diff options
Diffstat (limited to 'fpu')
| -rw-r--r-- | fpu/softfloat-macros.h | 720 | ||||
| -rw-r--r-- | fpu/softfloat-native.c | 262 | ||||
| -rw-r--r-- | fpu/softfloat-native.h | 312 | ||||
| -rw-r--r-- | fpu/softfloat-specialize.h | 464 | ||||
| -rw-r--r-- | fpu/softfloat.c | 5185 | ||||
| -rw-r--r-- | fpu/softfloat.h | 329 |
6 files changed, 7272 insertions, 0 deletions
diff --git a/fpu/softfloat-macros.h b/fpu/softfloat-macros.h new file mode 100644 index 0000000000..2c8f18b1ce --- /dev/null +++ b/fpu/softfloat-macros.h @@ -0,0 +1,720 @@ + +/*============================================================================ + +This C source fragment is part of the SoftFloat IEC/IEEE Floating-point +Arithmetic Package, Release 2b. + +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://www.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 ALL LOSSES, +COSTS, OR OTHER PROBLEMS THEY INCUR DUE TO THE SOFTWARE, AND WHO FURTHERMORE +EFFECTIVELY INDEMNIFY JOHN HAUSER AND THE INTERNATIONAL COMPUTER SCIENCE +INSTITUTE (possibly via similar legal notice) AGAINST ALL LOSSES, COSTS, OR +OTHER PROBLEMS INCURRED BY THEIR CUSTOMERS AND CLIENTS DUE TO THE SOFTWARE. + +Derivative works are acceptable, even for commercial purposes, so long as +(1) the source code for the derivative work includes prominent notice that +the work is derivative, and (2) the source code includes prominent notice with +these four paragraphs for those parts of this code that are retained. + +=============================================================================*/ + +/*---------------------------------------------------------------------------- +| 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'. +*----------------------------------------------------------------------------*/ + +INLINE void shift32RightJamming( bits32 a, int16 count, bits32 *zPtr ) +{ + bits32 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'. +*----------------------------------------------------------------------------*/ + +INLINE void shift64RightJamming( bits64 a, int16 count, bits64 *zPtr ) +{ + bits64 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'.) +*----------------------------------------------------------------------------*/ + +INLINE void + shift64ExtraRightJamming( + bits64 a0, bits64 a1, int16 count, bits64 *z0Ptr, bits64 *z1Ptr ) +{ + bits64 z0, z1; + int8 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'. +*----------------------------------------------------------------------------*/ + +INLINE void + shift128Right( + bits64 a0, bits64 a1, int16 count, bits64 *z0Ptr, bits64 *z1Ptr ) +{ + bits64 z0, z1; + int8 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 < 64 ) ? ( 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'. +*----------------------------------------------------------------------------*/ + +INLINE void + shift128RightJamming( + bits64 a0, bits64 a1, int16 count, bits64 *z0Ptr, bits64 *z1Ptr ) +{ + bits64 z0, z1; + int8 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'.) +*----------------------------------------------------------------------------*/ + +INLINE void + shift128ExtraRightJamming( + bits64 a0, + bits64 a1, + bits64 a2, + int16 count, + bits64 *z0Ptr, + bits64 *z1Ptr, + bits64 *z2Ptr + ) +{ + bits64 z0, z1, z2; + int8 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'. +*----------------------------------------------------------------------------*/ + +INLINE void + shortShift128Left( + bits64 a0, bits64 a1, int16 count, bits64 *z0Ptr, bits64 *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'. +*----------------------------------------------------------------------------*/ + +INLINE void + shortShift192Left( + bits64 a0, + bits64 a1, + bits64 a2, + int16 count, + bits64 *z0Ptr, + bits64 *z1Ptr, + bits64 *z2Ptr + ) +{ + bits64 z0, z1, z2; + int8 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'. +*----------------------------------------------------------------------------*/ + +INLINE void + add128( + bits64 a0, bits64 a1, bits64 b0, bits64 b1, bits64 *z0Ptr, bits64 *z1Ptr ) +{ + bits64 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'. +*----------------------------------------------------------------------------*/ + +INLINE void + add192( + bits64 a0, + bits64 a1, + bits64 a2, + bits64 b0, + bits64 b1, + bits64 b2, + bits64 *z0Ptr, + bits64 *z1Ptr, + bits64 *z2Ptr + ) +{ + bits64 z0, z1, z2; + int8 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'. +*----------------------------------------------------------------------------*/ + +INLINE void + sub128( + bits64 a0, bits64 a1, bits64 b0, bits64 b1, bits64 *z0Ptr, bits64 *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'. +*----------------------------------------------------------------------------*/ + +INLINE void + sub192( + bits64 a0, + bits64 a1, + bits64 a2, + bits64 b0, + bits64 b1, + bits64 b2, + bits64 *z0Ptr, + bits64 *z1Ptr, + bits64 *z2Ptr + ) +{ + bits64 z0, z1, z2; + int8 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'. +*----------------------------------------------------------------------------*/ + +INLINE void mul64To128( bits64 a, bits64 b, bits64 *z0Ptr, bits64 *z1Ptr ) +{ + bits32 aHigh, aLow, bHigh, bLow; + bits64 z0, zMiddleA, zMiddleB, z1; + + aLow = a; + aHigh = a>>32; + bLow = b; + bHigh = b>>32; + z1 = ( (bits64) aLow ) * bLow; + zMiddleA = ( (bits64) aLow ) * bHigh; + zMiddleB = ( (bits64) aHigh ) * bLow; + z0 = ( (bits64) aHigh ) * bHigh; + zMiddleA += zMiddleB; + z0 += ( ( (bits64) ( 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'. +*----------------------------------------------------------------------------*/ + +INLINE void + mul128By64To192( + bits64 a0, + bits64 a1, + bits64 b, + bits64 *z0Ptr, + bits64 *z1Ptr, + bits64 *z2Ptr + ) +{ + bits64 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'. +*----------------------------------------------------------------------------*/ + +INLINE void + mul128To256( + bits64 a0, + bits64 a1, + bits64 b0, + bits64 b1, + bits64 *z0Ptr, + bits64 *z1Ptr, + bits64 *z2Ptr, + bits64 *z3Ptr + ) +{ + bits64 z0, z1, z2, z3; + bits64 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 bits64 estimateDiv128To64( bits64 a0, bits64 a1, bits64 b ) +{ + bits64 b0, b1; + bits64 rem0, rem1, term0, term1; + bits64 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 ( ( (sbits64) 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; + +} + +/*---------------------------------------------------------------------------- +| 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 bits32 estimateSqrt32( int16 aExp, bits32 a ) +{ + static const bits16 sqrtOddAdjustments[] = { + 0x0004, 0x0022, 0x005D, 0x00B1, 0x011D, 0x019F, 0x0236, 0x02E0, + 0x039C, 0x0468, 0x0545, 0x0631, 0x072B, 0x0832, 0x0946, 0x0A67 + }; + static const bits16 sqrtEvenAdjustments[] = { + 0x0A2D, 0x08AF, 0x075A, 0x0629, 0x051A, 0x0429, 0x0356, 0x029E, + 0x0200, 0x0179, 0x0109, 0x00AF, 0x0068, 0x0034, 0x0012, 0x0002 + }; + int8 index; + bits32 z; + + index = ( a>>27 ) & 15; + if ( aExp & 1 ) { + z = 0x4000 + ( a>>17 ) - sqrtOddAdjustments[ index ]; + z = ( ( a / z )<<14 ) + ( z<<15 ); + a >>= 1; + } + else { + z = 0x8000 + ( a>>17 ) - sqrtEvenAdjustments[ index ]; + z = a / z + z; + z = ( 0x20000 <= z ) ? 0xFFFF8000 : ( z<<15 ); + if ( z <= a ) return (bits32) ( ( (sbits32) a )>>1 ); + } + return ( (bits32) ( ( ( (bits64) 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 countLeadingZeros32( bits32 a ) +{ + static const int8 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 shiftCount; + + shiftCount = 0; + if ( a < 0x10000 ) { + shiftCount += 16; + a <<= 16; + } + if ( a < 0x1000000 ) { + shiftCount += 8; + a <<= 8; + } + shiftCount += countLeadingZerosHigh[ a>>24 ]; + return shiftCount; + +} + +/*---------------------------------------------------------------------------- +| Returns the number of leading 0 bits before the most-significant 1 bit of +| `a'. If `a' is zero, 64 is returned. +*----------------------------------------------------------------------------*/ + +static int8 countLeadingZeros64( bits64 a ) +{ + int8 shiftCount; + + shiftCount = 0; + if ( a < ( (bits64) 1 )<<32 ) { + shiftCount += 32; + } + else { + a >>= 32; + } + shiftCount += countLeadingZeros32( a ); + return shiftCount; + +} + +/*---------------------------------------------------------------------------- +| 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. +*----------------------------------------------------------------------------*/ + +INLINE flag eq128( bits64 a0, bits64 a1, bits64 b0, bits64 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. +*----------------------------------------------------------------------------*/ + +INLINE flag le128( bits64 a0, bits64 a1, bits64 b0, bits64 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. +*----------------------------------------------------------------------------*/ + +INLINE flag lt128( bits64 a0, bits64 a1, bits64 b0, bits64 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. +*----------------------------------------------------------------------------*/ + +INLINE flag ne128( bits64 a0, bits64 a1, bits64 b0, bits64 b1 ) +{ + + return ( a0 != b0 ) || ( a1 != b1 ); + +} + diff --git a/fpu/softfloat-native.c b/fpu/softfloat-native.c new file mode 100644 index 0000000000..8259a7c27c --- /dev/null +++ b/fpu/softfloat-native.c @@ -0,0 +1,262 @@ +/* Native implementation of soft float functions. Only a single status + context is supported */ +#include "softfloat.h" +#include <math.h> + +void set_float_rounding_mode(int val STATUS_PARAM) +{ + STATUS(float_rounding_mode) = val; +#if defined(_BSD) && !defined(__APPLE__) + fpsetround(val); +#elif defined(__arm__) + /* nothing to do */ +#else + fesetround(val); +#endif +} + +#ifdef FLOATX80 +void set_floatx80_rounding_precision(int val STATUS_PARAM) +{ + STATUS(floatx80_rounding_precision) = val; +} +#endif + +#if defined(_BSD) +#define lrint(d) ((int32_t)rint(d)) +#define llrint(d) ((int64_t)rint(d)) +#endif + +#if defined(__powerpc__) + +/* correct (but slow) PowerPC rint() (glibc version is incorrect) */ +double qemu_rint(double x) +{ + double y = 4503599627370496.0; + if (fabs(x) >= y) + return x; + if (x < 0) + y = -y; + y = (x + y) - y; + if (y == 0.0) + y = copysign(y, x); + return y; +} + +#define rint qemu_rint +#endif + +/*---------------------------------------------------------------------------- +| Software IEC/IEEE integer-to-floating-point conversion routines. +*----------------------------------------------------------------------------*/ +float32 int32_to_float32(int v STATUS_PARAM) +{ + return (float32)v; +} + +float64 int32_to_float64(int v STATUS_PARAM) +{ + return (float64)v; +} + +#ifdef FLOATX80 +floatx80 int32_to_floatx80(int v STATUS_PARAM) +{ + return (floatx80)v; +} +#endif +float32 int64_to_float32( int64_t v STATUS_PARAM) +{ + return (float32)v; +} +float64 int64_to_float64( int64_t v STATUS_PARAM) +{ + return (float64)v; +} +#ifdef FLOATX80 +floatx80 int64_to_floatx80( int64_t v STATUS_PARAM) +{ + return (floatx80)v; +} +#endif + +/*---------------------------------------------------------------------------- +| Software IEC/IEEE single-precision conversion routines. +*----------------------------------------------------------------------------*/ +int float32_to_int32( float32 a STATUS_PARAM) +{ + return lrintf(a); +} +int float32_to_int32_round_to_zero( float32 a STATUS_PARAM) +{ + return (int)a; +} +int64_t float32_to_int64( float32 a STATUS_PARAM) +{ + return llrintf(a); +} + +int64_t float32_to_int64_round_to_zero( float32 a STATUS_PARAM) +{ + return (int64_t)a; +} + +float64 float32_to_float64( float32 a STATUS_PARAM) +{ + return a; +} +#ifdef FLOATX80 +floatx80 float32_to_floatx80( float32 a STATUS_PARAM) +{ + return a; +} +#endif + +/*---------------------------------------------------------------------------- +| Software IEC/IEEE single-precision operations. +*----------------------------------------------------------------------------*/ +float32 float32_round_to_int( float32 a STATUS_PARAM) +{ + return rintf(a); +} + +float32 float32_sqrt( float32 a STATUS_PARAM) +{ + return sqrtf(a); +} +char float32_is_signaling_nan( float32 a1) +{ + float32u u; + uint32_t a; + u.f = a1; + a = u.i; + return ( ( ( a>>22 ) & 0x1FF ) == 0x1FE ) && ( a & 0x003FFFFF ); +} + +/*---------------------------------------------------------------------------- +| Software IEC/IEEE double-precision conversion routines. +*----------------------------------------------------------------------------*/ +int float64_to_int32( float64 a STATUS_PARAM) +{ + return lrint(a); +} +int float64_to_int32_round_to_zero( float64 a STATUS_PARAM) +{ + return (int)a; +} +int64_t float64_to_int64( float64 a STATUS_PARAM) +{ + return llrint(a); +} +int64_t float64_to_int64_round_to_zero( float64 a STATUS_PARAM) +{ + return (int64_t)a; +} +float32 float64_to_float32( float64 a STATUS_PARAM) +{ + return a; +} +#ifdef FLOATX80 +floatx80 float64_to_floatx80( float64 a STATUS_PARAM) +{ + return a; +} +#endif +#ifdef FLOAT128 +float128 float64_to_float128( float64 a STATUS_PARAM) +{ + return a; +} +#endif + +/*---------------------------------------------------------------------------- +| Software IEC/IEEE double-precision operations. +*----------------------------------------------------------------------------*/ +float64 float64_round_to_int( float64 a STATUS_PARAM ) +{ +#if defined(__arm__) + switch(STATUS(float_rounding_mode)) { + default: + case float_round_nearest_even: + asm("rndd %0, %1" : "=f" (a) : "f"(a)); + break; + case float_round_down: + asm("rnddm %0, %1" : "=f" (a) : "f"(a)); + break; + case float_round_up: + asm("rnddp %0, %1" : "=f" (a) : "f"(a)); + break; + case float_round_to_zero: + asm("rnddz %0, %1" : "=f" (a) : "f"(a)); + break; + } +#else + return rint(a); +#endif +} + +float64 float64_sqrt( float64 a STATUS_PARAM) +{ + return sqrt(a); +} +char float64_is_signaling_nan( float64 a1) +{ + float64u u; + uint64_t a; + u.f = a1; + a = u.i; + return + ( ( ( a>>51 ) & 0xFFF ) == 0xFFE ) + && ( a & LIT64( 0x0007FFFFFFFFFFFF ) ); + +} + +#ifdef FLOATX80 + +/*---------------------------------------------------------------------------- +| Software IEC/IEEE extended double-precision conversion routines. +*----------------------------------------------------------------------------*/ +int floatx80_to_int32( floatx80 a STATUS_PARAM) +{ + return lrintl(a); +} +int floatx80_to_int32_round_to_zero( floatx80 a STATUS_PARAM) +{ + return (int)a; +} +int64_t floatx80_to_int64( floatx80 a STATUS_PARAM) +{ + return llrintl(a); +} +int64_t floatx80_to_int64_round_to_zero( floatx80 a STATUS_PARAM) +{ + return (int64_t)a; +} +float32 floatx80_to_float32( floatx80 a STATUS_PARAM) +{ + return a; +} +float64 floatx80_to_float64( floatx80 a STATUS_PARAM) +{ + return a; +} + +/*---------------------------------------------------------------------------- +| Software IEC/IEEE extended double-precision operations. +*----------------------------------------------------------------------------*/ +floatx80 floatx80_round_to_int( floatx80 a STATUS_PARAM) +{ + return rintl(a); +} +floatx80 floatx80_sqrt( floatx80 a STATUS_PARAM) +{ + return sqrtl(a); +} +char floatx80_is_signaling_nan( floatx80 a1) +{ + floatx80u u; + u.f = a1; + return ( ( u.i.high & 0x7FFF ) == 0x7FFF ) && (bits64) ( u.i.low<<1 ); +} + +#endif diff --git a/fpu/softfloat-native.h b/fpu/softfloat-native.h new file mode 100644 index 0000000000..709df51bcf --- /dev/null +++ b/fpu/softfloat-native.h @@ -0,0 +1,312 @@ +/* Native implementation of soft float functions */ +#include <math.h> +#if defined(_BSD) && !defined(__APPLE__) +#include <ieeefp.h> +#else +#include <fenv.h> +#endif + +typedef float float32; +typedef double float64; +#ifdef FLOATX80 +typedef long double floatx80; +#endif + +typedef union { + float32 f; + uint32_t i; +} float32u; +typedef union { + float64 f; + uint64_t i; +} float64u; +#ifdef FLOATX80 +typedef union { + floatx80 f; + struct { + uint64_t low; + uint16_t high; + } i; +} floatx80u; +#endif + +/*---------------------------------------------------------------------------- +| Software IEC/IEEE floating-point rounding mode. +*----------------------------------------------------------------------------*/ +#if defined(_BSD) && !defined(__APPLE__) +enum { + float_round_nearest_even = FP_RN, + float_round_down = FE_RM, + float_round_up = FE_RP, + float_round_to_zero = FE_RZ +}; +#elif defined(__arm__) +enum { + float_round_nearest_even = 0, + float_round_down = 1, + float_round_up = 2, + float_round_to_zero = 3 +}; +#else +enum { + float_round_nearest_even = FE_TONEAREST, + float_round_down = FE_DOWNWARD, + float_round_up = FE_UPWARD, + float_round_to_zero = FE_TOWARDZERO +}; +#endif + +typedef struct float_status { + signed char float_rounding_mode; +#ifdef FLOATX80 + signed char floatx80_rounding_precision; +#endif +} float_status; + +void set_float_rounding_mode(int val STATUS_PARAM); +#ifdef FLOATX80 +void set_floatx80_rounding_precision(int val STATUS_PARAM); +#endif + +/*---------------------------------------------------------------------------- +| Software IEC/IEEE integer-to-floating-point conversion routines. +*----------------------------------------------------------------------------*/ +float32 int32_to_float32( int STATUS_PARAM); +float64 int32_to_float64( int STATUS_PARAM); +#ifdef FLOATX80 +floatx80 int32_to_floatx80( int STATUS_PARAM); +#endif +#ifdef FLOAT128 +float128 int32_to_float128( int STATUS_PARAM); +#endif +float32 int64_to_float32( int64_t STATUS_PARAM); +float64 int64_to_float64( int64_t STATUS_PARAM); +#ifdef FLOATX80 +floatx80 int64_to_floatx80( int64_t STATUS_PARAM); +#endif +#ifdef FLOAT128 +float128 int64_to_float128( int64_t STATUS_PARAM); +#endif + +/*---------------------------------------------------------------------------- +| Software IEC/IEEE single-precision conversion routines. +*----------------------------------------------------------------------------*/ +int float32_to_int32( float32 STATUS_PARAM); +int float32_to_int32_round_to_zero( float32 STATUS_PARAM); +int64_t float32_to_int64( float32 STATUS_PARAM); +int64_t float32_to_int64_round_to_zero( float32 STATUS_PARAM); +float64 float32_to_float64( float32 STATUS_PARAM); +#ifdef FLOATX80 +floatx80 float32_to_floatx80( float32 STATUS_PARAM); +#endif +#ifdef FLOAT128 +float128 float32_to_float128( float32 STATUS_PARAM); +#endif + +/*---------------------------------------------------------------------------- +| Software IEC/IEEE single-precision operations. +*----------------------------------------------------------------------------*/ +float32 float32_round_to_int( float32 STATUS_PARAM); +INLINE float32 float32_add( float32 a, float32 b STATUS_PARAM) +{ + return a + b; +} +INLINE float32 float32_sub( float32 a, float32 b STATUS_PARAM) +{ + return a - b; +} +INLINE float32 float32_mul( float32 a, float32 b STATUS_PARAM) +{ + return a * b; +} +INLINE float32 float32_div( float32 a, float32 b STATUS_PARAM) +{ + return a / b; +} +float32 float32_rem( float32, float32 STATUS_PARAM); +float32 float32_sqrt( float32 STATUS_PARAM); +INLINE char float32_eq( float32 a, float32 b STATUS_PARAM) +{ + /* XXX: incorrect because it can raise an exception */ + return a == b; +} +INLINE char float32_le( float32 a, float32 b STATUS_PARAM) +{ + return a <= b; +} +INLINE char float32_lt( float32 a, float32 b STATUS_PARAM) +{ + return a < b; +} +INLINE char float32_eq_signaling( float32 a, float32 b STATUS_PARAM) +{ + return a == b; +} +INLINE char float32_le_quiet( float32 a, float32 b STATUS_PARAM) +{ + return islessequal(a, b); +} +INLINE char float32_lt_quiet( float32 a, float32 b STATUS_PARAM) +{ + return isless(a, b); +} +char float32_is_signaling_nan( float32 ); + +INLINE float32 float32_abs(float32 a) +{ + return fabsf(a); +} + +INLINE float32 float32_chs(float32 a) +{ + return -a; +} + +/*---------------------------------------------------------------------------- +| Software IEC/IEEE double-precision conversion routines. +*----------------------------------------------------------------------------*/ +int float64_to_int32( float64 STATUS_PARAM ); +int float64_to_int32_round_to_zero( float64 STATUS_PARAM ); +int64_t float64_to_int64( float64 STATUS_PARAM ); +int64_t float64_to_int64_round_to_zero( float64 STATUS_PARAM ); +float32 float64_to_float32( float64 STATUS_PARAM ); +#ifdef FLOATX80 +floatx80 float64_to_floatx80( float64 STATUS_PARAM ); +#endif +#ifdef FLOAT128 +float128 float64_to_float128( float64 STATUS_PARAM ); +#endif + +/*---------------------------------------------------------------------------- +| Software IEC/IEEE double-precision operations. +*----------------------------------------------------------------------------*/ +float64 float64_round_to_int( float64 STATUS_PARAM ); +INLINE float64 float64_add( float64 a, float64 b STATUS_PARAM) +{ + return a + b; +} +INLINE float64 float64_sub( float64 a, float64 b STATUS_PARAM) +{ + return a - b; +} +INLINE float64 float64_mul( float64 a, float64 b STATUS_PARAM) +{ + return a * b; +} +INLINE float64 float64_div( float64 a, float64 b STATUS_PARAM) +{ + return a / b; +} +float64 float64_rem( float64, float64 STATUS_PARAM ); +float64 float64_sqrt( float64 STATUS_PARAM ); +INLINE char float64_eq( float64 a, float64 b STATUS_PARAM) +{ + return a == b; +} +INLINE char float64_le( float64 a, float64 b STATUS_PARAM) +{ + return a <= b; +} +INLINE char float64_lt( float64 a, float64 b STATUS_PARAM) +{ + return a < b; +} +INLINE char float64_eq_signaling( float64 a, float64 b STATUS_PARAM) +{ + return a == b; +} +INLINE char float64_le_quiet( float64 a, float64 b STATUS_PARAM) +{ + return islessequal(a, b); +} +INLINE char float64_lt_quiet( float64 a, float64 b STATUS_PARAM) +{ + return isless(a, b); + +} +char float64_is_signaling_nan( float64 ); + +INLINE float64 float64_abs(float64 a) +{ + return fabs(a); +} + +INLINE float64 float64_chs(float64 a) +{ + return -a; +} + +#ifdef FLOATX80 + +/*---------------------------------------------------------------------------- +| Software IEC/IEEE extended double-precision conversion routines. +*----------------------------------------------------------------------------*/ +int floatx80_to_int32( floatx80 STATUS_PARAM ); +int floatx80_to_int32_round_to_zero( floatx80 STATUS_PARAM ); +int64_t floatx80_to_int64( floatx80 STATUS_PARAM); +int64_t floatx80_to_int64_round_to_zero( floatx80 STATUS_PARAM); +float32 floatx80_to_float32( floatx80 STATUS_PARAM ); +float64 floatx80_to_float64( floatx80 STATUS_PARAM ); +#ifdef FLOAT128 +float128 floatx80_to_float128( floatx80 STATUS_PARAM ); +#endif + +/*---------------------------------------------------------------------------- +| Software IEC/IEEE extended double-precision operations. +*----------------------------------------------------------------------------*/ +floatx80 floatx80_round_to_int( floatx80 STATUS_PARAM ); +INLINE floatx80 floatx80_add( floatx80 a, floatx80 b STATUS_PARAM) +{ + return a + b; +} +INLINE floatx80 floatx80_sub( floatx80 a, floatx80 b STATUS_PARAM) +{ + return a - b; +} +INLINE floatx80 floatx80_mul( floatx80 a, floatx80 b STATUS_PARAM) +{ + return a * b; +} +INLINE floatx80 floatx80_div( floatx80 a, floatx80 b STATUS_PARAM) +{ + return a / b; +} +floatx80 floatx80_rem( floatx80, floatx80 STATUS_PARAM ); +floatx80 floatx80_sqrt( floatx80 STATUS_PARAM ); +INLINE char floatx80_eq( floatx80 a, floatx80 b STATUS_PARAM) +{ + return a == b; +} +INLINE char floatx80_le( floatx80 a, floatx80 b STATUS_PARAM) +{ + return a <= b; +} +INLINE char floatx80_lt( floatx80 a, floatx80 b STATUS_PARAM) +{ + return a < b; +} +INLINE char floatx80_eq_signaling( floatx80 a, floatx80 b STATUS_PARAM) +{ + return a == b; +} +INLINE char floatx80_le_quiet( floatx80 a, floatx80 b STATUS_PARAM) +{ + return islessequal(a, b); +} +INLINE char floatx80_lt_quiet( floatx80 a, floatx80 b STATUS_PARAM) +{ + return isless(a, b); + +} +char floatx80_is_signaling_nan( floatx80 ); + +INLINE floatx80 floatx80_abs(floatx80 a) +{ + return fabsl(a); +} + +INLINE floatx80 floatx80_chs(floatx80 a) +{ + return -a; +} +#endif diff --git a/fpu/softfloat-specialize.h b/fpu/softfloat-specialize.h new file mode 100644 index 0000000000..d430f58a71 --- /dev/null +++ b/fpu/softfloat-specialize.h @@ -0,0 +1,464 @@ + +/*============================================================================ + +This C source fragment is part of the SoftFloat IEC/IEEE Floating-point +Arithmetic Package, Release 2b. + +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://www.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 ALL LOSSES, +COSTS, OR OTHER PROBLEMS THEY INCUR DUE TO THE SOFTWARE, AND WHO FURTHERMORE +EFFECTIVELY INDEMNIFY JOHN HAUSER AND THE INTERNATIONAL COMPUTER SCIENCE +INSTITUTE (possibly via similar legal warning) AGAINST ALL LOSSES, COSTS, OR +OTHER PROBLEMS INCURRED BY THEIR CUSTOMERS AND CLIENTS DUE TO THE SOFTWARE. + +Derivative works are acceptable, even for commercial purposes, so long as +(1) the source code for the derivative work includes prominent notice that +the work is derivative, and (2) the source code includes prominent notice with +these four paragraphs for those parts of this code that are retained. + +=============================================================================*/ + +/*---------------------------------------------------------------------------- +| Underflow tininess-detection mode, statically initialized to default value. +| (The declaration in `softfloat.h' must match the `int8' type here.) +*----------------------------------------------------------------------------*/ +int8 float_detect_tininess = float_tininess_after_rounding; + +/*---------------------------------------------------------------------------- +| Raises the exceptions specified by `flags'. Floating-point traps can be +| defined here if desired. It is currently not possible for such a trap +| to substitute a result value. If traps are not implemented, this routine +| should be simply `float_exception_flags |= flags;'. +*----------------------------------------------------------------------------*/ + +void float_raise( int8 flags STATUS_PARAM ) +{ + + STATUS(float_exception_flags) |= flags; + +} + +/*---------------------------------------------------------------------------- +| Internal canonical NaN format. +*----------------------------------------------------------------------------*/ +typedef struct { + flag sign; + bits64 high, low; +} commonNaNT; + +/*---------------------------------------------------------------------------- +| The pattern for a default generated single-precision NaN. +*----------------------------------------------------------------------------*/ +#define float32_default_nan 0xFFC00000 + +/*---------------------------------------------------------------------------- +| Returns 1 if the single-precision floating-point value `a' is a NaN; +| otherwise returns 0. +*----------------------------------------------------------------------------*/ + +flag float32_is_nan( float32 a ) +{ + + return ( 0xFF000000 < (bits32) ( a<<1 ) ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the single-precision floating-point value `a' is a signaling +| NaN; otherwise returns 0. +*----------------------------------------------------------------------------*/ + +flag float32_is_signaling_nan( float32 a ) +{ + + return ( ( ( a>>22 ) & 0x1FF ) == 0x1FE ) && ( a & 0x003FFFFF ); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the single-precision floating-point NaN +| `a' to the canonical NaN format. If `a' is a signaling NaN, the invalid +| exception is raised. +*----------------------------------------------------------------------------*/ + +static commonNaNT float32ToCommonNaN( float32 a STATUS_PARAM ) +{ + commonNaNT z; + + if ( float32_is_signaling_nan( a ) ) float_raise( float_flag_invalid STATUS_VAR ); + z.sign = a>>31; + z.low = 0; + z.high = ( (bits64) a )<<41; + return z; + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the canonical NaN `a' to the single- +| precision floating-point format. +*----------------------------------------------------------------------------*/ + +static float32 commonNaNToFloat32( commonNaNT a ) +{ + + return ( ( (bits32) a.sign )<<31 ) | 0x7FC00000 | ( a.high>>41 ); + +} + +/*---------------------------------------------------------------------------- +| Takes two single-precision floating-point values `a' and `b', one of which +| is a NaN, and returns the appropriate NaN result. If either `a' or `b' is a +| signaling NaN, the invalid exception is raised. +*----------------------------------------------------------------------------*/ + +static float32 propagateFloat32NaN( float32 a, float32 b STATUS_PARAM) +{ + flag aIsNaN, aIsSignalingNaN, bIsNaN, bIsSignalingNaN; + + aIsNaN = float32_is_nan( a ); + aIsSignalingNaN = float32_is_signaling_nan( a ); + bIsNaN = float32_is_nan( b ); + bIsSignalingNaN = float32_is_signaling_nan( b ); + a |= 0x00400000; + b |= 0x00400000; + if ( aIsSignalingNaN | bIsSignalingNaN ) float_raise( float_flag_invalid STATUS_VAR); + if ( aIsSignalingNaN ) { + if ( bIsSignalingNaN ) goto returnLargerSignificand; + return bIsNaN ? b : a; + } + else if ( aIsNaN ) { + if ( bIsSignalingNaN | ! bIsNaN ) return a; + returnLargerSignificand: + if ( (bits32) ( a<<1 ) < (bits32) ( b<<1 ) ) return b; + if ( (bits32) ( b<<1 ) < (bits32) ( a<<1 ) ) return a; + return ( a < b ) ? a : b; + } + else { + return b; + } + +} + +/*---------------------------------------------------------------------------- +| The pattern for a default generated double-precision NaN. +*----------------------------------------------------------------------------*/ +#define float64_default_nan LIT64( 0xFFF8000000000000 ) + +/*---------------------------------------------------------------------------- +| Returns 1 if the double-precision floating-point value `a' is a NaN; +| otherwise returns 0. +*----------------------------------------------------------------------------*/ + +flag float64_is_nan( float64 a ) +{ + + return ( LIT64( 0xFFE0000000000000 ) < (bits64) ( a<<1 ) ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the double-precision floating-point value `a' is a signaling +| NaN; otherwise returns 0. +*----------------------------------------------------------------------------*/ + +flag float64_is_signaling_nan( float64 a ) +{ + + return + ( ( ( a>>51 ) & 0xFFF ) == 0xFFE ) + && ( a & LIT64( 0x0007FFFFFFFFFFFF ) ); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the double-precision floating-point NaN +| `a' to the canonical NaN format. If `a' is a signaling NaN, the invalid +| exception is raised. +*----------------------------------------------------------------------------*/ + +static commonNaNT float64ToCommonNaN( float64 a STATUS_PARAM) +{ + commonNaNT z; + + if ( float64_is_signaling_nan( a ) ) float_raise( float_flag_invalid STATUS_VAR); + z.sign = a>>63; + z.low = 0; + z.high = a<<12; + return z; + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the canonical NaN `a' to the double- +| precision floating-point format. +*----------------------------------------------------------------------------*/ + +static float64 commonNaNToFloat64( commonNaNT a ) +{ + + return + ( ( (bits64) a.sign )<<63 ) + | LIT64( 0x7FF8000000000000 ) + | ( a.high>>12 ); + +} + +/*---------------------------------------------------------------------------- +| Takes two double-precision floating-point values `a' and `b', one of which +| is a NaN, and returns the appropriate NaN result. If either `a' or `b' is a +| signaling NaN, the invalid exception is raised. +*----------------------------------------------------------------------------*/ + +static float64 propagateFloat64NaN( float64 a, float64 b STATUS_PARAM) +{ + flag aIsNaN, aIsSignalingNaN, bIsNaN, bIsSignalingNaN; + + aIsNaN = float64_is_nan( a ); + aIsSignalingNaN = float64_is_signaling_nan( a ); + bIsNaN = float64_is_nan( b ); + bIsSignalingNaN = float64_is_signaling_nan( b ); + a |= LIT64( 0x0008000000000000 ); + b |= LIT64( 0x0008000000000000 ); + if ( aIsSignalingNaN | bIsSignalingNaN ) float_raise( float_flag_invalid STATUS_VAR); + if ( aIsSignalingNaN ) { + if ( bIsSignalingNaN ) goto returnLargerSignificand; + return bIsNaN ? b : a; + } + else if ( aIsNaN ) { + if ( bIsSignalingNaN | ! bIsNaN ) return a; + returnLargerSignificand: + if ( (bits64) ( a<<1 ) < (bits64) ( b<<1 ) ) return b; + if ( (bits64) ( b<<1 ) < (bits64) ( a<<1 ) ) return a; + return ( a < b ) ? a : b; + } + else { + return b; + } + +} + +#ifdef FLOATX80 + +/*---------------------------------------------------------------------------- +| The pattern for a default generated extended double-precision NaN. The +| `high' and `low' values hold the most- and least-significant bits, +| respectively. +*----------------------------------------------------------------------------*/ +#define floatx80_default_nan_high 0xFFFF +#define floatx80_default_nan_low LIT64( 0xC000000000000000 ) + +/*---------------------------------------------------------------------------- +| Returns 1 if the extended double-precision floating-point value `a' is a +| NaN; otherwise returns 0. +*----------------------------------------------------------------------------*/ + +flag floatx80_is_nan( floatx80 a ) +{ + + return ( ( a.high & 0x7FFF ) == 0x7FFF ) && (bits64) ( a.low<<1 ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the extended double-precision floating-point value `a' is a +| signaling NaN; otherwise returns 0. +*----------------------------------------------------------------------------*/ + +flag floatx80_is_signaling_nan( floatx80 a ) +{ + bits64 aLow; + + aLow = a.low & ~ LIT64( 0x4000000000000000 ); + return + ( ( a.high & 0x7FFF ) == 0x7FFF ) + && (bits64) ( aLow<<1 ) + && ( a.low == aLow ); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the extended double-precision floating- +| point NaN `a' to the canonical NaN format. If `a' is a signaling NaN, the +| invalid exception is raised. +*----------------------------------------------------------------------------*/ + +static commonNaNT floatx80ToCommonNaN( floatx80 a STATUS_PARAM) +{ + commonNaNT z; + + if ( floatx80_is_signaling_nan( a ) ) float_raise( float_flag_invalid STATUS_VAR); + z.sign = a.high>>15; + z.low = 0; + z.high = a.low<<1; + return z; + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the canonical NaN `a' to the extended +| double-precision floating-point format. +*----------------------------------------------------------------------------*/ + +static floatx80 commonNaNToFloatx80( commonNaNT a ) +{ + floatx80 z; + + z.low = LIT64( 0xC000000000000000 ) | ( a.high>>1 ); + z.high = ( ( (bits16) a.sign )<<15 ) | 0x7FFF; + return z; + +} + +/*---------------------------------------------------------------------------- +| Takes two extended double-precision floating-point values `a' and `b', one +| of which is a NaN, and returns the appropriate NaN result. If either `a' or +| `b' is a signaling NaN, the invalid exception is raised. +*----------------------------------------------------------------------------*/ + +static floatx80 propagateFloatx80NaN( floatx80 a, floatx80 b STATUS_PARAM) +{ + flag aIsNaN, aIsSignalingNaN, bIsNaN, bIsSignalingNaN; + + aIsNaN = floatx80_is_nan( a ); + aIsSignalingNaN = floatx80_is_signaling_nan( a ); + bIsNaN = floatx80_is_nan( b ); + bIsSignalingNaN = floatx80_is_signaling_nan( b ); + a.low |= LIT64( 0xC000000000000000 ); + b.low |= LIT64( 0xC000000000000000 ); + if ( aIsSignalingNaN | bIsSignalingNaN ) float_raise( float_flag_invalid STATUS_VAR); + if ( aIsSignalingNaN ) { + if ( bIsSignalingNaN ) goto returnLargerSignificand; + return bIsNaN ? b : a; + } + else if ( aIsNaN ) { + if ( bIsSignalingNaN | ! bIsNaN ) return a; + returnLargerSignificand: + if ( a.low < b.low ) return b; + if ( b.low < a.low ) return a; + return ( a.high < b.high ) ? a : b; + } + else { + return b; + } + +} + +#endif + +#ifdef FLOAT128 + +/*---------------------------------------------------------------------------- +| The pattern for a default generated quadruple-precision NaN. The `high' and +| `low' values hold the most- and least-significant bits, respectively. +*----------------------------------------------------------------------------*/ +#define float128_default_nan_high LIT64( 0xFFFF800000000000 ) +#define float128_default_nan_low LIT64( 0x0000000000000000 ) + +/*---------------------------------------------------------------------------- +| Returns 1 if the quadruple-precision floating-point value `a' is a NaN; +| otherwise returns 0. +*----------------------------------------------------------------------------*/ + +flag float128_is_nan( float128 a ) +{ + + return + ( LIT64( 0xFFFE000000000000 ) <= (bits64) ( a.high<<1 ) ) + && ( a.low || ( a.high & LIT64( 0x0000FFFFFFFFFFFF ) ) ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the quadruple-precision floating-point value `a' is a +| signaling NaN; otherwise returns 0. +*----------------------------------------------------------------------------*/ + +flag float128_is_signaling_nan( float128 a ) +{ + + return + ( ( ( a.high>>47 ) & 0xFFFF ) == 0xFFFE ) + && ( a.low || ( a.high & LIT64( 0x00007FFFFFFFFFFF ) ) ); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the quadruple-precision floating-point NaN +| `a' to the canonical NaN format. If `a' is a signaling NaN, the invalid +| exception is raised. +*----------------------------------------------------------------------------*/ + +static commonNaNT float128ToCommonNaN( float128 a STATUS_PARAM) +{ + commonNaNT z; + + if ( float128_is_signaling_nan( a ) ) float_raise( float_flag_invalid STATUS_VAR); + z.sign = a.high>>63; + shortShift128Left( a.high, a.low, 16, &z.high, &z.low ); + return z; + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the canonical NaN `a' to the quadruple- +| precision floating-point format. +*----------------------------------------------------------------------------*/ + +static float128 commonNaNToFloat128( commonNaNT a ) +{ + float128 z; + + shift128Right( a.high, a.low, 16, &z.high, &z.low ); + z.high |= ( ( (bits64) a.sign )<<63 ) | LIT64( 0x7FFF800000000000 ); + return z; + +} + +/*---------------------------------------------------------------------------- +| Takes two quadruple-precision floating-point values `a' and `b', one of +| which is a NaN, and returns the appropriate NaN result. If either `a' or +| `b' is a signaling NaN, the invalid exception is raised. +*----------------------------------------------------------------------------*/ + +static float128 propagateFloat128NaN( float128 a, float128 b STATUS_PARAM) +{ + flag aIsNaN, aIsSignalingNaN, bIsNaN, bIsSignalingNaN; + + aIsNaN = float128_is_nan( a ); + aIsSignalingNaN = float128_is_signaling_nan( a ); + bIsNaN = float128_is_nan( b ); + bIsSignalingNaN = float128_is_signaling_nan( b ); + a.high |= LIT64( 0x0000800000000000 ); + b.high |= LIT64( 0x0000800000000000 ); + if ( aIsSignalingNaN | bIsSignalingNaN ) float_raise( float_flag_invalid STATUS_VAR); + if ( aIsSignalingNaN ) { + if ( bIsSignalingNaN ) goto returnLargerSignificand; + return bIsNaN ? b : a; + } + else if ( aIsNaN ) { + if ( bIsSignalingNaN | ! bIsNaN ) return a; + returnLargerSignificand: + if ( lt128( a.high<<1, a.low, b.high<<1, b.low ) ) return b; + if ( lt128( b.high<<1, b.low, a.high<<1, a.low ) ) return a; + return ( a.high < b.high ) ? a : b; + } + else { + return b; + } + +} + +#endif + diff --git a/fpu/softfloat.c b/fpu/softfloat.c new file mode 100644 index 0000000000..ad57fd9e16 --- /dev/null +++ b/fpu/softfloat.c @@ -0,0 +1,5185 @@ + +/*============================================================================ + +This C source file is part of the SoftFloat IEC/IEEE Floating-point Arithmetic +Package, Release 2b. + +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://www.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 ALL LOSSES, +COSTS, OR OTHER PROBLEMS THEY INCUR DUE TO THE SOFTWARE, AND WHO FURTHERMORE +EFFECTIVELY INDEMNIFY JOHN HAUSER AND THE INTERNATIONAL COMPUTER SCIENCE +INSTITUTE (possibly via similar legal warning) AGAINST ALL LOSSES, COSTS, OR +OTHER PROBLEMS INCURRED BY THEIR CUSTOMERS AND CLIENTS DUE TO THE SOFTWARE. + +Derivative works are acceptable, even for commercial purposes, so long as +(1) the source code for the derivative work includes prominent notice that +the work is derivative, and (2) the source code includes prominent notice with +these four paragraphs for those parts of this code that are retained. + +=============================================================================*/ + +#include "softfloat.h" + +/*---------------------------------------------------------------------------- +| Primitive arithmetic functions, including multi-word arithmetic, and +| division and square root approximations. (Can be specialized to target if +| desired.) +*----------------------------------------------------------------------------*/ +#include "softfloat-macros.h" + +/*---------------------------------------------------------------------------- +| Functions and definitions to determine: (1) whether tininess for underflow +| is detected before or after rounding by default, (2) what (if anything) +| happens when exceptions are raised, (3) how signaling NaNs are distinguished +| from quiet NaNs, (4) the default generated quiet NaNs, and (5) how NaNs +| are propagated from function inputs to output. These details are target- +| specific. +*----------------------------------------------------------------------------*/ +#include "softfloat-specialize.h" + +void set_float_rounding_mode(int val STATUS_PARAM) +{ + STATUS(float_rounding_mode) = val; +} + +#ifdef FLOATX80 +void set_floatx80_rounding_precision(int val STATUS_PARAM) +{ + STATUS(floatx80_rounding_precision) = val; +} +#endif + +/*---------------------------------------------------------------------------- +| Takes a 64-bit fixed-point value `absZ' with binary point between bits 6 +| and 7, and returns the properly rounded 32-bit integer corresponding to the +| input. If `zSign' is 1, the input is negated before being converted to an +| integer. Bit 63 of `absZ' must be zero. Ordinarily, the fixed-point input +| is simply rounded to an integer, with the inexact exception raised if the +| input cannot be represented exactly as an integer. However, if the fixed- +| point input is too large, the invalid exception is raised and the largest +| positive or negative integer is returned. +*----------------------------------------------------------------------------*/ + +static int32 roundAndPackInt32( flag zSign, bits64 absZ STATUS_PARAM) +{ + int8 roundingMode; + flag roundNearestEven; + int8 roundIncrement, roundBits; + int32 z; + + roundingMode = STATUS(float_rounding_mode); + roundNearestEven = ( roundingMode == float_round_nearest_even ); + roundIncrement = 0x40; + if ( ! roundNearestEven ) { + if ( roundingMode == float_round_to_zero ) { + roundIncrement = 0; + } + else { + roundIncrement = 0x7F; + if ( zSign ) { + if ( roundingMode == float_round_up ) roundIncrement = 0; + } + else { + if ( roundingMode == float_round_down ) roundIncrement = 0; + } + } + } + roundBits = absZ & 0x7F; + absZ = ( absZ + roundIncrement )>>7; + absZ &= ~ ( ( ( roundBits ^ 0x40 ) == 0 ) & roundNearestEven ); + z = absZ; + if ( zSign ) z = - z; + if ( ( absZ>>32 ) || ( z && ( ( z < 0 ) ^ zSign ) ) ) { + float_raise( float_flag_invalid STATUS_VAR); + return zSign ? (sbits32) 0x80000000 : 0x7FFFFFFF; + } + if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact; + return z; + +} + +/*---------------------------------------------------------------------------- +| Takes the 128-bit fixed-point value formed by concatenating `absZ0' and +| `absZ1', with binary point between bits 63 and 64 (between the input words), +| and returns the properly rounded 64-bit integer corresponding to the input. +| If `zSign' is 1, the input is negated before being converted to an integer. +| Ordinarily, the fixed-point input is simply rounded to an integer, with +| the inexact exception raised if the input cannot be represented exactly as +| an integer. However, if the fixed-point input is too large, the invalid +| exception is raised and the largest positive or negative integer is +| returned. +*----------------------------------------------------------------------------*/ + +static int64 roundAndPackInt64( flag zSign, bits64 absZ0, bits64 absZ1 STATUS_PARAM) +{ + int8 roundingMode; + flag roundNearestEven, increment; + int64 z; + + roundingMode = STATUS(float_rounding_mode); + roundNearestEven = ( roundingMode == float_round_nearest_even ); + increment = ( (sbits64) absZ1 < 0 ); + if ( ! roundNearestEven ) { + if ( roundingMode == float_round_to_zero ) { + increment = 0; + } + else { + if ( zSign ) { + increment = ( roundingMode == float_round_down ) && absZ1; + } + else { + increment = ( roundingMode == float_round_up ) && absZ1; + } + } + } + if ( increment ) { + ++absZ0; + if ( absZ0 == 0 ) goto overflow; + absZ0 &= ~ ( ( (bits64) ( absZ1<<1 ) == 0 ) & roundNearestEven ); + } + z = absZ0; + if ( zSign ) z = - z; + if ( z && ( ( z < 0 ) ^ zSign ) ) { + overflow: + float_raise( float_flag_invalid STATUS_VAR); + return + zSign ? (sbits64) LIT64( 0x8000000000000000 ) + : LIT64( 0x7FFFFFFFFFFFFFFF ); + } + if ( absZ1 ) STATUS(float_exception_flags) |= float_flag_inexact; + return z; + +} + +/*---------------------------------------------------------------------------- +| Returns the fraction bits of the single-precision floating-point value `a'. +*----------------------------------------------------------------------------*/ + +INLINE bits32 extractFloat32Frac( float32 a ) +{ + + return a & 0x007FFFFF; + +} + +/*---------------------------------------------------------------------------- +| Returns the exponent bits of the single-precision floating-point value `a'. +*----------------------------------------------------------------------------*/ + +INLINE int16 extractFloat32Exp( float32 a ) +{ + + return ( a>>23 ) & 0xFF; + +} + +/*---------------------------------------------------------------------------- +| Returns the sign bit of the single-precision floating-point value `a'. +*----------------------------------------------------------------------------*/ + +INLINE flag extractFloat32Sign( float32 a ) +{ + + return a>>31; + +} + +/*---------------------------------------------------------------------------- +| Normalizes the subnormal single-precision floating-point value represented +| by the denormalized significand `aSig'. The normalized exponent and +| significand are stored at the locations pointed to by `zExpPtr' and +| `zSigPtr', respectively. +*----------------------------------------------------------------------------*/ + +static void + normalizeFloat32Subnormal( bits32 aSig, int16 *zExpPtr, bits32 *zSigPtr ) +{ + int8 shiftCount; + + shiftCount = countLeadingZeros32( aSig ) - 8; + *zSigPtr = aSig<<shiftCount; + *zExpPtr = 1 - shiftCount; + +} + +/*---------------------------------------------------------------------------- +| Packs the sign `zSign', exponent `zExp', and significand `zSig' into a +| single-precision floating-point value, returning the result. After being +| shifted into the proper positions, the three fields are simply added +| together to form the result. This means that any integer portion of `zSig' +| will be added into the exponent. Since a properly normalized significand +| will have an integer portion equal to 1, the `zExp' input should be 1 less +| than the desired result exponent whenever `zSig' is a complete, normalized +| significand. +*----------------------------------------------------------------------------*/ + +INLINE float32 packFloat32( flag zSign, int16 zExp, bits32 zSig ) +{ + + return ( ( (bits32) zSign )<<31 ) + ( ( (bits32) zExp )<<23 ) + zSig; + +} + +/*---------------------------------------------------------------------------- +| Takes an abstract floating-point value having sign `zSign', exponent `zExp', +| and significand `zSig', and returns the proper single-precision floating- +| point value corresponding to the abstract input. Ordinarily, the abstract +| value is simply rounded and packed into the single-precision format, with +| the inexact exception raised if the abstract input cannot be represented +| exactly. However, if the abstract value is too large, the overflow and +| inexact exceptions are raised and an infinity or maximal finite value is +| returned. If the abstract value is too small, the input value is rounded to +| a subnormal number, and the underflow and inexact exceptions are raised if +| the abstract input cannot be represented exactly as a subnormal single- +| precision floating-point number. +| The input significand `zSig' has its binary point between bits 30 +| and 29, which is 7 bits to the left of the usual location. This shifted +| significand must be normalized or smaller. If `zSig' is not normalized, +| `zExp' must be 0; in that case, the result returned is a subnormal number, +| and it must not require rounding. In the usual case that `zSig' is +| normalized, `zExp' must be 1 less than the ``true'' floating-point exponent. +| The handling of underflow and overflow follows the IEC/IEEE Standard for +| Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +static float32 roundAndPackFloat32( flag zSign, int16 zExp, bits32 zSig STATUS_PARAM) +{ + int8 roundingMode; + flag roundNearestEven; + int8 roundIncrement, roundBits; + flag isTiny; + + roundingMode = STATUS(float_rounding_mode); + roundNearestEven = ( roundingMode == float_round_nearest_even ); + roundIncrement = 0x40; + if ( ! roundNearestEven ) { + if ( roundingMode == float_round_to_zero ) { + roundIncrement = 0; + } + else { + roundIncrement = 0x7F; + if ( zSign ) { + if ( roundingMode == float_round_up ) roundIncrement = 0; + } + else { + if ( roundingMode == float_round_down ) roundIncrement = 0; + } + } + } + roundBits = zSig & 0x7F; + if ( 0xFD <= (bits16) zExp ) { + if ( ( 0xFD < zExp ) + || ( ( zExp == 0xFD ) + && ( (sbits32) ( zSig + roundIncrement ) < 0 ) ) + ) { + float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR); + return packFloat32( zSign, 0xFF, 0 ) - ( roundIncrement == 0 ); + } + if ( zExp < 0 ) { + isTiny = + ( STATUS(float_detect_tininess) == float_tininess_before_rounding ) + || ( zExp < -1 ) + || ( zSig + roundIncrement < 0x80000000 ); + shift32RightJamming( zSig, - zExp, &zSig ); + zExp = 0; + roundBits = zSig & 0x7F; + if ( isTiny && roundBits ) float_raise( float_flag_underflow STATUS_VAR); + } + } + if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact; + zSig = ( zSig + roundIncrement )>>7; + zSig &= ~ ( ( ( roundBits ^ 0x40 ) == 0 ) & roundNearestEven ); + if ( zSig == 0 ) zExp = 0; + return packFloat32( zSign, zExp, zSig ); + +} + +/*---------------------------------------------------------------------------- +| Takes an abstract floating-point value having sign `zSign', exponent `zExp', +| and significand `zSig', and returns the proper single-precision floating- +| point value corresponding to the abstract input. This routine is just like +| `roundAndPackFloat32' except that `zSig' does not have to be normalized. +| Bit 31 of `zSig' must be zero, and `zExp' must be 1 less than the ``true'' +| floating-point exponent. +*----------------------------------------------------------------------------*/ + +static float32 + normalizeRoundAndPackFloat32( flag zSign, int16 zExp, bits32 zSig STATUS_PARAM) +{ + int8 shiftCount; + + shiftCount = countLeadingZeros32( zSig ) - 1; + return roundAndPackFloat32( zSign, zExp - shiftCount, zSig<<shiftCount STATUS_VAR); + +} + +/*---------------------------------------------------------------------------- +| Returns the fraction bits of the double-precision floating-point value `a'. +*----------------------------------------------------------------------------*/ + +INLINE bits64 extractFloat64Frac( float64 a ) +{ + + return a & LIT64( 0x000FFFFFFFFFFFFF ); + +} + +/*---------------------------------------------------------------------------- +| Returns the exponent bits of the double-precision floating-point value `a'. +*----------------------------------------------------------------------------*/ + +INLINE int16 extractFloat64Exp( float64 a ) +{ + + return ( a>>52 ) & 0x7FF; + +} + +/*---------------------------------------------------------------------------- +| Returns the sign bit of the double-precision floating-point value `a'. +*----------------------------------------------------------------------------*/ + +INLINE flag extractFloat64Sign( float64 a ) +{ + + return a>>63; + +} + +/*---------------------------------------------------------------------------- +| Normalizes the subnormal double-precision floating-point value represented +| by the denormalized significand `aSig'. The normalized exponent and +| significand are stored at the locations pointed to by `zExpPtr' and +| `zSigPtr', respectively. +*----------------------------------------------------------------------------*/ + +static void + normalizeFloat64Subnormal( bits64 aSig, int16 *zExpPtr, bits64 *zSigPtr ) +{ + int8 shiftCount; + + shiftCount = countLeadingZeros64( aSig ) - 11; + *zSigPtr = aSig<<shiftCount; + *zExpPtr = 1 - shiftCount; + +} + +/*---------------------------------------------------------------------------- +| Packs the sign `zSign', exponent `zExp', and significand `zSig' into a +| double-precision floating-point value, returning the result. After being +| shifted into the proper positions, the three fields are simply added +| together to form the result. This means that any integer portion of `zSig' +| will be added into the exponent. Since a properly normalized significand +| will have an integer portion equal to 1, the `zExp' input should be 1 less +| than the desired result exponent whenever `zSig' is a complete, normalized +| significand. +*----------------------------------------------------------------------------*/ + +INLINE float64 packFloat64( flag zSign, int16 zExp, bits64 zSig ) +{ + + return ( ( (bits64) zSign )<<63 ) + ( ( (bits64) zExp )<<52 ) + zSig; + +} + +/*---------------------------------------------------------------------------- +| Takes an abstract floating-point value having sign `zSign', exponent `zExp', +| and significand `zSig', and returns the proper double-precision floating- +| point value corresponding to the abstract input. Ordinarily, the abstract +| value is simply rounded and packed into the double-precision format, with +| the inexact exception raised if the abstract input cannot be represented +| exactly. However, if the abstract value is too large, the overflow and +| inexact exceptions are raised and an infinity or maximal finite value is +| returned. If the abstract value is too small, the input value is rounded +| to a subnormal number, and the underflow and inexact exceptions are raised +| if the abstract input cannot be represented exactly as a subnormal double- +| precision floating-point number. +| The input significand `zSig' has its binary point between bits 62 +| and 61, which is 10 bits to the left of the usual location. This shifted +| significand must be normalized or smaller. If `zSig' is not normalized, +| `zExp' must be 0; in that case, the result returned is a subnormal number, +| and it must not require rounding. In the usual case that `zSig' is +| normalized, `zExp' must be 1 less than the ``true'' floating-point exponent. +| The handling of underflow and overflow follows the IEC/IEEE Standard for +| Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +static float64 roundAndPackFloat64( flag zSign, int16 zExp, bits64 zSig STATUS_PARAM) +{ + int8 roundingMode; + flag roundNearestEven; + int16 roundIncrement, roundBits; + flag isTiny; + + roundingMode = STATUS(float_rounding_mode); + roundNearestEven = ( roundingMode == float_round_nearest_even ); + roundIncrement = 0x200; + if ( ! roundNearestEven ) { + if ( roundingMode == float_round_to_zero ) { + roundIncrement = 0; + } + else { + roundIncrement = 0x3FF; + if ( zSign ) { + if ( roundingMode == float_round_up ) roundIncrement = 0; + } + else { + if ( roundingMode == float_round_down ) roundIncrement = 0; + } + } + } + roundBits = zSig & 0x3FF; + if ( 0x7FD <= (bits16) zExp ) { + if ( ( 0x7FD < zExp ) + || ( ( zExp == 0x7FD ) + && ( (sbits64) ( zSig + roundIncrement ) < 0 ) ) + ) { + float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR); + return packFloat64( zSign, 0x7FF, 0 ) - ( roundIncrement == 0 ); + } + if ( zExp < 0 ) { + isTiny = + ( STATUS(float_detect_tininess) == float_tininess_before_rounding ) + || ( zExp < -1 ) + || ( zSig + roundIncrement < LIT64( 0x8000000000000000 ) ); + shift64RightJamming( zSig, - zExp, &zSig ); + zExp = 0; + roundBits = zSig & 0x3FF; + if ( isTiny && roundBits ) float_raise( float_flag_underflow STATUS_VAR); + } + } + if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact; + zSig = ( zSig + roundIncrement )>>10; + zSig &= ~ ( ( ( roundBits ^ 0x200 ) == 0 ) & roundNearestEven ); + if ( zSig == 0 ) zExp = 0; + return packFloat64( zSign, zExp, zSig ); + +} + +/*---------------------------------------------------------------------------- +| Takes an abstract floating-point value having sign `zSign', exponent `zExp', +| and significand `zSig', and returns the proper double-precision floating- +| point value corresponding to the abstract input. This routine is just like +| `roundAndPackFloat64' except that `zSig' does not have to be normalized. +| Bit 63 of `zSig' must be zero, and `zExp' must be 1 less than the ``true'' +| floating-point exponent. +*----------------------------------------------------------------------------*/ + +static float64 + normalizeRoundAndPackFloat64( flag zSign, int16 zExp, bits64 zSig STATUS_PARAM) +{ + int8 shiftCount; + + shiftCount = countLeadingZeros64( zSig ) - 1; + return roundAndPackFloat64( zSign, zExp - shiftCount, zSig<<shiftCount STATUS_VAR); + +} + +#ifdef FLOATX80 + +/*---------------------------------------------------------------------------- +| Returns the fraction bits of the extended double-precision floating-point +| value `a'. +*----------------------------------------------------------------------------*/ + +INLINE bits64 extractFloatx80Frac( floatx80 a ) +{ + + return a.low; + +} + +/*---------------------------------------------------------------------------- +| Returns the exponent bits of the extended double-precision floating-point +| value `a'. +*----------------------------------------------------------------------------*/ + +INLINE int32 extractFloatx80Exp( floatx80 a ) +{ + + return a.high & 0x7FFF; + +} + +/*---------------------------------------------------------------------------- +| Returns the sign bit of the extended double-precision floating-point value +| `a'. +*----------------------------------------------------------------------------*/ + +INLINE flag extractFloatx80Sign( floatx80 a ) +{ + + return a.high>>15; + +} + +/*---------------------------------------------------------------------------- +| Normalizes the subnormal extended double-precision floating-point value +| represented by the denormalized significand `aSig'. The normalized exponent +| and significand are stored at the locations pointed to by `zExpPtr' and +| `zSigPtr', respectively. +*----------------------------------------------------------------------------*/ + +static void + normalizeFloatx80Subnormal( bits64 aSig, int32 *zExpPtr, bits64 *zSigPtr ) +{ + int8 shiftCount; + + shiftCount = countLeadingZeros64( aSig ); + *zSigPtr = aSig<<shiftCount; + *zExpPtr = 1 - shiftCount; + +} + +/*---------------------------------------------------------------------------- +| Packs the sign `zSign', exponent `zExp', and significand `zSig' into an +| extended double-precision floating-point value, returning the result. +*----------------------------------------------------------------------------*/ + +INLINE floatx80 packFloatx80( flag zSign, int32 zExp, bits64 zSig ) +{ + floatx80 z; + + z.low = zSig; + z.high = ( ( (bits16) zSign )<<15 ) + zExp; + return z; + +} + +/*---------------------------------------------------------------------------- +| Takes an abstract floating-point value having sign `zSign', exponent `zExp', +| and extended significand formed by the concatenation of `zSig0' and `zSig1', +| and returns the proper extended double-precision floating-point value +| corresponding to the abstract input. Ordinarily, the abstract value is +| rounded and packed into the extended double-precision format, with the +| inexact exception raised if the abstract input cannot be represented +| exactly. However, if the abstract value is too large, the overflow and +| inexact exceptions are raised and an infinity or maximal finite value is +| returned. If the abstract value is too small, the input value is rounded to +| a subnormal number, and the underflow and inexact exceptions are raised if +| the abstract input cannot be represented exactly as a subnormal extended +| double-precision floating-point number. +| If `roundingPrecision' is 32 or 64, the result is rounded to the same +| number of bits as single or double precision, respectively. Otherwise, the +| result is rounded to the full precision of the extended double-precision +| format. +| The input significand must be normalized or smaller. If the input +| significand is not normalized, `zExp' must be 0; in that case, the result +| returned is a subnormal number, and it must not require rounding. The +| handling of underflow and overflow follows the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +static floatx80 + roundAndPackFloatx80( + int8 roundingPrecision, flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1 + STATUS_PARAM) +{ + int8 roundingMode; + flag roundNearestEven, increment, isTiny; + int64 roundIncrement, roundMask, roundBits; + + roundingMode = STATUS(float_rounding_mode); + roundNearestEven = ( roundingMode == float_round_nearest_even ); + if ( roundingPrecision == 80 ) goto precision80; + if ( roundingPrecision == 64 ) { + roundIncrement = LIT64( 0x0000000000000400 ); + roundMask = LIT64( 0x00000000000007FF ); + } + else if ( roundingPrecision == 32 ) { + roundIncrement = LIT64( 0x0000008000000000 ); + roundMask = LIT64( 0x000000FFFFFFFFFF ); + } + else { + goto precision80; + } + zSig0 |= ( zSig1 != 0 ); + if ( ! roundNearestEven ) { + if ( roundingMode == float_round_to_zero ) { + roundIncrement = 0; + } + else { + roundIncrement = roundMask; + if ( zSign ) { + if ( roundingMode == float_round_up ) roundIncrement = 0; + } + else { + if ( roundingMode == float_round_down ) roundIncrement = 0; + } + } + } + roundBits = zSig0 & roundMask; + if ( 0x7FFD <= (bits32) ( zExp - 1 ) ) { + if ( ( 0x7FFE < zExp ) + || ( ( zExp == 0x7FFE ) && ( zSig0 + roundIncrement < zSig0 ) ) + ) { + goto overflow; + } + if ( zExp <= 0 ) { + isTiny = + ( STATUS(float_detect_tininess) == float_tininess_before_rounding ) + || ( zExp < 0 ) + || ( zSig0 <= zSig0 + roundIncrement ); + shift64RightJamming( zSig0, 1 - zExp, &zSig0 ); + zExp = 0; + roundBits = zSig0 & roundMask; + if ( isTiny && roundBits ) float_raise( float_flag_underflow STATUS_VAR); + if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact; + zSig0 += roundIncrement; + if ( (sbits64) zSig0 < 0 ) zExp = 1; + roundIncrement = roundMask + 1; + if ( roundNearestEven && ( roundBits<<1 == roundIncrement ) ) { + roundMask |= roundIncrement; + } + zSig0 &= ~ roundMask; + return packFloatx80( zSign, zExp, zSig0 ); + } + } + if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact; + zSig0 += roundIncrement; + if ( zSig0 < roundIncrement ) { + ++zExp; + zSig0 = LIT64( 0x8000000000000000 ); + } + roundIncrement = roundMask + 1; + if ( roundNearestEven && ( roundBits<<1 == roundIncrement ) ) { + roundMask |= roundIncrement; + } + zSig0 &= ~ roundMask; + if ( zSig0 == 0 ) zExp = 0; + return packFloatx80( zSign, zExp, zSig0 ); + precision80: + increment = ( (sbits64) zSig1 < 0 ); + if ( ! roundNearestEven ) { + if ( roundingMode == float_round_to_zero ) { + increment = 0; + } + else { + if ( zSign ) { + increment = ( roundingMode == float_round_down ) && zSig1; + } + else { + increment = ( roundingMode == float_round_up ) && zSig1; + } + } + } + if ( 0x7FFD <= (bits32) ( zExp - 1 ) ) { + if ( ( 0x7FFE < zExp ) + || ( ( zExp == 0x7FFE ) + && ( zSig0 == LIT64( 0xFFFFFFFFFFFFFFFF ) ) + && increment + ) + ) { + roundMask = 0; + overflow: + float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR); + if ( ( roundingMode == float_round_to_zero ) + || ( zSign && ( roundingMode == float_round_up ) ) + || ( ! zSign && ( roundingMode == float_round_down ) ) + ) { + return packFloatx80( zSign, 0x7FFE, ~ roundMask ); + } + return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); + } + if ( zExp <= 0 ) { + isTiny = + ( STATUS(float_detect_tininess) == float_tininess_before_rounding ) + || ( zExp < 0 ) + || ! increment + || ( zSig0 < LIT64( 0xFFFFFFFFFFFFFFFF ) ); + shift64ExtraRightJamming( zSig0, zSig1, 1 - zExp, &zSig0, &zSig1 ); + zExp = 0; + if ( isTiny && zSig1 ) float_raise( float_flag_underflow STATUS_VAR); + if ( zSig1 ) STATUS(float_exception_flags) |= float_flag_inexact; + if ( roundNearestEven ) { + increment = ( (sbits64) zSig1 < 0 ); + } + else { + if ( zSign ) { + increment = ( roundingMode == float_round_down ) && zSig1; + } + else { + increment = ( roundingMode == float_round_up ) && zSig1; + } + } + if ( increment ) { + ++zSig0; + zSig0 &= + ~ ( ( (bits64) ( zSig1<<1 ) == 0 ) & roundNearestEven ); + if ( (sbits64) zSig0 < 0 ) zExp = 1; + } + return packFloatx80( zSign, zExp, zSig0 ); + } + } + if ( zSig1 ) STATUS(float_exception_flags) |= float_flag_inexact; + if ( increment ) { + ++zSig0; + if ( zSig0 == 0 ) { + ++zExp; + zSig0 = LIT64( 0x8000000000000000 ); + } + else { + zSig0 &= ~ ( ( (bits64) ( zSig1<<1 ) == 0 ) & roundNearestEven ); + } + } + else { + if ( zSig0 == 0 ) zExp = 0; + } + return packFloatx80( zSign, zExp, zSig0 ); + +} + +/*---------------------------------------------------------------------------- +| Takes an abstract floating-point value having sign `zSign', exponent +| `zExp', and significand formed by the concatenation of `zSig0' and `zSig1', +| and returns the proper extended double-precision floating-point value +| corresponding to the abstract input. This routine is just like +| `roundAndPackFloatx80' except that the input significand does not have to be +| normalized. +*----------------------------------------------------------------------------*/ + +static floatx80 + normalizeRoundAndPackFloatx80( + int8 roundingPrecision, flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1 + STATUS_PARAM) +{ + int8 shiftCount; + + if ( zSig0 == 0 ) { + zSig0 = zSig1; + zSig1 = 0; + zExp -= 64; + } + shiftCount = countLeadingZeros64( zSig0 ); + shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 ); + zExp -= shiftCount; + return + roundAndPackFloatx80( roundingPrecision, zSign, zExp, zSig0, zSig1 STATUS_VAR); + +} + +#endif + +#ifdef FLOAT128 + +/*---------------------------------------------------------------------------- +| Returns the least-significant 64 fraction bits of the quadruple-precision +| floating-point value `a'. +*----------------------------------------------------------------------------*/ + +INLINE bits64 extractFloat128Frac1( float128 a ) +{ + + return a.low; + +} + +/*---------------------------------------------------------------------------- +| Returns the most-significant 48 fraction bits of the quadruple-precision +| floating-point value `a'. +*----------------------------------------------------------------------------*/ + +INLINE bits64 extractFloat128Frac0( float128 a ) +{ + + return a.high & LIT64( 0x0000FFFFFFFFFFFF ); + +} + +/*---------------------------------------------------------------------------- +| Returns the exponent bits of the quadruple-precision floating-point value +| `a'. +*----------------------------------------------------------------------------*/ + +INLINE int32 extractFloat128Exp( float128 a ) +{ + + return ( a.high>>48 ) & 0x7FFF; + +} + +/*---------------------------------------------------------------------------- +| Returns the sign bit of the quadruple-precision floating-point value `a'. +*----------------------------------------------------------------------------*/ + +INLINE flag extractFloat128Sign( float128 a ) +{ + + return a.high>>63; + +} + +/*---------------------------------------------------------------------------- +| Normalizes the subnormal quadruple-precision floating-point value +| represented by the denormalized significand formed by the concatenation of +| `aSig0' and `aSig1'. The normalized exponent is stored at the location +| pointed to by `zExpPtr'. The most significant 49 bits of the normalized +| significand are stored at the location pointed to by `zSig0Ptr', and the +| least significant 64 bits of the normalized significand are stored at the +| location pointed to by `zSig1Ptr'. +*----------------------------------------------------------------------------*/ + +static void + normalizeFloat128Subnormal( + bits64 aSig0, + bits64 aSig1, + int32 *zExpPtr, + bits64 *zSig0Ptr, + bits64 *zSig1Ptr + ) +{ + int8 shiftCount; + + if ( aSig0 == 0 ) { + shiftCount = countLeadingZeros64( aSig1 ) - 15; + if ( shiftCount < 0 ) { + *zSig0Ptr = aSig1>>( - shiftCount ); + *zSig1Ptr = aSig1<<( shiftCount & 63 ); + } + else { + *zSig0Ptr = aSig1<<shiftCount; + *zSig1Ptr = 0; + } + *zExpPtr = - shiftCount - 63; + } + else { + shiftCount = countLeadingZeros64( aSig0 ) - 15; + shortShift128Left( aSig0, aSig1, shiftCount, zSig0Ptr, zSig1Ptr ); + *zExpPtr = 1 - shiftCount; + } + +} + +/*---------------------------------------------------------------------------- +| Packs the sign `zSign', the exponent `zExp', and the significand formed +| by the concatenation of `zSig0' and `zSig1' into a quadruple-precision +| floating-point value, returning the result. After being shifted into the +| proper positions, the three fields `zSign', `zExp', and `zSig0' are simply +| added together to form the most significant 32 bits of the result. This +| means that any integer portion of `zSig0' will be added into the exponent. +| Since a properly normalized significand will have an integer portion equal +| to 1, the `zExp' input should be 1 less than the desired result exponent +| whenever `zSig0' and `zSig1' concatenated form a complete, normalized +| significand. +*----------------------------------------------------------------------------*/ + +INLINE float128 + packFloat128( flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1 ) +{ + float128 z; + + z.low = zSig1; + z.high = ( ( (bits64) zSign )<<63 ) + ( ( (bits64) zExp )<<48 ) + zSig0; + return z; + +} + +/*---------------------------------------------------------------------------- +| Takes an abstract floating-point value having sign `zSign', exponent `zExp', +| and extended significand formed by the concatenation of `zSig0', `zSig1', +| and `zSig2', and returns the proper quadruple-precision floating-point value +| corresponding to the abstract input. Ordinarily, the abstract value is +| simply rounded and packed into the quadruple-precision format, with the +| inexact exception raised if the abstract input cannot be represented +| exactly. However, if the abstract value is too large, the overflow and +| inexact exceptions are raised and an infinity or maximal finite value is +| returned. If the abstract value is too small, the input value is rounded to +| a subnormal number, and the underflow and inexact exceptions are raised if +| the abstract input cannot be represented exactly as a subnormal quadruple- +| precision floating-point number. +| The input significand must be normalized or smaller. If the input +| significand is not normalized, `zExp' must be 0; in that case, the result +| returned is a subnormal number, and it must not require rounding. In the +| usual case that the input significand is normalized, `zExp' must be 1 less +| than the ``true'' floating-point exponent. The handling of underflow and +| overflow follows the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +static float128 + roundAndPackFloat128( + flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1, bits64 zSig2 STATUS_PARAM) +{ + int8 roundingMode; + flag roundNearestEven, increment, isTiny; + + roundingMode = STATUS(float_rounding_mode); + roundNearestEven = ( roundingMode == float_round_nearest_even ); + increment = ( (sbits64) zSig2 < 0 ); + if ( ! roundNearestEven ) { + if ( roundingMode == float_round_to_zero ) { + increment = 0; + } + else { + if ( zSign ) { + increment = ( roundingMode == float_round_down ) && zSig2; + } + else { + increment = ( roundingMode == float_round_up ) && zSig2; + } + } + } + if ( 0x7FFD <= (bits32) zExp ) { + if ( ( 0x7FFD < zExp ) + || ( ( zExp == 0x7FFD ) + && eq128( + LIT64( 0x0001FFFFFFFFFFFF ), + LIT64( 0xFFFFFFFFFFFFFFFF ), + zSig0, + zSig1 + ) + && increment + ) + ) { + float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR); + if ( ( roundingMode == float_round_to_zero ) + || ( zSign && ( roundingMode == float_round_up ) ) + || ( ! zSign && ( roundingMode == float_round_down ) ) + ) { + return + packFloat128( + zSign, + 0x7FFE, + LIT64( 0x0000FFFFFFFFFFFF ), + LIT64( 0xFFFFFFFFFFFFFFFF ) + ); + } + return packFloat128( zSign, 0x7FFF, 0, 0 ); + } + if ( zExp < 0 ) { + isTiny = + ( STATUS(float_detect_tininess) == float_tininess_before_rounding ) + || ( zExp < -1 ) + || ! increment + || lt128( + zSig0, + zSig1, + LIT64( 0x0001FFFFFFFFFFFF ), + LIT64( 0xFFFFFFFFFFFFFFFF ) + ); + shift128ExtraRightJamming( + zSig0, zSig1, zSig2, - zExp, &zSig0, &zSig1, &zSig2 ); + zExp = 0; + if ( isTiny && zSig2 ) float_raise( float_flag_underflow STATUS_VAR); + if ( roundNearestEven ) { + increment = ( (sbits64) zSig2 < 0 ); + } + else { + if ( zSign ) { + increment = ( roundingMode == float_round_down ) && zSig2; + } + else { + increment = ( roundingMode == float_round_up ) && zSig2; + } + } + } + } + if ( zSig2 ) STATUS(float_exception_flags) |= float_flag_inexact; + if ( increment ) { + add128( zSig0, zSig1, 0, 1, &zSig0, &zSig1 ); + zSig1 &= ~ ( ( zSig2 + zSig2 == 0 ) & roundNearestEven ); + } + else { + if ( ( zSig0 | zSig1 ) == 0 ) zExp = 0; + } + return packFloat128( zSign, zExp, zSig0, zSig1 ); + +} + +/*---------------------------------------------------------------------------- +| Takes an abstract floating-point value having sign `zSign', exponent `zExp', +| and significand formed by the concatenation of `zSig0' and `zSig1', and +| returns the proper quadruple-precision floating-point value corresponding +| to the abstract input. This routine is just like `roundAndPackFloat128' +| except that the input significand has fewer bits and does not have to be +| normalized. In all cases, `zExp' must be 1 less than the ``true'' floating- +| point exponent. +*----------------------------------------------------------------------------*/ + +static float128 + normalizeRoundAndPackFloat128( + flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1 STATUS_PARAM) +{ + int8 shiftCount; + bits64 zSig2; + + if ( zSig0 == 0 ) { + zSig0 = zSig1; + zSig1 = 0; + zExp -= 64; + } + shiftCount = countLeadingZeros64( zSig0 ) - 15; + if ( 0 <= shiftCount ) { + zSig2 = 0; + shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 ); + } + else { + shift128ExtraRightJamming( + zSig0, zSig1, 0, - shiftCount, &zSig0, &zSig1, &zSig2 ); + } + zExp -= shiftCount; + return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 STATUS_VAR); + +} + +#endif + +/*---------------------------------------------------------------------------- +| Returns the result of converting the 32-bit two's complement integer `a' +| to the single-precision floating-point format. The conversion is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float32 int32_to_float32( int32 a STATUS_PARAM ) +{ + flag zSign; + + if ( a == 0 ) return 0; + if ( a == (sbits32) 0x80000000 ) return packFloat32( 1, 0x9E, 0 ); + zSign = ( a < 0 ); + return normalizeRoundAndPackFloat32( zSign, 0x9C, zSign ? - a : a STATUS_VAR ); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the 32-bit two's complement integer `a' +| to the double-precision floating-point format. The conversion is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float64 int32_to_float64( int32 a STATUS_PARAM ) +{ + flag zSign; + uint32 absA; + int8 shiftCount; + bits64 zSig; + + if ( a == 0 ) return 0; + zSign = ( a < 0 ); + absA = zSign ? - a : a; + shiftCount = countLeadingZeros32( absA ) + 21; + zSig = absA; + return packFloat64( zSign, 0x432 - shiftCount, zSig<<shiftCount ); + +} + +#ifdef FLOATX80 + +/*---------------------------------------------------------------------------- +| Returns the result of converting the 32-bit two's complement integer `a' +| to the extended double-precision floating-point format. The conversion +| is performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic. +*----------------------------------------------------------------------------*/ + +floatx80 int32_to_floatx80( int32 a STATUS_PARAM ) +{ + flag zSign; + uint32 absA; + int8 shiftCount; + bits64 zSig; + + if ( a == 0 ) return packFloatx80( 0, 0, 0 ); + zSign = ( a < 0 ); + absA = zSign ? - a : a; + shiftCount = countLeadingZeros32( absA ) + 32; + zSig = absA; + return packFloatx80( zSign, 0x403E - shiftCount, zSig<<shiftCount ); + +} + +#endif + +#ifdef FLOAT128 + +/*---------------------------------------------------------------------------- +| Returns the result of converting the 32-bit two's complement integer `a' to +| the quadruple-precision floating-point format. The conversion is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float128 int32_to_float128( int32 a STATUS_PARAM ) +{ + flag zSign; + uint32 absA; + int8 shiftCount; + bits64 zSig0; + + if ( a == 0 ) return packFloat128( 0, 0, 0, 0 ); + zSign = ( a < 0 ); + absA = zSign ? - a : a; + shiftCount = countLeadingZeros32( absA ) + 17; + zSig0 = absA; + return packFloat128( zSign, 0x402E - shiftCount, zSig0<<shiftCount, 0 ); + +} + +#endif + +/*---------------------------------------------------------------------------- +| Returns the result of converting the 64-bit two's complement integer `a' +| to the single-precision floating-point format. The conversion is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float32 int64_to_float32( int64 a STATUS_PARAM ) +{ + flag zSign; + uint64 absA; + int8 shiftCount; + + if ( a == 0 ) return 0; + zSign = ( a < 0 ); + absA = zSign ? - a : a; + shiftCount = countLeadingZeros64( absA ) - 40; + if ( 0 <= shiftCount ) { + return packFloat32( zSign, 0x95 - shiftCount, absA<<shiftCount ); + } + else { + shiftCount += 7; + if ( shiftCount < 0 ) { + shift64RightJamming( absA, - shiftCount, &absA ); + } + else { + absA <<= shiftCount; + } + return roundAndPackFloat32( zSign, 0x9C - shiftCount, absA STATUS_VAR ); + } + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the 64-bit two's complement integer `a' +| to the double-precision floating-point format. The conversion is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float64 int64_to_float64( int64 a STATUS_PARAM ) +{ + flag zSign; + + if ( a == 0 ) return 0; + if ( a == (sbits64) LIT64( 0x8000000000000000 ) ) { + return packFloat64( 1, 0x43E, 0 ); + } + zSign = ( a < 0 ); + return normalizeRoundAndPackFloat64( zSign, 0x43C, zSign ? - a : a STATUS_VAR ); + +} + +#ifdef FLOATX80 + +/*---------------------------------------------------------------------------- +| Returns the result of converting the 64-bit two's complement integer `a' +| to the extended double-precision floating-point format. The conversion +| is performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic. +*----------------------------------------------------------------------------*/ + +floatx80 int64_to_floatx80( int64 a STATUS_PARAM ) +{ + flag zSign; + uint64 absA; + int8 shiftCount; + + if ( a == 0 ) return packFloatx80( 0, 0, 0 ); + zSign = ( a < 0 ); + absA = zSign ? - a : a; + shiftCount = countLeadingZeros64( absA ); + return packFloatx80( zSign, 0x403E - shiftCount, absA<<shiftCount ); + +} + +#endif + +#ifdef FLOAT128 + +/*---------------------------------------------------------------------------- +| Returns the result of converting the 64-bit two's complement integer `a' to +| the quadruple-precision floating-point format. The conversion is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float128 int64_to_float128( int64 a STATUS_PARAM ) +{ + flag zSign; + uint64 absA; + int8 shiftCount; + int32 zExp; + bits64 zSig0, zSig1; + + if ( a == 0 ) return packFloat128( 0, 0, 0, 0 ); + zSign = ( a < 0 ); + absA = zSign ? - a : a; + shiftCount = countLeadingZeros64( absA ) + 49; + zExp = 0x406E - shiftCount; + if ( 64 <= shiftCount ) { + zSig1 = 0; + zSig0 = absA; + shiftCount -= 64; + } + else { + zSig1 = absA; + zSig0 = 0; + } + shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 ); + return packFloat128( zSign, zExp, zSig0, zSig1 ); + +} + +#endif + +/*---------------------------------------------------------------------------- +| Returns the result of converting the single-precision floating-point value +| `a' to the 32-bit two's complement integer format. The conversion is +| performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic---which means in particular that the conversion is rounded +| according to the current rounding mode. If `a' is a NaN, the largest +| positive integer is returned. Otherwise, if the conversion overflows, the +| largest integer with the same sign as `a' is returned. +*----------------------------------------------------------------------------*/ + +int32 float32_to_int32( float32 a STATUS_PARAM ) +{ + flag aSign; + int16 aExp, shiftCount; + bits32 aSig; + bits64 aSig64; + + aSig = extractFloat32Frac( a ); + aExp = extractFloat32Exp( a ); + aSign = extractFloat32Sign( a ); + if ( ( aExp == 0xFF ) && aSig ) aSign = 0; + if ( aExp ) aSig |= 0x00800000; + shiftCount = 0xAF - aExp; + aSig64 = aSig; + aSig64 <<= 32; + if ( 0 < shiftCount ) shift64RightJamming( aSig64, shiftCount, &aSig64 ); + return roundAndPackInt32( aSign, aSig64 STATUS_VAR ); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the single-precision floating-point value +| `a' to the 32-bit two's complement integer format. The conversion is +| performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic, except that the conversion is always rounded toward zero. +| If `a' is a NaN, the largest positive integer is returned. Otherwise, if +| the conversion overflows, the largest integer with the same sign as `a' is +| returned. +*----------------------------------------------------------------------------*/ + +int32 float32_to_int32_round_to_zero( float32 a STATUS_PARAM ) +{ + flag aSign; + int16 aExp, shiftCount; + bits32 aSig; + int32 z; + + aSig = extractFloat32Frac( a ); + aExp = extractFloat32Exp( a ); + aSign = extractFloat32Sign( a ); + shiftCount = aExp - 0x9E; + if ( 0 <= shiftCount ) { + if ( a != 0xCF000000 ) { + float_raise( float_flag_invalid STATUS_VAR); + if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) return 0x7FFFFFFF; + } + return (sbits32) 0x80000000; + } + else if ( aExp <= 0x7E ) { + if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact; + return 0; + } + aSig = ( aSig | 0x00800000 )<<8; + z = aSig>>( - shiftCount ); + if ( (bits32) ( aSig<<( shiftCount & 31 ) ) ) { + STATUS(float_exception_flags) |= float_flag_inexact; + } + if ( aSign ) z = - z; + return z; + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the single-precision floating-point value +| `a' to the 64-bit two's complement integer format. The conversion is +| performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic---which means in particular that the conversion is rounded +| according to the current rounding mode. If `a' is a NaN, the largest +| positive integer is returned. Otherwise, if the conversion overflows, the +| largest integer with the same sign as `a' is returned. +*----------------------------------------------------------------------------*/ + +int64 float32_to_int64( float32 a STATUS_PARAM ) +{ + flag aSign; + int16 aExp, shiftCount; + bits32 aSig; + bits64 aSig64, aSigExtra; + + aSig = extractFloat32Frac( a ); + aExp = extractFloat32Exp( a ); + aSign = extractFloat32Sign( a ); + shiftCount = 0xBE - aExp; + if ( shiftCount < 0 ) { + float_raise( float_flag_invalid STATUS_VAR); + if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) { + return LIT64( 0x7FFFFFFFFFFFFFFF ); + } + return (sbits64) LIT64( 0x8000000000000000 ); + } + if ( aExp ) aSig |= 0x00800000; + aSig64 = aSig; + aSig64 <<= 40; + shift64ExtraRightJamming( aSig64, 0, shiftCount, &aSig64, &aSigExtra ); + return roundAndPackInt64( aSign, aSig64, aSigExtra STATUS_VAR ); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the single-precision floating-point value +| `a' to the 64-bit two's complement integer format. The conversion is +| performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic, except that the conversion is always rounded toward zero. If +| `a' is a NaN, the largest positive integer is returned. Otherwise, if the +| conversion overflows, the largest integer with the same sign as `a' is +| returned. +*----------------------------------------------------------------------------*/ + +int64 float32_to_int64_round_to_zero( float32 a STATUS_PARAM ) +{ + flag aSign; + int16 aExp, shiftCount; + bits32 aSig; + bits64 aSig64; + int64 z; + + aSig = extractFloat32Frac( a ); + aExp = extractFloat32Exp( a ); + aSign = extractFloat32Sign( a ); + shiftCount = aExp - 0xBE; + if ( 0 <= shiftCount ) { + if ( a != 0xDF000000 ) { + float_raise( float_flag_invalid STATUS_VAR); + if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) { + return LIT64( 0x7FFFFFFFFFFFFFFF ); + } + } + return (sbits64) LIT64( 0x8000000000000000 ); + } + else if ( aExp <= 0x7E ) { + if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact; + return 0; + } + aSig64 = aSig | 0x00800000; + aSig64 <<= 40; + z = aSig64>>( - shiftCount ); + if ( (bits64) ( aSig64<<( shiftCount & 63 ) ) ) { + STATUS(float_exception_flags) |= float_flag_inexact; + } + if ( aSign ) z = - z; + return z; + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the single-precision floating-point value +| `a' to the double-precision floating-point format. The conversion is +| performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic. +*----------------------------------------------------------------------------*/ + +float64 float32_to_float64( float32 a STATUS_PARAM ) +{ + flag aSign; + int16 aExp; + bits32 aSig; + + aSig = extractFloat32Frac( a ); + aExp = extractFloat32Exp( a ); + aSign = extractFloat32Sign( a ); + if ( aExp == 0xFF ) { + if ( aSig ) return commonNaNToFloat64( float32ToCommonNaN( a STATUS_VAR )); + return packFloat64( aSign, 0x7FF, 0 ); + } + if ( aExp == 0 ) { + if ( aSig == 0 ) return packFloat64( aSign, 0, 0 ); + normalizeFloat32Subnormal( aSig, &aExp, &aSig ); + --aExp; + } + return packFloat64( aSign, aExp + 0x380, ( (bits64) aSig )<<29 ); + +} + +#ifdef FLOATX80 + +/*---------------------------------------------------------------------------- +| Returns the result of converting the single-precision floating-point value +| `a' to the extended double-precision floating-point format. The conversion +| is performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic. +*----------------------------------------------------------------------------*/ + +floatx80 float32_to_floatx80( float32 a STATUS_PARAM ) +{ + flag aSign; + int16 aExp; + bits32 aSig; + + aSig = extractFloat32Frac( a ); + aExp = extractFloat32Exp( a ); + aSign = extractFloat32Sign( a ); + if ( aExp == 0xFF ) { + if ( aSig ) return commonNaNToFloatx80( float32ToCommonNaN( a STATUS_VAR ) ); + return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); + } + if ( aExp == 0 ) { + if ( aSig == 0 ) return packFloatx80( aSign, 0, 0 ); + normalizeFloat32Subnormal( aSig, &aExp, &aSig ); + } + aSig |= 0x00800000; + return packFloatx80( aSign, aExp + 0x3F80, ( (bits64) aSig )<<40 ); + +} + +#endif + +#ifdef FLOAT128 + +/*---------------------------------------------------------------------------- +| Returns the result of converting the single-precision floating-point value +| `a' to the double-precision floating-point format. The conversion is +| performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic. +*----------------------------------------------------------------------------*/ + +float128 float32_to_float128( float32 a STATUS_PARAM ) +{ + flag aSign; + int16 aExp; + bits32 aSig; + + aSig = extractFloat32Frac( a ); + aExp = extractFloat32Exp( a ); + aSign = extractFloat32Sign( a ); + if ( aExp == 0xFF ) { + if ( aSig ) return commonNaNToFloat128( float32ToCommonNaN( a STATUS_VAR ) ); + return packFloat128( aSign, 0x7FFF, 0, 0 ); + } + if ( aExp == 0 ) { + if ( aSig == 0 ) return packFloat128( aSign, 0, 0, 0 ); + normalizeFloat32Subnormal( aSig, &aExp, &aSig ); + --aExp; + } + return packFloat128( aSign, aExp + 0x3F80, ( (bits64) aSig )<<25, 0 ); + +} + +#endif + +/*---------------------------------------------------------------------------- +| Rounds the single-precision floating-point value `a' to an integer, and +| returns the result as a single-precision floating-point value. The +| operation is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float32 float32_round_to_int( float32 a STATUS_PARAM) +{ + flag aSign; + int16 aExp; + bits32 lastBitMask, roundBitsMask; + int8 roundingMode; + float32 z; + + aExp = extractFloat32Exp( a ); + if ( 0x96 <= aExp ) { + if ( ( aExp == 0xFF ) && extractFloat32Frac( a ) ) { + return propagateFloat32NaN( a, a STATUS_VAR ); + } + return a; + } + if ( aExp <= 0x7E ) { + if ( (bits32) ( a<<1 ) == 0 ) return a; + STATUS(float_exception_flags) |= float_flag_inexact; + aSign = extractFloat32Sign( a ); + switch ( STATUS(float_rounding_mode) ) { + case float_round_nearest_even: + if ( ( aExp == 0x7E ) && extractFloat32Frac( a ) ) { + return packFloat32( aSign, 0x7F, 0 ); + } + break; + case float_round_down: + return aSign ? 0xBF800000 : 0; + case float_round_up: + return aSign ? 0x80000000 : 0x3F800000; + } + return packFloat32( aSign, 0, 0 ); + } + lastBitMask = 1; + lastBitMask <<= 0x96 - aExp; + roundBitsMask = lastBitMask - 1; + z = a; + roundingMode = STATUS(float_rounding_mode); + if ( roundingMode == float_round_nearest_even ) { + z += lastBitMask>>1; + if ( ( z & roundBitsMask ) == 0 ) z &= ~ lastBitMask; + } + else if ( roundingMode != float_round_to_zero ) { + if ( extractFloat32Sign( z ) ^ ( roundingMode == float_round_up ) ) { + z += roundBitsMask; + } + } + z &= ~ roundBitsMask; + if ( z != a ) STATUS(float_exception_flags) |= float_flag_inexact; + return z; + +} + +/*---------------------------------------------------------------------------- +| Returns the result of adding the absolute values of the single-precision +| floating-point values `a' and `b'. If `zSign' is 1, the sum is negated +| before being returned. `zSign' is ignored if the result is a NaN. +| The addition is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +static float32 addFloat32Sigs( float32 a, float32 b, flag zSign STATUS_PARAM) +{ + int16 aExp, bExp, zExp; + bits32 aSig, bSig, zSig; + int16 expDiff; + + aSig = extractFloat32Frac( a ); + aExp = extractFloat32Exp( a ); + bSig = extractFloat32Frac( b ); + bExp = extractFloat32Exp( b ); + expDiff = aExp - bExp; + aSig <<= 6; + bSig <<= 6; + if ( 0 < expDiff ) { + if ( aExp == 0xFF ) { + if ( aSig ) return propagateFloat32NaN( a, b STATUS_VAR ); + return a; + } + if ( bExp == 0 ) { + --expDiff; + } + else { + bSig |= 0x20000000; + } + shift32RightJamming( bSig, expDiff, &bSig ); + zExp = aExp; + } + else if ( expDiff < 0 ) { + if ( bExp == 0xFF ) { + if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); + return packFloat32( zSign, 0xFF, 0 ); + } + if ( aExp == 0 ) { + ++expDiff; + } + else { + aSig |= 0x20000000; + } + shift32RightJamming( aSig, - expDiff, &aSig ); + zExp = bExp; + } + else { + if ( aExp == 0xFF ) { + if ( aSig | bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); + return a; + } + if ( aExp == 0 ) return packFloat32( zSign, 0, ( aSig + bSig )>>6 ); + zSig = 0x40000000 + aSig + bSig; + zExp = aExp; + goto roundAndPack; + } + aSig |= 0x20000000; + zSig = ( aSig + bSig )<<1; + --zExp; + if ( (sbits32) zSig < 0 ) { + zSig = aSig + bSig; + ++zExp; + } + roundAndPack: + return roundAndPackFloat32( zSign, zExp, zSig STATUS_VAR ); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of subtracting the absolute values of the single- +| precision floating-point values `a' and `b'. If `zSign' is 1, the +| difference is negated before being returned. `zSign' is ignored if the +| result is a NaN. The subtraction is performed according to the IEC/IEEE +| Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +static float32 subFloat32Sigs( float32 a, float32 b, flag zSign STATUS_PARAM) +{ + int16 aExp, bExp, zExp; + bits32 aSig, bSig, zSig; + int16 expDiff; + + aSig = extractFloat32Frac( a ); + aExp = extractFloat32Exp( a ); + bSig = extractFloat32Frac( b ); + bExp = extractFloat32Exp( b ); + expDiff = aExp - bExp; + aSig <<= 7; + bSig <<= 7; + if ( 0 < expDiff ) goto aExpBigger; + if ( expDiff < 0 ) goto bExpBigger; + if ( aExp == 0xFF ) { + if ( aSig | bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); + float_raise( float_flag_invalid STATUS_VAR); + return float32_default_nan; + } + if ( aExp == 0 ) { + aExp = 1; + bExp = 1; + } + if ( bSig < aSig ) goto aBigger; + if ( aSig < bSig ) goto bBigger; + return packFloat32( STATUS(float_rounding_mode) == float_round_down, 0, 0 ); + bExpBigger: + if ( bExp == 0xFF ) { + if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); + return packFloat32( zSign ^ 1, 0xFF, 0 ); + } + if ( aExp == 0 ) { + ++expDiff; + } + else { + aSig |= 0x40000000; + } + shift32RightJamming( aSig, - expDiff, &aSig ); + bSig |= 0x40000000; + bBigger: + zSig = bSig - aSig; + zExp = bExp; + zSign ^= 1; + goto normalizeRoundAndPack; + aExpBigger: + if ( aExp == 0xFF ) { + if ( aSig ) return propagateFloat32NaN( a, b STATUS_VAR ); + return a; + } + if ( bExp == 0 ) { + --expDiff; + } + else { + bSig |= 0x40000000; + } + shift32RightJamming( bSig, expDiff, &bSig ); + aSig |= 0x40000000; + aBigger: + zSig = aSig - bSig; + zExp = aExp; + normalizeRoundAndPack: + --zExp; + return normalizeRoundAndPackFloat32( zSign, zExp, zSig STATUS_VAR ); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of adding the single-precision floating-point values `a' +| and `b'. The operation is performed according to the IEC/IEEE Standard for +| Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float32 float32_add( float32 a, float32 b STATUS_PARAM ) +{ + flag aSign, bSign; + + aSign = extractFloat32Sign( a ); + bSign = extractFloat32Sign( b ); + if ( aSign == bSign ) { + return addFloat32Sigs( a, b, aSign STATUS_VAR); + } + else { + return subFloat32Sigs( a, b, aSign STATUS_VAR ); + } + +} + +/*---------------------------------------------------------------------------- +| Returns the result of subtracting the single-precision floating-point values +| `a' and `b'. The operation is performed according to the IEC/IEEE Standard +| for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float32 float32_sub( float32 a, float32 b STATUS_PARAM ) +{ + flag aSign, bSign; + + aSign = extractFloat32Sign( a ); + bSign = extractFloat32Sign( b ); + if ( aSign == bSign ) { + return subFloat32Sigs( a, b, aSign STATUS_VAR ); + } + else { + return addFloat32Sigs( a, b, aSign STATUS_VAR ); + } + +} + +/*---------------------------------------------------------------------------- +| Returns the result of multiplying the single-precision floating-point values +| `a' and `b'. The operation is performed according to the IEC/IEEE Standard +| for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float32 float32_mul( float32 a, float32 b STATUS_PARAM ) +{ + flag aSign, bSign, zSign; + int16 aExp, bExp, zExp; + bits32 aSig, bSig; + bits64 zSig64; + bits32 zSig; + + aSig = extractFloat32Frac( a ); + aExp = extractFloat32Exp( a ); + aSign = extractFloat32Sign( a ); + bSig = extractFloat32Frac( b ); + bExp = extractFloat32Exp( b ); + bSign = extractFloat32Sign( b ); + zSign = aSign ^ bSign; + if ( aExp == 0xFF ) { + if ( aSig || ( ( bExp == 0xFF ) && bSig ) ) { + return propagateFloat32NaN( a, b STATUS_VAR ); + } + if ( ( bExp | bSig ) == 0 ) { + float_raise( float_flag_invalid STATUS_VAR); + return float32_default_nan; + } + return packFloat32( zSign, 0xFF, 0 ); + } + if ( bExp == 0xFF ) { + if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); + if ( ( aExp | aSig ) == 0 ) { + float_raise( float_flag_invalid STATUS_VAR); + return float32_default_nan; + } + return packFloat32( zSign, 0xFF, 0 ); + } + if ( aExp == 0 ) { + if ( aSig == 0 ) return packFloat32( zSign, 0, 0 ); + normalizeFloat32Subnormal( aSig, &aExp, &aSig ); + } + if ( bExp == 0 ) { + if ( bSig == 0 ) return packFloat32( zSign, 0, 0 ); + normalizeFloat32Subnormal( bSig, &bExp, &bSig ); + } + zExp = aExp + bExp - 0x7F; + aSig = ( aSig | 0x00800000 )<<7; + bSig = ( bSig | 0x00800000 )<<8; + shift64RightJamming( ( (bits64) aSig ) * bSig, 32, &zSig64 ); + zSig = zSig64; + if ( 0 <= (sbits32) ( zSig<<1 ) ) { + zSig <<= 1; + --zExp; + } + return roundAndPackFloat32( zSign, zExp, zSig STATUS_VAR ); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of dividing the single-precision floating-point value `a' +| by the corresponding value `b'. The operation is performed according to the +| IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float32 float32_div( float32 a, float32 b STATUS_PARAM ) +{ + flag aSign, bSign, zSign; + int16 aExp, bExp, zExp; + bits32 aSig, bSig, zSig; + + aSig = extractFloat32Frac( a ); + aExp = extractFloat32Exp( a ); + aSign = extractFloat32Sign( a ); + bSig = extractFloat32Frac( b ); + bExp = extractFloat32Exp( b ); + bSign = extractFloat32Sign( b ); + zSign = aSign ^ bSign; + if ( aExp == 0xFF ) { + if ( aSig ) return propagateFloat32NaN( a, b STATUS_VAR ); + if ( bExp == 0xFF ) { + if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); + float_raise( float_flag_invalid STATUS_VAR); + return float32_default_nan; + } + return packFloat32( zSign, 0xFF, 0 ); + } + if ( bExp == 0xFF ) { + if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); + return packFloat32( zSign, 0, 0 ); + } + if ( bExp == 0 ) { + if ( bSig == 0 ) { + if ( ( aExp | aSig ) == 0 ) { + float_raise( float_flag_invalid STATUS_VAR); + return float32_default_nan; + } + float_raise( float_flag_divbyzero STATUS_VAR); + return packFloat32( zSign, 0xFF, 0 ); + } + normalizeFloat32Subnormal( bSig, &bExp, &bSig ); + } + if ( aExp == 0 ) { + if ( aSig == 0 ) return packFloat32( zSign, 0, 0 ); + normalizeFloat32Subnormal( aSig, &aExp, &aSig ); + } + zExp = aExp - bExp + 0x7D; + aSig = ( aSig | 0x00800000 )<<7; + bSig = ( bSig | 0x00800000 )<<8; + if ( bSig <= ( aSig + aSig ) ) { + aSig >>= 1; + ++zExp; + } + zSig = ( ( (bits64) aSig )<<32 ) / bSig; + if ( ( zSig & 0x3F ) == 0 ) { + zSig |= ( (bits64) bSig * zSig != ( (bits64) aSig )<<32 ); + } + return roundAndPackFloat32( zSign, zExp, zSig STATUS_VAR ); + +} + +/*---------------------------------------------------------------------------- +| Returns the remainder of the single-precision floating-point value `a' +| with respect to the corresponding value `b'. The operation is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float32 float32_rem( float32 a, float32 b STATUS_PARAM ) +{ + flag aSign, bSign, zSign; + int16 aExp, bExp, expDiff; + bits32 aSig, bSig; + bits32 q; + bits64 aSig64, bSig64, q64; + bits32 alternateASig; + sbits32 sigMean; + + aSig = extractFloat32Frac( a ); + aExp = extractFloat32Exp( a ); + aSign = extractFloat32Sign( a ); + bSig = extractFloat32Frac( b ); + bExp = extractFloat32Exp( b ); + bSign = extractFloat32Sign( b ); + if ( aExp == 0xFF ) { + if ( aSig || ( ( bExp == 0xFF ) && bSig ) ) { + return propagateFloat32NaN( a, b STATUS_VAR ); + } + float_raise( float_flag_invalid STATUS_VAR); + return float32_default_nan; + } + if ( bExp == 0xFF ) { + if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); + return a; + } + if ( bExp == 0 ) { + if ( bSig == 0 ) { + float_raise( float_flag_invalid STATUS_VAR); + return float32_default_nan; + } + normalizeFloat32Subnormal( bSig, &bExp, &bSig ); + } + if ( aExp == 0 ) { + if ( aSig == 0 ) return a; + normalizeFloat32Subnormal( aSig, &aExp, &aSig ); + } + expDiff = aExp - bExp; + aSig |= 0x00800000; + bSig |= 0x00800000; + if ( expDiff < 32 ) { + aSig <<= 8; + bSig <<= 8; + if ( expDiff < 0 ) { + if ( expDiff < -1 ) return a; + aSig >>= 1; + } + q = ( bSig <= aSig ); + if ( q ) aSig -= bSig; + if ( 0 < expDiff ) { + q = ( ( (bits64) aSig )<<32 ) / bSig; + q >>= 32 - expDiff; + bSig >>= 2; + aSig = ( ( aSig>>1 )<<( expDiff - 1 ) ) - bSig * q; + } + else { + aSig >>= 2; + bSig >>= 2; + } + } + else { + if ( bSig <= aSig ) aSig -= bSig; + aSig64 = ( (bits64) aSig )<<40; + bSig64 = ( (bits64) bSig )<<40; + expDiff -= 64; + while ( 0 < expDiff ) { + q64 = estimateDiv128To64( aSig64, 0, bSig64 ); + q64 = ( 2 < q64 ) ? q64 - 2 : 0; + aSig64 = - ( ( bSig * q64 )<<38 ); + expDiff -= 62; + } + expDiff += 64; + q64 = estimateDiv128To64( aSig64, 0, bSig64 ); + q64 = ( 2 < q64 ) ? q64 - 2 : 0; + q = q64>>( 64 - expDiff ); + bSig <<= 6; + aSig = ( ( aSig64>>33 )<<( expDiff - 1 ) ) - bSig * q; + } + do { + alternateASig = aSig; + ++q; + aSig -= bSig; + } while ( 0 <= (sbits32) aSig ); + sigMean = aSig + alternateASig; + if ( ( sigMean < 0 ) || ( ( sigMean == 0 ) && ( q & 1 ) ) ) { + aSig = alternateASig; + } + zSign = ( (sbits32) aSig < 0 ); + if ( zSign ) aSig = - aSig; + return normalizeRoundAndPackFloat32( aSign ^ zSign, bExp, aSig STATUS_VAR ); + +} + +/*---------------------------------------------------------------------------- +| Returns the square root of the single-precision floating-point value `a'. +| The operation is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float32 float32_sqrt( float32 a STATUS_PARAM ) +{ + flag aSign; + int16 aExp, zExp; + bits32 aSig, zSig; + bits64 rem, term; + + aSig = extractFloat32Frac( a ); + aExp = extractFloat32Exp( a ); + aSign = extractFloat32Sign( a ); + if ( aExp == 0xFF ) { + if ( aSig ) return propagateFloat32NaN( a, 0 STATUS_VAR ); + if ( ! aSign ) return a; + float_raise( float_flag_invalid STATUS_VAR); + return float32_default_nan; + } + if ( aSign ) { + if ( ( aExp | aSig ) == 0 ) return a; + float_raise( float_flag_invalid STATUS_VAR); + return float32_default_nan; + } + if ( aExp == 0 ) { + if ( aSig == 0 ) return 0; + normalizeFloat32Subnormal( aSig, &aExp, &aSig ); + } + zExp = ( ( aExp - 0x7F )>>1 ) + 0x7E; + aSig = ( aSig | 0x00800000 )<<8; + zSig = estimateSqrt32( aExp, aSig ) + 2; + if ( ( zSig & 0x7F ) <= 5 ) { + if ( zSig < 2 ) { + zSig = 0x7FFFFFFF; + goto roundAndPack; + } + aSig >>= aExp & 1; + term = ( (bits64) zSig ) * zSig; + rem = ( ( (bits64) aSig )<<32 ) - term; + while ( (sbits64) rem < 0 ) { + --zSig; + rem += ( ( (bits64) zSig )<<1 ) | 1; + } + zSig |= ( rem != 0 ); + } + shift32RightJamming( zSig, 1, &zSig ); + roundAndPack: + return roundAndPackFloat32( 0, zExp, zSig STATUS_VAR ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the single-precision floating-point value `a' is equal to +| the corresponding value `b', and 0 otherwise. The comparison is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +flag float32_eq( float32 a, float32 b STATUS_PARAM ) +{ + + if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) + || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) + ) { + if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) { + float_raise( float_flag_invalid STATUS_VAR); + } + return 0; + } + return ( a == b ) || ( (bits32) ( ( a | b )<<1 ) == 0 ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the single-precision floating-point value `a' is less than +| or equal to the corresponding value `b', and 0 otherwise. The comparison +| is performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic. +*----------------------------------------------------------------------------*/ + +flag float32_le( float32 a, float32 b STATUS_PARAM ) +{ + flag aSign, bSign; + + if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) + || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) + ) { + float_raise( float_flag_invalid STATUS_VAR); + return 0; + } + aSign = extractFloat32Sign( a ); + bSign = extractFloat32Sign( b ); + if ( aSign != bSign ) return aSign || ( (bits32) ( ( a | b )<<1 ) == 0 ); + return ( a == b ) || ( aSign ^ ( a < b ) ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the single-precision floating-point value `a' is less than +| the corresponding value `b', and 0 otherwise. The comparison is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +flag float32_lt( float32 a, float32 b STATUS_PARAM ) +{ + flag aSign, bSign; + + if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) + || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) + ) { + float_raise( float_flag_invalid STATUS_VAR); + return 0; + } + aSign = extractFloat32Sign( a ); + bSign = extractFloat32Sign( b ); + if ( aSign != bSign ) return aSign && ( (bits32) ( ( a | b )<<1 ) != 0 ); + return ( a != b ) && ( aSign ^ ( a < b ) ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the single-precision floating-point value `a' is equal to +| the corresponding value `b', and 0 otherwise. The invalid exception is +| raised if either operand is a NaN. Otherwise, the comparison is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +flag float32_eq_signaling( float32 a, float32 b STATUS_PARAM ) +{ + + if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) + || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) + ) { + float_raise( float_flag_invalid STATUS_VAR); + return 0; + } + return ( a == b ) || ( (bits32) ( ( a | b )<<1 ) == 0 ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the single-precision floating-point value `a' is less than or +| equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not +| cause an exception. Otherwise, the comparison is performed according to the +| IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +flag float32_le_quiet( float32 a, float32 b STATUS_PARAM ) +{ + flag aSign, bSign; + + if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) + || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) + ) { + if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) { + float_raise( float_flag_invalid STATUS_VAR); + } + return 0; + } + aSign = extractFloat32Sign( a ); + bSign = extractFloat32Sign( b ); + if ( aSign != bSign ) return aSign || ( (bits32) ( ( a | b )<<1 ) == 0 ); + return ( a == b ) || ( aSign ^ ( a < b ) ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the single-precision floating-point value `a' is less than +| the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an +| exception. Otherwise, the comparison is performed according to the IEC/IEEE +| Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +flag float32_lt_quiet( float32 a, float32 b STATUS_PARAM ) +{ + flag aSign, bSign; + + if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) + || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) + ) { + if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) { + float_raise( float_flag_invalid STATUS_VAR); + } + return 0; + } + aSign = extractFloat32Sign( a ); + bSign = extractFloat32Sign( b ); + if ( aSign != bSign ) return aSign && ( (bits32) ( ( a | b )<<1 ) != 0 ); + return ( a != b ) && ( aSign ^ ( a < b ) ); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the double-precision floating-point value +| `a' to the 32-bit two's complement integer format. The conversion is +| performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic---which means in particular that the conversion is rounded +| according to the current rounding mode. If `a' is a NaN, the largest +| positive integer is returned. Otherwise, if the conversion overflows, the +| largest integer with the same sign as `a' is returned. +*----------------------------------------------------------------------------*/ + +int32 float64_to_int32( float64 a STATUS_PARAM ) +{ + flag aSign; + int16 aExp, shiftCount; + bits64 aSig; + + aSig = extractFloat64Frac( a ); + aExp = extractFloat64Exp( a ); + aSign = extractFloat64Sign( a ); + if ( ( aExp == 0x7FF ) && aSig ) aSign = 0; + if ( aExp ) aSig |= LIT64( 0x0010000000000000 ); + shiftCount = 0x42C - aExp; + if ( 0 < shiftCount ) shift64RightJamming( aSig, shiftCount, &aSig ); + return roundAndPackInt32( aSign, aSig STATUS_VAR ); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the double-precision floating-point value +| `a' to the 32-bit two's complement integer format. The conversion is +| performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic, except that the conversion is always rounded toward zero. +| If `a' is a NaN, the largest positive integer is returned. Otherwise, if +| the conversion overflows, the largest integer with the same sign as `a' is +| returned. +*----------------------------------------------------------------------------*/ + +int32 float64_to_int32_round_to_zero( float64 a STATUS_PARAM ) +{ + flag aSign; + int16 aExp, shiftCount; + bits64 aSig, savedASig; + int32 z; + + aSig = extractFloat64Frac( a ); + aExp = extractFloat64Exp( a ); + aSign = extractFloat64Sign( a ); + if ( 0x41E < aExp ) { + if ( ( aExp == 0x7FF ) && aSig ) aSign = 0; + goto invalid; + } + else if ( aExp < 0x3FF ) { + if ( aExp || aSig ) STATUS(float_exception_flags) |= float_flag_inexact; + return 0; + } + aSig |= LIT64( 0x0010000000000000 ); + shiftCount = 0x433 - aExp; + savedASig = aSig; + aSig >>= shiftCount; + z = aSig; + if ( aSign ) z = - z; + if ( ( z < 0 ) ^ aSign ) { + invalid: + float_raise( float_flag_invalid STATUS_VAR); + return aSign ? (sbits32) 0x80000000 : 0x7FFFFFFF; + } + if ( ( aSig<<shiftCount ) != savedASig ) { + STATUS(float_exception_flags) |= float_flag_inexact; + } + return z; + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the double-precision floating-point value +| `a' to the 64-bit two's complement integer format. The conversion is +| performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic---which means in particular that the conversion is rounded +| according to the current rounding mode. If `a' is a NaN, the largest +| positive integer is returned. Otherwise, if the conversion overflows, the +| largest integer with the same sign as `a' is returned. +*----------------------------------------------------------------------------*/ + +int64 float64_to_int64( float64 a STATUS_PARAM ) +{ + flag aSign; + int16 aExp, shiftCount; + bits64 aSig, aSigExtra; + + aSig = extractFloat64Frac( a ); + aExp = extractFloat64Exp( a ); + aSign = extractFloat64Sign( a ); + if ( aExp ) aSig |= LIT64( 0x0010000000000000 ); + shiftCount = 0x433 - aExp; + if ( shiftCount <= 0 ) { + if ( 0x43E < aExp ) { + float_raise( float_flag_invalid STATUS_VAR); + if ( ! aSign + || ( ( aExp == 0x7FF ) + && ( aSig != LIT64( 0x0010000000000000 ) ) ) + ) { + return LIT64( 0x7FFFFFFFFFFFFFFF ); + } + return (sbits64) LIT64( 0x8000000000000000 ); + } + aSigExtra = 0; + aSig <<= - shiftCount; + } + else { + shift64ExtraRightJamming( aSig, 0, shiftCount, &aSig, &aSigExtra ); + } + return roundAndPackInt64( aSign, aSig, aSigExtra STATUS_VAR ); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the double-precision floating-point value +| `a' to the 64-bit two's complement integer format. The conversion is +| performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic, except that the conversion is always rounded toward zero. +| If `a' is a NaN, the largest positive integer is returned. Otherwise, if +| the conversion overflows, the largest integer with the same sign as `a' is +| returned. +*----------------------------------------------------------------------------*/ + +int64 float64_to_int64_round_to_zero( float64 a STATUS_PARAM ) +{ + flag aSign; + int16 aExp, shiftCount; + bits64 aSig; + int64 z; + + aSig = extractFloat64Frac( a ); + aExp = extractFloat64Exp( a ); + aSign = extractFloat64Sign( a ); + if ( aExp ) aSig |= LIT64( 0x0010000000000000 ); + shiftCount = aExp - 0x433; + if ( 0 <= shiftCount ) { + if ( 0x43E <= aExp ) { + if ( a != LIT64( 0xC3E0000000000000 ) ) { + float_raise( float_flag_invalid STATUS_VAR); + if ( ! aSign + || ( ( aExp == 0x7FF ) + && ( aSig != LIT64( 0x0010000000000000 ) ) ) + ) { + return LIT64( 0x7FFFFFFFFFFFFFFF ); + } + } + return (sbits64) LIT64( 0x8000000000000000 ); + } + z = aSig<<shiftCount; + } + else { + if ( aExp < 0x3FE ) { + if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact; + return 0; + } + z = aSig>>( - shiftCount ); + if ( (bits64) ( aSig<<( shiftCount & 63 ) ) ) { + STATUS(float_exception_flags) |= float_flag_inexact; + } + } + if ( aSign ) z = - z; + return z; + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the double-precision floating-point value +| `a' to the single-precision floating-point format. The conversion is +| performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic. +*----------------------------------------------------------------------------*/ + +float32 float64_to_float32( float64 a STATUS_PARAM ) +{ + flag aSign; + int16 aExp; + bits64 aSig; + bits32 zSig; + + aSig = extractFloat64Frac( a ); + aExp = extractFloat64Exp( a ); + aSign = extractFloat64Sign( a ); + if ( aExp == 0x7FF ) { + if ( aSig ) return commonNaNToFloat32( float64ToCommonNaN( a STATUS_VAR ) ); + return packFloat32( aSign, 0xFF, 0 ); + } + shift64RightJamming( aSig, 22, &aSig ); + zSig = aSig; + if ( aExp || zSig ) { + zSig |= 0x40000000; + aExp -= 0x381; + } + return roundAndPackFloat32( aSign, aExp, zSig STATUS_VAR ); + +} + +#ifdef FLOATX80 + +/*---------------------------------------------------------------------------- +| Returns the result of converting the double-precision floating-point value +| `a' to the extended double-precision floating-point format. The conversion +| is performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic. +*----------------------------------------------------------------------------*/ + +floatx80 float64_to_floatx80( float64 a STATUS_PARAM ) +{ + flag aSign; + int16 aExp; + bits64 aSig; + + aSig = extractFloat64Frac( a ); + aExp = extractFloat64Exp( a ); + aSign = extractFloat64Sign( a ); + if ( aExp == 0x7FF ) { + if ( aSig ) return commonNaNToFloatx80( float64ToCommonNaN( a STATUS_VAR ) ); + return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); + } + if ( aExp == 0 ) { + if ( aSig == 0 ) return packFloatx80( aSign, 0, 0 ); + normalizeFloat64Subnormal( aSig, &aExp, &aSig ); + } + return + packFloatx80( + aSign, aExp + 0x3C00, ( aSig | LIT64( 0x0010000000000000 ) )<<11 ); + +} + +#endif + +#ifdef FLOAT128 + +/*---------------------------------------------------------------------------- +| Returns the result of converting the double-precision floating-point value +| `a' to the quadruple-precision floating-point format. The conversion is +| performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic. +*----------------------------------------------------------------------------*/ + +float128 float64_to_float128( float64 a STATUS_PARAM ) +{ + flag aSign; + int16 aExp; + bits64 aSig, zSig0, zSig1; + + aSig = extractFloat64Frac( a ); + aExp = extractFloat64Exp( a ); + aSign = extractFloat64Sign( a ); + if ( aExp == 0x7FF ) { + if ( aSig ) return commonNaNToFloat128( float64ToCommonNaN( a STATUS_VAR ) ); + return packFloat128( aSign, 0x7FFF, 0, 0 ); + } + if ( aExp == 0 ) { + if ( aSig == 0 ) return packFloat128( aSign, 0, 0, 0 ); + normalizeFloat64Subnormal( aSig, &aExp, &aSig ); + --aExp; + } + shift128Right( aSig, 0, 4, &zSig0, &zSig1 ); + return packFloat128( aSign, aExp + 0x3C00, zSig0, zSig1 ); + +} + +#endif + +/*---------------------------------------------------------------------------- +| Rounds the double-precision floating-point value `a' to an integer, and +| returns the result as a double-precision floating-point value. The +| operation is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float64 float64_round_to_int( float64 a STATUS_PARAM ) +{ + flag aSign; + int16 aExp; + bits64 lastBitMask, roundBitsMask; + int8 roundingMode; + float64 z; + + aExp = extractFloat64Exp( a ); + if ( 0x433 <= aExp ) { + if ( ( aExp == 0x7FF ) && extractFloat64Frac( a ) ) { + return propagateFloat64NaN( a, a STATUS_VAR ); + } + return a; + } + if ( aExp < 0x3FF ) { + if ( (bits64) ( a<<1 ) == 0 ) return a; + STATUS(float_exception_flags) |= float_flag_inexact; + aSign = extractFloat64Sign( a ); + switch ( STATUS(float_rounding_mode) ) { + case float_round_nearest_even: + if ( ( aExp == 0x3FE ) && extractFloat64Frac( a ) ) { + return packFloat64( aSign, 0x3FF, 0 ); + } + break; + case float_round_down: + return aSign ? LIT64( 0xBFF0000000000000 ) : 0; + case float_round_up: + return + aSign ? LIT64( 0x8000000000000000 ) : LIT64( 0x3FF0000000000000 ); + } + return packFloat64( aSign, 0, 0 ); + } + lastBitMask = 1; + lastBitMask <<= 0x433 - aExp; + roundBitsMask = lastBitMask - 1; + z = a; + roundingMode = STATUS(float_rounding_mode); + if ( roundingMode == float_round_nearest_even ) { + z += lastBitMask>>1; + if ( ( z & roundBitsMask ) == 0 ) z &= ~ lastBitMask; + } + else if ( roundingMode != float_round_to_zero ) { + if ( extractFloat64Sign( z ) ^ ( roundingMode == float_round_up ) ) { + z += roundBitsMask; + } + } + z &= ~ roundBitsMask; + if ( z != a ) STATUS(float_exception_flags) |= float_flag_inexact; + return z; + +} + +/*---------------------------------------------------------------------------- +| Returns the result of adding the absolute values of the double-precision +| floating-point values `a' and `b'. If `zSign' is 1, the sum is negated +| before being returned. `zSign' is ignored if the result is a NaN. +| The addition is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +static float64 addFloat64Sigs( float64 a, float64 b, flag zSign STATUS_PARAM ) +{ + int16 aExp, bExp, zExp; + bits64 aSig, bSig, zSig; + int16 expDiff; + + aSig = extractFloat64Frac( a ); + aExp = extractFloat64Exp( a ); + bSig = extractFloat64Frac( b ); + bExp = extractFloat64Exp( b ); + expDiff = aExp - bExp; + aSig <<= 9; + bSig <<= 9; + if ( 0 < expDiff ) { + if ( aExp == 0x7FF ) { + if ( aSig ) return propagateFloat64NaN( a, b STATUS_VAR ); + return a; + } + if ( bExp == 0 ) { + --expDiff; + } + else { + bSig |= LIT64( 0x2000000000000000 ); + } + shift64RightJamming( bSig, expDiff, &bSig ); + zExp = aExp; + } + else if ( expDiff < 0 ) { + if ( bExp == 0x7FF ) { + if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); + return packFloat64( zSign, 0x7FF, 0 ); + } + if ( aExp == 0 ) { + ++expDiff; + } + else { + aSig |= LIT64( 0x2000000000000000 ); + } + shift64RightJamming( aSig, - expDiff, &aSig ); + zExp = bExp; + } + else { + if ( aExp == 0x7FF ) { + if ( aSig | bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); + return a; + } + if ( aExp == 0 ) return packFloat64( zSign, 0, ( aSig + bSig )>>9 ); + zSig = LIT64( 0x4000000000000000 ) + aSig + bSig; + zExp = aExp; + goto roundAndPack; + } + aSig |= LIT64( 0x2000000000000000 ); + zSig = ( aSig + bSig )<<1; + --zExp; + if ( (sbits64) zSig < 0 ) { + zSig = aSig + bSig; + ++zExp; + } + roundAndPack: + return roundAndPackFloat64( zSign, zExp, zSig STATUS_VAR ); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of subtracting the absolute values of the double- +| precision floating-point values `a' and `b'. If `zSign' is 1, the +| difference is negated before being returned. `zSign' is ignored if the +| result is a NaN. The subtraction is performed according to the IEC/IEEE +| Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +static float64 subFloat64Sigs( float64 a, float64 b, flag zSign STATUS_PARAM ) +{ + int16 aExp, bExp, zExp; + bits64 aSig, bSig, zSig; + int16 expDiff; + + aSig = extractFloat64Frac( a ); + aExp = extractFloat64Exp( a ); + bSig = extractFloat64Frac( b ); + bExp = extractFloat64Exp( b ); + expDiff = aExp - bExp; + aSig <<= 10; + bSig <<= 10; + if ( 0 < expDiff ) goto aExpBigger; + if ( expDiff < 0 ) goto bExpBigger; + if ( aExp == 0x7FF ) { + if ( aSig | bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); + float_raise( float_flag_invalid STATUS_VAR); + return float64_default_nan; + } + if ( aExp == 0 ) { + aExp = 1; + bExp = 1; + } + if ( bSig < aSig ) goto aBigger; + if ( aSig < bSig ) goto bBigger; + return packFloat64( STATUS(float_rounding_mode) == float_round_down, 0, 0 ); + bExpBigger: + if ( bExp == 0x7FF ) { + if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); + return packFloat64( zSign ^ 1, 0x7FF, 0 ); + } + if ( aExp == 0 ) { + ++expDiff; + } + else { + aSig |= LIT64( 0x4000000000000000 ); + } + shift64RightJamming( aSig, - expDiff, &aSig ); + bSig |= LIT64( 0x4000000000000000 ); + bBigger: + zSig = bSig - aSig; + zExp = bExp; + zSign ^= 1; + goto normalizeRoundAndPack; + aExpBigger: + if ( aExp == 0x7FF ) { + if ( aSig ) return propagateFloat64NaN( a, b STATUS_VAR ); + return a; + } + if ( bExp == 0 ) { + --expDiff; + } + else { + bSig |= LIT64( 0x4000000000000000 ); + } + shift64RightJamming( bSig, expDiff, &bSig ); + aSig |= LIT64( 0x4000000000000000 ); + aBigger: + zSig = aSig - bSig; + zExp = aExp; + normalizeRoundAndPack: + --zExp; + return normalizeRoundAndPackFloat64( zSign, zExp, zSig STATUS_VAR ); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of adding the double-precision floating-point values `a' +| and `b'. The operation is performed according to the IEC/IEEE Standard for +| Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float64 float64_add( float64 a, float64 b STATUS_PARAM ) +{ + flag aSign, bSign; + + aSign = extractFloat64Sign( a ); + bSign = extractFloat64Sign( b ); + if ( aSign == bSign ) { + return addFloat64Sigs( a, b, aSign STATUS_VAR ); + } + else { + return subFloat64Sigs( a, b, aSign STATUS_VAR ); + } + +} + +/*---------------------------------------------------------------------------- +| Returns the result of subtracting the double-precision floating-point values +| `a' and `b'. The operation is performed according to the IEC/IEEE Standard +| for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float64 float64_sub( float64 a, float64 b STATUS_PARAM ) +{ + flag aSign, bSign; + + aSign = extractFloat64Sign( a ); + bSign = extractFloat64Sign( b ); + if ( aSign == bSign ) { + return subFloat64Sigs( a, b, aSign STATUS_VAR ); + } + else { + return addFloat64Sigs( a, b, aSign STATUS_VAR ); + } + +} + +/*---------------------------------------------------------------------------- +| Returns the result of multiplying the double-precision floating-point values +| `a' and `b'. The operation is performed according to the IEC/IEEE Standard +| for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float64 float64_mul( float64 a, float64 b STATUS_PARAM ) +{ + flag aSign, bSign, zSign; + int16 aExp, bExp, zExp; + bits64 aSig, bSig, zSig0, zSig1; + + aSig = extractFloat64Frac( a ); + aExp = extractFloat64Exp( a ); + aSign = extractFloat64Sign( a ); + bSig = extractFloat64Frac( b ); + bExp = extractFloat64Exp( b ); + bSign = extractFloat64Sign( b ); + zSign = aSign ^ bSign; + if ( aExp == 0x7FF ) { + if ( aSig || ( ( bExp == 0x7FF ) && bSig ) ) { + return propagateFloat64NaN( a, b STATUS_VAR ); + } + if ( ( bExp | bSig ) == 0 ) { + float_raise( float_flag_invalid STATUS_VAR); + return float64_default_nan; + } + return packFloat64( zSign, 0x7FF, 0 ); + } + if ( bExp == 0x7FF ) { + if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); + if ( ( aExp | aSig ) == 0 ) { + float_raise( float_flag_invalid STATUS_VAR); + return float64_default_nan; + } + return packFloat64( zSign, 0x7FF, 0 ); + } + if ( aExp == 0 ) { + if ( aSig == 0 ) return packFloat64( zSign, 0, 0 ); + normalizeFloat64Subnormal( aSig, &aExp, &aSig ); + } + if ( bExp == 0 ) { + if ( bSig == 0 ) return packFloat64( zSign, 0, 0 ); + normalizeFloat64Subnormal( bSig, &bExp, &bSig ); + } + zExp = aExp + bExp - 0x3FF; + aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<10; + bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11; + mul64To128( aSig, bSig, &zSig0, &zSig1 ); + zSig0 |= ( zSig1 != 0 ); + if ( 0 <= (sbits64) ( zSig0<<1 ) ) { + zSig0 <<= 1; + --zExp; + } + return roundAndPackFloat64( zSign, zExp, zSig0 STATUS_VAR ); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of dividing the double-precision floating-point value `a' +| by the corresponding value `b'. The operation is performed according to +| the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float64 float64_div( float64 a, float64 b STATUS_PARAM ) +{ + flag aSign, bSign, zSign; + int16 aExp, bExp, zExp; + bits64 aSig, bSig, zSig; + bits64 rem0, rem1; + bits64 term0, term1; + + aSig = extractFloat64Frac( a ); + aExp = extractFloat64Exp( a ); + aSign = extractFloat64Sign( a ); + bSig = extractFloat64Frac( b ); + bExp = extractFloat64Exp( b ); + bSign = extractFloat64Sign( b ); + zSign = aSign ^ bSign; + if ( aExp == 0x7FF ) { + if ( aSig ) return propagateFloat64NaN( a, b STATUS_VAR ); + if ( bExp == 0x7FF ) { + if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); + float_raise( float_flag_invalid STATUS_VAR); + return float64_default_nan; + } + return packFloat64( zSign, 0x7FF, 0 ); + } + if ( bExp == 0x7FF ) { + if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); + return packFloat64( zSign, 0, 0 ); + } + if ( bExp == 0 ) { + if ( bSig == 0 ) { + if ( ( aExp | aSig ) == 0 ) { + float_raise( float_flag_invalid STATUS_VAR); + return float64_default_nan; + } + float_raise( float_flag_divbyzero STATUS_VAR); + return packFloat64( zSign, 0x7FF, 0 ); + } + normalizeFloat64Subnormal( bSig, &bExp, &bSig ); + } + if ( aExp == 0 ) { + if ( aSig == 0 ) return packFloat64( zSign, 0, 0 ); + normalizeFloat64Subnormal( aSig, &aExp, &aSig ); + } + zExp = aExp - bExp + 0x3FD; + aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<10; + bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11; + if ( bSig <= ( aSig + aSig ) ) { + aSig >>= 1; + ++zExp; + } + zSig = estimateDiv128To64( aSig, 0, bSig ); + if ( ( zSig & 0x1FF ) <= 2 ) { + mul64To128( bSig, zSig, &term0, &term1 ); + sub128( aSig, 0, term0, term1, &rem0, &rem1 ); + while ( (sbits64) rem0 < 0 ) { + --zSig; + add128( rem0, rem1, 0, bSig, &rem0, &rem1 ); + } + zSig |= ( rem1 != 0 ); + } + return roundAndPackFloat64( zSign, zExp, zSig STATUS_VAR ); + +} + +/*---------------------------------------------------------------------------- +| Returns the remainder of the double-precision floating-point value `a' +| with respect to the corresponding value `b'. The operation is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float64 float64_rem( float64 a, float64 b STATUS_PARAM ) +{ + flag aSign, bSign, zSign; + int16 aExp, bExp, expDiff; + bits64 aSig, bSig; + bits64 q, alternateASig; + sbits64 sigMean; + + aSig = extractFloat64Frac( a ); + aExp = extractFloat64Exp( a ); + aSign = extractFloat64Sign( a ); + bSig = extractFloat64Frac( b ); + bExp = extractFloat64Exp( b ); + bSign = extractFloat64Sign( b ); + if ( aExp == 0x7FF ) { + if ( aSig || ( ( bExp == 0x7FF ) && bSig ) ) { + return propagateFloat64NaN( a, b STATUS_VAR ); + } + float_raise( float_flag_invalid STATUS_VAR); + return float64_default_nan; + } + if ( bExp == 0x7FF ) { + if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); + return a; + } + if ( bExp == 0 ) { + if ( bSig == 0 ) { + float_raise( float_flag_invalid STATUS_VAR); + return float64_default_nan; + } + normalizeFloat64Subnormal( bSig, &bExp, &bSig ); + } + if ( aExp == 0 ) { + if ( aSig == 0 ) return a; + normalizeFloat64Subnormal( aSig, &aExp, &aSig ); + } + expDiff = aExp - bExp; + aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<11; + bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11; + if ( expDiff < 0 ) { + if ( expDiff < -1 ) return a; + aSig >>= 1; + } + q = ( bSig <= aSig ); + if ( q ) aSig -= bSig; + expDiff -= 64; + while ( 0 < expDiff ) { + q = estimateDiv128To64( aSig, 0, bSig ); + q = ( 2 < q ) ? q - 2 : 0; + aSig = - ( ( bSig>>2 ) * q ); + expDiff -= 62; + } + expDiff += 64; + if ( 0 < expDiff ) { + q = estimateDiv128To64( aSig, 0, bSig ); + q = ( 2 < q ) ? q - 2 : 0; + q >>= 64 - expDiff; + bSig >>= 2; + aSig = ( ( aSig>>1 )<<( expDiff - 1 ) ) - bSig * q; + } + else { + aSig >>= 2; + bSig >>= 2; + } + do { + alternateASig = aSig; + ++q; + aSig -= bSig; + } while ( 0 <= (sbits64) aSig ); + sigMean = aSig + alternateASig; + if ( ( sigMean < 0 ) || ( ( sigMean == 0 ) && ( q & 1 ) ) ) { + aSig = alternateASig; + } + zSign = ( (sbits64) aSig < 0 ); + if ( zSign ) aSig = - aSig; + return normalizeRoundAndPackFloat64( aSign ^ zSign, bExp, aSig STATUS_VAR ); + +} + +/*---------------------------------------------------------------------------- +| Returns the square root of the double-precision floating-point value `a'. +| The operation is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float64 float64_sqrt( float64 a STATUS_PARAM ) +{ + flag aSign; + int16 aExp, zExp; + bits64 aSig, zSig, doubleZSig; + bits64 rem0, rem1, term0, term1; + + aSig = extractFloat64Frac( a ); + aExp = extractFloat64Exp( a ); + aSign = extractFloat64Sign( a ); + if ( aExp == 0x7FF ) { + if ( aSig ) return propagateFloat64NaN( a, a STATUS_VAR ); + if ( ! aSign ) return a; + float_raise( float_flag_invalid STATUS_VAR); + return float64_default_nan; + } + if ( aSign ) { + if ( ( aExp | aSig ) == 0 ) return a; + float_raise( float_flag_invalid STATUS_VAR); + return float64_default_nan; + } + if ( aExp == 0 ) { + if ( aSig == 0 ) return 0; + normalizeFloat64Subnormal( aSig, &aExp, &aSig ); + } + zExp = ( ( aExp - 0x3FF )>>1 ) + 0x3FE; + aSig |= LIT64( 0x0010000000000000 ); + zSig = estimateSqrt32( aExp, aSig>>21 ); + aSig <<= 9 - ( aExp & 1 ); + zSig = estimateDiv128To64( aSig, 0, zSig<<32 ) + ( zSig<<30 ); + if ( ( zSig & 0x1FF ) <= 5 ) { + doubleZSig = zSig<<1; + mul64To128( zSig, zSig, &term0, &term1 ); + sub128( aSig, 0, term0, term1, &rem0, &rem1 ); + while ( (sbits64) rem0 < 0 ) { + --zSig; + doubleZSig -= 2; + add128( rem0, rem1, zSig>>63, doubleZSig | 1, &rem0, &rem1 ); + } + zSig |= ( ( rem0 | rem1 ) != 0 ); + } + return roundAndPackFloat64( 0, zExp, zSig STATUS_VAR ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the double-precision floating-point value `a' is equal to the +| corresponding value `b', and 0 otherwise. The comparison is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +flag float64_eq( float64 a, float64 b STATUS_PARAM ) +{ + + if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) + || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) + ) { + if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) { + float_raise( float_flag_invalid STATUS_VAR); + } + return 0; + } + return ( a == b ) || ( (bits64) ( ( a | b )<<1 ) == 0 ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the double-precision floating-point value `a' is less than or +| equal to the corresponding value `b', and 0 otherwise. The comparison is +| performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic. +*----------------------------------------------------------------------------*/ + +flag float64_le( float64 a, float64 b STATUS_PARAM ) +{ + flag aSign, bSign; + + if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) + || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) + ) { + float_raise( float_flag_invalid STATUS_VAR); + return 0; + } + aSign = extractFloat64Sign( a ); + bSign = extractFloat64Sign( b ); + if ( aSign != bSign ) return aSign || ( (bits64) ( ( a | b )<<1 ) == 0 ); + return ( a == b ) || ( aSign ^ ( a < b ) ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the double-precision floating-point value `a' is less than +| the corresponding value `b', and 0 otherwise. The comparison is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +flag float64_lt( float64 a, float64 b STATUS_PARAM ) +{ + flag aSign, bSign; + + if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) + || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) + ) { + float_raise( float_flag_invalid STATUS_VAR); + return 0; + } + aSign = extractFloat64Sign( a ); + bSign = extractFloat64Sign( b ); + if ( aSign != bSign ) return aSign && ( (bits64) ( ( a | b )<<1 ) != 0 ); + return ( a != b ) && ( aSign ^ ( a < b ) ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the double-precision floating-point value `a' is equal to the +| corresponding value `b', and 0 otherwise. The invalid exception is raised +| if either operand is a NaN. Otherwise, the comparison is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +flag float64_eq_signaling( float64 a, float64 b STATUS_PARAM ) +{ + + if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) + || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) + ) { + float_raise( float_flag_invalid STATUS_VAR); + return 0; + } + return ( a == b ) || ( (bits64) ( ( a | b )<<1 ) == 0 ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the double-precision floating-point value `a' is less than or +| equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not +| cause an exception. Otherwise, the comparison is performed according to the +| IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +flag float64_le_quiet( float64 a, float64 b STATUS_PARAM ) +{ + flag aSign, bSign; + + if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) + || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) + ) { + if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) { + float_raise( float_flag_invalid STATUS_VAR); + } + return 0; + } + aSign = extractFloat64Sign( a ); + bSign = extractFloat64Sign( b ); + if ( aSign != bSign ) return aSign || ( (bits64) ( ( a | b )<<1 ) == 0 ); + return ( a == b ) || ( aSign ^ ( a < b ) ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the double-precision floating-point value `a' is less than +| the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an +| exception. Otherwise, the comparison is performed according to the IEC/IEEE +| Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +flag float64_lt_quiet( float64 a, float64 b STATUS_PARAM ) +{ + flag aSign, bSign; + + if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) + || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) + ) { + if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) { + float_raise( float_flag_invalid STATUS_VAR); + } + return 0; + } + aSign = extractFloat64Sign( a ); + bSign = extractFloat64Sign( b ); + if ( aSign != bSign ) return aSign && ( (bits64) ( ( a | b )<<1 ) != 0 ); + return ( a != b ) && ( aSign ^ ( a < b ) ); + +} + +#ifdef FLOATX80 + +/*---------------------------------------------------------------------------- +| Returns the result of converting the extended double-precision floating- +| point value `a' to the 32-bit two's complement integer format. The +| conversion is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic---which means in particular that the conversion +| is rounded according to the current rounding mode. If `a' is a NaN, the +| largest positive integer is returned. Otherwise, if the conversion +| overflows, the largest integer with the same sign as `a' is returned. +*----------------------------------------------------------------------------*/ + +int32 floatx80_to_int32( floatx80 a STATUS_PARAM ) +{ + flag aSign; + int32 aExp, shiftCount; + bits64 aSig; + + aSig = extractFloatx80Frac( a ); + aExp = extractFloatx80Exp( a ); + aSign = extractFloatx80Sign( a ); + if ( ( aExp == 0x7FFF ) && (bits64) ( aSig<<1 ) ) aSign = 0; + shiftCount = 0x4037 - aExp; + if ( shiftCount <= 0 ) shiftCount = 1; + shift64RightJamming( aSig, shiftCount, &aSig ); + return roundAndPackInt32( aSign, aSig STATUS_VAR ); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the extended double-precision floating- +| point value `a' to the 32-bit two's complement integer format. The +| conversion is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic, except that the conversion is always rounded +| toward zero. If `a' is a NaN, the largest positive integer is returned. +| Otherwise, if the conversion overflows, the largest integer with the same +| sign as `a' is returned. +*----------------------------------------------------------------------------*/ + +int32 floatx80_to_int32_round_to_zero( floatx80 a STATUS_PARAM ) +{ + flag aSign; + int32 aExp, shiftCount; + bits64 aSig, savedASig; + int32 z; + + aSig = extractFloatx80Frac( a ); + aExp = extractFloatx80Exp( a ); + aSign = extractFloatx80Sign( a ); + if ( 0x401E < aExp ) { + if ( ( aExp == 0x7FFF ) && (bits64) ( aSig<<1 ) ) aSign = 0; + goto invalid; + } + else if ( aExp < 0x3FFF ) { + if ( aExp || aSig ) STATUS(float_exception_flags) |= float_flag_inexact; + return 0; + } + shiftCount = 0x403E - aExp; + savedASig = aSig; + aSig >>= shiftCount; + z = aSig; + if ( aSign ) z = - z; + if ( ( z < 0 ) ^ aSign ) { + invalid: + float_raise( float_flag_invalid STATUS_VAR); + return aSign ? (sbits32) 0x80000000 : 0x7FFFFFFF; + } + if ( ( aSig<<shiftCount ) != savedASig ) { + STATUS(float_exception_flags) |= float_flag_inexact; + } + return z; + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the extended double-precision floating- +| point value `a' to the 64-bit two's complement integer format. The +| conversion is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic---which means in particular that the conversion +| is rounded according to the current rounding mode. If `a' is a NaN, +| the largest positive integer is returned. Otherwise, if the conversion +| overflows, the largest integer with the same sign as `a' is returned. +*----------------------------------------------------------------------------*/ + +int64 floatx80_to_int64( floatx80 a STATUS_PARAM ) +{ + flag aSign; + int32 aExp, shiftCount; + bits64 aSig, aSigExtra; + + aSig = extractFloatx80Frac( a ); + aExp = extractFloatx80Exp( a ); + aSign = extractFloatx80Sign( a ); + shiftCount = 0x403E - aExp; + if ( shiftCount <= 0 ) { + if ( shiftCount ) { + float_raise( float_flag_invalid STATUS_VAR); + if ( ! aSign + || ( ( aExp == 0x7FFF ) + && ( aSig != LIT64( 0x8000000000000000 ) ) ) + ) { + return LIT64( 0x7FFFFFFFFFFFFFFF ); + } + return (sbits64) LIT64( 0x8000000000000000 ); + } + aSigExtra = 0; + } + else { + shift64ExtraRightJamming( aSig, 0, shiftCount, &aSig, &aSigExtra ); + } + return roundAndPackInt64( aSign, aSig, aSigExtra STATUS_VAR ); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the extended double-precision floating- +| point value `a' to the 64-bit two's complement integer format. The +| conversion is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic, except that the conversion is always rounded +| toward zero. If `a' is a NaN, the largest positive integer is returned. +| Otherwise, if the conversion overflows, the largest integer with the same +| sign as `a' is returned. +*----------------------------------------------------------------------------*/ + +int64 floatx80_to_int64_round_to_zero( floatx80 a STATUS_PARAM ) +{ + flag aSign; + int32 aExp, shiftCount; + bits64 aSig; + int64 z; + + aSig = extractFloatx80Frac( a ); + aExp = extractFloatx80Exp( a ); + aSign = extractFloatx80Sign( a ); + shiftCount = aExp - 0x403E; + if ( 0 <= shiftCount ) { + aSig &= LIT64( 0x7FFFFFFFFFFFFFFF ); + if ( ( a.high != 0xC03E ) || aSig ) { + float_raise( float_flag_invalid STATUS_VAR); + if ( ! aSign || ( ( aExp == 0x7FFF ) && aSig ) ) { + return LIT64( 0x7FFFFFFFFFFFFFFF ); + } + } + return (sbits64) LIT64( 0x8000000000000000 ); + } + else if ( aExp < 0x3FFF ) { + if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact; + return 0; + } + z = aSig>>( - shiftCount ); + if ( (bits64) ( aSig<<( shiftCount & 63 ) ) ) { + STATUS(float_exception_flags) |= float_flag_inexact; + } + if ( aSign ) z = - z; + return z; + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the extended double-precision floating- +| point value `a' to the single-precision floating-point format. The +| conversion is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float32 floatx80_to_float32( floatx80 a STATUS_PARAM ) +{ + flag aSign; + int32 aExp; + bits64 aSig; + + aSig = extractFloatx80Frac( a ); + aExp = extractFloatx80Exp( a ); + aSign = extractFloatx80Sign( a ); + if ( aExp == 0x7FFF ) { + if ( (bits64) ( aSig<<1 ) ) { + return commonNaNToFloat32( floatx80ToCommonNaN( a STATUS_VAR ) ); + } + return packFloat32( aSign, 0xFF, 0 ); + } + shift64RightJamming( aSig, 33, &aSig ); + if ( aExp || aSig ) aExp -= 0x3F81; + return roundAndPackFloat32( aSign, aExp, aSig STATUS_VAR ); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the extended double-precision floating- +| point value `a' to the double-precision floating-point format. The +| conversion is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float64 floatx80_to_float64( floatx80 a STATUS_PARAM ) +{ + flag aSign; + int32 aExp; + bits64 aSig, zSig; + + aSig = extractFloatx80Frac( a ); + aExp = extractFloatx80Exp( a ); + aSign = extractFloatx80Sign( a ); + if ( aExp == 0x7FFF ) { + if ( (bits64) ( aSig<<1 ) ) { + return commonNaNToFloat64( floatx80ToCommonNaN( a STATUS_VAR ) ); + } + return packFloat64( aSign, 0x7FF, 0 ); + } + shift64RightJamming( aSig, 1, &zSig ); + if ( aExp || aSig ) aExp -= 0x3C01; + return roundAndPackFloat64( aSign, aExp, zSig STATUS_VAR ); + +} + +#ifdef FLOAT128 + +/*---------------------------------------------------------------------------- +| Returns the result of converting the extended double-precision floating- +| point value `a' to the quadruple-precision floating-point format. The +| conversion is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float128 floatx80_to_float128( floatx80 a STATUS_PARAM ) +{ + flag aSign; + int16 aExp; + bits64 aSig, zSig0, zSig1; + + aSig = extractFloatx80Frac( a ); + aExp = extractFloatx80Exp( a ); + aSign = extractFloatx80Sign( a ); + if ( ( aExp == 0x7FFF ) && (bits64) ( aSig<<1 ) ) { + return commonNaNToFloat128( floatx80ToCommonNaN( a STATUS_VAR ) ); + } + shift128Right( aSig<<1, 0, 16, &zSig0, &zSig1 ); + return packFloat128( aSign, aExp, zSig0, zSig1 ); + +} + +#endif + +/*---------------------------------------------------------------------------- +| Rounds the extended double-precision floating-point value `a' to an integer, +| and returns the result as an extended quadruple-precision floating-point +| value. The operation is performed according to the IEC/IEEE Standard for +| Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +floatx80 floatx80_round_to_int( floatx80 a STATUS_PARAM ) +{ + flag aSign; + int32 aExp; + bits64 lastBitMask, roundBitsMask; + int8 roundingMode; + floatx80 z; + + aExp = extractFloatx80Exp( a ); + if ( 0x403E <= aExp ) { + if ( ( aExp == 0x7FFF ) && (bits64) ( extractFloatx80Frac( a )<<1 ) ) { + return propagateFloatx80NaN( a, a STATUS_VAR ); + } + return a; + } + if ( aExp < 0x3FFF ) { + if ( ( aExp == 0 ) + && ( (bits64) ( extractFloatx80Frac( a )<<1 ) == 0 ) ) { + return a; + } + STATUS(float_exception_flags) |= float_flag_inexact; + aSign = extractFloatx80Sign( a ); + switch ( STATUS(float_rounding_mode) ) { + case float_round_nearest_even: + if ( ( aExp == 0x3FFE ) && (bits64) ( extractFloatx80Frac( a )<<1 ) + ) { + return + packFloatx80( aSign, 0x3FFF, LIT64( 0x8000000000000000 ) ); + } + break; + case float_round_down: + return + aSign ? + packFloatx80( 1, 0x3FFF, LIT64( 0x8000000000000000 ) ) + : packFloatx80( 0, 0, 0 ); + case float_round_up: + return + aSign ? packFloatx80( 1, 0, 0 ) + : packFloatx80( 0, 0x3FFF, LIT64( 0x8000000000000000 ) ); + } + return packFloatx80( aSign, 0, 0 ); + } + lastBitMask = 1; + lastBitMask <<= 0x403E - aExp; + roundBitsMask = lastBitMask - 1; + z = a; + roundingMode = STATUS(float_rounding_mode); + if ( roundingMode == float_round_nearest_even ) { + z.low += lastBitMask>>1; + if ( ( z.low & roundBitsMask ) == 0 ) z.low &= ~ lastBitMask; + } + else if ( roundingMode != float_round_to_zero ) { + if ( extractFloatx80Sign( z ) ^ ( roundingMode == float_round_up ) ) { + z.low += roundBitsMask; + } + } + z.low &= ~ roundBitsMask; + if ( z.low == 0 ) { + ++z.high; + z.low = LIT64( 0x8000000000000000 ); + } + if ( z.low != a.low ) STATUS(float_exception_flags) |= float_flag_inexact; + return z; + +} + +/*---------------------------------------------------------------------------- +| Returns the result of adding the absolute values of the extended double- +| precision floating-point values `a' and `b'. If `zSign' is 1, the sum is +| negated before being returned. `zSign' is ignored if the result is a NaN. +| The addition is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +static floatx80 addFloatx80Sigs( floatx80 a, floatx80 b, flag zSign STATUS_PARAM) +{ + int32 aExp, bExp, zExp; + bits64 aSig, bSig, zSig0, zSig1; + int32 expDiff; + + aSig = extractFloatx80Frac( a ); + aExp = extractFloatx80Exp( a ); + bSig = extractFloatx80Frac( b ); + bExp = extractFloatx80Exp( b ); + expDiff = aExp - bExp; + if ( 0 < expDiff ) { + if ( aExp == 0x7FFF ) { + if ( (bits64) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); + return a; + } + if ( bExp == 0 ) --expDiff; + shift64ExtraRightJamming( bSig, 0, expDiff, &bSig, &zSig1 ); + zExp = aExp; + } + else if ( expDiff < 0 ) { + if ( bExp == 0x7FFF ) { + if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); + return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); + } + if ( aExp == 0 ) ++expDiff; + shift64ExtraRightJamming( aSig, 0, - expDiff, &aSig, &zSig1 ); + zExp = bExp; + } + else { + if ( aExp == 0x7FFF ) { + if ( (bits64) ( ( aSig | bSig )<<1 ) ) { + return propagateFloatx80NaN( a, b STATUS_VAR ); + } + return a; + } + zSig1 = 0; + zSig0 = aSig + bSig; + if ( aExp == 0 ) { + normalizeFloatx80Subnormal( zSig0, &zExp, &zSig0 ); + goto roundAndPack; + } + zExp = aExp; + goto shiftRight1; + } + zSig0 = aSig + bSig; + if ( (sbits64) zSig0 < 0 ) goto roundAndPack; + shiftRight1: + shift64ExtraRightJamming( zSig0, zSig1, 1, &zSig0, &zSig1 ); + zSig0 |= LIT64( 0x8000000000000000 ); + ++zExp; + roundAndPack: + return + roundAndPackFloatx80( + STATUS(floatx80_rounding_precision), zSign, zExp, zSig0, zSig1 STATUS_VAR ); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of subtracting the absolute values of the extended +| double-precision floating-point values `a' and `b'. If `zSign' is 1, the +| difference is negated before being returned. `zSign' is ignored if the +| result is a NaN. The subtraction is performed according to the IEC/IEEE +| Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +static floatx80 subFloatx80Sigs( floatx80 a, floatx80 b, flag zSign STATUS_PARAM ) +{ + int32 aExp, bExp, zExp; + bits64 aSig, bSig, zSig0, zSig1; + int32 expDiff; + floatx80 z; + + aSig = extractFloatx80Frac( a ); + aExp = extractFloatx80Exp( a ); + bSig = extractFloatx80Frac( b ); + bExp = extractFloatx80Exp( b ); + expDiff = aExp - bExp; + if ( 0 < expDiff ) goto aExpBigger; + if ( expDiff < 0 ) goto bExpBigger; + if ( aExp == 0x7FFF ) { + if ( (bits64) ( ( aSig | bSig )<<1 ) ) { + return propagateFloatx80NaN( a, b STATUS_VAR ); + } + float_raise( float_flag_invalid STATUS_VAR); + z.low = floatx80_default_nan_low; + z.high = floatx80_default_nan_high; + return z; + } + if ( aExp == 0 ) { + aExp = 1; + bExp = 1; + } + zSig1 = 0; + if ( bSig < aSig ) goto aBigger; + if ( aSig < bSig ) goto bBigger; + return packFloatx80( STATUS(float_rounding_mode) == float_round_down, 0, 0 ); + bExpBigger: + if ( bExp == 0x7FFF ) { + if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); + return packFloatx80( zSign ^ 1, 0x7FFF, LIT64( 0x8000000000000000 ) ); + } + if ( aExp == 0 ) ++expDiff; + shift128RightJamming( aSig, 0, - expDiff, &aSig, &zSig1 ); + bBigger: + sub128( bSig, 0, aSig, zSig1, &zSig0, &zSig1 ); + zExp = bExp; + zSign ^= 1; + goto normalizeRoundAndPack; + aExpBigger: + if ( aExp == 0x7FFF ) { + if ( (bits64) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); + return a; + } + if ( bExp == 0 ) --expDiff; + shift128RightJamming( bSig, 0, expDiff, &bSig, &zSig1 ); + aBigger: + sub128( aSig, 0, bSig, zSig1, &zSig0, &zSig1 ); + zExp = aExp; + normalizeRoundAndPack: + return + normalizeRoundAndPackFloatx80( + STATUS(floatx80_rounding_precision), zSign, zExp, zSig0, zSig1 STATUS_VAR ); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of adding the extended double-precision floating-point +| values `a' and `b'. The operation is performed according to the IEC/IEEE +| Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +floatx80 floatx80_add( floatx80 a, floatx80 b STATUS_PARAM ) +{ + flag aSign, bSign; + + aSign = extractFloatx80Sign( a ); + bSign = extractFloatx80Sign( b ); + if ( aSign == bSign ) { + return addFloatx80Sigs( a, b, aSign STATUS_VAR ); + } + else { + return subFloatx80Sigs( a, b, aSign STATUS_VAR ); + } + +} + +/*---------------------------------------------------------------------------- +| Returns the result of subtracting the extended double-precision floating- +| point values `a' and `b'. The operation is performed according to the +| IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +floatx80 floatx80_sub( floatx80 a, floatx80 b STATUS_PARAM ) +{ + flag aSign, bSign; + + aSign = extractFloatx80Sign( a ); + bSign = extractFloatx80Sign( b ); + if ( aSign == bSign ) { + return subFloatx80Sigs( a, b, aSign STATUS_VAR ); + } + else { + return addFloatx80Sigs( a, b, aSign STATUS_VAR ); + } + +} + +/*---------------------------------------------------------------------------- +| Returns the result of multiplying the extended double-precision floating- +| point values `a' and `b'. The operation is performed according to the +| IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +floatx80 floatx80_mul( floatx80 a, floatx80 b STATUS_PARAM ) +{ + flag aSign, bSign, zSign; + int32 aExp, bExp, zExp; + bits64 aSig, bSig, zSig0, zSig1; + floatx80 z; + + aSig = extractFloatx80Frac( a ); + aExp = extractFloatx80Exp( a ); + aSign = extractFloatx80Sign( a ); + bSig = extractFloatx80Frac( b ); + bExp = extractFloatx80Exp( b ); + bSign = extractFloatx80Sign( b ); + zSign = aSign ^ bSign; + if ( aExp == 0x7FFF ) { + if ( (bits64) ( aSig<<1 ) + || ( ( bExp == 0x7FFF ) && (bits64) ( bSig<<1 ) ) ) { + return propagateFloatx80NaN( a, b STATUS_VAR ); + } + if ( ( bExp | bSig ) == 0 ) goto invalid; + return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); + } + if ( bExp == 0x7FFF ) { + if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); + if ( ( aExp | aSig ) == 0 ) { + invalid: + float_raise( float_flag_invalid STATUS_VAR); + z.low = floatx80_default_nan_low; + z.high = floatx80_default_nan_high; + return z; + } + return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); + } + if ( aExp == 0 ) { + if ( aSig == 0 ) return packFloatx80( zSign, 0, 0 ); + normalizeFloatx80Subnormal( aSig, &aExp, &aSig ); + } + if ( bExp == 0 ) { + if ( bSig == 0 ) return packFloatx80( zSign, 0, 0 ); + normalizeFloatx80Subnormal( bSig, &bExp, &bSig ); + } + zExp = aExp + bExp - 0x3FFE; + mul64To128( aSig, bSig, &zSig0, &zSig1 ); + if ( 0 < (sbits64) zSig0 ) { + shortShift128Left( zSig0, zSig1, 1, &zSig0, &zSig1 ); + --zExp; + } + return + roundAndPackFloatx80( + STATUS(floatx80_rounding_precision), zSign, zExp, zSig0, zSig1 STATUS_VAR ); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of dividing the extended double-precision floating-point +| value `a' by the corresponding value `b'. The operation is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +floatx80 floatx80_div( floatx80 a, floatx80 b STATUS_PARAM ) +{ + flag aSign, bSign, zSign; + int32 aExp, bExp, zExp; + bits64 aSig, bSig, zSig0, zSig1; + bits64 rem0, rem1, rem2, term0, term1, term2; + floatx80 z; + + aSig = extractFloatx80Frac( a ); + aExp = extractFloatx80Exp( a ); + aSign = extractFloatx80Sign( a ); + bSig = extractFloatx80Frac( b ); + bExp = extractFloatx80Exp( b ); + bSign = extractFloatx80Sign( b ); + zSign = aSign ^ bSign; + if ( aExp == 0x7FFF ) { + if ( (bits64) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); + if ( bExp == 0x7FFF ) { + if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); + goto invalid; + } + return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); + } + if ( bExp == 0x7FFF ) { + if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); + return packFloatx80( zSign, 0, 0 ); + } + if ( bExp == 0 ) { + if ( bSig == 0 ) { + if ( ( aExp | aSig ) == 0 ) { + invalid: + float_raise( float_flag_invalid STATUS_VAR); + z.low = floatx80_default_nan_low; + z.high = floatx80_default_nan_high; + return z; + } + float_raise( float_flag_divbyzero STATUS_VAR); + return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); + } + normalizeFloatx80Subnormal( bSig, &bExp, &bSig ); + } + if ( aExp == 0 ) { + if ( aSig == 0 ) return packFloatx80( zSign, 0, 0 ); + normalizeFloatx80Subnormal( aSig, &aExp, &aSig ); + } + zExp = aExp - bExp + 0x3FFE; + rem1 = 0; + if ( bSig <= aSig ) { + shift128Right( aSig, 0, 1, &aSig, &rem1 ); + ++zExp; + } + zSig0 = estimateDiv128To64( aSig, rem1, bSig ); + mul64To128( bSig, zSig0, &term0, &term1 ); + sub128( aSig, rem1, term0, term1, &rem0, &rem1 ); + while ( (sbits64) rem0 < 0 ) { + --zSig0; + add128( rem0, rem1, 0, bSig, &rem0, &rem1 ); + } + zSig1 = estimateDiv128To64( rem1, 0, bSig ); + if ( (bits64) ( zSig1<<1 ) <= 8 ) { + mul64To128( bSig, zSig1, &term1, &term2 ); + sub128( rem1, 0, term1, term2, &rem1, &rem2 ); + while ( (sbits64) rem1 < 0 ) { + --zSig1; + add128( rem1, rem2, 0, bSig, &rem1, &rem2 ); + } + zSig1 |= ( ( rem1 | rem2 ) != 0 ); + } + return + roundAndPackFloatx80( + STATUS(floatx80_rounding_precision), zSign, zExp, zSig0, zSig1 STATUS_VAR ); + +} + +/*---------------------------------------------------------------------------- +| Returns the remainder of the extended double-precision floating-point value +| `a' with respect to the corresponding value `b'. The operation is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +floatx80 floatx80_rem( floatx80 a, floatx80 b STATUS_PARAM ) +{ + flag aSign, bSign, zSign; + int32 aExp, bExp, expDiff; + bits64 aSig0, aSig1, bSig; + bits64 q, term0, term1, alternateASig0, alternateASig1; + floatx80 z; + + aSig0 = extractFloatx80Frac( a ); + aExp = extractFloatx80Exp( a ); + aSign = extractFloatx80Sign( a ); + bSig = extractFloatx80Frac( b ); + bExp = extractFloatx80Exp( b ); + bSign = extractFloatx80Sign( b ); + if ( aExp == 0x7FFF ) { + if ( (bits64) ( aSig0<<1 ) + || ( ( bExp == 0x7FFF ) && (bits64) ( bSig<<1 ) ) ) { + return propagateFloatx80NaN( a, b STATUS_VAR ); + } + goto invalid; + } + if ( bExp == 0x7FFF ) { + if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); + return a; + } + if ( bExp == 0 ) { + if ( bSig == 0 ) { + invalid: + float_raise( float_flag_invalid STATUS_VAR); + z.low = floatx80_default_nan_low; + z.high = floatx80_default_nan_high; + return z; + } + normalizeFloatx80Subnormal( bSig, &bExp, &bSig ); + } + if ( aExp == 0 ) { + if ( (bits64) ( aSig0<<1 ) == 0 ) return a; + normalizeFloatx80Subnormal( aSig0, &aExp, &aSig0 ); + } + bSig |= LIT64( 0x8000000000000000 ); + zSign = aSign; + expDiff = aExp - bExp; + aSig1 = 0; + if ( expDiff < 0 ) { + if ( expDiff < -1 ) return a; + shift128Right( aSig0, 0, 1, &aSig0, &aSig1 ); + expDiff = 0; + } + q = ( bSig <= aSig0 ); + if ( q ) aSig0 -= bSig; + expDiff -= 64; + while ( 0 < expDiff ) { + q = estimateDiv128To64( aSig0, aSig1, bSig ); + q = ( 2 < q ) ? q - 2 : 0; + mul64To128( bSig, q, &term0, &term1 ); + sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 ); + shortShift128Left( aSig0, aSig1, 62, &aSig0, &aSig1 ); + expDiff -= 62; + } + expDiff += 64; + if ( 0 < expDiff ) { + q = estimateDiv128To64( aSig0, aSig1, bSig ); + q = ( 2 < q ) ? q - 2 : 0; + q >>= 64 - expDiff; + mul64To128( bSig, q<<( 64 - expDiff ), &term0, &term1 ); + sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 ); + shortShift128Left( 0, bSig, 64 - expDiff, &term0, &term1 ); + while ( le128( term0, term1, aSig0, aSig1 ) ) { + ++q; + sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 ); + } + } + else { + term1 = 0; + term0 = bSig; + } + sub128( term0, term1, aSig0, aSig1, &alternateASig0, &alternateASig1 ); + if ( lt128( alternateASig0, alternateASig1, aSig0, aSig1 ) + || ( eq128( alternateASig0, alternateASig1, aSig0, aSig1 ) + && ( q & 1 ) ) + ) { + aSig0 = alternateASig0; + aSig1 = alternateASig1; + zSign = ! zSign; + } + return + normalizeRoundAndPackFloatx80( + 80, zSign, bExp + expDiff, aSig0, aSig1 STATUS_VAR ); + +} + +/*---------------------------------------------------------------------------- +| Returns the square root of the extended double-precision floating-point +| value `a'. The operation is performed according to the IEC/IEEE Standard +| for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +floatx80 floatx80_sqrt( floatx80 a STATUS_PARAM ) +{ + flag aSign; + int32 aExp, zExp; + bits64 aSig0, aSig1, zSig0, zSig1, doubleZSig0; + bits64 rem0, rem1, rem2, rem3, term0, term1, term2, term3; + floatx80 z; + + aSig0 = extractFloatx80Frac( a ); + aExp = extractFloatx80Exp( a ); + aSign = extractFloatx80Sign( a ); + if ( aExp == 0x7FFF ) { + if ( (bits64) ( aSig0<<1 ) ) return propagateFloatx80NaN( a, a STATUS_VAR ); + if ( ! aSign ) return a; + goto invalid; + } + if ( aSign ) { + if ( ( aExp | aSig0 ) == 0 ) return a; + invalid: + float_raise( float_flag_invalid STATUS_VAR); + z.low = floatx80_default_nan_low; + z.high = floatx80_default_nan_high; + return z; + } + if ( aExp == 0 ) { + if ( aSig0 == 0 ) return packFloatx80( 0, 0, 0 ); + normalizeFloatx80Subnormal( aSig0, &aExp, &aSig0 ); + } + zExp = ( ( aExp - 0x3FFF )>>1 ) + 0x3FFF; + zSig0 = estimateSqrt32( aExp, aSig0>>32 ); + shift128Right( aSig0, 0, 2 + ( aExp & 1 ), &aSig0, &aSig1 ); + zSig0 = estimateDiv128To64( aSig0, aSig1, zSig0<<32 ) + ( zSig0<<30 ); + doubleZSig0 = zSig0<<1; + mul64To128( zSig0, zSig0, &term0, &term1 ); + sub128( aSig0, aSig1, term0, term1, &rem0, &rem1 ); + while ( (sbits64) rem0 < 0 ) { + --zSig0; + doubleZSig0 -= 2; + add128( rem0, rem1, zSig0>>63, doubleZSig0 | 1, &rem0, &rem1 ); + } + zSig1 = estimateDiv128To64( rem1, 0, doubleZSig0 ); + if ( ( zSig1 & LIT64( 0x3FFFFFFFFFFFFFFF ) ) <= 5 ) { + if ( zSig1 == 0 ) zSig1 = 1; + mul64To128( doubleZSig0, zSig1, &term1, &term2 ); + sub128( rem1, 0, term1, term2, &rem1, &rem2 ); + mul64To128( zSig1, zSig1, &term2, &term3 ); + sub192( rem1, rem2, 0, 0, term2, term3, &rem1, &rem2, &rem3 ); + while ( (sbits64) rem1 < 0 ) { + --zSig1; + shortShift128Left( 0, zSig1, 1, &term2, &term3 ); + term3 |= 1; + term2 |= doubleZSig0; + add192( rem1, rem2, rem3, 0, term2, term3, &rem1, &rem2, &rem3 ); + } + zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 ); + } + shortShift128Left( 0, zSig1, 1, &zSig0, &zSig1 ); + zSig0 |= doubleZSig0; + return + roundAndPackFloatx80( + STATUS(floatx80_rounding_precision), 0, zExp, zSig0, zSig1 STATUS_VAR ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the extended double-precision floating-point value `a' is +| equal to the corresponding value `b', and 0 otherwise. The comparison is +| performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic. +*----------------------------------------------------------------------------*/ + +flag floatx80_eq( floatx80 a, floatx80 b STATUS_PARAM ) +{ + + if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) + && (bits64) ( extractFloatx80Frac( a )<<1 ) ) + || ( ( extractFloatx80Exp( b ) == 0x7FFF ) + && (bits64) ( extractFloatx80Frac( b )<<1 ) ) + ) { + if ( floatx80_is_signaling_nan( a ) + || floatx80_is_signaling_nan( b ) ) { + float_raise( float_flag_invalid STATUS_VAR); + } + return 0; + } + return + ( a.low == b.low ) + && ( ( a.high == b.high ) + || ( ( a.low == 0 ) + && ( (bits16) ( ( a.high | b.high )<<1 ) == 0 ) ) + ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the extended double-precision floating-point value `a' is +| less than or equal to the corresponding value `b', and 0 otherwise. The +| comparison is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +flag floatx80_le( floatx80 a, floatx80 b STATUS_PARAM ) +{ + flag aSign, bSign; + + if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) + && (bits64) ( extractFloatx80Frac( a )<<1 ) ) + || ( ( extractFloatx80Exp( b ) == 0x7FFF ) + && (bits64) ( extractFloatx80Frac( b )<<1 ) ) + ) { + float_raise( float_flag_invalid STATUS_VAR); + return 0; + } + aSign = extractFloatx80Sign( a ); + bSign = extractFloatx80Sign( b ); + if ( aSign != bSign ) { + return + aSign + || ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) + == 0 ); + } + return + aSign ? le128( b.high, b.low, a.high, a.low ) + : le128( a.high, a.low, b.high, b.low ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the extended double-precision floating-point value `a' is +| less than the corresponding value `b', and 0 otherwise. The comparison +| is performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic. +*----------------------------------------------------------------------------*/ + +flag floatx80_lt( floatx80 a, floatx80 b STATUS_PARAM ) +{ + flag aSign, bSign; + + if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) + && (bits64) ( extractFloatx80Frac( a )<<1 ) ) + || ( ( extractFloatx80Exp( b ) == 0x7FFF ) + && (bits64) ( extractFloatx80Frac( b )<<1 ) ) + ) { + float_raise( float_flag_invalid STATUS_VAR); + return 0; + } + aSign = extractFloatx80Sign( a ); + bSign = extractFloatx80Sign( b ); + if ( aSign != bSign ) { + return + aSign + && ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) + != 0 ); + } + return + aSign ? lt128( b.high, b.low, a.high, a.low ) + : lt128( a.high, a.low, b.high, b.low ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the extended double-precision floating-point value `a' is equal +| to the corresponding value `b', and 0 otherwise. The invalid exception is +| raised if either operand is a NaN. Otherwise, the comparison is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +flag floatx80_eq_signaling( floatx80 a, floatx80 b STATUS_PARAM ) +{ + + if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) + && (bits64) ( extractFloatx80Frac( a )<<1 ) ) + || ( ( extractFloatx80Exp( b ) == 0x7FFF ) + && (bits64) ( extractFloatx80Frac( b )<<1 ) ) + ) { + float_raise( float_flag_invalid STATUS_VAR); + return 0; + } + return + ( a.low == b.low ) + && ( ( a.high == b.high ) + || ( ( a.low == 0 ) + && ( (bits16) ( ( a.high | b.high )<<1 ) == 0 ) ) + ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the extended double-precision floating-point value `a' is less +| than or equal to the corresponding value `b', and 0 otherwise. Quiet NaNs +| do not cause an exception. Otherwise, the comparison is performed according +| to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +flag floatx80_le_quiet( floatx80 a, floatx80 b STATUS_PARAM ) +{ + flag aSign, bSign; + + if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) + && (bits64) ( extractFloatx80Frac( a )<<1 ) ) + || ( ( extractFloatx80Exp( b ) == 0x7FFF ) + && (bits64) ( extractFloatx80Frac( b )<<1 ) ) + ) { + if ( floatx80_is_signaling_nan( a ) + || floatx80_is_signaling_nan( b ) ) { + float_raise( float_flag_invalid STATUS_VAR); + } + return 0; + } + aSign = extractFloatx80Sign( a ); + bSign = extractFloatx80Sign( b ); + if ( aSign != bSign ) { + return + aSign + || ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) + == 0 ); + } + return + aSign ? le128( b.high, b.low, a.high, a.low ) + : le128( a.high, a.low, b.high, b.low ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the extended double-precision floating-point value `a' is less +| than the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause +| an exception. Otherwise, the comparison is performed according to the +| IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +flag floatx80_lt_quiet( floatx80 a, floatx80 b STATUS_PARAM ) +{ + flag aSign, bSign; + + if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) + && (bits64) ( extractFloatx80Frac( a )<<1 ) ) + || ( ( extractFloatx80Exp( b ) == 0x7FFF ) + && (bits64) ( extractFloatx80Frac( b )<<1 ) ) + ) { + if ( floatx80_is_signaling_nan( a ) + || floatx80_is_signaling_nan( b ) ) { + float_raise( float_flag_invalid STATUS_VAR); + } + return 0; + } + aSign = extractFloatx80Sign( a ); + bSign = extractFloatx80Sign( b ); + if ( aSign != bSign ) { + return + aSign + && ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) + != 0 ); + } + return + aSign ? lt128( b.high, b.low, a.high, a.low ) + : lt128( a.high, a.low, b.high, b.low ); + +} + +#endif + +#ifdef FLOAT128 + +/*---------------------------------------------------------------------------- +| Returns the result of converting the quadruple-precision floating-point +| value `a' to the 32-bit two's complement integer format. The conversion +| is performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic---which means in particular that the conversion is rounded +| according to the current rounding mode. If `a' is a NaN, the largest +| positive integer is returned. Otherwise, if the conversion overflows, the +| largest integer with the same sign as `a' is returned. +*----------------------------------------------------------------------------*/ + +int32 float128_to_int32( float128 a STATUS_PARAM ) +{ + flag aSign; + int32 aExp, shiftCount; + bits64 aSig0, aSig1; + + aSig1 = extractFloat128Frac1( a ); + aSig0 = extractFloat128Frac0( a ); + aExp = extractFloat128Exp( a ); + aSign = extractFloat128Sign( a ); + if ( ( aExp == 0x7FFF ) && ( aSig0 | aSig1 ) ) aSign = 0; + if ( aExp ) aSig0 |= LIT64( 0x0001000000000000 ); + aSig0 |= ( aSig1 != 0 ); + shiftCount = 0x4028 - aExp; + if ( 0 < shiftCount ) shift64RightJamming( aSig0, shiftCount, &aSig0 ); + return roundAndPackInt32( aSign, aSig0 STATUS_VAR ); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the quadruple-precision floating-point +| value `a' to the 32-bit two's complement integer format. The conversion +| is performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic, except that the conversion is always rounded toward zero. If +| `a' is a NaN, the largest positive integer is returned. Otherwise, if the +| conversion overflows, the largest integer with the same sign as `a' is +| returned. +*----------------------------------------------------------------------------*/ + +int32 float128_to_int32_round_to_zero( float128 a STATUS_PARAM ) +{ + flag aSign; + int32 aExp, shiftCount; + bits64 aSig0, aSig1, savedASig; + int32 z; + + aSig1 = extractFloat128Frac1( a ); + aSig0 = extractFloat128Frac0( a ); + aExp = extractFloat128Exp( a ); + aSign = extractFloat128Sign( a ); + aSig0 |= ( aSig1 != 0 ); + if ( 0x401E < aExp ) { + if ( ( aExp == 0x7FFF ) && aSig0 ) aSign = 0; + goto invalid; + } + else if ( aExp < 0x3FFF ) { + if ( aExp || aSig0 ) STATUS(float_exception_flags) |= float_flag_inexact; + return 0; + } + aSig0 |= LIT64( 0x0001000000000000 ); + shiftCount = 0x402F - aExp; + savedASig = aSig0; + aSig0 >>= shiftCount; + z = aSig0; + if ( aSign ) z = - z; + if ( ( z < 0 ) ^ aSign ) { + invalid: + float_raise( float_flag_invalid STATUS_VAR); + return aSign ? (sbits32) 0x80000000 : 0x7FFFFFFF; + } + if ( ( aSig0<<shiftCount ) != savedASig ) { + STATUS(float_exception_flags) |= float_flag_inexact; + } + return z; + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the quadruple-precision floating-point +| value `a' to the 64-bit two's complement integer format. The conversion +| is performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic---which means in particular that the conversion is rounded +| according to the current rounding mode. If `a' is a NaN, the largest +| positive integer is returned. Otherwise, if the conversion overflows, the +| largest integer with the same sign as `a' is returned. +*----------------------------------------------------------------------------*/ + +int64 float128_to_int64( float128 a STATUS_PARAM ) +{ + flag aSign; + int32 aExp, shiftCount; + bits64 aSig0, aSig1; + + aSig1 = extractFloat128Frac1( a ); + aSig0 = extractFloat128Frac0( a ); + aExp = extractFloat128Exp( a ); + aSign = extractFloat128Sign( a ); + if ( aExp ) aSig0 |= LIT64( 0x0001000000000000 ); + shiftCount = 0x402F - aExp; + if ( shiftCount <= 0 ) { + if ( 0x403E < aExp ) { + float_raise( float_flag_invalid STATUS_VAR); + if ( ! aSign + || ( ( aExp == 0x7FFF ) + && ( aSig1 || ( aSig0 != LIT64( 0x0001000000000000 ) ) ) + ) + ) { + return LIT64( 0x7FFFFFFFFFFFFFFF ); + } + return (sbits64) LIT64( 0x8000000000000000 ); + } + shortShift128Left( aSig0, aSig1, - shiftCount, &aSig0, &aSig1 ); + } + else { + shift64ExtraRightJamming( aSig0, aSig1, shiftCount, &aSig0, &aSig1 ); + } + return roundAndPackInt64( aSign, aSig0, aSig1 STATUS_VAR ); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the quadruple-precision floating-point +| value `a' to the 64-bit two's complement integer format. The conversion +| is performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic, except that the conversion is always rounded toward zero. +| If `a' is a NaN, the largest positive integer is returned. Otherwise, if +| the conversion overflows, the largest integer with the same sign as `a' is +| returned. +*----------------------------------------------------------------------------*/ + +int64 float128_to_int64_round_to_zero( float128 a STATUS_PARAM ) +{ + flag aSign; + int32 aExp, shiftCount; + bits64 aSig0, aSig1; + int64 z; + + aSig1 = extractFloat128Frac1( a ); + aSig0 = extractFloat128Frac0( a ); + aExp = extractFloat128Exp( a ); + aSign = extractFloat128Sign( a ); + if ( aExp ) aSig0 |= LIT64( 0x0001000000000000 ); + shiftCount = aExp - 0x402F; + if ( 0 < shiftCount ) { + if ( 0x403E <= aExp ) { + aSig0 &= LIT64( 0x0000FFFFFFFFFFFF ); + if ( ( a.high == LIT64( 0xC03E000000000000 ) ) + && ( aSig1 < LIT64( 0x0002000000000000 ) ) ) { + if ( aSig1 ) STATUS(float_exception_flags) |= float_flag_inexact; + } + else { + float_raise( float_flag_invalid STATUS_VAR); + if ( ! aSign || ( ( aExp == 0x7FFF ) && ( aSig0 | aSig1 ) ) ) { + return LIT64( 0x7FFFFFFFFFFFFFFF ); + } + } + return (sbits64) LIT64( 0x8000000000000000 ); + } + z = ( aSig0<<shiftCount ) | ( aSig1>>( ( - shiftCount ) & 63 ) ); + if ( (bits64) ( aSig1<<shiftCount ) ) { + STATUS(float_exception_flags) |= float_flag_inexact; + } + } + else { + if ( aExp < 0x3FFF ) { + if ( aExp | aSig0 | aSig1 ) { + STATUS(float_exception_flags) |= float_flag_inexact; + } + return 0; + } + z = aSig0>>( - shiftCount ); + if ( aSig1 + || ( shiftCount && (bits64) ( aSig0<<( shiftCount & 63 ) ) ) ) { + STATUS(float_exception_flags) |= float_flag_inexact; + } + } + if ( aSign ) z = - z; + return z; + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the quadruple-precision floating-point +| value `a' to the single-precision floating-point format. The conversion +| is performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic. +*----------------------------------------------------------------------------*/ + +float32 float128_to_float32( float128 a STATUS_PARAM ) +{ + flag aSign; + int32 aExp; + bits64 aSig0, aSig1; + bits32 zSig; + + aSig1 = extractFloat128Frac1( a ); + aSig0 = extractFloat128Frac0( a ); + aExp = extractFloat128Exp( a ); + aSign = extractFloat128Sign( a ); + if ( aExp == 0x7FFF ) { + if ( aSig0 | aSig1 ) { + return commonNaNToFloat32( float128ToCommonNaN( a STATUS_VAR ) ); + } + return packFloat32( aSign, 0xFF, 0 ); + } + aSig0 |= ( aSig1 != 0 ); + shift64RightJamming( aSig0, 18, &aSig0 ); + zSig = aSig0; + if ( aExp || zSig ) { + zSig |= 0x40000000; + aExp -= 0x3F81; + } + return roundAndPackFloat32( aSign, aExp, zSig STATUS_VAR ); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of converting the quadruple-precision floating-point +| value `a' to the double-precision floating-point format. The conversion +| is performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic. +*----------------------------------------------------------------------------*/ + +float64 float128_to_float64( float128 a STATUS_PARAM ) +{ + flag aSign; + int32 aExp; + bits64 aSig0, aSig1; + + aSig1 = extractFloat128Frac1( a ); + aSig0 = extractFloat128Frac0( a ); + aExp = extractFloat128Exp( a ); + aSign = extractFloat128Sign( a ); + if ( aExp == 0x7FFF ) { + if ( aSig0 | aSig1 ) { + return commonNaNToFloat64( float128ToCommonNaN( a STATUS_VAR ) ); + } + return packFloat64( aSign, 0x7FF, 0 ); + } + shortShift128Left( aSig0, aSig1, 14, &aSig0, &aSig1 ); + aSig0 |= ( aSig1 != 0 ); + if ( aExp || aSig0 ) { + aSig0 |= LIT64( 0x4000000000000000 ); + aExp -= 0x3C01; + } + return roundAndPackFloat64( aSign, aExp, aSig0 STATUS_VAR ); + +} + +#ifdef FLOATX80 + +/*---------------------------------------------------------------------------- +| Returns the result of converting the quadruple-precision floating-point +| value `a' to the extended double-precision floating-point format. The +| conversion is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +floatx80 float128_to_floatx80( float128 a STATUS_PARAM ) +{ + flag aSign; + int32 aExp; + bits64 aSig0, aSig1; + + aSig1 = extractFloat128Frac1( a ); + aSig0 = extractFloat128Frac0( a ); + aExp = extractFloat128Exp( a ); + aSign = extractFloat128Sign( a ); + if ( aExp == 0x7FFF ) { + if ( aSig0 | aSig1 ) { + return commonNaNToFloatx80( float128ToCommonNaN( a STATUS_VAR ) ); + } + return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); + } + if ( aExp == 0 ) { + if ( ( aSig0 | aSig1 ) == 0 ) return packFloatx80( aSign, 0, 0 ); + normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); + } + else { + aSig0 |= LIT64( 0x0001000000000000 ); + } + shortShift128Left( aSig0, aSig1, 15, &aSig0, &aSig1 ); + return roundAndPackFloatx80( 80, aSign, aExp, aSig0, aSig1 STATUS_VAR ); + +} + +#endif + +/*---------------------------------------------------------------------------- +| Rounds the quadruple-precision floating-point value `a' to an integer, and +| returns the result as a quadruple-precision floating-point value. The +| operation is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float128 float128_round_to_int( float128 a STATUS_PARAM ) +{ + flag aSign; + int32 aExp; + bits64 lastBitMask, roundBitsMask; + int8 roundingMode; + float128 z; + + aExp = extractFloat128Exp( a ); + if ( 0x402F <= aExp ) { + if ( 0x406F <= aExp ) { + if ( ( aExp == 0x7FFF ) + && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) + ) { + return propagateFloat128NaN( a, a STATUS_VAR ); + } + return a; + } + lastBitMask = 1; + lastBitMask = ( lastBitMask<<( 0x406E - aExp ) )<<1; + roundBitsMask = lastBitMask - 1; + z = a; + roundingMode = STATUS(float_rounding_mode); + if ( roundingMode == float_round_nearest_even ) { + if ( lastBitMask ) { + add128( z.high, z.low, 0, lastBitMask>>1, &z.high, &z.low ); + if ( ( z.low & roundBitsMask ) == 0 ) z.low &= ~ lastBitMask; + } + else { + if ( (sbits64) z.low < 0 ) { + ++z.high; + if ( (bits64) ( z.low<<1 ) == 0 ) z.high &= ~1; + } + } + } + else if ( roundingMode != float_round_to_zero ) { + if ( extractFloat128Sign( z ) + ^ ( roundingMode == float_round_up ) ) { + add128( z.high, z.low, 0, roundBitsMask, &z.high, &z.low ); + } + } + z.low &= ~ roundBitsMask; + } + else { + if ( aExp < 0x3FFF ) { + if ( ( ( (bits64) ( a.high<<1 ) ) | a.low ) == 0 ) return a; + STATUS(float_exception_flags) |= float_flag_inexact; + aSign = extractFloat128Sign( a ); + switch ( STATUS(float_rounding_mode) ) { + case float_round_nearest_even: + if ( ( aExp == 0x3FFE ) + && ( extractFloat128Frac0( a ) + | extractFloat128Frac1( a ) ) + ) { + return packFloat128( aSign, 0x3FFF, 0, 0 ); + } + break; + case float_round_down: + return + aSign ? packFloat128( 1, 0x3FFF, 0, 0 ) + : packFloat128( 0, 0, 0, 0 ); + case float_round_up: + return + aSign ? packFloat128( 1, 0, 0, 0 ) + : packFloat128( 0, 0x3FFF, 0, 0 ); + } + return packFloat128( aSign, 0, 0, 0 ); + } + lastBitMask = 1; + lastBitMask <<= 0x402F - aExp; + roundBitsMask = lastBitMask - 1; + z.low = 0; + z.high = a.high; + roundingMode = STATUS(float_rounding_mode); + if ( roundingMode == float_round_nearest_even ) { + z.high += lastBitMask>>1; + if ( ( ( z.high & roundBitsMask ) | a.low ) == 0 ) { + z.high &= ~ lastBitMask; + } + } + else if ( roundingMode != float_round_to_zero ) { + if ( extractFloat128Sign( z ) + ^ ( roundingMode == float_round_up ) ) { + z.high |= ( a.low != 0 ); + z.high += roundBitsMask; + } + } + z.high &= ~ roundBitsMask; + } + if ( ( z.low != a.low ) || ( z.high != a.high ) ) { + STATUS(float_exception_flags) |= float_flag_inexact; + } + return z; + +} + +/*---------------------------------------------------------------------------- +| Returns the result of adding the absolute values of the quadruple-precision +| floating-point values `a' and `b'. If `zSign' is 1, the sum is negated +| before being returned. `zSign' is ignored if the result is a NaN. +| The addition is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +static float128 addFloat128Sigs( float128 a, float128 b, flag zSign STATUS_PARAM) +{ + int32 aExp, bExp, zExp; + bits64 aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2; + int32 expDiff; + + aSig1 = extractFloat128Frac1( a ); + aSig0 = extractFloat128Frac0( a ); + aExp = extractFloat128Exp( a ); + bSig1 = extractFloat128Frac1( b ); + bSig0 = extractFloat128Frac0( b ); + bExp = extractFloat128Exp( b ); + expDiff = aExp - bExp; + if ( 0 < expDiff ) { + if ( aExp == 0x7FFF ) { + if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); + return a; + } + if ( bExp == 0 ) { + --expDiff; + } + else { + bSig0 |= LIT64( 0x0001000000000000 ); + } + shift128ExtraRightJamming( + bSig0, bSig1, 0, expDiff, &bSig0, &bSig1, &zSig2 ); + zExp = aExp; + } + else if ( expDiff < 0 ) { + if ( bExp == 0x7FFF ) { + if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); + return packFloat128( zSign, 0x7FFF, 0, 0 ); + } + if ( aExp == 0 ) { + ++expDiff; + } + else { + aSig0 |= LIT64( 0x0001000000000000 ); + } + shift128ExtraRightJamming( + aSig0, aSig1, 0, - expDiff, &aSig0, &aSig1, &zSig2 ); + zExp = bExp; + } + else { + if ( aExp == 0x7FFF ) { + if ( aSig0 | aSig1 | bSig0 | bSig1 ) { + return propagateFloat128NaN( a, b STATUS_VAR ); + } + return a; + } + add128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 ); + if ( aExp == 0 ) return packFloat128( zSign, 0, zSig0, zSig1 ); + zSig2 = 0; + zSig0 |= LIT64( 0x0002000000000000 ); + zExp = aExp; + goto shiftRight1; + } + aSig0 |= LIT64( 0x0001000000000000 ); + add128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 ); + --zExp; + if ( zSig0 < LIT64( 0x0002000000000000 ) ) goto roundAndPack; + ++zExp; + shiftRight1: + shift128ExtraRightJamming( + zSig0, zSig1, zSig2, 1, &zSig0, &zSig1, &zSig2 ); + roundAndPack: + return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 STATUS_VAR ); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of subtracting the absolute values of the quadruple- +| precision floating-point values `a' and `b'. If `zSign' is 1, the +| difference is negated before being returned. `zSign' is ignored if the +| result is a NaN. The subtraction is performed according to the IEC/IEEE +| Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +static float128 subFloat128Sigs( float128 a, float128 b, flag zSign STATUS_PARAM) +{ + int32 aExp, bExp, zExp; + bits64 aSig0, aSig1, bSig0, bSig1, zSig0, zSig1; + int32 expDiff; + float128 z; + + aSig1 = extractFloat128Frac1( a ); + aSig0 = extractFloat128Frac0( a ); + aExp = extractFloat128Exp( a ); + bSig1 = extractFloat128Frac1( b ); + bSig0 = extractFloat128Frac0( b ); + bExp = extractFloat128Exp( b ); + expDiff = aExp - bExp; + shortShift128Left( aSig0, aSig1, 14, &aSig0, &aSig1 ); + shortShift128Left( bSig0, bSig1, 14, &bSig0, &bSig1 ); + if ( 0 < expDiff ) goto aExpBigger; + if ( expDiff < 0 ) goto bExpBigger; + if ( aExp == 0x7FFF ) { + if ( aSig0 | aSig1 | bSig0 | bSig1 ) { + return propagateFloat128NaN( a, b STATUS_VAR ); + } + float_raise( float_flag_invalid STATUS_VAR); + z.low = float128_default_nan_low; + z.high = float128_default_nan_high; + return z; + } + if ( aExp == 0 ) { + aExp = 1; + bExp = 1; + } + if ( bSig0 < aSig0 ) goto aBigger; + if ( aSig0 < bSig0 ) goto bBigger; + if ( bSig1 < aSig1 ) goto aBigger; + if ( aSig1 < bSig1 ) goto bBigger; + return packFloat128( STATUS(float_rounding_mode) == float_round_down, 0, 0, 0 ); + bExpBigger: + if ( bExp == 0x7FFF ) { + if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); + return packFloat128( zSign ^ 1, 0x7FFF, 0, 0 ); + } + if ( aExp == 0 ) { + ++expDiff; + } + else { + aSig0 |= LIT64( 0x4000000000000000 ); + } + shift128RightJamming( aSig0, aSig1, - expDiff, &aSig0, &aSig1 ); + bSig0 |= LIT64( 0x4000000000000000 ); + bBigger: + sub128( bSig0, bSig1, aSig0, aSig1, &zSig0, &zSig1 ); + zExp = bExp; + zSign ^= 1; + goto normalizeRoundAndPack; + aExpBigger: + if ( aExp == 0x7FFF ) { + if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); + return a; + } + if ( bExp == 0 ) { + --expDiff; + } + else { + bSig0 |= LIT64( 0x4000000000000000 ); + } + shift128RightJamming( bSig0, bSig1, expDiff, &bSig0, &bSig1 ); + aSig0 |= LIT64( 0x4000000000000000 ); + aBigger: + sub128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 ); + zExp = aExp; + normalizeRoundAndPack: + --zExp; + return normalizeRoundAndPackFloat128( zSign, zExp - 14, zSig0, zSig1 STATUS_VAR ); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of adding the quadruple-precision floating-point values +| `a' and `b'. The operation is performed according to the IEC/IEEE Standard +| for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float128 float128_add( float128 a, float128 b STATUS_PARAM ) +{ + flag aSign, bSign; + + aSign = extractFloat128Sign( a ); + bSign = extractFloat128Sign( b ); + if ( aSign == bSign ) { + return addFloat128Sigs( a, b, aSign STATUS_VAR ); + } + else { + return subFloat128Sigs( a, b, aSign STATUS_VAR ); + } + +} + +/*---------------------------------------------------------------------------- +| Returns the result of subtracting the quadruple-precision floating-point +| values `a' and `b'. The operation is performed according to the IEC/IEEE +| Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float128 float128_sub( float128 a, float128 b STATUS_PARAM ) +{ + flag aSign, bSign; + + aSign = extractFloat128Sign( a ); + bSign = extractFloat128Sign( b ); + if ( aSign == bSign ) { + return subFloat128Sigs( a, b, aSign STATUS_VAR ); + } + else { + return addFloat128Sigs( a, b, aSign STATUS_VAR ); + } + +} + +/*---------------------------------------------------------------------------- +| Returns the result of multiplying the quadruple-precision floating-point +| values `a' and `b'. The operation is performed according to the IEC/IEEE +| Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float128 float128_mul( float128 a, float128 b STATUS_PARAM ) +{ + flag aSign, bSign, zSign; + int32 aExp, bExp, zExp; + bits64 aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2, zSig3; + float128 z; + + aSig1 = extractFloat128Frac1( a ); + aSig0 = extractFloat128Frac0( a ); + aExp = extractFloat128Exp( a ); + aSign = extractFloat128Sign( a ); + bSig1 = extractFloat128Frac1( b ); + bSig0 = extractFloat128Frac0( b ); + bExp = extractFloat128Exp( b ); + bSign = extractFloat128Sign( b ); + zSign = aSign ^ bSign; + if ( aExp == 0x7FFF ) { + if ( ( aSig0 | aSig1 ) + || ( ( bExp == 0x7FFF ) && ( bSig0 | bSig1 ) ) ) { + return propagateFloat128NaN( a, b STATUS_VAR ); + } + if ( ( bExp | bSig0 | bSig1 ) == 0 ) goto invalid; + return packFloat128( zSign, 0x7FFF, 0, 0 ); + } + if ( bExp == 0x7FFF ) { + if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); + if ( ( aExp | aSig0 | aSig1 ) == 0 ) { + invalid: + float_raise( float_flag_invalid STATUS_VAR); + z.low = float128_default_nan_low; + z.high = float128_default_nan_high; + return z; + } + return packFloat128( zSign, 0x7FFF, 0, 0 ); + } + if ( aExp == 0 ) { + if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 ); + normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); + } + if ( bExp == 0 ) { + if ( ( bSig0 | bSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 ); + normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 ); + } + zExp = aExp + bExp - 0x4000; + aSig0 |= LIT64( 0x0001000000000000 ); + shortShift128Left( bSig0, bSig1, 16, &bSig0, &bSig1 ); + mul128To256( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1, &zSig2, &zSig3 ); + add128( zSig0, zSig1, aSig0, aSig1, &zSig0, &zSig1 ); + zSig2 |= ( zSig3 != 0 ); + if ( LIT64( 0x0002000000000000 ) <= zSig0 ) { + shift128ExtraRightJamming( + zSig0, zSig1, zSig2, 1, &zSig0, &zSig1, &zSig2 ); + ++zExp; + } + return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 STATUS_VAR ); + +} + +/*---------------------------------------------------------------------------- +| Returns the result of dividing the quadruple-precision floating-point value +| `a' by the corresponding value `b'. The operation is performed according to +| the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float128 float128_div( float128 a, float128 b STATUS_PARAM ) +{ + flag aSign, bSign, zSign; + int32 aExp, bExp, zExp; + bits64 aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2; + bits64 rem0, rem1, rem2, rem3, term0, term1, term2, term3; + float128 z; + + aSig1 = extractFloat128Frac1( a ); + aSig0 = extractFloat128Frac0( a ); + aExp = extractFloat128Exp( a ); + aSign = extractFloat128Sign( a ); + bSig1 = extractFloat128Frac1( b ); + bSig0 = extractFloat128Frac0( b ); + bExp = extractFloat128Exp( b ); + bSign = extractFloat128Sign( b ); + zSign = aSign ^ bSign; + if ( aExp == 0x7FFF ) { + if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); + if ( bExp == 0x7FFF ) { + if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); + goto invalid; + } + return packFloat128( zSign, 0x7FFF, 0, 0 ); + } + if ( bExp == 0x7FFF ) { + if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); + return packFloat128( zSign, 0, 0, 0 ); + } + if ( bExp == 0 ) { + if ( ( bSig0 | bSig1 ) == 0 ) { + if ( ( aExp | aSig0 | aSig1 ) == 0 ) { + invalid: + float_raise( float_flag_invalid STATUS_VAR); + z.low = float128_default_nan_low; + z.high = float128_default_nan_high; + return z; + } + float_raise( float_flag_divbyzero STATUS_VAR); + return packFloat128( zSign, 0x7FFF, 0, 0 ); + } + normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 ); + } + if ( aExp == 0 ) { + if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 ); + normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); + } + zExp = aExp - bExp + 0x3FFD; + shortShift128Left( + aSig0 | LIT64( 0x0001000000000000 ), aSig1, 15, &aSig0, &aSig1 ); + shortShift128Left( + bSig0 | LIT64( 0x0001000000000000 ), bSig1, 15, &bSig0, &bSig1 ); + if ( le128( bSig0, bSig1, aSig0, aSig1 ) ) { + shift128Right( aSig0, aSig1, 1, &aSig0, &aSig1 ); + ++zExp; + } + zSig0 = estimateDiv128To64( aSig0, aSig1, bSig0 ); + mul128By64To192( bSig0, bSig1, zSig0, &term0, &term1, &term2 ); + sub192( aSig0, aSig1, 0, term0, term1, term2, &rem0, &rem1, &rem2 ); + while ( (sbits64) rem0 < 0 ) { + --zSig0; + add192( rem0, rem1, rem2, 0, bSig0, bSig1, &rem0, &rem1, &rem2 ); + } + zSig1 = estimateDiv128To64( rem1, rem2, bSig0 ); + if ( ( zSig1 & 0x3FFF ) <= 4 ) { + mul128By64To192( bSig0, bSig1, zSig1, &term1, &term2, &term3 ); + sub192( rem1, rem2, 0, term1, term2, term3, &rem1, &rem2, &rem3 ); + while ( (sbits64) rem1 < 0 ) { + --zSig1; + add192( rem1, rem2, rem3, 0, bSig0, bSig1, &rem1, &rem2, &rem3 ); + } + zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 ); + } + shift128ExtraRightJamming( zSig0, zSig1, 0, 15, &zSig0, &zSig1, &zSig2 ); + return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 STATUS_VAR ); + +} + +/*---------------------------------------------------------------------------- +| Returns the remainder of the quadruple-precision floating-point value `a' +| with respect to the corresponding value `b'. The operation is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float128 float128_rem( float128 a, float128 b STATUS_PARAM ) +{ + flag aSign, bSign, zSign; + int32 aExp, bExp, expDiff; + bits64 aSig0, aSig1, bSig0, bSig1, q, term0, term1, term2; + bits64 allZero, alternateASig0, alternateASig1, sigMean1; + sbits64 sigMean0; + float128 z; + + aSig1 = extractFloat128Frac1( a ); + aSig0 = extractFloat128Frac0( a ); + aExp = extractFloat128Exp( a ); + aSign = extractFloat128Sign( a ); + bSig1 = extractFloat128Frac1( b ); + bSig0 = extractFloat128Frac0( b ); + bExp = extractFloat128Exp( b ); + bSign = extractFloat128Sign( b ); + if ( aExp == 0x7FFF ) { + if ( ( aSig0 | aSig1 ) + || ( ( bExp == 0x7FFF ) && ( bSig0 | bSig1 ) ) ) { + return propagateFloat128NaN( a, b STATUS_VAR ); + } + goto invalid; + } + if ( bExp == 0x7FFF ) { + if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); + return a; + } + if ( bExp == 0 ) { + if ( ( bSig0 | bSig1 ) == 0 ) { + invalid: + float_raise( float_flag_invalid STATUS_VAR); + z.low = float128_default_nan_low; + z.high = float128_default_nan_high; + return z; + } + normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 ); + } + if ( aExp == 0 ) { + if ( ( aSig0 | aSig1 ) == 0 ) return a; + normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); + } + expDiff = aExp - bExp; + if ( expDiff < -1 ) return a; + shortShift128Left( + aSig0 | LIT64( 0x0001000000000000 ), + aSig1, + 15 - ( expDiff < 0 ), + &aSig0, + &aSig1 + ); + shortShift128Left( + bSig0 | LIT64( 0x0001000000000000 ), bSig1, 15, &bSig0, &bSig1 ); + q = le128( bSig0, bSig1, aSig0, aSig1 ); + if ( q ) sub128( aSig0, aSig1, bSig0, bSig1, &aSig0, &aSig1 ); + expDiff -= 64; + while ( 0 < expDiff ) { + q = estimateDiv128To64( aSig0, aSig1, bSig0 ); + q = ( 4 < q ) ? q - 4 : 0; + mul128By64To192( bSig0, bSig1, q, &term0, &term1, &term2 ); + shortShift192Left( term0, term1, term2, 61, &term1, &term2, &allZero ); + shortShift128Left( aSig0, aSig1, 61, &aSig0, &allZero ); + sub128( aSig0, 0, term1, term2, &aSig0, &aSig1 ); + expDiff -= 61; + } + if ( -64 < expDiff ) { + q = estimateDiv128To64( aSig0, aSig1, bSig0 ); + q = ( 4 < q ) ? q - 4 : 0; + q >>= - expDiff; + shift128Right( bSig0, bSig1, 12, &bSig0, &bSig1 ); + expDiff += 52; + if ( expDiff < 0 ) { + shift128Right( aSig0, aSig1, - expDiff, &aSig0, &aSig1 ); + } + else { + shortShift128Left( aSig0, aSig1, expDiff, &aSig0, &aSig1 ); + } + mul128By64To192( bSig0, bSig1, q, &term0, &term1, &term2 ); + sub128( aSig0, aSig1, term1, term2, &aSig0, &aSig1 ); + } + else { + shift128Right( aSig0, aSig1, 12, &aSig0, &aSig1 ); + shift128Right( bSig0, bSig1, 12, &bSig0, &bSig1 ); + } + do { + alternateASig0 = aSig0; + alternateASig1 = aSig1; + ++q; + sub128( aSig0, aSig1, bSig0, bSig1, &aSig0, &aSig1 ); + } while ( 0 <= (sbits64) aSig0 ); + add128( + aSig0, aSig1, alternateASig0, alternateASig1, &sigMean0, &sigMean1 ); + if ( ( sigMean0 < 0 ) + || ( ( ( sigMean0 | sigMean1 ) == 0 ) && ( q & 1 ) ) ) { + aSig0 = alternateASig0; + aSig1 = alternateASig1; + } + zSign = ( (sbits64) aSig0 < 0 ); + if ( zSign ) sub128( 0, 0, aSig0, aSig1, &aSig0, &aSig1 ); + return + normalizeRoundAndPackFloat128( aSign ^ zSign, bExp - 4, aSig0, aSig1 STATUS_VAR ); + +} + +/*---------------------------------------------------------------------------- +| Returns the square root of the quadruple-precision floating-point value `a'. +| The operation is performed according to the IEC/IEEE Standard for Binary +| Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +float128 float128_sqrt( float128 a STATUS_PARAM ) +{ + flag aSign; + int32 aExp, zExp; + bits64 aSig0, aSig1, zSig0, zSig1, zSig2, doubleZSig0; + bits64 rem0, rem1, rem2, rem3, term0, term1, term2, term3; + float128 z; + + aSig1 = extractFloat128Frac1( a ); + aSig0 = extractFloat128Frac0( a ); + aExp = extractFloat128Exp( a ); + aSign = extractFloat128Sign( a ); + if ( aExp == 0x7FFF ) { + if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, a STATUS_VAR ); + if ( ! aSign ) return a; + goto invalid; + } + if ( aSign ) { + if ( ( aExp | aSig0 | aSig1 ) == 0 ) return a; + invalid: + float_raise( float_flag_invalid STATUS_VAR); + z.low = float128_default_nan_low; + z.high = float128_default_nan_high; + return z; + } + if ( aExp == 0 ) { + if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( 0, 0, 0, 0 ); + normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); + } + zExp = ( ( aExp - 0x3FFF )>>1 ) + 0x3FFE; + aSig0 |= LIT64( 0x0001000000000000 ); + zSig0 = estimateSqrt32( aExp, aSig0>>17 ); + shortShift128Left( aSig0, aSig1, 13 - ( aExp & 1 ), &aSig0, &aSig1 ); + zSig0 = estimateDiv128To64( aSig0, aSig1, zSig0<<32 ) + ( zSig0<<30 ); + doubleZSig0 = zSig0<<1; + mul64To128( zSig0, zSig0, &term0, &term1 ); + sub128( aSig0, aSig1, term0, term1, &rem0, &rem1 ); + while ( (sbits64) rem0 < 0 ) { + --zSig0; + doubleZSig0 -= 2; + add128( rem0, rem1, zSig0>>63, doubleZSig0 | 1, &rem0, &rem1 ); + } + zSig1 = estimateDiv128To64( rem1, 0, doubleZSig0 ); + if ( ( zSig1 & 0x1FFF ) <= 5 ) { + if ( zSig1 == 0 ) zSig1 = 1; + mul64To128( doubleZSig0, zSig1, &term1, &term2 ); + sub128( rem1, 0, term1, term2, &rem1, &rem2 ); + mul64To128( zSig1, zSig1, &term2, &term3 ); + sub192( rem1, rem2, 0, 0, term2, term3, &rem1, &rem2, &rem3 ); + while ( (sbits64) rem1 < 0 ) { + --zSig1; + shortShift128Left( 0, zSig1, 1, &term2, &term3 ); + term3 |= 1; + term2 |= doubleZSig0; + add192( rem1, rem2, rem3, 0, term2, term3, &rem1, &rem2, &rem3 ); + } + zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 ); + } + shift128ExtraRightJamming( zSig0, zSig1, 0, 14, &zSig0, &zSig1, &zSig2 ); + return roundAndPackFloat128( 0, zExp, zSig0, zSig1, zSig2 STATUS_VAR ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the quadruple-precision floating-point value `a' is equal to +| the corresponding value `b', and 0 otherwise. The comparison is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +flag float128_eq( float128 a, float128 b STATUS_PARAM ) +{ + + if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) + && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) + || ( ( extractFloat128Exp( b ) == 0x7FFF ) + && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) + ) { + if ( float128_is_signaling_nan( a ) + || float128_is_signaling_nan( b ) ) { + float_raise( float_flag_invalid STATUS_VAR); + } + return 0; + } + return + ( a.low == b.low ) + && ( ( a.high == b.high ) + || ( ( a.low == 0 ) + && ( (bits64) ( ( a.high | b.high )<<1 ) == 0 ) ) + ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the quadruple-precision floating-point value `a' is less than +| or equal to the corresponding value `b', and 0 otherwise. The comparison +| is performed according to the IEC/IEEE Standard for Binary Floating-Point +| Arithmetic. +*----------------------------------------------------------------------------*/ + +flag float128_le( float128 a, float128 b STATUS_PARAM ) +{ + flag aSign, bSign; + + if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) + && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) + || ( ( extractFloat128Exp( b ) == 0x7FFF ) + && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) + ) { + float_raise( float_flag_invalid STATUS_VAR); + return 0; + } + aSign = extractFloat128Sign( a ); + bSign = extractFloat128Sign( b ); + if ( aSign != bSign ) { + return + aSign + || ( ( ( (bits64) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) + == 0 ); + } + return + aSign ? le128( b.high, b.low, a.high, a.low ) + : le128( a.high, a.low, b.high, b.low ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the quadruple-precision floating-point value `a' is less than +| the corresponding value `b', and 0 otherwise. The comparison is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +flag float128_lt( float128 a, float128 b STATUS_PARAM ) +{ + flag aSign, bSign; + + if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) + && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) + || ( ( extractFloat128Exp( b ) == 0x7FFF ) + && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) + ) { + float_raise( float_flag_invalid STATUS_VAR); + return 0; + } + aSign = extractFloat128Sign( a ); + bSign = extractFloat128Sign( b ); + if ( aSign != bSign ) { + return + aSign + && ( ( ( (bits64) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) + != 0 ); + } + return + aSign ? lt128( b.high, b.low, a.high, a.low ) + : lt128( a.high, a.low, b.high, b.low ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the quadruple-precision floating-point value `a' is equal to +| the corresponding value `b', and 0 otherwise. The invalid exception is +| raised if either operand is a NaN. Otherwise, the comparison is performed +| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +flag float128_eq_signaling( float128 a, float128 b STATUS_PARAM ) +{ + + if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) + && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) + || ( ( extractFloat128Exp( b ) == 0x7FFF ) + && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) + ) { + float_raise( float_flag_invalid STATUS_VAR); + return 0; + } + return + ( a.low == b.low ) + && ( ( a.high == b.high ) + || ( ( a.low == 0 ) + && ( (bits64) ( ( a.high | b.high )<<1 ) == 0 ) ) + ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the quadruple-precision floating-point value `a' is less than +| or equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not +| cause an exception. Otherwise, the comparison is performed according to the +| IEC/IEEE Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +flag float128_le_quiet( float128 a, float128 b STATUS_PARAM ) +{ + flag aSign, bSign; + + if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) + && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) + || ( ( extractFloat128Exp( b ) == 0x7FFF ) + && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) + ) { + if ( float128_is_signaling_nan( a ) + || float128_is_signaling_nan( b ) ) { + float_raise( float_flag_invalid STATUS_VAR); + } + return 0; + } + aSign = extractFloat128Sign( a ); + bSign = extractFloat128Sign( b ); + if ( aSign != bSign ) { + return + aSign + || ( ( ( (bits64) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) + == 0 ); + } + return + aSign ? le128( b.high, b.low, a.high, a.low ) + : le128( a.high, a.low, b.high, b.low ); + +} + +/*---------------------------------------------------------------------------- +| Returns 1 if the quadruple-precision floating-point value `a' is less than +| the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an +| exception. Otherwise, the comparison is performed according to the IEC/IEEE +| Standard for Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +flag float128_lt_quiet( float128 a, float128 b STATUS_PARAM ) +{ + flag aSign, bSign; + + if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) + && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) + || ( ( extractFloat128Exp( b ) == 0x7FFF ) + && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) + ) { + if ( float128_is_signaling_nan( a ) + || float128_is_signaling_nan( b ) ) { + float_raise( float_flag_invalid STATUS_VAR); + } + return 0; + } + aSign = extractFloat128Sign( a ); + bSign = extractFloat128Sign( b ); + if ( aSign != bSign ) { + return + aSign + && ( ( ( (bits64) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) + != 0 ); + } + return + aSign ? lt128( b.high, b.low, a.high, a.low ) + : lt128( a.high, a.low, b.high, b.low ); + +} + +#endif + diff --git a/fpu/softfloat.h b/fpu/softfloat.h new file mode 100644 index 0000000000..9aefbf75ac --- /dev/null +++ b/fpu/softfloat.h @@ -0,0 +1,329 @@ +/*============================================================================ + +This C header file is part of the SoftFloat IEC/IEEE Floating-point Arithmetic +Package, Release 2b. + +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://www.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 ALL LOSSES, +COSTS, OR OTHER PROBLEMS THEY INCUR DUE TO THE SOFTWARE, AND WHO FURTHERMORE +EFFECTIVELY INDEMNIFY JOHN HAUSER AND THE INTERNATIONAL COMPUTER SCIENCE +INSTITUTE (possibly via similar legal warning) AGAINST ALL LOSSES, COSTS, OR +OTHER PROBLEMS INCURRED BY THEIR CUSTOMERS AND CLIENTS DUE TO THE SOFTWARE. + +Derivative works are acceptable, even for commercial purposes, so long as +(1) the source code for the derivative work includes prominent notice that +the work is derivative, and (2) the source code includes prominent notice with +these four paragraphs for those parts of this code that are retained. + +=============================================================================*/ + +#ifndef SOFTFLOAT_H +#define SOFTFLOAT_H + +#include <inttypes.h> +#include "config.h" + +/*---------------------------------------------------------------------------- +| Each of the following `typedef's defines the most convenient type that holds +| integers of at least as many bits as specified. For example, `uint8' should +| be the most convenient type that can hold unsigned integers of as many as +| 8 bits. The `flag' type must be able to hold either a 0 or 1. For most +| implementations of C, `flag', `uint8', and `int8' should all be `typedef'ed +| to the same as `int'. +*----------------------------------------------------------------------------*/ +typedef char flag; +typedef uint8_t uint8; +typedef int8_t int8; +typedef int uint16; +typedef int int16; +typedef unsigned int uint32; +typedef signed int int32; +typedef uint64_t uint64; +typedef int64_t int64; + +/*---------------------------------------------------------------------------- +| Each of the following `typedef's defines a type that holds integers +| of _exactly_ the number of bits specified. For instance, for most +| implementation of C, `bits16' and `sbits16' should be `typedef'ed to +| `unsigned short int' and `signed short int' (or `short int'), respectively. +*----------------------------------------------------------------------------*/ +typedef uint8_t bits8; +typedef int8_t sbits8; +typedef uint16_t bits16; +typedef int16_t sbits16; +typedef uint32_t bits32; +typedef int32_t sbits32; +typedef uint64_t bits64; +typedef int64_t sbits64; + +#define LIT64( a ) a##LL +#define INLINE static inline + +/*---------------------------------------------------------------------------- +| The macro `FLOATX80' must be defined to enable the extended double-precision +| floating-point format `floatx80'. If this macro is not defined, the +| `floatx80' type will not be defined, and none of the functions that either +| input or output the `floatx80' type will be defined. The same applies to +| the `FLOAT128' macro and the quadruple-precision format `float128'. +*----------------------------------------------------------------------------*/ +#ifdef CONFIG_SOFTFLOAT +/* bit exact soft float support */ +#define FLOATX80 +#define FLOAT128 +#else +/* native float support */ +#if (defined(__i386__) || defined(__x86_64__)) && !defined(_BSD) +#define FLOATX80 +#endif +#endif /* !CONFIG_SOFTFLOAT */ + +#define STATUS_PARAM , float_status *status +#define STATUS(field) status->field +#define STATUS_VAR , status + +#ifdef CONFIG_SOFTFLOAT +/*---------------------------------------------------------------------------- +| Software IEC/IEEE floating-point types. +*----------------------------------------------------------------------------*/ +typedef uint32_t float32; +typedef uint64_t float64; +#ifdef FLOATX80 +typedef struct { + uint64_t low; + uint16_t high; +} floatx80; +#endif +#ifdef FLOAT128 +typedef struct { +#ifdef WORDS_BIGENDIAN + uint64_t high, low; +#else + uint64_t low, high; +#endif +} float128; +#endif + +/*---------------------------------------------------------------------------- +| Software IEC/IEEE floating-point underflow tininess-detection mode. +*----------------------------------------------------------------------------*/ +enum { + float_tininess_after_rounding = 0, + float_tininess_before_rounding = 1 +}; + +/*---------------------------------------------------------------------------- +| Software IEC/IEEE floating-point rounding mode. +*----------------------------------------------------------------------------*/ +enum { + float_round_nearest_even = 0, + float_round_down = 1, + float_round_up = 2, + float_round_to_zero = 3 +}; + +/*---------------------------------------------------------------------------- +| Software IEC/IEEE floating-point exception flags. +*----------------------------------------------------------------------------*/ +enum { + float_flag_invalid = 1, + float_flag_divbyzero = 4, + float_flag_overflow = 8, + float_flag_underflow = 16, + float_flag_inexact = 32 +}; + +typedef struct float_status { + signed char float_detect_tininess; + signed char float_rounding_mode; + signed char float_exception_flags; +#ifdef FLOATX80 + signed char floatx80_rounding_precision; +#endif +} float_status; + +void set_float_rounding_mode(int val STATUS_PARAM); +#ifdef FLOATX80 +void set_floatx80_rounding_precision(int val STATUS_PARAM); +#endif + +/*---------------------------------------------------------------------------- +| Routine to raise any or all of the software IEC/IEEE floating-point +| exception flags. +*----------------------------------------------------------------------------*/ +void float_raise( signed char STATUS_PARAM); + +/*---------------------------------------------------------------------------- +| Software IEC/IEEE integer-to-floating-point conversion routines. +*----------------------------------------------------------------------------*/ +float32 int32_to_float32( int STATUS_PARAM ); +float64 int32_to_float64( int STATUS_PARAM ); +#ifdef FLOATX80 +floatx80 int32_to_floatx80( int STATUS_PARAM ); +#endif +#ifdef FLOAT128 +float128 int32_to_float128( int STATUS_PARAM ); +#endif +float32 int64_to_float32( int64_t STATUS_PARAM ); +float64 int64_to_float64( int64_t STATUS_PARAM ); +#ifdef FLOATX80 +floatx80 int64_to_floatx80( int64_t STATUS_PARAM ); +#endif +#ifdef FLOAT128 +float128 int64_to_float128( int64_t STATUS_PARAM ); +#endif + +/*---------------------------------------------------------------------------- +| Software IEC/IEEE single-precision conversion routines. +*----------------------------------------------------------------------------*/ +int float32_to_int32( float32 STATUS_PARAM ); +int float32_to_int32_round_to_zero( float32 STATUS_PARAM ); +int64_t float32_to_int64( float32 STATUS_PARAM ); +int64_t float32_to_int64_round_to_zero( float32 STATUS_PARAM ); +float64 float32_to_float64( float32 STATUS_PARAM ); +#ifdef FLOATX80 +floatx80 float32_to_floatx80( float32 STATUS_PARAM ); +#endif +#ifdef FLOAT128 +float128 float32_to_float128( float32 STATUS_PARAM ); +#endif + +/*---------------------------------------------------------------------------- +| Software IEC/IEEE single-precision operations. +*----------------------------------------------------------------------------*/ +float32 float32_round_to_int( float32 STATUS_PARAM ); +float32 float32_add( float32, float32 STATUS_PARAM ); +float32 float32_sub( float32, float32 STATUS_PARAM ); +float32 float32_mul( float32, float32 STATUS_PARAM ); +float32 float32_div( float32, float32 STATUS_PARAM ); +float32 float32_rem( float32, float32 STATUS_PARAM ); +float32 float32_sqrt( float32 STATUS_PARAM ); +char float32_eq( float32, float32 STATUS_PARAM ); +char float32_le( float32, float32 STATUS_PARAM ); +char float32_lt( float32, float32 STATUS_PARAM ); +char float32_eq_signaling( float32, float32 STATUS_PARAM ); +char float32_le_quiet( float32, float32 STATUS_PARAM ); +char float32_lt_quiet( float32, float32 STATUS_PARAM ); +char float32_is_signaling_nan( float32 ); + +/*---------------------------------------------------------------------------- +| Software IEC/IEEE double-precision conversion routines. +*----------------------------------------------------------------------------*/ +int float64_to_int32( float64 STATUS_PARAM ); +int float64_to_int32_round_to_zero( float64 STATUS_PARAM ); +int64_t float64_to_int64( float64 STATUS_PARAM ); +int64_t float64_to_int64_round_to_zero( float64 STATUS_PARAM ); +float32 float64_to_float32( float64 STATUS_PARAM ); +#ifdef FLOATX80 +floatx80 float64_to_floatx80( float64 STATUS_PARAM ); +#endif +#ifdef FLOAT128 +float128 float64_to_float128( float64 STATUS_PARAM ); +#endif + +/*---------------------------------------------------------------------------- +| Software IEC/IEEE double-precision operations. +*----------------------------------------------------------------------------*/ +float64 float64_round_to_int( float64 STATUS_PARAM ); +float64 float64_add( float64, float64 STATUS_PARAM ); +float64 float64_sub( float64, float64 STATUS_PARAM ); +float64 float64_mul( float64, float64 STATUS_PARAM ); +float64 float64_div( float64, float64 STATUS_PARAM ); +float64 float64_rem( float64, float64 STATUS_PARAM ); +float64 float64_sqrt( float64 STATUS_PARAM ); +char float64_eq( float64, float64 STATUS_PARAM ); +char float64_le( float64, float64 STATUS_PARAM ); +char float64_lt( float64, float64 STATUS_PARAM ); +char float64_eq_signaling( float64, float64 STATUS_PARAM ); +char float64_le_quiet( float64, float64 STATUS_PARAM ); +char float64_lt_quiet( float64, float64 STATUS_PARAM ); +char float64_is_signaling_nan( float64 ); + +#ifdef FLOATX80 + +/*---------------------------------------------------------------------------- +| Software IEC/IEEE extended double-precision conversion routines. +*----------------------------------------------------------------------------*/ +int floatx80_to_int32( floatx80 STATUS_PARAM ); +int floatx80_to_int32_round_to_zero( floatx80 STATUS_PARAM ); +int64_t floatx80_to_int64( floatx80 STATUS_PARAM ); +int64_t floatx80_to_int64_round_to_zero( floatx80 STATUS_PARAM ); +float32 floatx80_to_float32( floatx80 STATUS_PARAM ); +float64 floatx80_to_float64( floatx80 STATUS_PARAM ); +#ifdef FLOAT128 +float128 floatx80_to_float128( floatx80 STATUS_PARAM ); +#endif + +/*---------------------------------------------------------------------------- +| Software IEC/IEEE extended double-precision operations. +*----------------------------------------------------------------------------*/ +floatx80 floatx80_round_to_int( floatx80 STATUS_PARAM ); +floatx80 floatx80_add( floatx80, floatx80 STATUS_PARAM ); +floatx80 floatx80_sub( floatx80, floatx80 STATUS_PARAM ); +floatx80 floatx80_mul( floatx80, floatx80 STATUS_PARAM ); +floatx80 floatx80_div( floatx80, floatx80 STATUS_PARAM ); +floatx80 floatx80_rem( floatx80, floatx80 STATUS_PARAM ); +floatx80 floatx80_sqrt( floatx80 STATUS_PARAM ); +char floatx80_eq( floatx80, floatx80 STATUS_PARAM ); +char floatx80_le( floatx80, floatx80 STATUS_PARAM ); +char floatx80_lt( floatx80, floatx80 STATUS_PARAM ); +char floatx80_eq_signaling( floatx80, floatx80 STATUS_PARAM ); +char floatx80_le_quiet( floatx80, floatx80 STATUS_PARAM ); +char floatx80_lt_quiet( floatx80, floatx80 STATUS_PARAM ); +char floatx80_is_signaling_nan( floatx80 ); + +#endif + +#ifdef FLOAT128 + +/*---------------------------------------------------------------------------- +| Software IEC/IEEE quadruple-precision conversion routines. +*----------------------------------------------------------------------------*/ +int float128_to_int32( float128 STATUS_PARAM ); +int float128_to_int32_round_to_zero( float128 STATUS_PARAM ); +int64_t float128_to_int64( float128 STATUS_PARAM ); +int64_t float128_to_int64_round_to_zero( float128 STATUS_PARAM ); +float32 float128_to_float32( float128 STATUS_PARAM ); +float64 float128_to_float64( float128 STATUS_PARAM ); +#ifdef FLOATX80 +floatx80 float128_to_floatx80( float128 STATUS_PARAM ); +#endif + +/*---------------------------------------------------------------------------- +| Software IEC/IEEE quadruple-precision operations. +*----------------------------------------------------------------------------*/ +float128 float128_round_to_int( float128 STATUS_PARAM ); +float128 float128_add( float128, float128 STATUS_PARAM ); +float128 float128_sub( float128, float128 STATUS_PARAM ); +float128 float128_mul( float128, float128 STATUS_PARAM ); +float128 float128_div( float128, float128 STATUS_PARAM ); +float128 float128_rem( float128, float128 STATUS_PARAM ); +float128 float128_sqrt( float128 STATUS_PARAM ); +char float128_eq( float128, float128 STATUS_PARAM ); +char float128_le( float128, float128 STATUS_PARAM ); +char float128_lt( float128, float128 STATUS_PARAM ); +char float128_eq_signaling( float128, float128 STATUS_PARAM ); +char float128_le_quiet( float128, float128 STATUS_PARAM ); +char float128_lt_quiet( float128, float128 STATUS_PARAM ); +char float128_is_signaling_nan( float128 ); + +#endif + +#else /* CONFIG_SOFTFLOAT */ + +#include "softfloat-native.h" + +#endif /* !CONFIG_SOFTFLOAT */ + +#endif /* !SOFTFLOAT_H */ |