+++ /dev/null
-
-/*
-===============================================================================
-
-This C source fragment is part of the SoftFloat IEC/IEEE Floating-point
-Arithmetic Package, Release 2.
-
-Written by John R. Hauser. This work was made possible in part by the
-International Computer Science Institute, located at Suite 600, 1947 Center
-Street, Berkeley, California 94704. Funding was partially provided by the
-National Science Foundation under grant MIP-9311980. The original version
-of this code was written as part of a project to build a fixed-point vector
-processor in collaboration with the University of California at Berkeley,
-overseen by Profs. Nelson Morgan and John Wawrzynek. More information
-is available through the web page `http://HTTP.CS.Berkeley.EDU/~jhauser/
-arithmetic/softfloat.html'.
-
-THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort
-has been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT
-TIMES RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO
-PERSONS AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ANY
-AND ALL LOSSES, COSTS, OR OTHER PROBLEMS ARISING FROM ITS USE.
-
-Derivative works are acceptable, even for commercial purposes, so long as
-(1) they include prominent notice that the work is derivative, and (2) they
-include prominent notice akin to these three 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;
-
-// __asm__("@shift64RightJamming -- start");
- if ( count == 0 ) {
- z = a;
- }
- else if ( count < 64 ) {
- z = ( a>>count ) | ( ( a<<( ( - count ) & 63 ) ) != 0 );
- }
- else {
- z = ( a != 0 );
- }
-// __asm__("@shift64RightJamming -- end");
- *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 );
-
-}
-
+++ /dev/null
-/*
-===============================================================================
-
-This C source file is part of the SoftFloat IEC/IEEE Floating-point
-Arithmetic Package, Release 2.
-
-Written by John R. Hauser. This work was made possible in part by the
-International Computer Science Institute, located at Suite 600, 1947 Center
-Street, Berkeley, California 94704. Funding was partially provided by the
-National Science Foundation under grant MIP-9311980. The original version
-of this code was written as part of a project to build a fixed-point vector
-processor in collaboration with the University of California at Berkeley,
-overseen by Profs. Nelson Morgan and John Wawrzynek. More information
-is available through the web page `http://HTTP.CS.Berkeley.EDU/~jhauser/
-arithmetic/softfloat.html'.
-
-THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort
-has been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT
-TIMES RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO
-PERSONS AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ANY
-AND ALL LOSSES, COSTS, OR OTHER PROBLEMS ARISING FROM ITS USE.
-
-Derivative works are acceptable, even for commercial purposes, so long as
-(1) they include prominent notice that the work is derivative, and (2) they
-include prominent notice akin to these three paragraphs for those parts of
-this code that are retained.
-
-===============================================================================
-*/
-
-#include "fpa11.h"
-#include "milieu.h"
-#include "softfloat.h"
-
-/*
--------------------------------------------------------------------------------
-Floating-point rounding mode, extended double-precision rounding precision,
-and exception flags.
--------------------------------------------------------------------------------
-*/
-int8 float_rounding_mode = float_round_nearest_even;
-int8 floatx80_rounding_precision = 80;
-int8 float_exception_flags;
-
-/*
--------------------------------------------------------------------------------
-Primitive arithmetic functions, including multi-word arithmetic, and
-division and square root approximations. (Can be specialized to target if
-desired.)
--------------------------------------------------------------------------------
-*/
-#include "softfloat-macros"
-
-/*
--------------------------------------------------------------------------------
-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"
-
-/*
--------------------------------------------------------------------------------
-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 nonzero, 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. If the fixed-point
-input is too large, however, the invalid exception is raised and the largest
-positive or negative integer is returned.
--------------------------------------------------------------------------------
-*/
-static int32 roundAndPackInt32( flag zSign, bits64 absZ )
-{
- int8 roundingMode;
- flag roundNearestEven;
- int8 roundIncrement, roundBits;
- int32 z;
-
- roundingMode = 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_exception_flags |= float_flag_invalid;
- return zSign ? 0x80000000 : 0x7FFFFFFF;
- }
- if ( roundBits ) 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. If the abstract value is too large, however, 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 )
-{
- int8 roundingMode;
- flag roundNearestEven;
- int8 roundIncrement, roundBits;
- flag isTiny;
-
- roundingMode = 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 );
- return packFloat32( zSign, 0xFF, 0 ) - ( roundIncrement == 0 );
- }
- if ( zExp < 0 ) {
- isTiny =
- ( 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 );
- }
- }
- if ( roundBits ) 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 in
-any way. In all cases, `zExp' must be 1 less than the ``true'' floating-
-point exponent.
--------------------------------------------------------------------------------
-*/
-static float32
- normalizeRoundAndPackFloat32( flag zSign, int16 zExp, bits32 zSig )
-{
- int8 shiftCount;
-
- shiftCount = countLeadingZeros32( zSig ) - 1;
- return roundAndPackFloat32( zSign, zExp - shiftCount, zSig<<shiftCount );
-
-}
-
-/*
--------------------------------------------------------------------------------
-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. If the abstract value is too large, however, 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 )
-{
- int8 roundingMode;
- flag roundNearestEven;
- int16 roundIncrement, roundBits;
- flag isTiny;
-
- roundingMode = 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 ) )
- ) {
- //register int lr = __builtin_return_address(0);
- //printk("roundAndPackFloat64 called from 0x%08x\n",lr);
- float_raise( float_flag_overflow | float_flag_inexact );
- return packFloat64( zSign, 0x7FF, 0 ) - ( roundIncrement == 0 );
- }
- if ( zExp < 0 ) {
- isTiny =
- ( 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 );
- }
- }
- if ( roundBits ) 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 in
-any way. In all cases, `zExp' must be 1 less than the ``true'' floating-
-point exponent.
--------------------------------------------------------------------------------
-*/
-static float64
- normalizeRoundAndPackFloat64( flag zSign, int16 zExp, bits64 zSig )
-{
- int8 shiftCount;
-
- shiftCount = countLeadingZeros64( zSig ) - 1;
- return roundAndPackFloat64( zSign, zExp - shiftCount, zSig<<shiftCount );
-
-}
-
-#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. If the abstract value is too large, however, 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
- )
-{
- int8 roundingMode;
- flag roundNearestEven, increment, isTiny;
- int64 roundIncrement, roundMask, roundBits;
-
- roundingMode = 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 =
- ( 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 );
- if ( roundBits ) 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 ) 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 );
- 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 =
- ( 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 );
- if ( zSig1 ) 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 &= ~ ( ( zSig1 + zSig1 == 0 ) & roundNearestEven );
- if ( (sbits64) zSig0 < 0 ) zExp = 1;
- }
- return packFloatx80( zSign, zExp, zSig0 );
- }
- }
- if ( zSig1 ) float_exception_flags |= float_flag_inexact;
- if ( increment ) {
- ++zSig0;
- if ( zSig0 == 0 ) {
- ++zExp;
- zSig0 = LIT64( 0x8000000000000000 );
- }
- else {
- zSig0 &= ~ ( ( zSig1 + zSig1 == 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
- )
-{
- 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 );
-
-}
-
-#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 )
-{
- flag zSign;
-
- if ( a == 0 ) return 0;
- if ( a == 0x80000000 ) return packFloat32( 1, 0x9E, 0 );
- zSign = ( a < 0 );
- return normalizeRoundAndPackFloat32( zSign, 0x9C, zSign ? - a : a );
-
-}
-
-/*
--------------------------------------------------------------------------------
-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 )
-{
- flag aSign;
- uint32 absA;
- int8 shiftCount;
- bits64 zSig;
-
- if ( a == 0 ) return 0;
- aSign = ( a < 0 );
- absA = aSign ? - a : a;
- shiftCount = countLeadingZeros32( absA ) + 21;
- zSig = absA;
- return packFloat64( aSign, 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 )
-{
- 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
-
-/*
--------------------------------------------------------------------------------
-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 )
-{
- flag aSign;
- int16 aExp, shiftCount;
- bits32 aSig;
- bits64 zSig;
-
- aSig = extractFloat32Frac( a );
- aExp = extractFloat32Exp( a );
- aSign = extractFloat32Sign( a );
- if ( ( aExp == 0x7FF ) && aSig ) aSign = 0;
- if ( aExp ) aSig |= 0x00800000;
- shiftCount = 0xAF - aExp;
- zSig = aSig;
- zSig <<= 32;
- if ( 0 < shiftCount ) shift64RightJamming( zSig, shiftCount, &zSig );
- return roundAndPackInt32( aSign, zSig );
-
-}
-
-/*
--------------------------------------------------------------------------------
-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 )
-{
- 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 ) return 0x80000000;
- float_raise( float_flag_invalid );
- if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) return 0x7FFFFFFF;
- return 0x80000000;
- }
- else if ( aExp <= 0x7E ) {
- if ( aExp | aSig ) float_exception_flags |= float_flag_inexact;
- return 0;
- }
- aSig = ( aSig | 0x00800000 )<<8;
- z = aSig>>( - shiftCount );
- if ( (bits32) ( aSig<<( shiftCount & 31 ) ) ) {
- float_exception_flags |= float_flag_inexact;
- }
- return aSign ? - z : 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 )
-{
- flag aSign;
- int16 aExp;
- bits32 aSig;
-
- aSig = extractFloat32Frac( a );
- aExp = extractFloat32Exp( a );
- aSign = extractFloat32Sign( a );
- if ( aExp == 0xFF ) {
- if ( aSig ) return commonNaNToFloat64( float32ToCommonNaN( a ) );
- 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 )
-{
- flag aSign;
- int16 aExp;
- bits32 aSig;
-
- aSig = extractFloat32Frac( a );
- aExp = extractFloat32Exp( a );
- aSign = extractFloat32Sign( a );
- if ( aExp == 0xFF ) {
- if ( aSig ) return commonNaNToFloatx80( float32ToCommonNaN( a ) );
- 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
-
-/*
--------------------------------------------------------------------------------
-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 )
-{
- 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 );
- }
- return a;
- }
- if ( aExp <= 0x7E ) {
- if ( (bits32) ( a<<1 ) == 0 ) return a;
- float_exception_flags |= float_flag_inexact;
- aSign = extractFloat32Sign( a );
- switch ( 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 = 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 ) 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 true, 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 )
-{
- 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 );
- 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 );
- 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 );
- 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 );
-
-}
-
-/*
--------------------------------------------------------------------------------
-Returns the result of subtracting the absolute values of the single-
-precision floating-point values `a' and `b'. If `zSign' is true, 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 )
-{
- 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 );
- float_raise( float_flag_invalid );
- return float32_default_nan;
- }
- if ( aExp == 0 ) {
- aExp = 1;
- bExp = 1;
- }
- if ( bSig < aSig ) goto aBigger;
- if ( aSig < bSig ) goto bBigger;
- return packFloat32( float_rounding_mode == float_round_down, 0, 0 );
- bExpBigger:
- if ( bExp == 0xFF ) {
- if ( bSig ) return propagateFloat32NaN( a, b );
- 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 );
- 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 );
-
-}
-
-/*
--------------------------------------------------------------------------------
-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 )
-{
- flag aSign, bSign;
-
- aSign = extractFloat32Sign( a );
- bSign = extractFloat32Sign( b );
- if ( aSign == bSign ) {
- return addFloat32Sigs( a, b, aSign );
- }
- else {
- return subFloat32Sigs( a, b, aSign );
- }
-
-}
-
-/*
--------------------------------------------------------------------------------
-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 )
-{
- flag aSign, bSign;
-
- aSign = extractFloat32Sign( a );
- bSign = extractFloat32Sign( b );
- if ( aSign == bSign ) {
- return subFloat32Sigs( a, b, aSign );
- }
- else {
- return addFloat32Sigs( a, b, aSign );
- }
-
-}
-
-/*
--------------------------------------------------------------------------------
-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 )
-{
- 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 );
- }
- if ( ( bExp | bSig ) == 0 ) {
- float_raise( float_flag_invalid );
- return float32_default_nan;
- }
- return packFloat32( zSign, 0xFF, 0 );
- }
- if ( bExp == 0xFF ) {
- if ( bSig ) return propagateFloat32NaN( a, b );
- if ( ( aExp | aSig ) == 0 ) {
- float_raise( float_flag_invalid );
- 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 );
-
-}
-
-/*
--------------------------------------------------------------------------------
-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 )
-{
- 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 );
- if ( bExp == 0xFF ) {
- if ( bSig ) return propagateFloat32NaN( a, b );
- float_raise( float_flag_invalid );
- return float32_default_nan;
- }
- return packFloat32( zSign, 0xFF, 0 );
- }
- if ( bExp == 0xFF ) {
- if ( bSig ) return propagateFloat32NaN( a, b );
- return packFloat32( zSign, 0, 0 );
- }
- if ( bExp == 0 ) {
- if ( bSig == 0 ) {
- if ( ( aExp | aSig ) == 0 ) {
- float_raise( float_flag_invalid );
- return float32_default_nan;
- }
- float_raise( float_flag_divbyzero );
- 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 );
-
-}
-
-/*
--------------------------------------------------------------------------------
-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 )
-{
- 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 );
- }
- float_raise( float_flag_invalid );
- return float32_default_nan;
- }
- if ( bExp == 0xFF ) {
- if ( bSig ) return propagateFloat32NaN( a, b );
- return a;
- }
- if ( bExp == 0 ) {
- if ( bSig == 0 ) {
- float_raise( float_flag_invalid );
- 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 );
-
-}
-
-/*
--------------------------------------------------------------------------------
-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 )
-{
- 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 );
- if ( ! aSign ) return a;
- float_raise( float_flag_invalid );
- return float32_default_nan;
- }
- if ( aSign ) {
- if ( ( aExp | aSig ) == 0 ) return a;
- float_raise( float_flag_invalid );
- 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 = 0xFFFFFFFF;
- }
- else {
- 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 );
- return roundAndPackFloat32( 0, zExp, zSig );
-
-}
-
-/*
--------------------------------------------------------------------------------
-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 )
-{
-
- 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 );
- }
- 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 )
-{
- flag aSign, bSign;
-
- if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
- || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
- ) {
- float_raise( float_flag_invalid );
- 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 )
-{
- flag aSign, bSign;
-
- if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
- || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
- ) {
- float_raise( float_flag_invalid );
- 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 )
-{
-
- if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
- || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
- ) {
- float_raise( float_flag_invalid );
- 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 )
-{
- flag aSign, bSign;
- //int16 aExp, bExp;
-
- 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 );
- }
- 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 )
-{
- 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 );
- }
- 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 )
-{
- 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 );
-
-}
-
-/*
--------------------------------------------------------------------------------
-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 )
-{
- flag aSign;
- int16 aExp, shiftCount;
- bits64 aSig, savedASig;
- int32 z;
-
- aSig = extractFloat64Frac( a );
- aExp = extractFloat64Exp( a );
- aSign = extractFloat64Sign( a );
- shiftCount = 0x433 - aExp;
- if ( shiftCount < 21 ) {
- if ( ( aExp == 0x7FF ) && aSig ) aSign = 0;
- goto invalid;
- }
- else if ( 52 < shiftCount ) {
- if ( aExp || aSig ) float_exception_flags |= float_flag_inexact;
- return 0;
- }
- aSig |= LIT64( 0x0010000000000000 );
- savedASig = aSig;
- aSig >>= shiftCount;
- z = aSig;
- if ( aSign ) z = - z;
- if ( ( z < 0 ) ^ aSign ) {
- invalid:
- float_exception_flags |= float_flag_invalid;
- return aSign ? 0x80000000 : 0x7FFFFFFF;
- }
- if ( ( aSig<<shiftCount ) != savedASig ) {
- float_exception_flags |= float_flag_inexact;
- }
- return z;
-
-}
-
-/*
--------------------------------------------------------------------------------
-Returns the result of converting the double-precision floating-point value
-`a' to the 32-bit two's complement unsigned 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 positive integer is returned.
--------------------------------------------------------------------------------
-*/
-int32 float64_to_uint32( float64 a )
-{
- flag aSign;
- int16 aExp, shiftCount;
- bits64 aSig;
-
- aSig = extractFloat64Frac( a );
- aExp = extractFloat64Exp( a );
- aSign = 0; //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 );
-}
-
-/*
--------------------------------------------------------------------------------
-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 positive integer is returned.
--------------------------------------------------------------------------------
-*/
-int32 float64_to_uint32_round_to_zero( float64 a )
-{
- flag aSign;
- int16 aExp, shiftCount;
- bits64 aSig, savedASig;
- int32 z;
-
- aSig = extractFloat64Frac( a );
- aExp = extractFloat64Exp( a );
- aSign = extractFloat64Sign( a );
- shiftCount = 0x433 - aExp;
- if ( shiftCount < 21 ) {
- if ( ( aExp == 0x7FF ) && aSig ) aSign = 0;
- goto invalid;
- }
- else if ( 52 < shiftCount ) {
- if ( aExp || aSig ) float_exception_flags |= float_flag_inexact;
- return 0;
- }
- aSig |= LIT64( 0x0010000000000000 );
- savedASig = aSig;
- aSig >>= shiftCount;
- z = aSig;
- if ( aSign ) z = - z;
- if ( ( z < 0 ) ^ aSign ) {
- invalid:
- float_exception_flags |= float_flag_invalid;
- return aSign ? 0x80000000 : 0x7FFFFFFF;
- }
- if ( ( aSig<<shiftCount ) != savedASig ) {
- float_exception_flags |= float_flag_inexact;
- }
- 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 )
-{
- 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 ) );
- return packFloat32( aSign, 0xFF, 0 );
- }
- shift64RightJamming( aSig, 22, &aSig );
- zSig = aSig;
- if ( aExp || zSig ) {
- zSig |= 0x40000000;
- aExp -= 0x381;
- }
- return roundAndPackFloat32( aSign, aExp, zSig );
-
-}
-
-#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 )
-{
- flag aSign;
- int16 aExp;
- bits64 aSig;
-
- aSig = extractFloat64Frac( a );
- aExp = extractFloat64Exp( a );
- aSign = extractFloat64Sign( a );
- if ( aExp == 0x7FF ) {
- if ( aSig ) return commonNaNToFloatx80( float64ToCommonNaN( a ) );
- 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
-
-/*
--------------------------------------------------------------------------------
-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 )
-{
- 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 );
- }
- return a;
- }
- if ( aExp <= 0x3FE ) {
- if ( (bits64) ( a<<1 ) == 0 ) return a;
- float_exception_flags |= float_flag_inexact;
- aSign = extractFloat64Sign( a );
- switch ( 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 = 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 ) 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 true, 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 )
-{
- 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 );
- 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 );
- 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 );
- 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 );
-
-}
-
-/*
--------------------------------------------------------------------------------
-Returns the result of subtracting the absolute values of the double-
-precision floating-point values `a' and `b'. If `zSign' is true, 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 )
-{
- 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 );
- float_raise( float_flag_invalid );
- return float64_default_nan;
- }
- if ( aExp == 0 ) {
- aExp = 1;
- bExp = 1;
- }
- if ( bSig < aSig ) goto aBigger;
- if ( aSig < bSig ) goto bBigger;
- return packFloat64( float_rounding_mode == float_round_down, 0, 0 );
- bExpBigger:
- if ( bExp == 0x7FF ) {
- if ( bSig ) return propagateFloat64NaN( a, b );
- 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 );
- 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 );
-
-}
-
-/*
--------------------------------------------------------------------------------
-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 )
-{
- flag aSign, bSign;
-
- aSign = extractFloat64Sign( a );
- bSign = extractFloat64Sign( b );
- if ( aSign == bSign ) {
- return addFloat64Sigs( a, b, aSign );
- }
- else {
- return subFloat64Sigs( a, b, aSign );
- }
-
-}
-
-/*
--------------------------------------------------------------------------------
-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 )
-{
- flag aSign, bSign;
-
- aSign = extractFloat64Sign( a );
- bSign = extractFloat64Sign( b );
- if ( aSign == bSign ) {
- return subFloat64Sigs( a, b, aSign );
- }
- else {
- return addFloat64Sigs( a, b, aSign );
- }
-
-}
-
-/*
--------------------------------------------------------------------------------
-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 )
-{
- 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 );
- }
- if ( ( bExp | bSig ) == 0 ) {
- float_raise( float_flag_invalid );
- return float64_default_nan;
- }
- return packFloat64( zSign, 0x7FF, 0 );
- }
- if ( bExp == 0x7FF ) {
- if ( bSig ) return propagateFloat64NaN( a, b );
- if ( ( aExp | aSig ) == 0 ) {
- float_raise( float_flag_invalid );
- 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 );
-
-}
-
-/*
--------------------------------------------------------------------------------
-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 )
-{
- 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 );
- if ( bExp == 0x7FF ) {
- if ( bSig ) return propagateFloat64NaN( a, b );
- float_raise( float_flag_invalid );
- return float64_default_nan;
- }
- return packFloat64( zSign, 0x7FF, 0 );
- }
- if ( bExp == 0x7FF ) {
- if ( bSig ) return propagateFloat64NaN( a, b );
- return packFloat64( zSign, 0, 0 );
- }
- if ( bExp == 0 ) {
- if ( bSig == 0 ) {
- if ( ( aExp | aSig ) == 0 ) {
- float_raise( float_flag_invalid );
- return float64_default_nan;
- }
- float_raise( float_flag_divbyzero );
- 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 );
-
-}
-
-/*
--------------------------------------------------------------------------------
-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 )
-{
- 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 );
- }
- float_raise( float_flag_invalid );
- return float64_default_nan;
- }
- if ( bExp == 0x7FF ) {
- if ( bSig ) return propagateFloat64NaN( a, b );
- return a;
- }
- if ( bExp == 0 ) {
- if ( bSig == 0 ) {
- float_raise( float_flag_invalid );
- 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 );
-
-}
-
-/*
--------------------------------------------------------------------------------
-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 )
-{
- flag aSign;
- int16 aExp, zExp;
- bits64 aSig, zSig;
- bits64 rem0, rem1, term0, term1; //, shiftedRem;
- //float64 z;
-
- aSig = extractFloat64Frac( a );
- aExp = extractFloat64Exp( a );
- aSign = extractFloat64Sign( a );
- if ( aExp == 0x7FF ) {
- if ( aSig ) return propagateFloat64NaN( a, a );
- if ( ! aSign ) return a;
- float_raise( float_flag_invalid );
- return float64_default_nan;
- }
- if ( aSign ) {
- if ( ( aExp | aSig ) == 0 ) return a;
- float_raise( float_flag_invalid );
- 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 );
- zSig <<= 31;
- aSig <<= 9 - ( aExp & 1 );
- zSig = estimateDiv128To64( aSig, 0, zSig ) + zSig + 2;
- if ( ( zSig & 0x3FF ) <= 5 ) {
- if ( zSig < 2 ) {
- zSig = LIT64( 0xFFFFFFFFFFFFFFFF );
- }
- else {
- aSig <<= 2;
- mul64To128( zSig, zSig, &term0, &term1 );
- sub128( aSig, 0, term0, term1, &rem0, &rem1 );
- while ( (sbits64) rem0 < 0 ) {
- --zSig;
- shortShift128Left( 0, zSig, 1, &term0, &term1 );
- term1 |= 1;
- add128( rem0, rem1, term0, term1, &rem0, &rem1 );
- }
- zSig |= ( ( rem0 | rem1 ) != 0 );
- }
- }
- shift64RightJamming( zSig, 1, &zSig );
- return roundAndPackFloat64( 0, zExp, zSig );
-
-}
-
-/*
--------------------------------------------------------------------------------
-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 )
-{
-
- 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 );
- }
- 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 )
-{
- flag aSign, bSign;
-
- if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
- || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
- ) {
- float_raise( float_flag_invalid );
- 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 )
-{
- flag aSign, bSign;
-
- if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
- || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
- ) {
- float_raise( float_flag_invalid );
- 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 )
-{
-
- if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
- || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
- ) {
- float_raise( float_flag_invalid );
- 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 )
-{
- flag aSign, bSign;
- //int16 aExp, bExp;
-
- 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 );
- }
- 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 )
-{
- 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 );
- }
- 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 )
-{
- 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 );
-
-}
-
-/*
--------------------------------------------------------------------------------
-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 )
-{
- flag aSign;
- int32 aExp, shiftCount;
- bits64 aSig, savedASig;
- int32 z;
-
- aSig = extractFloatx80Frac( a );
- aExp = extractFloatx80Exp( a );
- aSign = extractFloatx80Sign( a );
- shiftCount = 0x403E - aExp;
- if ( shiftCount < 32 ) {
- if ( ( aExp == 0x7FFF ) && (bits64) ( aSig<<1 ) ) aSign = 0;
- goto invalid;
- }
- else if ( 63 < shiftCount ) {
- if ( aExp || aSig ) float_exception_flags |= float_flag_inexact;
- return 0;
- }
- savedASig = aSig;
- aSig >>= shiftCount;
- z = aSig;
- if ( aSign ) z = - z;
- if ( ( z < 0 ) ^ aSign ) {
- invalid:
- float_exception_flags |= float_flag_invalid;
- return aSign ? 0x80000000 : 0x7FFFFFFF;
- }
- if ( ( aSig<<shiftCount ) != savedASig ) {
- float_exception_flags |= float_flag_inexact;
- }
- 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 )
-{
- 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 ) );
- }
- return packFloat32( aSign, 0xFF, 0 );
- }
- shift64RightJamming( aSig, 33, &aSig );
- if ( aExp || aSig ) aExp -= 0x3F81;
- return roundAndPackFloat32( aSign, aExp, aSig );
-
-}
-
-/*
--------------------------------------------------------------------------------
-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 )
-{
- 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 ) );
- }
- return packFloat64( aSign, 0x7FF, 0 );
- }
- shift64RightJamming( aSig, 1, &zSig );
- if ( aExp || aSig ) aExp -= 0x3C01;
- return roundAndPackFloat64( aSign, aExp, zSig );
-
-}
-
-/*
--------------------------------------------------------------------------------
-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 )
-{
- 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 );
- }
- return a;
- }
- if ( aExp <= 0x3FFE ) {
- if ( ( aExp == 0 )
- && ( (bits64) ( extractFloatx80Frac( a )<<1 ) == 0 ) ) {
- return a;
- }
- float_exception_flags |= float_flag_inexact;
- aSign = extractFloatx80Sign( a );
- switch ( 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 = 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 ) 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 true, 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 )
-{
- 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 );
- 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 );
- 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 );
- }
- 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(
- floatx80_rounding_precision, zSign, zExp, zSig0, zSig1 );
-
-}
-
-/*
--------------------------------------------------------------------------------
-Returns the result of subtracting the absolute values of the extended
-double-precision floating-point values `a' and `b'. If `zSign' is true,
-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 )
-{
- 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 );
- }
- float_raise( float_flag_invalid );
- 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( float_rounding_mode == float_round_down, 0, 0 );
- bExpBigger:
- if ( bExp == 0x7FFF ) {
- if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b );
- 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 );
- 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(
- floatx80_rounding_precision, zSign, zExp, zSig0, zSig1 );
-
-}
-
-/*
--------------------------------------------------------------------------------
-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 )
-{
- flag aSign, bSign;
-
- aSign = extractFloatx80Sign( a );
- bSign = extractFloatx80Sign( b );
- if ( aSign == bSign ) {
- return addFloatx80Sigs( a, b, aSign );
- }
- else {
- return subFloatx80Sigs( a, b, aSign );
- }
-
-}
-
-/*
--------------------------------------------------------------------------------
-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 )
-{
- flag aSign, bSign;
-
- aSign = extractFloatx80Sign( a );
- bSign = extractFloatx80Sign( b );
- if ( aSign == bSign ) {
- return subFloatx80Sigs( a, b, aSign );
- }
- else {
- return addFloatx80Sigs( a, b, aSign );
- }
-
-}
-
-/*
--------------------------------------------------------------------------------
-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 )
-{
- 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 );
- }
- if ( ( bExp | bSig ) == 0 ) goto invalid;
- return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
- }
- if ( bExp == 0x7FFF ) {
- if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b );
- if ( ( aExp | aSig ) == 0 ) {
- invalid:
- float_raise( float_flag_invalid );
- 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(
- floatx80_rounding_precision, zSign, zExp, zSig0, zSig1 );
-
-}
-
-/*
--------------------------------------------------------------------------------
-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 )
-{
- 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 );
- if ( bExp == 0x7FFF ) {
- if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b );
- goto invalid;
- }
- return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
- }
- if ( bExp == 0x7FFF ) {
- if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b );
- return packFloatx80( zSign, 0, 0 );
- }
- if ( bExp == 0 ) {
- if ( bSig == 0 ) {
- if ( ( aExp | aSig ) == 0 ) {
- invalid:
- float_raise( float_flag_invalid );
- z.low = floatx80_default_nan_low;
- z.high = floatx80_default_nan_high;
- return z;
- }
- float_raise( float_flag_divbyzero );
- 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(
- floatx80_rounding_precision, zSign, zExp, zSig0, zSig1 );
-
-}
-
-/*
--------------------------------------------------------------------------------
-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 )
-{
- 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 );
- }
- goto invalid;
- }
- if ( bExp == 0x7FFF ) {
- if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b );
- return a;
- }
- if ( bExp == 0 ) {
- if ( bSig == 0 ) {
- invalid:
- float_raise( float_flag_invalid );
- 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 );
-
-}
-
-/*
--------------------------------------------------------------------------------
-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 )
-{
- flag aSign;
- int32 aExp, zExp;
- bits64 aSig0, aSig1, zSig0, zSig1;
- bits64 rem0, rem1, rem2, rem3, term0, term1, term2, term3;
- bits64 shiftedRem0, shiftedRem1;
- floatx80 z;
-
- aSig0 = extractFloatx80Frac( a );
- aExp = extractFloatx80Exp( a );
- aSign = extractFloatx80Sign( a );
- if ( aExp == 0x7FFF ) {
- if ( (bits64) ( aSig0<<1 ) ) return propagateFloatx80NaN( a, a );
- if ( ! aSign ) return a;
- goto invalid;
- }
- if ( aSign ) {
- if ( ( aExp | aSig0 ) == 0 ) return a;
- invalid:
- float_raise( float_flag_invalid );
- 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 );
- zSig0 <<= 31;
- aSig1 = 0;
- shift128Right( aSig0, 0, ( aExp & 1 ) + 2, &aSig0, &aSig1 );
- zSig0 = estimateDiv128To64( aSig0, aSig1, zSig0 ) + zSig0 + 4;
- if ( 0 <= (sbits64) zSig0 ) zSig0 = LIT64( 0xFFFFFFFFFFFFFFFF );
- shortShift128Left( aSig0, aSig1, 2, &aSig0, &aSig1 );
- mul64To128( zSig0, zSig0, &term0, &term1 );
- sub128( aSig0, aSig1, term0, term1, &rem0, &rem1 );
- while ( (sbits64) rem0 < 0 ) {
- --zSig0;
- shortShift128Left( 0, zSig0, 1, &term0, &term1 );
- term1 |= 1;
- add128( rem0, rem1, term0, term1, &rem0, &rem1 );
- }
- shortShift128Left( rem0, rem1, 63, &shiftedRem0, &shiftedRem1 );
- zSig1 = estimateDiv128To64( shiftedRem0, shiftedRem1, zSig0 );
- if ( (bits64) ( zSig1<<1 ) <= 10 ) {
- if ( zSig1 == 0 ) zSig1 = 1;
- mul64To128( zSig0, zSig1, &term1, &term2 );
- shortShift128Left( term1, term2, 1, &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;
- shortShift192Left( 0, zSig0, zSig1, 1, &term1, &term2, &term3 );
- term3 |= 1;
- add192(
- rem1, rem2, rem3, term1, term2, term3, &rem1, &rem2, &rem3 );
- }
- zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 );
- }
- return
- roundAndPackFloatx80(
- floatx80_rounding_precision, 0, zExp, zSig0, zSig1 );
-
-}
-
-/*
--------------------------------------------------------------------------------
-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 )
-{
-
- 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 );
- }
- 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 )
-{
- flag aSign, bSign;
-
- if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
- && (bits64) ( extractFloatx80Frac( a )<<1 ) )
- || ( ( extractFloatx80Exp( b ) == 0x7FFF )
- && (bits64) ( extractFloatx80Frac( b )<<1 ) )
- ) {
- float_raise( float_flag_invalid );
- 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 )
-{
- flag aSign, bSign;
-
- if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
- && (bits64) ( extractFloatx80Frac( a )<<1 ) )
- || ( ( extractFloatx80Exp( b ) == 0x7FFF )
- && (bits64) ( extractFloatx80Frac( b )<<1 ) )
- ) {
- float_raise( float_flag_invalid );
- 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 )
-{
-
- if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
- && (bits64) ( extractFloatx80Frac( a )<<1 ) )
- || ( ( extractFloatx80Exp( b ) == 0x7FFF )
- && (bits64) ( extractFloatx80Frac( b )<<1 ) )
- ) {
- float_raise( float_flag_invalid );
- 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 )
-{
- 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 );
- }
- 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 )
-{
- 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 );
- }
- 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
-
projects / sdk / emulator / qemu.git / commitdiff