soft float support
git-svn-id: svn://svn.savannah.nongnu.org/qemu/trunk@1332 c046a42c-6fe2-441c-8c8c-71466251a162
diff --git a/fpu/softfloat-macros.h b/fpu/softfloat-macros.h
new file mode 100644
index 0000000..2c8f18b
--- /dev/null
+++ b/fpu/softfloat-macros.h
@@ -0,0 +1,720 @@
+
+/*============================================================================
+
+This C source fragment is part of the SoftFloat IEC/IEEE Floating-point
+Arithmetic Package, Release 2b.
+
+Written by John R. Hauser. This work was made possible in part by the
+International Computer Science Institute, located at Suite 600, 1947 Center
+Street, Berkeley, California 94704. Funding was partially provided by the
+National Science Foundation under grant MIP-9311980. The original version
+of this code was written as part of a project to build a fixed-point vector
+processor in collaboration with the University of California at Berkeley,
+overseen by Profs. Nelson Morgan and John Wawrzynek. More information
+is available through the Web page `http://www.cs.berkeley.edu/~jhauser/
+arithmetic/SoftFloat.html'.
+
+THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort has
+been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT TIMES
+RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO PERSONS
+AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ALL LOSSES,
+COSTS, OR OTHER PROBLEMS THEY INCUR DUE TO THE SOFTWARE, AND WHO FURTHERMORE
+EFFECTIVELY INDEMNIFY JOHN HAUSER AND THE INTERNATIONAL COMPUTER SCIENCE
+INSTITUTE (possibly via similar legal notice) AGAINST ALL LOSSES, COSTS, OR
+OTHER PROBLEMS INCURRED BY THEIR CUSTOMERS AND CLIENTS DUE TO THE SOFTWARE.
+
+Derivative works are acceptable, even for commercial purposes, so long as
+(1) the source code for the derivative work includes prominent notice that
+the work is derivative, and (2) the source code includes prominent notice with
+these four paragraphs for those parts of this code that are retained.
+
+=============================================================================*/
+
+/*----------------------------------------------------------------------------
+| Shifts `a' right by the number of bits given in `count'. If any nonzero
+| bits are shifted off, they are ``jammed'' into the least significant bit of
+| the result by setting the least significant bit to 1. The value of `count'
+| can be arbitrarily large; in particular, if `count' is greater than 32, the
+| result will be either 0 or 1, depending on whether `a' is zero or nonzero.
+| The result is stored in the location pointed to by `zPtr'.
+*----------------------------------------------------------------------------*/
+
+INLINE void shift32RightJamming( bits32 a, int16 count, bits32 *zPtr )
+{
+ bits32 z;
+
+ if ( count == 0 ) {
+ z = a;
+ }
+ else if ( count < 32 ) {
+ z = ( a>>count ) | ( ( a<<( ( - count ) & 31 ) ) != 0 );
+ }
+ else {
+ z = ( a != 0 );
+ }
+ *zPtr = z;
+
+}
+
+/*----------------------------------------------------------------------------
+| Shifts `a' right by the number of bits given in `count'. If any nonzero
+| bits are shifted off, they are ``jammed'' into the least significant bit of
+| the result by setting the least significant bit to 1. The value of `count'
+| can be arbitrarily large; in particular, if `count' is greater than 64, the
+| result will be either 0 or 1, depending on whether `a' is zero or nonzero.
+| The result is stored in the location pointed to by `zPtr'.
+*----------------------------------------------------------------------------*/
+
+INLINE void shift64RightJamming( bits64 a, int16 count, bits64 *zPtr )
+{
+ bits64 z;
+
+ if ( count == 0 ) {
+ z = a;
+ }
+ else if ( count < 64 ) {
+ z = ( a>>count ) | ( ( a<<( ( - count ) & 63 ) ) != 0 );
+ }
+ else {
+ z = ( a != 0 );
+ }
+ *zPtr = z;
+
+}
+
+/*----------------------------------------------------------------------------
+| Shifts the 128-bit value formed by concatenating `a0' and `a1' right by 64
+| _plus_ the number of bits given in `count'. The shifted result is at most
+| 64 nonzero bits; this is stored at the location pointed to by `z0Ptr'. The
+| bits shifted off form a second 64-bit result as follows: The _last_ bit
+| shifted off is the most-significant bit of the extra result, and the other
+| 63 bits of the extra result are all zero if and only if _all_but_the_last_
+| bits shifted off were all zero. This extra result is stored in the location
+| pointed to by `z1Ptr'. The value of `count' can be arbitrarily large.
+| (This routine makes more sense if `a0' and `a1' are considered to form
+| a fixed-point value with binary point between `a0' and `a1'. This fixed-
+| point value is shifted right by the number of bits given in `count', and
+| the integer part of the result is returned at the location pointed to by
+| `z0Ptr'. The fractional part of the result may be slightly corrupted as
+| described above, and is returned at the location pointed to by `z1Ptr'.)
+*----------------------------------------------------------------------------*/
+
+INLINE void
+ shift64ExtraRightJamming(
+ bits64 a0, bits64 a1, int16 count, bits64 *z0Ptr, bits64 *z1Ptr )
+{
+ bits64 z0, z1;
+ int8 negCount = ( - count ) & 63;
+
+ if ( count == 0 ) {
+ z1 = a1;
+ z0 = a0;
+ }
+ else if ( count < 64 ) {
+ z1 = ( a0<<negCount ) | ( a1 != 0 );
+ z0 = a0>>count;
+ }
+ else {
+ if ( count == 64 ) {
+ z1 = a0 | ( a1 != 0 );
+ }
+ else {
+ z1 = ( ( a0 | a1 ) != 0 );
+ }
+ z0 = 0;
+ }
+ *z1Ptr = z1;
+ *z0Ptr = z0;
+
+}
+
+/*----------------------------------------------------------------------------
+| Shifts the 128-bit value formed by concatenating `a0' and `a1' right by the
+| number of bits given in `count'. Any bits shifted off are lost. The value
+| of `count' can be arbitrarily large; in particular, if `count' is greater
+| than 128, the result will be 0. The result is broken into two 64-bit pieces
+| which are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
+*----------------------------------------------------------------------------*/
+
+INLINE void
+ shift128Right(
+ bits64 a0, bits64 a1, int16 count, bits64 *z0Ptr, bits64 *z1Ptr )
+{
+ bits64 z0, z1;
+ int8 negCount = ( - count ) & 63;
+
+ if ( count == 0 ) {
+ z1 = a1;
+ z0 = a0;
+ }
+ else if ( count < 64 ) {
+ z1 = ( a0<<negCount ) | ( a1>>count );
+ z0 = a0>>count;
+ }
+ else {
+ z1 = ( count < 64 ) ? ( a0>>( count & 63 ) ) : 0;
+ z0 = 0;
+ }
+ *z1Ptr = z1;
+ *z0Ptr = z0;
+
+}
+
+/*----------------------------------------------------------------------------
+| Shifts the 128-bit value formed by concatenating `a0' and `a1' right by the
+| number of bits given in `count'. If any nonzero bits are shifted off, they
+| are ``jammed'' into the least significant bit of the result by setting the
+| least significant bit to 1. The value of `count' can be arbitrarily large;
+| in particular, if `count' is greater than 128, the result will be either
+| 0 or 1, depending on whether the concatenation of `a0' and `a1' is zero or
+| nonzero. The result is broken into two 64-bit pieces which are stored at
+| the locations pointed to by `z0Ptr' and `z1Ptr'.
+*----------------------------------------------------------------------------*/
+
+INLINE void
+ shift128RightJamming(
+ bits64 a0, bits64 a1, int16 count, bits64 *z0Ptr, bits64 *z1Ptr )
+{
+ bits64 z0, z1;
+ int8 negCount = ( - count ) & 63;
+
+ if ( count == 0 ) {
+ z1 = a1;
+ z0 = a0;
+ }
+ else if ( count < 64 ) {
+ z1 = ( a0<<negCount ) | ( a1>>count ) | ( ( a1<<negCount ) != 0 );
+ z0 = a0>>count;
+ }
+ else {
+ if ( count == 64 ) {
+ z1 = a0 | ( a1 != 0 );
+ }
+ else if ( count < 128 ) {
+ z1 = ( a0>>( count & 63 ) ) | ( ( ( a0<<negCount ) | a1 ) != 0 );
+ }
+ else {
+ z1 = ( ( a0 | a1 ) != 0 );
+ }
+ z0 = 0;
+ }
+ *z1Ptr = z1;
+ *z0Ptr = z0;
+
+}
+
+/*----------------------------------------------------------------------------
+| Shifts the 192-bit value formed by concatenating `a0', `a1', and `a2' right
+| by 64 _plus_ the number of bits given in `count'. The shifted result is
+| at most 128 nonzero bits; these are broken into two 64-bit pieces which are
+| stored at the locations pointed to by `z0Ptr' and `z1Ptr'. The bits shifted
+| off form a third 64-bit result as follows: The _last_ bit shifted off is
+| the most-significant bit of the extra result, and the other 63 bits of the
+| extra result are all zero if and only if _all_but_the_last_ bits shifted off
+| were all zero. This extra result is stored in the location pointed to by
+| `z2Ptr'. The value of `count' can be arbitrarily large.
+| (This routine makes more sense if `a0', `a1', and `a2' are considered
+| to form a fixed-point value with binary point between `a1' and `a2'. This
+| fixed-point value is shifted right by the number of bits given in `count',
+| and the integer part of the result is returned at the locations pointed to
+| by `z0Ptr' and `z1Ptr'. The fractional part of the result may be slightly
+| corrupted as described above, and is returned at the location pointed to by
+| `z2Ptr'.)
+*----------------------------------------------------------------------------*/
+
+INLINE void
+ shift128ExtraRightJamming(
+ bits64 a0,
+ bits64 a1,
+ bits64 a2,
+ int16 count,
+ bits64 *z0Ptr,
+ bits64 *z1Ptr,
+ bits64 *z2Ptr
+ )
+{
+ bits64 z0, z1, z2;
+ int8 negCount = ( - count ) & 63;
+
+ if ( count == 0 ) {
+ z2 = a2;
+ z1 = a1;
+ z0 = a0;
+ }
+ else {
+ if ( count < 64 ) {
+ z2 = a1<<negCount;
+ z1 = ( a0<<negCount ) | ( a1>>count );
+ z0 = a0>>count;
+ }
+ else {
+ if ( count == 64 ) {
+ z2 = a1;
+ z1 = a0;
+ }
+ else {
+ a2 |= a1;
+ if ( count < 128 ) {
+ z2 = a0<<negCount;
+ z1 = a0>>( count & 63 );
+ }
+ else {
+ z2 = ( count == 128 ) ? a0 : ( a0 != 0 );
+ z1 = 0;
+ }
+ }
+ z0 = 0;
+ }
+ z2 |= ( a2 != 0 );
+ }
+ *z2Ptr = z2;
+ *z1Ptr = z1;
+ *z0Ptr = z0;
+
+}
+
+/*----------------------------------------------------------------------------
+| Shifts the 128-bit value formed by concatenating `a0' and `a1' left by the
+| number of bits given in `count'. Any bits shifted off are lost. The value
+| of `count' must be less than 64. The result is broken into two 64-bit
+| pieces which are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
+*----------------------------------------------------------------------------*/
+
+INLINE void
+ shortShift128Left(
+ bits64 a0, bits64 a1, int16 count, bits64 *z0Ptr, bits64 *z1Ptr )
+{
+
+ *z1Ptr = a1<<count;
+ *z0Ptr =
+ ( count == 0 ) ? a0 : ( a0<<count ) | ( a1>>( ( - count ) & 63 ) );
+
+}
+
+/*----------------------------------------------------------------------------
+| Shifts the 192-bit value formed by concatenating `a0', `a1', and `a2' left
+| by the number of bits given in `count'. Any bits shifted off are lost.
+| The value of `count' must be less than 64. The result is broken into three
+| 64-bit pieces which are stored at the locations pointed to by `z0Ptr',
+| `z1Ptr', and `z2Ptr'.
+*----------------------------------------------------------------------------*/
+
+INLINE void
+ shortShift192Left(
+ bits64 a0,
+ bits64 a1,
+ bits64 a2,
+ int16 count,
+ bits64 *z0Ptr,
+ bits64 *z1Ptr,
+ bits64 *z2Ptr
+ )
+{
+ bits64 z0, z1, z2;
+ int8 negCount;
+
+ z2 = a2<<count;
+ z1 = a1<<count;
+ z0 = a0<<count;
+ if ( 0 < count ) {
+ negCount = ( ( - count ) & 63 );
+ z1 |= a2>>negCount;
+ z0 |= a1>>negCount;
+ }
+ *z2Ptr = z2;
+ *z1Ptr = z1;
+ *z0Ptr = z0;
+
+}
+
+/*----------------------------------------------------------------------------
+| Adds the 128-bit value formed by concatenating `a0' and `a1' to the 128-bit
+| value formed by concatenating `b0' and `b1'. Addition is modulo 2^128, so
+| any carry out is lost. The result is broken into two 64-bit pieces which
+| are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
+*----------------------------------------------------------------------------*/
+
+INLINE void
+ add128(
+ bits64 a0, bits64 a1, bits64 b0, bits64 b1, bits64 *z0Ptr, bits64 *z1Ptr )
+{
+ bits64 z1;
+
+ z1 = a1 + b1;
+ *z1Ptr = z1;
+ *z0Ptr = a0 + b0 + ( z1 < a1 );
+
+}
+
+/*----------------------------------------------------------------------------
+| Adds the 192-bit value formed by concatenating `a0', `a1', and `a2' to the
+| 192-bit value formed by concatenating `b0', `b1', and `b2'. Addition is
+| modulo 2^192, so any carry out is lost. The result is broken into three
+| 64-bit pieces which are stored at the locations pointed to by `z0Ptr',
+| `z1Ptr', and `z2Ptr'.
+*----------------------------------------------------------------------------*/
+
+INLINE void
+ add192(
+ bits64 a0,
+ bits64 a1,
+ bits64 a2,
+ bits64 b0,
+ bits64 b1,
+ bits64 b2,
+ bits64 *z0Ptr,
+ bits64 *z1Ptr,
+ bits64 *z2Ptr
+ )
+{
+ bits64 z0, z1, z2;
+ int8 carry0, carry1;
+
+ z2 = a2 + b2;
+ carry1 = ( z2 < a2 );
+ z1 = a1 + b1;
+ carry0 = ( z1 < a1 );
+ z0 = a0 + b0;
+ z1 += carry1;
+ z0 += ( z1 < carry1 );
+ z0 += carry0;
+ *z2Ptr = z2;
+ *z1Ptr = z1;
+ *z0Ptr = z0;
+
+}
+
+/*----------------------------------------------------------------------------
+| Subtracts the 128-bit value formed by concatenating `b0' and `b1' from the
+| 128-bit value formed by concatenating `a0' and `a1'. Subtraction is modulo
+| 2^128, so any borrow out (carry out) is lost. The result is broken into two
+| 64-bit pieces which are stored at the locations pointed to by `z0Ptr' and
+| `z1Ptr'.
+*----------------------------------------------------------------------------*/
+
+INLINE void
+ sub128(
+ bits64 a0, bits64 a1, bits64 b0, bits64 b1, bits64 *z0Ptr, bits64 *z1Ptr )
+{
+
+ *z1Ptr = a1 - b1;
+ *z0Ptr = a0 - b0 - ( a1 < b1 );
+
+}
+
+/*----------------------------------------------------------------------------
+| Subtracts the 192-bit value formed by concatenating `b0', `b1', and `b2'
+| from the 192-bit value formed by concatenating `a0', `a1', and `a2'.
+| Subtraction is modulo 2^192, so any borrow out (carry out) is lost. The
+| result is broken into three 64-bit pieces which are stored at the locations
+| pointed to by `z0Ptr', `z1Ptr', and `z2Ptr'.
+*----------------------------------------------------------------------------*/
+
+INLINE void
+ sub192(
+ bits64 a0,
+ bits64 a1,
+ bits64 a2,
+ bits64 b0,
+ bits64 b1,
+ bits64 b2,
+ bits64 *z0Ptr,
+ bits64 *z1Ptr,
+ bits64 *z2Ptr
+ )
+{
+ bits64 z0, z1, z2;
+ int8 borrow0, borrow1;
+
+ z2 = a2 - b2;
+ borrow1 = ( a2 < b2 );
+ z1 = a1 - b1;
+ borrow0 = ( a1 < b1 );
+ z0 = a0 - b0;
+ z0 -= ( z1 < borrow1 );
+ z1 -= borrow1;
+ z0 -= borrow0;
+ *z2Ptr = z2;
+ *z1Ptr = z1;
+ *z0Ptr = z0;
+
+}
+
+/*----------------------------------------------------------------------------
+| Multiplies `a' by `b' to obtain a 128-bit product. The product is broken
+| into two 64-bit pieces which are stored at the locations pointed to by
+| `z0Ptr' and `z1Ptr'.
+*----------------------------------------------------------------------------*/
+
+INLINE void mul64To128( bits64 a, bits64 b, bits64 *z0Ptr, bits64 *z1Ptr )
+{
+ bits32 aHigh, aLow, bHigh, bLow;
+ bits64 z0, zMiddleA, zMiddleB, z1;
+
+ aLow = a;
+ aHigh = a>>32;
+ bLow = b;
+ bHigh = b>>32;
+ z1 = ( (bits64) aLow ) * bLow;
+ zMiddleA = ( (bits64) aLow ) * bHigh;
+ zMiddleB = ( (bits64) aHigh ) * bLow;
+ z0 = ( (bits64) aHigh ) * bHigh;
+ zMiddleA += zMiddleB;
+ z0 += ( ( (bits64) ( zMiddleA < zMiddleB ) )<<32 ) + ( zMiddleA>>32 );
+ zMiddleA <<= 32;
+ z1 += zMiddleA;
+ z0 += ( z1 < zMiddleA );
+ *z1Ptr = z1;
+ *z0Ptr = z0;
+
+}
+
+/*----------------------------------------------------------------------------
+| Multiplies the 128-bit value formed by concatenating `a0' and `a1' by
+| `b' to obtain a 192-bit product. The product is broken into three 64-bit
+| pieces which are stored at the locations pointed to by `z0Ptr', `z1Ptr', and
+| `z2Ptr'.
+*----------------------------------------------------------------------------*/
+
+INLINE void
+ mul128By64To192(
+ bits64 a0,
+ bits64 a1,
+ bits64 b,
+ bits64 *z0Ptr,
+ bits64 *z1Ptr,
+ bits64 *z2Ptr
+ )
+{
+ bits64 z0, z1, z2, more1;
+
+ mul64To128( a1, b, &z1, &z2 );
+ mul64To128( a0, b, &z0, &more1 );
+ add128( z0, more1, 0, z1, &z0, &z1 );
+ *z2Ptr = z2;
+ *z1Ptr = z1;
+ *z0Ptr = z0;
+
+}
+
+/*----------------------------------------------------------------------------
+| Multiplies the 128-bit value formed by concatenating `a0' and `a1' to the
+| 128-bit value formed by concatenating `b0' and `b1' to obtain a 256-bit
+| product. The product is broken into four 64-bit pieces which are stored at
+| the locations pointed to by `z0Ptr', `z1Ptr', `z2Ptr', and `z3Ptr'.
+*----------------------------------------------------------------------------*/
+
+INLINE void
+ mul128To256(
+ bits64 a0,
+ bits64 a1,
+ bits64 b0,
+ bits64 b1,
+ bits64 *z0Ptr,
+ bits64 *z1Ptr,
+ bits64 *z2Ptr,
+ bits64 *z3Ptr
+ )
+{
+ bits64 z0, z1, z2, z3;
+ bits64 more1, more2;
+
+ mul64To128( a1, b1, &z2, &z3 );
+ mul64To128( a1, b0, &z1, &more2 );
+ add128( z1, more2, 0, z2, &z1, &z2 );
+ mul64To128( a0, b0, &z0, &more1 );
+ add128( z0, more1, 0, z1, &z0, &z1 );
+ mul64To128( a0, b1, &more1, &more2 );
+ add128( more1, more2, 0, z2, &more1, &z2 );
+ add128( z0, z1, 0, more1, &z0, &z1 );
+ *z3Ptr = z3;
+ *z2Ptr = z2;
+ *z1Ptr = z1;
+ *z0Ptr = z0;
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns an approximation to the 64-bit integer quotient obtained by dividing
+| `b' into the 128-bit value formed by concatenating `a0' and `a1'. The
+| divisor `b' must be at least 2^63. If q is the exact quotient truncated
+| toward zero, the approximation returned lies between q and q + 2 inclusive.
+| If the exact quotient q is larger than 64 bits, the maximum positive 64-bit
+| unsigned integer is returned.
+*----------------------------------------------------------------------------*/
+
+static bits64 estimateDiv128To64( bits64 a0, bits64 a1, bits64 b )
+{
+ bits64 b0, b1;
+ bits64 rem0, rem1, term0, term1;
+ bits64 z;
+
+ if ( b <= a0 ) return LIT64( 0xFFFFFFFFFFFFFFFF );
+ b0 = b>>32;
+ z = ( b0<<32 <= a0 ) ? LIT64( 0xFFFFFFFF00000000 ) : ( a0 / b0 )<<32;
+ mul64To128( b, z, &term0, &term1 );
+ sub128( a0, a1, term0, term1, &rem0, &rem1 );
+ while ( ( (sbits64) rem0 ) < 0 ) {
+ z -= LIT64( 0x100000000 );
+ b1 = b<<32;
+ add128( rem0, rem1, b0, b1, &rem0, &rem1 );
+ }
+ rem0 = ( rem0<<32 ) | ( rem1>>32 );
+ z |= ( b0<<32 <= rem0 ) ? 0xFFFFFFFF : rem0 / b0;
+ return z;
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns an approximation to the square root of the 32-bit significand given
+| by `a'. Considered as an integer, `a' must be at least 2^31. If bit 0 of
+| `aExp' (the least significant bit) is 1, the integer returned approximates
+| 2^31*sqrt(`a'/2^31), where `a' is considered an integer. If bit 0 of `aExp'
+| is 0, the integer returned approximates 2^31*sqrt(`a'/2^30). In either
+| case, the approximation returned lies strictly within +/-2 of the exact
+| value.
+*----------------------------------------------------------------------------*/
+
+static bits32 estimateSqrt32( int16 aExp, bits32 a )
+{
+ static const bits16 sqrtOddAdjustments[] = {
+ 0x0004, 0x0022, 0x005D, 0x00B1, 0x011D, 0x019F, 0x0236, 0x02E0,
+ 0x039C, 0x0468, 0x0545, 0x0631, 0x072B, 0x0832, 0x0946, 0x0A67
+ };
+ static const bits16 sqrtEvenAdjustments[] = {
+ 0x0A2D, 0x08AF, 0x075A, 0x0629, 0x051A, 0x0429, 0x0356, 0x029E,
+ 0x0200, 0x0179, 0x0109, 0x00AF, 0x0068, 0x0034, 0x0012, 0x0002
+ };
+ int8 index;
+ bits32 z;
+
+ index = ( a>>27 ) & 15;
+ if ( aExp & 1 ) {
+ z = 0x4000 + ( a>>17 ) - sqrtOddAdjustments[ index ];
+ z = ( ( a / z )<<14 ) + ( z<<15 );
+ a >>= 1;
+ }
+ else {
+ z = 0x8000 + ( a>>17 ) - sqrtEvenAdjustments[ index ];
+ z = a / z + z;
+ z = ( 0x20000 <= z ) ? 0xFFFF8000 : ( z<<15 );
+ if ( z <= a ) return (bits32) ( ( (sbits32) a )>>1 );
+ }
+ return ( (bits32) ( ( ( (bits64) a )<<31 ) / z ) ) + ( z>>1 );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the number of leading 0 bits before the most-significant 1 bit of
+| `a'. If `a' is zero, 32 is returned.
+*----------------------------------------------------------------------------*/
+
+static int8 countLeadingZeros32( bits32 a )
+{
+ static const int8 countLeadingZerosHigh[] = {
+ 8, 7, 6, 6, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4,
+ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
+ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
+ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
+ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
+ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
+ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
+ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
+ };
+ int8 shiftCount;
+
+ shiftCount = 0;
+ if ( a < 0x10000 ) {
+ shiftCount += 16;
+ a <<= 16;
+ }
+ if ( a < 0x1000000 ) {
+ shiftCount += 8;
+ a <<= 8;
+ }
+ shiftCount += countLeadingZerosHigh[ a>>24 ];
+ return shiftCount;
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the number of leading 0 bits before the most-significant 1 bit of
+| `a'. If `a' is zero, 64 is returned.
+*----------------------------------------------------------------------------*/
+
+static int8 countLeadingZeros64( bits64 a )
+{
+ int8 shiftCount;
+
+ shiftCount = 0;
+ if ( a < ( (bits64) 1 )<<32 ) {
+ shiftCount += 32;
+ }
+ else {
+ a >>= 32;
+ }
+ shiftCount += countLeadingZeros32( a );
+ return shiftCount;
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the 128-bit value formed by concatenating `a0' and `a1'
+| is equal to the 128-bit value formed by concatenating `b0' and `b1'.
+| Otherwise, returns 0.
+*----------------------------------------------------------------------------*/
+
+INLINE flag eq128( bits64 a0, bits64 a1, bits64 b0, bits64 b1 )
+{
+
+ return ( a0 == b0 ) && ( a1 == b1 );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is less
+| than or equal to the 128-bit value formed by concatenating `b0' and `b1'.
+| Otherwise, returns 0.
+*----------------------------------------------------------------------------*/
+
+INLINE flag le128( bits64 a0, bits64 a1, bits64 b0, bits64 b1 )
+{
+
+ return ( a0 < b0 ) || ( ( a0 == b0 ) && ( a1 <= b1 ) );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is less
+| than the 128-bit value formed by concatenating `b0' and `b1'. Otherwise,
+| returns 0.
+*----------------------------------------------------------------------------*/
+
+INLINE flag lt128( bits64 a0, bits64 a1, bits64 b0, bits64 b1 )
+{
+
+ return ( a0 < b0 ) || ( ( a0 == b0 ) && ( a1 < b1 ) );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is
+| not equal to the 128-bit value formed by concatenating `b0' and `b1'.
+| Otherwise, returns 0.
+*----------------------------------------------------------------------------*/
+
+INLINE flag ne128( bits64 a0, bits64 a1, bits64 b0, bits64 b1 )
+{
+
+ return ( a0 != b0 ) || ( a1 != b1 );
+
+}
+
diff --git a/fpu/softfloat-native.c b/fpu/softfloat-native.c
new file mode 100644
index 0000000..8259a7c
--- /dev/null
+++ b/fpu/softfloat-native.c
@@ -0,0 +1,262 @@
+/* Native implementation of soft float functions. Only a single status
+ context is supported */
+#include "softfloat.h"
+#include <math.h>
+
+void set_float_rounding_mode(int val STATUS_PARAM)
+{
+ STATUS(float_rounding_mode) = val;
+#if defined(_BSD) && !defined(__APPLE__)
+ fpsetround(val);
+#elif defined(__arm__)
+ /* nothing to do */
+#else
+ fesetround(val);
+#endif
+}
+
+#ifdef FLOATX80
+void set_floatx80_rounding_precision(int val STATUS_PARAM)
+{
+ STATUS(floatx80_rounding_precision) = val;
+}
+#endif
+
+#if defined(_BSD)
+#define lrint(d) ((int32_t)rint(d))
+#define llrint(d) ((int64_t)rint(d))
+#endif
+
+#if defined(__powerpc__)
+
+/* correct (but slow) PowerPC rint() (glibc version is incorrect) */
+double qemu_rint(double x)
+{
+ double y = 4503599627370496.0;
+ if (fabs(x) >= y)
+ return x;
+ if (x < 0)
+ y = -y;
+ y = (x + y) - y;
+ if (y == 0.0)
+ y = copysign(y, x);
+ return y;
+}
+
+#define rint qemu_rint
+#endif
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE integer-to-floating-point conversion routines.
+*----------------------------------------------------------------------------*/
+float32 int32_to_float32(int v STATUS_PARAM)
+{
+ return (float32)v;
+}
+
+float64 int32_to_float64(int v STATUS_PARAM)
+{
+ return (float64)v;
+}
+
+#ifdef FLOATX80
+floatx80 int32_to_floatx80(int v STATUS_PARAM)
+{
+ return (floatx80)v;
+}
+#endif
+float32 int64_to_float32( int64_t v STATUS_PARAM)
+{
+ return (float32)v;
+}
+float64 int64_to_float64( int64_t v STATUS_PARAM)
+{
+ return (float64)v;
+}
+#ifdef FLOATX80
+floatx80 int64_to_floatx80( int64_t v STATUS_PARAM)
+{
+ return (floatx80)v;
+}
+#endif
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE single-precision conversion routines.
+*----------------------------------------------------------------------------*/
+int float32_to_int32( float32 a STATUS_PARAM)
+{
+ return lrintf(a);
+}
+int float32_to_int32_round_to_zero( float32 a STATUS_PARAM)
+{
+ return (int)a;
+}
+int64_t float32_to_int64( float32 a STATUS_PARAM)
+{
+ return llrintf(a);
+}
+
+int64_t float32_to_int64_round_to_zero( float32 a STATUS_PARAM)
+{
+ return (int64_t)a;
+}
+
+float64 float32_to_float64( float32 a STATUS_PARAM)
+{
+ return a;
+}
+#ifdef FLOATX80
+floatx80 float32_to_floatx80( float32 a STATUS_PARAM)
+{
+ return a;
+}
+#endif
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE single-precision operations.
+*----------------------------------------------------------------------------*/
+float32 float32_round_to_int( float32 a STATUS_PARAM)
+{
+ return rintf(a);
+}
+
+float32 float32_sqrt( float32 a STATUS_PARAM)
+{
+ return sqrtf(a);
+}
+char float32_is_signaling_nan( float32 a1)
+{
+ float32u u;
+ uint32_t a;
+ u.f = a1;
+ a = u.i;
+ return ( ( ( a>>22 ) & 0x1FF ) == 0x1FE ) && ( a & 0x003FFFFF );
+}
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE double-precision conversion routines.
+*----------------------------------------------------------------------------*/
+int float64_to_int32( float64 a STATUS_PARAM)
+{
+ return lrint(a);
+}
+int float64_to_int32_round_to_zero( float64 a STATUS_PARAM)
+{
+ return (int)a;
+}
+int64_t float64_to_int64( float64 a STATUS_PARAM)
+{
+ return llrint(a);
+}
+int64_t float64_to_int64_round_to_zero( float64 a STATUS_PARAM)
+{
+ return (int64_t)a;
+}
+float32 float64_to_float32( float64 a STATUS_PARAM)
+{
+ return a;
+}
+#ifdef FLOATX80
+floatx80 float64_to_floatx80( float64 a STATUS_PARAM)
+{
+ return a;
+}
+#endif
+#ifdef FLOAT128
+float128 float64_to_float128( float64 a STATUS_PARAM)
+{
+ return a;
+}
+#endif
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE double-precision operations.
+*----------------------------------------------------------------------------*/
+float64 float64_round_to_int( float64 a STATUS_PARAM )
+{
+#if defined(__arm__)
+ switch(STATUS(float_rounding_mode)) {
+ default:
+ case float_round_nearest_even:
+ asm("rndd %0, %1" : "=f" (a) : "f"(a));
+ break;
+ case float_round_down:
+ asm("rnddm %0, %1" : "=f" (a) : "f"(a));
+ break;
+ case float_round_up:
+ asm("rnddp %0, %1" : "=f" (a) : "f"(a));
+ break;
+ case float_round_to_zero:
+ asm("rnddz %0, %1" : "=f" (a) : "f"(a));
+ break;
+ }
+#else
+ return rint(a);
+#endif
+}
+
+float64 float64_sqrt( float64 a STATUS_PARAM)
+{
+ return sqrt(a);
+}
+char float64_is_signaling_nan( float64 a1)
+{
+ float64u u;
+ uint64_t a;
+ u.f = a1;
+ a = u.i;
+ return
+ ( ( ( a>>51 ) & 0xFFF ) == 0xFFE )
+ && ( a & LIT64( 0x0007FFFFFFFFFFFF ) );
+
+}
+
+#ifdef FLOATX80
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE extended double-precision conversion routines.
+*----------------------------------------------------------------------------*/
+int floatx80_to_int32( floatx80 a STATUS_PARAM)
+{
+ return lrintl(a);
+}
+int floatx80_to_int32_round_to_zero( floatx80 a STATUS_PARAM)
+{
+ return (int)a;
+}
+int64_t floatx80_to_int64( floatx80 a STATUS_PARAM)
+{
+ return llrintl(a);
+}
+int64_t floatx80_to_int64_round_to_zero( floatx80 a STATUS_PARAM)
+{
+ return (int64_t)a;
+}
+float32 floatx80_to_float32( floatx80 a STATUS_PARAM)
+{
+ return a;
+}
+float64 floatx80_to_float64( floatx80 a STATUS_PARAM)
+{
+ return a;
+}
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE extended double-precision operations.
+*----------------------------------------------------------------------------*/
+floatx80 floatx80_round_to_int( floatx80 a STATUS_PARAM)
+{
+ return rintl(a);
+}
+floatx80 floatx80_sqrt( floatx80 a STATUS_PARAM)
+{
+ return sqrtl(a);
+}
+char floatx80_is_signaling_nan( floatx80 a1)
+{
+ floatx80u u;
+ u.f = a1;
+ return ( ( u.i.high & 0x7FFF ) == 0x7FFF ) && (bits64) ( u.i.low<<1 );
+}
+
+#endif
diff --git a/fpu/softfloat-native.h b/fpu/softfloat-native.h
new file mode 100644
index 0000000..709df51
--- /dev/null
+++ b/fpu/softfloat-native.h
@@ -0,0 +1,312 @@
+/* Native implementation of soft float functions */
+#include <math.h>
+#if defined(_BSD) && !defined(__APPLE__)
+#include <ieeefp.h>
+#else
+#include <fenv.h>
+#endif
+
+typedef float float32;
+typedef double float64;
+#ifdef FLOATX80
+typedef long double floatx80;
+#endif
+
+typedef union {
+ float32 f;
+ uint32_t i;
+} float32u;
+typedef union {
+ float64 f;
+ uint64_t i;
+} float64u;
+#ifdef FLOATX80
+typedef union {
+ floatx80 f;
+ struct {
+ uint64_t low;
+ uint16_t high;
+ } i;
+} floatx80u;
+#endif
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE floating-point rounding mode.
+*----------------------------------------------------------------------------*/
+#if defined(_BSD) && !defined(__APPLE__)
+enum {
+ float_round_nearest_even = FP_RN,
+ float_round_down = FE_RM,
+ float_round_up = FE_RP,
+ float_round_to_zero = FE_RZ
+};
+#elif defined(__arm__)
+enum {
+ float_round_nearest_even = 0,
+ float_round_down = 1,
+ float_round_up = 2,
+ float_round_to_zero = 3
+};
+#else
+enum {
+ float_round_nearest_even = FE_TONEAREST,
+ float_round_down = FE_DOWNWARD,
+ float_round_up = FE_UPWARD,
+ float_round_to_zero = FE_TOWARDZERO
+};
+#endif
+
+typedef struct float_status {
+ signed char float_rounding_mode;
+#ifdef FLOATX80
+ signed char floatx80_rounding_precision;
+#endif
+} float_status;
+
+void set_float_rounding_mode(int val STATUS_PARAM);
+#ifdef FLOATX80
+void set_floatx80_rounding_precision(int val STATUS_PARAM);
+#endif
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE integer-to-floating-point conversion routines.
+*----------------------------------------------------------------------------*/
+float32 int32_to_float32( int STATUS_PARAM);
+float64 int32_to_float64( int STATUS_PARAM);
+#ifdef FLOATX80
+floatx80 int32_to_floatx80( int STATUS_PARAM);
+#endif
+#ifdef FLOAT128
+float128 int32_to_float128( int STATUS_PARAM);
+#endif
+float32 int64_to_float32( int64_t STATUS_PARAM);
+float64 int64_to_float64( int64_t STATUS_PARAM);
+#ifdef FLOATX80
+floatx80 int64_to_floatx80( int64_t STATUS_PARAM);
+#endif
+#ifdef FLOAT128
+float128 int64_to_float128( int64_t STATUS_PARAM);
+#endif
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE single-precision conversion routines.
+*----------------------------------------------------------------------------*/
+int float32_to_int32( float32 STATUS_PARAM);
+int float32_to_int32_round_to_zero( float32 STATUS_PARAM);
+int64_t float32_to_int64( float32 STATUS_PARAM);
+int64_t float32_to_int64_round_to_zero( float32 STATUS_PARAM);
+float64 float32_to_float64( float32 STATUS_PARAM);
+#ifdef FLOATX80
+floatx80 float32_to_floatx80( float32 STATUS_PARAM);
+#endif
+#ifdef FLOAT128
+float128 float32_to_float128( float32 STATUS_PARAM);
+#endif
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE single-precision operations.
+*----------------------------------------------------------------------------*/
+float32 float32_round_to_int( float32 STATUS_PARAM);
+INLINE float32 float32_add( float32 a, float32 b STATUS_PARAM)
+{
+ return a + b;
+}
+INLINE float32 float32_sub( float32 a, float32 b STATUS_PARAM)
+{
+ return a - b;
+}
+INLINE float32 float32_mul( float32 a, float32 b STATUS_PARAM)
+{
+ return a * b;
+}
+INLINE float32 float32_div( float32 a, float32 b STATUS_PARAM)
+{
+ return a / b;
+}
+float32 float32_rem( float32, float32 STATUS_PARAM);
+float32 float32_sqrt( float32 STATUS_PARAM);
+INLINE char float32_eq( float32 a, float32 b STATUS_PARAM)
+{
+ /* XXX: incorrect because it can raise an exception */
+ return a == b;
+}
+INLINE char float32_le( float32 a, float32 b STATUS_PARAM)
+{
+ return a <= b;
+}
+INLINE char float32_lt( float32 a, float32 b STATUS_PARAM)
+{
+ return a < b;
+}
+INLINE char float32_eq_signaling( float32 a, float32 b STATUS_PARAM)
+{
+ return a == b;
+}
+INLINE char float32_le_quiet( float32 a, float32 b STATUS_PARAM)
+{
+ return islessequal(a, b);
+}
+INLINE char float32_lt_quiet( float32 a, float32 b STATUS_PARAM)
+{
+ return isless(a, b);
+}
+char float32_is_signaling_nan( float32 );
+
+INLINE float32 float32_abs(float32 a)
+{
+ return fabsf(a);
+}
+
+INLINE float32 float32_chs(float32 a)
+{
+ return -a;
+}
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE double-precision conversion routines.
+*----------------------------------------------------------------------------*/
+int float64_to_int32( float64 STATUS_PARAM );
+int float64_to_int32_round_to_zero( float64 STATUS_PARAM );
+int64_t float64_to_int64( float64 STATUS_PARAM );
+int64_t float64_to_int64_round_to_zero( float64 STATUS_PARAM );
+float32 float64_to_float32( float64 STATUS_PARAM );
+#ifdef FLOATX80
+floatx80 float64_to_floatx80( float64 STATUS_PARAM );
+#endif
+#ifdef FLOAT128
+float128 float64_to_float128( float64 STATUS_PARAM );
+#endif
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE double-precision operations.
+*----------------------------------------------------------------------------*/
+float64 float64_round_to_int( float64 STATUS_PARAM );
+INLINE float64 float64_add( float64 a, float64 b STATUS_PARAM)
+{
+ return a + b;
+}
+INLINE float64 float64_sub( float64 a, float64 b STATUS_PARAM)
+{
+ return a - b;
+}
+INLINE float64 float64_mul( float64 a, float64 b STATUS_PARAM)
+{
+ return a * b;
+}
+INLINE float64 float64_div( float64 a, float64 b STATUS_PARAM)
+{
+ return a / b;
+}
+float64 float64_rem( float64, float64 STATUS_PARAM );
+float64 float64_sqrt( float64 STATUS_PARAM );
+INLINE char float64_eq( float64 a, float64 b STATUS_PARAM)
+{
+ return a == b;
+}
+INLINE char float64_le( float64 a, float64 b STATUS_PARAM)
+{
+ return a <= b;
+}
+INLINE char float64_lt( float64 a, float64 b STATUS_PARAM)
+{
+ return a < b;
+}
+INLINE char float64_eq_signaling( float64 a, float64 b STATUS_PARAM)
+{
+ return a == b;
+}
+INLINE char float64_le_quiet( float64 a, float64 b STATUS_PARAM)
+{
+ return islessequal(a, b);
+}
+INLINE char float64_lt_quiet( float64 a, float64 b STATUS_PARAM)
+{
+ return isless(a, b);
+
+}
+char float64_is_signaling_nan( float64 );
+
+INLINE float64 float64_abs(float64 a)
+{
+ return fabs(a);
+}
+
+INLINE float64 float64_chs(float64 a)
+{
+ return -a;
+}
+
+#ifdef FLOATX80
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE extended double-precision conversion routines.
+*----------------------------------------------------------------------------*/
+int floatx80_to_int32( floatx80 STATUS_PARAM );
+int floatx80_to_int32_round_to_zero( floatx80 STATUS_PARAM );
+int64_t floatx80_to_int64( floatx80 STATUS_PARAM);
+int64_t floatx80_to_int64_round_to_zero( floatx80 STATUS_PARAM);
+float32 floatx80_to_float32( floatx80 STATUS_PARAM );
+float64 floatx80_to_float64( floatx80 STATUS_PARAM );
+#ifdef FLOAT128
+float128 floatx80_to_float128( floatx80 STATUS_PARAM );
+#endif
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE extended double-precision operations.
+*----------------------------------------------------------------------------*/
+floatx80 floatx80_round_to_int( floatx80 STATUS_PARAM );
+INLINE floatx80 floatx80_add( floatx80 a, floatx80 b STATUS_PARAM)
+{
+ return a + b;
+}
+INLINE floatx80 floatx80_sub( floatx80 a, floatx80 b STATUS_PARAM)
+{
+ return a - b;
+}
+INLINE floatx80 floatx80_mul( floatx80 a, floatx80 b STATUS_PARAM)
+{
+ return a * b;
+}
+INLINE floatx80 floatx80_div( floatx80 a, floatx80 b STATUS_PARAM)
+{
+ return a / b;
+}
+floatx80 floatx80_rem( floatx80, floatx80 STATUS_PARAM );
+floatx80 floatx80_sqrt( floatx80 STATUS_PARAM );
+INLINE char floatx80_eq( floatx80 a, floatx80 b STATUS_PARAM)
+{
+ return a == b;
+}
+INLINE char floatx80_le( floatx80 a, floatx80 b STATUS_PARAM)
+{
+ return a <= b;
+}
+INLINE char floatx80_lt( floatx80 a, floatx80 b STATUS_PARAM)
+{
+ return a < b;
+}
+INLINE char floatx80_eq_signaling( floatx80 a, floatx80 b STATUS_PARAM)
+{
+ return a == b;
+}
+INLINE char floatx80_le_quiet( floatx80 a, floatx80 b STATUS_PARAM)
+{
+ return islessequal(a, b);
+}
+INLINE char floatx80_lt_quiet( floatx80 a, floatx80 b STATUS_PARAM)
+{
+ return isless(a, b);
+
+}
+char floatx80_is_signaling_nan( floatx80 );
+
+INLINE floatx80 floatx80_abs(floatx80 a)
+{
+ return fabsl(a);
+}
+
+INLINE floatx80 floatx80_chs(floatx80 a)
+{
+ return -a;
+}
+#endif
diff --git a/fpu/softfloat-specialize.h b/fpu/softfloat-specialize.h
new file mode 100644
index 0000000..d430f58
--- /dev/null
+++ b/fpu/softfloat-specialize.h
@@ -0,0 +1,464 @@
+
+/*============================================================================
+
+This C source fragment is part of the SoftFloat IEC/IEEE Floating-point
+Arithmetic Package, Release 2b.
+
+Written by John R. Hauser. This work was made possible in part by the
+International Computer Science Institute, located at Suite 600, 1947 Center
+Street, Berkeley, California 94704. Funding was partially provided by the
+National Science Foundation under grant MIP-9311980. The original version
+of this code was written as part of a project to build a fixed-point vector
+processor in collaboration with the University of California at Berkeley,
+overseen by Profs. Nelson Morgan and John Wawrzynek. More information
+is available through the Web page `http://www.cs.berkeley.edu/~jhauser/
+arithmetic/SoftFloat.html'.
+
+THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort has
+been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT TIMES
+RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO PERSONS
+AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ALL LOSSES,
+COSTS, OR OTHER PROBLEMS THEY INCUR DUE TO THE SOFTWARE, AND WHO FURTHERMORE
+EFFECTIVELY INDEMNIFY JOHN HAUSER AND THE INTERNATIONAL COMPUTER SCIENCE
+INSTITUTE (possibly via similar legal warning) AGAINST ALL LOSSES, COSTS, OR
+OTHER PROBLEMS INCURRED BY THEIR CUSTOMERS AND CLIENTS DUE TO THE SOFTWARE.
+
+Derivative works are acceptable, even for commercial purposes, so long as
+(1) the source code for the derivative work includes prominent notice that
+the work is derivative, and (2) the source code includes prominent notice with
+these four paragraphs for those parts of this code that are retained.
+
+=============================================================================*/
+
+/*----------------------------------------------------------------------------
+| Underflow tininess-detection mode, statically initialized to default value.
+| (The declaration in `softfloat.h' must match the `int8' type here.)
+*----------------------------------------------------------------------------*/
+int8 float_detect_tininess = float_tininess_after_rounding;
+
+/*----------------------------------------------------------------------------
+| Raises the exceptions specified by `flags'. Floating-point traps can be
+| defined here if desired. It is currently not possible for such a trap
+| to substitute a result value. If traps are not implemented, this routine
+| should be simply `float_exception_flags |= flags;'.
+*----------------------------------------------------------------------------*/
+
+void float_raise( int8 flags STATUS_PARAM )
+{
+
+ STATUS(float_exception_flags) |= flags;
+
+}
+
+/*----------------------------------------------------------------------------
+| Internal canonical NaN format.
+*----------------------------------------------------------------------------*/
+typedef struct {
+ flag sign;
+ bits64 high, low;
+} commonNaNT;
+
+/*----------------------------------------------------------------------------
+| The pattern for a default generated single-precision NaN.
+*----------------------------------------------------------------------------*/
+#define float32_default_nan 0xFFC00000
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the single-precision floating-point value `a' is a NaN;
+| otherwise returns 0.
+*----------------------------------------------------------------------------*/
+
+flag float32_is_nan( float32 a )
+{
+
+ return ( 0xFF000000 < (bits32) ( a<<1 ) );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the single-precision floating-point value `a' is a signaling
+| NaN; otherwise returns 0.
+*----------------------------------------------------------------------------*/
+
+flag float32_is_signaling_nan( float32 a )
+{
+
+ return ( ( ( a>>22 ) & 0x1FF ) == 0x1FE ) && ( a & 0x003FFFFF );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the single-precision floating-point NaN
+| `a' to the canonical NaN format. If `a' is a signaling NaN, the invalid
+| exception is raised.
+*----------------------------------------------------------------------------*/
+
+static commonNaNT float32ToCommonNaN( float32 a STATUS_PARAM )
+{
+ commonNaNT z;
+
+ if ( float32_is_signaling_nan( a ) ) float_raise( float_flag_invalid STATUS_VAR );
+ z.sign = a>>31;
+ z.low = 0;
+ z.high = ( (bits64) a )<<41;
+ return z;
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the canonical NaN `a' to the single-
+| precision floating-point format.
+*----------------------------------------------------------------------------*/
+
+static float32 commonNaNToFloat32( commonNaNT a )
+{
+
+ return ( ( (bits32) a.sign )<<31 ) | 0x7FC00000 | ( a.high>>41 );
+
+}
+
+/*----------------------------------------------------------------------------
+| Takes two single-precision floating-point values `a' and `b', one of which
+| is a NaN, and returns the appropriate NaN result. If either `a' or `b' is a
+| signaling NaN, the invalid exception is raised.
+*----------------------------------------------------------------------------*/
+
+static float32 propagateFloat32NaN( float32 a, float32 b STATUS_PARAM)
+{
+ flag aIsNaN, aIsSignalingNaN, bIsNaN, bIsSignalingNaN;
+
+ aIsNaN = float32_is_nan( a );
+ aIsSignalingNaN = float32_is_signaling_nan( a );
+ bIsNaN = float32_is_nan( b );
+ bIsSignalingNaN = float32_is_signaling_nan( b );
+ a |= 0x00400000;
+ b |= 0x00400000;
+ if ( aIsSignalingNaN | bIsSignalingNaN ) float_raise( float_flag_invalid STATUS_VAR);
+ if ( aIsSignalingNaN ) {
+ if ( bIsSignalingNaN ) goto returnLargerSignificand;
+ return bIsNaN ? b : a;
+ }
+ else if ( aIsNaN ) {
+ if ( bIsSignalingNaN | ! bIsNaN ) return a;
+ returnLargerSignificand:
+ if ( (bits32) ( a<<1 ) < (bits32) ( b<<1 ) ) return b;
+ if ( (bits32) ( b<<1 ) < (bits32) ( a<<1 ) ) return a;
+ return ( a < b ) ? a : b;
+ }
+ else {
+ return b;
+ }
+
+}
+
+/*----------------------------------------------------------------------------
+| The pattern for a default generated double-precision NaN.
+*----------------------------------------------------------------------------*/
+#define float64_default_nan LIT64( 0xFFF8000000000000 )
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the double-precision floating-point value `a' is a NaN;
+| otherwise returns 0.
+*----------------------------------------------------------------------------*/
+
+flag float64_is_nan( float64 a )
+{
+
+ return ( LIT64( 0xFFE0000000000000 ) < (bits64) ( a<<1 ) );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the double-precision floating-point value `a' is a signaling
+| NaN; otherwise returns 0.
+*----------------------------------------------------------------------------*/
+
+flag float64_is_signaling_nan( float64 a )
+{
+
+ return
+ ( ( ( a>>51 ) & 0xFFF ) == 0xFFE )
+ && ( a & LIT64( 0x0007FFFFFFFFFFFF ) );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the double-precision floating-point NaN
+| `a' to the canonical NaN format. If `a' is a signaling NaN, the invalid
+| exception is raised.
+*----------------------------------------------------------------------------*/
+
+static commonNaNT float64ToCommonNaN( float64 a STATUS_PARAM)
+{
+ commonNaNT z;
+
+ if ( float64_is_signaling_nan( a ) ) float_raise( float_flag_invalid STATUS_VAR);
+ z.sign = a>>63;
+ z.low = 0;
+ z.high = a<<12;
+ return z;
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the canonical NaN `a' to the double-
+| precision floating-point format.
+*----------------------------------------------------------------------------*/
+
+static float64 commonNaNToFloat64( commonNaNT a )
+{
+
+ return
+ ( ( (bits64) a.sign )<<63 )
+ | LIT64( 0x7FF8000000000000 )
+ | ( a.high>>12 );
+
+}
+
+/*----------------------------------------------------------------------------
+| Takes two double-precision floating-point values `a' and `b', one of which
+| is a NaN, and returns the appropriate NaN result. If either `a' or `b' is a
+| signaling NaN, the invalid exception is raised.
+*----------------------------------------------------------------------------*/
+
+static float64 propagateFloat64NaN( float64 a, float64 b STATUS_PARAM)
+{
+ flag aIsNaN, aIsSignalingNaN, bIsNaN, bIsSignalingNaN;
+
+ aIsNaN = float64_is_nan( a );
+ aIsSignalingNaN = float64_is_signaling_nan( a );
+ bIsNaN = float64_is_nan( b );
+ bIsSignalingNaN = float64_is_signaling_nan( b );
+ a |= LIT64( 0x0008000000000000 );
+ b |= LIT64( 0x0008000000000000 );
+ if ( aIsSignalingNaN | bIsSignalingNaN ) float_raise( float_flag_invalid STATUS_VAR);
+ if ( aIsSignalingNaN ) {
+ if ( bIsSignalingNaN ) goto returnLargerSignificand;
+ return bIsNaN ? b : a;
+ }
+ else if ( aIsNaN ) {
+ if ( bIsSignalingNaN | ! bIsNaN ) return a;
+ returnLargerSignificand:
+ if ( (bits64) ( a<<1 ) < (bits64) ( b<<1 ) ) return b;
+ if ( (bits64) ( b<<1 ) < (bits64) ( a<<1 ) ) return a;
+ return ( a < b ) ? a : b;
+ }
+ else {
+ return b;
+ }
+
+}
+
+#ifdef FLOATX80
+
+/*----------------------------------------------------------------------------
+| The pattern for a default generated extended double-precision NaN. The
+| `high' and `low' values hold the most- and least-significant bits,
+| respectively.
+*----------------------------------------------------------------------------*/
+#define floatx80_default_nan_high 0xFFFF
+#define floatx80_default_nan_low LIT64( 0xC000000000000000 )
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the extended double-precision floating-point value `a' is a
+| NaN; otherwise returns 0.
+*----------------------------------------------------------------------------*/
+
+flag floatx80_is_nan( floatx80 a )
+{
+
+ return ( ( a.high & 0x7FFF ) == 0x7FFF ) && (bits64) ( a.low<<1 );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the extended double-precision floating-point value `a' is a
+| signaling NaN; otherwise returns 0.
+*----------------------------------------------------------------------------*/
+
+flag floatx80_is_signaling_nan( floatx80 a )
+{
+ bits64 aLow;
+
+ aLow = a.low & ~ LIT64( 0x4000000000000000 );
+ return
+ ( ( a.high & 0x7FFF ) == 0x7FFF )
+ && (bits64) ( aLow<<1 )
+ && ( a.low == aLow );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the extended double-precision floating-
+| point NaN `a' to the canonical NaN format. If `a' is a signaling NaN, the
+| invalid exception is raised.
+*----------------------------------------------------------------------------*/
+
+static commonNaNT floatx80ToCommonNaN( floatx80 a STATUS_PARAM)
+{
+ commonNaNT z;
+
+ if ( floatx80_is_signaling_nan( a ) ) float_raise( float_flag_invalid STATUS_VAR);
+ z.sign = a.high>>15;
+ z.low = 0;
+ z.high = a.low<<1;
+ return z;
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the canonical NaN `a' to the extended
+| double-precision floating-point format.
+*----------------------------------------------------------------------------*/
+
+static floatx80 commonNaNToFloatx80( commonNaNT a )
+{
+ floatx80 z;
+
+ z.low = LIT64( 0xC000000000000000 ) | ( a.high>>1 );
+ z.high = ( ( (bits16) a.sign )<<15 ) | 0x7FFF;
+ return z;
+
+}
+
+/*----------------------------------------------------------------------------
+| Takes two extended double-precision floating-point values `a' and `b', one
+| of which is a NaN, and returns the appropriate NaN result. If either `a' or
+| `b' is a signaling NaN, the invalid exception is raised.
+*----------------------------------------------------------------------------*/
+
+static floatx80 propagateFloatx80NaN( floatx80 a, floatx80 b STATUS_PARAM)
+{
+ flag aIsNaN, aIsSignalingNaN, bIsNaN, bIsSignalingNaN;
+
+ aIsNaN = floatx80_is_nan( a );
+ aIsSignalingNaN = floatx80_is_signaling_nan( a );
+ bIsNaN = floatx80_is_nan( b );
+ bIsSignalingNaN = floatx80_is_signaling_nan( b );
+ a.low |= LIT64( 0xC000000000000000 );
+ b.low |= LIT64( 0xC000000000000000 );
+ if ( aIsSignalingNaN | bIsSignalingNaN ) float_raise( float_flag_invalid STATUS_VAR);
+ if ( aIsSignalingNaN ) {
+ if ( bIsSignalingNaN ) goto returnLargerSignificand;
+ return bIsNaN ? b : a;
+ }
+ else if ( aIsNaN ) {
+ if ( bIsSignalingNaN | ! bIsNaN ) return a;
+ returnLargerSignificand:
+ if ( a.low < b.low ) return b;
+ if ( b.low < a.low ) return a;
+ return ( a.high < b.high ) ? a : b;
+ }
+ else {
+ return b;
+ }
+
+}
+
+#endif
+
+#ifdef FLOAT128
+
+/*----------------------------------------------------------------------------
+| The pattern for a default generated quadruple-precision NaN. The `high' and
+| `low' values hold the most- and least-significant bits, respectively.
+*----------------------------------------------------------------------------*/
+#define float128_default_nan_high LIT64( 0xFFFF800000000000 )
+#define float128_default_nan_low LIT64( 0x0000000000000000 )
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the quadruple-precision floating-point value `a' is a NaN;
+| otherwise returns 0.
+*----------------------------------------------------------------------------*/
+
+flag float128_is_nan( float128 a )
+{
+
+ return
+ ( LIT64( 0xFFFE000000000000 ) <= (bits64) ( a.high<<1 ) )
+ && ( a.low || ( a.high & LIT64( 0x0000FFFFFFFFFFFF ) ) );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the quadruple-precision floating-point value `a' is a
+| signaling NaN; otherwise returns 0.
+*----------------------------------------------------------------------------*/
+
+flag float128_is_signaling_nan( float128 a )
+{
+
+ return
+ ( ( ( a.high>>47 ) & 0xFFFF ) == 0xFFFE )
+ && ( a.low || ( a.high & LIT64( 0x00007FFFFFFFFFFF ) ) );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the quadruple-precision floating-point NaN
+| `a' to the canonical NaN format. If `a' is a signaling NaN, the invalid
+| exception is raised.
+*----------------------------------------------------------------------------*/
+
+static commonNaNT float128ToCommonNaN( float128 a STATUS_PARAM)
+{
+ commonNaNT z;
+
+ if ( float128_is_signaling_nan( a ) ) float_raise( float_flag_invalid STATUS_VAR);
+ z.sign = a.high>>63;
+ shortShift128Left( a.high, a.low, 16, &z.high, &z.low );
+ return z;
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the canonical NaN `a' to the quadruple-
+| precision floating-point format.
+*----------------------------------------------------------------------------*/
+
+static float128 commonNaNToFloat128( commonNaNT a )
+{
+ float128 z;
+
+ shift128Right( a.high, a.low, 16, &z.high, &z.low );
+ z.high |= ( ( (bits64) a.sign )<<63 ) | LIT64( 0x7FFF800000000000 );
+ return z;
+
+}
+
+/*----------------------------------------------------------------------------
+| Takes two quadruple-precision floating-point values `a' and `b', one of
+| which is a NaN, and returns the appropriate NaN result. If either `a' or
+| `b' is a signaling NaN, the invalid exception is raised.
+*----------------------------------------------------------------------------*/
+
+static float128 propagateFloat128NaN( float128 a, float128 b STATUS_PARAM)
+{
+ flag aIsNaN, aIsSignalingNaN, bIsNaN, bIsSignalingNaN;
+
+ aIsNaN = float128_is_nan( a );
+ aIsSignalingNaN = float128_is_signaling_nan( a );
+ bIsNaN = float128_is_nan( b );
+ bIsSignalingNaN = float128_is_signaling_nan( b );
+ a.high |= LIT64( 0x0000800000000000 );
+ b.high |= LIT64( 0x0000800000000000 );
+ if ( aIsSignalingNaN | bIsSignalingNaN ) float_raise( float_flag_invalid STATUS_VAR);
+ if ( aIsSignalingNaN ) {
+ if ( bIsSignalingNaN ) goto returnLargerSignificand;
+ return bIsNaN ? b : a;
+ }
+ else if ( aIsNaN ) {
+ if ( bIsSignalingNaN | ! bIsNaN ) return a;
+ returnLargerSignificand:
+ if ( lt128( a.high<<1, a.low, b.high<<1, b.low ) ) return b;
+ if ( lt128( b.high<<1, b.low, a.high<<1, a.low ) ) return a;
+ return ( a.high < b.high ) ? a : b;
+ }
+ else {
+ return b;
+ }
+
+}
+
+#endif
+
diff --git a/fpu/softfloat.c b/fpu/softfloat.c
new file mode 100644
index 0000000..ad57fd9
--- /dev/null
+++ b/fpu/softfloat.c
@@ -0,0 +1,5185 @@
+
+/*============================================================================
+
+This C source file is part of the SoftFloat IEC/IEEE Floating-point Arithmetic
+Package, Release 2b.
+
+Written by John R. Hauser. This work was made possible in part by the
+International Computer Science Institute, located at Suite 600, 1947 Center
+Street, Berkeley, California 94704. Funding was partially provided by the
+National Science Foundation under grant MIP-9311980. The original version
+of this code was written as part of a project to build a fixed-point vector
+processor in collaboration with the University of California at Berkeley,
+overseen by Profs. Nelson Morgan and John Wawrzynek. More information
+is available through the Web page `http://www.cs.berkeley.edu/~jhauser/
+arithmetic/SoftFloat.html'.
+
+THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort has
+been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT TIMES
+RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO PERSONS
+AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ALL LOSSES,
+COSTS, OR OTHER PROBLEMS THEY INCUR DUE TO THE SOFTWARE, AND WHO FURTHERMORE
+EFFECTIVELY INDEMNIFY JOHN HAUSER AND THE INTERNATIONAL COMPUTER SCIENCE
+INSTITUTE (possibly via similar legal warning) AGAINST ALL LOSSES, COSTS, OR
+OTHER PROBLEMS INCURRED BY THEIR CUSTOMERS AND CLIENTS DUE TO THE SOFTWARE.
+
+Derivative works are acceptable, even for commercial purposes, so long as
+(1) the source code for the derivative work includes prominent notice that
+the work is derivative, and (2) the source code includes prominent notice with
+these four paragraphs for those parts of this code that are retained.
+
+=============================================================================*/
+
+#include "softfloat.h"
+
+/*----------------------------------------------------------------------------
+| Primitive arithmetic functions, including multi-word arithmetic, and
+| division and square root approximations. (Can be specialized to target if
+| desired.)
+*----------------------------------------------------------------------------*/
+#include "softfloat-macros.h"
+
+/*----------------------------------------------------------------------------
+| Functions and definitions to determine: (1) whether tininess for underflow
+| is detected before or after rounding by default, (2) what (if anything)
+| happens when exceptions are raised, (3) how signaling NaNs are distinguished
+| from quiet NaNs, (4) the default generated quiet NaNs, and (5) how NaNs
+| are propagated from function inputs to output. These details are target-
+| specific.
+*----------------------------------------------------------------------------*/
+#include "softfloat-specialize.h"
+
+void set_float_rounding_mode(int val STATUS_PARAM)
+{
+ STATUS(float_rounding_mode) = val;
+}
+
+#ifdef FLOATX80
+void set_floatx80_rounding_precision(int val STATUS_PARAM)
+{
+ STATUS(floatx80_rounding_precision) = val;
+}
+#endif
+
+/*----------------------------------------------------------------------------
+| Takes a 64-bit fixed-point value `absZ' with binary point between bits 6
+| and 7, and returns the properly rounded 32-bit integer corresponding to the
+| input. If `zSign' is 1, the input is negated before being converted to an
+| integer. Bit 63 of `absZ' must be zero. Ordinarily, the fixed-point input
+| is simply rounded to an integer, with the inexact exception raised if the
+| input cannot be represented exactly as an integer. However, if the fixed-
+| point input is too large, the invalid exception is raised and the largest
+| positive or negative integer is returned.
+*----------------------------------------------------------------------------*/
+
+static int32 roundAndPackInt32( flag zSign, bits64 absZ STATUS_PARAM)
+{
+ int8 roundingMode;
+ flag roundNearestEven;
+ int8 roundIncrement, roundBits;
+ int32 z;
+
+ roundingMode = STATUS(float_rounding_mode);
+ roundNearestEven = ( roundingMode == float_round_nearest_even );
+ roundIncrement = 0x40;
+ if ( ! roundNearestEven ) {
+ if ( roundingMode == float_round_to_zero ) {
+ roundIncrement = 0;
+ }
+ else {
+ roundIncrement = 0x7F;
+ if ( zSign ) {
+ if ( roundingMode == float_round_up ) roundIncrement = 0;
+ }
+ else {
+ if ( roundingMode == float_round_down ) roundIncrement = 0;
+ }
+ }
+ }
+ roundBits = absZ & 0x7F;
+ absZ = ( absZ + roundIncrement )>>7;
+ absZ &= ~ ( ( ( roundBits ^ 0x40 ) == 0 ) & roundNearestEven );
+ z = absZ;
+ if ( zSign ) z = - z;
+ if ( ( absZ>>32 ) || ( z && ( ( z < 0 ) ^ zSign ) ) ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ return zSign ? (sbits32) 0x80000000 : 0x7FFFFFFF;
+ }
+ if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact;
+ return z;
+
+}
+
+/*----------------------------------------------------------------------------
+| Takes the 128-bit fixed-point value formed by concatenating `absZ0' and
+| `absZ1', with binary point between bits 63 and 64 (between the input words),
+| and returns the properly rounded 64-bit integer corresponding to the input.
+| If `zSign' is 1, the input is negated before being converted to an integer.
+| Ordinarily, the fixed-point input is simply rounded to an integer, with
+| the inexact exception raised if the input cannot be represented exactly as
+| an integer. However, if the fixed-point input is too large, the invalid
+| exception is raised and the largest positive or negative integer is
+| returned.
+*----------------------------------------------------------------------------*/
+
+static int64 roundAndPackInt64( flag zSign, bits64 absZ0, bits64 absZ1 STATUS_PARAM)
+{
+ int8 roundingMode;
+ flag roundNearestEven, increment;
+ int64 z;
+
+ roundingMode = STATUS(float_rounding_mode);
+ roundNearestEven = ( roundingMode == float_round_nearest_even );
+ increment = ( (sbits64) absZ1 < 0 );
+ if ( ! roundNearestEven ) {
+ if ( roundingMode == float_round_to_zero ) {
+ increment = 0;
+ }
+ else {
+ if ( zSign ) {
+ increment = ( roundingMode == float_round_down ) && absZ1;
+ }
+ else {
+ increment = ( roundingMode == float_round_up ) && absZ1;
+ }
+ }
+ }
+ if ( increment ) {
+ ++absZ0;
+ if ( absZ0 == 0 ) goto overflow;
+ absZ0 &= ~ ( ( (bits64) ( absZ1<<1 ) == 0 ) & roundNearestEven );
+ }
+ z = absZ0;
+ if ( zSign ) z = - z;
+ if ( z && ( ( z < 0 ) ^ zSign ) ) {
+ overflow:
+ float_raise( float_flag_invalid STATUS_VAR);
+ return
+ zSign ? (sbits64) LIT64( 0x8000000000000000 )
+ : LIT64( 0x7FFFFFFFFFFFFFFF );
+ }
+ if ( absZ1 ) STATUS(float_exception_flags) |= float_flag_inexact;
+ return z;
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the fraction bits of the single-precision floating-point value `a'.
+*----------------------------------------------------------------------------*/
+
+INLINE bits32 extractFloat32Frac( float32 a )
+{
+
+ return a & 0x007FFFFF;
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the exponent bits of the single-precision floating-point value `a'.
+*----------------------------------------------------------------------------*/
+
+INLINE int16 extractFloat32Exp( float32 a )
+{
+
+ return ( a>>23 ) & 0xFF;
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the sign bit of the single-precision floating-point value `a'.
+*----------------------------------------------------------------------------*/
+
+INLINE flag extractFloat32Sign( float32 a )
+{
+
+ return a>>31;
+
+}
+
+/*----------------------------------------------------------------------------
+| Normalizes the subnormal single-precision floating-point value represented
+| by the denormalized significand `aSig'. The normalized exponent and
+| significand are stored at the locations pointed to by `zExpPtr' and
+| `zSigPtr', respectively.
+*----------------------------------------------------------------------------*/
+
+static void
+ normalizeFloat32Subnormal( bits32 aSig, int16 *zExpPtr, bits32 *zSigPtr )
+{
+ int8 shiftCount;
+
+ shiftCount = countLeadingZeros32( aSig ) - 8;
+ *zSigPtr = aSig<<shiftCount;
+ *zExpPtr = 1 - shiftCount;
+
+}
+
+/*----------------------------------------------------------------------------
+| Packs the sign `zSign', exponent `zExp', and significand `zSig' into a
+| single-precision floating-point value, returning the result. After being
+| shifted into the proper positions, the three fields are simply added
+| together to form the result. This means that any integer portion of `zSig'
+| will be added into the exponent. Since a properly normalized significand
+| will have an integer portion equal to 1, the `zExp' input should be 1 less
+| than the desired result exponent whenever `zSig' is a complete, normalized
+| significand.
+*----------------------------------------------------------------------------*/
+
+INLINE float32 packFloat32( flag zSign, int16 zExp, bits32 zSig )
+{
+
+ return ( ( (bits32) zSign )<<31 ) + ( ( (bits32) zExp )<<23 ) + zSig;
+
+}
+
+/*----------------------------------------------------------------------------
+| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
+| and significand `zSig', and returns the proper single-precision floating-
+| point value corresponding to the abstract input. Ordinarily, the abstract
+| value is simply rounded and packed into the single-precision format, with
+| the inexact exception raised if the abstract input cannot be represented
+| exactly. However, if the abstract value is too large, the overflow and
+| inexact exceptions are raised and an infinity or maximal finite value is
+| returned. If the abstract value is too small, the input value is rounded to
+| a subnormal number, and the underflow and inexact exceptions are raised if
+| the abstract input cannot be represented exactly as a subnormal single-
+| precision floating-point number.
+| The input significand `zSig' has its binary point between bits 30
+| and 29, which is 7 bits to the left of the usual location. This shifted
+| significand must be normalized or smaller. If `zSig' is not normalized,
+| `zExp' must be 0; in that case, the result returned is a subnormal number,
+| and it must not require rounding. In the usual case that `zSig' is
+| normalized, `zExp' must be 1 less than the ``true'' floating-point exponent.
+| The handling of underflow and overflow follows the IEC/IEEE Standard for
+| Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+static float32 roundAndPackFloat32( flag zSign, int16 zExp, bits32 zSig STATUS_PARAM)
+{
+ int8 roundingMode;
+ flag roundNearestEven;
+ int8 roundIncrement, roundBits;
+ flag isTiny;
+
+ roundingMode = STATUS(float_rounding_mode);
+ roundNearestEven = ( roundingMode == float_round_nearest_even );
+ roundIncrement = 0x40;
+ if ( ! roundNearestEven ) {
+ if ( roundingMode == float_round_to_zero ) {
+ roundIncrement = 0;
+ }
+ else {
+ roundIncrement = 0x7F;
+ if ( zSign ) {
+ if ( roundingMode == float_round_up ) roundIncrement = 0;
+ }
+ else {
+ if ( roundingMode == float_round_down ) roundIncrement = 0;
+ }
+ }
+ }
+ roundBits = zSig & 0x7F;
+ if ( 0xFD <= (bits16) zExp ) {
+ if ( ( 0xFD < zExp )
+ || ( ( zExp == 0xFD )
+ && ( (sbits32) ( zSig + roundIncrement ) < 0 ) )
+ ) {
+ float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR);
+ return packFloat32( zSign, 0xFF, 0 ) - ( roundIncrement == 0 );
+ }
+ if ( zExp < 0 ) {
+ isTiny =
+ ( STATUS(float_detect_tininess) == float_tininess_before_rounding )
+ || ( zExp < -1 )
+ || ( zSig + roundIncrement < 0x80000000 );
+ shift32RightJamming( zSig, - zExp, &zSig );
+ zExp = 0;
+ roundBits = zSig & 0x7F;
+ if ( isTiny && roundBits ) float_raise( float_flag_underflow STATUS_VAR);
+ }
+ }
+ if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact;
+ zSig = ( zSig + roundIncrement )>>7;
+ zSig &= ~ ( ( ( roundBits ^ 0x40 ) == 0 ) & roundNearestEven );
+ if ( zSig == 0 ) zExp = 0;
+ return packFloat32( zSign, zExp, zSig );
+
+}
+
+/*----------------------------------------------------------------------------
+| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
+| and significand `zSig', and returns the proper single-precision floating-
+| point value corresponding to the abstract input. This routine is just like
+| `roundAndPackFloat32' except that `zSig' does not have to be normalized.
+| Bit 31 of `zSig' must be zero, and `zExp' must be 1 less than the ``true''
+| floating-point exponent.
+*----------------------------------------------------------------------------*/
+
+static float32
+ normalizeRoundAndPackFloat32( flag zSign, int16 zExp, bits32 zSig STATUS_PARAM)
+{
+ int8 shiftCount;
+
+ shiftCount = countLeadingZeros32( zSig ) - 1;
+ return roundAndPackFloat32( zSign, zExp - shiftCount, zSig<<shiftCount STATUS_VAR);
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the fraction bits of the double-precision floating-point value `a'.
+*----------------------------------------------------------------------------*/
+
+INLINE bits64 extractFloat64Frac( float64 a )
+{
+
+ return a & LIT64( 0x000FFFFFFFFFFFFF );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the exponent bits of the double-precision floating-point value `a'.
+*----------------------------------------------------------------------------*/
+
+INLINE int16 extractFloat64Exp( float64 a )
+{
+
+ return ( a>>52 ) & 0x7FF;
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the sign bit of the double-precision floating-point value `a'.
+*----------------------------------------------------------------------------*/
+
+INLINE flag extractFloat64Sign( float64 a )
+{
+
+ return a>>63;
+
+}
+
+/*----------------------------------------------------------------------------
+| Normalizes the subnormal double-precision floating-point value represented
+| by the denormalized significand `aSig'. The normalized exponent and
+| significand are stored at the locations pointed to by `zExpPtr' and
+| `zSigPtr', respectively.
+*----------------------------------------------------------------------------*/
+
+static void
+ normalizeFloat64Subnormal( bits64 aSig, int16 *zExpPtr, bits64 *zSigPtr )
+{
+ int8 shiftCount;
+
+ shiftCount = countLeadingZeros64( aSig ) - 11;
+ *zSigPtr = aSig<<shiftCount;
+ *zExpPtr = 1 - shiftCount;
+
+}
+
+/*----------------------------------------------------------------------------
+| Packs the sign `zSign', exponent `zExp', and significand `zSig' into a
+| double-precision floating-point value, returning the result. After being
+| shifted into the proper positions, the three fields are simply added
+| together to form the result. This means that any integer portion of `zSig'
+| will be added into the exponent. Since a properly normalized significand
+| will have an integer portion equal to 1, the `zExp' input should be 1 less
+| than the desired result exponent whenever `zSig' is a complete, normalized
+| significand.
+*----------------------------------------------------------------------------*/
+
+INLINE float64 packFloat64( flag zSign, int16 zExp, bits64 zSig )
+{
+
+ return ( ( (bits64) zSign )<<63 ) + ( ( (bits64) zExp )<<52 ) + zSig;
+
+}
+
+/*----------------------------------------------------------------------------
+| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
+| and significand `zSig', and returns the proper double-precision floating-
+| point value corresponding to the abstract input. Ordinarily, the abstract
+| value is simply rounded and packed into the double-precision format, with
+| the inexact exception raised if the abstract input cannot be represented
+| exactly. However, if the abstract value is too large, the overflow and
+| inexact exceptions are raised and an infinity or maximal finite value is
+| returned. If the abstract value is too small, the input value is rounded
+| to a subnormal number, and the underflow and inexact exceptions are raised
+| if the abstract input cannot be represented exactly as a subnormal double-
+| precision floating-point number.
+| The input significand `zSig' has its binary point between bits 62
+| and 61, which is 10 bits to the left of the usual location. This shifted
+| significand must be normalized or smaller. If `zSig' is not normalized,
+| `zExp' must be 0; in that case, the result returned is a subnormal number,
+| and it must not require rounding. In the usual case that `zSig' is
+| normalized, `zExp' must be 1 less than the ``true'' floating-point exponent.
+| The handling of underflow and overflow follows the IEC/IEEE Standard for
+| Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+static float64 roundAndPackFloat64( flag zSign, int16 zExp, bits64 zSig STATUS_PARAM)
+{
+ int8 roundingMode;
+ flag roundNearestEven;
+ int16 roundIncrement, roundBits;
+ flag isTiny;
+
+ roundingMode = STATUS(float_rounding_mode);
+ roundNearestEven = ( roundingMode == float_round_nearest_even );
+ roundIncrement = 0x200;
+ if ( ! roundNearestEven ) {
+ if ( roundingMode == float_round_to_zero ) {
+ roundIncrement = 0;
+ }
+ else {
+ roundIncrement = 0x3FF;
+ if ( zSign ) {
+ if ( roundingMode == float_round_up ) roundIncrement = 0;
+ }
+ else {
+ if ( roundingMode == float_round_down ) roundIncrement = 0;
+ }
+ }
+ }
+ roundBits = zSig & 0x3FF;
+ if ( 0x7FD <= (bits16) zExp ) {
+ if ( ( 0x7FD < zExp )
+ || ( ( zExp == 0x7FD )
+ && ( (sbits64) ( zSig + roundIncrement ) < 0 ) )
+ ) {
+ float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR);
+ return packFloat64( zSign, 0x7FF, 0 ) - ( roundIncrement == 0 );
+ }
+ if ( zExp < 0 ) {
+ isTiny =
+ ( STATUS(float_detect_tininess) == float_tininess_before_rounding )
+ || ( zExp < -1 )
+ || ( zSig + roundIncrement < LIT64( 0x8000000000000000 ) );
+ shift64RightJamming( zSig, - zExp, &zSig );
+ zExp = 0;
+ roundBits = zSig & 0x3FF;
+ if ( isTiny && roundBits ) float_raise( float_flag_underflow STATUS_VAR);
+ }
+ }
+ if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact;
+ zSig = ( zSig + roundIncrement )>>10;
+ zSig &= ~ ( ( ( roundBits ^ 0x200 ) == 0 ) & roundNearestEven );
+ if ( zSig == 0 ) zExp = 0;
+ return packFloat64( zSign, zExp, zSig );
+
+}
+
+/*----------------------------------------------------------------------------
+| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
+| and significand `zSig', and returns the proper double-precision floating-
+| point value corresponding to the abstract input. This routine is just like
+| `roundAndPackFloat64' except that `zSig' does not have to be normalized.
+| Bit 63 of `zSig' must be zero, and `zExp' must be 1 less than the ``true''
+| floating-point exponent.
+*----------------------------------------------------------------------------*/
+
+static float64
+ normalizeRoundAndPackFloat64( flag zSign, int16 zExp, bits64 zSig STATUS_PARAM)
+{
+ int8 shiftCount;
+
+ shiftCount = countLeadingZeros64( zSig ) - 1;
+ return roundAndPackFloat64( zSign, zExp - shiftCount, zSig<<shiftCount STATUS_VAR);
+
+}
+
+#ifdef FLOATX80
+
+/*----------------------------------------------------------------------------
+| Returns the fraction bits of the extended double-precision floating-point
+| value `a'.
+*----------------------------------------------------------------------------*/
+
+INLINE bits64 extractFloatx80Frac( floatx80 a )
+{
+
+ return a.low;
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the exponent bits of the extended double-precision floating-point
+| value `a'.
+*----------------------------------------------------------------------------*/
+
+INLINE int32 extractFloatx80Exp( floatx80 a )
+{
+
+ return a.high & 0x7FFF;
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the sign bit of the extended double-precision floating-point value
+| `a'.
+*----------------------------------------------------------------------------*/
+
+INLINE flag extractFloatx80Sign( floatx80 a )
+{
+
+ return a.high>>15;
+
+}
+
+/*----------------------------------------------------------------------------
+| Normalizes the subnormal extended double-precision floating-point value
+| represented by the denormalized significand `aSig'. The normalized exponent
+| and significand are stored at the locations pointed to by `zExpPtr' and
+| `zSigPtr', respectively.
+*----------------------------------------------------------------------------*/
+
+static void
+ normalizeFloatx80Subnormal( bits64 aSig, int32 *zExpPtr, bits64 *zSigPtr )
+{
+ int8 shiftCount;
+
+ shiftCount = countLeadingZeros64( aSig );
+ *zSigPtr = aSig<<shiftCount;
+ *zExpPtr = 1 - shiftCount;
+
+}
+
+/*----------------------------------------------------------------------------
+| Packs the sign `zSign', exponent `zExp', and significand `zSig' into an
+| extended double-precision floating-point value, returning the result.
+*----------------------------------------------------------------------------*/
+
+INLINE floatx80 packFloatx80( flag zSign, int32 zExp, bits64 zSig )
+{
+ floatx80 z;
+
+ z.low = zSig;
+ z.high = ( ( (bits16) zSign )<<15 ) + zExp;
+ return z;
+
+}
+
+/*----------------------------------------------------------------------------
+| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
+| and extended significand formed by the concatenation of `zSig0' and `zSig1',
+| and returns the proper extended double-precision floating-point value
+| corresponding to the abstract input. Ordinarily, the abstract value is
+| rounded and packed into the extended double-precision format, with the
+| inexact exception raised if the abstract input cannot be represented
+| exactly. However, if the abstract value is too large, the overflow and
+| inexact exceptions are raised and an infinity or maximal finite value is
+| returned. If the abstract value is too small, the input value is rounded to
+| a subnormal number, and the underflow and inexact exceptions are raised if
+| the abstract input cannot be represented exactly as a subnormal extended
+| double-precision floating-point number.
+| If `roundingPrecision' is 32 or 64, the result is rounded to the same
+| number of bits as single or double precision, respectively. Otherwise, the
+| result is rounded to the full precision of the extended double-precision
+| format.
+| The input significand must be normalized or smaller. If the input
+| significand is not normalized, `zExp' must be 0; in that case, the result
+| returned is a subnormal number, and it must not require rounding. The
+| handling of underflow and overflow follows the IEC/IEEE Standard for Binary
+| Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+static floatx80
+ roundAndPackFloatx80(
+ int8 roundingPrecision, flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1
+ STATUS_PARAM)
+{
+ int8 roundingMode;
+ flag roundNearestEven, increment, isTiny;
+ int64 roundIncrement, roundMask, roundBits;
+
+ roundingMode = STATUS(float_rounding_mode);
+ roundNearestEven = ( roundingMode == float_round_nearest_even );
+ if ( roundingPrecision == 80 ) goto precision80;
+ if ( roundingPrecision == 64 ) {
+ roundIncrement = LIT64( 0x0000000000000400 );
+ roundMask = LIT64( 0x00000000000007FF );
+ }
+ else if ( roundingPrecision == 32 ) {
+ roundIncrement = LIT64( 0x0000008000000000 );
+ roundMask = LIT64( 0x000000FFFFFFFFFF );
+ }
+ else {
+ goto precision80;
+ }
+ zSig0 |= ( zSig1 != 0 );
+ if ( ! roundNearestEven ) {
+ if ( roundingMode == float_round_to_zero ) {
+ roundIncrement = 0;
+ }
+ else {
+ roundIncrement = roundMask;
+ if ( zSign ) {
+ if ( roundingMode == float_round_up ) roundIncrement = 0;
+ }
+ else {
+ if ( roundingMode == float_round_down ) roundIncrement = 0;
+ }
+ }
+ }
+ roundBits = zSig0 & roundMask;
+ if ( 0x7FFD <= (bits32) ( zExp - 1 ) ) {
+ if ( ( 0x7FFE < zExp )
+ || ( ( zExp == 0x7FFE ) && ( zSig0 + roundIncrement < zSig0 ) )
+ ) {
+ goto overflow;
+ }
+ if ( zExp <= 0 ) {
+ isTiny =
+ ( STATUS(float_detect_tininess) == float_tininess_before_rounding )
+ || ( zExp < 0 )
+ || ( zSig0 <= zSig0 + roundIncrement );
+ shift64RightJamming( zSig0, 1 - zExp, &zSig0 );
+ zExp = 0;
+ roundBits = zSig0 & roundMask;
+ if ( isTiny && roundBits ) float_raise( float_flag_underflow STATUS_VAR);
+ if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact;
+ zSig0 += roundIncrement;
+ if ( (sbits64) zSig0 < 0 ) zExp = 1;
+ roundIncrement = roundMask + 1;
+ if ( roundNearestEven && ( roundBits<<1 == roundIncrement ) ) {
+ roundMask |= roundIncrement;
+ }
+ zSig0 &= ~ roundMask;
+ return packFloatx80( zSign, zExp, zSig0 );
+ }
+ }
+ if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact;
+ zSig0 += roundIncrement;
+ if ( zSig0 < roundIncrement ) {
+ ++zExp;
+ zSig0 = LIT64( 0x8000000000000000 );
+ }
+ roundIncrement = roundMask + 1;
+ if ( roundNearestEven && ( roundBits<<1 == roundIncrement ) ) {
+ roundMask |= roundIncrement;
+ }
+ zSig0 &= ~ roundMask;
+ if ( zSig0 == 0 ) zExp = 0;
+ return packFloatx80( zSign, zExp, zSig0 );
+ precision80:
+ increment = ( (sbits64) zSig1 < 0 );
+ if ( ! roundNearestEven ) {
+ if ( roundingMode == float_round_to_zero ) {
+ increment = 0;
+ }
+ else {
+ if ( zSign ) {
+ increment = ( roundingMode == float_round_down ) && zSig1;
+ }
+ else {
+ increment = ( roundingMode == float_round_up ) && zSig1;
+ }
+ }
+ }
+ if ( 0x7FFD <= (bits32) ( zExp - 1 ) ) {
+ if ( ( 0x7FFE < zExp )
+ || ( ( zExp == 0x7FFE )
+ && ( zSig0 == LIT64( 0xFFFFFFFFFFFFFFFF ) )
+ && increment
+ )
+ ) {
+ roundMask = 0;
+ overflow:
+ float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR);
+ if ( ( roundingMode == float_round_to_zero )
+ || ( zSign && ( roundingMode == float_round_up ) )
+ || ( ! zSign && ( roundingMode == float_round_down ) )
+ ) {
+ return packFloatx80( zSign, 0x7FFE, ~ roundMask );
+ }
+ return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
+ }
+ if ( zExp <= 0 ) {
+ isTiny =
+ ( STATUS(float_detect_tininess) == float_tininess_before_rounding )
+ || ( zExp < 0 )
+ || ! increment
+ || ( zSig0 < LIT64( 0xFFFFFFFFFFFFFFFF ) );
+ shift64ExtraRightJamming( zSig0, zSig1, 1 - zExp, &zSig0, &zSig1 );
+ zExp = 0;
+ if ( isTiny && zSig1 ) float_raise( float_flag_underflow STATUS_VAR);
+ if ( zSig1 ) STATUS(float_exception_flags) |= float_flag_inexact;
+ if ( roundNearestEven ) {
+ increment = ( (sbits64) zSig1 < 0 );
+ }
+ else {
+ if ( zSign ) {
+ increment = ( roundingMode == float_round_down ) && zSig1;
+ }
+ else {
+ increment = ( roundingMode == float_round_up ) && zSig1;
+ }
+ }
+ if ( increment ) {
+ ++zSig0;
+ zSig0 &=
+ ~ ( ( (bits64) ( zSig1<<1 ) == 0 ) & roundNearestEven );
+ if ( (sbits64) zSig0 < 0 ) zExp = 1;
+ }
+ return packFloatx80( zSign, zExp, zSig0 );
+ }
+ }
+ if ( zSig1 ) STATUS(float_exception_flags) |= float_flag_inexact;
+ if ( increment ) {
+ ++zSig0;
+ if ( zSig0 == 0 ) {
+ ++zExp;
+ zSig0 = LIT64( 0x8000000000000000 );
+ }
+ else {
+ zSig0 &= ~ ( ( (bits64) ( zSig1<<1 ) == 0 ) & roundNearestEven );
+ }
+ }
+ else {
+ if ( zSig0 == 0 ) zExp = 0;
+ }
+ return packFloatx80( zSign, zExp, zSig0 );
+
+}
+
+/*----------------------------------------------------------------------------
+| Takes an abstract floating-point value having sign `zSign', exponent
+| `zExp', and significand formed by the concatenation of `zSig0' and `zSig1',
+| and returns the proper extended double-precision floating-point value
+| corresponding to the abstract input. This routine is just like
+| `roundAndPackFloatx80' except that the input significand does not have to be
+| normalized.
+*----------------------------------------------------------------------------*/
+
+static floatx80
+ normalizeRoundAndPackFloatx80(
+ int8 roundingPrecision, flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1
+ STATUS_PARAM)
+{
+ int8 shiftCount;
+
+ if ( zSig0 == 0 ) {
+ zSig0 = zSig1;
+ zSig1 = 0;
+ zExp -= 64;
+ }
+ shiftCount = countLeadingZeros64( zSig0 );
+ shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 );
+ zExp -= shiftCount;
+ return
+ roundAndPackFloatx80( roundingPrecision, zSign, zExp, zSig0, zSig1 STATUS_VAR);
+
+}
+
+#endif
+
+#ifdef FLOAT128
+
+/*----------------------------------------------------------------------------
+| Returns the least-significant 64 fraction bits of the quadruple-precision
+| floating-point value `a'.
+*----------------------------------------------------------------------------*/
+
+INLINE bits64 extractFloat128Frac1( float128 a )
+{
+
+ return a.low;
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the most-significant 48 fraction bits of the quadruple-precision
+| floating-point value `a'.
+*----------------------------------------------------------------------------*/
+
+INLINE bits64 extractFloat128Frac0( float128 a )
+{
+
+ return a.high & LIT64( 0x0000FFFFFFFFFFFF );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the exponent bits of the quadruple-precision floating-point value
+| `a'.
+*----------------------------------------------------------------------------*/
+
+INLINE int32 extractFloat128Exp( float128 a )
+{
+
+ return ( a.high>>48 ) & 0x7FFF;
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the sign bit of the quadruple-precision floating-point value `a'.
+*----------------------------------------------------------------------------*/
+
+INLINE flag extractFloat128Sign( float128 a )
+{
+
+ return a.high>>63;
+
+}
+
+/*----------------------------------------------------------------------------
+| Normalizes the subnormal quadruple-precision floating-point value
+| represented by the denormalized significand formed by the concatenation of
+| `aSig0' and `aSig1'. The normalized exponent is stored at the location
+| pointed to by `zExpPtr'. The most significant 49 bits of the normalized
+| significand are stored at the location pointed to by `zSig0Ptr', and the
+| least significant 64 bits of the normalized significand are stored at the
+| location pointed to by `zSig1Ptr'.
+*----------------------------------------------------------------------------*/
+
+static void
+ normalizeFloat128Subnormal(
+ bits64 aSig0,
+ bits64 aSig1,
+ int32 *zExpPtr,
+ bits64 *zSig0Ptr,
+ bits64 *zSig1Ptr
+ )
+{
+ int8 shiftCount;
+
+ if ( aSig0 == 0 ) {
+ shiftCount = countLeadingZeros64( aSig1 ) - 15;
+ if ( shiftCount < 0 ) {
+ *zSig0Ptr = aSig1>>( - shiftCount );
+ *zSig1Ptr = aSig1<<( shiftCount & 63 );
+ }
+ else {
+ *zSig0Ptr = aSig1<<shiftCount;
+ *zSig1Ptr = 0;
+ }
+ *zExpPtr = - shiftCount - 63;
+ }
+ else {
+ shiftCount = countLeadingZeros64( aSig0 ) - 15;
+ shortShift128Left( aSig0, aSig1, shiftCount, zSig0Ptr, zSig1Ptr );
+ *zExpPtr = 1 - shiftCount;
+ }
+
+}
+
+/*----------------------------------------------------------------------------
+| Packs the sign `zSign', the exponent `zExp', and the significand formed
+| by the concatenation of `zSig0' and `zSig1' into a quadruple-precision
+| floating-point value, returning the result. After being shifted into the
+| proper positions, the three fields `zSign', `zExp', and `zSig0' are simply
+| added together to form the most significant 32 bits of the result. This
+| means that any integer portion of `zSig0' will be added into the exponent.
+| Since a properly normalized significand will have an integer portion equal
+| to 1, the `zExp' input should be 1 less than the desired result exponent
+| whenever `zSig0' and `zSig1' concatenated form a complete, normalized
+| significand.
+*----------------------------------------------------------------------------*/
+
+INLINE float128
+ packFloat128( flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1 )
+{
+ float128 z;
+
+ z.low = zSig1;
+ z.high = ( ( (bits64) zSign )<<63 ) + ( ( (bits64) zExp )<<48 ) + zSig0;
+ return z;
+
+}
+
+/*----------------------------------------------------------------------------
+| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
+| and extended significand formed by the concatenation of `zSig0', `zSig1',
+| and `zSig2', and returns the proper quadruple-precision floating-point value
+| corresponding to the abstract input. Ordinarily, the abstract value is
+| simply rounded and packed into the quadruple-precision format, with the
+| inexact exception raised if the abstract input cannot be represented
+| exactly. However, if the abstract value is too large, the overflow and
+| inexact exceptions are raised and an infinity or maximal finite value is
+| returned. If the abstract value is too small, the input value is rounded to
+| a subnormal number, and the underflow and inexact exceptions are raised if
+| the abstract input cannot be represented exactly as a subnormal quadruple-
+| precision floating-point number.
+| The input significand must be normalized or smaller. If the input
+| significand is not normalized, `zExp' must be 0; in that case, the result
+| returned is a subnormal number, and it must not require rounding. In the
+| usual case that the input significand is normalized, `zExp' must be 1 less
+| than the ``true'' floating-point exponent. The handling of underflow and
+| overflow follows the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+static float128
+ roundAndPackFloat128(
+ flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1, bits64 zSig2 STATUS_PARAM)
+{
+ int8 roundingMode;
+ flag roundNearestEven, increment, isTiny;
+
+ roundingMode = STATUS(float_rounding_mode);
+ roundNearestEven = ( roundingMode == float_round_nearest_even );
+ increment = ( (sbits64) zSig2 < 0 );
+ if ( ! roundNearestEven ) {
+ if ( roundingMode == float_round_to_zero ) {
+ increment = 0;
+ }
+ else {
+ if ( zSign ) {
+ increment = ( roundingMode == float_round_down ) && zSig2;
+ }
+ else {
+ increment = ( roundingMode == float_round_up ) && zSig2;
+ }
+ }
+ }
+ if ( 0x7FFD <= (bits32) zExp ) {
+ if ( ( 0x7FFD < zExp )
+ || ( ( zExp == 0x7FFD )
+ && eq128(
+ LIT64( 0x0001FFFFFFFFFFFF ),
+ LIT64( 0xFFFFFFFFFFFFFFFF ),
+ zSig0,
+ zSig1
+ )
+ && increment
+ )
+ ) {
+ float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR);
+ if ( ( roundingMode == float_round_to_zero )
+ || ( zSign && ( roundingMode == float_round_up ) )
+ || ( ! zSign && ( roundingMode == float_round_down ) )
+ ) {
+ return
+ packFloat128(
+ zSign,
+ 0x7FFE,
+ LIT64( 0x0000FFFFFFFFFFFF ),
+ LIT64( 0xFFFFFFFFFFFFFFFF )
+ );
+ }
+ return packFloat128( zSign, 0x7FFF, 0, 0 );
+ }
+ if ( zExp < 0 ) {
+ isTiny =
+ ( STATUS(float_detect_tininess) == float_tininess_before_rounding )
+ || ( zExp < -1 )
+ || ! increment
+ || lt128(
+ zSig0,
+ zSig1,
+ LIT64( 0x0001FFFFFFFFFFFF ),
+ LIT64( 0xFFFFFFFFFFFFFFFF )
+ );
+ shift128ExtraRightJamming(
+ zSig0, zSig1, zSig2, - zExp, &zSig0, &zSig1, &zSig2 );
+ zExp = 0;
+ if ( isTiny && zSig2 ) float_raise( float_flag_underflow STATUS_VAR);
+ if ( roundNearestEven ) {
+ increment = ( (sbits64) zSig2 < 0 );
+ }
+ else {
+ if ( zSign ) {
+ increment = ( roundingMode == float_round_down ) && zSig2;
+ }
+ else {
+ increment = ( roundingMode == float_round_up ) && zSig2;
+ }
+ }
+ }
+ }
+ if ( zSig2 ) STATUS(float_exception_flags) |= float_flag_inexact;
+ if ( increment ) {
+ add128( zSig0, zSig1, 0, 1, &zSig0, &zSig1 );
+ zSig1 &= ~ ( ( zSig2 + zSig2 == 0 ) & roundNearestEven );
+ }
+ else {
+ if ( ( zSig0 | zSig1 ) == 0 ) zExp = 0;
+ }
+ return packFloat128( zSign, zExp, zSig0, zSig1 );
+
+}
+
+/*----------------------------------------------------------------------------
+| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
+| and significand formed by the concatenation of `zSig0' and `zSig1', and
+| returns the proper quadruple-precision floating-point value corresponding
+| to the abstract input. This routine is just like `roundAndPackFloat128'
+| except that the input significand has fewer bits and does not have to be
+| normalized. In all cases, `zExp' must be 1 less than the ``true'' floating-
+| point exponent.
+*----------------------------------------------------------------------------*/
+
+static float128
+ normalizeRoundAndPackFloat128(
+ flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1 STATUS_PARAM)
+{
+ int8 shiftCount;
+ bits64 zSig2;
+
+ if ( zSig0 == 0 ) {
+ zSig0 = zSig1;
+ zSig1 = 0;
+ zExp -= 64;
+ }
+ shiftCount = countLeadingZeros64( zSig0 ) - 15;
+ if ( 0 <= shiftCount ) {
+ zSig2 = 0;
+ shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 );
+ }
+ else {
+ shift128ExtraRightJamming(
+ zSig0, zSig1, 0, - shiftCount, &zSig0, &zSig1, &zSig2 );
+ }
+ zExp -= shiftCount;
+ return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 STATUS_VAR);
+
+}
+
+#endif
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the 32-bit two's complement integer `a'
+| to the single-precision floating-point format. The conversion is performed
+| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+float32 int32_to_float32( int32 a STATUS_PARAM )
+{
+ flag zSign;
+
+ if ( a == 0 ) return 0;
+ if ( a == (sbits32) 0x80000000 ) return packFloat32( 1, 0x9E, 0 );
+ zSign = ( a < 0 );
+ return normalizeRoundAndPackFloat32( zSign, 0x9C, zSign ? - a : a STATUS_VAR );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the 32-bit two's complement integer `a'
+| to the double-precision floating-point format. The conversion is performed
+| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+float64 int32_to_float64( int32 a STATUS_PARAM )
+{
+ flag zSign;
+ uint32 absA;
+ int8 shiftCount;
+ bits64 zSig;
+
+ if ( a == 0 ) return 0;
+ zSign = ( a < 0 );
+ absA = zSign ? - a : a;
+ shiftCount = countLeadingZeros32( absA ) + 21;
+ zSig = absA;
+ return packFloat64( zSign, 0x432 - shiftCount, zSig<<shiftCount );
+
+}
+
+#ifdef FLOATX80
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the 32-bit two's complement integer `a'
+| to the extended double-precision floating-point format. The conversion
+| is performed according to the IEC/IEEE Standard for Binary Floating-Point
+| Arithmetic.
+*----------------------------------------------------------------------------*/
+
+floatx80 int32_to_floatx80( int32 a STATUS_PARAM )
+{
+ flag zSign;
+ uint32 absA;
+ int8 shiftCount;
+ bits64 zSig;
+
+ if ( a == 0 ) return packFloatx80( 0, 0, 0 );
+ zSign = ( a < 0 );
+ absA = zSign ? - a : a;
+ shiftCount = countLeadingZeros32( absA ) + 32;
+ zSig = absA;
+ return packFloatx80( zSign, 0x403E - shiftCount, zSig<<shiftCount );
+
+}
+
+#endif
+
+#ifdef FLOAT128
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the 32-bit two's complement integer `a' to
+| the quadruple-precision floating-point format. The conversion is performed
+| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+float128 int32_to_float128( int32 a STATUS_PARAM )
+{
+ flag zSign;
+ uint32 absA;
+ int8 shiftCount;
+ bits64 zSig0;
+
+ if ( a == 0 ) return packFloat128( 0, 0, 0, 0 );
+ zSign = ( a < 0 );
+ absA = zSign ? - a : a;
+ shiftCount = countLeadingZeros32( absA ) + 17;
+ zSig0 = absA;
+ return packFloat128( zSign, 0x402E - shiftCount, zSig0<<shiftCount, 0 );
+
+}
+
+#endif
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the 64-bit two's complement integer `a'
+| to the single-precision floating-point format. The conversion is performed
+| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+float32 int64_to_float32( int64 a STATUS_PARAM )
+{
+ flag zSign;
+ uint64 absA;
+ int8 shiftCount;
+
+ if ( a == 0 ) return 0;
+ zSign = ( a < 0 );
+ absA = zSign ? - a : a;
+ shiftCount = countLeadingZeros64( absA ) - 40;
+ if ( 0 <= shiftCount ) {
+ return packFloat32( zSign, 0x95 - shiftCount, absA<<shiftCount );
+ }
+ else {
+ shiftCount += 7;
+ if ( shiftCount < 0 ) {
+ shift64RightJamming( absA, - shiftCount, &absA );
+ }
+ else {
+ absA <<= shiftCount;
+ }
+ return roundAndPackFloat32( zSign, 0x9C - shiftCount, absA STATUS_VAR );
+ }
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the 64-bit two's complement integer `a'
+| to the double-precision floating-point format. The conversion is performed
+| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+float64 int64_to_float64( int64 a STATUS_PARAM )
+{
+ flag zSign;
+
+ if ( a == 0 ) return 0;
+ if ( a == (sbits64) LIT64( 0x8000000000000000 ) ) {
+ return packFloat64( 1, 0x43E, 0 );
+ }
+ zSign = ( a < 0 );
+ return normalizeRoundAndPackFloat64( zSign, 0x43C, zSign ? - a : a STATUS_VAR );
+
+}
+
+#ifdef FLOATX80
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the 64-bit two's complement integer `a'
+| to the extended double-precision floating-point format. The conversion
+| is performed according to the IEC/IEEE Standard for Binary Floating-Point
+| Arithmetic.
+*----------------------------------------------------------------------------*/
+
+floatx80 int64_to_floatx80( int64 a STATUS_PARAM )
+{
+ flag zSign;
+ uint64 absA;
+ int8 shiftCount;
+
+ if ( a == 0 ) return packFloatx80( 0, 0, 0 );
+ zSign = ( a < 0 );
+ absA = zSign ? - a : a;
+ shiftCount = countLeadingZeros64( absA );
+ return packFloatx80( zSign, 0x403E - shiftCount, absA<<shiftCount );
+
+}
+
+#endif
+
+#ifdef FLOAT128
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the 64-bit two's complement integer `a' to
+| the quadruple-precision floating-point format. The conversion is performed
+| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+float128 int64_to_float128( int64 a STATUS_PARAM )
+{
+ flag zSign;
+ uint64 absA;
+ int8 shiftCount;
+ int32 zExp;
+ bits64 zSig0, zSig1;
+
+ if ( a == 0 ) return packFloat128( 0, 0, 0, 0 );
+ zSign = ( a < 0 );
+ absA = zSign ? - a : a;
+ shiftCount = countLeadingZeros64( absA ) + 49;
+ zExp = 0x406E - shiftCount;
+ if ( 64 <= shiftCount ) {
+ zSig1 = 0;
+ zSig0 = absA;
+ shiftCount -= 64;
+ }
+ else {
+ zSig1 = absA;
+ zSig0 = 0;
+ }
+ shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 );
+ return packFloat128( zSign, zExp, zSig0, zSig1 );
+
+}
+
+#endif
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the single-precision floating-point value
+| `a' to the 32-bit two's complement integer format. The conversion is
+| performed according to the IEC/IEEE Standard for Binary Floating-Point
+| Arithmetic---which means in particular that the conversion is rounded
+| according to the current rounding mode. If `a' is a NaN, the largest
+| positive integer is returned. Otherwise, if the conversion overflows, the
+| largest integer with the same sign as `a' is returned.
+*----------------------------------------------------------------------------*/
+
+int32 float32_to_int32( float32 a STATUS_PARAM )
+{
+ flag aSign;
+ int16 aExp, shiftCount;
+ bits32 aSig;
+ bits64 aSig64;
+
+ aSig = extractFloat32Frac( a );
+ aExp = extractFloat32Exp( a );
+ aSign = extractFloat32Sign( a );
+ if ( ( aExp == 0xFF ) && aSig ) aSign = 0;
+ if ( aExp ) aSig |= 0x00800000;
+ shiftCount = 0xAF - aExp;
+ aSig64 = aSig;
+ aSig64 <<= 32;
+ if ( 0 < shiftCount ) shift64RightJamming( aSig64, shiftCount, &aSig64 );
+ return roundAndPackInt32( aSign, aSig64 STATUS_VAR );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the single-precision floating-point value
+| `a' to the 32-bit two's complement integer format. The conversion is
+| performed according to the IEC/IEEE Standard for Binary Floating-Point
+| Arithmetic, except that the conversion is always rounded toward zero.
+| If `a' is a NaN, the largest positive integer is returned. Otherwise, if
+| the conversion overflows, the largest integer with the same sign as `a' is
+| returned.
+*----------------------------------------------------------------------------*/
+
+int32 float32_to_int32_round_to_zero( float32 a STATUS_PARAM )
+{
+ flag aSign;
+ int16 aExp, shiftCount;
+ bits32 aSig;
+ int32 z;
+
+ aSig = extractFloat32Frac( a );
+ aExp = extractFloat32Exp( a );
+ aSign = extractFloat32Sign( a );
+ shiftCount = aExp - 0x9E;
+ if ( 0 <= shiftCount ) {
+ if ( a != 0xCF000000 ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) return 0x7FFFFFFF;
+ }
+ return (sbits32) 0x80000000;
+ }
+ else if ( aExp <= 0x7E ) {
+ if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact;
+ return 0;
+ }
+ aSig = ( aSig | 0x00800000 )<<8;
+ z = aSig>>( - shiftCount );
+ if ( (bits32) ( aSig<<( shiftCount & 31 ) ) ) {
+ STATUS(float_exception_flags) |= float_flag_inexact;
+ }
+ if ( aSign ) z = - z;
+ return z;
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the single-precision floating-point value
+| `a' to the 64-bit two's complement integer format. The conversion is
+| performed according to the IEC/IEEE Standard for Binary Floating-Point
+| Arithmetic---which means in particular that the conversion is rounded
+| according to the current rounding mode. If `a' is a NaN, the largest
+| positive integer is returned. Otherwise, if the conversion overflows, the
+| largest integer with the same sign as `a' is returned.
+*----------------------------------------------------------------------------*/
+
+int64 float32_to_int64( float32 a STATUS_PARAM )
+{
+ flag aSign;
+ int16 aExp, shiftCount;
+ bits32 aSig;
+ bits64 aSig64, aSigExtra;
+
+ aSig = extractFloat32Frac( a );
+ aExp = extractFloat32Exp( a );
+ aSign = extractFloat32Sign( a );
+ shiftCount = 0xBE - aExp;
+ if ( shiftCount < 0 ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) {
+ return LIT64( 0x7FFFFFFFFFFFFFFF );
+ }
+ return (sbits64) LIT64( 0x8000000000000000 );
+ }
+ if ( aExp ) aSig |= 0x00800000;
+ aSig64 = aSig;
+ aSig64 <<= 40;
+ shift64ExtraRightJamming( aSig64, 0, shiftCount, &aSig64, &aSigExtra );
+ return roundAndPackInt64( aSign, aSig64, aSigExtra STATUS_VAR );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the single-precision floating-point value
+| `a' to the 64-bit two's complement integer format. The conversion is
+| performed according to the IEC/IEEE Standard for Binary Floating-Point
+| Arithmetic, except that the conversion is always rounded toward zero. If
+| `a' is a NaN, the largest positive integer is returned. Otherwise, if the
+| conversion overflows, the largest integer with the same sign as `a' is
+| returned.
+*----------------------------------------------------------------------------*/
+
+int64 float32_to_int64_round_to_zero( float32 a STATUS_PARAM )
+{
+ flag aSign;
+ int16 aExp, shiftCount;
+ bits32 aSig;
+ bits64 aSig64;
+ int64 z;
+
+ aSig = extractFloat32Frac( a );
+ aExp = extractFloat32Exp( a );
+ aSign = extractFloat32Sign( a );
+ shiftCount = aExp - 0xBE;
+ if ( 0 <= shiftCount ) {
+ if ( a != 0xDF000000 ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) {
+ return LIT64( 0x7FFFFFFFFFFFFFFF );
+ }
+ }
+ return (sbits64) LIT64( 0x8000000000000000 );
+ }
+ else if ( aExp <= 0x7E ) {
+ if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact;
+ return 0;
+ }
+ aSig64 = aSig | 0x00800000;
+ aSig64 <<= 40;
+ z = aSig64>>( - shiftCount );
+ if ( (bits64) ( aSig64<<( shiftCount & 63 ) ) ) {
+ STATUS(float_exception_flags) |= float_flag_inexact;
+ }
+ if ( aSign ) z = - z;
+ return z;
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the single-precision floating-point value
+| `a' to the double-precision floating-point format. The conversion is
+| performed according to the IEC/IEEE Standard for Binary Floating-Point
+| Arithmetic.
+*----------------------------------------------------------------------------*/
+
+float64 float32_to_float64( float32 a STATUS_PARAM )
+{
+ flag aSign;
+ int16 aExp;
+ bits32 aSig;
+
+ aSig = extractFloat32Frac( a );
+ aExp = extractFloat32Exp( a );
+ aSign = extractFloat32Sign( a );
+ if ( aExp == 0xFF ) {
+ if ( aSig ) return commonNaNToFloat64( float32ToCommonNaN( a STATUS_VAR ));
+ return packFloat64( aSign, 0x7FF, 0 );
+ }
+ if ( aExp == 0 ) {
+ if ( aSig == 0 ) return packFloat64( aSign, 0, 0 );
+ normalizeFloat32Subnormal( aSig, &aExp, &aSig );
+ --aExp;
+ }
+ return packFloat64( aSign, aExp + 0x380, ( (bits64) aSig )<<29 );
+
+}
+
+#ifdef FLOATX80
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the single-precision floating-point value
+| `a' to the extended double-precision floating-point format. The conversion
+| is performed according to the IEC/IEEE Standard for Binary Floating-Point
+| Arithmetic.
+*----------------------------------------------------------------------------*/
+
+floatx80 float32_to_floatx80( float32 a STATUS_PARAM )
+{
+ flag aSign;
+ int16 aExp;
+ bits32 aSig;
+
+ aSig = extractFloat32Frac( a );
+ aExp = extractFloat32Exp( a );
+ aSign = extractFloat32Sign( a );
+ if ( aExp == 0xFF ) {
+ if ( aSig ) return commonNaNToFloatx80( float32ToCommonNaN( a STATUS_VAR ) );
+ return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
+ }
+ if ( aExp == 0 ) {
+ if ( aSig == 0 ) return packFloatx80( aSign, 0, 0 );
+ normalizeFloat32Subnormal( aSig, &aExp, &aSig );
+ }
+ aSig |= 0x00800000;
+ return packFloatx80( aSign, aExp + 0x3F80, ( (bits64) aSig )<<40 );
+
+}
+
+#endif
+
+#ifdef FLOAT128
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the single-precision floating-point value
+| `a' to the double-precision floating-point format. The conversion is
+| performed according to the IEC/IEEE Standard for Binary Floating-Point
+| Arithmetic.
+*----------------------------------------------------------------------------*/
+
+float128 float32_to_float128( float32 a STATUS_PARAM )
+{
+ flag aSign;
+ int16 aExp;
+ bits32 aSig;
+
+ aSig = extractFloat32Frac( a );
+ aExp = extractFloat32Exp( a );
+ aSign = extractFloat32Sign( a );
+ if ( aExp == 0xFF ) {
+ if ( aSig ) return commonNaNToFloat128( float32ToCommonNaN( a STATUS_VAR ) );
+ return packFloat128( aSign, 0x7FFF, 0, 0 );
+ }
+ if ( aExp == 0 ) {
+ if ( aSig == 0 ) return packFloat128( aSign, 0, 0, 0 );
+ normalizeFloat32Subnormal( aSig, &aExp, &aSig );
+ --aExp;
+ }
+ return packFloat128( aSign, aExp + 0x3F80, ( (bits64) aSig )<<25, 0 );
+
+}
+
+#endif
+
+/*----------------------------------------------------------------------------
+| Rounds the single-precision floating-point value `a' to an integer, and
+| returns the result as a single-precision floating-point value. The
+| operation is performed according to the IEC/IEEE Standard for Binary
+| Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+float32 float32_round_to_int( float32 a STATUS_PARAM)
+{
+ flag aSign;
+ int16 aExp;
+ bits32 lastBitMask, roundBitsMask;
+ int8 roundingMode;
+ float32 z;
+
+ aExp = extractFloat32Exp( a );
+ if ( 0x96 <= aExp ) {
+ if ( ( aExp == 0xFF ) && extractFloat32Frac( a ) ) {
+ return propagateFloat32NaN( a, a STATUS_VAR );
+ }
+ return a;
+ }
+ if ( aExp <= 0x7E ) {
+ if ( (bits32) ( a<<1 ) == 0 ) return a;
+ STATUS(float_exception_flags) |= float_flag_inexact;
+ aSign = extractFloat32Sign( a );
+ switch ( STATUS(float_rounding_mode) ) {
+ case float_round_nearest_even:
+ if ( ( aExp == 0x7E ) && extractFloat32Frac( a ) ) {
+ return packFloat32( aSign, 0x7F, 0 );
+ }
+ break;
+ case float_round_down:
+ return aSign ? 0xBF800000 : 0;
+ case float_round_up:
+ return aSign ? 0x80000000 : 0x3F800000;
+ }
+ return packFloat32( aSign, 0, 0 );
+ }
+ lastBitMask = 1;
+ lastBitMask <<= 0x96 - aExp;
+ roundBitsMask = lastBitMask - 1;
+ z = a;
+ roundingMode = STATUS(float_rounding_mode);
+ if ( roundingMode == float_round_nearest_even ) {
+ z += lastBitMask>>1;
+ if ( ( z & roundBitsMask ) == 0 ) z &= ~ lastBitMask;
+ }
+ else if ( roundingMode != float_round_to_zero ) {
+ if ( extractFloat32Sign( z ) ^ ( roundingMode == float_round_up ) ) {
+ z += roundBitsMask;
+ }
+ }
+ z &= ~ roundBitsMask;
+ if ( z != a ) STATUS(float_exception_flags) |= float_flag_inexact;
+ return z;
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of adding the absolute values of the single-precision
+| floating-point values `a' and `b'. If `zSign' is 1, the sum is negated
+| before being returned. `zSign' is ignored if the result is a NaN.
+| The addition is performed according to the IEC/IEEE Standard for Binary
+| Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+static float32 addFloat32Sigs( float32 a, float32 b, flag zSign STATUS_PARAM)
+{
+ int16 aExp, bExp, zExp;
+ bits32 aSig, bSig, zSig;
+ int16 expDiff;
+
+ aSig = extractFloat32Frac( a );
+ aExp = extractFloat32Exp( a );
+ bSig = extractFloat32Frac( b );
+ bExp = extractFloat32Exp( b );
+ expDiff = aExp - bExp;
+ aSig <<= 6;
+ bSig <<= 6;
+ if ( 0 < expDiff ) {
+ if ( aExp == 0xFF ) {
+ if ( aSig ) return propagateFloat32NaN( a, b STATUS_VAR );
+ return a;
+ }
+ if ( bExp == 0 ) {
+ --expDiff;
+ }
+ else {
+ bSig |= 0x20000000;
+ }
+ shift32RightJamming( bSig, expDiff, &bSig );
+ zExp = aExp;
+ }
+ else if ( expDiff < 0 ) {
+ if ( bExp == 0xFF ) {
+ if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR );
+ return packFloat32( zSign, 0xFF, 0 );
+ }
+ if ( aExp == 0 ) {
+ ++expDiff;
+ }
+ else {
+ aSig |= 0x20000000;
+ }
+ shift32RightJamming( aSig, - expDiff, &aSig );
+ zExp = bExp;
+ }
+ else {
+ if ( aExp == 0xFF ) {
+ if ( aSig | bSig ) return propagateFloat32NaN( a, b STATUS_VAR );
+ return a;
+ }
+ if ( aExp == 0 ) return packFloat32( zSign, 0, ( aSig + bSig )>>6 );
+ zSig = 0x40000000 + aSig + bSig;
+ zExp = aExp;
+ goto roundAndPack;
+ }
+ aSig |= 0x20000000;
+ zSig = ( aSig + bSig )<<1;
+ --zExp;
+ if ( (sbits32) zSig < 0 ) {
+ zSig = aSig + bSig;
+ ++zExp;
+ }
+ roundAndPack:
+ return roundAndPackFloat32( zSign, zExp, zSig STATUS_VAR );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of subtracting the absolute values of the single-
+| precision floating-point values `a' and `b'. If `zSign' is 1, the
+| difference is negated before being returned. `zSign' is ignored if the
+| result is a NaN. The subtraction is performed according to the IEC/IEEE
+| Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+static float32 subFloat32Sigs( float32 a, float32 b, flag zSign STATUS_PARAM)
+{
+ int16 aExp, bExp, zExp;
+ bits32 aSig, bSig, zSig;
+ int16 expDiff;
+
+ aSig = extractFloat32Frac( a );
+ aExp = extractFloat32Exp( a );
+ bSig = extractFloat32Frac( b );
+ bExp = extractFloat32Exp( b );
+ expDiff = aExp - bExp;
+ aSig <<= 7;
+ bSig <<= 7;
+ if ( 0 < expDiff ) goto aExpBigger;
+ if ( expDiff < 0 ) goto bExpBigger;
+ if ( aExp == 0xFF ) {
+ if ( aSig | bSig ) return propagateFloat32NaN( a, b STATUS_VAR );
+ float_raise( float_flag_invalid STATUS_VAR);
+ return float32_default_nan;
+ }
+ if ( aExp == 0 ) {
+ aExp = 1;
+ bExp = 1;
+ }
+ if ( bSig < aSig ) goto aBigger;
+ if ( aSig < bSig ) goto bBigger;
+ return packFloat32( STATUS(float_rounding_mode) == float_round_down, 0, 0 );
+ bExpBigger:
+ if ( bExp == 0xFF ) {
+ if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR );
+ return packFloat32( zSign ^ 1, 0xFF, 0 );
+ }
+ if ( aExp == 0 ) {
+ ++expDiff;
+ }
+ else {
+ aSig |= 0x40000000;
+ }
+ shift32RightJamming( aSig, - expDiff, &aSig );
+ bSig |= 0x40000000;
+ bBigger:
+ zSig = bSig - aSig;
+ zExp = bExp;
+ zSign ^= 1;
+ goto normalizeRoundAndPack;
+ aExpBigger:
+ if ( aExp == 0xFF ) {
+ if ( aSig ) return propagateFloat32NaN( a, b STATUS_VAR );
+ return a;
+ }
+ if ( bExp == 0 ) {
+ --expDiff;
+ }
+ else {
+ bSig |= 0x40000000;
+ }
+ shift32RightJamming( bSig, expDiff, &bSig );
+ aSig |= 0x40000000;
+ aBigger:
+ zSig = aSig - bSig;
+ zExp = aExp;
+ normalizeRoundAndPack:
+ --zExp;
+ return normalizeRoundAndPackFloat32( zSign, zExp, zSig STATUS_VAR );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of adding the single-precision floating-point values `a'
+| and `b'. The operation is performed according to the IEC/IEEE Standard for
+| Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+float32 float32_add( float32 a, float32 b STATUS_PARAM )
+{
+ flag aSign, bSign;
+
+ aSign = extractFloat32Sign( a );
+ bSign = extractFloat32Sign( b );
+ if ( aSign == bSign ) {
+ return addFloat32Sigs( a, b, aSign STATUS_VAR);
+ }
+ else {
+ return subFloat32Sigs( a, b, aSign STATUS_VAR );
+ }
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of subtracting the single-precision floating-point values
+| `a' and `b'. The operation is performed according to the IEC/IEEE Standard
+| for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+float32 float32_sub( float32 a, float32 b STATUS_PARAM )
+{
+ flag aSign, bSign;
+
+ aSign = extractFloat32Sign( a );
+ bSign = extractFloat32Sign( b );
+ if ( aSign == bSign ) {
+ return subFloat32Sigs( a, b, aSign STATUS_VAR );
+ }
+ else {
+ return addFloat32Sigs( a, b, aSign STATUS_VAR );
+ }
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of multiplying the single-precision floating-point values
+| `a' and `b'. The operation is performed according to the IEC/IEEE Standard
+| for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+float32 float32_mul( float32 a, float32 b STATUS_PARAM )
+{
+ flag aSign, bSign, zSign;
+ int16 aExp, bExp, zExp;
+ bits32 aSig, bSig;
+ bits64 zSig64;
+ bits32 zSig;
+
+ aSig = extractFloat32Frac( a );
+ aExp = extractFloat32Exp( a );
+ aSign = extractFloat32Sign( a );
+ bSig = extractFloat32Frac( b );
+ bExp = extractFloat32Exp( b );
+ bSign = extractFloat32Sign( b );
+ zSign = aSign ^ bSign;
+ if ( aExp == 0xFF ) {
+ if ( aSig || ( ( bExp == 0xFF ) && bSig ) ) {
+ return propagateFloat32NaN( a, b STATUS_VAR );
+ }
+ if ( ( bExp | bSig ) == 0 ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ return float32_default_nan;
+ }
+ return packFloat32( zSign, 0xFF, 0 );
+ }
+ if ( bExp == 0xFF ) {
+ if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR );
+ if ( ( aExp | aSig ) == 0 ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ return float32_default_nan;
+ }
+ return packFloat32( zSign, 0xFF, 0 );
+ }
+ if ( aExp == 0 ) {
+ if ( aSig == 0 ) return packFloat32( zSign, 0, 0 );
+ normalizeFloat32Subnormal( aSig, &aExp, &aSig );
+ }
+ if ( bExp == 0 ) {
+ if ( bSig == 0 ) return packFloat32( zSign, 0, 0 );
+ normalizeFloat32Subnormal( bSig, &bExp, &bSig );
+ }
+ zExp = aExp + bExp - 0x7F;
+ aSig = ( aSig | 0x00800000 )<<7;
+ bSig = ( bSig | 0x00800000 )<<8;
+ shift64RightJamming( ( (bits64) aSig ) * bSig, 32, &zSig64 );
+ zSig = zSig64;
+ if ( 0 <= (sbits32) ( zSig<<1 ) ) {
+ zSig <<= 1;
+ --zExp;
+ }
+ return roundAndPackFloat32( zSign, zExp, zSig STATUS_VAR );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of dividing the single-precision floating-point value `a'
+| by the corresponding value `b'. The operation is performed according to the
+| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+float32 float32_div( float32 a, float32 b STATUS_PARAM )
+{
+ flag aSign, bSign, zSign;
+ int16 aExp, bExp, zExp;
+ bits32 aSig, bSig, zSig;
+
+ aSig = extractFloat32Frac( a );
+ aExp = extractFloat32Exp( a );
+ aSign = extractFloat32Sign( a );
+ bSig = extractFloat32Frac( b );
+ bExp = extractFloat32Exp( b );
+ bSign = extractFloat32Sign( b );
+ zSign = aSign ^ bSign;
+ if ( aExp == 0xFF ) {
+ if ( aSig ) return propagateFloat32NaN( a, b STATUS_VAR );
+ if ( bExp == 0xFF ) {
+ if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR );
+ float_raise( float_flag_invalid STATUS_VAR);
+ return float32_default_nan;
+ }
+ return packFloat32( zSign, 0xFF, 0 );
+ }
+ if ( bExp == 0xFF ) {
+ if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR );
+ return packFloat32( zSign, 0, 0 );
+ }
+ if ( bExp == 0 ) {
+ if ( bSig == 0 ) {
+ if ( ( aExp | aSig ) == 0 ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ return float32_default_nan;
+ }
+ float_raise( float_flag_divbyzero STATUS_VAR);
+ return packFloat32( zSign, 0xFF, 0 );
+ }
+ normalizeFloat32Subnormal( bSig, &bExp, &bSig );
+ }
+ if ( aExp == 0 ) {
+ if ( aSig == 0 ) return packFloat32( zSign, 0, 0 );
+ normalizeFloat32Subnormal( aSig, &aExp, &aSig );
+ }
+ zExp = aExp - bExp + 0x7D;
+ aSig = ( aSig | 0x00800000 )<<7;
+ bSig = ( bSig | 0x00800000 )<<8;
+ if ( bSig <= ( aSig + aSig ) ) {
+ aSig >>= 1;
+ ++zExp;
+ }
+ zSig = ( ( (bits64) aSig )<<32 ) / bSig;
+ if ( ( zSig & 0x3F ) == 0 ) {
+ zSig |= ( (bits64) bSig * zSig != ( (bits64) aSig )<<32 );
+ }
+ return roundAndPackFloat32( zSign, zExp, zSig STATUS_VAR );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the remainder of the single-precision floating-point value `a'
+| with respect to the corresponding value `b'. The operation is performed
+| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+float32 float32_rem( float32 a, float32 b STATUS_PARAM )
+{
+ flag aSign, bSign, zSign;
+ int16 aExp, bExp, expDiff;
+ bits32 aSig, bSig;
+ bits32 q;
+ bits64 aSig64, bSig64, q64;
+ bits32 alternateASig;
+ sbits32 sigMean;
+
+ aSig = extractFloat32Frac( a );
+ aExp = extractFloat32Exp( a );
+ aSign = extractFloat32Sign( a );
+ bSig = extractFloat32Frac( b );
+ bExp = extractFloat32Exp( b );
+ bSign = extractFloat32Sign( b );
+ if ( aExp == 0xFF ) {
+ if ( aSig || ( ( bExp == 0xFF ) && bSig ) ) {
+ return propagateFloat32NaN( a, b STATUS_VAR );
+ }
+ float_raise( float_flag_invalid STATUS_VAR);
+ return float32_default_nan;
+ }
+ if ( bExp == 0xFF ) {
+ if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR );
+ return a;
+ }
+ if ( bExp == 0 ) {
+ if ( bSig == 0 ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ return float32_default_nan;
+ }
+ normalizeFloat32Subnormal( bSig, &bExp, &bSig );
+ }
+ if ( aExp == 0 ) {
+ if ( aSig == 0 ) return a;
+ normalizeFloat32Subnormal( aSig, &aExp, &aSig );
+ }
+ expDiff = aExp - bExp;
+ aSig |= 0x00800000;
+ bSig |= 0x00800000;
+ if ( expDiff < 32 ) {
+ aSig <<= 8;
+ bSig <<= 8;
+ if ( expDiff < 0 ) {
+ if ( expDiff < -1 ) return a;
+ aSig >>= 1;
+ }
+ q = ( bSig <= aSig );
+ if ( q ) aSig -= bSig;
+ if ( 0 < expDiff ) {
+ q = ( ( (bits64) aSig )<<32 ) / bSig;
+ q >>= 32 - expDiff;
+ bSig >>= 2;
+ aSig = ( ( aSig>>1 )<<( expDiff - 1 ) ) - bSig * q;
+ }
+ else {
+ aSig >>= 2;
+ bSig >>= 2;
+ }
+ }
+ else {
+ if ( bSig <= aSig ) aSig -= bSig;
+ aSig64 = ( (bits64) aSig )<<40;
+ bSig64 = ( (bits64) bSig )<<40;
+ expDiff -= 64;
+ while ( 0 < expDiff ) {
+ q64 = estimateDiv128To64( aSig64, 0, bSig64 );
+ q64 = ( 2 < q64 ) ? q64 - 2 : 0;
+ aSig64 = - ( ( bSig * q64 )<<38 );
+ expDiff -= 62;
+ }
+ expDiff += 64;
+ q64 = estimateDiv128To64( aSig64, 0, bSig64 );
+ q64 = ( 2 < q64 ) ? q64 - 2 : 0;
+ q = q64>>( 64 - expDiff );
+ bSig <<= 6;
+ aSig = ( ( aSig64>>33 )<<( expDiff - 1 ) ) - bSig * q;
+ }
+ do {
+ alternateASig = aSig;
+ ++q;
+ aSig -= bSig;
+ } while ( 0 <= (sbits32) aSig );
+ sigMean = aSig + alternateASig;
+ if ( ( sigMean < 0 ) || ( ( sigMean == 0 ) && ( q & 1 ) ) ) {
+ aSig = alternateASig;
+ }
+ zSign = ( (sbits32) aSig < 0 );
+ if ( zSign ) aSig = - aSig;
+ return normalizeRoundAndPackFloat32( aSign ^ zSign, bExp, aSig STATUS_VAR );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the square root of the single-precision floating-point value `a'.
+| The operation is performed according to the IEC/IEEE Standard for Binary
+| Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+float32 float32_sqrt( float32 a STATUS_PARAM )
+{
+ flag aSign;
+ int16 aExp, zExp;
+ bits32 aSig, zSig;
+ bits64 rem, term;
+
+ aSig = extractFloat32Frac( a );
+ aExp = extractFloat32Exp( a );
+ aSign = extractFloat32Sign( a );
+ if ( aExp == 0xFF ) {
+ if ( aSig ) return propagateFloat32NaN( a, 0 STATUS_VAR );
+ if ( ! aSign ) return a;
+ float_raise( float_flag_invalid STATUS_VAR);
+ return float32_default_nan;
+ }
+ if ( aSign ) {
+ if ( ( aExp | aSig ) == 0 ) return a;
+ float_raise( float_flag_invalid STATUS_VAR);
+ return float32_default_nan;
+ }
+ if ( aExp == 0 ) {
+ if ( aSig == 0 ) return 0;
+ normalizeFloat32Subnormal( aSig, &aExp, &aSig );
+ }
+ zExp = ( ( aExp - 0x7F )>>1 ) + 0x7E;
+ aSig = ( aSig | 0x00800000 )<<8;
+ zSig = estimateSqrt32( aExp, aSig ) + 2;
+ if ( ( zSig & 0x7F ) <= 5 ) {
+ if ( zSig < 2 ) {
+ zSig = 0x7FFFFFFF;
+ goto roundAndPack;
+ }
+ aSig >>= aExp & 1;
+ term = ( (bits64) zSig ) * zSig;
+ rem = ( ( (bits64) aSig )<<32 ) - term;
+ while ( (sbits64) rem < 0 ) {
+ --zSig;
+ rem += ( ( (bits64) zSig )<<1 ) | 1;
+ }
+ zSig |= ( rem != 0 );
+ }
+ shift32RightJamming( zSig, 1, &zSig );
+ roundAndPack:
+ return roundAndPackFloat32( 0, zExp, zSig STATUS_VAR );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the single-precision floating-point value `a' is equal to
+| the corresponding value `b', and 0 otherwise. The comparison is performed
+| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+flag float32_eq( float32 a, float32 b STATUS_PARAM )
+{
+
+ if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
+ || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
+ ) {
+ if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ }
+ return 0;
+ }
+ return ( a == b ) || ( (bits32) ( ( a | b )<<1 ) == 0 );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the single-precision floating-point value `a' is less than
+| or equal to the corresponding value `b', and 0 otherwise. The comparison
+| is performed according to the IEC/IEEE Standard for Binary Floating-Point
+| Arithmetic.
+*----------------------------------------------------------------------------*/
+
+flag float32_le( float32 a, float32 b STATUS_PARAM )
+{
+ flag aSign, bSign;
+
+ if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
+ || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
+ ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ return 0;
+ }
+ aSign = extractFloat32Sign( a );
+ bSign = extractFloat32Sign( b );
+ if ( aSign != bSign ) return aSign || ( (bits32) ( ( a | b )<<1 ) == 0 );
+ return ( a == b ) || ( aSign ^ ( a < b ) );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the single-precision floating-point value `a' is less than
+| the corresponding value `b', and 0 otherwise. The comparison is performed
+| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+flag float32_lt( float32 a, float32 b STATUS_PARAM )
+{
+ flag aSign, bSign;
+
+ if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
+ || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
+ ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ return 0;
+ }
+ aSign = extractFloat32Sign( a );
+ bSign = extractFloat32Sign( b );
+ if ( aSign != bSign ) return aSign && ( (bits32) ( ( a | b )<<1 ) != 0 );
+ return ( a != b ) && ( aSign ^ ( a < b ) );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the single-precision floating-point value `a' is equal to
+| the corresponding value `b', and 0 otherwise. The invalid exception is
+| raised if either operand is a NaN. Otherwise, the comparison is performed
+| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+flag float32_eq_signaling( float32 a, float32 b STATUS_PARAM )
+{
+
+ if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
+ || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
+ ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ return 0;
+ }
+ return ( a == b ) || ( (bits32) ( ( a | b )<<1 ) == 0 );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the single-precision floating-point value `a' is less than or
+| equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not
+| cause an exception. Otherwise, the comparison is performed according to the
+| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+flag float32_le_quiet( float32 a, float32 b STATUS_PARAM )
+{
+ flag aSign, bSign;
+
+ if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
+ || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
+ ) {
+ if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ }
+ return 0;
+ }
+ aSign = extractFloat32Sign( a );
+ bSign = extractFloat32Sign( b );
+ if ( aSign != bSign ) return aSign || ( (bits32) ( ( a | b )<<1 ) == 0 );
+ return ( a == b ) || ( aSign ^ ( a < b ) );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the single-precision floating-point value `a' is less than
+| the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an
+| exception. Otherwise, the comparison is performed according to the IEC/IEEE
+| Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+flag float32_lt_quiet( float32 a, float32 b STATUS_PARAM )
+{
+ flag aSign, bSign;
+
+ if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) )
+ || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) )
+ ) {
+ if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ }
+ return 0;
+ }
+ aSign = extractFloat32Sign( a );
+ bSign = extractFloat32Sign( b );
+ if ( aSign != bSign ) return aSign && ( (bits32) ( ( a | b )<<1 ) != 0 );
+ return ( a != b ) && ( aSign ^ ( a < b ) );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the double-precision floating-point value
+| `a' to the 32-bit two's complement integer format. The conversion is
+| performed according to the IEC/IEEE Standard for Binary Floating-Point
+| Arithmetic---which means in particular that the conversion is rounded
+| according to the current rounding mode. If `a' is a NaN, the largest
+| positive integer is returned. Otherwise, if the conversion overflows, the
+| largest integer with the same sign as `a' is returned.
+*----------------------------------------------------------------------------*/
+
+int32 float64_to_int32( float64 a STATUS_PARAM )
+{
+ flag aSign;
+ int16 aExp, shiftCount;
+ bits64 aSig;
+
+ aSig = extractFloat64Frac( a );
+ aExp = extractFloat64Exp( a );
+ aSign = extractFloat64Sign( a );
+ if ( ( aExp == 0x7FF ) && aSig ) aSign = 0;
+ if ( aExp ) aSig |= LIT64( 0x0010000000000000 );
+ shiftCount = 0x42C - aExp;
+ if ( 0 < shiftCount ) shift64RightJamming( aSig, shiftCount, &aSig );
+ return roundAndPackInt32( aSign, aSig STATUS_VAR );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the double-precision floating-point value
+| `a' to the 32-bit two's complement integer format. The conversion is
+| performed according to the IEC/IEEE Standard for Binary Floating-Point
+| Arithmetic, except that the conversion is always rounded toward zero.
+| If `a' is a NaN, the largest positive integer is returned. Otherwise, if
+| the conversion overflows, the largest integer with the same sign as `a' is
+| returned.
+*----------------------------------------------------------------------------*/
+
+int32 float64_to_int32_round_to_zero( float64 a STATUS_PARAM )
+{
+ flag aSign;
+ int16 aExp, shiftCount;
+ bits64 aSig, savedASig;
+ int32 z;
+
+ aSig = extractFloat64Frac( a );
+ aExp = extractFloat64Exp( a );
+ aSign = extractFloat64Sign( a );
+ if ( 0x41E < aExp ) {
+ if ( ( aExp == 0x7FF ) && aSig ) aSign = 0;
+ goto invalid;
+ }
+ else if ( aExp < 0x3FF ) {
+ if ( aExp || aSig ) STATUS(float_exception_flags) |= float_flag_inexact;
+ return 0;
+ }
+ aSig |= LIT64( 0x0010000000000000 );
+ shiftCount = 0x433 - aExp;
+ savedASig = aSig;
+ aSig >>= shiftCount;
+ z = aSig;
+ if ( aSign ) z = - z;
+ if ( ( z < 0 ) ^ aSign ) {
+ invalid:
+ float_raise( float_flag_invalid STATUS_VAR);
+ return aSign ? (sbits32) 0x80000000 : 0x7FFFFFFF;
+ }
+ if ( ( aSig<<shiftCount ) != savedASig ) {
+ STATUS(float_exception_flags) |= float_flag_inexact;
+ }
+ return z;
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the double-precision floating-point value
+| `a' to the 64-bit two's complement integer format. The conversion is
+| performed according to the IEC/IEEE Standard for Binary Floating-Point
+| Arithmetic---which means in particular that the conversion is rounded
+| according to the current rounding mode. If `a' is a NaN, the largest
+| positive integer is returned. Otherwise, if the conversion overflows, the
+| largest integer with the same sign as `a' is returned.
+*----------------------------------------------------------------------------*/
+
+int64 float64_to_int64( float64 a STATUS_PARAM )
+{
+ flag aSign;
+ int16 aExp, shiftCount;
+ bits64 aSig, aSigExtra;
+
+ aSig = extractFloat64Frac( a );
+ aExp = extractFloat64Exp( a );
+ aSign = extractFloat64Sign( a );
+ if ( aExp ) aSig |= LIT64( 0x0010000000000000 );
+ shiftCount = 0x433 - aExp;
+ if ( shiftCount <= 0 ) {
+ if ( 0x43E < aExp ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ if ( ! aSign
+ || ( ( aExp == 0x7FF )
+ && ( aSig != LIT64( 0x0010000000000000 ) ) )
+ ) {
+ return LIT64( 0x7FFFFFFFFFFFFFFF );
+ }
+ return (sbits64) LIT64( 0x8000000000000000 );
+ }
+ aSigExtra = 0;
+ aSig <<= - shiftCount;
+ }
+ else {
+ shift64ExtraRightJamming( aSig, 0, shiftCount, &aSig, &aSigExtra );
+ }
+ return roundAndPackInt64( aSign, aSig, aSigExtra STATUS_VAR );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the double-precision floating-point value
+| `a' to the 64-bit two's complement integer format. The conversion is
+| performed according to the IEC/IEEE Standard for Binary Floating-Point
+| Arithmetic, except that the conversion is always rounded toward zero.
+| If `a' is a NaN, the largest positive integer is returned. Otherwise, if
+| the conversion overflows, the largest integer with the same sign as `a' is
+| returned.
+*----------------------------------------------------------------------------*/
+
+int64 float64_to_int64_round_to_zero( float64 a STATUS_PARAM )
+{
+ flag aSign;
+ int16 aExp, shiftCount;
+ bits64 aSig;
+ int64 z;
+
+ aSig = extractFloat64Frac( a );
+ aExp = extractFloat64Exp( a );
+ aSign = extractFloat64Sign( a );
+ if ( aExp ) aSig |= LIT64( 0x0010000000000000 );
+ shiftCount = aExp - 0x433;
+ if ( 0 <= shiftCount ) {
+ if ( 0x43E <= aExp ) {
+ if ( a != LIT64( 0xC3E0000000000000 ) ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ if ( ! aSign
+ || ( ( aExp == 0x7FF )
+ && ( aSig != LIT64( 0x0010000000000000 ) ) )
+ ) {
+ return LIT64( 0x7FFFFFFFFFFFFFFF );
+ }
+ }
+ return (sbits64) LIT64( 0x8000000000000000 );
+ }
+ z = aSig<<shiftCount;
+ }
+ else {
+ if ( aExp < 0x3FE ) {
+ if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact;
+ return 0;
+ }
+ z = aSig>>( - shiftCount );
+ if ( (bits64) ( aSig<<( shiftCount & 63 ) ) ) {
+ STATUS(float_exception_flags) |= float_flag_inexact;
+ }
+ }
+ if ( aSign ) z = - z;
+ return z;
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the double-precision floating-point value
+| `a' to the single-precision floating-point format. The conversion is
+| performed according to the IEC/IEEE Standard for Binary Floating-Point
+| Arithmetic.
+*----------------------------------------------------------------------------*/
+
+float32 float64_to_float32( float64 a STATUS_PARAM )
+{
+ flag aSign;
+ int16 aExp;
+ bits64 aSig;
+ bits32 zSig;
+
+ aSig = extractFloat64Frac( a );
+ aExp = extractFloat64Exp( a );
+ aSign = extractFloat64Sign( a );
+ if ( aExp == 0x7FF ) {
+ if ( aSig ) return commonNaNToFloat32( float64ToCommonNaN( a STATUS_VAR ) );
+ return packFloat32( aSign, 0xFF, 0 );
+ }
+ shift64RightJamming( aSig, 22, &aSig );
+ zSig = aSig;
+ if ( aExp || zSig ) {
+ zSig |= 0x40000000;
+ aExp -= 0x381;
+ }
+ return roundAndPackFloat32( aSign, aExp, zSig STATUS_VAR );
+
+}
+
+#ifdef FLOATX80
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the double-precision floating-point value
+| `a' to the extended double-precision floating-point format. The conversion
+| is performed according to the IEC/IEEE Standard for Binary Floating-Point
+| Arithmetic.
+*----------------------------------------------------------------------------*/
+
+floatx80 float64_to_floatx80( float64 a STATUS_PARAM )
+{
+ flag aSign;
+ int16 aExp;
+ bits64 aSig;
+
+ aSig = extractFloat64Frac( a );
+ aExp = extractFloat64Exp( a );
+ aSign = extractFloat64Sign( a );
+ if ( aExp == 0x7FF ) {
+ if ( aSig ) return commonNaNToFloatx80( float64ToCommonNaN( a STATUS_VAR ) );
+ return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
+ }
+ if ( aExp == 0 ) {
+ if ( aSig == 0 ) return packFloatx80( aSign, 0, 0 );
+ normalizeFloat64Subnormal( aSig, &aExp, &aSig );
+ }
+ return
+ packFloatx80(
+ aSign, aExp + 0x3C00, ( aSig | LIT64( 0x0010000000000000 ) )<<11 );
+
+}
+
+#endif
+
+#ifdef FLOAT128
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the double-precision floating-point value
+| `a' to the quadruple-precision floating-point format. The conversion is
+| performed according to the IEC/IEEE Standard for Binary Floating-Point
+| Arithmetic.
+*----------------------------------------------------------------------------*/
+
+float128 float64_to_float128( float64 a STATUS_PARAM )
+{
+ flag aSign;
+ int16 aExp;
+ bits64 aSig, zSig0, zSig1;
+
+ aSig = extractFloat64Frac( a );
+ aExp = extractFloat64Exp( a );
+ aSign = extractFloat64Sign( a );
+ if ( aExp == 0x7FF ) {
+ if ( aSig ) return commonNaNToFloat128( float64ToCommonNaN( a STATUS_VAR ) );
+ return packFloat128( aSign, 0x7FFF, 0, 0 );
+ }
+ if ( aExp == 0 ) {
+ if ( aSig == 0 ) return packFloat128( aSign, 0, 0, 0 );
+ normalizeFloat64Subnormal( aSig, &aExp, &aSig );
+ --aExp;
+ }
+ shift128Right( aSig, 0, 4, &zSig0, &zSig1 );
+ return packFloat128( aSign, aExp + 0x3C00, zSig0, zSig1 );
+
+}
+
+#endif
+
+/*----------------------------------------------------------------------------
+| Rounds the double-precision floating-point value `a' to an integer, and
+| returns the result as a double-precision floating-point value. The
+| operation is performed according to the IEC/IEEE Standard for Binary
+| Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+float64 float64_round_to_int( float64 a STATUS_PARAM )
+{
+ flag aSign;
+ int16 aExp;
+ bits64 lastBitMask, roundBitsMask;
+ int8 roundingMode;
+ float64 z;
+
+ aExp = extractFloat64Exp( a );
+ if ( 0x433 <= aExp ) {
+ if ( ( aExp == 0x7FF ) && extractFloat64Frac( a ) ) {
+ return propagateFloat64NaN( a, a STATUS_VAR );
+ }
+ return a;
+ }
+ if ( aExp < 0x3FF ) {
+ if ( (bits64) ( a<<1 ) == 0 ) return a;
+ STATUS(float_exception_flags) |= float_flag_inexact;
+ aSign = extractFloat64Sign( a );
+ switch ( STATUS(float_rounding_mode) ) {
+ case float_round_nearest_even:
+ if ( ( aExp == 0x3FE ) && extractFloat64Frac( a ) ) {
+ return packFloat64( aSign, 0x3FF, 0 );
+ }
+ break;
+ case float_round_down:
+ return aSign ? LIT64( 0xBFF0000000000000 ) : 0;
+ case float_round_up:
+ return
+ aSign ? LIT64( 0x8000000000000000 ) : LIT64( 0x3FF0000000000000 );
+ }
+ return packFloat64( aSign, 0, 0 );
+ }
+ lastBitMask = 1;
+ lastBitMask <<= 0x433 - aExp;
+ roundBitsMask = lastBitMask - 1;
+ z = a;
+ roundingMode = STATUS(float_rounding_mode);
+ if ( roundingMode == float_round_nearest_even ) {
+ z += lastBitMask>>1;
+ if ( ( z & roundBitsMask ) == 0 ) z &= ~ lastBitMask;
+ }
+ else if ( roundingMode != float_round_to_zero ) {
+ if ( extractFloat64Sign( z ) ^ ( roundingMode == float_round_up ) ) {
+ z += roundBitsMask;
+ }
+ }
+ z &= ~ roundBitsMask;
+ if ( z != a ) STATUS(float_exception_flags) |= float_flag_inexact;
+ return z;
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of adding the absolute values of the double-precision
+| floating-point values `a' and `b'. If `zSign' is 1, the sum is negated
+| before being returned. `zSign' is ignored if the result is a NaN.
+| The addition is performed according to the IEC/IEEE Standard for Binary
+| Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+static float64 addFloat64Sigs( float64 a, float64 b, flag zSign STATUS_PARAM )
+{
+ int16 aExp, bExp, zExp;
+ bits64 aSig, bSig, zSig;
+ int16 expDiff;
+
+ aSig = extractFloat64Frac( a );
+ aExp = extractFloat64Exp( a );
+ bSig = extractFloat64Frac( b );
+ bExp = extractFloat64Exp( b );
+ expDiff = aExp - bExp;
+ aSig <<= 9;
+ bSig <<= 9;
+ if ( 0 < expDiff ) {
+ if ( aExp == 0x7FF ) {
+ if ( aSig ) return propagateFloat64NaN( a, b STATUS_VAR );
+ return a;
+ }
+ if ( bExp == 0 ) {
+ --expDiff;
+ }
+ else {
+ bSig |= LIT64( 0x2000000000000000 );
+ }
+ shift64RightJamming( bSig, expDiff, &bSig );
+ zExp = aExp;
+ }
+ else if ( expDiff < 0 ) {
+ if ( bExp == 0x7FF ) {
+ if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR );
+ return packFloat64( zSign, 0x7FF, 0 );
+ }
+ if ( aExp == 0 ) {
+ ++expDiff;
+ }
+ else {
+ aSig |= LIT64( 0x2000000000000000 );
+ }
+ shift64RightJamming( aSig, - expDiff, &aSig );
+ zExp = bExp;
+ }
+ else {
+ if ( aExp == 0x7FF ) {
+ if ( aSig | bSig ) return propagateFloat64NaN( a, b STATUS_VAR );
+ return a;
+ }
+ if ( aExp == 0 ) return packFloat64( zSign, 0, ( aSig + bSig )>>9 );
+ zSig = LIT64( 0x4000000000000000 ) + aSig + bSig;
+ zExp = aExp;
+ goto roundAndPack;
+ }
+ aSig |= LIT64( 0x2000000000000000 );
+ zSig = ( aSig + bSig )<<1;
+ --zExp;
+ if ( (sbits64) zSig < 0 ) {
+ zSig = aSig + bSig;
+ ++zExp;
+ }
+ roundAndPack:
+ return roundAndPackFloat64( zSign, zExp, zSig STATUS_VAR );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of subtracting the absolute values of the double-
+| precision floating-point values `a' and `b'. If `zSign' is 1, the
+| difference is negated before being returned. `zSign' is ignored if the
+| result is a NaN. The subtraction is performed according to the IEC/IEEE
+| Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+static float64 subFloat64Sigs( float64 a, float64 b, flag zSign STATUS_PARAM )
+{
+ int16 aExp, bExp, zExp;
+ bits64 aSig, bSig, zSig;
+ int16 expDiff;
+
+ aSig = extractFloat64Frac( a );
+ aExp = extractFloat64Exp( a );
+ bSig = extractFloat64Frac( b );
+ bExp = extractFloat64Exp( b );
+ expDiff = aExp - bExp;
+ aSig <<= 10;
+ bSig <<= 10;
+ if ( 0 < expDiff ) goto aExpBigger;
+ if ( expDiff < 0 ) goto bExpBigger;
+ if ( aExp == 0x7FF ) {
+ if ( aSig | bSig ) return propagateFloat64NaN( a, b STATUS_VAR );
+ float_raise( float_flag_invalid STATUS_VAR);
+ return float64_default_nan;
+ }
+ if ( aExp == 0 ) {
+ aExp = 1;
+ bExp = 1;
+ }
+ if ( bSig < aSig ) goto aBigger;
+ if ( aSig < bSig ) goto bBigger;
+ return packFloat64( STATUS(float_rounding_mode) == float_round_down, 0, 0 );
+ bExpBigger:
+ if ( bExp == 0x7FF ) {
+ if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR );
+ return packFloat64( zSign ^ 1, 0x7FF, 0 );
+ }
+ if ( aExp == 0 ) {
+ ++expDiff;
+ }
+ else {
+ aSig |= LIT64( 0x4000000000000000 );
+ }
+ shift64RightJamming( aSig, - expDiff, &aSig );
+ bSig |= LIT64( 0x4000000000000000 );
+ bBigger:
+ zSig = bSig - aSig;
+ zExp = bExp;
+ zSign ^= 1;
+ goto normalizeRoundAndPack;
+ aExpBigger:
+ if ( aExp == 0x7FF ) {
+ if ( aSig ) return propagateFloat64NaN( a, b STATUS_VAR );
+ return a;
+ }
+ if ( bExp == 0 ) {
+ --expDiff;
+ }
+ else {
+ bSig |= LIT64( 0x4000000000000000 );
+ }
+ shift64RightJamming( bSig, expDiff, &bSig );
+ aSig |= LIT64( 0x4000000000000000 );
+ aBigger:
+ zSig = aSig - bSig;
+ zExp = aExp;
+ normalizeRoundAndPack:
+ --zExp;
+ return normalizeRoundAndPackFloat64( zSign, zExp, zSig STATUS_VAR );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of adding the double-precision floating-point values `a'
+| and `b'. The operation is performed according to the IEC/IEEE Standard for
+| Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+float64 float64_add( float64 a, float64 b STATUS_PARAM )
+{
+ flag aSign, bSign;
+
+ aSign = extractFloat64Sign( a );
+ bSign = extractFloat64Sign( b );
+ if ( aSign == bSign ) {
+ return addFloat64Sigs( a, b, aSign STATUS_VAR );
+ }
+ else {
+ return subFloat64Sigs( a, b, aSign STATUS_VAR );
+ }
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of subtracting the double-precision floating-point values
+| `a' and `b'. The operation is performed according to the IEC/IEEE Standard
+| for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+float64 float64_sub( float64 a, float64 b STATUS_PARAM )
+{
+ flag aSign, bSign;
+
+ aSign = extractFloat64Sign( a );
+ bSign = extractFloat64Sign( b );
+ if ( aSign == bSign ) {
+ return subFloat64Sigs( a, b, aSign STATUS_VAR );
+ }
+ else {
+ return addFloat64Sigs( a, b, aSign STATUS_VAR );
+ }
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of multiplying the double-precision floating-point values
+| `a' and `b'. The operation is performed according to the IEC/IEEE Standard
+| for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+float64 float64_mul( float64 a, float64 b STATUS_PARAM )
+{
+ flag aSign, bSign, zSign;
+ int16 aExp, bExp, zExp;
+ bits64 aSig, bSig, zSig0, zSig1;
+
+ aSig = extractFloat64Frac( a );
+ aExp = extractFloat64Exp( a );
+ aSign = extractFloat64Sign( a );
+ bSig = extractFloat64Frac( b );
+ bExp = extractFloat64Exp( b );
+ bSign = extractFloat64Sign( b );
+ zSign = aSign ^ bSign;
+ if ( aExp == 0x7FF ) {
+ if ( aSig || ( ( bExp == 0x7FF ) && bSig ) ) {
+ return propagateFloat64NaN( a, b STATUS_VAR );
+ }
+ if ( ( bExp | bSig ) == 0 ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ return float64_default_nan;
+ }
+ return packFloat64( zSign, 0x7FF, 0 );
+ }
+ if ( bExp == 0x7FF ) {
+ if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR );
+ if ( ( aExp | aSig ) == 0 ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ return float64_default_nan;
+ }
+ return packFloat64( zSign, 0x7FF, 0 );
+ }
+ if ( aExp == 0 ) {
+ if ( aSig == 0 ) return packFloat64( zSign, 0, 0 );
+ normalizeFloat64Subnormal( aSig, &aExp, &aSig );
+ }
+ if ( bExp == 0 ) {
+ if ( bSig == 0 ) return packFloat64( zSign, 0, 0 );
+ normalizeFloat64Subnormal( bSig, &bExp, &bSig );
+ }
+ zExp = aExp + bExp - 0x3FF;
+ aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<10;
+ bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11;
+ mul64To128( aSig, bSig, &zSig0, &zSig1 );
+ zSig0 |= ( zSig1 != 0 );
+ if ( 0 <= (sbits64) ( zSig0<<1 ) ) {
+ zSig0 <<= 1;
+ --zExp;
+ }
+ return roundAndPackFloat64( zSign, zExp, zSig0 STATUS_VAR );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of dividing the double-precision floating-point value `a'
+| by the corresponding value `b'. The operation is performed according to
+| the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+float64 float64_div( float64 a, float64 b STATUS_PARAM )
+{
+ flag aSign, bSign, zSign;
+ int16 aExp, bExp, zExp;
+ bits64 aSig, bSig, zSig;
+ bits64 rem0, rem1;
+ bits64 term0, term1;
+
+ aSig = extractFloat64Frac( a );
+ aExp = extractFloat64Exp( a );
+ aSign = extractFloat64Sign( a );
+ bSig = extractFloat64Frac( b );
+ bExp = extractFloat64Exp( b );
+ bSign = extractFloat64Sign( b );
+ zSign = aSign ^ bSign;
+ if ( aExp == 0x7FF ) {
+ if ( aSig ) return propagateFloat64NaN( a, b STATUS_VAR );
+ if ( bExp == 0x7FF ) {
+ if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR );
+ float_raise( float_flag_invalid STATUS_VAR);
+ return float64_default_nan;
+ }
+ return packFloat64( zSign, 0x7FF, 0 );
+ }
+ if ( bExp == 0x7FF ) {
+ if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR );
+ return packFloat64( zSign, 0, 0 );
+ }
+ if ( bExp == 0 ) {
+ if ( bSig == 0 ) {
+ if ( ( aExp | aSig ) == 0 ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ return float64_default_nan;
+ }
+ float_raise( float_flag_divbyzero STATUS_VAR);
+ return packFloat64( zSign, 0x7FF, 0 );
+ }
+ normalizeFloat64Subnormal( bSig, &bExp, &bSig );
+ }
+ if ( aExp == 0 ) {
+ if ( aSig == 0 ) return packFloat64( zSign, 0, 0 );
+ normalizeFloat64Subnormal( aSig, &aExp, &aSig );
+ }
+ zExp = aExp - bExp + 0x3FD;
+ aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<10;
+ bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11;
+ if ( bSig <= ( aSig + aSig ) ) {
+ aSig >>= 1;
+ ++zExp;
+ }
+ zSig = estimateDiv128To64( aSig, 0, bSig );
+ if ( ( zSig & 0x1FF ) <= 2 ) {
+ mul64To128( bSig, zSig, &term0, &term1 );
+ sub128( aSig, 0, term0, term1, &rem0, &rem1 );
+ while ( (sbits64) rem0 < 0 ) {
+ --zSig;
+ add128( rem0, rem1, 0, bSig, &rem0, &rem1 );
+ }
+ zSig |= ( rem1 != 0 );
+ }
+ return roundAndPackFloat64( zSign, zExp, zSig STATUS_VAR );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the remainder of the double-precision floating-point value `a'
+| with respect to the corresponding value `b'. The operation is performed
+| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+float64 float64_rem( float64 a, float64 b STATUS_PARAM )
+{
+ flag aSign, bSign, zSign;
+ int16 aExp, bExp, expDiff;
+ bits64 aSig, bSig;
+ bits64 q, alternateASig;
+ sbits64 sigMean;
+
+ aSig = extractFloat64Frac( a );
+ aExp = extractFloat64Exp( a );
+ aSign = extractFloat64Sign( a );
+ bSig = extractFloat64Frac( b );
+ bExp = extractFloat64Exp( b );
+ bSign = extractFloat64Sign( b );
+ if ( aExp == 0x7FF ) {
+ if ( aSig || ( ( bExp == 0x7FF ) && bSig ) ) {
+ return propagateFloat64NaN( a, b STATUS_VAR );
+ }
+ float_raise( float_flag_invalid STATUS_VAR);
+ return float64_default_nan;
+ }
+ if ( bExp == 0x7FF ) {
+ if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR );
+ return a;
+ }
+ if ( bExp == 0 ) {
+ if ( bSig == 0 ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ return float64_default_nan;
+ }
+ normalizeFloat64Subnormal( bSig, &bExp, &bSig );
+ }
+ if ( aExp == 0 ) {
+ if ( aSig == 0 ) return a;
+ normalizeFloat64Subnormal( aSig, &aExp, &aSig );
+ }
+ expDiff = aExp - bExp;
+ aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<11;
+ bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11;
+ if ( expDiff < 0 ) {
+ if ( expDiff < -1 ) return a;
+ aSig >>= 1;
+ }
+ q = ( bSig <= aSig );
+ if ( q ) aSig -= bSig;
+ expDiff -= 64;
+ while ( 0 < expDiff ) {
+ q = estimateDiv128To64( aSig, 0, bSig );
+ q = ( 2 < q ) ? q - 2 : 0;
+ aSig = - ( ( bSig>>2 ) * q );
+ expDiff -= 62;
+ }
+ expDiff += 64;
+ if ( 0 < expDiff ) {
+ q = estimateDiv128To64( aSig, 0, bSig );
+ q = ( 2 < q ) ? q - 2 : 0;
+ q >>= 64 - expDiff;
+ bSig >>= 2;
+ aSig = ( ( aSig>>1 )<<( expDiff - 1 ) ) - bSig * q;
+ }
+ else {
+ aSig >>= 2;
+ bSig >>= 2;
+ }
+ do {
+ alternateASig = aSig;
+ ++q;
+ aSig -= bSig;
+ } while ( 0 <= (sbits64) aSig );
+ sigMean = aSig + alternateASig;
+ if ( ( sigMean < 0 ) || ( ( sigMean == 0 ) && ( q & 1 ) ) ) {
+ aSig = alternateASig;
+ }
+ zSign = ( (sbits64) aSig < 0 );
+ if ( zSign ) aSig = - aSig;
+ return normalizeRoundAndPackFloat64( aSign ^ zSign, bExp, aSig STATUS_VAR );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the square root of the double-precision floating-point value `a'.
+| The operation is performed according to the IEC/IEEE Standard for Binary
+| Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+float64 float64_sqrt( float64 a STATUS_PARAM )
+{
+ flag aSign;
+ int16 aExp, zExp;
+ bits64 aSig, zSig, doubleZSig;
+ bits64 rem0, rem1, term0, term1;
+
+ aSig = extractFloat64Frac( a );
+ aExp = extractFloat64Exp( a );
+ aSign = extractFloat64Sign( a );
+ if ( aExp == 0x7FF ) {
+ if ( aSig ) return propagateFloat64NaN( a, a STATUS_VAR );
+ if ( ! aSign ) return a;
+ float_raise( float_flag_invalid STATUS_VAR);
+ return float64_default_nan;
+ }
+ if ( aSign ) {
+ if ( ( aExp | aSig ) == 0 ) return a;
+ float_raise( float_flag_invalid STATUS_VAR);
+ return float64_default_nan;
+ }
+ if ( aExp == 0 ) {
+ if ( aSig == 0 ) return 0;
+ normalizeFloat64Subnormal( aSig, &aExp, &aSig );
+ }
+ zExp = ( ( aExp - 0x3FF )>>1 ) + 0x3FE;
+ aSig |= LIT64( 0x0010000000000000 );
+ zSig = estimateSqrt32( aExp, aSig>>21 );
+ aSig <<= 9 - ( aExp & 1 );
+ zSig = estimateDiv128To64( aSig, 0, zSig<<32 ) + ( zSig<<30 );
+ if ( ( zSig & 0x1FF ) <= 5 ) {
+ doubleZSig = zSig<<1;
+ mul64To128( zSig, zSig, &term0, &term1 );
+ sub128( aSig, 0, term0, term1, &rem0, &rem1 );
+ while ( (sbits64) rem0 < 0 ) {
+ --zSig;
+ doubleZSig -= 2;
+ add128( rem0, rem1, zSig>>63, doubleZSig | 1, &rem0, &rem1 );
+ }
+ zSig |= ( ( rem0 | rem1 ) != 0 );
+ }
+ return roundAndPackFloat64( 0, zExp, zSig STATUS_VAR );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the double-precision floating-point value `a' is equal to the
+| corresponding value `b', and 0 otherwise. The comparison is performed
+| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+flag float64_eq( float64 a, float64 b STATUS_PARAM )
+{
+
+ if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
+ || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
+ ) {
+ if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ }
+ return 0;
+ }
+ return ( a == b ) || ( (bits64) ( ( a | b )<<1 ) == 0 );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the double-precision floating-point value `a' is less than or
+| equal to the corresponding value `b', and 0 otherwise. The comparison is
+| performed according to the IEC/IEEE Standard for Binary Floating-Point
+| Arithmetic.
+*----------------------------------------------------------------------------*/
+
+flag float64_le( float64 a, float64 b STATUS_PARAM )
+{
+ flag aSign, bSign;
+
+ if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
+ || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
+ ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ return 0;
+ }
+ aSign = extractFloat64Sign( a );
+ bSign = extractFloat64Sign( b );
+ if ( aSign != bSign ) return aSign || ( (bits64) ( ( a | b )<<1 ) == 0 );
+ return ( a == b ) || ( aSign ^ ( a < b ) );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the double-precision floating-point value `a' is less than
+| the corresponding value `b', and 0 otherwise. The comparison is performed
+| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+flag float64_lt( float64 a, float64 b STATUS_PARAM )
+{
+ flag aSign, bSign;
+
+ if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
+ || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
+ ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ return 0;
+ }
+ aSign = extractFloat64Sign( a );
+ bSign = extractFloat64Sign( b );
+ if ( aSign != bSign ) return aSign && ( (bits64) ( ( a | b )<<1 ) != 0 );
+ return ( a != b ) && ( aSign ^ ( a < b ) );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the double-precision floating-point value `a' is equal to the
+| corresponding value `b', and 0 otherwise. The invalid exception is raised
+| if either operand is a NaN. Otherwise, the comparison is performed
+| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+flag float64_eq_signaling( float64 a, float64 b STATUS_PARAM )
+{
+
+ if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
+ || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
+ ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ return 0;
+ }
+ return ( a == b ) || ( (bits64) ( ( a | b )<<1 ) == 0 );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the double-precision floating-point value `a' is less than or
+| equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not
+| cause an exception. Otherwise, the comparison is performed according to the
+| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+flag float64_le_quiet( float64 a, float64 b STATUS_PARAM )
+{
+ flag aSign, bSign;
+
+ if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
+ || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
+ ) {
+ if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ }
+ return 0;
+ }
+ aSign = extractFloat64Sign( a );
+ bSign = extractFloat64Sign( b );
+ if ( aSign != bSign ) return aSign || ( (bits64) ( ( a | b )<<1 ) == 0 );
+ return ( a == b ) || ( aSign ^ ( a < b ) );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the double-precision floating-point value `a' is less than
+| the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an
+| exception. Otherwise, the comparison is performed according to the IEC/IEEE
+| Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+flag float64_lt_quiet( float64 a, float64 b STATUS_PARAM )
+{
+ flag aSign, bSign;
+
+ if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) )
+ || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) )
+ ) {
+ if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ }
+ return 0;
+ }
+ aSign = extractFloat64Sign( a );
+ bSign = extractFloat64Sign( b );
+ if ( aSign != bSign ) return aSign && ( (bits64) ( ( a | b )<<1 ) != 0 );
+ return ( a != b ) && ( aSign ^ ( a < b ) );
+
+}
+
+#ifdef FLOATX80
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the extended double-precision floating-
+| point value `a' to the 32-bit two's complement integer format. The
+| conversion is performed according to the IEC/IEEE Standard for Binary
+| Floating-Point Arithmetic---which means in particular that the conversion
+| is rounded according to the current rounding mode. If `a' is a NaN, the
+| largest positive integer is returned. Otherwise, if the conversion
+| overflows, the largest integer with the same sign as `a' is returned.
+*----------------------------------------------------------------------------*/
+
+int32 floatx80_to_int32( floatx80 a STATUS_PARAM )
+{
+ flag aSign;
+ int32 aExp, shiftCount;
+ bits64 aSig;
+
+ aSig = extractFloatx80Frac( a );
+ aExp = extractFloatx80Exp( a );
+ aSign = extractFloatx80Sign( a );
+ if ( ( aExp == 0x7FFF ) && (bits64) ( aSig<<1 ) ) aSign = 0;
+ shiftCount = 0x4037 - aExp;
+ if ( shiftCount <= 0 ) shiftCount = 1;
+ shift64RightJamming( aSig, shiftCount, &aSig );
+ return roundAndPackInt32( aSign, aSig STATUS_VAR );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the extended double-precision floating-
+| point value `a' to the 32-bit two's complement integer format. The
+| conversion is performed according to the IEC/IEEE Standard for Binary
+| Floating-Point Arithmetic, except that the conversion is always rounded
+| toward zero. If `a' is a NaN, the largest positive integer is returned.
+| Otherwise, if the conversion overflows, the largest integer with the same
+| sign as `a' is returned.
+*----------------------------------------------------------------------------*/
+
+int32 floatx80_to_int32_round_to_zero( floatx80 a STATUS_PARAM )
+{
+ flag aSign;
+ int32 aExp, shiftCount;
+ bits64 aSig, savedASig;
+ int32 z;
+
+ aSig = extractFloatx80Frac( a );
+ aExp = extractFloatx80Exp( a );
+ aSign = extractFloatx80Sign( a );
+ if ( 0x401E < aExp ) {
+ if ( ( aExp == 0x7FFF ) && (bits64) ( aSig<<1 ) ) aSign = 0;
+ goto invalid;
+ }
+ else if ( aExp < 0x3FFF ) {
+ if ( aExp || aSig ) STATUS(float_exception_flags) |= float_flag_inexact;
+ return 0;
+ }
+ shiftCount = 0x403E - aExp;
+ savedASig = aSig;
+ aSig >>= shiftCount;
+ z = aSig;
+ if ( aSign ) z = - z;
+ if ( ( z < 0 ) ^ aSign ) {
+ invalid:
+ float_raise( float_flag_invalid STATUS_VAR);
+ return aSign ? (sbits32) 0x80000000 : 0x7FFFFFFF;
+ }
+ if ( ( aSig<<shiftCount ) != savedASig ) {
+ STATUS(float_exception_flags) |= float_flag_inexact;
+ }
+ return z;
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the extended double-precision floating-
+| point value `a' to the 64-bit two's complement integer format. The
+| conversion is performed according to the IEC/IEEE Standard for Binary
+| Floating-Point Arithmetic---which means in particular that the conversion
+| is rounded according to the current rounding mode. If `a' is a NaN,
+| the largest positive integer is returned. Otherwise, if the conversion
+| overflows, the largest integer with the same sign as `a' is returned.
+*----------------------------------------------------------------------------*/
+
+int64 floatx80_to_int64( floatx80 a STATUS_PARAM )
+{
+ flag aSign;
+ int32 aExp, shiftCount;
+ bits64 aSig, aSigExtra;
+
+ aSig = extractFloatx80Frac( a );
+ aExp = extractFloatx80Exp( a );
+ aSign = extractFloatx80Sign( a );
+ shiftCount = 0x403E - aExp;
+ if ( shiftCount <= 0 ) {
+ if ( shiftCount ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ if ( ! aSign
+ || ( ( aExp == 0x7FFF )
+ && ( aSig != LIT64( 0x8000000000000000 ) ) )
+ ) {
+ return LIT64( 0x7FFFFFFFFFFFFFFF );
+ }
+ return (sbits64) LIT64( 0x8000000000000000 );
+ }
+ aSigExtra = 0;
+ }
+ else {
+ shift64ExtraRightJamming( aSig, 0, shiftCount, &aSig, &aSigExtra );
+ }
+ return roundAndPackInt64( aSign, aSig, aSigExtra STATUS_VAR );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the extended double-precision floating-
+| point value `a' to the 64-bit two's complement integer format. The
+| conversion is performed according to the IEC/IEEE Standard for Binary
+| Floating-Point Arithmetic, except that the conversion is always rounded
+| toward zero. If `a' is a NaN, the largest positive integer is returned.
+| Otherwise, if the conversion overflows, the largest integer with the same
+| sign as `a' is returned.
+*----------------------------------------------------------------------------*/
+
+int64 floatx80_to_int64_round_to_zero( floatx80 a STATUS_PARAM )
+{
+ flag aSign;
+ int32 aExp, shiftCount;
+ bits64 aSig;
+ int64 z;
+
+ aSig = extractFloatx80Frac( a );
+ aExp = extractFloatx80Exp( a );
+ aSign = extractFloatx80Sign( a );
+ shiftCount = aExp - 0x403E;
+ if ( 0 <= shiftCount ) {
+ aSig &= LIT64( 0x7FFFFFFFFFFFFFFF );
+ if ( ( a.high != 0xC03E ) || aSig ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ if ( ! aSign || ( ( aExp == 0x7FFF ) && aSig ) ) {
+ return LIT64( 0x7FFFFFFFFFFFFFFF );
+ }
+ }
+ return (sbits64) LIT64( 0x8000000000000000 );
+ }
+ else if ( aExp < 0x3FFF ) {
+ if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact;
+ return 0;
+ }
+ z = aSig>>( - shiftCount );
+ if ( (bits64) ( aSig<<( shiftCount & 63 ) ) ) {
+ STATUS(float_exception_flags) |= float_flag_inexact;
+ }
+ if ( aSign ) z = - z;
+ return z;
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the extended double-precision floating-
+| point value `a' to the single-precision floating-point format. The
+| conversion is performed according to the IEC/IEEE Standard for Binary
+| Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+float32 floatx80_to_float32( floatx80 a STATUS_PARAM )
+{
+ flag aSign;
+ int32 aExp;
+ bits64 aSig;
+
+ aSig = extractFloatx80Frac( a );
+ aExp = extractFloatx80Exp( a );
+ aSign = extractFloatx80Sign( a );
+ if ( aExp == 0x7FFF ) {
+ if ( (bits64) ( aSig<<1 ) ) {
+ return commonNaNToFloat32( floatx80ToCommonNaN( a STATUS_VAR ) );
+ }
+ return packFloat32( aSign, 0xFF, 0 );
+ }
+ shift64RightJamming( aSig, 33, &aSig );
+ if ( aExp || aSig ) aExp -= 0x3F81;
+ return roundAndPackFloat32( aSign, aExp, aSig STATUS_VAR );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the extended double-precision floating-
+| point value `a' to the double-precision floating-point format. The
+| conversion is performed according to the IEC/IEEE Standard for Binary
+| Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+float64 floatx80_to_float64( floatx80 a STATUS_PARAM )
+{
+ flag aSign;
+ int32 aExp;
+ bits64 aSig, zSig;
+
+ aSig = extractFloatx80Frac( a );
+ aExp = extractFloatx80Exp( a );
+ aSign = extractFloatx80Sign( a );
+ if ( aExp == 0x7FFF ) {
+ if ( (bits64) ( aSig<<1 ) ) {
+ return commonNaNToFloat64( floatx80ToCommonNaN( a STATUS_VAR ) );
+ }
+ return packFloat64( aSign, 0x7FF, 0 );
+ }
+ shift64RightJamming( aSig, 1, &zSig );
+ if ( aExp || aSig ) aExp -= 0x3C01;
+ return roundAndPackFloat64( aSign, aExp, zSig STATUS_VAR );
+
+}
+
+#ifdef FLOAT128
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the extended double-precision floating-
+| point value `a' to the quadruple-precision floating-point format. The
+| conversion is performed according to the IEC/IEEE Standard for Binary
+| Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+float128 floatx80_to_float128( floatx80 a STATUS_PARAM )
+{
+ flag aSign;
+ int16 aExp;
+ bits64 aSig, zSig0, zSig1;
+
+ aSig = extractFloatx80Frac( a );
+ aExp = extractFloatx80Exp( a );
+ aSign = extractFloatx80Sign( a );
+ if ( ( aExp == 0x7FFF ) && (bits64) ( aSig<<1 ) ) {
+ return commonNaNToFloat128( floatx80ToCommonNaN( a STATUS_VAR ) );
+ }
+ shift128Right( aSig<<1, 0, 16, &zSig0, &zSig1 );
+ return packFloat128( aSign, aExp, zSig0, zSig1 );
+
+}
+
+#endif
+
+/*----------------------------------------------------------------------------
+| Rounds the extended double-precision floating-point value `a' to an integer,
+| and returns the result as an extended quadruple-precision floating-point
+| value. The operation is performed according to the IEC/IEEE Standard for
+| Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+floatx80 floatx80_round_to_int( floatx80 a STATUS_PARAM )
+{
+ flag aSign;
+ int32 aExp;
+ bits64 lastBitMask, roundBitsMask;
+ int8 roundingMode;
+ floatx80 z;
+
+ aExp = extractFloatx80Exp( a );
+ if ( 0x403E <= aExp ) {
+ if ( ( aExp == 0x7FFF ) && (bits64) ( extractFloatx80Frac( a )<<1 ) ) {
+ return propagateFloatx80NaN( a, a STATUS_VAR );
+ }
+ return a;
+ }
+ if ( aExp < 0x3FFF ) {
+ if ( ( aExp == 0 )
+ && ( (bits64) ( extractFloatx80Frac( a )<<1 ) == 0 ) ) {
+ return a;
+ }
+ STATUS(float_exception_flags) |= float_flag_inexact;
+ aSign = extractFloatx80Sign( a );
+ switch ( STATUS(float_rounding_mode) ) {
+ case float_round_nearest_even:
+ if ( ( aExp == 0x3FFE ) && (bits64) ( extractFloatx80Frac( a )<<1 )
+ ) {
+ return
+ packFloatx80( aSign, 0x3FFF, LIT64( 0x8000000000000000 ) );
+ }
+ break;
+ case float_round_down:
+ return
+ aSign ?
+ packFloatx80( 1, 0x3FFF, LIT64( 0x8000000000000000 ) )
+ : packFloatx80( 0, 0, 0 );
+ case float_round_up:
+ return
+ aSign ? packFloatx80( 1, 0, 0 )
+ : packFloatx80( 0, 0x3FFF, LIT64( 0x8000000000000000 ) );
+ }
+ return packFloatx80( aSign, 0, 0 );
+ }
+ lastBitMask = 1;
+ lastBitMask <<= 0x403E - aExp;
+ roundBitsMask = lastBitMask - 1;
+ z = a;
+ roundingMode = STATUS(float_rounding_mode);
+ if ( roundingMode == float_round_nearest_even ) {
+ z.low += lastBitMask>>1;
+ if ( ( z.low & roundBitsMask ) == 0 ) z.low &= ~ lastBitMask;
+ }
+ else if ( roundingMode != float_round_to_zero ) {
+ if ( extractFloatx80Sign( z ) ^ ( roundingMode == float_round_up ) ) {
+ z.low += roundBitsMask;
+ }
+ }
+ z.low &= ~ roundBitsMask;
+ if ( z.low == 0 ) {
+ ++z.high;
+ z.low = LIT64( 0x8000000000000000 );
+ }
+ if ( z.low != a.low ) STATUS(float_exception_flags) |= float_flag_inexact;
+ return z;
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of adding the absolute values of the extended double-
+| precision floating-point values `a' and `b'. If `zSign' is 1, the sum is
+| negated before being returned. `zSign' is ignored if the result is a NaN.
+| The addition is performed according to the IEC/IEEE Standard for Binary
+| Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+static floatx80 addFloatx80Sigs( floatx80 a, floatx80 b, flag zSign STATUS_PARAM)
+{
+ int32 aExp, bExp, zExp;
+ bits64 aSig, bSig, zSig0, zSig1;
+ int32 expDiff;
+
+ aSig = extractFloatx80Frac( a );
+ aExp = extractFloatx80Exp( a );
+ bSig = extractFloatx80Frac( b );
+ bExp = extractFloatx80Exp( b );
+ expDiff = aExp - bExp;
+ if ( 0 < expDiff ) {
+ if ( aExp == 0x7FFF ) {
+ if ( (bits64) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR );
+ return a;
+ }
+ if ( bExp == 0 ) --expDiff;
+ shift64ExtraRightJamming( bSig, 0, expDiff, &bSig, &zSig1 );
+ zExp = aExp;
+ }
+ else if ( expDiff < 0 ) {
+ if ( bExp == 0x7FFF ) {
+ if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR );
+ return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
+ }
+ if ( aExp == 0 ) ++expDiff;
+ shift64ExtraRightJamming( aSig, 0, - expDiff, &aSig, &zSig1 );
+ zExp = bExp;
+ }
+ else {
+ if ( aExp == 0x7FFF ) {
+ if ( (bits64) ( ( aSig | bSig )<<1 ) ) {
+ return propagateFloatx80NaN( a, b STATUS_VAR );
+ }
+ return a;
+ }
+ zSig1 = 0;
+ zSig0 = aSig + bSig;
+ if ( aExp == 0 ) {
+ normalizeFloatx80Subnormal( zSig0, &zExp, &zSig0 );
+ goto roundAndPack;
+ }
+ zExp = aExp;
+ goto shiftRight1;
+ }
+ zSig0 = aSig + bSig;
+ if ( (sbits64) zSig0 < 0 ) goto roundAndPack;
+ shiftRight1:
+ shift64ExtraRightJamming( zSig0, zSig1, 1, &zSig0, &zSig1 );
+ zSig0 |= LIT64( 0x8000000000000000 );
+ ++zExp;
+ roundAndPack:
+ return
+ roundAndPackFloatx80(
+ STATUS(floatx80_rounding_precision), zSign, zExp, zSig0, zSig1 STATUS_VAR );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of subtracting the absolute values of the extended
+| double-precision floating-point values `a' and `b'. If `zSign' is 1, the
+| difference is negated before being returned. `zSign' is ignored if the
+| result is a NaN. The subtraction is performed according to the IEC/IEEE
+| Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+static floatx80 subFloatx80Sigs( floatx80 a, floatx80 b, flag zSign STATUS_PARAM )
+{
+ int32 aExp, bExp, zExp;
+ bits64 aSig, bSig, zSig0, zSig1;
+ int32 expDiff;
+ floatx80 z;
+
+ aSig = extractFloatx80Frac( a );
+ aExp = extractFloatx80Exp( a );
+ bSig = extractFloatx80Frac( b );
+ bExp = extractFloatx80Exp( b );
+ expDiff = aExp - bExp;
+ if ( 0 < expDiff ) goto aExpBigger;
+ if ( expDiff < 0 ) goto bExpBigger;
+ if ( aExp == 0x7FFF ) {
+ if ( (bits64) ( ( aSig | bSig )<<1 ) ) {
+ return propagateFloatx80NaN( a, b STATUS_VAR );
+ }
+ float_raise( float_flag_invalid STATUS_VAR);
+ z.low = floatx80_default_nan_low;
+ z.high = floatx80_default_nan_high;
+ return z;
+ }
+ if ( aExp == 0 ) {
+ aExp = 1;
+ bExp = 1;
+ }
+ zSig1 = 0;
+ if ( bSig < aSig ) goto aBigger;
+ if ( aSig < bSig ) goto bBigger;
+ return packFloatx80( STATUS(float_rounding_mode) == float_round_down, 0, 0 );
+ bExpBigger:
+ if ( bExp == 0x7FFF ) {
+ if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR );
+ return packFloatx80( zSign ^ 1, 0x7FFF, LIT64( 0x8000000000000000 ) );
+ }
+ if ( aExp == 0 ) ++expDiff;
+ shift128RightJamming( aSig, 0, - expDiff, &aSig, &zSig1 );
+ bBigger:
+ sub128( bSig, 0, aSig, zSig1, &zSig0, &zSig1 );
+ zExp = bExp;
+ zSign ^= 1;
+ goto normalizeRoundAndPack;
+ aExpBigger:
+ if ( aExp == 0x7FFF ) {
+ if ( (bits64) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR );
+ return a;
+ }
+ if ( bExp == 0 ) --expDiff;
+ shift128RightJamming( bSig, 0, expDiff, &bSig, &zSig1 );
+ aBigger:
+ sub128( aSig, 0, bSig, zSig1, &zSig0, &zSig1 );
+ zExp = aExp;
+ normalizeRoundAndPack:
+ return
+ normalizeRoundAndPackFloatx80(
+ STATUS(floatx80_rounding_precision), zSign, zExp, zSig0, zSig1 STATUS_VAR );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of adding the extended double-precision floating-point
+| values `a' and `b'. The operation is performed according to the IEC/IEEE
+| Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+floatx80 floatx80_add( floatx80 a, floatx80 b STATUS_PARAM )
+{
+ flag aSign, bSign;
+
+ aSign = extractFloatx80Sign( a );
+ bSign = extractFloatx80Sign( b );
+ if ( aSign == bSign ) {
+ return addFloatx80Sigs( a, b, aSign STATUS_VAR );
+ }
+ else {
+ return subFloatx80Sigs( a, b, aSign STATUS_VAR );
+ }
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of subtracting the extended double-precision floating-
+| point values `a' and `b'. The operation is performed according to the
+| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+floatx80 floatx80_sub( floatx80 a, floatx80 b STATUS_PARAM )
+{
+ flag aSign, bSign;
+
+ aSign = extractFloatx80Sign( a );
+ bSign = extractFloatx80Sign( b );
+ if ( aSign == bSign ) {
+ return subFloatx80Sigs( a, b, aSign STATUS_VAR );
+ }
+ else {
+ return addFloatx80Sigs( a, b, aSign STATUS_VAR );
+ }
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of multiplying the extended double-precision floating-
+| point values `a' and `b'. The operation is performed according to the
+| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+floatx80 floatx80_mul( floatx80 a, floatx80 b STATUS_PARAM )
+{
+ flag aSign, bSign, zSign;
+ int32 aExp, bExp, zExp;
+ bits64 aSig, bSig, zSig0, zSig1;
+ floatx80 z;
+
+ aSig = extractFloatx80Frac( a );
+ aExp = extractFloatx80Exp( a );
+ aSign = extractFloatx80Sign( a );
+ bSig = extractFloatx80Frac( b );
+ bExp = extractFloatx80Exp( b );
+ bSign = extractFloatx80Sign( b );
+ zSign = aSign ^ bSign;
+ if ( aExp == 0x7FFF ) {
+ if ( (bits64) ( aSig<<1 )
+ || ( ( bExp == 0x7FFF ) && (bits64) ( bSig<<1 ) ) ) {
+ return propagateFloatx80NaN( a, b STATUS_VAR );
+ }
+ if ( ( bExp | bSig ) == 0 ) goto invalid;
+ return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
+ }
+ if ( bExp == 0x7FFF ) {
+ if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR );
+ if ( ( aExp | aSig ) == 0 ) {
+ invalid:
+ float_raise( float_flag_invalid STATUS_VAR);
+ z.low = floatx80_default_nan_low;
+ z.high = floatx80_default_nan_high;
+ return z;
+ }
+ return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
+ }
+ if ( aExp == 0 ) {
+ if ( aSig == 0 ) return packFloatx80( zSign, 0, 0 );
+ normalizeFloatx80Subnormal( aSig, &aExp, &aSig );
+ }
+ if ( bExp == 0 ) {
+ if ( bSig == 0 ) return packFloatx80( zSign, 0, 0 );
+ normalizeFloatx80Subnormal( bSig, &bExp, &bSig );
+ }
+ zExp = aExp + bExp - 0x3FFE;
+ mul64To128( aSig, bSig, &zSig0, &zSig1 );
+ if ( 0 < (sbits64) zSig0 ) {
+ shortShift128Left( zSig0, zSig1, 1, &zSig0, &zSig1 );
+ --zExp;
+ }
+ return
+ roundAndPackFloatx80(
+ STATUS(floatx80_rounding_precision), zSign, zExp, zSig0, zSig1 STATUS_VAR );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of dividing the extended double-precision floating-point
+| value `a' by the corresponding value `b'. The operation is performed
+| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+floatx80 floatx80_div( floatx80 a, floatx80 b STATUS_PARAM )
+{
+ flag aSign, bSign, zSign;
+ int32 aExp, bExp, zExp;
+ bits64 aSig, bSig, zSig0, zSig1;
+ bits64 rem0, rem1, rem2, term0, term1, term2;
+ floatx80 z;
+
+ aSig = extractFloatx80Frac( a );
+ aExp = extractFloatx80Exp( a );
+ aSign = extractFloatx80Sign( a );
+ bSig = extractFloatx80Frac( b );
+ bExp = extractFloatx80Exp( b );
+ bSign = extractFloatx80Sign( b );
+ zSign = aSign ^ bSign;
+ if ( aExp == 0x7FFF ) {
+ if ( (bits64) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR );
+ if ( bExp == 0x7FFF ) {
+ if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR );
+ goto invalid;
+ }
+ return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
+ }
+ if ( bExp == 0x7FFF ) {
+ if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR );
+ return packFloatx80( zSign, 0, 0 );
+ }
+ if ( bExp == 0 ) {
+ if ( bSig == 0 ) {
+ if ( ( aExp | aSig ) == 0 ) {
+ invalid:
+ float_raise( float_flag_invalid STATUS_VAR);
+ z.low = floatx80_default_nan_low;
+ z.high = floatx80_default_nan_high;
+ return z;
+ }
+ float_raise( float_flag_divbyzero STATUS_VAR);
+ return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
+ }
+ normalizeFloatx80Subnormal( bSig, &bExp, &bSig );
+ }
+ if ( aExp == 0 ) {
+ if ( aSig == 0 ) return packFloatx80( zSign, 0, 0 );
+ normalizeFloatx80Subnormal( aSig, &aExp, &aSig );
+ }
+ zExp = aExp - bExp + 0x3FFE;
+ rem1 = 0;
+ if ( bSig <= aSig ) {
+ shift128Right( aSig, 0, 1, &aSig, &rem1 );
+ ++zExp;
+ }
+ zSig0 = estimateDiv128To64( aSig, rem1, bSig );
+ mul64To128( bSig, zSig0, &term0, &term1 );
+ sub128( aSig, rem1, term0, term1, &rem0, &rem1 );
+ while ( (sbits64) rem0 < 0 ) {
+ --zSig0;
+ add128( rem0, rem1, 0, bSig, &rem0, &rem1 );
+ }
+ zSig1 = estimateDiv128To64( rem1, 0, bSig );
+ if ( (bits64) ( zSig1<<1 ) <= 8 ) {
+ mul64To128( bSig, zSig1, &term1, &term2 );
+ sub128( rem1, 0, term1, term2, &rem1, &rem2 );
+ while ( (sbits64) rem1 < 0 ) {
+ --zSig1;
+ add128( rem1, rem2, 0, bSig, &rem1, &rem2 );
+ }
+ zSig1 |= ( ( rem1 | rem2 ) != 0 );
+ }
+ return
+ roundAndPackFloatx80(
+ STATUS(floatx80_rounding_precision), zSign, zExp, zSig0, zSig1 STATUS_VAR );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the remainder of the extended double-precision floating-point value
+| `a' with respect to the corresponding value `b'. The operation is performed
+| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+floatx80 floatx80_rem( floatx80 a, floatx80 b STATUS_PARAM )
+{
+ flag aSign, bSign, zSign;
+ int32 aExp, bExp, expDiff;
+ bits64 aSig0, aSig1, bSig;
+ bits64 q, term0, term1, alternateASig0, alternateASig1;
+ floatx80 z;
+
+ aSig0 = extractFloatx80Frac( a );
+ aExp = extractFloatx80Exp( a );
+ aSign = extractFloatx80Sign( a );
+ bSig = extractFloatx80Frac( b );
+ bExp = extractFloatx80Exp( b );
+ bSign = extractFloatx80Sign( b );
+ if ( aExp == 0x7FFF ) {
+ if ( (bits64) ( aSig0<<1 )
+ || ( ( bExp == 0x7FFF ) && (bits64) ( bSig<<1 ) ) ) {
+ return propagateFloatx80NaN( a, b STATUS_VAR );
+ }
+ goto invalid;
+ }
+ if ( bExp == 0x7FFF ) {
+ if ( (bits64) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR );
+ return a;
+ }
+ if ( bExp == 0 ) {
+ if ( bSig == 0 ) {
+ invalid:
+ float_raise( float_flag_invalid STATUS_VAR);
+ z.low = floatx80_default_nan_low;
+ z.high = floatx80_default_nan_high;
+ return z;
+ }
+ normalizeFloatx80Subnormal( bSig, &bExp, &bSig );
+ }
+ if ( aExp == 0 ) {
+ if ( (bits64) ( aSig0<<1 ) == 0 ) return a;
+ normalizeFloatx80Subnormal( aSig0, &aExp, &aSig0 );
+ }
+ bSig |= LIT64( 0x8000000000000000 );
+ zSign = aSign;
+ expDiff = aExp - bExp;
+ aSig1 = 0;
+ if ( expDiff < 0 ) {
+ if ( expDiff < -1 ) return a;
+ shift128Right( aSig0, 0, 1, &aSig0, &aSig1 );
+ expDiff = 0;
+ }
+ q = ( bSig <= aSig0 );
+ if ( q ) aSig0 -= bSig;
+ expDiff -= 64;
+ while ( 0 < expDiff ) {
+ q = estimateDiv128To64( aSig0, aSig1, bSig );
+ q = ( 2 < q ) ? q - 2 : 0;
+ mul64To128( bSig, q, &term0, &term1 );
+ sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 );
+ shortShift128Left( aSig0, aSig1, 62, &aSig0, &aSig1 );
+ expDiff -= 62;
+ }
+ expDiff += 64;
+ if ( 0 < expDiff ) {
+ q = estimateDiv128To64( aSig0, aSig1, bSig );
+ q = ( 2 < q ) ? q - 2 : 0;
+ q >>= 64 - expDiff;
+ mul64To128( bSig, q<<( 64 - expDiff ), &term0, &term1 );
+ sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 );
+ shortShift128Left( 0, bSig, 64 - expDiff, &term0, &term1 );
+ while ( le128( term0, term1, aSig0, aSig1 ) ) {
+ ++q;
+ sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 );
+ }
+ }
+ else {
+ term1 = 0;
+ term0 = bSig;
+ }
+ sub128( term0, term1, aSig0, aSig1, &alternateASig0, &alternateASig1 );
+ if ( lt128( alternateASig0, alternateASig1, aSig0, aSig1 )
+ || ( eq128( alternateASig0, alternateASig1, aSig0, aSig1 )
+ && ( q & 1 ) )
+ ) {
+ aSig0 = alternateASig0;
+ aSig1 = alternateASig1;
+ zSign = ! zSign;
+ }
+ return
+ normalizeRoundAndPackFloatx80(
+ 80, zSign, bExp + expDiff, aSig0, aSig1 STATUS_VAR );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the square root of the extended double-precision floating-point
+| value `a'. The operation is performed according to the IEC/IEEE Standard
+| for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+floatx80 floatx80_sqrt( floatx80 a STATUS_PARAM )
+{
+ flag aSign;
+ int32 aExp, zExp;
+ bits64 aSig0, aSig1, zSig0, zSig1, doubleZSig0;
+ bits64 rem0, rem1, rem2, rem3, term0, term1, term2, term3;
+ floatx80 z;
+
+ aSig0 = extractFloatx80Frac( a );
+ aExp = extractFloatx80Exp( a );
+ aSign = extractFloatx80Sign( a );
+ if ( aExp == 0x7FFF ) {
+ if ( (bits64) ( aSig0<<1 ) ) return propagateFloatx80NaN( a, a STATUS_VAR );
+ if ( ! aSign ) return a;
+ goto invalid;
+ }
+ if ( aSign ) {
+ if ( ( aExp | aSig0 ) == 0 ) return a;
+ invalid:
+ float_raise( float_flag_invalid STATUS_VAR);
+ z.low = floatx80_default_nan_low;
+ z.high = floatx80_default_nan_high;
+ return z;
+ }
+ if ( aExp == 0 ) {
+ if ( aSig0 == 0 ) return packFloatx80( 0, 0, 0 );
+ normalizeFloatx80Subnormal( aSig0, &aExp, &aSig0 );
+ }
+ zExp = ( ( aExp - 0x3FFF )>>1 ) + 0x3FFF;
+ zSig0 = estimateSqrt32( aExp, aSig0>>32 );
+ shift128Right( aSig0, 0, 2 + ( aExp & 1 ), &aSig0, &aSig1 );
+ zSig0 = estimateDiv128To64( aSig0, aSig1, zSig0<<32 ) + ( zSig0<<30 );
+ doubleZSig0 = zSig0<<1;
+ mul64To128( zSig0, zSig0, &term0, &term1 );
+ sub128( aSig0, aSig1, term0, term1, &rem0, &rem1 );
+ while ( (sbits64) rem0 < 0 ) {
+ --zSig0;
+ doubleZSig0 -= 2;
+ add128( rem0, rem1, zSig0>>63, doubleZSig0 | 1, &rem0, &rem1 );
+ }
+ zSig1 = estimateDiv128To64( rem1, 0, doubleZSig0 );
+ if ( ( zSig1 & LIT64( 0x3FFFFFFFFFFFFFFF ) ) <= 5 ) {
+ if ( zSig1 == 0 ) zSig1 = 1;
+ mul64To128( doubleZSig0, zSig1, &term1, &term2 );
+ sub128( rem1, 0, term1, term2, &rem1, &rem2 );
+ mul64To128( zSig1, zSig1, &term2, &term3 );
+ sub192( rem1, rem2, 0, 0, term2, term3, &rem1, &rem2, &rem3 );
+ while ( (sbits64) rem1 < 0 ) {
+ --zSig1;
+ shortShift128Left( 0, zSig1, 1, &term2, &term3 );
+ term3 |= 1;
+ term2 |= doubleZSig0;
+ add192( rem1, rem2, rem3, 0, term2, term3, &rem1, &rem2, &rem3 );
+ }
+ zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 );
+ }
+ shortShift128Left( 0, zSig1, 1, &zSig0, &zSig1 );
+ zSig0 |= doubleZSig0;
+ return
+ roundAndPackFloatx80(
+ STATUS(floatx80_rounding_precision), 0, zExp, zSig0, zSig1 STATUS_VAR );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the extended double-precision floating-point value `a' is
+| equal to the corresponding value `b', and 0 otherwise. The comparison is
+| performed according to the IEC/IEEE Standard for Binary Floating-Point
+| Arithmetic.
+*----------------------------------------------------------------------------*/
+
+flag floatx80_eq( floatx80 a, floatx80 b STATUS_PARAM )
+{
+
+ if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
+ && (bits64) ( extractFloatx80Frac( a )<<1 ) )
+ || ( ( extractFloatx80Exp( b ) == 0x7FFF )
+ && (bits64) ( extractFloatx80Frac( b )<<1 ) )
+ ) {
+ if ( floatx80_is_signaling_nan( a )
+ || floatx80_is_signaling_nan( b ) ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ }
+ return 0;
+ }
+ return
+ ( a.low == b.low )
+ && ( ( a.high == b.high )
+ || ( ( a.low == 0 )
+ && ( (bits16) ( ( a.high | b.high )<<1 ) == 0 ) )
+ );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the extended double-precision floating-point value `a' is
+| less than or equal to the corresponding value `b', and 0 otherwise. The
+| comparison is performed according to the IEC/IEEE Standard for Binary
+| Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+flag floatx80_le( floatx80 a, floatx80 b STATUS_PARAM )
+{
+ flag aSign, bSign;
+
+ if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
+ && (bits64) ( extractFloatx80Frac( a )<<1 ) )
+ || ( ( extractFloatx80Exp( b ) == 0x7FFF )
+ && (bits64) ( extractFloatx80Frac( b )<<1 ) )
+ ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ return 0;
+ }
+ aSign = extractFloatx80Sign( a );
+ bSign = extractFloatx80Sign( b );
+ if ( aSign != bSign ) {
+ return
+ aSign
+ || ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
+ == 0 );
+ }
+ return
+ aSign ? le128( b.high, b.low, a.high, a.low )
+ : le128( a.high, a.low, b.high, b.low );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the extended double-precision floating-point value `a' is
+| less than the corresponding value `b', and 0 otherwise. The comparison
+| is performed according to the IEC/IEEE Standard for Binary Floating-Point
+| Arithmetic.
+*----------------------------------------------------------------------------*/
+
+flag floatx80_lt( floatx80 a, floatx80 b STATUS_PARAM )
+{
+ flag aSign, bSign;
+
+ if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
+ && (bits64) ( extractFloatx80Frac( a )<<1 ) )
+ || ( ( extractFloatx80Exp( b ) == 0x7FFF )
+ && (bits64) ( extractFloatx80Frac( b )<<1 ) )
+ ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ return 0;
+ }
+ aSign = extractFloatx80Sign( a );
+ bSign = extractFloatx80Sign( b );
+ if ( aSign != bSign ) {
+ return
+ aSign
+ && ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
+ != 0 );
+ }
+ return
+ aSign ? lt128( b.high, b.low, a.high, a.low )
+ : lt128( a.high, a.low, b.high, b.low );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the extended double-precision floating-point value `a' is equal
+| to the corresponding value `b', and 0 otherwise. The invalid exception is
+| raised if either operand is a NaN. Otherwise, the comparison is performed
+| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+flag floatx80_eq_signaling( floatx80 a, floatx80 b STATUS_PARAM )
+{
+
+ if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
+ && (bits64) ( extractFloatx80Frac( a )<<1 ) )
+ || ( ( extractFloatx80Exp( b ) == 0x7FFF )
+ && (bits64) ( extractFloatx80Frac( b )<<1 ) )
+ ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ return 0;
+ }
+ return
+ ( a.low == b.low )
+ && ( ( a.high == b.high )
+ || ( ( a.low == 0 )
+ && ( (bits16) ( ( a.high | b.high )<<1 ) == 0 ) )
+ );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the extended double-precision floating-point value `a' is less
+| than or equal to the corresponding value `b', and 0 otherwise. Quiet NaNs
+| do not cause an exception. Otherwise, the comparison is performed according
+| to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+flag floatx80_le_quiet( floatx80 a, floatx80 b STATUS_PARAM )
+{
+ flag aSign, bSign;
+
+ if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
+ && (bits64) ( extractFloatx80Frac( a )<<1 ) )
+ || ( ( extractFloatx80Exp( b ) == 0x7FFF )
+ && (bits64) ( extractFloatx80Frac( b )<<1 ) )
+ ) {
+ if ( floatx80_is_signaling_nan( a )
+ || floatx80_is_signaling_nan( b ) ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ }
+ return 0;
+ }
+ aSign = extractFloatx80Sign( a );
+ bSign = extractFloatx80Sign( b );
+ if ( aSign != bSign ) {
+ return
+ aSign
+ || ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
+ == 0 );
+ }
+ return
+ aSign ? le128( b.high, b.low, a.high, a.low )
+ : le128( a.high, a.low, b.high, b.low );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the extended double-precision floating-point value `a' is less
+| than the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause
+| an exception. Otherwise, the comparison is performed according to the
+| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+flag floatx80_lt_quiet( floatx80 a, floatx80 b STATUS_PARAM )
+{
+ flag aSign, bSign;
+
+ if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
+ && (bits64) ( extractFloatx80Frac( a )<<1 ) )
+ || ( ( extractFloatx80Exp( b ) == 0x7FFF )
+ && (bits64) ( extractFloatx80Frac( b )<<1 ) )
+ ) {
+ if ( floatx80_is_signaling_nan( a )
+ || floatx80_is_signaling_nan( b ) ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ }
+ return 0;
+ }
+ aSign = extractFloatx80Sign( a );
+ bSign = extractFloatx80Sign( b );
+ if ( aSign != bSign ) {
+ return
+ aSign
+ && ( ( ( (bits16) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
+ != 0 );
+ }
+ return
+ aSign ? lt128( b.high, b.low, a.high, a.low )
+ : lt128( a.high, a.low, b.high, b.low );
+
+}
+
+#endif
+
+#ifdef FLOAT128
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the quadruple-precision floating-point
+| value `a' to the 32-bit two's complement integer format. The conversion
+| is performed according to the IEC/IEEE Standard for Binary Floating-Point
+| Arithmetic---which means in particular that the conversion is rounded
+| according to the current rounding mode. If `a' is a NaN, the largest
+| positive integer is returned. Otherwise, if the conversion overflows, the
+| largest integer with the same sign as `a' is returned.
+*----------------------------------------------------------------------------*/
+
+int32 float128_to_int32( float128 a STATUS_PARAM )
+{
+ flag aSign;
+ int32 aExp, shiftCount;
+ bits64 aSig0, aSig1;
+
+ aSig1 = extractFloat128Frac1( a );
+ aSig0 = extractFloat128Frac0( a );
+ aExp = extractFloat128Exp( a );
+ aSign = extractFloat128Sign( a );
+ if ( ( aExp == 0x7FFF ) && ( aSig0 | aSig1 ) ) aSign = 0;
+ if ( aExp ) aSig0 |= LIT64( 0x0001000000000000 );
+ aSig0 |= ( aSig1 != 0 );
+ shiftCount = 0x4028 - aExp;
+ if ( 0 < shiftCount ) shift64RightJamming( aSig0, shiftCount, &aSig0 );
+ return roundAndPackInt32( aSign, aSig0 STATUS_VAR );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the quadruple-precision floating-point
+| value `a' to the 32-bit two's complement integer format. The conversion
+| is performed according to the IEC/IEEE Standard for Binary Floating-Point
+| Arithmetic, except that the conversion is always rounded toward zero. If
+| `a' is a NaN, the largest positive integer is returned. Otherwise, if the
+| conversion overflows, the largest integer with the same sign as `a' is
+| returned.
+*----------------------------------------------------------------------------*/
+
+int32 float128_to_int32_round_to_zero( float128 a STATUS_PARAM )
+{
+ flag aSign;
+ int32 aExp, shiftCount;
+ bits64 aSig0, aSig1, savedASig;
+ int32 z;
+
+ aSig1 = extractFloat128Frac1( a );
+ aSig0 = extractFloat128Frac0( a );
+ aExp = extractFloat128Exp( a );
+ aSign = extractFloat128Sign( a );
+ aSig0 |= ( aSig1 != 0 );
+ if ( 0x401E < aExp ) {
+ if ( ( aExp == 0x7FFF ) && aSig0 ) aSign = 0;
+ goto invalid;
+ }
+ else if ( aExp < 0x3FFF ) {
+ if ( aExp || aSig0 ) STATUS(float_exception_flags) |= float_flag_inexact;
+ return 0;
+ }
+ aSig0 |= LIT64( 0x0001000000000000 );
+ shiftCount = 0x402F - aExp;
+ savedASig = aSig0;
+ aSig0 >>= shiftCount;
+ z = aSig0;
+ if ( aSign ) z = - z;
+ if ( ( z < 0 ) ^ aSign ) {
+ invalid:
+ float_raise( float_flag_invalid STATUS_VAR);
+ return aSign ? (sbits32) 0x80000000 : 0x7FFFFFFF;
+ }
+ if ( ( aSig0<<shiftCount ) != savedASig ) {
+ STATUS(float_exception_flags) |= float_flag_inexact;
+ }
+ return z;
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the quadruple-precision floating-point
+| value `a' to the 64-bit two's complement integer format. The conversion
+| is performed according to the IEC/IEEE Standard for Binary Floating-Point
+| Arithmetic---which means in particular that the conversion is rounded
+| according to the current rounding mode. If `a' is a NaN, the largest
+| positive integer is returned. Otherwise, if the conversion overflows, the
+| largest integer with the same sign as `a' is returned.
+*----------------------------------------------------------------------------*/
+
+int64 float128_to_int64( float128 a STATUS_PARAM )
+{
+ flag aSign;
+ int32 aExp, shiftCount;
+ bits64 aSig0, aSig1;
+
+ aSig1 = extractFloat128Frac1( a );
+ aSig0 = extractFloat128Frac0( a );
+ aExp = extractFloat128Exp( a );
+ aSign = extractFloat128Sign( a );
+ if ( aExp ) aSig0 |= LIT64( 0x0001000000000000 );
+ shiftCount = 0x402F - aExp;
+ if ( shiftCount <= 0 ) {
+ if ( 0x403E < aExp ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ if ( ! aSign
+ || ( ( aExp == 0x7FFF )
+ && ( aSig1 || ( aSig0 != LIT64( 0x0001000000000000 ) ) )
+ )
+ ) {
+ return LIT64( 0x7FFFFFFFFFFFFFFF );
+ }
+ return (sbits64) LIT64( 0x8000000000000000 );
+ }
+ shortShift128Left( aSig0, aSig1, - shiftCount, &aSig0, &aSig1 );
+ }
+ else {
+ shift64ExtraRightJamming( aSig0, aSig1, shiftCount, &aSig0, &aSig1 );
+ }
+ return roundAndPackInt64( aSign, aSig0, aSig1 STATUS_VAR );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the quadruple-precision floating-point
+| value `a' to the 64-bit two's complement integer format. The conversion
+| is performed according to the IEC/IEEE Standard for Binary Floating-Point
+| Arithmetic, except that the conversion is always rounded toward zero.
+| If `a' is a NaN, the largest positive integer is returned. Otherwise, if
+| the conversion overflows, the largest integer with the same sign as `a' is
+| returned.
+*----------------------------------------------------------------------------*/
+
+int64 float128_to_int64_round_to_zero( float128 a STATUS_PARAM )
+{
+ flag aSign;
+ int32 aExp, shiftCount;
+ bits64 aSig0, aSig1;
+ int64 z;
+
+ aSig1 = extractFloat128Frac1( a );
+ aSig0 = extractFloat128Frac0( a );
+ aExp = extractFloat128Exp( a );
+ aSign = extractFloat128Sign( a );
+ if ( aExp ) aSig0 |= LIT64( 0x0001000000000000 );
+ shiftCount = aExp - 0x402F;
+ if ( 0 < shiftCount ) {
+ if ( 0x403E <= aExp ) {
+ aSig0 &= LIT64( 0x0000FFFFFFFFFFFF );
+ if ( ( a.high == LIT64( 0xC03E000000000000 ) )
+ && ( aSig1 < LIT64( 0x0002000000000000 ) ) ) {
+ if ( aSig1 ) STATUS(float_exception_flags) |= float_flag_inexact;
+ }
+ else {
+ float_raise( float_flag_invalid STATUS_VAR);
+ if ( ! aSign || ( ( aExp == 0x7FFF ) && ( aSig0 | aSig1 ) ) ) {
+ return LIT64( 0x7FFFFFFFFFFFFFFF );
+ }
+ }
+ return (sbits64) LIT64( 0x8000000000000000 );
+ }
+ z = ( aSig0<<shiftCount ) | ( aSig1>>( ( - shiftCount ) & 63 ) );
+ if ( (bits64) ( aSig1<<shiftCount ) ) {
+ STATUS(float_exception_flags) |= float_flag_inexact;
+ }
+ }
+ else {
+ if ( aExp < 0x3FFF ) {
+ if ( aExp | aSig0 | aSig1 ) {
+ STATUS(float_exception_flags) |= float_flag_inexact;
+ }
+ return 0;
+ }
+ z = aSig0>>( - shiftCount );
+ if ( aSig1
+ || ( shiftCount && (bits64) ( aSig0<<( shiftCount & 63 ) ) ) ) {
+ STATUS(float_exception_flags) |= float_flag_inexact;
+ }
+ }
+ if ( aSign ) z = - z;
+ return z;
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the quadruple-precision floating-point
+| value `a' to the single-precision floating-point format. The conversion
+| is performed according to the IEC/IEEE Standard for Binary Floating-Point
+| Arithmetic.
+*----------------------------------------------------------------------------*/
+
+float32 float128_to_float32( float128 a STATUS_PARAM )
+{
+ flag aSign;
+ int32 aExp;
+ bits64 aSig0, aSig1;
+ bits32 zSig;
+
+ aSig1 = extractFloat128Frac1( a );
+ aSig0 = extractFloat128Frac0( a );
+ aExp = extractFloat128Exp( a );
+ aSign = extractFloat128Sign( a );
+ if ( aExp == 0x7FFF ) {
+ if ( aSig0 | aSig1 ) {
+ return commonNaNToFloat32( float128ToCommonNaN( a STATUS_VAR ) );
+ }
+ return packFloat32( aSign, 0xFF, 0 );
+ }
+ aSig0 |= ( aSig1 != 0 );
+ shift64RightJamming( aSig0, 18, &aSig0 );
+ zSig = aSig0;
+ if ( aExp || zSig ) {
+ zSig |= 0x40000000;
+ aExp -= 0x3F81;
+ }
+ return roundAndPackFloat32( aSign, aExp, zSig STATUS_VAR );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the quadruple-precision floating-point
+| value `a' to the double-precision floating-point format. The conversion
+| is performed according to the IEC/IEEE Standard for Binary Floating-Point
+| Arithmetic.
+*----------------------------------------------------------------------------*/
+
+float64 float128_to_float64( float128 a STATUS_PARAM )
+{
+ flag aSign;
+ int32 aExp;
+ bits64 aSig0, aSig1;
+
+ aSig1 = extractFloat128Frac1( a );
+ aSig0 = extractFloat128Frac0( a );
+ aExp = extractFloat128Exp( a );
+ aSign = extractFloat128Sign( a );
+ if ( aExp == 0x7FFF ) {
+ if ( aSig0 | aSig1 ) {
+ return commonNaNToFloat64( float128ToCommonNaN( a STATUS_VAR ) );
+ }
+ return packFloat64( aSign, 0x7FF, 0 );
+ }
+ shortShift128Left( aSig0, aSig1, 14, &aSig0, &aSig1 );
+ aSig0 |= ( aSig1 != 0 );
+ if ( aExp || aSig0 ) {
+ aSig0 |= LIT64( 0x4000000000000000 );
+ aExp -= 0x3C01;
+ }
+ return roundAndPackFloat64( aSign, aExp, aSig0 STATUS_VAR );
+
+}
+
+#ifdef FLOATX80
+
+/*----------------------------------------------------------------------------
+| Returns the result of converting the quadruple-precision floating-point
+| value `a' to the extended double-precision floating-point format. The
+| conversion is performed according to the IEC/IEEE Standard for Binary
+| Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+floatx80 float128_to_floatx80( float128 a STATUS_PARAM )
+{
+ flag aSign;
+ int32 aExp;
+ bits64 aSig0, aSig1;
+
+ aSig1 = extractFloat128Frac1( a );
+ aSig0 = extractFloat128Frac0( a );
+ aExp = extractFloat128Exp( a );
+ aSign = extractFloat128Sign( a );
+ if ( aExp == 0x7FFF ) {
+ if ( aSig0 | aSig1 ) {
+ return commonNaNToFloatx80( float128ToCommonNaN( a STATUS_VAR ) );
+ }
+ return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
+ }
+ if ( aExp == 0 ) {
+ if ( ( aSig0 | aSig1 ) == 0 ) return packFloatx80( aSign, 0, 0 );
+ normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 );
+ }
+ else {
+ aSig0 |= LIT64( 0x0001000000000000 );
+ }
+ shortShift128Left( aSig0, aSig1, 15, &aSig0, &aSig1 );
+ return roundAndPackFloatx80( 80, aSign, aExp, aSig0, aSig1 STATUS_VAR );
+
+}
+
+#endif
+
+/*----------------------------------------------------------------------------
+| Rounds the quadruple-precision floating-point value `a' to an integer, and
+| returns the result as a quadruple-precision floating-point value. The
+| operation is performed according to the IEC/IEEE Standard for Binary
+| Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+float128 float128_round_to_int( float128 a STATUS_PARAM )
+{
+ flag aSign;
+ int32 aExp;
+ bits64 lastBitMask, roundBitsMask;
+ int8 roundingMode;
+ float128 z;
+
+ aExp = extractFloat128Exp( a );
+ if ( 0x402F <= aExp ) {
+ if ( 0x406F <= aExp ) {
+ if ( ( aExp == 0x7FFF )
+ && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) )
+ ) {
+ return propagateFloat128NaN( a, a STATUS_VAR );
+ }
+ return a;
+ }
+ lastBitMask = 1;
+ lastBitMask = ( lastBitMask<<( 0x406E - aExp ) )<<1;
+ roundBitsMask = lastBitMask - 1;
+ z = a;
+ roundingMode = STATUS(float_rounding_mode);
+ if ( roundingMode == float_round_nearest_even ) {
+ if ( lastBitMask ) {
+ add128( z.high, z.low, 0, lastBitMask>>1, &z.high, &z.low );
+ if ( ( z.low & roundBitsMask ) == 0 ) z.low &= ~ lastBitMask;
+ }
+ else {
+ if ( (sbits64) z.low < 0 ) {
+ ++z.high;
+ if ( (bits64) ( z.low<<1 ) == 0 ) z.high &= ~1;
+ }
+ }
+ }
+ else if ( roundingMode != float_round_to_zero ) {
+ if ( extractFloat128Sign( z )
+ ^ ( roundingMode == float_round_up ) ) {
+ add128( z.high, z.low, 0, roundBitsMask, &z.high, &z.low );
+ }
+ }
+ z.low &= ~ roundBitsMask;
+ }
+ else {
+ if ( aExp < 0x3FFF ) {
+ if ( ( ( (bits64) ( a.high<<1 ) ) | a.low ) == 0 ) return a;
+ STATUS(float_exception_flags) |= float_flag_inexact;
+ aSign = extractFloat128Sign( a );
+ switch ( STATUS(float_rounding_mode) ) {
+ case float_round_nearest_even:
+ if ( ( aExp == 0x3FFE )
+ && ( extractFloat128Frac0( a )
+ | extractFloat128Frac1( a ) )
+ ) {
+ return packFloat128( aSign, 0x3FFF, 0, 0 );
+ }
+ break;
+ case float_round_down:
+ return
+ aSign ? packFloat128( 1, 0x3FFF, 0, 0 )
+ : packFloat128( 0, 0, 0, 0 );
+ case float_round_up:
+ return
+ aSign ? packFloat128( 1, 0, 0, 0 )
+ : packFloat128( 0, 0x3FFF, 0, 0 );
+ }
+ return packFloat128( aSign, 0, 0, 0 );
+ }
+ lastBitMask = 1;
+ lastBitMask <<= 0x402F - aExp;
+ roundBitsMask = lastBitMask - 1;
+ z.low = 0;
+ z.high = a.high;
+ roundingMode = STATUS(float_rounding_mode);
+ if ( roundingMode == float_round_nearest_even ) {
+ z.high += lastBitMask>>1;
+ if ( ( ( z.high & roundBitsMask ) | a.low ) == 0 ) {
+ z.high &= ~ lastBitMask;
+ }
+ }
+ else if ( roundingMode != float_round_to_zero ) {
+ if ( extractFloat128Sign( z )
+ ^ ( roundingMode == float_round_up ) ) {
+ z.high |= ( a.low != 0 );
+ z.high += roundBitsMask;
+ }
+ }
+ z.high &= ~ roundBitsMask;
+ }
+ if ( ( z.low != a.low ) || ( z.high != a.high ) ) {
+ STATUS(float_exception_flags) |= float_flag_inexact;
+ }
+ return z;
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of adding the absolute values of the quadruple-precision
+| floating-point values `a' and `b'. If `zSign' is 1, the sum is negated
+| before being returned. `zSign' is ignored if the result is a NaN.
+| The addition is performed according to the IEC/IEEE Standard for Binary
+| Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+static float128 addFloat128Sigs( float128 a, float128 b, flag zSign STATUS_PARAM)
+{
+ int32 aExp, bExp, zExp;
+ bits64 aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2;
+ int32 expDiff;
+
+ aSig1 = extractFloat128Frac1( a );
+ aSig0 = extractFloat128Frac0( a );
+ aExp = extractFloat128Exp( a );
+ bSig1 = extractFloat128Frac1( b );
+ bSig0 = extractFloat128Frac0( b );
+ bExp = extractFloat128Exp( b );
+ expDiff = aExp - bExp;
+ if ( 0 < expDiff ) {
+ if ( aExp == 0x7FFF ) {
+ if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, b STATUS_VAR );
+ return a;
+ }
+ if ( bExp == 0 ) {
+ --expDiff;
+ }
+ else {
+ bSig0 |= LIT64( 0x0001000000000000 );
+ }
+ shift128ExtraRightJamming(
+ bSig0, bSig1, 0, expDiff, &bSig0, &bSig1, &zSig2 );
+ zExp = aExp;
+ }
+ else if ( expDiff < 0 ) {
+ if ( bExp == 0x7FFF ) {
+ if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR );
+ return packFloat128( zSign, 0x7FFF, 0, 0 );
+ }
+ if ( aExp == 0 ) {
+ ++expDiff;
+ }
+ else {
+ aSig0 |= LIT64( 0x0001000000000000 );
+ }
+ shift128ExtraRightJamming(
+ aSig0, aSig1, 0, - expDiff, &aSig0, &aSig1, &zSig2 );
+ zExp = bExp;
+ }
+ else {
+ if ( aExp == 0x7FFF ) {
+ if ( aSig0 | aSig1 | bSig0 | bSig1 ) {
+ return propagateFloat128NaN( a, b STATUS_VAR );
+ }
+ return a;
+ }
+ add128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 );
+ if ( aExp == 0 ) return packFloat128( zSign, 0, zSig0, zSig1 );
+ zSig2 = 0;
+ zSig0 |= LIT64( 0x0002000000000000 );
+ zExp = aExp;
+ goto shiftRight1;
+ }
+ aSig0 |= LIT64( 0x0001000000000000 );
+ add128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 );
+ --zExp;
+ if ( zSig0 < LIT64( 0x0002000000000000 ) ) goto roundAndPack;
+ ++zExp;
+ shiftRight1:
+ shift128ExtraRightJamming(
+ zSig0, zSig1, zSig2, 1, &zSig0, &zSig1, &zSig2 );
+ roundAndPack:
+ return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 STATUS_VAR );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of subtracting the absolute values of the quadruple-
+| precision floating-point values `a' and `b'. If `zSign' is 1, the
+| difference is negated before being returned. `zSign' is ignored if the
+| result is a NaN. The subtraction is performed according to the IEC/IEEE
+| Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+static float128 subFloat128Sigs( float128 a, float128 b, flag zSign STATUS_PARAM)
+{
+ int32 aExp, bExp, zExp;
+ bits64 aSig0, aSig1, bSig0, bSig1, zSig0, zSig1;
+ int32 expDiff;
+ float128 z;
+
+ aSig1 = extractFloat128Frac1( a );
+ aSig0 = extractFloat128Frac0( a );
+ aExp = extractFloat128Exp( a );
+ bSig1 = extractFloat128Frac1( b );
+ bSig0 = extractFloat128Frac0( b );
+ bExp = extractFloat128Exp( b );
+ expDiff = aExp - bExp;
+ shortShift128Left( aSig0, aSig1, 14, &aSig0, &aSig1 );
+ shortShift128Left( bSig0, bSig1, 14, &bSig0, &bSig1 );
+ if ( 0 < expDiff ) goto aExpBigger;
+ if ( expDiff < 0 ) goto bExpBigger;
+ if ( aExp == 0x7FFF ) {
+ if ( aSig0 | aSig1 | bSig0 | bSig1 ) {
+ return propagateFloat128NaN( a, b STATUS_VAR );
+ }
+ float_raise( float_flag_invalid STATUS_VAR);
+ z.low = float128_default_nan_low;
+ z.high = float128_default_nan_high;
+ return z;
+ }
+ if ( aExp == 0 ) {
+ aExp = 1;
+ bExp = 1;
+ }
+ if ( bSig0 < aSig0 ) goto aBigger;
+ if ( aSig0 < bSig0 ) goto bBigger;
+ if ( bSig1 < aSig1 ) goto aBigger;
+ if ( aSig1 < bSig1 ) goto bBigger;
+ return packFloat128( STATUS(float_rounding_mode) == float_round_down, 0, 0, 0 );
+ bExpBigger:
+ if ( bExp == 0x7FFF ) {
+ if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR );
+ return packFloat128( zSign ^ 1, 0x7FFF, 0, 0 );
+ }
+ if ( aExp == 0 ) {
+ ++expDiff;
+ }
+ else {
+ aSig0 |= LIT64( 0x4000000000000000 );
+ }
+ shift128RightJamming( aSig0, aSig1, - expDiff, &aSig0, &aSig1 );
+ bSig0 |= LIT64( 0x4000000000000000 );
+ bBigger:
+ sub128( bSig0, bSig1, aSig0, aSig1, &zSig0, &zSig1 );
+ zExp = bExp;
+ zSign ^= 1;
+ goto normalizeRoundAndPack;
+ aExpBigger:
+ if ( aExp == 0x7FFF ) {
+ if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, b STATUS_VAR );
+ return a;
+ }
+ if ( bExp == 0 ) {
+ --expDiff;
+ }
+ else {
+ bSig0 |= LIT64( 0x4000000000000000 );
+ }
+ shift128RightJamming( bSig0, bSig1, expDiff, &bSig0, &bSig1 );
+ aSig0 |= LIT64( 0x4000000000000000 );
+ aBigger:
+ sub128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 );
+ zExp = aExp;
+ normalizeRoundAndPack:
+ --zExp;
+ return normalizeRoundAndPackFloat128( zSign, zExp - 14, zSig0, zSig1 STATUS_VAR );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of adding the quadruple-precision floating-point values
+| `a' and `b'. The operation is performed according to the IEC/IEEE Standard
+| for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+float128 float128_add( float128 a, float128 b STATUS_PARAM )
+{
+ flag aSign, bSign;
+
+ aSign = extractFloat128Sign( a );
+ bSign = extractFloat128Sign( b );
+ if ( aSign == bSign ) {
+ return addFloat128Sigs( a, b, aSign STATUS_VAR );
+ }
+ else {
+ return subFloat128Sigs( a, b, aSign STATUS_VAR );
+ }
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of subtracting the quadruple-precision floating-point
+| values `a' and `b'. The operation is performed according to the IEC/IEEE
+| Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+float128 float128_sub( float128 a, float128 b STATUS_PARAM )
+{
+ flag aSign, bSign;
+
+ aSign = extractFloat128Sign( a );
+ bSign = extractFloat128Sign( b );
+ if ( aSign == bSign ) {
+ return subFloat128Sigs( a, b, aSign STATUS_VAR );
+ }
+ else {
+ return addFloat128Sigs( a, b, aSign STATUS_VAR );
+ }
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of multiplying the quadruple-precision floating-point
+| values `a' and `b'. The operation is performed according to the IEC/IEEE
+| Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+float128 float128_mul( float128 a, float128 b STATUS_PARAM )
+{
+ flag aSign, bSign, zSign;
+ int32 aExp, bExp, zExp;
+ bits64 aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2, zSig3;
+ float128 z;
+
+ aSig1 = extractFloat128Frac1( a );
+ aSig0 = extractFloat128Frac0( a );
+ aExp = extractFloat128Exp( a );
+ aSign = extractFloat128Sign( a );
+ bSig1 = extractFloat128Frac1( b );
+ bSig0 = extractFloat128Frac0( b );
+ bExp = extractFloat128Exp( b );
+ bSign = extractFloat128Sign( b );
+ zSign = aSign ^ bSign;
+ if ( aExp == 0x7FFF ) {
+ if ( ( aSig0 | aSig1 )
+ || ( ( bExp == 0x7FFF ) && ( bSig0 | bSig1 ) ) ) {
+ return propagateFloat128NaN( a, b STATUS_VAR );
+ }
+ if ( ( bExp | bSig0 | bSig1 ) == 0 ) goto invalid;
+ return packFloat128( zSign, 0x7FFF, 0, 0 );
+ }
+ if ( bExp == 0x7FFF ) {
+ if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR );
+ if ( ( aExp | aSig0 | aSig1 ) == 0 ) {
+ invalid:
+ float_raise( float_flag_invalid STATUS_VAR);
+ z.low = float128_default_nan_low;
+ z.high = float128_default_nan_high;
+ return z;
+ }
+ return packFloat128( zSign, 0x7FFF, 0, 0 );
+ }
+ if ( aExp == 0 ) {
+ if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 );
+ normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 );
+ }
+ if ( bExp == 0 ) {
+ if ( ( bSig0 | bSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 );
+ normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 );
+ }
+ zExp = aExp + bExp - 0x4000;
+ aSig0 |= LIT64( 0x0001000000000000 );
+ shortShift128Left( bSig0, bSig1, 16, &bSig0, &bSig1 );
+ mul128To256( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1, &zSig2, &zSig3 );
+ add128( zSig0, zSig1, aSig0, aSig1, &zSig0, &zSig1 );
+ zSig2 |= ( zSig3 != 0 );
+ if ( LIT64( 0x0002000000000000 ) <= zSig0 ) {
+ shift128ExtraRightJamming(
+ zSig0, zSig1, zSig2, 1, &zSig0, &zSig1, &zSig2 );
+ ++zExp;
+ }
+ return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 STATUS_VAR );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the result of dividing the quadruple-precision floating-point value
+| `a' by the corresponding value `b'. The operation is performed according to
+| the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+float128 float128_div( float128 a, float128 b STATUS_PARAM )
+{
+ flag aSign, bSign, zSign;
+ int32 aExp, bExp, zExp;
+ bits64 aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2;
+ bits64 rem0, rem1, rem2, rem3, term0, term1, term2, term3;
+ float128 z;
+
+ aSig1 = extractFloat128Frac1( a );
+ aSig0 = extractFloat128Frac0( a );
+ aExp = extractFloat128Exp( a );
+ aSign = extractFloat128Sign( a );
+ bSig1 = extractFloat128Frac1( b );
+ bSig0 = extractFloat128Frac0( b );
+ bExp = extractFloat128Exp( b );
+ bSign = extractFloat128Sign( b );
+ zSign = aSign ^ bSign;
+ if ( aExp == 0x7FFF ) {
+ if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, b STATUS_VAR );
+ if ( bExp == 0x7FFF ) {
+ if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR );
+ goto invalid;
+ }
+ return packFloat128( zSign, 0x7FFF, 0, 0 );
+ }
+ if ( bExp == 0x7FFF ) {
+ if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR );
+ return packFloat128( zSign, 0, 0, 0 );
+ }
+ if ( bExp == 0 ) {
+ if ( ( bSig0 | bSig1 ) == 0 ) {
+ if ( ( aExp | aSig0 | aSig1 ) == 0 ) {
+ invalid:
+ float_raise( float_flag_invalid STATUS_VAR);
+ z.low = float128_default_nan_low;
+ z.high = float128_default_nan_high;
+ return z;
+ }
+ float_raise( float_flag_divbyzero STATUS_VAR);
+ return packFloat128( zSign, 0x7FFF, 0, 0 );
+ }
+ normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 );
+ }
+ if ( aExp == 0 ) {
+ if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 );
+ normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 );
+ }
+ zExp = aExp - bExp + 0x3FFD;
+ shortShift128Left(
+ aSig0 | LIT64( 0x0001000000000000 ), aSig1, 15, &aSig0, &aSig1 );
+ shortShift128Left(
+ bSig0 | LIT64( 0x0001000000000000 ), bSig1, 15, &bSig0, &bSig1 );
+ if ( le128( bSig0, bSig1, aSig0, aSig1 ) ) {
+ shift128Right( aSig0, aSig1, 1, &aSig0, &aSig1 );
+ ++zExp;
+ }
+ zSig0 = estimateDiv128To64( aSig0, aSig1, bSig0 );
+ mul128By64To192( bSig0, bSig1, zSig0, &term0, &term1, &term2 );
+ sub192( aSig0, aSig1, 0, term0, term1, term2, &rem0, &rem1, &rem2 );
+ while ( (sbits64) rem0 < 0 ) {
+ --zSig0;
+ add192( rem0, rem1, rem2, 0, bSig0, bSig1, &rem0, &rem1, &rem2 );
+ }
+ zSig1 = estimateDiv128To64( rem1, rem2, bSig0 );
+ if ( ( zSig1 & 0x3FFF ) <= 4 ) {
+ mul128By64To192( bSig0, bSig1, zSig1, &term1, &term2, &term3 );
+ sub192( rem1, rem2, 0, term1, term2, term3, &rem1, &rem2, &rem3 );
+ while ( (sbits64) rem1 < 0 ) {
+ --zSig1;
+ add192( rem1, rem2, rem3, 0, bSig0, bSig1, &rem1, &rem2, &rem3 );
+ }
+ zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 );
+ }
+ shift128ExtraRightJamming( zSig0, zSig1, 0, 15, &zSig0, &zSig1, &zSig2 );
+ return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 STATUS_VAR );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the remainder of the quadruple-precision floating-point value `a'
+| with respect to the corresponding value `b'. The operation is performed
+| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+float128 float128_rem( float128 a, float128 b STATUS_PARAM )
+{
+ flag aSign, bSign, zSign;
+ int32 aExp, bExp, expDiff;
+ bits64 aSig0, aSig1, bSig0, bSig1, q, term0, term1, term2;
+ bits64 allZero, alternateASig0, alternateASig1, sigMean1;
+ sbits64 sigMean0;
+ float128 z;
+
+ aSig1 = extractFloat128Frac1( a );
+ aSig0 = extractFloat128Frac0( a );
+ aExp = extractFloat128Exp( a );
+ aSign = extractFloat128Sign( a );
+ bSig1 = extractFloat128Frac1( b );
+ bSig0 = extractFloat128Frac0( b );
+ bExp = extractFloat128Exp( b );
+ bSign = extractFloat128Sign( b );
+ if ( aExp == 0x7FFF ) {
+ if ( ( aSig0 | aSig1 )
+ || ( ( bExp == 0x7FFF ) && ( bSig0 | bSig1 ) ) ) {
+ return propagateFloat128NaN( a, b STATUS_VAR );
+ }
+ goto invalid;
+ }
+ if ( bExp == 0x7FFF ) {
+ if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR );
+ return a;
+ }
+ if ( bExp == 0 ) {
+ if ( ( bSig0 | bSig1 ) == 0 ) {
+ invalid:
+ float_raise( float_flag_invalid STATUS_VAR);
+ z.low = float128_default_nan_low;
+ z.high = float128_default_nan_high;
+ return z;
+ }
+ normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 );
+ }
+ if ( aExp == 0 ) {
+ if ( ( aSig0 | aSig1 ) == 0 ) return a;
+ normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 );
+ }
+ expDiff = aExp - bExp;
+ if ( expDiff < -1 ) return a;
+ shortShift128Left(
+ aSig0 | LIT64( 0x0001000000000000 ),
+ aSig1,
+ 15 - ( expDiff < 0 ),
+ &aSig0,
+ &aSig1
+ );
+ shortShift128Left(
+ bSig0 | LIT64( 0x0001000000000000 ), bSig1, 15, &bSig0, &bSig1 );
+ q = le128( bSig0, bSig1, aSig0, aSig1 );
+ if ( q ) sub128( aSig0, aSig1, bSig0, bSig1, &aSig0, &aSig1 );
+ expDiff -= 64;
+ while ( 0 < expDiff ) {
+ q = estimateDiv128To64( aSig0, aSig1, bSig0 );
+ q = ( 4 < q ) ? q - 4 : 0;
+ mul128By64To192( bSig0, bSig1, q, &term0, &term1, &term2 );
+ shortShift192Left( term0, term1, term2, 61, &term1, &term2, &allZero );
+ shortShift128Left( aSig0, aSig1, 61, &aSig0, &allZero );
+ sub128( aSig0, 0, term1, term2, &aSig0, &aSig1 );
+ expDiff -= 61;
+ }
+ if ( -64 < expDiff ) {
+ q = estimateDiv128To64( aSig0, aSig1, bSig0 );
+ q = ( 4 < q ) ? q - 4 : 0;
+ q >>= - expDiff;
+ shift128Right( bSig0, bSig1, 12, &bSig0, &bSig1 );
+ expDiff += 52;
+ if ( expDiff < 0 ) {
+ shift128Right( aSig0, aSig1, - expDiff, &aSig0, &aSig1 );
+ }
+ else {
+ shortShift128Left( aSig0, aSig1, expDiff, &aSig0, &aSig1 );
+ }
+ mul128By64To192( bSig0, bSig1, q, &term0, &term1, &term2 );
+ sub128( aSig0, aSig1, term1, term2, &aSig0, &aSig1 );
+ }
+ else {
+ shift128Right( aSig0, aSig1, 12, &aSig0, &aSig1 );
+ shift128Right( bSig0, bSig1, 12, &bSig0, &bSig1 );
+ }
+ do {
+ alternateASig0 = aSig0;
+ alternateASig1 = aSig1;
+ ++q;
+ sub128( aSig0, aSig1, bSig0, bSig1, &aSig0, &aSig1 );
+ } while ( 0 <= (sbits64) aSig0 );
+ add128(
+ aSig0, aSig1, alternateASig0, alternateASig1, &sigMean0, &sigMean1 );
+ if ( ( sigMean0 < 0 )
+ || ( ( ( sigMean0 | sigMean1 ) == 0 ) && ( q & 1 ) ) ) {
+ aSig0 = alternateASig0;
+ aSig1 = alternateASig1;
+ }
+ zSign = ( (sbits64) aSig0 < 0 );
+ if ( zSign ) sub128( 0, 0, aSig0, aSig1, &aSig0, &aSig1 );
+ return
+ normalizeRoundAndPackFloat128( aSign ^ zSign, bExp - 4, aSig0, aSig1 STATUS_VAR );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the square root of the quadruple-precision floating-point value `a'.
+| The operation is performed according to the IEC/IEEE Standard for Binary
+| Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+float128 float128_sqrt( float128 a STATUS_PARAM )
+{
+ flag aSign;
+ int32 aExp, zExp;
+ bits64 aSig0, aSig1, zSig0, zSig1, zSig2, doubleZSig0;
+ bits64 rem0, rem1, rem2, rem3, term0, term1, term2, term3;
+ float128 z;
+
+ aSig1 = extractFloat128Frac1( a );
+ aSig0 = extractFloat128Frac0( a );
+ aExp = extractFloat128Exp( a );
+ aSign = extractFloat128Sign( a );
+ if ( aExp == 0x7FFF ) {
+ if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, a STATUS_VAR );
+ if ( ! aSign ) return a;
+ goto invalid;
+ }
+ if ( aSign ) {
+ if ( ( aExp | aSig0 | aSig1 ) == 0 ) return a;
+ invalid:
+ float_raise( float_flag_invalid STATUS_VAR);
+ z.low = float128_default_nan_low;
+ z.high = float128_default_nan_high;
+ return z;
+ }
+ if ( aExp == 0 ) {
+ if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( 0, 0, 0, 0 );
+ normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 );
+ }
+ zExp = ( ( aExp - 0x3FFF )>>1 ) + 0x3FFE;
+ aSig0 |= LIT64( 0x0001000000000000 );
+ zSig0 = estimateSqrt32( aExp, aSig0>>17 );
+ shortShift128Left( aSig0, aSig1, 13 - ( aExp & 1 ), &aSig0, &aSig1 );
+ zSig0 = estimateDiv128To64( aSig0, aSig1, zSig0<<32 ) + ( zSig0<<30 );
+ doubleZSig0 = zSig0<<1;
+ mul64To128( zSig0, zSig0, &term0, &term1 );
+ sub128( aSig0, aSig1, term0, term1, &rem0, &rem1 );
+ while ( (sbits64) rem0 < 0 ) {
+ --zSig0;
+ doubleZSig0 -= 2;
+ add128( rem0, rem1, zSig0>>63, doubleZSig0 | 1, &rem0, &rem1 );
+ }
+ zSig1 = estimateDiv128To64( rem1, 0, doubleZSig0 );
+ if ( ( zSig1 & 0x1FFF ) <= 5 ) {
+ if ( zSig1 == 0 ) zSig1 = 1;
+ mul64To128( doubleZSig0, zSig1, &term1, &term2 );
+ sub128( rem1, 0, term1, term2, &rem1, &rem2 );
+ mul64To128( zSig1, zSig1, &term2, &term3 );
+ sub192( rem1, rem2, 0, 0, term2, term3, &rem1, &rem2, &rem3 );
+ while ( (sbits64) rem1 < 0 ) {
+ --zSig1;
+ shortShift128Left( 0, zSig1, 1, &term2, &term3 );
+ term3 |= 1;
+ term2 |= doubleZSig0;
+ add192( rem1, rem2, rem3, 0, term2, term3, &rem1, &rem2, &rem3 );
+ }
+ zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 );
+ }
+ shift128ExtraRightJamming( zSig0, zSig1, 0, 14, &zSig0, &zSig1, &zSig2 );
+ return roundAndPackFloat128( 0, zExp, zSig0, zSig1, zSig2 STATUS_VAR );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the quadruple-precision floating-point value `a' is equal to
+| the corresponding value `b', and 0 otherwise. The comparison is performed
+| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+flag float128_eq( float128 a, float128 b STATUS_PARAM )
+{
+
+ if ( ( ( extractFloat128Exp( a ) == 0x7FFF )
+ && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) )
+ || ( ( extractFloat128Exp( b ) == 0x7FFF )
+ && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) )
+ ) {
+ if ( float128_is_signaling_nan( a )
+ || float128_is_signaling_nan( b ) ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ }
+ return 0;
+ }
+ return
+ ( a.low == b.low )
+ && ( ( a.high == b.high )
+ || ( ( a.low == 0 )
+ && ( (bits64) ( ( a.high | b.high )<<1 ) == 0 ) )
+ );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the quadruple-precision floating-point value `a' is less than
+| or equal to the corresponding value `b', and 0 otherwise. The comparison
+| is performed according to the IEC/IEEE Standard for Binary Floating-Point
+| Arithmetic.
+*----------------------------------------------------------------------------*/
+
+flag float128_le( float128 a, float128 b STATUS_PARAM )
+{
+ flag aSign, bSign;
+
+ if ( ( ( extractFloat128Exp( a ) == 0x7FFF )
+ && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) )
+ || ( ( extractFloat128Exp( b ) == 0x7FFF )
+ && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) )
+ ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ return 0;
+ }
+ aSign = extractFloat128Sign( a );
+ bSign = extractFloat128Sign( b );
+ if ( aSign != bSign ) {
+ return
+ aSign
+ || ( ( ( (bits64) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
+ == 0 );
+ }
+ return
+ aSign ? le128( b.high, b.low, a.high, a.low )
+ : le128( a.high, a.low, b.high, b.low );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the quadruple-precision floating-point value `a' is less than
+| the corresponding value `b', and 0 otherwise. The comparison is performed
+| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+flag float128_lt( float128 a, float128 b STATUS_PARAM )
+{
+ flag aSign, bSign;
+
+ if ( ( ( extractFloat128Exp( a ) == 0x7FFF )
+ && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) )
+ || ( ( extractFloat128Exp( b ) == 0x7FFF )
+ && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) )
+ ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ return 0;
+ }
+ aSign = extractFloat128Sign( a );
+ bSign = extractFloat128Sign( b );
+ if ( aSign != bSign ) {
+ return
+ aSign
+ && ( ( ( (bits64) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
+ != 0 );
+ }
+ return
+ aSign ? lt128( b.high, b.low, a.high, a.low )
+ : lt128( a.high, a.low, b.high, b.low );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the quadruple-precision floating-point value `a' is equal to
+| the corresponding value `b', and 0 otherwise. The invalid exception is
+| raised if either operand is a NaN. Otherwise, the comparison is performed
+| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+flag float128_eq_signaling( float128 a, float128 b STATUS_PARAM )
+{
+
+ if ( ( ( extractFloat128Exp( a ) == 0x7FFF )
+ && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) )
+ || ( ( extractFloat128Exp( b ) == 0x7FFF )
+ && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) )
+ ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ return 0;
+ }
+ return
+ ( a.low == b.low )
+ && ( ( a.high == b.high )
+ || ( ( a.low == 0 )
+ && ( (bits64) ( ( a.high | b.high )<<1 ) == 0 ) )
+ );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the quadruple-precision floating-point value `a' is less than
+| or equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not
+| cause an exception. Otherwise, the comparison is performed according to the
+| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+flag float128_le_quiet( float128 a, float128 b STATUS_PARAM )
+{
+ flag aSign, bSign;
+
+ if ( ( ( extractFloat128Exp( a ) == 0x7FFF )
+ && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) )
+ || ( ( extractFloat128Exp( b ) == 0x7FFF )
+ && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) )
+ ) {
+ if ( float128_is_signaling_nan( a )
+ || float128_is_signaling_nan( b ) ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ }
+ return 0;
+ }
+ aSign = extractFloat128Sign( a );
+ bSign = extractFloat128Sign( b );
+ if ( aSign != bSign ) {
+ return
+ aSign
+ || ( ( ( (bits64) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
+ == 0 );
+ }
+ return
+ aSign ? le128( b.high, b.low, a.high, a.low )
+ : le128( a.high, a.low, b.high, b.low );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the quadruple-precision floating-point value `a' is less than
+| the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an
+| exception. Otherwise, the comparison is performed according to the IEC/IEEE
+| Standard for Binary Floating-Point Arithmetic.
+*----------------------------------------------------------------------------*/
+
+flag float128_lt_quiet( float128 a, float128 b STATUS_PARAM )
+{
+ flag aSign, bSign;
+
+ if ( ( ( extractFloat128Exp( a ) == 0x7FFF )
+ && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) )
+ || ( ( extractFloat128Exp( b ) == 0x7FFF )
+ && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) )
+ ) {
+ if ( float128_is_signaling_nan( a )
+ || float128_is_signaling_nan( b ) ) {
+ float_raise( float_flag_invalid STATUS_VAR);
+ }
+ return 0;
+ }
+ aSign = extractFloat128Sign( a );
+ bSign = extractFloat128Sign( b );
+ if ( aSign != bSign ) {
+ return
+ aSign
+ && ( ( ( (bits64) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
+ != 0 );
+ }
+ return
+ aSign ? lt128( b.high, b.low, a.high, a.low )
+ : lt128( a.high, a.low, b.high, b.low );
+
+}
+
+#endif
+
diff --git a/fpu/softfloat.h b/fpu/softfloat.h
new file mode 100644
index 0000000..9aefbf7
--- /dev/null
+++ b/fpu/softfloat.h
@@ -0,0 +1,329 @@
+/*============================================================================
+
+This C header file is part of the SoftFloat IEC/IEEE Floating-point Arithmetic
+Package, Release 2b.
+
+Written by John R. Hauser. This work was made possible in part by the
+International Computer Science Institute, located at Suite 600, 1947 Center
+Street, Berkeley, California 94704. Funding was partially provided by the
+National Science Foundation under grant MIP-9311980. The original version
+of this code was written as part of a project to build a fixed-point vector
+processor in collaboration with the University of California at Berkeley,
+overseen by Profs. Nelson Morgan and John Wawrzynek. More information
+is available through the Web page `http://www.cs.berkeley.edu/~jhauser/
+arithmetic/SoftFloat.html'.
+
+THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort has
+been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT TIMES
+RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO PERSONS
+AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ALL LOSSES,
+COSTS, OR OTHER PROBLEMS THEY INCUR DUE TO THE SOFTWARE, AND WHO FURTHERMORE
+EFFECTIVELY INDEMNIFY JOHN HAUSER AND THE INTERNATIONAL COMPUTER SCIENCE
+INSTITUTE (possibly via similar legal warning) AGAINST ALL LOSSES, COSTS, OR
+OTHER PROBLEMS INCURRED BY THEIR CUSTOMERS AND CLIENTS DUE TO THE SOFTWARE.
+
+Derivative works are acceptable, even for commercial purposes, so long as
+(1) the source code for the derivative work includes prominent notice that
+the work is derivative, and (2) the source code includes prominent notice with
+these four paragraphs for those parts of this code that are retained.
+
+=============================================================================*/
+
+#ifndef SOFTFLOAT_H
+#define SOFTFLOAT_H
+
+#include <inttypes.h>
+#include "config.h"
+
+/*----------------------------------------------------------------------------
+| Each of the following `typedef's defines the most convenient type that holds
+| integers of at least as many bits as specified. For example, `uint8' should
+| be the most convenient type that can hold unsigned integers of as many as
+| 8 bits. The `flag' type must be able to hold either a 0 or 1. For most
+| implementations of C, `flag', `uint8', and `int8' should all be `typedef'ed
+| to the same as `int'.
+*----------------------------------------------------------------------------*/
+typedef char flag;
+typedef uint8_t uint8;
+typedef int8_t int8;
+typedef int uint16;
+typedef int int16;
+typedef unsigned int uint32;
+typedef signed int int32;
+typedef uint64_t uint64;
+typedef int64_t int64;
+
+/*----------------------------------------------------------------------------
+| Each of the following `typedef's defines a type that holds integers
+| of _exactly_ the number of bits specified. For instance, for most
+| implementation of C, `bits16' and `sbits16' should be `typedef'ed to
+| `unsigned short int' and `signed short int' (or `short int'), respectively.
+*----------------------------------------------------------------------------*/
+typedef uint8_t bits8;
+typedef int8_t sbits8;
+typedef uint16_t bits16;
+typedef int16_t sbits16;
+typedef uint32_t bits32;
+typedef int32_t sbits32;
+typedef uint64_t bits64;
+typedef int64_t sbits64;
+
+#define LIT64( a ) a##LL
+#define INLINE static inline
+
+/*----------------------------------------------------------------------------
+| The macro `FLOATX80' must be defined to enable the extended double-precision
+| floating-point format `floatx80'. If this macro is not defined, the
+| `floatx80' type will not be defined, and none of the functions that either
+| input or output the `floatx80' type will be defined. The same applies to
+| the `FLOAT128' macro and the quadruple-precision format `float128'.
+*----------------------------------------------------------------------------*/
+#ifdef CONFIG_SOFTFLOAT
+/* bit exact soft float support */
+#define FLOATX80
+#define FLOAT128
+#else
+/* native float support */
+#if (defined(__i386__) || defined(__x86_64__)) && !defined(_BSD)
+#define FLOATX80
+#endif
+#endif /* !CONFIG_SOFTFLOAT */
+
+#define STATUS_PARAM , float_status *status
+#define STATUS(field) status->field
+#define STATUS_VAR , status
+
+#ifdef CONFIG_SOFTFLOAT
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE floating-point types.
+*----------------------------------------------------------------------------*/
+typedef uint32_t float32;
+typedef uint64_t float64;
+#ifdef FLOATX80
+typedef struct {
+ uint64_t low;
+ uint16_t high;
+} floatx80;
+#endif
+#ifdef FLOAT128
+typedef struct {
+#ifdef WORDS_BIGENDIAN
+ uint64_t high, low;
+#else
+ uint64_t low, high;
+#endif
+} float128;
+#endif
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE floating-point underflow tininess-detection mode.
+*----------------------------------------------------------------------------*/
+enum {
+ float_tininess_after_rounding = 0,
+ float_tininess_before_rounding = 1
+};
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE floating-point rounding mode.
+*----------------------------------------------------------------------------*/
+enum {
+ float_round_nearest_even = 0,
+ float_round_down = 1,
+ float_round_up = 2,
+ float_round_to_zero = 3
+};
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE floating-point exception flags.
+*----------------------------------------------------------------------------*/
+enum {
+ float_flag_invalid = 1,
+ float_flag_divbyzero = 4,
+ float_flag_overflow = 8,
+ float_flag_underflow = 16,
+ float_flag_inexact = 32
+};
+
+typedef struct float_status {
+ signed char float_detect_tininess;
+ signed char float_rounding_mode;
+ signed char float_exception_flags;
+#ifdef FLOATX80
+ signed char floatx80_rounding_precision;
+#endif
+} float_status;
+
+void set_float_rounding_mode(int val STATUS_PARAM);
+#ifdef FLOATX80
+void set_floatx80_rounding_precision(int val STATUS_PARAM);
+#endif
+
+/*----------------------------------------------------------------------------
+| Routine to raise any or all of the software IEC/IEEE floating-point
+| exception flags.
+*----------------------------------------------------------------------------*/
+void float_raise( signed char STATUS_PARAM);
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE integer-to-floating-point conversion routines.
+*----------------------------------------------------------------------------*/
+float32 int32_to_float32( int STATUS_PARAM );
+float64 int32_to_float64( int STATUS_PARAM );
+#ifdef FLOATX80
+floatx80 int32_to_floatx80( int STATUS_PARAM );
+#endif
+#ifdef FLOAT128
+float128 int32_to_float128( int STATUS_PARAM );
+#endif
+float32 int64_to_float32( int64_t STATUS_PARAM );
+float64 int64_to_float64( int64_t STATUS_PARAM );
+#ifdef FLOATX80
+floatx80 int64_to_floatx80( int64_t STATUS_PARAM );
+#endif
+#ifdef FLOAT128
+float128 int64_to_float128( int64_t STATUS_PARAM );
+#endif
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE single-precision conversion routines.
+*----------------------------------------------------------------------------*/
+int float32_to_int32( float32 STATUS_PARAM );
+int float32_to_int32_round_to_zero( float32 STATUS_PARAM );
+int64_t float32_to_int64( float32 STATUS_PARAM );
+int64_t float32_to_int64_round_to_zero( float32 STATUS_PARAM );
+float64 float32_to_float64( float32 STATUS_PARAM );
+#ifdef FLOATX80
+floatx80 float32_to_floatx80( float32 STATUS_PARAM );
+#endif
+#ifdef FLOAT128
+float128 float32_to_float128( float32 STATUS_PARAM );
+#endif
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE single-precision operations.
+*----------------------------------------------------------------------------*/
+float32 float32_round_to_int( float32 STATUS_PARAM );
+float32 float32_add( float32, float32 STATUS_PARAM );
+float32 float32_sub( float32, float32 STATUS_PARAM );
+float32 float32_mul( float32, float32 STATUS_PARAM );
+float32 float32_div( float32, float32 STATUS_PARAM );
+float32 float32_rem( float32, float32 STATUS_PARAM );
+float32 float32_sqrt( float32 STATUS_PARAM );
+char float32_eq( float32, float32 STATUS_PARAM );
+char float32_le( float32, float32 STATUS_PARAM );
+char float32_lt( float32, float32 STATUS_PARAM );
+char float32_eq_signaling( float32, float32 STATUS_PARAM );
+char float32_le_quiet( float32, float32 STATUS_PARAM );
+char float32_lt_quiet( float32, float32 STATUS_PARAM );
+char float32_is_signaling_nan( float32 );
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE double-precision conversion routines.
+*----------------------------------------------------------------------------*/
+int float64_to_int32( float64 STATUS_PARAM );
+int float64_to_int32_round_to_zero( float64 STATUS_PARAM );
+int64_t float64_to_int64( float64 STATUS_PARAM );
+int64_t float64_to_int64_round_to_zero( float64 STATUS_PARAM );
+float32 float64_to_float32( float64 STATUS_PARAM );
+#ifdef FLOATX80
+floatx80 float64_to_floatx80( float64 STATUS_PARAM );
+#endif
+#ifdef FLOAT128
+float128 float64_to_float128( float64 STATUS_PARAM );
+#endif
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE double-precision operations.
+*----------------------------------------------------------------------------*/
+float64 float64_round_to_int( float64 STATUS_PARAM );
+float64 float64_add( float64, float64 STATUS_PARAM );
+float64 float64_sub( float64, float64 STATUS_PARAM );
+float64 float64_mul( float64, float64 STATUS_PARAM );
+float64 float64_div( float64, float64 STATUS_PARAM );
+float64 float64_rem( float64, float64 STATUS_PARAM );
+float64 float64_sqrt( float64 STATUS_PARAM );
+char float64_eq( float64, float64 STATUS_PARAM );
+char float64_le( float64, float64 STATUS_PARAM );
+char float64_lt( float64, float64 STATUS_PARAM );
+char float64_eq_signaling( float64, float64 STATUS_PARAM );
+char float64_le_quiet( float64, float64 STATUS_PARAM );
+char float64_lt_quiet( float64, float64 STATUS_PARAM );
+char float64_is_signaling_nan( float64 );
+
+#ifdef FLOATX80
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE extended double-precision conversion routines.
+*----------------------------------------------------------------------------*/
+int floatx80_to_int32( floatx80 STATUS_PARAM );
+int floatx80_to_int32_round_to_zero( floatx80 STATUS_PARAM );
+int64_t floatx80_to_int64( floatx80 STATUS_PARAM );
+int64_t floatx80_to_int64_round_to_zero( floatx80 STATUS_PARAM );
+float32 floatx80_to_float32( floatx80 STATUS_PARAM );
+float64 floatx80_to_float64( floatx80 STATUS_PARAM );
+#ifdef FLOAT128
+float128 floatx80_to_float128( floatx80 STATUS_PARAM );
+#endif
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE extended double-precision operations.
+*----------------------------------------------------------------------------*/
+floatx80 floatx80_round_to_int( floatx80 STATUS_PARAM );
+floatx80 floatx80_add( floatx80, floatx80 STATUS_PARAM );
+floatx80 floatx80_sub( floatx80, floatx80 STATUS_PARAM );
+floatx80 floatx80_mul( floatx80, floatx80 STATUS_PARAM );
+floatx80 floatx80_div( floatx80, floatx80 STATUS_PARAM );
+floatx80 floatx80_rem( floatx80, floatx80 STATUS_PARAM );
+floatx80 floatx80_sqrt( floatx80 STATUS_PARAM );
+char floatx80_eq( floatx80, floatx80 STATUS_PARAM );
+char floatx80_le( floatx80, floatx80 STATUS_PARAM );
+char floatx80_lt( floatx80, floatx80 STATUS_PARAM );
+char floatx80_eq_signaling( floatx80, floatx80 STATUS_PARAM );
+char floatx80_le_quiet( floatx80, floatx80 STATUS_PARAM );
+char floatx80_lt_quiet( floatx80, floatx80 STATUS_PARAM );
+char floatx80_is_signaling_nan( floatx80 );
+
+#endif
+
+#ifdef FLOAT128
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE quadruple-precision conversion routines.
+*----------------------------------------------------------------------------*/
+int float128_to_int32( float128 STATUS_PARAM );
+int float128_to_int32_round_to_zero( float128 STATUS_PARAM );
+int64_t float128_to_int64( float128 STATUS_PARAM );
+int64_t float128_to_int64_round_to_zero( float128 STATUS_PARAM );
+float32 float128_to_float32( float128 STATUS_PARAM );
+float64 float128_to_float64( float128 STATUS_PARAM );
+#ifdef FLOATX80
+floatx80 float128_to_floatx80( float128 STATUS_PARAM );
+#endif
+
+/*----------------------------------------------------------------------------
+| Software IEC/IEEE quadruple-precision operations.
+*----------------------------------------------------------------------------*/
+float128 float128_round_to_int( float128 STATUS_PARAM );
+float128 float128_add( float128, float128 STATUS_PARAM );
+float128 float128_sub( float128, float128 STATUS_PARAM );
+float128 float128_mul( float128, float128 STATUS_PARAM );
+float128 float128_div( float128, float128 STATUS_PARAM );
+float128 float128_rem( float128, float128 STATUS_PARAM );
+float128 float128_sqrt( float128 STATUS_PARAM );
+char float128_eq( float128, float128 STATUS_PARAM );
+char float128_le( float128, float128 STATUS_PARAM );
+char float128_lt( float128, float128 STATUS_PARAM );
+char float128_eq_signaling( float128, float128 STATUS_PARAM );
+char float128_le_quiet( float128, float128 STATUS_PARAM );
+char float128_lt_quiet( float128, float128 STATUS_PARAM );
+char float128_is_signaling_nan( float128 );
+
+#endif
+
+#else /* CONFIG_SOFTFLOAT */
+
+#include "softfloat-native.h"
+
+#endif /* !CONFIG_SOFTFLOAT */
+
+#endif /* !SOFTFLOAT_H */
