+++ /dev/null
-/*
- * QEMU float support macros
- *
- * The code in this source file is derived from release 2a of the SoftFloat
- * IEC/IEEE Floating-point Arithmetic Package. Those parts of the code (and
- * some later contributions) are provided under that license, as detailed below.
- * It has subsequently been modified by contributors to the QEMU Project,
- * so some portions are provided under:
- * the SoftFloat-2a license
- * the BSD license
- * GPL-v2-or-later
- *
- * Any future contributions to this file after December 1st 2014 will be
- * taken to be licensed under the Softfloat-2a license unless specifically
- * indicated otherwise.
- */
-
-/*
-===============================================================================
-This C source fragment is part of the SoftFloat IEC/IEEE Floating-point
-Arithmetic Package, Release 2a.
-
-Written by John R. Hauser. This work was made possible in part by the
-International Computer Science Institute, located at Suite 600, 1947 Center
-Street, Berkeley, California 94704. Funding was partially provided by the
-National Science Foundation under grant MIP-9311980. The original version
-of this code was written as part of a project to build a fixed-point vector
-processor in collaboration with the University of California at Berkeley,
-overseen by Profs. Nelson Morgan and John Wawrzynek. More information
-is available through the Web page `http://HTTP.CS.Berkeley.EDU/~jhauser/
-arithmetic/SoftFloat.html'.
-
-THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort
-has been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT
-TIMES RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO
-PERSONS AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ANY
-AND ALL LOSSES, COSTS, OR OTHER PROBLEMS ARISING FROM ITS USE.
-
-Derivative works are acceptable, even for commercial purposes, so long as
-(1) they include prominent notice that the work is derivative, and (2) they
-include prominent notice akin to these four paragraphs for those parts of
-this code that are retained.
-
-===============================================================================
-*/
-
-/* BSD licensing:
- * Copyright (c) 2006, Fabrice Bellard
- * All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions are met:
- *
- * 1. Redistributions of source code must retain the above copyright notice,
- * this list of conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright notice,
- * this list of conditions and the following disclaimer in the documentation
- * and/or other materials provided with the distribution.
- *
- * 3. Neither the name of the copyright holder nor the names of its contributors
- * may be used to endorse or promote products derived from this software without
- * specific prior written permission.
- *
- * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
- * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
- * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
- * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
- * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
- * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
- * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
- * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
- * THE POSSIBILITY OF SUCH DAMAGE.
- */
-
-/* Portions of this work are licensed under the terms of the GNU GPL,
- * version 2 or later. See the COPYING file in the top-level directory.
- */
-
-/*----------------------------------------------------------------------------
-| This macro tests for minimum version of the GNU C compiler.
-*----------------------------------------------------------------------------*/
-#if defined(__GNUC__) && defined(__GNUC_MINOR__)
-# define SOFTFLOAT_GNUC_PREREQ(maj, min) \
- ((__GNUC__ << 16) + __GNUC_MINOR__ >= ((maj) << 16) + (min))
-#else
-# define SOFTFLOAT_GNUC_PREREQ(maj, min) 0
-#endif
-
-
-/*----------------------------------------------------------------------------
-| Shifts `a' right by the number of bits given in `count'. If any nonzero
-| bits are shifted off, they are ``jammed'' into the least significant bit of
-| the result by setting the least significant bit to 1. The value of `count'
-| can be arbitrarily large; in particular, if `count' is greater than 32, the
-| result will be either 0 or 1, depending on whether `a' is zero or nonzero.
-| The result is stored in the location pointed to by `zPtr'.
-*----------------------------------------------------------------------------*/
-
-static inline void shift32RightJamming(uint32_t a, int count, uint32_t *zPtr)
-{
- uint32_t z;
-
- if ( count == 0 ) {
- z = a;
- }
- else if ( count < 32 ) {
- z = ( a>>count ) | ( ( a<<( ( - count ) & 31 ) ) != 0 );
- }
- else {
- z = ( a != 0 );
- }
- *zPtr = z;
-
-}
-
-/*----------------------------------------------------------------------------
-| Shifts `a' right by the number of bits given in `count'. If any nonzero
-| bits are shifted off, they are ``jammed'' into the least significant bit of
-| the result by setting the least significant bit to 1. The value of `count'
-| can be arbitrarily large; in particular, if `count' is greater than 64, the
-| result will be either 0 or 1, depending on whether `a' is zero or nonzero.
-| The result is stored in the location pointed to by `zPtr'.
-*----------------------------------------------------------------------------*/
-
-static inline void shift64RightJamming(uint64_t a, int count, uint64_t *zPtr)
-{
- uint64_t z;
-
- if ( count == 0 ) {
- z = a;
- }
- else if ( count < 64 ) {
- z = ( a>>count ) | ( ( a<<( ( - count ) & 63 ) ) != 0 );
- }
- else {
- z = ( a != 0 );
- }
- *zPtr = z;
-
-}
-
-/*----------------------------------------------------------------------------
-| Shifts the 128-bit value formed by concatenating `a0' and `a1' right by 64
-| _plus_ the number of bits given in `count'. The shifted result is at most
-| 64 nonzero bits; this is stored at the location pointed to by `z0Ptr'. The
-| bits shifted off form a second 64-bit result as follows: The _last_ bit
-| shifted off is the most-significant bit of the extra result, and the other
-| 63 bits of the extra result are all zero if and only if _all_but_the_last_
-| bits shifted off were all zero. This extra result is stored in the location
-| pointed to by `z1Ptr'. The value of `count' can be arbitrarily large.
-| (This routine makes more sense if `a0' and `a1' are considered to form a
-| fixed-point value with binary point between `a0' and `a1'. This fixed-point
-| value is shifted right by the number of bits given in `count', and the
-| integer part of the result is returned at the location pointed to by
-| `z0Ptr'. The fractional part of the result may be slightly corrupted as
-| described above, and is returned at the location pointed to by `z1Ptr'.)
-*----------------------------------------------------------------------------*/
-
-static inline void
- shift64ExtraRightJamming(
- uint64_t a0, uint64_t a1, int count, uint64_t *z0Ptr, uint64_t *z1Ptr)
-{
- uint64_t z0, z1;
- int8_t negCount = ( - count ) & 63;
-
- if ( count == 0 ) {
- z1 = a1;
- z0 = a0;
- }
- else if ( count < 64 ) {
- z1 = ( a0<<negCount ) | ( a1 != 0 );
- z0 = a0>>count;
- }
- else {
- if ( count == 64 ) {
- z1 = a0 | ( a1 != 0 );
- }
- else {
- z1 = ( ( a0 | a1 ) != 0 );
- }
- z0 = 0;
- }
- *z1Ptr = z1;
- *z0Ptr = z0;
-
-}
-
-/*----------------------------------------------------------------------------
-| Shifts the 128-bit value formed by concatenating `a0' and `a1' right by the
-| number of bits given in `count'. Any bits shifted off are lost. The value
-| of `count' can be arbitrarily large; in particular, if `count' is greater
-| than 128, the result will be 0. The result is broken into two 64-bit pieces
-| which are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
-*----------------------------------------------------------------------------*/
-
-static inline void
- shift128Right(
- uint64_t a0, uint64_t a1, int count, uint64_t *z0Ptr, uint64_t *z1Ptr)
-{
- uint64_t z0, z1;
- int8_t negCount = ( - count ) & 63;
-
- if ( count == 0 ) {
- z1 = a1;
- z0 = a0;
- }
- else if ( count < 64 ) {
- z1 = ( a0<<negCount ) | ( a1>>count );
- z0 = a0>>count;
- }
- else {
- z1 = (count < 128) ? (a0 >> (count & 63)) : 0;
- z0 = 0;
- }
- *z1Ptr = z1;
- *z0Ptr = z0;
-
-}
-
-/*----------------------------------------------------------------------------
-| Shifts the 128-bit value formed by concatenating `a0' and `a1' right by the
-| number of bits given in `count'. If any nonzero bits are shifted off, they
-| are ``jammed'' into the least significant bit of the result by setting the
-| least significant bit to 1. The value of `count' can be arbitrarily large;
-| in particular, if `count' is greater than 128, the result will be either
-| 0 or 1, depending on whether the concatenation of `a0' and `a1' is zero or
-| nonzero. The result is broken into two 64-bit pieces which are stored at
-| the locations pointed to by `z0Ptr' and `z1Ptr'.
-*----------------------------------------------------------------------------*/
-
-static inline void
- shift128RightJamming(
- uint64_t a0, uint64_t a1, int count, uint64_t *z0Ptr, uint64_t *z1Ptr)
-{
- uint64_t z0, z1;
- int8_t negCount = ( - count ) & 63;
-
- if ( count == 0 ) {
- z1 = a1;
- z0 = a0;
- }
- else if ( count < 64 ) {
- z1 = ( a0<<negCount ) | ( a1>>count ) | ( ( a1<<negCount ) != 0 );
- z0 = a0>>count;
- }
- else {
- if ( count == 64 ) {
- z1 = a0 | ( a1 != 0 );
- }
- else if ( count < 128 ) {
- z1 = ( a0>>( count & 63 ) ) | ( ( ( a0<<negCount ) | a1 ) != 0 );
- }
- else {
- z1 = ( ( a0 | a1 ) != 0 );
- }
- z0 = 0;
- }
- *z1Ptr = z1;
- *z0Ptr = z0;
-
-}
-
-/*----------------------------------------------------------------------------
-| Shifts the 192-bit value formed by concatenating `a0', `a1', and `a2' right
-| by 64 _plus_ the number of bits given in `count'. The shifted result is
-| at most 128 nonzero bits; these are broken into two 64-bit pieces which are
-| stored at the locations pointed to by `z0Ptr' and `z1Ptr'. The bits shifted
-| off form a third 64-bit result as follows: The _last_ bit shifted off is
-| the most-significant bit of the extra result, and the other 63 bits of the
-| extra result are all zero if and only if _all_but_the_last_ bits shifted off
-| were all zero. This extra result is stored in the location pointed to by
-| `z2Ptr'. The value of `count' can be arbitrarily large.
-| (This routine makes more sense if `a0', `a1', and `a2' are considered
-| to form a fixed-point value with binary point between `a1' and `a2'. This
-| fixed-point value is shifted right by the number of bits given in `count',
-| and the integer part of the result is returned at the locations pointed to
-| by `z0Ptr' and `z1Ptr'. The fractional part of the result may be slightly
-| corrupted as described above, and is returned at the location pointed to by
-| `z2Ptr'.)
-*----------------------------------------------------------------------------*/
-
-static inline void
- shift128ExtraRightJamming(
- uint64_t a0,
- uint64_t a1,
- uint64_t a2,
- int count,
- uint64_t *z0Ptr,
- uint64_t *z1Ptr,
- uint64_t *z2Ptr
- )
-{
- uint64_t z0, z1, z2;
- int8_t negCount = ( - count ) & 63;
-
- if ( count == 0 ) {
- z2 = a2;
- z1 = a1;
- z0 = a0;
- }
- else {
- if ( count < 64 ) {
- z2 = a1<<negCount;
- z1 = ( a0<<negCount ) | ( a1>>count );
- z0 = a0>>count;
- }
- else {
- if ( count == 64 ) {
- z2 = a1;
- z1 = a0;
- }
- else {
- a2 |= a1;
- if ( count < 128 ) {
- z2 = a0<<negCount;
- z1 = a0>>( count & 63 );
- }
- else {
- z2 = ( count == 128 ) ? a0 : ( a0 != 0 );
- z1 = 0;
- }
- }
- z0 = 0;
- }
- z2 |= ( a2 != 0 );
- }
- *z2Ptr = z2;
- *z1Ptr = z1;
- *z0Ptr = z0;
-
-}
-
-/*----------------------------------------------------------------------------
-| Shifts the 128-bit value formed by concatenating `a0' and `a1' left by the
-| number of bits given in `count'. Any bits shifted off are lost. The value
-| of `count' must be less than 64. The result is broken into two 64-bit
-| pieces which are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
-*----------------------------------------------------------------------------*/
-
-static inline void
- shortShift128Left(
- uint64_t a0, uint64_t a1, int count, uint64_t *z0Ptr, uint64_t *z1Ptr)
-{
-
- *z1Ptr = a1<<count;
- *z0Ptr =
- ( count == 0 ) ? a0 : ( a0<<count ) | ( a1>>( ( - count ) & 63 ) );
-
-}
-
-/*----------------------------------------------------------------------------
-| Shifts the 192-bit value formed by concatenating `a0', `a1', and `a2' left
-| by the number of bits given in `count'. Any bits shifted off are lost.
-| The value of `count' must be less than 64. The result is broken into three
-| 64-bit pieces which are stored at the locations pointed to by `z0Ptr',
-| `z1Ptr', and `z2Ptr'.
-*----------------------------------------------------------------------------*/
-
-static inline void
- shortShift192Left(
- uint64_t a0,
- uint64_t a1,
- uint64_t a2,
- int count,
- uint64_t *z0Ptr,
- uint64_t *z1Ptr,
- uint64_t *z2Ptr
- )
-{
- uint64_t z0, z1, z2;
- int8_t negCount;
-
- z2 = a2<<count;
- z1 = a1<<count;
- z0 = a0<<count;
- if ( 0 < count ) {
- negCount = ( ( - count ) & 63 );
- z1 |= a2>>negCount;
- z0 |= a1>>negCount;
- }
- *z2Ptr = z2;
- *z1Ptr = z1;
- *z0Ptr = z0;
-
-}
-
-/*----------------------------------------------------------------------------
-| Adds the 128-bit value formed by concatenating `a0' and `a1' to the 128-bit
-| value formed by concatenating `b0' and `b1'. Addition is modulo 2^128, so
-| any carry out is lost. The result is broken into two 64-bit pieces which
-| are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
-*----------------------------------------------------------------------------*/
-
-static inline void
- add128(
- uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1, uint64_t *z0Ptr, uint64_t *z1Ptr )
-{
- uint64_t z1;
-
- z1 = a1 + b1;
- *z1Ptr = z1;
- *z0Ptr = a0 + b0 + ( z1 < a1 );
-
-}
-
-/*----------------------------------------------------------------------------
-| Adds the 192-bit value formed by concatenating `a0', `a1', and `a2' to the
-| 192-bit value formed by concatenating `b0', `b1', and `b2'. Addition is
-| modulo 2^192, so any carry out is lost. The result is broken into three
-| 64-bit pieces which are stored at the locations pointed to by `z0Ptr',
-| `z1Ptr', and `z2Ptr'.
-*----------------------------------------------------------------------------*/
-
-static inline void
- add192(
- uint64_t a0,
- uint64_t a1,
- uint64_t a2,
- uint64_t b0,
- uint64_t b1,
- uint64_t b2,
- uint64_t *z0Ptr,
- uint64_t *z1Ptr,
- uint64_t *z2Ptr
- )
-{
- uint64_t z0, z1, z2;
- int8_t carry0, carry1;
-
- z2 = a2 + b2;
- carry1 = ( z2 < a2 );
- z1 = a1 + b1;
- carry0 = ( z1 < a1 );
- z0 = a0 + b0;
- z1 += carry1;
- z0 += ( z1 < carry1 );
- z0 += carry0;
- *z2Ptr = z2;
- *z1Ptr = z1;
- *z0Ptr = z0;
-
-}
-
-/*----------------------------------------------------------------------------
-| Subtracts the 128-bit value formed by concatenating `b0' and `b1' from the
-| 128-bit value formed by concatenating `a0' and `a1'. Subtraction is modulo
-| 2^128, so any borrow out (carry out) is lost. The result is broken into two
-| 64-bit pieces which are stored at the locations pointed to by `z0Ptr' and
-| `z1Ptr'.
-*----------------------------------------------------------------------------*/
-
-static inline void
- sub128(
- uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1, uint64_t *z0Ptr, uint64_t *z1Ptr )
-{
-
- *z1Ptr = a1 - b1;
- *z0Ptr = a0 - b0 - ( a1 < b1 );
-
-}
-
-/*----------------------------------------------------------------------------
-| Subtracts the 192-bit value formed by concatenating `b0', `b1', and `b2'
-| from the 192-bit value formed by concatenating `a0', `a1', and `a2'.
-| Subtraction is modulo 2^192, so any borrow out (carry out) is lost. The
-| result is broken into three 64-bit pieces which are stored at the locations
-| pointed to by `z0Ptr', `z1Ptr', and `z2Ptr'.
-*----------------------------------------------------------------------------*/
-
-static inline void
- sub192(
- uint64_t a0,
- uint64_t a1,
- uint64_t a2,
- uint64_t b0,
- uint64_t b1,
- uint64_t b2,
- uint64_t *z0Ptr,
- uint64_t *z1Ptr,
- uint64_t *z2Ptr
- )
-{
- uint64_t z0, z1, z2;
- int8_t borrow0, borrow1;
-
- z2 = a2 - b2;
- borrow1 = ( a2 < b2 );
- z1 = a1 - b1;
- borrow0 = ( a1 < b1 );
- z0 = a0 - b0;
- z0 -= ( z1 < borrow1 );
- z1 -= borrow1;
- z0 -= borrow0;
- *z2Ptr = z2;
- *z1Ptr = z1;
- *z0Ptr = z0;
-
-}
-
-/*----------------------------------------------------------------------------
-| Multiplies `a' by `b' to obtain a 128-bit product. The product is broken
-| into two 64-bit pieces which are stored at the locations pointed to by
-| `z0Ptr' and `z1Ptr'.
-*----------------------------------------------------------------------------*/
-
-static inline void mul64To128( uint64_t a, uint64_t b, uint64_t *z0Ptr, uint64_t *z1Ptr )
-{
- uint32_t aHigh, aLow, bHigh, bLow;
- uint64_t z0, zMiddleA, zMiddleB, z1;
-
- aLow = a;
- aHigh = a>>32;
- bLow = b;
- bHigh = b>>32;
- z1 = ( (uint64_t) aLow ) * bLow;
- zMiddleA = ( (uint64_t) aLow ) * bHigh;
- zMiddleB = ( (uint64_t) aHigh ) * bLow;
- z0 = ( (uint64_t) aHigh ) * bHigh;
- zMiddleA += zMiddleB;
- z0 += ( ( (uint64_t) ( zMiddleA < zMiddleB ) )<<32 ) + ( zMiddleA>>32 );
- zMiddleA <<= 32;
- z1 += zMiddleA;
- z0 += ( z1 < zMiddleA );
- *z1Ptr = z1;
- *z0Ptr = z0;
-
-}
-
-/*----------------------------------------------------------------------------
-| Multiplies the 128-bit value formed by concatenating `a0' and `a1' by
-| `b' to obtain a 192-bit product. The product is broken into three 64-bit
-| pieces which are stored at the locations pointed to by `z0Ptr', `z1Ptr', and
-| `z2Ptr'.
-*----------------------------------------------------------------------------*/
-
-static inline void
- mul128By64To192(
- uint64_t a0,
- uint64_t a1,
- uint64_t b,
- uint64_t *z0Ptr,
- uint64_t *z1Ptr,
- uint64_t *z2Ptr
- )
-{
- uint64_t z0, z1, z2, more1;
-
- mul64To128( a1, b, &z1, &z2 );
- mul64To128( a0, b, &z0, &more1 );
- add128( z0, more1, 0, z1, &z0, &z1 );
- *z2Ptr = z2;
- *z1Ptr = z1;
- *z0Ptr = z0;
-
-}
-
-/*----------------------------------------------------------------------------
-| Multiplies the 128-bit value formed by concatenating `a0' and `a1' to the
-| 128-bit value formed by concatenating `b0' and `b1' to obtain a 256-bit
-| product. The product is broken into four 64-bit pieces which are stored at
-| the locations pointed to by `z0Ptr', `z1Ptr', `z2Ptr', and `z3Ptr'.
-*----------------------------------------------------------------------------*/
-
-static inline void
- mul128To256(
- uint64_t a0,
- uint64_t a1,
- uint64_t b0,
- uint64_t b1,
- uint64_t *z0Ptr,
- uint64_t *z1Ptr,
- uint64_t *z2Ptr,
- uint64_t *z3Ptr
- )
-{
- uint64_t z0, z1, z2, z3;
- uint64_t more1, more2;
-
- mul64To128( a1, b1, &z2, &z3 );
- mul64To128( a1, b0, &z1, &more2 );
- add128( z1, more2, 0, z2, &z1, &z2 );
- mul64To128( a0, b0, &z0, &more1 );
- add128( z0, more1, 0, z1, &z0, &z1 );
- mul64To128( a0, b1, &more1, &more2 );
- add128( more1, more2, 0, z2, &more1, &z2 );
- add128( z0, z1, 0, more1, &z0, &z1 );
- *z3Ptr = z3;
- *z2Ptr = z2;
- *z1Ptr = z1;
- *z0Ptr = z0;
-
-}
-
-/*----------------------------------------------------------------------------
-| Returns an approximation to the 64-bit integer quotient obtained by dividing
-| `b' into the 128-bit value formed by concatenating `a0' and `a1'. The
-| divisor `b' must be at least 2^63. If q is the exact quotient truncated
-| toward zero, the approximation returned lies between q and q + 2 inclusive.
-| If the exact quotient q is larger than 64 bits, the maximum positive 64-bit
-| unsigned integer is returned.
-*----------------------------------------------------------------------------*/
-
-static uint64_t estimateDiv128To64( uint64_t a0, uint64_t a1, uint64_t b )
-{
- uint64_t b0, b1;
- uint64_t rem0, rem1, term0, term1;
- uint64_t z;
-
- if ( b <= a0 ) return LIT64( 0xFFFFFFFFFFFFFFFF );
- b0 = b>>32;
- z = ( b0<<32 <= a0 ) ? LIT64( 0xFFFFFFFF00000000 ) : ( a0 / b0 )<<32;
- mul64To128( b, z, &term0, &term1 );
- sub128( a0, a1, term0, term1, &rem0, &rem1 );
- while ( ( (int64_t) rem0 ) < 0 ) {
- z -= LIT64( 0x100000000 );
- b1 = b<<32;
- add128( rem0, rem1, b0, b1, &rem0, &rem1 );
- }
- rem0 = ( rem0<<32 ) | ( rem1>>32 );
- z |= ( b0<<32 <= rem0 ) ? 0xFFFFFFFF : rem0 / b0;
- return z;
-
-}
-
-/* From the GNU Multi Precision Library - longlong.h __udiv_qrnnd
- * (https://gmplib.org/repo/gmp/file/tip/longlong.h)
- *
- * Licensed under the GPLv2/LGPLv3
- */
-static uint64_t div128To64(uint64_t n0, uint64_t n1, uint64_t d)
-{
- uint64_t d0, d1, q0, q1, r1, r0, m;
-
- d0 = (uint32_t)d;
- d1 = d >> 32;
-
- r1 = n1 % d1;
- q1 = n1 / d1;
- m = q1 * d0;
- r1 = (r1 << 32) | (n0 >> 32);
- if (r1 < m) {
- q1 -= 1;
- r1 += d;
- if (r1 >= d) {
- if (r1 < m) {
- q1 -= 1;
- r1 += d;
- }
- }
- }
- r1 -= m;
-
- r0 = r1 % d1;
- q0 = r1 / d1;
- m = q0 * d0;
- r0 = (r0 << 32) | (uint32_t)n0;
- if (r0 < m) {
- q0 -= 1;
- r0 += d;
- if (r0 >= d) {
- if (r0 < m) {
- q0 -= 1;
- r0 += d;
- }
- }
- }
- r0 -= m;
-
- /* Return remainder in LSB */
- return (q1 << 32) | q0 | (r0 != 0);
-}
-
-/*----------------------------------------------------------------------------
-| Returns an approximation to the square root of the 32-bit significand given
-| by `a'. Considered as an integer, `a' must be at least 2^31. If bit 0 of
-| `aExp' (the least significant bit) is 1, the integer returned approximates
-| 2^31*sqrt(`a'/2^31), where `a' is considered an integer. If bit 0 of `aExp'
-| is 0, the integer returned approximates 2^31*sqrt(`a'/2^30). In either
-| case, the approximation returned lies strictly within +/-2 of the exact
-| value.
-*----------------------------------------------------------------------------*/
-
-static uint32_t estimateSqrt32(int aExp, uint32_t a)
-{
- static const uint16_t sqrtOddAdjustments[] = {
- 0x0004, 0x0022, 0x005D, 0x00B1, 0x011D, 0x019F, 0x0236, 0x02E0,
- 0x039C, 0x0468, 0x0545, 0x0631, 0x072B, 0x0832, 0x0946, 0x0A67
- };
- static const uint16_t sqrtEvenAdjustments[] = {
- 0x0A2D, 0x08AF, 0x075A, 0x0629, 0x051A, 0x0429, 0x0356, 0x029E,
- 0x0200, 0x0179, 0x0109, 0x00AF, 0x0068, 0x0034, 0x0012, 0x0002
- };
- int8_t index;
- uint32_t z;
-
- index = ( a>>27 ) & 15;
- if ( aExp & 1 ) {
- z = 0x4000 + ( a>>17 ) - sqrtOddAdjustments[ (int)index ];
- z = ( ( a / z )<<14 ) + ( z<<15 );
- a >>= 1;
- }
- else {
- z = 0x8000 + ( a>>17 ) - sqrtEvenAdjustments[ (int)index ];
- z = a / z + z;
- z = ( 0x20000 <= z ) ? 0xFFFF8000 : ( z<<15 );
- if ( z <= a ) return (uint32_t) ( ( (int32_t) a )>>1 );
- }
- return ( (uint32_t) ( ( ( (uint64_t) a )<<31 ) / z ) ) + ( z>>1 );
-
-}
-
-/*----------------------------------------------------------------------------
-| Returns the number of leading 0 bits before the most-significant 1 bit of
-| `a'. If `a' is zero, 32 is returned.
-*----------------------------------------------------------------------------*/
-
-static int8_t countLeadingZeros32( uint32_t a )
-{
-#if SOFTFLOAT_GNUC_PREREQ(3, 4)
- if (a) {
- return __builtin_clz(a);
- } else {
- return 32;
- }
-#else
- static const int8_t countLeadingZerosHigh[] = {
- 8, 7, 6, 6, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4,
- 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
- 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
- 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
- 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
- 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
- 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
- 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
- 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
- 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
- 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
- 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
- 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
- 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
- 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
- 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
- };
- int8_t shiftCount;
-
- shiftCount = 0;
- if ( a < 0x10000 ) {
- shiftCount += 16;
- a <<= 16;
- }
- if ( a < 0x1000000 ) {
- shiftCount += 8;
- a <<= 8;
- }
- shiftCount += countLeadingZerosHigh[ a>>24 ];
- return shiftCount;
-#endif
-}
-
-/*----------------------------------------------------------------------------
-| Returns the number of leading 0 bits before the most-significant 1 bit of
-| `a'. If `a' is zero, 64 is returned.
-*----------------------------------------------------------------------------*/
-
-static int8_t countLeadingZeros64( uint64_t a )
-{
-#if SOFTFLOAT_GNUC_PREREQ(3, 4)
- if (a) {
- return __builtin_clzll(a);
- } else {
- return 64;
- }
-#else
- int8_t shiftCount;
-
- shiftCount = 0;
- if ( a < ( (uint64_t) 1 )<<32 ) {
- shiftCount += 32;
- }
- else {
- a >>= 32;
- }
- shiftCount += countLeadingZeros32( a );
- return shiftCount;
-#endif
-}
-
-/*----------------------------------------------------------------------------
-| Returns 1 if the 128-bit value formed by concatenating `a0' and `a1'
-| is equal to the 128-bit value formed by concatenating `b0' and `b1'.
-| Otherwise, returns 0.
-*----------------------------------------------------------------------------*/
-
-static inline flag eq128( uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1 )
-{
-
- return ( a0 == b0 ) && ( a1 == b1 );
-
-}
-
-/*----------------------------------------------------------------------------
-| Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is less
-| than or equal to the 128-bit value formed by concatenating `b0' and `b1'.
-| Otherwise, returns 0.
-*----------------------------------------------------------------------------*/
-
-static inline flag le128( uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1 )
-{
-
- return ( a0 < b0 ) || ( ( a0 == b0 ) && ( a1 <= b1 ) );
-
-}
-
-/*----------------------------------------------------------------------------
-| Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is less
-| than the 128-bit value formed by concatenating `b0' and `b1'. Otherwise,
-| returns 0.
-*----------------------------------------------------------------------------*/
-
-static inline flag lt128( uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1 )
-{
-
- return ( a0 < b0 ) || ( ( a0 == b0 ) && ( a1 < b1 ) );
-
-}
-
-/*----------------------------------------------------------------------------
-| Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is
-| not equal to the 128-bit value formed by concatenating `b0' and `b1'.
-| Otherwise, returns 0.
-*----------------------------------------------------------------------------*/
-
-static inline flag ne128( uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1 )
-{
-
- return ( a0 != b0 ) || ( a1 != b1 );
-
-}
| `b' is a signaling NaN, the invalid exception is raised.
*----------------------------------------------------------------------------*/
-static floatx80 propagateFloatx80NaN(floatx80 a, floatx80 b,
- float_status *status)
+floatx80 propagateFloatx80NaN(floatx80 a, floatx80 b, float_status *status)
{
flag aIsQuietNaN, aIsSignalingNaN, bIsQuietNaN, bIsSignalingNaN;
flag aIsLargerSignificand;
| division and square root approximations. (Can be specialized to target if
| desired.)
*----------------------------------------------------------------------------*/
-#include "softfloat-macros.h"
+#include "fpu/softfloat-macros.h"
/*----------------------------------------------------------------------------
| Functions and definitions to determine: (1) whether tininess for underflow
}
-/*----------------------------------------------------------------------------
-| 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.
-*----------------------------------------------------------------------------*/
-
-static inline float32 packFloat32(flag zSign, int zExp, uint32_t zSig)
-{
-
- return make_float32(
- ( ( (uint32_t) zSign )<<31 ) + ( ( (uint32_t) zExp )<<23 ) + zSig);
-
-}
-
/*----------------------------------------------------------------------------
| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
| and significand `zSig', and returns the proper single-precision floating-
}
-/*----------------------------------------------------------------------------
-| Returns the fraction bits of the extended double-precision floating-point
-| value `a'.
-*----------------------------------------------------------------------------*/
-
-static inline uint64_t extractFloatx80Frac( floatx80 a )
-{
-
- return a.low;
-
-}
-
-/*----------------------------------------------------------------------------
-| Returns the exponent bits of the extended double-precision floating-point
-| value `a'.
-*----------------------------------------------------------------------------*/
-
-static inline int32_t extractFloatx80Exp( floatx80 a )
-{
-
- return a.high & 0x7FFF;
-
-}
-
-/*----------------------------------------------------------------------------
-| Returns the sign bit of the extended double-precision floating-point value
-| `a'.
-*----------------------------------------------------------------------------*/
-
-static 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
| `zSigPtr', respectively.
*----------------------------------------------------------------------------*/
-static void
- normalizeFloatx80Subnormal( uint64_t aSig, int32_t *zExpPtr, uint64_t *zSigPtr )
+void normalizeFloatx80Subnormal(uint64_t aSig, int32_t *zExpPtr,
+ uint64_t *zSigPtr)
{
int8_t 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.
-*----------------------------------------------------------------------------*/
-
-static inline floatx80 packFloatx80( flag zSign, int32_t zExp, uint64_t zSig )
-{
- floatx80 z;
-
- z.low = zSig;
- z.high = ( ( (uint16_t) zSign )<<15 ) + zExp;
- return z;
-
}
/*----------------------------------------------------------------------------
| Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/
-static floatx80 roundAndPackFloatx80(int8_t roundingPrecision, flag zSign,
- int32_t zExp, uint64_t zSig0, uint64_t zSig1,
- float_status *status)
+floatx80 roundAndPackFloatx80(int8_t roundingPrecision, flag zSign,
+ int32_t zExp, uint64_t zSig0, uint64_t zSig1,
+ float_status *status)
{
int8_t roundingMode;
flag roundNearestEven, increment, isTiny;
| normalized.
*----------------------------------------------------------------------------*/
-static floatx80 normalizeRoundAndPackFloatx80(int8_t roundingPrecision,
- flag zSign, int32_t zExp,
- uint64_t zSig0, uint64_t zSig1,
- float_status *status)
+floatx80 normalizeRoundAndPackFloatx80(int8_t roundingPrecision,
+ flag zSign, int32_t zExp,
+ uint64_t zSig0, uint64_t zSig1,
+ float_status *status)
{
int8_t shiftCount;
--- /dev/null
+/*
+ * QEMU float support macros
+ *
+ * The code in this source file is derived from release 2a of the SoftFloat
+ * IEC/IEEE Floating-point Arithmetic Package. Those parts of the code (and
+ * some later contributions) are provided under that license, as detailed below.
+ * It has subsequently been modified by contributors to the QEMU Project,
+ * so some portions are provided under:
+ * the SoftFloat-2a license
+ * the BSD license
+ * GPL-v2-or-later
+ *
+ * Any future contributions to this file after December 1st 2014 will be
+ * taken to be licensed under the Softfloat-2a license unless specifically
+ * indicated otherwise.
+ */
+
+/*
+===============================================================================
+This C source fragment is part of the SoftFloat IEC/IEEE Floating-point
+Arithmetic Package, Release 2a.
+
+Written by John R. Hauser. This work was made possible in part by the
+International Computer Science Institute, located at Suite 600, 1947 Center
+Street, Berkeley, California 94704. Funding was partially provided by the
+National Science Foundation under grant MIP-9311980. The original version
+of this code was written as part of a project to build a fixed-point vector
+processor in collaboration with the University of California at Berkeley,
+overseen by Profs. Nelson Morgan and John Wawrzynek. More information
+is available through the Web page `http://HTTP.CS.Berkeley.EDU/~jhauser/
+arithmetic/SoftFloat.html'.
+
+THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort
+has been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT
+TIMES RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO
+PERSONS AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ANY
+AND ALL LOSSES, COSTS, OR OTHER PROBLEMS ARISING FROM ITS USE.
+
+Derivative works are acceptable, even for commercial purposes, so long as
+(1) they include prominent notice that the work is derivative, and (2) they
+include prominent notice akin to these four paragraphs for those parts of
+this code that are retained.
+
+===============================================================================
+*/
+
+/* BSD licensing:
+ * Copyright (c) 2006, Fabrice Bellard
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright notice,
+ * this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright notice,
+ * this list of conditions and the following disclaimer in the documentation
+ * and/or other materials provided with the distribution.
+ *
+ * 3. Neither the name of the copyright holder nor the names of its contributors
+ * may be used to endorse or promote products derived from this software without
+ * specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+ * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
+ * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+ * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+ * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+ * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+ * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+ * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
+ * THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+/* Portions of this work are licensed under the terms of the GNU GPL,
+ * version 2 or later. See the COPYING file in the top-level directory.
+ */
+
+/*----------------------------------------------------------------------------
+| This macro tests for minimum version of the GNU C compiler.
+*----------------------------------------------------------------------------*/
+#if defined(__GNUC__) && defined(__GNUC_MINOR__)
+# define SOFTFLOAT_GNUC_PREREQ(maj, min) \
+ ((__GNUC__ << 16) + __GNUC_MINOR__ >= ((maj) << 16) + (min))
+#else
+# define SOFTFLOAT_GNUC_PREREQ(maj, min) 0
+#endif
+
+
+/*----------------------------------------------------------------------------
+| Shifts `a' right by the number of bits given in `count'. If any nonzero
+| bits are shifted off, they are ``jammed'' into the least significant bit of
+| the result by setting the least significant bit to 1. The value of `count'
+| can be arbitrarily large; in particular, if `count' is greater than 32, the
+| result will be either 0 or 1, depending on whether `a' is zero or nonzero.
+| The result is stored in the location pointed to by `zPtr'.
+*----------------------------------------------------------------------------*/
+
+static inline void shift32RightJamming(uint32_t a, int count, uint32_t *zPtr)
+{
+ uint32_t z;
+
+ if ( count == 0 ) {
+ z = a;
+ }
+ else if ( count < 32 ) {
+ z = ( a>>count ) | ( ( a<<( ( - count ) & 31 ) ) != 0 );
+ }
+ else {
+ z = ( a != 0 );
+ }
+ *zPtr = z;
+
+}
+
+/*----------------------------------------------------------------------------
+| Shifts `a' right by the number of bits given in `count'. If any nonzero
+| bits are shifted off, they are ``jammed'' into the least significant bit of
+| the result by setting the least significant bit to 1. The value of `count'
+| can be arbitrarily large; in particular, if `count' is greater than 64, the
+| result will be either 0 or 1, depending on whether `a' is zero or nonzero.
+| The result is stored in the location pointed to by `zPtr'.
+*----------------------------------------------------------------------------*/
+
+static inline void shift64RightJamming(uint64_t a, int count, uint64_t *zPtr)
+{
+ uint64_t z;
+
+ if ( count == 0 ) {
+ z = a;
+ }
+ else if ( count < 64 ) {
+ z = ( a>>count ) | ( ( a<<( ( - count ) & 63 ) ) != 0 );
+ }
+ else {
+ z = ( a != 0 );
+ }
+ *zPtr = z;
+
+}
+
+/*----------------------------------------------------------------------------
+| Shifts the 128-bit value formed by concatenating `a0' and `a1' right by 64
+| _plus_ the number of bits given in `count'. The shifted result is at most
+| 64 nonzero bits; this is stored at the location pointed to by `z0Ptr'. The
+| bits shifted off form a second 64-bit result as follows: The _last_ bit
+| shifted off is the most-significant bit of the extra result, and the other
+| 63 bits of the extra result are all zero if and only if _all_but_the_last_
+| bits shifted off were all zero. This extra result is stored in the location
+| pointed to by `z1Ptr'. The value of `count' can be arbitrarily large.
+| (This routine makes more sense if `a0' and `a1' are considered to form a
+| fixed-point value with binary point between `a0' and `a1'. This fixed-point
+| value is shifted right by the number of bits given in `count', and the
+| integer part of the result is returned at the location pointed to by
+| `z0Ptr'. The fractional part of the result may be slightly corrupted as
+| described above, and is returned at the location pointed to by `z1Ptr'.)
+*----------------------------------------------------------------------------*/
+
+static inline void
+ shift64ExtraRightJamming(
+ uint64_t a0, uint64_t a1, int count, uint64_t *z0Ptr, uint64_t *z1Ptr)
+{
+ uint64_t z0, z1;
+ int8_t negCount = ( - count ) & 63;
+
+ if ( count == 0 ) {
+ z1 = a1;
+ z0 = a0;
+ }
+ else if ( count < 64 ) {
+ z1 = ( a0<<negCount ) | ( a1 != 0 );
+ z0 = a0>>count;
+ }
+ else {
+ if ( count == 64 ) {
+ z1 = a0 | ( a1 != 0 );
+ }
+ else {
+ z1 = ( ( a0 | a1 ) != 0 );
+ }
+ z0 = 0;
+ }
+ *z1Ptr = z1;
+ *z0Ptr = z0;
+
+}
+
+/*----------------------------------------------------------------------------
+| Shifts the 128-bit value formed by concatenating `a0' and `a1' right by the
+| number of bits given in `count'. Any bits shifted off are lost. The value
+| of `count' can be arbitrarily large; in particular, if `count' is greater
+| than 128, the result will be 0. The result is broken into two 64-bit pieces
+| which are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
+*----------------------------------------------------------------------------*/
+
+static inline void
+ shift128Right(
+ uint64_t a0, uint64_t a1, int count, uint64_t *z0Ptr, uint64_t *z1Ptr)
+{
+ uint64_t z0, z1;
+ int8_t negCount = ( - count ) & 63;
+
+ if ( count == 0 ) {
+ z1 = a1;
+ z0 = a0;
+ }
+ else if ( count < 64 ) {
+ z1 = ( a0<<negCount ) | ( a1>>count );
+ z0 = a0>>count;
+ }
+ else {
+ z1 = (count < 128) ? (a0 >> (count & 63)) : 0;
+ z0 = 0;
+ }
+ *z1Ptr = z1;
+ *z0Ptr = z0;
+
+}
+
+/*----------------------------------------------------------------------------
+| Shifts the 128-bit value formed by concatenating `a0' and `a1' right by the
+| number of bits given in `count'. If any nonzero bits are shifted off, they
+| are ``jammed'' into the least significant bit of the result by setting the
+| least significant bit to 1. The value of `count' can be arbitrarily large;
+| in particular, if `count' is greater than 128, the result will be either
+| 0 or 1, depending on whether the concatenation of `a0' and `a1' is zero or
+| nonzero. The result is broken into two 64-bit pieces which are stored at
+| the locations pointed to by `z0Ptr' and `z1Ptr'.
+*----------------------------------------------------------------------------*/
+
+static inline void
+ shift128RightJamming(
+ uint64_t a0, uint64_t a1, int count, uint64_t *z0Ptr, uint64_t *z1Ptr)
+{
+ uint64_t z0, z1;
+ int8_t negCount = ( - count ) & 63;
+
+ if ( count == 0 ) {
+ z1 = a1;
+ z0 = a0;
+ }
+ else if ( count < 64 ) {
+ z1 = ( a0<<negCount ) | ( a1>>count ) | ( ( a1<<negCount ) != 0 );
+ z0 = a0>>count;
+ }
+ else {
+ if ( count == 64 ) {
+ z1 = a0 | ( a1 != 0 );
+ }
+ else if ( count < 128 ) {
+ z1 = ( a0>>( count & 63 ) ) | ( ( ( a0<<negCount ) | a1 ) != 0 );
+ }
+ else {
+ z1 = ( ( a0 | a1 ) != 0 );
+ }
+ z0 = 0;
+ }
+ *z1Ptr = z1;
+ *z0Ptr = z0;
+
+}
+
+/*----------------------------------------------------------------------------
+| Shifts the 192-bit value formed by concatenating `a0', `a1', and `a2' right
+| by 64 _plus_ the number of bits given in `count'. The shifted result is
+| at most 128 nonzero bits; these are broken into two 64-bit pieces which are
+| stored at the locations pointed to by `z0Ptr' and `z1Ptr'. The bits shifted
+| off form a third 64-bit result as follows: The _last_ bit shifted off is
+| the most-significant bit of the extra result, and the other 63 bits of the
+| extra result are all zero if and only if _all_but_the_last_ bits shifted off
+| were all zero. This extra result is stored in the location pointed to by
+| `z2Ptr'. The value of `count' can be arbitrarily large.
+| (This routine makes more sense if `a0', `a1', and `a2' are considered
+| to form a fixed-point value with binary point between `a1' and `a2'. This
+| fixed-point value is shifted right by the number of bits given in `count',
+| and the integer part of the result is returned at the locations pointed to
+| by `z0Ptr' and `z1Ptr'. The fractional part of the result may be slightly
+| corrupted as described above, and is returned at the location pointed to by
+| `z2Ptr'.)
+*----------------------------------------------------------------------------*/
+
+static inline void
+ shift128ExtraRightJamming(
+ uint64_t a0,
+ uint64_t a1,
+ uint64_t a2,
+ int count,
+ uint64_t *z0Ptr,
+ uint64_t *z1Ptr,
+ uint64_t *z2Ptr
+ )
+{
+ uint64_t z0, z1, z2;
+ int8_t negCount = ( - count ) & 63;
+
+ if ( count == 0 ) {
+ z2 = a2;
+ z1 = a1;
+ z0 = a0;
+ }
+ else {
+ if ( count < 64 ) {
+ z2 = a1<<negCount;
+ z1 = ( a0<<negCount ) | ( a1>>count );
+ z0 = a0>>count;
+ }
+ else {
+ if ( count == 64 ) {
+ z2 = a1;
+ z1 = a0;
+ }
+ else {
+ a2 |= a1;
+ if ( count < 128 ) {
+ z2 = a0<<negCount;
+ z1 = a0>>( count & 63 );
+ }
+ else {
+ z2 = ( count == 128 ) ? a0 : ( a0 != 0 );
+ z1 = 0;
+ }
+ }
+ z0 = 0;
+ }
+ z2 |= ( a2 != 0 );
+ }
+ *z2Ptr = z2;
+ *z1Ptr = z1;
+ *z0Ptr = z0;
+
+}
+
+/*----------------------------------------------------------------------------
+| Shifts the 128-bit value formed by concatenating `a0' and `a1' left by the
+| number of bits given in `count'. Any bits shifted off are lost. The value
+| of `count' must be less than 64. The result is broken into two 64-bit
+| pieces which are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
+*----------------------------------------------------------------------------*/
+
+static inline void
+ shortShift128Left(
+ uint64_t a0, uint64_t a1, int count, uint64_t *z0Ptr, uint64_t *z1Ptr)
+{
+
+ *z1Ptr = a1<<count;
+ *z0Ptr =
+ ( count == 0 ) ? a0 : ( a0<<count ) | ( a1>>( ( - count ) & 63 ) );
+
+}
+
+/*----------------------------------------------------------------------------
+| Shifts the 192-bit value formed by concatenating `a0', `a1', and `a2' left
+| by the number of bits given in `count'. Any bits shifted off are lost.
+| The value of `count' must be less than 64. The result is broken into three
+| 64-bit pieces which are stored at the locations pointed to by `z0Ptr',
+| `z1Ptr', and `z2Ptr'.
+*----------------------------------------------------------------------------*/
+
+static inline void
+ shortShift192Left(
+ uint64_t a0,
+ uint64_t a1,
+ uint64_t a2,
+ int count,
+ uint64_t *z0Ptr,
+ uint64_t *z1Ptr,
+ uint64_t *z2Ptr
+ )
+{
+ uint64_t z0, z1, z2;
+ int8_t negCount;
+
+ z2 = a2<<count;
+ z1 = a1<<count;
+ z0 = a0<<count;
+ if ( 0 < count ) {
+ negCount = ( ( - count ) & 63 );
+ z1 |= a2>>negCount;
+ z0 |= a1>>negCount;
+ }
+ *z2Ptr = z2;
+ *z1Ptr = z1;
+ *z0Ptr = z0;
+
+}
+
+/*----------------------------------------------------------------------------
+| Adds the 128-bit value formed by concatenating `a0' and `a1' to the 128-bit
+| value formed by concatenating `b0' and `b1'. Addition is modulo 2^128, so
+| any carry out is lost. The result is broken into two 64-bit pieces which
+| are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
+*----------------------------------------------------------------------------*/
+
+static inline void
+ add128(
+ uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1, uint64_t *z0Ptr, uint64_t *z1Ptr )
+{
+ uint64_t z1;
+
+ z1 = a1 + b1;
+ *z1Ptr = z1;
+ *z0Ptr = a0 + b0 + ( z1 < a1 );
+
+}
+
+/*----------------------------------------------------------------------------
+| Adds the 192-bit value formed by concatenating `a0', `a1', and `a2' to the
+| 192-bit value formed by concatenating `b0', `b1', and `b2'. Addition is
+| modulo 2^192, so any carry out is lost. The result is broken into three
+| 64-bit pieces which are stored at the locations pointed to by `z0Ptr',
+| `z1Ptr', and `z2Ptr'.
+*----------------------------------------------------------------------------*/
+
+static inline void
+ add192(
+ uint64_t a0,
+ uint64_t a1,
+ uint64_t a2,
+ uint64_t b0,
+ uint64_t b1,
+ uint64_t b2,
+ uint64_t *z0Ptr,
+ uint64_t *z1Ptr,
+ uint64_t *z2Ptr
+ )
+{
+ uint64_t z0, z1, z2;
+ int8_t carry0, carry1;
+
+ z2 = a2 + b2;
+ carry1 = ( z2 < a2 );
+ z1 = a1 + b1;
+ carry0 = ( z1 < a1 );
+ z0 = a0 + b0;
+ z1 += carry1;
+ z0 += ( z1 < carry1 );
+ z0 += carry0;
+ *z2Ptr = z2;
+ *z1Ptr = z1;
+ *z0Ptr = z0;
+
+}
+
+/*----------------------------------------------------------------------------
+| Subtracts the 128-bit value formed by concatenating `b0' and `b1' from the
+| 128-bit value formed by concatenating `a0' and `a1'. Subtraction is modulo
+| 2^128, so any borrow out (carry out) is lost. The result is broken into two
+| 64-bit pieces which are stored at the locations pointed to by `z0Ptr' and
+| `z1Ptr'.
+*----------------------------------------------------------------------------*/
+
+static inline void
+ sub128(
+ uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1, uint64_t *z0Ptr, uint64_t *z1Ptr )
+{
+
+ *z1Ptr = a1 - b1;
+ *z0Ptr = a0 - b0 - ( a1 < b1 );
+
+}
+
+/*----------------------------------------------------------------------------
+| Subtracts the 192-bit value formed by concatenating `b0', `b1', and `b2'
+| from the 192-bit value formed by concatenating `a0', `a1', and `a2'.
+| Subtraction is modulo 2^192, so any borrow out (carry out) is lost. The
+| result is broken into three 64-bit pieces which are stored at the locations
+| pointed to by `z0Ptr', `z1Ptr', and `z2Ptr'.
+*----------------------------------------------------------------------------*/
+
+static inline void
+ sub192(
+ uint64_t a0,
+ uint64_t a1,
+ uint64_t a2,
+ uint64_t b0,
+ uint64_t b1,
+ uint64_t b2,
+ uint64_t *z0Ptr,
+ uint64_t *z1Ptr,
+ uint64_t *z2Ptr
+ )
+{
+ uint64_t z0, z1, z2;
+ int8_t borrow0, borrow1;
+
+ z2 = a2 - b2;
+ borrow1 = ( a2 < b2 );
+ z1 = a1 - b1;
+ borrow0 = ( a1 < b1 );
+ z0 = a0 - b0;
+ z0 -= ( z1 < borrow1 );
+ z1 -= borrow1;
+ z0 -= borrow0;
+ *z2Ptr = z2;
+ *z1Ptr = z1;
+ *z0Ptr = z0;
+
+}
+
+/*----------------------------------------------------------------------------
+| Multiplies `a' by `b' to obtain a 128-bit product. The product is broken
+| into two 64-bit pieces which are stored at the locations pointed to by
+| `z0Ptr' and `z1Ptr'.
+*----------------------------------------------------------------------------*/
+
+static inline void mul64To128( uint64_t a, uint64_t b, uint64_t *z0Ptr, uint64_t *z1Ptr )
+{
+ uint32_t aHigh, aLow, bHigh, bLow;
+ uint64_t z0, zMiddleA, zMiddleB, z1;
+
+ aLow = a;
+ aHigh = a>>32;
+ bLow = b;
+ bHigh = b>>32;
+ z1 = ( (uint64_t) aLow ) * bLow;
+ zMiddleA = ( (uint64_t) aLow ) * bHigh;
+ zMiddleB = ( (uint64_t) aHigh ) * bLow;
+ z0 = ( (uint64_t) aHigh ) * bHigh;
+ zMiddleA += zMiddleB;
+ z0 += ( ( (uint64_t) ( zMiddleA < zMiddleB ) )<<32 ) + ( zMiddleA>>32 );
+ zMiddleA <<= 32;
+ z1 += zMiddleA;
+ z0 += ( z1 < zMiddleA );
+ *z1Ptr = z1;
+ *z0Ptr = z0;
+
+}
+
+/*----------------------------------------------------------------------------
+| Multiplies the 128-bit value formed by concatenating `a0' and `a1' by
+| `b' to obtain a 192-bit product. The product is broken into three 64-bit
+| pieces which are stored at the locations pointed to by `z0Ptr', `z1Ptr', and
+| `z2Ptr'.
+*----------------------------------------------------------------------------*/
+
+static inline void
+ mul128By64To192(
+ uint64_t a0,
+ uint64_t a1,
+ uint64_t b,
+ uint64_t *z0Ptr,
+ uint64_t *z1Ptr,
+ uint64_t *z2Ptr
+ )
+{
+ uint64_t z0, z1, z2, more1;
+
+ mul64To128( a1, b, &z1, &z2 );
+ mul64To128( a0, b, &z0, &more1 );
+ add128( z0, more1, 0, z1, &z0, &z1 );
+ *z2Ptr = z2;
+ *z1Ptr = z1;
+ *z0Ptr = z0;
+
+}
+
+/*----------------------------------------------------------------------------
+| Multiplies the 128-bit value formed by concatenating `a0' and `a1' to the
+| 128-bit value formed by concatenating `b0' and `b1' to obtain a 256-bit
+| product. The product is broken into four 64-bit pieces which are stored at
+| the locations pointed to by `z0Ptr', `z1Ptr', `z2Ptr', and `z3Ptr'.
+*----------------------------------------------------------------------------*/
+
+static inline void
+ mul128To256(
+ uint64_t a0,
+ uint64_t a1,
+ uint64_t b0,
+ uint64_t b1,
+ uint64_t *z0Ptr,
+ uint64_t *z1Ptr,
+ uint64_t *z2Ptr,
+ uint64_t *z3Ptr
+ )
+{
+ uint64_t z0, z1, z2, z3;
+ uint64_t more1, more2;
+
+ mul64To128( a1, b1, &z2, &z3 );
+ mul64To128( a1, b0, &z1, &more2 );
+ add128( z1, more2, 0, z2, &z1, &z2 );
+ mul64To128( a0, b0, &z0, &more1 );
+ add128( z0, more1, 0, z1, &z0, &z1 );
+ mul64To128( a0, b1, &more1, &more2 );
+ add128( more1, more2, 0, z2, &more1, &z2 );
+ add128( z0, z1, 0, more1, &z0, &z1 );
+ *z3Ptr = z3;
+ *z2Ptr = z2;
+ *z1Ptr = z1;
+ *z0Ptr = z0;
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns an approximation to the 64-bit integer quotient obtained by dividing
+| `b' into the 128-bit value formed by concatenating `a0' and `a1'. The
+| divisor `b' must be at least 2^63. If q is the exact quotient truncated
+| toward zero, the approximation returned lies between q and q + 2 inclusive.
+| If the exact quotient q is larger than 64 bits, the maximum positive 64-bit
+| unsigned integer is returned.
+*----------------------------------------------------------------------------*/
+
+static inline uint64_t estimateDiv128To64(uint64_t a0, uint64_t a1, uint64_t b)
+{
+ uint64_t b0, b1;
+ uint64_t rem0, rem1, term0, term1;
+ uint64_t z;
+
+ if ( b <= a0 ) return LIT64( 0xFFFFFFFFFFFFFFFF );
+ b0 = b>>32;
+ z = ( b0<<32 <= a0 ) ? LIT64( 0xFFFFFFFF00000000 ) : ( a0 / b0 )<<32;
+ mul64To128( b, z, &term0, &term1 );
+ sub128( a0, a1, term0, term1, &rem0, &rem1 );
+ while ( ( (int64_t) rem0 ) < 0 ) {
+ z -= LIT64( 0x100000000 );
+ b1 = b<<32;
+ add128( rem0, rem1, b0, b1, &rem0, &rem1 );
+ }
+ rem0 = ( rem0<<32 ) | ( rem1>>32 );
+ z |= ( b0<<32 <= rem0 ) ? 0xFFFFFFFF : rem0 / b0;
+ return z;
+
+}
+
+/* From the GNU Multi Precision Library - longlong.h __udiv_qrnnd
+ * (https://gmplib.org/repo/gmp/file/tip/longlong.h)
+ *
+ * Licensed under the GPLv2/LGPLv3
+ */
+static inline uint64_t div128To64(uint64_t n0, uint64_t n1, uint64_t d)
+{
+ uint64_t d0, d1, q0, q1, r1, r0, m;
+
+ d0 = (uint32_t)d;
+ d1 = d >> 32;
+
+ r1 = n1 % d1;
+ q1 = n1 / d1;
+ m = q1 * d0;
+ r1 = (r1 << 32) | (n0 >> 32);
+ if (r1 < m) {
+ q1 -= 1;
+ r1 += d;
+ if (r1 >= d) {
+ if (r1 < m) {
+ q1 -= 1;
+ r1 += d;
+ }
+ }
+ }
+ r1 -= m;
+
+ r0 = r1 % d1;
+ q0 = r1 / d1;
+ m = q0 * d0;
+ r0 = (r0 << 32) | (uint32_t)n0;
+ if (r0 < m) {
+ q0 -= 1;
+ r0 += d;
+ if (r0 >= d) {
+ if (r0 < m) {
+ q0 -= 1;
+ r0 += d;
+ }
+ }
+ }
+ r0 -= m;
+
+ /* Return remainder in LSB */
+ return (q1 << 32) | q0 | (r0 != 0);
+}
+
+/*----------------------------------------------------------------------------
+| Returns an approximation to the square root of the 32-bit significand given
+| by `a'. Considered as an integer, `a' must be at least 2^31. If bit 0 of
+| `aExp' (the least significant bit) is 1, the integer returned approximates
+| 2^31*sqrt(`a'/2^31), where `a' is considered an integer. If bit 0 of `aExp'
+| is 0, the integer returned approximates 2^31*sqrt(`a'/2^30). In either
+| case, the approximation returned lies strictly within +/-2 of the exact
+| value.
+*----------------------------------------------------------------------------*/
+
+static inline uint32_t estimateSqrt32(int aExp, uint32_t a)
+{
+ static const uint16_t sqrtOddAdjustments[] = {
+ 0x0004, 0x0022, 0x005D, 0x00B1, 0x011D, 0x019F, 0x0236, 0x02E0,
+ 0x039C, 0x0468, 0x0545, 0x0631, 0x072B, 0x0832, 0x0946, 0x0A67
+ };
+ static const uint16_t sqrtEvenAdjustments[] = {
+ 0x0A2D, 0x08AF, 0x075A, 0x0629, 0x051A, 0x0429, 0x0356, 0x029E,
+ 0x0200, 0x0179, 0x0109, 0x00AF, 0x0068, 0x0034, 0x0012, 0x0002
+ };
+ int8_t index;
+ uint32_t z;
+
+ index = ( a>>27 ) & 15;
+ if ( aExp & 1 ) {
+ z = 0x4000 + ( a>>17 ) - sqrtOddAdjustments[ (int)index ];
+ z = ( ( a / z )<<14 ) + ( z<<15 );
+ a >>= 1;
+ }
+ else {
+ z = 0x8000 + ( a>>17 ) - sqrtEvenAdjustments[ (int)index ];
+ z = a / z + z;
+ z = ( 0x20000 <= z ) ? 0xFFFF8000 : ( z<<15 );
+ if ( z <= a ) return (uint32_t) ( ( (int32_t) a )>>1 );
+ }
+ return ( (uint32_t) ( ( ( (uint64_t) a )<<31 ) / z ) ) + ( z>>1 );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns the number of leading 0 bits before the most-significant 1 bit of
+| `a'. If `a' is zero, 32 is returned.
+*----------------------------------------------------------------------------*/
+
+static inline int8_t countLeadingZeros32(uint32_t a)
+{
+#if SOFTFLOAT_GNUC_PREREQ(3, 4)
+ if (a) {
+ return __builtin_clz(a);
+ } else {
+ return 32;
+ }
+#else
+ static const int8_t countLeadingZerosHigh[] = {
+ 8, 7, 6, 6, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4,
+ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
+ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
+ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
+ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
+ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
+ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
+ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
+ };
+ int8_t shiftCount;
+
+ shiftCount = 0;
+ if ( a < 0x10000 ) {
+ shiftCount += 16;
+ a <<= 16;
+ }
+ if ( a < 0x1000000 ) {
+ shiftCount += 8;
+ a <<= 8;
+ }
+ shiftCount += countLeadingZerosHigh[ a>>24 ];
+ return shiftCount;
+#endif
+}
+
+/*----------------------------------------------------------------------------
+| Returns the number of leading 0 bits before the most-significant 1 bit of
+| `a'. If `a' is zero, 64 is returned.
+*----------------------------------------------------------------------------*/
+
+static inline int8_t countLeadingZeros64(uint64_t a)
+{
+#if SOFTFLOAT_GNUC_PREREQ(3, 4)
+ if (a) {
+ return __builtin_clzll(a);
+ } else {
+ return 64;
+ }
+#else
+ int8_t shiftCount;
+
+ shiftCount = 0;
+ if ( a < ( (uint64_t) 1 )<<32 ) {
+ shiftCount += 32;
+ }
+ else {
+ a >>= 32;
+ }
+ shiftCount += countLeadingZeros32( a );
+ return shiftCount;
+#endif
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the 128-bit value formed by concatenating `a0' and `a1'
+| is equal to the 128-bit value formed by concatenating `b0' and `b1'.
+| Otherwise, returns 0.
+*----------------------------------------------------------------------------*/
+
+static inline flag eq128( uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1 )
+{
+
+ return ( a0 == b0 ) && ( a1 == b1 );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is less
+| than or equal to the 128-bit value formed by concatenating `b0' and `b1'.
+| Otherwise, returns 0.
+*----------------------------------------------------------------------------*/
+
+static inline flag le128( uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1 )
+{
+
+ return ( a0 < b0 ) || ( ( a0 == b0 ) && ( a1 <= b1 ) );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is less
+| than the 128-bit value formed by concatenating `b0' and `b1'. Otherwise,
+| returns 0.
+*----------------------------------------------------------------------------*/
+
+static inline flag lt128( uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1 )
+{
+
+ return ( a0 < b0 ) || ( ( a0 == b0 ) && ( a1 < b1 ) );
+
+}
+
+/*----------------------------------------------------------------------------
+| Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is
+| not equal to the 128-bit value formed by concatenating `b0' and `b1'.
+| Otherwise, returns 0.
+*----------------------------------------------------------------------------*/
+
+static inline flag ne128( uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1 )
+{
+
+ return ( a0 != b0 ) || ( a1 != b1 );
+
+}
#define float32_three make_float32(0x40400000)
#define float32_infinity make_float32(0x7f800000)
+/*----------------------------------------------------------------------------
+| 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.
+*----------------------------------------------------------------------------*/
+
+static inline float32 packFloat32(flag zSign, int zExp, uint32_t zSig)
+{
+ return make_float32(
+ (((uint32_t)zSign) << 31) + (((uint32_t)zExp) << 23) + zSig);
+}
+
/*----------------------------------------------------------------------------
| The pattern for a default generated single-precision NaN.
*----------------------------------------------------------------------------*/
#define floatx80_half make_floatx80(0x3ffe, 0x8000000000000000LL)
#define floatx80_infinity make_floatx80(0x7fff, 0x8000000000000000LL)
+/*----------------------------------------------------------------------------
+| Returns the fraction bits of the extended double-precision floating-point
+| value `a'.
+*----------------------------------------------------------------------------*/
+
+static inline uint64_t extractFloatx80Frac(floatx80 a)
+{
+ return a.low;
+}
+
+/*----------------------------------------------------------------------------
+| Returns the exponent bits of the extended double-precision floating-point
+| value `a'.
+*----------------------------------------------------------------------------*/
+
+static inline int32_t extractFloatx80Exp(floatx80 a)
+{
+ return a.high & 0x7FFF;
+}
+
+/*----------------------------------------------------------------------------
+| Returns the sign bit of the extended double-precision floating-point value
+| `a'.
+*----------------------------------------------------------------------------*/
+
+static inline flag extractFloatx80Sign(floatx80 a)
+{
+ return a.high >> 15;
+}
+
+/*----------------------------------------------------------------------------
+| Packs the sign `zSign', exponent `zExp', and significand `zSig' into an
+| extended double-precision floating-point value, returning the result.
+*----------------------------------------------------------------------------*/
+
+static inline floatx80 packFloatx80(flag zSign, int32_t zExp, uint64_t zSig)
+{
+ floatx80 z;
+
+ z.low = zSig;
+ z.high = (((uint16_t)zSign) << 15) + zExp;
+ return z;
+}
+
+/*----------------------------------------------------------------------------
+| 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.
+*----------------------------------------------------------------------------*/
+
+void normalizeFloatx80Subnormal(uint64_t aSig, int32_t *zExpPtr,
+ uint64_t *zSigPtr);
+
+/*----------------------------------------------------------------------------
+| 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.
+*----------------------------------------------------------------------------*/
+
+floatx80 propagateFloatx80NaN(floatx80 a, floatx80 b, float_status *status);
+
+/*----------------------------------------------------------------------------
+| 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.
+*----------------------------------------------------------------------------*/
+
+floatx80 roundAndPackFloatx80(int8_t roundingPrecision, flag zSign,
+ int32_t zExp, uint64_t zSig0, uint64_t zSig1,
+ float_status *status);
+
+/*----------------------------------------------------------------------------
+| 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.
+*----------------------------------------------------------------------------*/
+
+floatx80 normalizeRoundAndPackFloatx80(int8_t roundingPrecision,
+ flag zSign, int32_t zExp,
+ uint64_t zSig0, uint64_t zSig1,
+ float_status *status);
+
/*----------------------------------------------------------------------------
| The pattern for a default generated extended double-precision NaN.
*----------------------------------------------------------------------------*/
projects / qemu.git / commitdiff