2c00542c70
Clang v7.0.1 does not like the __int128 variable type for inline
assembly on s390x:
In file included from fpu/softfloat.c:97:
include/fpu/softfloat-macros.h:647:9: error: inline asm error:
This value type register class is not natively supported!
asm("dlgr %0, %1" : "+r"(n) : "r"(d));
^
Disable this code part there now when compiling with Clang, so that
the generic code gets used instead.
Signed-off-by: Thomas Huth <thuth@redhat.com>
Reviewed-by: Richard Henderson <richard.henderson@linaro.org>
Acked-by: Cornelia Huck <cohuck@redhat.com>
Signed-off-by: Alex Bennée <alex.bennee@linaro.org>
799 lines
27 KiB
C
799 lines
27 KiB
C
/*
|
|
* 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.
|
|
*/
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| 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 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' may be greater 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 shift128Left(uint64_t a0, uint64_t a1, int count,
|
|
uint64_t *z0Ptr, uint64_t *z1Ptr)
|
|
{
|
|
if (count < 64) {
|
|
*z1Ptr = a1 << count;
|
|
*z0Ptr = count == 0 ? a0 : (a0 << count) | (a1 >> (-count & 63));
|
|
} else {
|
|
*z1Ptr = 0;
|
|
*z0Ptr = a1 << (count - 64);
|
|
}
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| 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 udiv_qrnnd(uint64_t *r, uint64_t n1,
|
|
uint64_t n0, uint64_t d)
|
|
{
|
|
#if defined(__x86_64__)
|
|
uint64_t q;
|
|
asm("divq %4" : "=a"(q), "=d"(*r) : "0"(n0), "1"(n1), "rm"(d));
|
|
return q;
|
|
#elif defined(__s390x__) && !defined(__clang__)
|
|
/* Need to use a TImode type to get an even register pair for DLGR. */
|
|
unsigned __int128 n = (unsigned __int128)n1 << 64 | n0;
|
|
asm("dlgr %0, %1" : "+r"(n) : "r"(d));
|
|
*r = n >> 64;
|
|
return n;
|
|
#elif defined(_ARCH_PPC64) && defined(_ARCH_PWR7)
|
|
/* From Power ISA 2.06, programming note for divdeu. */
|
|
uint64_t q1, q2, Q, r1, r2, R;
|
|
asm("divdeu %0,%2,%4; divdu %1,%3,%4"
|
|
: "=&r"(q1), "=r"(q2)
|
|
: "r"(n1), "r"(n0), "r"(d));
|
|
r1 = -(q1 * d); /* low part of (n1<<64) - (q1 * d) */
|
|
r2 = n0 - (q2 * d);
|
|
Q = q1 + q2;
|
|
R = r1 + r2;
|
|
if (R >= d || R < r2) { /* overflow implies R > d */
|
|
Q += 1;
|
|
R -= d;
|
|
}
|
|
*r = R;
|
|
return Q;
|
|
#else
|
|
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;
|
|
|
|
*r = r0;
|
|
return (q1 << 32) | q0;
|
|
#endif
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| 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 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 );
|
|
|
|
}
|