diff options
Diffstat (limited to 'StdLib/LibC/Softfloat/bits32')
| -rw-r--r-- | StdLib/LibC/Softfloat/bits32/softfloat-macros | 648 | ||||
| -rw-r--r-- | StdLib/LibC/Softfloat/bits32/softfloat.c | 2355 |
2 files changed, 3003 insertions, 0 deletions
diff --git a/StdLib/LibC/Softfloat/bits32/softfloat-macros b/StdLib/LibC/Softfloat/bits32/softfloat-macros new file mode 100644 index 0000000000..8e1f2d8b9a --- /dev/null +++ b/StdLib/LibC/Softfloat/bits32/softfloat-macros @@ -0,0 +1,648 @@ +
+/*
+===============================================================================
+
+This C source fragment is part of the SoftFloat IEC/IEEE Floating-point
+Arithmetic Package, Release 2a.
+
+Written by John R. Hauser. This work was made possible in part by the
+International Computer Science Institute, located at Suite 600, 1947 Center
+Street, Berkeley, California 94704. Funding was partially provided by the
+National Science Foundation under grant MIP-9311980. The original version
+of this code was written as part of a project to build a fixed-point vector
+processor in collaboration with the University of California at Berkeley,
+overseen by Profs. Nelson Morgan and John Wawrzynek. More information
+is available through the Web page `http://HTTP.CS.Berkeley.EDU/~jhauser/
+arithmetic/SoftFloat.html'.
+
+THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort
+has been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT
+TIMES RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO
+PERSONS AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ANY
+AND ALL LOSSES, COSTS, OR OTHER PROBLEMS ARISING FROM ITS USE.
+
+Derivative works are acceptable, even for commercial purposes, so long as
+(1) they include prominent notice that the work is derivative, and (2) they
+include prominent notice akin to these four paragraphs for those parts of
+this code that are retained.
+
+===============================================================================
+*/
+
+/*
+-------------------------------------------------------------------------------
+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 the 64-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 64, the result will be 0. The result is broken into two 32-bit pieces
+which are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
+-------------------------------------------------------------------------------
+*/
+INLINE void
+ shift64Right(
+ bits32 a0, bits32 a1, int16 count, bits32 *z0Ptr, bits32 *z1Ptr )
+{
+ bits32 z0, z1;
+ int8 negCount = ( - count ) & 31;
+
+ if ( count == 0 ) {
+ z1 = a1;
+ z0 = a0;
+ }
+ else if ( count < 32 ) {
+ z1 = ( a0<<negCount ) | ( a1>>count );
+ z0 = a0>>count;
+ }
+ else {
+ z1 = ( count < 64 ) ? ( a0>>( count & 31 ) ) : 0;
+ z0 = 0;
+ }
+ *z1Ptr = z1;
+ *z0Ptr = z0;
+
+}
+
+/*
+-------------------------------------------------------------------------------
+Shifts the 64-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 64, 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 32-bit pieces which are stored at
+the locations pointed to by `z0Ptr' and `z1Ptr'.
+-------------------------------------------------------------------------------
+*/
+INLINE void
+ shift64RightJamming(
+ bits32 a0, bits32 a1, int16 count, bits32 *z0Ptr, bits32 *z1Ptr )
+{
+ bits32 z0, z1;
+ int8 negCount = ( - count ) & 31;
+
+ if ( count == 0 ) {
+ z1 = a1;
+ z0 = a0;
+ }
+ else if ( count < 32 ) {
+ z1 = ( a0<<negCount ) | ( a1>>count ) | ( ( a1<<negCount ) != 0 );
+ z0 = a0>>count;
+ }
+ else {
+ if ( count == 32 ) {
+ z1 = a0 | ( a1 != 0 );
+ }
+ else if ( count < 64 ) {
+ z1 = ( a0>>( count & 31 ) ) | ( ( ( a0<<negCount ) | a1 ) != 0 );
+ }
+ else {
+ z1 = ( ( a0 | a1 ) != 0 );
+ }
+ z0 = 0;
+ }
+ *z1Ptr = z1;
+ *z0Ptr = z0;
+
+}
+
+/*
+-------------------------------------------------------------------------------
+Shifts the 96-bit value formed by concatenating `a0', `a1', and `a2' right
+by 32 _plus_ the number of bits given in `count'. The shifted result is
+at most 64 nonzero bits; these are broken into two 32-bit pieces which are
+stored at the locations pointed to by `z0Ptr' and `z1Ptr'. The bits shifted
+off form a third 32-bit result as follows: The _last_ bit shifted off is
+the most-significant bit of the extra result, and the other 31 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
+ shift64ExtraRightJamming(
+ bits32 a0,
+ bits32 a1,
+ bits32 a2,
+ int16 count,
+ bits32 *z0Ptr,
+ bits32 *z1Ptr,
+ bits32 *z2Ptr
+ )
+{
+ bits32 z0, z1, z2;
+ int8 negCount = ( - count ) & 31;
+
+ if ( count == 0 ) {
+ z2 = a2;
+ z1 = a1;
+ z0 = a0;
+ }
+ else {
+ if ( count < 32 ) {
+ z2 = a1<<negCount;
+ z1 = ( a0<<negCount ) | ( a1>>count );
+ z0 = a0>>count;
+ }
+ else {
+ if ( count == 32 ) {
+ z2 = a1;
+ z1 = a0;
+ }
+ else {
+ a2 |= a1;
+ if ( count < 64 ) {
+ z2 = a0<<negCount;
+ z1 = a0>>( count & 31 );
+ }
+ else {
+ z2 = ( count == 64 ) ? a0 : ( a0 != 0 );
+ z1 = 0;
+ }
+ }
+ z0 = 0;
+ }
+ z2 |= ( a2 != 0 );
+ }
+ *z2Ptr = z2;
+ *z1Ptr = z1;
+ *z0Ptr = z0;
+
+}
+
+/*
+-------------------------------------------------------------------------------
+Shifts the 64-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 32. The result is broken into two 32-bit
+pieces which are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
+-------------------------------------------------------------------------------
+*/
+INLINE void
+ shortShift64Left(
+ bits32 a0, bits32 a1, int16 count, bits32 *z0Ptr, bits32 *z1Ptr )
+{
+
+ *z1Ptr = a1<<count;
+ *z0Ptr =
+ ( count == 0 ) ? a0 : ( a0<<count ) | ( a1>>( ( - count ) & 31 ) );
+
+}
+
+/*
+-------------------------------------------------------------------------------
+Shifts the 96-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 32. The result is broken into three
+32-bit pieces which are stored at the locations pointed to by `z0Ptr',
+`z1Ptr', and `z2Ptr'.
+-------------------------------------------------------------------------------
+*/
+INLINE void
+ shortShift96Left(
+ bits32 a0,
+ bits32 a1,
+ bits32 a2,
+ int16 count,
+ bits32 *z0Ptr,
+ bits32 *z1Ptr,
+ bits32 *z2Ptr
+ )
+{
+ bits32 z0, z1, z2;
+ int8 negCount;
+
+ z2 = a2<<count;
+ z1 = a1<<count;
+ z0 = a0<<count;
+ if ( 0 < count ) {
+ negCount = ( ( - count ) & 31 );
+ z1 |= a2>>negCount;
+ z0 |= a1>>negCount;
+ }
+ *z2Ptr = z2;
+ *z1Ptr = z1;
+ *z0Ptr = z0;
+
+}
+
+/*
+-------------------------------------------------------------------------------
+Adds the 64-bit value formed by concatenating `a0' and `a1' to the 64-bit
+value formed by concatenating `b0' and `b1'. Addition is modulo 2^64, so
+any carry out is lost. The result is broken into two 32-bit pieces which
+are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
+-------------------------------------------------------------------------------
+*/
+INLINE void
+ add64(
+ bits32 a0, bits32 a1, bits32 b0, bits32 b1, bits32 *z0Ptr, bits32 *z1Ptr )
+{
+ bits32 z1;
+
+ z1 = a1 + b1;
+ *z1Ptr = z1;
+ *z0Ptr = a0 + b0 + ( z1 < a1 );
+
+}
+
+/*
+-------------------------------------------------------------------------------
+Adds the 96-bit value formed by concatenating `a0', `a1', and `a2' to the
+96-bit value formed by concatenating `b0', `b1', and `b2'. Addition is
+modulo 2^96, so any carry out is lost. The result is broken into three
+32-bit pieces which are stored at the locations pointed to by `z0Ptr',
+`z1Ptr', and `z2Ptr'.
+-------------------------------------------------------------------------------
+*/
+INLINE void
+ add96(
+ bits32 a0,
+ bits32 a1,
+ bits32 a2,
+ bits32 b0,
+ bits32 b1,
+ bits32 b2,
+ bits32 *z0Ptr,
+ bits32 *z1Ptr,
+ bits32 *z2Ptr
+ )
+{
+ bits32 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 < (bits32)carry1 );
+ z0 += carry0;
+ *z2Ptr = z2;
+ *z1Ptr = z1;
+ *z0Ptr = z0;
+
+}
+
+/*
+-------------------------------------------------------------------------------
+Subtracts the 64-bit value formed by concatenating `b0' and `b1' from the
+64-bit value formed by concatenating `a0' and `a1'. Subtraction is modulo
+2^64, so any borrow out (carry out) is lost. The result is broken into two
+32-bit pieces which are stored at the locations pointed to by `z0Ptr' and
+`z1Ptr'.
+-------------------------------------------------------------------------------
+*/
+INLINE void
+ sub64(
+ bits32 a0, bits32 a1, bits32 b0, bits32 b1, bits32 *z0Ptr, bits32 *z1Ptr )
+{
+
+ *z1Ptr = a1 - b1;
+ *z0Ptr = a0 - b0 - ( a1 < b1 );
+
+}
+
+/*
+-------------------------------------------------------------------------------
+Subtracts the 96-bit value formed by concatenating `b0', `b1', and `b2' from
+the 96-bit value formed by concatenating `a0', `a1', and `a2'. Subtraction
+is modulo 2^96, so any borrow out (carry out) is lost. The result is broken
+into three 32-bit pieces which are stored at the locations pointed to by
+`z0Ptr', `z1Ptr', and `z2Ptr'.
+-------------------------------------------------------------------------------
+*/
+INLINE void
+ sub96(
+ bits32 a0,
+ bits32 a1,
+ bits32 a2,
+ bits32 b0,
+ bits32 b1,
+ bits32 b2,
+ bits32 *z0Ptr,
+ bits32 *z1Ptr,
+ bits32 *z2Ptr
+ )
+{
+ bits32 z0, z1, z2;
+ int8 borrow0, borrow1;
+
+ z2 = a2 - b2;
+ borrow1 = ( a2 < b2 );
+ z1 = a1 - b1;
+ borrow0 = ( a1 < b1 );
+ z0 = a0 - b0;
+ z0 -= ( z1 < (bits32)borrow1 );
+ z1 -= borrow1;
+ z0 -= borrow0;
+ *z2Ptr = z2;
+ *z1Ptr = z1;
+ *z0Ptr = z0;
+
+}
+
+/*
+-------------------------------------------------------------------------------
+Multiplies `a' by `b' to obtain a 64-bit product. The product is broken
+into two 32-bit pieces which are stored at the locations pointed to by
+`z0Ptr' and `z1Ptr'.
+-------------------------------------------------------------------------------
+*/
+INLINE void mul32To64( bits32 a, bits32 b, bits32 *z0Ptr, bits32 *z1Ptr )
+{
+ bits16 aHigh, aLow, bHigh, bLow;
+ bits32 z0, zMiddleA, zMiddleB, z1;
+
+ aLow = a;
+ aHigh = a>>16;
+ bLow = b;
+ bHigh = b>>16;
+ z1 = ( (bits32) aLow ) * bLow;
+ zMiddleA = ( (bits32) aLow ) * bHigh;
+ zMiddleB = ( (bits32) aHigh ) * bLow;
+ z0 = ( (bits32) aHigh ) * bHigh;
+ zMiddleA += zMiddleB;
+ z0 += ( ( (bits32) ( zMiddleA < zMiddleB ) )<<16 ) + ( zMiddleA>>16 );
+ zMiddleA <<= 16;
+ z1 += zMiddleA;
+ z0 += ( z1 < zMiddleA );
+ *z1Ptr = z1;
+ *z0Ptr = z0;
+
+}
+
+/*
+-------------------------------------------------------------------------------
+Multiplies the 64-bit value formed by concatenating `a0' and `a1' by `b'
+to obtain a 96-bit product. The product is broken into three 32-bit pieces
+which are stored at the locations pointed to by `z0Ptr', `z1Ptr', and
+`z2Ptr'.
+-------------------------------------------------------------------------------
+*/
+INLINE void
+ mul64By32To96(
+ bits32 a0,
+ bits32 a1,
+ bits32 b,
+ bits32 *z0Ptr,
+ bits32 *z1Ptr,
+ bits32 *z2Ptr
+ )
+{
+ bits32 z0, z1, z2, more1;
+
+ mul32To64( a1, b, &z1, &z2 );
+ mul32To64( a0, b, &z0, &more1 );
+ add64( z0, more1, 0, z1, &z0, &z1 );
+ *z2Ptr = z2;
+ *z1Ptr = z1;
+ *z0Ptr = z0;
+
+}
+
+/*
+-------------------------------------------------------------------------------
+Multiplies the 64-bit value formed by concatenating `a0' and `a1' to the
+64-bit value formed by concatenating `b0' and `b1' to obtain a 128-bit
+product. The product is broken into four 32-bit pieces which are stored at
+the locations pointed to by `z0Ptr', `z1Ptr', `z2Ptr', and `z3Ptr'.
+-------------------------------------------------------------------------------
+*/
+INLINE void
+ mul64To128(
+ bits32 a0,
+ bits32 a1,
+ bits32 b0,
+ bits32 b1,
+ bits32 *z0Ptr,
+ bits32 *z1Ptr,
+ bits32 *z2Ptr,
+ bits32 *z3Ptr
+ )
+{
+ bits32 z0, z1, z2, z3;
+ bits32 more1, more2;
+
+ mul32To64( a1, b1, &z2, &z3 );
+ mul32To64( a1, b0, &z1, &more2 );
+ add64( z1, more2, 0, z2, &z1, &z2 );
+ mul32To64( a0, b0, &z0, &more1 );
+ add64( z0, more1, 0, z1, &z0, &z1 );
+ mul32To64( a0, b1, &more1, &more2 );
+ add64( more1, more2, 0, z2, &more1, &z2 );
+ add64( z0, z1, 0, more1, &z0, &z1 );
+ *z3Ptr = z3;
+ *z2Ptr = z2;
+ *z1Ptr = z1;
+ *z0Ptr = z0;
+
+}
+
+/*
+-------------------------------------------------------------------------------
+Returns an approximation to the 32-bit integer quotient obtained by dividing
+`b' into the 64-bit value formed by concatenating `a0' and `a1'. The
+divisor `b' must be at least 2^31. 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 32 bits, the maximum positive 32-bit
+unsigned integer is returned.
+-------------------------------------------------------------------------------
+*/
+static bits32 estimateDiv64To32( bits32 a0, bits32 a1, bits32 b )
+{
+ bits32 b0, b1;
+ bits32 rem0, rem1, term0, term1;
+ bits32 z;
+
+ if ( b <= a0 ) return 0xFFFFFFFF;
+ b0 = b>>16;
+ z = ( b0<<16 <= a0 ) ? 0xFFFF0000 : ( a0 / b0 )<<16;
+ mul32To64( b, z, &term0, &term1 );
+ sub64( a0, a1, term0, term1, &rem0, &rem1 );
+ while ( ( (sbits32) rem0 ) < 0 ) {
+ z -= 0x10000;
+ b1 = b<<16;
+ add64( rem0, rem1, b0, b1, &rem0, &rem1 );
+ }
+ rem0 = ( rem0<<16 ) | ( rem1>>16 );
+ z |= ( b0<<16 <= rem0 ) ? 0xFFFF : rem0 / b0;
+ return z;
+
+}
+
+#ifndef SOFTFLOAT_FOR_GCC
+/*
+-------------------------------------------------------------------------------
+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 ( ( estimateDiv64To32( a, 0, z ) )>>1 ) + ( z>>1 );
+
+}
+#endif
+
+/*
+-------------------------------------------------------------------------------
+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 1 if the 64-bit value formed by concatenating `a0' and `a1' is
+equal to the 64-bit value formed by concatenating `b0' and `b1'. Otherwise,
+returns 0.
+-------------------------------------------------------------------------------
+*/
+INLINE flag eq64( bits32 a0, bits32 a1, bits32 b0, bits32 b1 )
+{
+
+ return ( a0 == b0 ) && ( a1 == b1 );
+
+}
+
+/*
+-------------------------------------------------------------------------------
+Returns 1 if the 64-bit value formed by concatenating `a0' and `a1' is less
+than or equal to the 64-bit value formed by concatenating `b0' and `b1'.
+Otherwise, returns 0.
+-------------------------------------------------------------------------------
+*/
+INLINE flag le64( bits32 a0, bits32 a1, bits32 b0, bits32 b1 )
+{
+
+ return ( a0 < b0 ) || ( ( a0 == b0 ) && ( a1 <= b1 ) );
+
+}
+
+/*
+-------------------------------------------------------------------------------
+Returns 1 if the 64-bit value formed by concatenating `a0' and `a1' is less
+than the 64-bit value formed by concatenating `b0' and `b1'. Otherwise,
+returns 0.
+-------------------------------------------------------------------------------
+*/
+INLINE flag lt64( bits32 a0, bits32 a1, bits32 b0, bits32 b1 )
+{
+
+ return ( a0 < b0 ) || ( ( a0 == b0 ) && ( a1 < b1 ) );
+
+}
+
+/*
+-------------------------------------------------------------------------------
+Returns 1 if the 64-bit value formed by concatenating `a0' and `a1' is not
+equal to the 64-bit value formed by concatenating `b0' and `b1'. Otherwise,
+returns 0.
+-------------------------------------------------------------------------------
+*/
+INLINE flag ne64( bits32 a0, bits32 a1, bits32 b0, bits32 b1 )
+{
+
+ return ( a0 != b0 ) || ( a1 != b1 );
+
+}
+
diff --git a/StdLib/LibC/Softfloat/bits32/softfloat.c b/StdLib/LibC/Softfloat/bits32/softfloat.c new file mode 100644 index 0000000000..a513bf94e1 --- /dev/null +++ b/StdLib/LibC/Softfloat/bits32/softfloat.c @@ -0,0 +1,2355 @@ +/* $NetBSD: softfloat.c,v 1.3 2013/01/10 08:16:11 matt Exp $ */
+
+/*
+ * This version hacked for use with gcc -msoft-float by bjh21.
+ * (Mostly a case of #ifdefing out things GCC doesn't need or provides
+ * itself).
+ */
+
+/*
+ * Things you may want to define:
+ *
+ * SOFTFLOAT_FOR_GCC - build only those functions necessary for GCC (with
+ * -msoft-float) to work. Include "softfloat-for-gcc.h" to get them
+ * properly renamed.
+ */
+
+/*
+ * This differs from the standard bits32/softfloat.c in that float64
+ * is defined to be a 64-bit integer rather than a structure. The
+ * structure is float64s, with translation between the two going via
+ * float64u.
+ */
+
+/*
+===============================================================================
+
+This C source file is part of the SoftFloat IEC/IEEE Floating-Point
+Arithmetic Package, Release 2a.
+
+Written by John R. Hauser. This work was made possible in part by the
+International Computer Science Institute, located at Suite 600, 1947 Center
+Street, Berkeley, California 94704. Funding was partially provided by the
+National Science Foundation under grant MIP-9311980. The original version
+of this code was written as part of a project to build a fixed-point vector
+processor in collaboration with the University of California at Berkeley,
+overseen by Profs. Nelson Morgan and John Wawrzynek. More information
+is available through the Web page `http://HTTP.CS.Berkeley.EDU/~jhauser/
+arithmetic/SoftFloat.html'.
+
+THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort
+has been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT
+TIMES RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO
+PERSONS AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ANY
+AND ALL LOSSES, COSTS, OR OTHER PROBLEMS ARISING FROM ITS USE.
+
+Derivative works are acceptable, even for commercial purposes, so long as
+(1) they include prominent notice that the work is derivative, and (2) they
+include prominent notice akin to these four paragraphs for those parts of
+this code that are retained.
+
+===============================================================================
+*/
+
+#include <sys/cdefs.h>
+#if defined(LIBC_SCCS) && !defined(lint)
+__RCSID("$NetBSD: softfloat.c,v 1.3 2013/01/10 08:16:11 matt Exp $");
+#endif /* LIBC_SCCS and not lint */
+
+#ifdef SOFTFLOAT_FOR_GCC
+#include "softfloat-for-gcc.h"
+#endif
+
+#include "milieu.h"
+#include "softfloat.h"
+
+/*
+ * Conversions between floats as stored in memory and floats as
+ * SoftFloat uses them
+ */
+#ifndef FLOAT64_DEMANGLE
+#define FLOAT64_DEMANGLE(a) (a)
+#endif
+#ifndef FLOAT64_MANGLE
+#define FLOAT64_MANGLE(a) (a)
+#endif
+
+/*
+-------------------------------------------------------------------------------
+Floating-point rounding mode and exception flags.
+-------------------------------------------------------------------------------
+*/
+#ifndef set_float_rounding_mode
+fp_rnd float_rounding_mode = float_round_nearest_even;
+fp_except float_exception_flags = 0;
+#endif
+#ifndef set_float_exception_inexact_flag
+#define set_float_exception_inexact_flag() \
+ ((void)(float_exception_flags |= float_flag_inexact))
+#endif
+
+/*
+-------------------------------------------------------------------------------
+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 (4) how NaNs
+are propagated from function inputs to output. These details are target-
+specific.
+-------------------------------------------------------------------------------
+*/
+#include "softfloat-specialize"
+
+/*
+-------------------------------------------------------------------------------
+Returns the fraction bits of the single-precision floating-point value `a'.
+-------------------------------------------------------------------------------
+*/
+INLINE bits32 extractFloat32Frac( float32 a )
+{
+
+ return a & 0x007FFFFF;
+
+}
+
+/*
+-------------------------------------------------------------------------------
+Returns the exponent bits of the single-precision floating-point value `a'.
+-------------------------------------------------------------------------------
+*/
+INLINE int16 extractFloat32Exp( float32 a )
+{
+
+ return ( a>>23 ) & 0xFF;
+
+}
+
+/*
+-------------------------------------------------------------------------------
+Returns the sign bit of the single-precision floating-point value `a'.
+-------------------------------------------------------------------------------
+*/
+INLINE flag extractFloat32Sign( float32 a )
+{
+
+ return a>>31;
+
+}
+
+/*
+-------------------------------------------------------------------------------
+Normalizes the subnormal single-precision floating-point value represented
+by the denormalized significand `aSig'. The normalized exponent and
+significand are stored at the locations pointed to by `zExpPtr' and
+`zSigPtr', respectively.
+-------------------------------------------------------------------------------
+*/
+static void
+ normalizeFloat32Subnormal( bits32 aSig, int16 *zExpPtr, bits32 *zSigPtr )
+{
+ int8 shiftCount;
+
+ shiftCount = countLeadingZeros32( aSig ) - 8;
+ *zSigPtr = aSig<<shiftCount;
+ *zExpPtr = 1 - shiftCount;
+
+}
+
+/*
+-------------------------------------------------------------------------------
+Packs the sign `zSign', exponent `zExp', and significand `zSig' into a
+single-precision floating-point value, returning the result. After being
+shifted into the proper positions, the three fields are simply added
+together to form the result. This means that any integer portion of `zSig'
+will be added into the exponent. Since a properly normalized significand
+will have an integer portion equal to 1, the `zExp' input should be 1 less
+than the desired result exponent whenever `zSig' is a complete, normalized
+significand.
+-------------------------------------------------------------------------------
+*/
+INLINE float32 packFloat32( flag zSign, int16 zExp, bits32 zSig )
+{
+
+ return ( ( (bits32) zSign )<<31 ) + ( ( (bits32) zExp )<<23 ) + zSig;
+
+}
+
+/*
+-------------------------------------------------------------------------------
+Takes an abstract floating-point value having sign `zSign', exponent `zExp',
+and significand `zSig', and returns the proper single-precision floating-
+point value corresponding to the abstract input. Ordinarily, the abstract
+value is simply rounded and packed into the single-precision format, with
+the inexact exception raised if the abstract input cannot be represented
+exactly. However, if the abstract value is too large, the overflow and
+inexact exceptions are raised and an infinity or maximal finite value is
+returned. If the abstract value is too small, the input value is rounded to
+a subnormal number, and the underflow and inexact exceptions are raised if
+the abstract input cannot be represented exactly as a subnormal single-
+precision floating-point number.
+ The input significand `zSig' has its binary point between bits 30
+and 29, which is 7 bits to the left of the usual location. This shifted
+significand must be normalized or smaller. If `zSig' is not normalized,
+`zExp' must be 0; in that case, the result returned is a subnormal number,
+and it must not require rounding. In the usual case that `zSig' is
+normalized, `zExp' must be 1 less than the ``true'' floating-point exponent.
+The handling of underflow and overflow follows the IEC/IEEE Standard for
+Binary Floating-Point Arithmetic.
+-------------------------------------------------------------------------------
+*/
+static float32 roundAndPackFloat32( flag zSign, int16 zExp, bits32 zSig )
+{
+ 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 < (uint32)0x80000000 );
+ shift32RightJamming( zSig, - zExp, &zSig );
+ zExp = 0;
+ roundBits = zSig & 0x7F;
+ if ( isTiny && roundBits ) float_raise( float_flag_underflow );
+ }
+ }
+ if ( roundBits ) set_float_exception_inexact_flag();
+ zSig = ( zSig + roundIncrement )>>7;
+ zSig &= ~ ( ( ( roundBits ^ 0x40 ) == 0 ) & roundNearestEven );
+ if ( zSig == 0 ) zExp = 0;
+ return packFloat32( zSign, zExp, zSig );
+
+}
+
+/*
+-------------------------------------------------------------------------------
+Takes an abstract floating-point value having sign `zSign', exponent `zExp',
+and significand `zSig', and returns the proper single-precision floating-
+point value corresponding to the abstract input. This routine is just like
+`roundAndPackFloat32' except that `zSig' does not have to be normalized.
+Bit 31 of `zSig' must be zero, and `zExp' must be 1 less than the ``true''
+floating-point exponent.
+-------------------------------------------------------------------------------
+*/
+static float32
+ normalizeRoundAndPackFloat32( flag zSign, int16 zExp, bits32 zSig )
+{
+ int8 shiftCount;
+
+ shiftCount = countLeadingZeros32( zSig ) - 1;
+ return roundAndPackFloat32( zSign, zExp - shiftCount, zSig<<shiftCount );
+
+}
+
+/*
+-------------------------------------------------------------------------------
+Returns the least-significant 32 fraction bits of the double-precision
+floating-point value `a'.
+-------------------------------------------------------------------------------
+*/
+INLINE bits32 extractFloat64Frac1( float64 a )
+{
+
+ return (bits32)(FLOAT64_DEMANGLE(a) & LIT64(0x00000000FFFFFFFF));
+
+}
+
+/*
+-------------------------------------------------------------------------------
+Returns the most-significant 20 fraction bits of the double-precision
+floating-point value `a'.
+-------------------------------------------------------------------------------
+*/
+INLINE bits32 extractFloat64Frac0( float64 a )
+{
+
+ return (bits32)((FLOAT64_DEMANGLE(a) >> 32) & 0x000FFFFF);
+
+}
+
+/*
+-------------------------------------------------------------------------------
+Returns the exponent bits of the double-precision floating-point value `a'.
+-------------------------------------------------------------------------------
+*/
+INLINE int16 extractFloat64Exp( float64 a )
+{
+
+ return (int16)((FLOAT64_DEMANGLE(a) >> 52) & 0x7FF);
+
+}
+
+/*
+-------------------------------------------------------------------------------
+Returns the sign bit of the double-precision floating-point value `a'.
+-------------------------------------------------------------------------------
+*/
+INLINE flag extractFloat64Sign( float64 a )
+{
+
+ return (flag)(FLOAT64_DEMANGLE(a) >> 63);
+
+}
+
+/*
+-------------------------------------------------------------------------------
+Normalizes the subnormal double-precision floating-point value represented
+by the denormalized significand formed by the concatenation of `aSig0' and
+`aSig1'. The normalized exponent is stored at the location pointed to by
+`zExpPtr'. The most significant 21 bits of the normalized significand are
+stored at the location pointed to by `zSig0Ptr', and the least significant
+32 bits of the normalized significand are stored at the location pointed to
+by `zSig1Ptr'.
+-------------------------------------------------------------------------------
+*/
+static void
+ normalizeFloat64Subnormal(
+ bits32 aSig0,
+ bits32 aSig1,
+ int16 *zExpPtr,
+ bits32 *zSig0Ptr,
+ bits32 *zSig1Ptr
+ )
+{
+ int8 shiftCount;
+
+ if ( aSig0 == 0 ) {
+ shiftCount = countLeadingZeros32( aSig1 ) - 11;
+ if ( shiftCount < 0 ) {
+ *zSig0Ptr = aSig1>>( - shiftCount );
+ *zSig1Ptr = aSig1<<( shiftCount & 31 );
+ }
+ else {
+ *zSig0Ptr = aSig1<<shiftCount;
+ *zSig1Ptr = 0;
+ }
+ *zExpPtr = - shiftCount - 31;
+ }
+ else {
+ shiftCount = countLeadingZeros32( aSig0 ) - 11;
+ shortShift64Left( aSig0, aSig1, shiftCount, zSig0Ptr, zSig1Ptr );
+ *zExpPtr = 1 - shiftCount;
+ }
+
+}
+
+/*
+-------------------------------------------------------------------------------
+Packs the sign `zSign', the exponent `zExp', and the significand formed by
+the concatenation of `zSig0' and `zSig1' into a double-precision floating-
+point value, returning the result. After being shifted into the proper
+positions, the three fields `zSign', `zExp', and `zSig0' are simply added
+together to form the most significant 32 bits of the result. This means
+that any integer portion of `zSig0' will be added into the exponent. Since
+a properly normalized significand will have an integer portion equal to 1,
+the `zExp' input should be 1 less than the desired result exponent whenever
+`zSig0' and `zSig1' concatenated form a complete, normalized significand.
+-------------------------------------------------------------------------------
+*/
+INLINE float64
+ packFloat64( flag zSign, int16 zExp, bits32 zSig0, bits32 zSig1 )
+{
+
+ return FLOAT64_MANGLE( ( ( (bits64) zSign )<<63 ) +
+ ( ( (bits64) zExp )<<52 ) +
+ ( ( (bits64) zSig0 )<<32 ) + zSig1 );
+
+
+}
+
+/*
+-------------------------------------------------------------------------------
+Takes an abstract floating-point value having sign `zSign', exponent `zExp',
+and extended significand formed by the concatenation of `zSig0', `zSig1',
+and `zSig2', and returns the proper double-precision floating-point value
+corresponding to the abstract input. Ordinarily, the abstract value is
+simply rounded and packed into the double-precision format, with the inexact
+exception raised if the abstract input cannot be represented exactly.
+However, if the abstract value is too large, the overflow and inexact
+exceptions are raised and an infinity or maximal finite value is returned.
+If the abstract value is too small, the input value is rounded to a
+subnormal number, and the underflow and inexact exceptions are raised if the
+abstract input cannot be represented exactly as a subnormal double-precision
+floating-point number.
+ The input significand must be normalized or smaller. If the input
+significand is not normalized, `zExp' must be 0; in that case, the result
+returned is a subnormal number, and it must not require rounding. In the
+usual case that the input significand is normalized, `zExp' must be 1 less
+than the ``true'' floating-point exponent. The handling of underflow and
+overflow follows the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+-------------------------------------------------------------------------------
+*/
+static float64
+ roundAndPackFloat64(
+ flag zSign, int16 zExp, bits32 zSig0, bits32 zSig1, bits32 zSig2 )
+{
+ int8 roundingMode;
+ flag roundNearestEven, increment, isTiny;
+
+ roundingMode = float_rounding_mode;
+ roundNearestEven = ( roundingMode == float_round_nearest_even );
+ increment = ( (sbits32) zSig2 < 0 );
+ if ( ! roundNearestEven ) {
+ if ( roundingMode == float_round_to_zero ) {
+ increment = 0;
+ }
+ else {
+ if ( zSign ) {
+ increment = ( roundingMode == float_round_down ) && zSig2;
+ }
+ else {
+ increment = ( roundingMode == float_round_up ) && zSig2;
+ }
+ }
+ }
+ if ( 0x7FD <= (bits16) zExp ) {
+ if ( ( 0x7FD < zExp )
+ || ( ( zExp == 0x7FD )
+ && eq64( 0x001FFFFF, 0xFFFFFFFF, zSig0, zSig1 )
+ && increment
+ )
+ ) {
+ 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 packFloat64( zSign, 0x7FE, 0x000FFFFF, 0xFFFFFFFF );
+ }
+ return packFloat64( zSign, 0x7FF, 0, 0 );
+ }
+ if ( zExp < 0 ) {
+ isTiny =
+ ( float_detect_tininess == float_tininess_before_rounding )
+ || ( zExp < -1 )
+ || ! increment
+ || lt64( zSig0, zSig1, 0x001FFFFF, 0xFFFFFFFF );
+ shift64ExtraRightJamming(
+ zSig0, zSig1, zSig2, - zExp, &zSig0, &zSig1, &zSig2 );
+ zExp = 0;
+ if ( isTiny && zSig2 ) float_raise( float_flag_underflow );
+ if ( roundNearestEven ) {
+ increment = ( (sbits32) zSig2 < 0 );
+ }
+ else {
+ if ( zSign ) {
+ increment = ( roundingMode == float_round_down ) && zSig2;
+ }
+ else {
+ increment = ( roundingMode == float_round_up ) && zSig2;
+ }
+ }
+ }
+ }
+ if ( zSig2 ) set_float_exception_inexact_flag();
+ if ( increment ) {
+ add64( zSig0, zSig1, 0, 1, &zSig0, &zSig1 );
+ zSig1 &= ~ ( ( zSig2 + zSig2 == 0 ) & roundNearestEven );
+ }
+ else {
+ if ( ( zSig0 | zSig1 ) == 0 ) zExp = 0;
+ }
+ return packFloat64( zSign, zExp, zSig0, zSig1 );
+
+}
+
+/*
+-------------------------------------------------------------------------------
+Takes an abstract floating-point value having sign `zSign', exponent `zExp',
+and significand formed by the concatenation of `zSig0' and `zSig1', and
+returns the proper double-precision floating-point value corresponding
+to the abstract input. This routine is just like `roundAndPackFloat64'
+except that the input significand has fewer bits and does not have to be
+normalized. In all cases, `zExp' must be 1 less than the ``true'' floating-
+point exponent.
+-------------------------------------------------------------------------------
+*/
+static float64
+ normalizeRoundAndPackFloat64(
+ flag zSign, int16 zExp, bits32 zSig0, bits32 zSig1 )
+{
+ int8 shiftCount;
+ bits32 zSig2;
+
+ if ( zSig0 == 0 ) {
+ zSig0 = zSig1;
+ zSig1 = 0;
+ zExp -= 32;
+ }
+ shiftCount = countLeadingZeros32( zSig0 ) - 11;
+ if ( 0 <= shiftCount ) {
+ zSig2 = 0;
+ shortShift64Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 );
+ }
+ else {
+ shift64ExtraRightJamming(
+ zSig0, zSig1, 0, - shiftCount, &zSig0, &zSig1, &zSig2 );
+ }
+ zExp -= shiftCount;
+ return roundAndPackFloat64( zSign, zExp, zSig0, zSig1, zSig2 );
+
+}
+
+/*
+-------------------------------------------------------------------------------
+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 == (sbits32) 0x80000000 ) return packFloat32( 1, 0x9E, 0 );
+ zSign = ( a < 0 );
+ return normalizeRoundAndPackFloat32(zSign, 0x9C, (uint32)(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 zSign;
+ bits32 absA;
+ int8 shiftCount;
+ bits32 zSig0, zSig1;
+
+ if ( a == 0 ) return packFloat64( 0, 0, 0, 0 );
+ zSign = ( a < 0 );
+ absA = zSign ? - a : a;
+ shiftCount = countLeadingZeros32( absA ) - 11;
+ if ( 0 <= shiftCount ) {
+ zSig0 = absA<<shiftCount;
+ zSig1 = 0;
+ }
+ else {
+ shift64Right( absA, 0, - shiftCount, &zSig0, &zSig1 );
+ }
+ return packFloat64( zSign, 0x412 - shiftCount, zSig0, zSig1 );
+
+}
+
+#ifndef SOFTFLOAT_FOR_GCC
+/*
+-------------------------------------------------------------------------------
+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, aSigExtra;
+ int32 z;
+ int8 roundingMode;
+
+ aSig = extractFloat32Frac( a );
+ aExp = extractFloat32Exp( a );
+ aSign = extractFloat32Sign( a );
+ shiftCount = aExp - 0x96;
+ if ( 0 <= shiftCount ) {
+ if ( 0x9E <= aExp ) {
+ if ( a != 0xCF000000 ) {
+ float_raise( float_flag_invalid );
+ if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) {
+ return 0x7FFFFFFF;
+ }
+ }
+ return (sbits32) 0x80000000;
+ }
+ z = ( aSig | 0x00800000 )<<shiftCount;
+ if ( aSign ) z = - z;
+ }
+ else {
+ if ( aExp < 0x7E ) {
+ aSigExtra = aExp | aSig;
+ z = 0;
+ }
+ else {
+ aSig |= 0x00800000;
+ aSigExtra = aSig<<( shiftCount & 31 );
+ z = aSig>>( - shiftCount );
+ }
+ if ( aSigExtra ) set_float_exception_inexact_flag();
+ roundingMode = float_rounding_mode;
+ if ( roundingMode == float_round_nearest_even ) {
+ if ( (sbits32) aSigExtra < 0 ) {
+ ++z;
+ if ( (bits32) ( aSigExtra<<1 ) == 0 ) z &= ~1;
+ }
+ if ( aSign ) z = - z;
+ }
+ else {
+ aSigExtra = ( aSigExtra != 0 );
+ if ( aSign ) {
+ z += ( roundingMode == float_round_down ) & aSigExtra;
+ z = - z;
+ }
+ else {
+ z += ( roundingMode == float_round_up ) & aSigExtra;
+ }
+ }
+ }
+ return z;
+
+}
+#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, 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 ) {
+ float_raise( float_flag_invalid );
+ if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) return 0x7FFFFFFF;
+ }
+ return (sbits32) 0x80000000;
+ }
+ else if ( aExp <= 0x7E ) {
+ if ( aExp | aSig ) set_float_exception_inexact_flag();
+ return 0;
+ }
+ aSig = ( aSig | 0x00800000 )<<8;
+ z = aSig>>( - shiftCount );
+ if ( (bits32) ( aSig<<( shiftCount & 31 ) ) ) {
+ set_float_exception_inexact_flag();
+ }
+ if ( aSign ) z = - z;
+ return z;
+
+}
+
+/*
+-------------------------------------------------------------------------------
+Returns the result of converting the single-precision floating-point value
+`a' to the double-precision floating-point format. The conversion is
+performed according to the IEC/IEEE Standard for Binary Floating-Point
+Arithmetic.
+-------------------------------------------------------------------------------
+*/
+float64 float32_to_float64( float32 a )
+{
+ flag aSign;
+ int16 aExp;
+ bits32 aSig, zSig0, zSig1;
+
+ aSig = extractFloat32Frac( a );
+ aExp = extractFloat32Exp( a );
+ aSign = extractFloat32Sign( a );
+ if ( aExp == 0xFF ) {
+ if ( aSig ) return commonNaNToFloat64( float32ToCommonNaN( a ) );
+ return packFloat64( aSign, 0x7FF, 0, 0 );
+ }
+ if ( aExp == 0 ) {
+ if ( aSig == 0 ) return packFloat64( aSign, 0, 0, 0 );
+ normalizeFloat32Subnormal( aSig, &aExp, &aSig );
+ --aExp;
+ }
+ shift64Right( aSig, 0, 3, &zSig0, &zSig1 );
+ return packFloat64( aSign, aExp + 0x380, zSig0, zSig1 );
+
+}
+
+#ifndef SOFTFLOAT_FOR_GCC
+/*
+-------------------------------------------------------------------------------
+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;
+ set_float_exception_inexact_flag();
+ 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_to_zero:
+ 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 ) set_float_exception_inexact_flag();
+ return z;
+
+}
+#endif
+
+/*
+-------------------------------------------------------------------------------
+Returns the result of adding the absolute values of the single-precision
+floating-point values `a' and `b'. If `zSign' is 1, the sum is negated
+before being returned. `zSign' is ignored if the result is a NaN.
+The addition is performed according to the IEC/IEEE Standard for Binary
+Floating-Point Arithmetic.
+-------------------------------------------------------------------------------
+*/
+static float32 addFloat32Sigs( float32 a, float32 b, flag zSign )
+{
+ 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 1, the
+difference is negated before being returned. `zSign' is ignored if the
+result is a NaN. The subtraction is performed according to the IEC/IEEE
+Standard for Binary Floating-Point Arithmetic.
+-------------------------------------------------------------------------------
+*/
+static float32 subFloat32Sigs( float32 a, float32 b, flag zSign )
+{
+ 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, zSig0, zSig1;
+
+ 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;
+ mul32To64( aSig, bSig, &zSig0, &zSig1 );
+ zSig0 |= ( zSig1 != 0 );
+ if ( 0 <= (sbits32) ( zSig0<<1 ) ) {
+ zSig0 <<= 1;
+ --zExp;
+ }
+ return roundAndPackFloat32( zSign, zExp, zSig0 );
+
+}
+
+/*
+-------------------------------------------------------------------------------
+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, rem0, rem1, term0, term1;
+
+ 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 = estimateDiv64To32( aSig, 0, bSig );
+ if ( ( zSig & 0x3F ) <= 2 ) {
+ mul32To64( bSig, zSig, &term0, &term1 );
+ sub64( aSig, 0, term0, term1, &rem0, &rem1 );
+ while ( (sbits32) rem0 < 0 ) {
+ --zSig;
+ add64( rem0, rem1, 0, bSig, &rem0, &rem1 );
+ }
+ zSig |= ( rem1 != 0 );
+ }
+ return roundAndPackFloat32( zSign, zExp, zSig );
+
+}
+
+#ifndef SOFTFLOAT_FOR_GCC
+/*
+-------------------------------------------------------------------------------
+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, q, allZero, 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 = ( aSig | 0x00800000 )<<8;
+ bSig = ( bSig | 0x00800000 )<<8;
+ if ( expDiff < 0 ) {
+ if ( expDiff < -1 ) return a;
+ aSig >>= 1;
+ }
+ q = ( bSig <= aSig );
+ if ( q ) aSig -= bSig;
+ expDiff -= 32;
+ while ( 0 < expDiff ) {
+ q = estimateDiv64To32( aSig, 0, bSig );
+ q = ( 2 < q ) ? q - 2 : 0;
+ aSig = - ( ( bSig>>2 ) * q );
+ expDiff -= 30;
+ }
+ expDiff += 32;
+ if ( 0 < expDiff ) {
+ q = estimateDiv64To32( aSig, 0, bSig );
+ q = ( 2 < q ) ? q - 2 : 0;
+ q >>= 32 - expDiff;
+ bSig >>= 2;
+ aSig = ( ( aSig>>1 )<<( expDiff - 1 ) ) - bSig * q;
+ }
+ else {
+ aSig >>= 2;
+ bSig >>= 2;
+ }
+ 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 );
+
+}
+#endif
+
+#ifndef SOFTFLOAT_FOR_GCC
+/*
+-------------------------------------------------------------------------------
+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, rem0, rem1, term0, term1;
+
+ 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 = 0x7FFFFFFF;
+ goto roundAndPack;
+ }
+ else {
+ aSig >>= aExp & 1;
+ mul32To64( zSig, zSig, &term0, &term1 );
+ sub64( aSig, 0, term0, term1, &rem0, &rem1 );
+ while ( (sbits32) rem0 < 0 ) {
+ --zSig;
+ shortShift64Left( 0, zSig, 1, &term0, &term1 );
+ term1 |= 1;
+ add64( rem0, rem1, term0, term1, &rem0, &rem1 );
+ }
+ zSig |= ( ( rem0 | rem1 ) != 0 );
+ }
+ }
+ shift32RightJamming( zSig, 1, &zSig );
+ roundAndPack:
+ return roundAndPackFloat32( 0, zExp, zSig );
+
+}
+#endif
+
+/*
+-------------------------------------------------------------------------------
+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 ) );
+
+}
+
+#ifndef SOFTFLOAT_FOR_GCC /* Not needed */
+/*
+-------------------------------------------------------------------------------
+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 ) );
+
+}
+#endif /* !SOFTFLOAT_FOR_GCC */
+
+#ifndef SOFTFLOAT_FOR_GCC /* Not needed */
+/*
+-------------------------------------------------------------------------------
+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;
+ bits32 aSig0, aSig1, absZ, aSigExtra;
+ int32 z;
+ int8 roundingMode;
+
+ aSig1 = extractFloat64Frac1( a );
+ aSig0 = extractFloat64Frac0( a );
+ aExp = extractFloat64Exp( a );
+ aSign = extractFloat64Sign( a );
+ shiftCount = aExp - 0x413;
+ if ( 0 <= shiftCount ) {
+ if ( 0x41E < aExp ) {
+ if ( ( aExp == 0x7FF ) && ( aSig0 | aSig1 ) ) aSign = 0;
+ goto invalid;
+ }
+ shortShift64Left(
+ aSig0 | 0x00100000, aSig1, shiftCount, &absZ, &aSigExtra );
+ if ( 0x80000000 < absZ ) goto invalid;
+ }
+ else {
+ aSig1 = ( aSig1 != 0 );
+ if ( aExp < 0x3FE ) {
+ aSigExtra = aExp | aSig0 | aSig1;
+ absZ = 0;
+ }
+ else {
+ aSig0 |= 0x00100000;
+ aSigExtra = ( aSig0<<( shiftCount & 31 ) ) | aSig1;
+ absZ = aSig0>>( - shiftCount );
+ }
+ }
+ roundingMode = float_rounding_mode;
+ if ( roundingMode == float_round_nearest_even ) {
+ if ( (sbits32) aSigExtra < 0 ) {
+ ++absZ;
+ if ( (bits32) ( aSigExtra<<1 ) == 0 ) absZ &= ~1;
+ }
+ z = aSign ? - absZ : absZ;
+ }
+ else {
+ aSigExtra = ( aSigExtra != 0 );
+ if ( aSign ) {
+ z = - ( absZ
+ + ( ( roundingMode == float_round_down ) & aSigExtra ) );
+ }
+ else {
+ z = absZ + ( ( roundingMode == float_round_up ) & aSigExtra );
+ }
+ }
+ if ( ( aSign ^ ( z < 0 ) ) && z ) {
+ invalid:
+ float_raise( float_flag_invalid );
+ return aSign ? (sbits32) 0x80000000 : 0x7FFFFFFF;
+ }
+ if ( aSigExtra ) set_float_exception_inexact_flag();
+ return z;
+
+}
+#endif /* !SOFTFLOAT_FOR_GCC */
+
+/*
+-------------------------------------------------------------------------------
+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;
+ bits32 aSig0, aSig1, absZ, aSigExtra;
+ int32 z;
+
+ aSig1 = extractFloat64Frac1( a );
+ aSig0 = extractFloat64Frac0( a );
+ aExp = extractFloat64Exp( a );
+ aSign = extractFloat64Sign( a );
+ shiftCount = aExp - 0x413;
+ if ( 0 <= shiftCount ) {
+ if ( 0x41E < aExp ) {
+ if ( ( aExp == 0x7FF ) && ( aSig0 | aSig1 ) ) aSign = 0;
+ goto invalid;
+ }
+ shortShift64Left(
+ aSig0 | 0x00100000, aSig1, shiftCount, &absZ, &aSigExtra );
+ }
+ else {
+ if ( aExp < 0x3FF ) {
+ if ( aExp | aSig0 | aSig1 ) {
+ set_float_exception_inexact_flag();
+ }
+ return 0;
+ }
+ aSig0 |= 0x00100000;
+ aSigExtra = ( aSig0<<( shiftCount & 31 ) ) | aSig1;
+ absZ = aSig0>>( - shiftCount );
+ }
+ z = aSign ? - absZ : absZ;
+ if ( ( aSign ^ ( z < 0 ) ) && z ) {
+ invalid:
+ float_raise( float_flag_invalid );
+ return aSign ? (sbits32) 0x80000000 : 0x7FFFFFFF;
+ }
+ if ( aSigExtra ) set_float_exception_inexact_flag();
+ 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;
+ bits32 aSig0, aSig1, zSig;
+ bits32 allZero;
+
+ aSig1 = extractFloat64Frac1( a );
+ aSig0 = extractFloat64Frac0( a );
+ aExp = extractFloat64Exp( a );
+ aSign = extractFloat64Sign( a );
+ if ( aExp == 0x7FF ) {
+ if ( aSig0 | aSig1 ) {
+ return commonNaNToFloat32( float64ToCommonNaN( a ) );
+ }
+ return packFloat32( aSign, 0xFF, 0 );
+ }
+ shift64RightJamming( aSig0, aSig1, 22, &allZero, &zSig );
+ if ( aExp ) zSig |= 0x40000000;
+ return roundAndPackFloat32( aSign, aExp - 0x381, zSig );
+
+}
+
+#ifndef SOFTFLOAT_FOR_GCC
+/*
+-------------------------------------------------------------------------------
+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;
+ bits32 lastBitMask, roundBitsMask;
+ int8 roundingMode;
+ float64 z;
+
+ aExp = extractFloat64Exp( a );
+ if ( 0x413 <= aExp ) {
+ if ( 0x433 <= aExp ) {
+ if ( ( aExp == 0x7FF )
+ && ( extractFloat64Frac0( a ) | extractFloat64Frac1( a ) ) ) {
+ return propagateFloat64NaN( a, a );
+ }
+ return a;
+ }
+ lastBitMask = 1;
+ lastBitMask = ( lastBitMask<<( 0x432 - aExp ) )<<1;
+ roundBitsMask = lastBitMask - 1;
+ z = a;
+ roundingMode = float_rounding_mode;
+ if ( roundingMode == float_round_nearest_even ) {
+ if ( lastBitMask ) {
+ add64( z.high, z.low, 0, lastBitMask>>1, &z.high, &z.low );
+ if ( ( z.low & roundBitsMask ) == 0 ) z.low &= ~ lastBitMask;
+ }
+ else {
+ if ( (sbits32) z.low < 0 ) {
+ ++z.high;
+ if ( (bits32) ( z.low<<1 ) == 0 ) z.high &= ~1;
+ }
+ }
+ }
+ else if ( roundingMode != float_round_to_zero ) {
+ if ( extractFloat64Sign( z )
+ ^ ( roundingMode == float_round_up ) ) {
+ add64( z.high, z.low, 0, roundBitsMask, &z.high, &z.low );
+ }
+ }
+ z.low &= ~ roundBitsMask;
+ }
+ else {
+ if ( aExp <= 0x3FE ) {
+ if ( ( ( (bits32) ( a.high<<1 ) ) | a.low ) == 0 ) return a;
+ set_float_exception_inexact_flag();
+ aSign = extractFloat64Sign( a );
+ switch ( float_rounding_mode ) {
+ case float_round_nearest_even:
+ if ( ( aExp == 0x3FE )
+ && ( extractFloat64Frac0( a ) | extractFloat64Frac1( a ) )
+ ) {
+ return packFloat64( aSign, 0x3FF, 0, 0 );
+ }
+ break;
+ case float_round_down:
+ return
+ aSign ? packFloat64( 1, 0x3FF, 0, 0 )
+ : packFloat64( 0, 0, 0, 0 );
+ case float_round_up:
+ return
+ aSign ? packFloat64( 1, 0, 0, 0 )
+ : packFloat64( 0, 0x3FF, 0, 0 );
+ }
+ return packFloat64( aSign, 0, 0, 0 );
+ }
+ lastBitMask = 1;
+ lastBitMask <<= 0x413 - aExp;
+ roundBitsMask = lastBitMask - 1;
+ z.low = 0;
+ z.high = a.high;
+ roundingMode = float_rounding_mode;
+ if ( roundingMode == float_round_nearest_even ) {
+ z.high += lastBitMask>>1;
+ if ( ( ( z.high & roundBitsMask ) | a.low ) == 0 ) {
+ z.high &= ~ lastBitMask;
+ }
+ }
+ else if ( roundingMode != float_round_to_zero ) {
+ if ( extractFloat64Sign( z )
+ ^ ( roundingMode == float_round_up ) ) {
+ z.high |= ( a.low != 0 );
+ z.high += roundBitsMask;
+ }
+ }
+ z.high &= ~ roundBitsMask;
+ }
+ if ( ( z.low != a.low ) || ( z.high != a.high ) ) {
+ set_float_exception_inexact_flag();
+ }
+ return z;
+
+}
+#endif
+
+/*
+-------------------------------------------------------------------------------
+Returns the result of adding the absolute values of the double-precision
+floating-point values `a' and `b'. If `zSign' is 1, the sum is negated
+before being returned. `zSign' is ignored if the result is a NaN.
+The addition is performed according to the IEC/IEEE Standard for Binary
+Floating-Point Arithmetic.
+-------------------------------------------------------------------------------
+*/
+static float64 addFloat64Sigs( float64 a, float64 b, flag zSign )
+{
+ int16 aExp, bExp, zExp;
+ bits32 aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2;
+ int16 expDiff;
+
+ aSig1 = extractFloat64Frac1( a );
+ aSig0 = extractFloat64Frac0( a );
+ aExp = extractFloat64Exp( a );
+ bSig1 = extractFloat64Frac1( b );
+ bSig0 = extractFloat64Frac0( b );
+ bExp = extractFloat64Exp( b );
+ expDiff = aExp - bExp;
+ if ( 0 < expDiff ) {
+ if ( aExp == 0x7FF ) {
+ if ( aSig0 | aSig1 ) return propagateFloat64NaN( a, b );
+ return a;
+ }
+ if ( bExp == 0 ) {
+ --expDiff;
+ }
+ else {
+ bSig0 |= 0x00100000;
+ }
+ shift64ExtraRightJamming(
+ bSig0, bSig1, 0, expDiff, &bSig0, &bSig1, &zSig2 );
+ zExp = aExp;
+ }
+ else if ( expDiff < 0 ) {
+ if ( bExp == 0x7FF ) {
+ if ( bSig0 | bSig1 ) return propagateFloat64NaN( a, b );
+ return packFloat64( zSign, 0x7FF, 0, 0 );
+ }
+ if ( aExp == 0 ) {
+ ++expDiff;
+ }
+ else {
+ aSig0 |= 0x00100000;
+ }
+ shift64ExtraRightJamming(
+ aSig0, aSig1, 0, - expDiff, &aSig0, &aSig1, &zSig2 );
+ zExp = bExp;
+ }
+ else {
+ if ( aExp == 0x7FF ) {
+ if ( aSig0 | aSig1 | bSig0 | bSig1 ) {
+ return propagateFloat64NaN( a, b );
+ }
+ return a;
+ }
+ add64( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 );
+ if ( aExp == 0 ) return packFloat64( zSign, 0, zSig0, zSig1 );
+ zSig2 = 0;
+ zSig0 |= 0x00200000;
+ zExp = aExp;
+ goto shiftRight1;
+ }
+ aSig0 |= 0x00100000;
+ add64( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 );
+ --zExp;
+ if ( zSig0 < 0x00200000 ) goto roundAndPack;
+ ++zExp;
+ shiftRight1:
+ shift64ExtraRightJamming( zSig0, zSig1, zSig2, 1, &zSig0, &zSig1, &zSig2 );
+ roundAndPack:
+ return roundAndPackFloat64( zSign, zExp, zSig0, zSig1, zSig2 );
+
+}
+
+/*
+-------------------------------------------------------------------------------
+Returns the result of subtracting the absolute values of the double-
+precision floating-point values `a' and `b'. If `zSign' is 1, the
+difference is negated before being returned. `zSign' is ignored if the
+result is a NaN. The subtraction is performed according to the IEC/IEEE
+Standard for Binary Floating-Point Arithmetic.
+-------------------------------------------------------------------------------
+*/
+static float64 subFloat64Sigs( float64 a, float64 b, flag zSign )
+{
+ int16 aExp, bExp, zExp;
+ bits32 aSig0, aSig1, bSig0, bSig1, zSig0, zSig1;
+ int16 expDiff;
+
+ aSig1 = extractFloat64Frac1( a );
+ aSig0 = extractFloat64Frac0( a );
+ aExp = extractFloat64Exp( a );
+ bSig1 = extractFloat64Frac1( b );
+ bSig0 = extractFloat64Frac0( b );
+ bExp = extractFloat64Exp( b );
+ expDiff = aExp - bExp;
+ shortShift64Left( aSig0, aSig1, 10, &aSig0, &aSig1 );
+ shortShift64Left( bSig0, bSig1, 10, &bSig0, &bSig1 );
+ if ( 0 < expDiff ) goto aExpBigger;
+ if ( expDiff < 0 ) goto bExpBigger;
+ if ( aExp == 0x7FF ) {
+ if ( aSig0 | aSig1 | bSig0 | bSig1 ) {
+ return propagateFloat64NaN( a, b );
+ }
+ float_raise( float_flag_invalid );
+ return float64_default_nan;
+ }
+ if ( aExp == 0 ) {
+ aExp = 1;
+ bExp = 1;
+ }
+ if ( bSig0 < aSig0 ) goto aBigger;
+ if ( aSig0 < bSig0 ) goto bBigger;
+ if ( bSig1 < aSig1 ) goto aBigger;
+ if ( aSig1 < bSig1 ) goto bBigger;
+ return packFloat64( float_rounding_mode == float_round_down, 0, 0, 0 );
+ bExpBigger:
+ if ( bExp == 0x7FF ) {
+ if ( bSig0 | bSig1 ) return propagateFloat64NaN( a, b );
+ return packFloat64( zSign ^ 1, 0x7FF, 0, 0 );
+ }
+ if ( aExp == 0 ) {
+ ++expDiff;
+ }
+ else {
+ aSig0 |= 0x40000000;
+ }
+ shift64RightJamming( aSig0, aSig1, - expDiff, &aSig0, &aSig1 );
+ bSig0 |= 0x40000000;
+ bBigger:
+ sub64( bSig0, bSig1, aSig0, aSig1, &zSig0, &zSig1 );
+ zExp = bExp;
+ zSign ^= 1;
+ goto normalizeRoundAndPack;
+ aExpBigger:
+ if ( aExp == 0x7FF ) {
+ if ( aSig0 | aSig1 ) return propagateFloat64NaN( a, b );
+ return a;
+ }
+ if ( bExp == 0 ) {
+ --expDiff;
+ }
+ else {
+ bSig0 |= 0x40000000;
+ }
+ shift64RightJamming( bSig0, bSig1, expDiff, &bSig0, &bSig1 );
+ aSig0 |= 0x40000000;
+ aBigger:
+ sub64( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 );
+ zExp = aExp;
+ normalizeRoundAndPack:
+ --zExp;
+ return normalizeRoundAndPackFloat64( zSign, zExp - 10, zSig0, zSig1 );
+
+}
+
+/*
+-------------------------------------------------------------------------------
+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;
+ bits32 aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2, zSig3;
+
+ aSig1 = extractFloat64Frac1( a );
+ aSig0 = extractFloat64Frac0( a );
+ aExp = extractFloat64Exp( a );
+ aSign = extractFloat64Sign( a );
+ bSig1 = extractFloat64Frac1( b );
+ bSig0 = extractFloat64Frac0( b );
+ bExp = extractFloat64Exp( b );
+ bSign = extractFloat64Sign( b );
+ zSign = aSign ^ bSign;
+ if ( aExp == 0x7FF ) {
+ if ( ( aSig0 | aSig1 )
+ || ( ( bExp == 0x7FF ) && ( bSig0 | bSig1 ) ) ) {
+ return propagateFloat64NaN( a, b );
+ }
+ if ( ( bExp | bSig0 | bSig1 ) == 0 ) goto invalid;
+ return packFloat64( zSign, 0x7FF, 0, 0 );
+ }
+ if ( bExp == 0x7FF ) {
+ if ( bSig0 | bSig1 ) return propagateFloat64NaN( a, b );
+ if ( ( aExp | aSig0 | aSig1 ) == 0 ) {
+ invalid:
+ float_raise( float_flag_invalid );
+ return float64_default_nan;
+ }
+ return packFloat64( zSign, 0x7FF, 0, 0 );
+ }
+ if ( aExp == 0 ) {
+ if ( ( aSig0 | aSig1 ) == 0 ) return packFloat64( zSign, 0, 0, 0 );
+ normalizeFloat64Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 );
+ }
+ if ( bExp == 0 ) {
+ if ( ( bSig0 | bSig1 ) == 0 ) return packFloat64( zSign, 0, 0, 0 );
+ normalizeFloat64Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 );
+ }
+ zExp = aExp + bExp - 0x400;
+ aSig0 |= 0x00100000;
+ shortShift64Left( bSig0, bSig1, 12, &bSig0, &bSig1 );
+ mul64To128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1, &zSig2, &zSig3 );
+ add64( zSig0, zSig1, aSig0, aSig1, &zSig0, &zSig1 );
+ zSig2 |= ( zSig3 != 0 );
+ if ( 0x00200000 <= zSig0 ) {
+ shift64ExtraRightJamming(
+ zSig0, zSig1, zSig2, 1, &zSig0, &zSig1, &zSig2 );
+ ++zExp;
+ }
+ return roundAndPackFloat64( zSign, zExp, zSig0, zSig1, zSig2 );
+
+}
+
+/*
+-------------------------------------------------------------------------------
+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;
+ bits32 aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2;
+ bits32 rem0, rem1, rem2, rem3, term0, term1, term2, term3;
+
+ aSig1 = extractFloat64Frac1( a );
+ aSig0 = extractFloat64Frac0( a );
+ aExp = extractFloat64Exp( a );
+ aSign = extractFloat64Sign( a );
+ bSig1 = extractFloat64Frac1( b );
+ bSig0 = extractFloat64Frac0( b );
+ bExp = extractFloat64Exp( b );
+ bSign = extractFloat64Sign( b );
+ zSign = aSign ^ bSign;
+ if ( aExp == 0x7FF ) {
+ if ( aSig0 | aSig1 ) return propagateFloat64NaN( a, b );
+ if ( bExp == 0x7FF ) {
+ if ( bSig0 | bSig1 ) return propagateFloat64NaN( a, b );
+ goto invalid;
+ }
+ return packFloat64( zSign, 0x7FF, 0, 0 );
+ }
+ if ( bExp == 0x7FF ) {
+ if ( bSig0 | bSig1 ) return propagateFloat64NaN( a, b );
+ return packFloat64( zSign, 0, 0, 0 );
+ }
+ if ( bExp == 0 ) {
+ if ( ( bSig0 | bSig1 ) == 0 ) {
+ if ( ( aExp | aSig0 | aSig1 ) == 0 ) {
+ invalid:
+ float_raise( float_flag_invalid );
+ return float64_default_nan;
+ }
+ float_raise( float_flag_divbyzero );
+ return packFloat64( zSign, 0x7FF, 0, 0 );
+ }
+ normalizeFloat64Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 );
+ }
+ if ( aExp == 0 ) {
+ if ( ( aSig0 | aSig1 ) == 0 ) return packFloat64( zSign, 0, 0, 0 );
+ normalizeFloat64Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 );
+ }
+ zExp = aExp - bExp + 0x3FD;
+ shortShift64Left( aSig0 | 0x00100000, aSig1, 11, &aSig0, &aSig1 );
+ shortShift64Left( bSig0 | 0x00100000, bSig1, 11, &bSig0, &bSig1 );
+ if ( le64( bSig0, bSig1, aSig0, aSig1 ) ) {
+ shift64Right( aSig0, aSig1, 1, &aSig0, &aSig1 );
+ ++zExp;
+ }
+ zSig0 = estimateDiv64To32( aSig0, aSig1, bSig0 );
+ mul64By32To96( bSig0, bSig1, zSig0, &term0, &term1, &term2 );
+ sub96( aSig0, aSig1, 0, term0, term1, term2, &rem0, &rem1, &rem2 );
+ while ( (sbits32) rem0 < 0 ) {
+ --zSig0;
+ add96( rem0, rem1, rem2, 0, bSig0, bSig1, &rem0, &rem1, &rem2 );
+ }
+ zSig1 = estimateDiv64To32( rem1, rem2, bSig0 );
+ if ( ( zSig1 & 0x3FF ) <= 4 ) {
+ mul64By32To96( bSig0, bSig1, zSig1, &term1, &term2, &term3 );
+ sub96( rem1, rem2, 0, term1, term2, term3, &rem1, &rem2, &rem3 );
+ while ( (sbits32) rem1 < 0 ) {
+ --zSig1;
+ add96( rem1, rem2, rem3, 0, bSig0, bSig1, &rem1, &rem2, &rem3 );
+ }
+ zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 );
+ }
+ shift64ExtraRightJamming( zSig0, zSig1, 0, 11, &zSig0, &zSig1, &zSig2 );
+ return roundAndPackFloat64( zSign, zExp, zSig0, zSig1, zSig2 );
+
+}
+
+#ifndef SOFTFLOAT_FOR_GCC
+/*
+-------------------------------------------------------------------------------
+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;
+ bits32 aSig0, aSig1, bSig0, bSig1, q, term0, term1, term2;
+ bits32 allZero, alternateASig0, alternateASig1, sigMean1;
+ sbits32 sigMean0;
+ float64 z;
+
+ aSig1 = extractFloat64Frac1( a );
+ aSig0 = extractFloat64Frac0( a );
+ aExp = extractFloat64Exp( a );
+ aSign = extractFloat64Sign( a );
+ bSig1 = extractFloat64Frac1( b );
+ bSig0 = extractFloat64Frac0( b );
+ bExp = extractFloat64Exp( b );
+ bSign = extractFloat64Sign( b );
+ if ( aExp == 0x7FF ) {
+ if ( ( aSig0 | aSig1 )
+ || ( ( bExp == 0x7FF ) && ( bSig0 | bSig1 ) ) ) {
+ return propagateFloat64NaN( a, b );
+ }
+ goto invalid;
+ }
+ if ( bExp == 0x7FF ) {
+ if ( bSig0 | bSig1 ) return propagateFloat64NaN( a, b );
+ return a;
+ }
+ if ( bExp == 0 ) {
+ if ( ( bSig0 | bSig1 ) == 0 ) {
+ invalid:
+ float_raise( float_flag_invalid );
+ return float64_default_nan;
+ }
+ normalizeFloat64Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 );
+ }
+ if ( aExp == 0 ) {
+ if ( ( aSig0 | aSig1 ) == 0 ) return a;
+ normalizeFloat64Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 );
+ }
+ expDiff = aExp - bExp;
+ if ( expDiff < -1 ) return a;
+ shortShift64Left(
+ aSig0 | 0x00100000, aSig1, 11 - ( expDiff < 0 ), &aSig0, &aSig1 );
+ shortShift64Left( bSig0 | 0x00100000, bSig1, 11, &bSig0, &bSig1 );
+ q = le64( bSig0, bSig1, aSig0, aSig1 );
+ if ( q ) sub64( aSig0, aSig1, bSig0, bSig1, &aSig0, &aSig1 );
+ expDiff -= 32;
+ while ( 0 < expDiff ) {
+ q = estimateDiv64To32( aSig0, aSig1, bSig0 );
+ q = ( 4 < q ) ? q - 4 : 0;
+ mul64By32To96( bSig0, bSig1, q, &term0, &term1, &term2 );
+ shortShift96Left( term0, term1, term2, 29, &term1, &term2, &allZero );
+ shortShift64Left( aSig0, aSig1, 29, &aSig0, &allZero );
+ sub64( aSig0, 0, term1, term2, &aSig0, &aSig1 );
+ expDiff -= 29;
+ }
+ if ( -32 < expDiff ) {
+ q = estimateDiv64To32( aSig0, aSig1, bSig0 );
+ q = ( 4 < q ) ? q - 4 : 0;
+ q >>= - expDiff;
+ shift64Right( bSig0, bSig1, 8, &bSig0, &bSig1 );
+ expDiff += 24;
+ if ( expDiff < 0 ) {
+ shift64Right( aSig0, aSig1, - expDiff, &aSig0, &aSig1 );
+ }
+ else {
+ shortShift64Left( aSig0, aSig1, expDiff, &aSig0, &aSig1 );
+ }
+ mul64By32To96( bSig0, bSig1, q, &term0, &term1, &term2 );
+ sub64( aSig0, aSig1, term1, term2, &aSig0, &aSig1 );
+ }
+ else {
+ shift64Right( aSig0, aSig1, 8, &aSig0, &aSig1 );
+ shift64Right( bSig0, bSig1, 8, &bSig0, &bSig1 );
+ }
+ do {
+ alternateASig0 = aSig0;
+ alternateASig1 = aSig1;
+ ++q;
+ sub64( aSig0, aSig1, bSig0, bSig1, &aSig0, &aSig1 );
+ } while ( 0 <= (sbits32) aSig0 );
+ add64(
+ aSig0, aSig1, alternateASig0, alternateASig1, &sigMean0, &sigMean1 );
+ if ( ( sigMean0 < 0 )
+ || ( ( ( sigMean0 | sigMean1 ) == 0 ) && ( q & 1 ) ) ) {
+ aSig0 = alternateASig0;
+ aSig1 = alternateASig1;
+ }
+ zSign = ( (sbits32) aSig0 < 0 );
+ if ( zSign ) sub64( 0, 0, aSig0, aSig1, &aSig0, &aSig1 );
+ return
+ normalizeRoundAndPackFloat64( aSign ^ zSign, bExp - 4, aSig0, aSig1 );
+
+}
+#endif
+
+#ifndef SOFTFLOAT_FOR_GCC
+/*
+-------------------------------------------------------------------------------
+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;
+ bits32 aSig0, aSig1, zSig0, zSig1, zSig2, doubleZSig0;
+ bits32 rem0, rem1, rem2, rem3, term0, term1, term2, term3;
+ float64 z;
+
+ aSig1 = extractFloat64Frac1( a );
+ aSig0 = extractFloat64Frac0( a );
+ aExp = extractFloat64Exp( a );
+ aSign = extractFloat64Sign( a );
+ if ( aExp == 0x7FF ) {
+ if ( aSig0 | aSig1 ) return propagateFloat64NaN( a, a );
+ if ( ! aSign ) return a;
+ goto invalid;
+ }
+ if ( aSign ) {
+ if ( ( aExp | aSig0 | aSig1 ) == 0 ) return a;
+ invalid:
+ float_raise( float_flag_invalid );
+ return float64_default_nan;
+ }
+ if ( aExp == 0 ) {
+ if ( ( aSig0 | aSig1 ) == 0 ) return packFloat64( 0, 0, 0, 0 );
+ normalizeFloat64Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 );
+ }
+ zExp = ( ( aExp - 0x3FF )>>1 ) + 0x3FE;
+ aSig0 |= 0x00100000;
+ shortShift64Left( aSig0, aSig1, 11, &term0, &term1 );
+ zSig0 = ( estimateSqrt32( aExp, term0 )>>1 ) + 1;
+ if ( zSig0 == 0 ) zSig0 = 0x7FFFFFFF;
+ doubleZSig0 = zSig0 + zSig0;
+ shortShift64Left( aSig0, aSig1, 9 - ( aExp & 1 ), &aSig0, &aSig1 );
+ mul32To64( zSig0, zSig0, &term0, &term1 );
+ sub64( aSig0, aSig1, term0, term1, &rem0, &rem1 );
+ while ( (sbits32) rem0 < 0 ) {
+ --zSig0;
+ doubleZSig0 -= 2;
+ add64( rem0, rem1, 0, doubleZSig0 | 1, &rem0, &rem1 );
+ }
+ zSig1 = estimateDiv64To32( rem1, 0, doubleZSig0 );
+ if ( ( zSig1 & 0x1FF ) <= 5 ) {
+ if ( zSig1 == 0 ) zSig1 = 1;
+ mul32To64( doubleZSig0, zSig1, &term1, &term2 );
+ sub64( rem1, 0, term1, term2, &rem1, &rem2 );
+ mul32To64( zSig1, zSig1, &term2, &term3 );
+ sub96( rem1, rem2, 0, 0, term2, term3, &rem1, &rem2, &rem3 );
+ while ( (sbits32) rem1 < 0 ) {
+ --zSig1;
+ shortShift64Left( 0, zSig1, 1, &term2, &term3 );
+ term3 |= 1;
+ term2 |= doubleZSig0;
+ add96( rem1, rem2, rem3, 0, term2, term3, &rem1, &rem2, &rem3 );
+ }
+ zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 );
+ }
+ shift64ExtraRightJamming( zSig0, zSig1, 0, 10, &zSig0, &zSig1, &zSig2 );
+ return roundAndPackFloat64( 0, zExp, zSig0, zSig1, zSig2 );
+
+}
+#endif
+
+/*
+-------------------------------------------------------------------------------
+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 )
+ && ( extractFloat64Frac0( a ) | extractFloat64Frac1( a ) ) )
+ || ( ( extractFloat64Exp( b ) == 0x7FF )
+ && ( extractFloat64Frac0( b ) | extractFloat64Frac1( b ) ) )
+ ) {
+ if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) {
+ float_raise( float_flag_invalid );
+ }
+ return 0;
+ }
+ return ( a == b ) ||
+ ( (bits64) ( ( FLOAT64_DEMANGLE(a) | FLOAT64_DEMANGLE(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 )
+ && ( extractFloat64Frac0( a ) | extractFloat64Frac1( a ) ) )
+ || ( ( extractFloat64Exp( b ) == 0x7FF )
+ && ( extractFloat64Frac0( b ) | extractFloat64Frac1( b ) ) )
+ ) {
+ float_raise( float_flag_invalid );
+ return 0;
+ }
+ aSign = extractFloat64Sign( a );
+ bSign = extractFloat64Sign( b );
+ if ( aSign != bSign )
+ return aSign ||
+ ( (bits64) ( ( FLOAT64_DEMANGLE(a) | FLOAT64_DEMANGLE(b) )<<1 ) ==
+ 0 );
+ return ( a == b ) ||
+ ( aSign ^ ( FLOAT64_DEMANGLE(a) < FLOAT64_DEMANGLE(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 )
+ && ( extractFloat64Frac0( a ) | extractFloat64Frac1( a ) ) )
+ || ( ( extractFloat64Exp( b ) == 0x7FF )
+ && ( extractFloat64Frac0( b ) | extractFloat64Frac1( b ) ) )
+ ) {
+ float_raise( float_flag_invalid );
+ return 0;
+ }
+ aSign = extractFloat64Sign( a );
+ bSign = extractFloat64Sign( b );
+ if ( aSign != bSign )
+ return aSign &&
+ ( (bits64) ( ( FLOAT64_DEMANGLE(a) | FLOAT64_DEMANGLE(b) )<<1 ) !=
+ 0 );
+ return ( a != b ) &&
+ ( aSign ^ ( FLOAT64_DEMANGLE(a) < FLOAT64_DEMANGLE(b) ) );
+
+}
+
+#ifndef SOFTFLOAT_FOR_GCC
+/*
+-------------------------------------------------------------------------------
+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 )
+ && ( extractFloat64Frac0( a ) | extractFloat64Frac1( a ) ) )
+ || ( ( extractFloat64Exp( b ) == 0x7FF )
+ && ( extractFloat64Frac0( b ) | extractFloat64Frac1( 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;
+
+ if ( ( ( extractFloat64Exp( a ) == 0x7FF )
+ && ( extractFloat64Frac0( a ) | extractFloat64Frac1( a ) ) )
+ || ( ( extractFloat64Exp( b ) == 0x7FF )
+ && ( extractFloat64Frac0( b ) | extractFloat64Frac1( 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 )
+ && ( extractFloat64Frac0( a ) | extractFloat64Frac1( a ) ) )
+ || ( ( extractFloat64Exp( b ) == 0x7FF )
+ && ( extractFloat64Frac0( b ) | extractFloat64Frac1( 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 ) );
+
+}
+
+#endif
|