 0x4000 + ( a>>17 ) - sqrtOddAdjustments[ (int)index ]; - z = ( ( a / z )<<14 ) + ( z<<15 ); - a >>= 1; - } - else { - z = 0x8000 + ( a>>17 ) - sqrtEvenAdjustments[ (int)index ]; - z = a / z + z; - z = ( 0x20000 <= z ) ? 0xFFFF8000 : ( z<<15 ); - if ( z <= a ) return (uint32_t) ( ( (int32_t) a )>>1 ); - } - return ( (uint32_t) ( ( ( (uint64_t) a )<<31 ) / z ) ) + ( z>>1 ); - -} - -/*---------------------------------------------------------------------------- -| Returns the number of leading 0 bits before the most-significant 1 bit of -| `a'. If `a' is zero, 32 is returned. -*----------------------------------------------------------------------------*/ - -static int8_t countLeadingZeros32( uint32_t a ) -{ -#if SOFTFLOAT_GNUC_PREREQ(3, 4) - if (a) { - return __builtin_clz(a); - } else { - return 32; - } -#else - static const int8_t countLeadingZerosHigh[] = { - 8, 7, 6, 6, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, - 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, - 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, - 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, - 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 - }; - int8_t shiftCount; - - shiftCount = 0; - if ( a < 0x10000 ) { - shiftCount += 16; - a <<= 16; - } - if ( a < 0x1000000 ) { - shiftCount += 8; - a <<= 8; - } - shiftCount += countLeadingZerosHigh[ a>>24 ]; - return shiftCount; -#endif -} - -/*---------------------------------------------------------------------------- -| Returns the number of leading 0 bits before the most-significant 1 bit of -| `a'. If `a' is zero, 64 is returned. -*----------------------------------------------------------------------------*/ - -static int8_t countLeadingZeros64( uint64_t a ) -{ -#if SOFTFLOAT_GNUC_PREREQ(3, 4) - if (a) { - return __builtin_clzll(a); - } else { - return 64; - } -#else - int8_t shiftCount; - - shiftCount = 0; - if ( a < ( (uint64_t) 1 )<<32 ) { - shiftCount += 32; - } - else { - a >>= 32; - } - shiftCount += countLeadingZeros32( a ); - return shiftCount; -#endif -} - -/*---------------------------------------------------------------------------- -| Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' -| is equal to the 128-bit value formed by concatenating `b0' and `b1'. -| Otherwise, returns 0. -*----------------------------------------------------------------------------*/ - -static inline flag eq128( uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1 ) -{ - - return ( a0 == b0 ) && ( a1 == b1 ); - -} - -/*---------------------------------------------------------------------------- -| Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is less -| than or equal to the 128-bit value formed by concatenating `b0' and `b1'. -| Otherwise, returns 0. -*----------------------------------------------------------------------------*/ - -static inline flag le128( uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1 ) -{ - - return ( a0 < b0 ) || ( ( a0 == b0 ) && ( a1 <= b1 ) ); - -} - -/*---------------------------------------------------------------------------- -| Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is less -| than the 128-bit value formed by concatenating `b0' and `b1'. Otherwise, -| returns 0. -*----------------------------------------------------------------------------*/ - -static inline flag lt128( uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1 ) -{ - - return ( a0 < b0 ) || ( ( a0 == b0 ) && ( a1 < b1 ) ); - -} - -/*---------------------------------------------------------------------------- -| Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is -| not equal to the 128-bit value formed by concatenating `b0' and `b1'. -| Otherwise, returns 0. -*----------------------------------------------------------------------------*/ - -static inline flag ne128( uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1 ) -{ - - return ( a0 != b0 ) || ( a1 != b1 ); - -} |