cf07323d49
We can now add float16_div and use the common decompose and canonicalize functions to have a single implementation for float16/32/64 versions. Signed-off-by: Alex Bennée <alex.bennee@linaro.org> Signed-off-by: Richard Henderson <richard.henderson@linaro.org> Reviewed-by: Peter Maydell <peter.maydell@linaro.org>
842 lines
28 KiB
C
842 lines
28 KiB
C
/*
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* QEMU float support macros
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*
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* The code in this source file is derived from release 2a of the SoftFloat
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* IEC/IEEE Floating-point Arithmetic Package. Those parts of the code (and
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* some later contributions) are provided under that license, as detailed below.
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* It has subsequently been modified by contributors to the QEMU Project,
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* so some portions are provided under:
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* the SoftFloat-2a license
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* the BSD license
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* GPL-v2-or-later
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*
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* Any future contributions to this file after December 1st 2014 will be
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* taken to be licensed under the Softfloat-2a license unless specifically
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* indicated otherwise.
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*/
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/*
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===============================================================================
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This C source fragment is part of the SoftFloat IEC/IEEE Floating-point
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Arithmetic Package, Release 2a.
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Written by John R. Hauser. This work was made possible in part by the
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International Computer Science Institute, located at Suite 600, 1947 Center
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Street, Berkeley, California 94704. Funding was partially provided by the
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National Science Foundation under grant MIP-9311980. The original version
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of this code was written as part of a project to build a fixed-point vector
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processor in collaboration with the University of California at Berkeley,
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overseen by Profs. Nelson Morgan and John Wawrzynek. More information
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is available through the Web page `http://HTTP.CS.Berkeley.EDU/~jhauser/
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arithmetic/SoftFloat.html'.
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THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort
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has been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT
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TIMES RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO
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PERSONS AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ANY
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AND ALL LOSSES, COSTS, OR OTHER PROBLEMS ARISING FROM ITS USE.
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Derivative works are acceptable, even for commercial purposes, so long as
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(1) they include prominent notice that the work is derivative, and (2) they
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include prominent notice akin to these four paragraphs for those parts of
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this code that are retained.
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===============================================================================
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*/
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/* BSD licensing:
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* Copyright (c) 2006, Fabrice Bellard
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions are met:
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*
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* 1. Redistributions of source code must retain the above copyright notice,
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* this list of conditions and the following disclaimer.
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*
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* 2. Redistributions in binary form must reproduce the above copyright notice,
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* this list of conditions and the following disclaimer in the documentation
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* and/or other materials provided with the distribution.
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*
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* 3. Neither the name of the copyright holder nor the names of its contributors
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* may be used to endorse or promote products derived from this software without
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* specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
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* LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
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* THE POSSIBILITY OF SUCH DAMAGE.
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*/
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/* Portions of this work are licensed under the terms of the GNU GPL,
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* version 2 or later. See the COPYING file in the top-level directory.
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*/
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/*----------------------------------------------------------------------------
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| This macro tests for minimum version of the GNU C compiler.
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*----------------------------------------------------------------------------*/
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#if defined(__GNUC__) && defined(__GNUC_MINOR__)
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# define SOFTFLOAT_GNUC_PREREQ(maj, min) \
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((__GNUC__ << 16) + __GNUC_MINOR__ >= ((maj) << 16) + (min))
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#else
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# define SOFTFLOAT_GNUC_PREREQ(maj, min) 0
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#endif
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/*----------------------------------------------------------------------------
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| Shifts `a' right by the number of bits given in `count'. If any nonzero
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| bits are shifted off, they are ``jammed'' into the least significant bit of
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| the result by setting the least significant bit to 1. The value of `count'
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| can be arbitrarily large; in particular, if `count' is greater than 32, the
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| result will be either 0 or 1, depending on whether `a' is zero or nonzero.
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| The result is stored in the location pointed to by `zPtr'.
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*----------------------------------------------------------------------------*/
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static inline void shift32RightJamming(uint32_t a, int count, uint32_t *zPtr)
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{
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uint32_t z;
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if ( count == 0 ) {
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z = a;
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}
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else if ( count < 32 ) {
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z = ( a>>count ) | ( ( a<<( ( - count ) & 31 ) ) != 0 );
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}
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else {
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z = ( a != 0 );
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}
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*zPtr = z;
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}
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/*----------------------------------------------------------------------------
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| Shifts `a' right by the number of bits given in `count'. If any nonzero
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| bits are shifted off, they are ``jammed'' into the least significant bit of
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| the result by setting the least significant bit to 1. The value of `count'
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| can be arbitrarily large; in particular, if `count' is greater than 64, the
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| result will be either 0 or 1, depending on whether `a' is zero or nonzero.
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| The result is stored in the location pointed to by `zPtr'.
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*----------------------------------------------------------------------------*/
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static inline void shift64RightJamming(uint64_t a, int count, uint64_t *zPtr)
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{
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uint64_t z;
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if ( count == 0 ) {
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z = a;
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}
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else if ( count < 64 ) {
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z = ( a>>count ) | ( ( a<<( ( - count ) & 63 ) ) != 0 );
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}
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else {
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z = ( a != 0 );
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}
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*zPtr = z;
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}
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/*----------------------------------------------------------------------------
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| Shifts the 128-bit value formed by concatenating `a0' and `a1' right by 64
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| _plus_ the number of bits given in `count'. The shifted result is at most
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| 64 nonzero bits; this is stored at the location pointed to by `z0Ptr'. The
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| bits shifted off form a second 64-bit result as follows: The _last_ bit
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| shifted off is the most-significant bit of the extra result, and the other
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| 63 bits of the extra result are all zero if and only if _all_but_the_last_
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| bits shifted off were all zero. This extra result is stored in the location
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| pointed to by `z1Ptr'. The value of `count' can be arbitrarily large.
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| (This routine makes more sense if `a0' and `a1' are considered to form a
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| fixed-point value with binary point between `a0' and `a1'. This fixed-point
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| value is shifted right by the number of bits given in `count', and the
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| integer part of the result is returned at the location pointed to by
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| `z0Ptr'. The fractional part of the result may be slightly corrupted as
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| described above, and is returned at the location pointed to by `z1Ptr'.)
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*----------------------------------------------------------------------------*/
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static inline void
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shift64ExtraRightJamming(
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uint64_t a0, uint64_t a1, int count, uint64_t *z0Ptr, uint64_t *z1Ptr)
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{
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uint64_t z0, z1;
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int8_t negCount = ( - count ) & 63;
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if ( count == 0 ) {
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z1 = a1;
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z0 = a0;
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}
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else if ( count < 64 ) {
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z1 = ( a0<<negCount ) | ( a1 != 0 );
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z0 = a0>>count;
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}
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else {
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if ( count == 64 ) {
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z1 = a0 | ( a1 != 0 );
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}
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else {
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z1 = ( ( a0 | a1 ) != 0 );
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}
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z0 = 0;
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}
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*z1Ptr = z1;
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*z0Ptr = z0;
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}
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/*----------------------------------------------------------------------------
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| Shifts the 128-bit value formed by concatenating `a0' and `a1' right by the
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| number of bits given in `count'. Any bits shifted off are lost. The value
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| of `count' can be arbitrarily large; in particular, if `count' is greater
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| than 128, the result will be 0. The result is broken into two 64-bit pieces
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| which are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
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*----------------------------------------------------------------------------*/
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static inline void
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shift128Right(
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uint64_t a0, uint64_t a1, int count, uint64_t *z0Ptr, uint64_t *z1Ptr)
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{
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uint64_t z0, z1;
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int8_t negCount = ( - count ) & 63;
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if ( count == 0 ) {
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z1 = a1;
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z0 = a0;
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}
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else if ( count < 64 ) {
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z1 = ( a0<<negCount ) | ( a1>>count );
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z0 = a0>>count;
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}
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else {
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z1 = (count < 128) ? (a0 >> (count & 63)) : 0;
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z0 = 0;
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}
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*z1Ptr = z1;
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*z0Ptr = z0;
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}
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/*----------------------------------------------------------------------------
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| Shifts the 128-bit value formed by concatenating `a0' and `a1' right by the
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| number of bits given in `count'. If any nonzero bits are shifted off, they
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| are ``jammed'' into the least significant bit of the result by setting the
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| least significant bit to 1. The value of `count' can be arbitrarily large;
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| in particular, if `count' is greater than 128, the result will be either
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| 0 or 1, depending on whether the concatenation of `a0' and `a1' is zero or
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| nonzero. The result is broken into two 64-bit pieces which are stored at
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| the locations pointed to by `z0Ptr' and `z1Ptr'.
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*----------------------------------------------------------------------------*/
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static inline void
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shift128RightJamming(
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uint64_t a0, uint64_t a1, int count, uint64_t *z0Ptr, uint64_t *z1Ptr)
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{
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uint64_t z0, z1;
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int8_t negCount = ( - count ) & 63;
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if ( count == 0 ) {
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z1 = a1;
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z0 = a0;
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}
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else if ( count < 64 ) {
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z1 = ( a0<<negCount ) | ( a1>>count ) | ( ( a1<<negCount ) != 0 );
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z0 = a0>>count;
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}
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else {
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if ( count == 64 ) {
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z1 = a0 | ( a1 != 0 );
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}
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else if ( count < 128 ) {
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z1 = ( a0>>( count & 63 ) ) | ( ( ( a0<<negCount ) | a1 ) != 0 );
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}
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else {
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z1 = ( ( a0 | a1 ) != 0 );
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}
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z0 = 0;
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}
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*z1Ptr = z1;
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*z0Ptr = z0;
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}
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/*----------------------------------------------------------------------------
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| Shifts the 192-bit value formed by concatenating `a0', `a1', and `a2' right
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| by 64 _plus_ the number of bits given in `count'. The shifted result is
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| at most 128 nonzero bits; these are broken into two 64-bit pieces which are
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| stored at the locations pointed to by `z0Ptr' and `z1Ptr'. The bits shifted
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| off form a third 64-bit result as follows: The _last_ bit shifted off is
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| the most-significant bit of the extra result, and the other 63 bits of the
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| extra result are all zero if and only if _all_but_the_last_ bits shifted off
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| were all zero. This extra result is stored in the location pointed to by
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| `z2Ptr'. The value of `count' can be arbitrarily large.
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| (This routine makes more sense if `a0', `a1', and `a2' are considered
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| to form a fixed-point value with binary point between `a1' and `a2'. This
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| fixed-point value is shifted right by the number of bits given in `count',
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| and the integer part of the result is returned at the locations pointed to
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| by `z0Ptr' and `z1Ptr'. The fractional part of the result may be slightly
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| corrupted as described above, and is returned at the location pointed to by
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| `z2Ptr'.)
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*----------------------------------------------------------------------------*/
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static inline void
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shift128ExtraRightJamming(
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uint64_t a0,
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uint64_t a1,
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uint64_t a2,
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int count,
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uint64_t *z0Ptr,
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uint64_t *z1Ptr,
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uint64_t *z2Ptr
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)
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{
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uint64_t z0, z1, z2;
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int8_t negCount = ( - count ) & 63;
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if ( count == 0 ) {
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z2 = a2;
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z1 = a1;
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z0 = a0;
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}
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else {
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if ( count < 64 ) {
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z2 = a1<<negCount;
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z1 = ( a0<<negCount ) | ( a1>>count );
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z0 = a0>>count;
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}
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else {
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if ( count == 64 ) {
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z2 = a1;
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z1 = a0;
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}
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else {
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a2 |= a1;
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if ( count < 128 ) {
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z2 = a0<<negCount;
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z1 = a0>>( count & 63 );
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}
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else {
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z2 = ( count == 128 ) ? a0 : ( a0 != 0 );
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z1 = 0;
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}
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}
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z0 = 0;
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}
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z2 |= ( a2 != 0 );
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}
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*z2Ptr = z2;
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*z1Ptr = z1;
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*z0Ptr = z0;
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}
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/*----------------------------------------------------------------------------
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| Shifts the 128-bit value formed by concatenating `a0' and `a1' left by the
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| number of bits given in `count'. Any bits shifted off are lost. The value
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| of `count' must be less than 64. The result is broken into two 64-bit
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| pieces which are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
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*----------------------------------------------------------------------------*/
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static inline void
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shortShift128Left(
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uint64_t a0, uint64_t a1, int count, uint64_t *z0Ptr, uint64_t *z1Ptr)
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{
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*z1Ptr = a1<<count;
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*z0Ptr =
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( count == 0 ) ? a0 : ( a0<<count ) | ( a1>>( ( - count ) & 63 ) );
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}
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/*----------------------------------------------------------------------------
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| Shifts the 192-bit value formed by concatenating `a0', `a1', and `a2' left
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| by the number of bits given in `count'. Any bits shifted off are lost.
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| The value of `count' must be less than 64. The result is broken into three
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| 64-bit pieces which are stored at the locations pointed to by `z0Ptr',
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| `z1Ptr', and `z2Ptr'.
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*----------------------------------------------------------------------------*/
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static inline void
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shortShift192Left(
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uint64_t a0,
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uint64_t a1,
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uint64_t a2,
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int count,
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uint64_t *z0Ptr,
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uint64_t *z1Ptr,
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uint64_t *z2Ptr
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)
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{
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uint64_t z0, z1, z2;
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int8_t negCount;
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z2 = a2<<count;
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z1 = a1<<count;
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z0 = a0<<count;
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if ( 0 < count ) {
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negCount = ( ( - count ) & 63 );
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z1 |= a2>>negCount;
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z0 |= a1>>negCount;
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}
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*z2Ptr = z2;
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*z1Ptr = z1;
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*z0Ptr = z0;
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}
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|
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/*----------------------------------------------------------------------------
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| Adds the 128-bit value formed by concatenating `a0' and `a1' to the 128-bit
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| value formed by concatenating `b0' and `b1'. Addition is modulo 2^128, so
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| any carry out is lost. The result is broken into two 64-bit pieces which
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| are stored at the locations pointed to by `z0Ptr' and `z1Ptr'.
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|
*----------------------------------------------------------------------------*/
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|
|
static inline void
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add128(
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uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1, uint64_t *z0Ptr, uint64_t *z1Ptr )
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{
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uint64_t z1;
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z1 = a1 + b1;
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*z1Ptr = z1;
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*z0Ptr = a0 + b0 + ( z1 < a1 );
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|
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}
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|
|
/*----------------------------------------------------------------------------
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| Adds the 192-bit value formed by concatenating `a0', `a1', and `a2' to the
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| 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
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| 64-bit pieces which are stored at the locations pointed to by `z0Ptr',
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| `z1Ptr', and `z2Ptr'.
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|
*----------------------------------------------------------------------------*/
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|
|
static inline void
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add192(
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uint64_t a0,
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uint64_t a1,
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uint64_t a2,
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uint64_t b0,
|
|
uint64_t b1,
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|
uint64_t b2,
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uint64_t *z0Ptr,
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|
uint64_t *z1Ptr,
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|
uint64_t *z2Ptr
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|
)
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{
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uint64_t z0, z1, z2;
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int8_t carry0, carry1;
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z2 = a2 + b2;
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carry1 = ( z2 < a2 );
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z1 = a1 + b1;
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carry0 = ( z1 < a1 );
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z0 = a0 + b0;
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z1 += carry1;
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z0 += ( z1 < carry1 );
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z0 += carry0;
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*z2Ptr = z2;
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*z1Ptr = z1;
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*z0Ptr = z0;
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|
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}
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|
|
/*----------------------------------------------------------------------------
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| Subtracts the 128-bit value formed by concatenating `b0' and `b1' from the
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| 128-bit value formed by concatenating `a0' and `a1'. Subtraction is modulo
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| 2^128, so any borrow out (carry out) is lost. The result is broken into two
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| 64-bit pieces which are stored at the locations pointed to by `z0Ptr' and
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| `z1Ptr'.
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|
*----------------------------------------------------------------------------*/
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|
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static inline void
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sub128(
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uint64_t a0, uint64_t a1, uint64_t b0, uint64_t b1, uint64_t *z0Ptr, uint64_t *z1Ptr )
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{
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*z1Ptr = a1 - b1;
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*z0Ptr = a0 - b0 - ( a1 < b1 );
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|
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}
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|
|
/*----------------------------------------------------------------------------
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| Subtracts the 192-bit value formed by concatenating `b0', `b1', and `b2'
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| from the 192-bit value formed by concatenating `a0', `a1', and `a2'.
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| Subtraction is modulo 2^192, so any borrow out (carry out) is lost. The
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|
| result is broken into three 64-bit pieces which are stored at the locations
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| pointed to by `z0Ptr', `z1Ptr', and `z2Ptr'.
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|
*----------------------------------------------------------------------------*/
|
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|
|
static inline void
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sub192(
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uint64_t a0,
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uint64_t a1,
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uint64_t a2,
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|
uint64_t b0,
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|
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 );
|
|
|
|
}
|