mirror of
https://github.com/yuzu-emu/unicorn.git
synced 2024-12-23 04:35:36 +00:00
57d2419cd3
Replace the float128 compare specializations with inline functions
that call the standard float128_compare{,_quiet} functions.
Use bool as the return type.
Backports commit b7b1ac684fea49c6bfe1ad8b706aed7b09116d15 from qemu
7361 lines
244 KiB
C
7361 lines
244 KiB
C
/*
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* QEMU float support
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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 file 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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/* softfloat (and in particular the code in softfloat-specialize.h) is
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* target-dependent and needs the TARGET_* macros.
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*/
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#include "qemu/osdep.h"
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#include <float.h>
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#include <math.h>
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#include "qemu/bitops.h"
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#include "fpu/softfloat.h"
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/* We only need stdlib for abort() */
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/*----------------------------------------------------------------------------
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| Primitive arithmetic functions, including multi-word arithmetic, and
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| division and square root approximations. (Can be specialized to target if
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| desired.)
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*----------------------------------------------------------------------------*/
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#include "fpu/softfloat-macros.h"
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/*
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* Hardfloat
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*
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* Fast emulation of guest FP instructions is challenging for two reasons.
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* First, FP instruction semantics are similar but not identical, particularly
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* when handling NaNs. Second, emulating at reasonable speed the guest FP
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* exception flags is not trivial: reading the host's flags register with a
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* feclearexcept & fetestexcept pair is slow [slightly slower than soft-fp],
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* and trapping on every FP exception is not fast nor pleasant to work with.
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*
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* We address these challenges by leveraging the host FPU for a subset of the
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* operations. To do this we expand on the idea presented in this paper:
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*
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* Guo, Yu-Chuan, et al. "Translating the ARM Neon and VFP instructions in a
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* binary translator." Software: Practice and Experience 46.12 (2016):1591-1615.
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*
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* The idea is thus to leverage the host FPU to (1) compute FP operations
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* and (2) identify whether FP exceptions occurred while avoiding
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* expensive exception flag register accesses.
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*
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* An important optimization shown in the paper is that given that exception
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* flags are rarely cleared by the guest, we can avoid recomputing some flags.
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* This is particularly useful for the inexact flag, which is very frequently
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* raised in floating-point workloads.
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*
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* We optimize the code further by deferring to soft-fp whenever FP exception
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* detection might get hairy. Two examples: (1) when at least one operand is
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* denormal/inf/NaN; (2) when operands are not guaranteed to lead to a 0 result
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* and the result is < the minimum normal.
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*/
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#define GEN_INPUT_FLUSH__NOCHECK(name, soft_t) \
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static inline void name(soft_t *a, float_status *s) \
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{ \
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if (unlikely(soft_t ## _is_denormal(*a))) { \
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*a = soft_t ## _set_sign(soft_t ## _zero, \
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soft_t ## _is_neg(*a)); \
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s->float_exception_flags |= float_flag_input_denormal; \
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} \
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}
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GEN_INPUT_FLUSH__NOCHECK(float32_input_flush__nocheck, float32)
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GEN_INPUT_FLUSH__NOCHECK(float64_input_flush__nocheck, float64)
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#undef GEN_INPUT_FLUSH__NOCHECK
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#define GEN_INPUT_FLUSH1(name, soft_t) \
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static inline void name(soft_t *a, float_status *s) \
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{ \
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if (likely(!s->flush_inputs_to_zero)) { \
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return; \
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} \
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soft_t ## _input_flush__nocheck(a, s); \
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}
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GEN_INPUT_FLUSH1(float32_input_flush1, float32)
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GEN_INPUT_FLUSH1(float64_input_flush1, float64)
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#undef GEN_INPUT_FLUSH1
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#define GEN_INPUT_FLUSH2(name, soft_t) \
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static inline void name(soft_t *a, soft_t *b, float_status *s) \
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{ \
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if (likely(!s->flush_inputs_to_zero)) { \
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return; \
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} \
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soft_t ## _input_flush__nocheck(a, s); \
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soft_t ## _input_flush__nocheck(b, s); \
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}
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GEN_INPUT_FLUSH2(float32_input_flush2, float32)
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GEN_INPUT_FLUSH2(float64_input_flush2, float64)
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#undef GEN_INPUT_FLUSH2
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#define GEN_INPUT_FLUSH3(name, soft_t) \
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static inline void name(soft_t *a, soft_t *b, soft_t *c, float_status *s) \
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{ \
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if (likely(!s->flush_inputs_to_zero)) { \
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return; \
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} \
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soft_t ## _input_flush__nocheck(a, s); \
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soft_t ## _input_flush__nocheck(b, s); \
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soft_t ## _input_flush__nocheck(c, s); \
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}
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GEN_INPUT_FLUSH3(float32_input_flush3, float32)
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GEN_INPUT_FLUSH3(float64_input_flush3, float64)
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#undef GEN_INPUT_FLUSH3
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/*
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* Choose whether to use fpclassify or float32/64_* primitives in the generated
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* hardfloat functions. Each combination of number of inputs and float size
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* gets its own value.
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*/
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#if defined(__x86_64__)
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# define QEMU_HARDFLOAT_1F32_USE_FP 0
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# define QEMU_HARDFLOAT_1F64_USE_FP 1
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# define QEMU_HARDFLOAT_2F32_USE_FP 0
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# define QEMU_HARDFLOAT_2F64_USE_FP 1
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# define QEMU_HARDFLOAT_3F32_USE_FP 0
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# define QEMU_HARDFLOAT_3F64_USE_FP 1
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#else
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# define QEMU_HARDFLOAT_1F32_USE_FP 0
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# define QEMU_HARDFLOAT_1F64_USE_FP 0
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# define QEMU_HARDFLOAT_2F32_USE_FP 0
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# define QEMU_HARDFLOAT_2F64_USE_FP 0
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# define QEMU_HARDFLOAT_3F32_USE_FP 0
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# define QEMU_HARDFLOAT_3F64_USE_FP 0
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#endif
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/*
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* QEMU_HARDFLOAT_USE_ISINF chooses whether to use isinf() over
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* float{32,64}_is_infinity when !USE_FP.
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* On x86_64/aarch64, using the former over the latter can yield a ~6% speedup.
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* On power64 however, using isinf() reduces fp-bench performance by up to 50%.
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*/
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#if defined(__x86_64__) || defined(__aarch64__)
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# define QEMU_HARDFLOAT_USE_ISINF 1
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#else
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# define QEMU_HARDFLOAT_USE_ISINF 0
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#endif
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/*
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* Some targets clear the FP flags before most FP operations. This prevents
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* the use of hardfloat, since hardfloat relies on the inexact flag being
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* already set.
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*/
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#if defined(TARGET_PPC) || defined(__FAST_MATH__)
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# if defined(__FAST_MATH__)
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# warning disabling hardfloat due to -ffast-math: hardfloat requires an exact \
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IEEE implementation
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# endif
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# define QEMU_NO_HARDFLOAT 1
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# define QEMU_SOFTFLOAT_ATTR QEMU_FLATTEN
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#else
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# define QEMU_NO_HARDFLOAT 0
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# define QEMU_SOFTFLOAT_ATTR QEMU_FLATTEN __attribute__((noinline))
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#endif
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static inline bool can_use_fpu(const float_status *s)
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{
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if (QEMU_NO_HARDFLOAT) {
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return false;
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}
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return likely(s->float_exception_flags & float_flag_inexact &&
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s->float_rounding_mode == float_round_nearest_even);
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}
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/*
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* Hardfloat generation functions. Each operation can have two flavors:
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* either using softfloat primitives (e.g. float32_is_zero_or_normal) for
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* most condition checks, or native ones (e.g. fpclassify).
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*
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* The flavor is chosen by the callers. Instead of using macros, we rely on the
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* compiler to propagate constants and inline everything into the callers.
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*
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* We only generate functions for operations with two inputs, since only
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* these are common enough to justify consolidating them into common code.
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*/
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typedef union {
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float32 s;
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float h;
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} union_float32;
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typedef union {
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float64 s;
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double h;
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} union_float64;
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typedef bool (*f32_check_fn)(union_float32 a, union_float32 b);
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typedef bool (*f64_check_fn)(union_float64 a, union_float64 b);
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typedef float32 (*soft_f32_op2_fn)(float32 a, float32 b, float_status *s);
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typedef float64 (*soft_f64_op2_fn)(float64 a, float64 b, float_status *s);
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typedef float (*hard_f32_op2_fn)(float a, float b);
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typedef double (*hard_f64_op2_fn)(double a, double b);
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|
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/* 2-input is-zero-or-normal */
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static inline bool f32_is_zon2(union_float32 a, union_float32 b)
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{
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if (QEMU_HARDFLOAT_2F32_USE_FP) {
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/*
|
|
* Not using a temp variable for consecutive fpclassify calls ends up
|
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* generating faster code.
|
|
*/
|
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return (fpclassify(a.h) == FP_NORMAL || fpclassify(a.h) == FP_ZERO) &&
|
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(fpclassify(b.h) == FP_NORMAL || fpclassify(b.h) == FP_ZERO);
|
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}
|
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return float32_is_zero_or_normal(a.s) &&
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float32_is_zero_or_normal(b.s);
|
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}
|
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|
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static inline bool f64_is_zon2(union_float64 a, union_float64 b)
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{
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if (QEMU_HARDFLOAT_2F64_USE_FP) {
|
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return (fpclassify(a.h) == FP_NORMAL || fpclassify(a.h) == FP_ZERO) &&
|
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(fpclassify(b.h) == FP_NORMAL || fpclassify(b.h) == FP_ZERO);
|
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}
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return float64_is_zero_or_normal(a.s) &&
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float64_is_zero_or_normal(b.s);
|
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}
|
|
|
|
/* 3-input is-zero-or-normal */
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static inline
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bool f32_is_zon3(union_float32 a, union_float32 b, union_float32 c)
|
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{
|
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if (QEMU_HARDFLOAT_3F32_USE_FP) {
|
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return (fpclassify(a.h) == FP_NORMAL || fpclassify(a.h) == FP_ZERO) &&
|
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(fpclassify(b.h) == FP_NORMAL || fpclassify(b.h) == FP_ZERO) &&
|
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(fpclassify(c.h) == FP_NORMAL || fpclassify(c.h) == FP_ZERO);
|
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}
|
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return float32_is_zero_or_normal(a.s) &&
|
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float32_is_zero_or_normal(b.s) &&
|
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float32_is_zero_or_normal(c.s);
|
|
}
|
|
|
|
static inline
|
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bool f64_is_zon3(union_float64 a, union_float64 b, union_float64 c)
|
|
{
|
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if (QEMU_HARDFLOAT_3F64_USE_FP) {
|
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return (fpclassify(a.h) == FP_NORMAL || fpclassify(a.h) == FP_ZERO) &&
|
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(fpclassify(b.h) == FP_NORMAL || fpclassify(b.h) == FP_ZERO) &&
|
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(fpclassify(c.h) == FP_NORMAL || fpclassify(c.h) == FP_ZERO);
|
|
}
|
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return float64_is_zero_or_normal(a.s) &&
|
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float64_is_zero_or_normal(b.s) &&
|
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float64_is_zero_or_normal(c.s);
|
|
}
|
|
|
|
static inline bool f32_is_inf(union_float32 a)
|
|
{
|
|
if (QEMU_HARDFLOAT_USE_ISINF) {
|
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return isinf(a.h);
|
|
}
|
|
return float32_is_infinity(a.s);
|
|
}
|
|
|
|
static inline bool f64_is_inf(union_float64 a)
|
|
{
|
|
if (QEMU_HARDFLOAT_USE_ISINF) {
|
|
return isinf(a.h);
|
|
}
|
|
return float64_is_infinity(a.s);
|
|
}
|
|
|
|
static inline float32
|
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float32_gen2(float32 xa, float32 xb, float_status *s,
|
|
hard_f32_op2_fn hard, soft_f32_op2_fn soft,
|
|
f32_check_fn pre, f32_check_fn post)
|
|
{
|
|
union_float32 ua, ub, ur;
|
|
|
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ua.s = xa;
|
|
ub.s = xb;
|
|
|
|
if (unlikely(!can_use_fpu(s))) {
|
|
goto soft;
|
|
}
|
|
|
|
float32_input_flush2(&ua.s, &ub.s, s);
|
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if (unlikely(!pre(ua, ub))) {
|
|
goto soft;
|
|
}
|
|
|
|
ur.h = hard(ua.h, ub.h);
|
|
if (unlikely(f32_is_inf(ur))) {
|
|
s->float_exception_flags |= float_flag_overflow;
|
|
} else if (unlikely(fabsf(ur.h) <= FLT_MIN) && post(ua, ub)) {
|
|
goto soft;
|
|
}
|
|
return ur.s;
|
|
|
|
soft:
|
|
return soft(ua.s, ub.s, s);
|
|
}
|
|
|
|
static inline float64
|
|
float64_gen2(float64 xa, float64 xb, float_status *s,
|
|
hard_f64_op2_fn hard, soft_f64_op2_fn soft,
|
|
f64_check_fn pre, f64_check_fn post)
|
|
{
|
|
union_float64 ua, ub, ur;
|
|
|
|
ua.s = xa;
|
|
ub.s = xb;
|
|
|
|
if (unlikely(!can_use_fpu(s))) {
|
|
goto soft;
|
|
}
|
|
|
|
float64_input_flush2(&ua.s, &ub.s, s);
|
|
if (unlikely(!pre(ua, ub))) {
|
|
goto soft;
|
|
}
|
|
|
|
ur.h = hard(ua.h, ub.h);
|
|
if (unlikely(f64_is_inf(ur))) {
|
|
s->float_exception_flags |= float_flag_overflow;
|
|
} else if (unlikely(fabs(ur.h) <= DBL_MIN) && post(ua, ub)) {
|
|
goto soft;
|
|
}
|
|
return ur.s;
|
|
|
|
soft:
|
|
return soft(ua.s, ub.s, s);
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the fraction bits of the single-precision floating-point value `a'.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
static inline uint32_t extractFloat32Frac(float32 a)
|
|
{
|
|
return float32_val(a) & 0x007FFFFF;
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the exponent bits of the single-precision floating-point value `a'.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
static inline int extractFloat32Exp(float32 a)
|
|
{
|
|
return (float32_val(a) >> 23) & 0xFF;
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the sign bit of the single-precision floating-point value `a'.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
static inline bool extractFloat32Sign(float32 a)
|
|
{
|
|
return float32_val(a) >> 31;
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the fraction bits of the double-precision floating-point value `a'.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
static inline uint64_t extractFloat64Frac(float64 a)
|
|
{
|
|
return float64_val(a) & UINT64_C(0x000FFFFFFFFFFFFF);
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the exponent bits of the double-precision floating-point value `a'.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
static inline int extractFloat64Exp(float64 a)
|
|
{
|
|
return (float64_val(a) >> 52) & 0x7FF;
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the sign bit of the double-precision floating-point value `a'.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
static inline bool extractFloat64Sign(float64 a)
|
|
{
|
|
return float64_val(a) >> 63;
|
|
}
|
|
|
|
/*
|
|
* Classify a floating point number. Everything above float_class_qnan
|
|
* is a NaN so cls >= float_class_qnan is any NaN.
|
|
*/
|
|
|
|
typedef enum __attribute__ ((__packed__)) {
|
|
float_class_unclassified,
|
|
float_class_zero,
|
|
float_class_normal,
|
|
float_class_inf,
|
|
float_class_qnan, /* all NaNs from here */
|
|
float_class_snan,
|
|
} FloatClass;
|
|
|
|
/* Simple helpers for checking if, or what kind of, NaN we have */
|
|
static inline bool is_nan(FloatClass c)
|
|
{
|
|
return unlikely(c >= float_class_qnan);
|
|
}
|
|
|
|
static inline bool is_snan(FloatClass c)
|
|
{
|
|
return c == float_class_snan;
|
|
}
|
|
|
|
static inline bool is_qnan(FloatClass c)
|
|
{
|
|
return c == float_class_qnan;
|
|
}
|
|
|
|
/*
|
|
* Structure holding all of the decomposed parts of a float. The
|
|
* exponent is unbiased and the fraction is normalized. All
|
|
* calculations are done with a 64 bit fraction and then rounded as
|
|
* appropriate for the final format.
|
|
*
|
|
* Thanks to the packed FloatClass a decent compiler should be able to
|
|
* fit the whole structure into registers and avoid using the stack
|
|
* for parameter passing.
|
|
*/
|
|
|
|
typedef struct {
|
|
uint64_t frac;
|
|
int32_t exp;
|
|
FloatClass cls;
|
|
bool sign;
|
|
} FloatParts;
|
|
|
|
#define DECOMPOSED_BINARY_POINT (64 - 2)
|
|
#define DECOMPOSED_IMPLICIT_BIT (1ull << DECOMPOSED_BINARY_POINT)
|
|
#define DECOMPOSED_OVERFLOW_BIT (DECOMPOSED_IMPLICIT_BIT << 1)
|
|
|
|
/* Structure holding all of the relevant parameters for a format.
|
|
* exp_size: the size of the exponent field
|
|
* exp_bias: the offset applied to the exponent field
|
|
* exp_max: the maximum normalised exponent
|
|
* frac_size: the size of the fraction field
|
|
* frac_shift: shift to normalise the fraction with DECOMPOSED_BINARY_POINT
|
|
* The following are computed based the size of fraction
|
|
* frac_lsb: least significant bit of fraction
|
|
* frac_lsbm1: the bit below the least significant bit (for rounding)
|
|
* round_mask/roundeven_mask: masks used for rounding
|
|
* The following optional modifiers are available:
|
|
* arm_althp: handle ARM Alternative Half Precision
|
|
*/
|
|
typedef struct {
|
|
int exp_size;
|
|
int exp_bias;
|
|
int exp_max;
|
|
int frac_size;
|
|
int frac_shift;
|
|
uint64_t frac_lsb;
|
|
uint64_t frac_lsbm1;
|
|
uint64_t round_mask;
|
|
uint64_t roundeven_mask;
|
|
bool arm_althp;
|
|
} FloatFmt;
|
|
|
|
/* Expand fields based on the size of exponent and fraction */
|
|
#define FLOAT_PARAMS(E, F) \
|
|
.exp_size = E, \
|
|
.exp_bias = ((1 << E) - 1) >> 1, \
|
|
.exp_max = (1 << E) - 1, \
|
|
.frac_size = F, \
|
|
.frac_shift = DECOMPOSED_BINARY_POINT - F, \
|
|
.frac_lsb = 1ull << (DECOMPOSED_BINARY_POINT - F), \
|
|
.frac_lsbm1 = 1ull << ((DECOMPOSED_BINARY_POINT - F) - 1), \
|
|
.round_mask = (1ull << (DECOMPOSED_BINARY_POINT - F)) - 1, \
|
|
.roundeven_mask = (2ull << (DECOMPOSED_BINARY_POINT - F)) - 1
|
|
|
|
static const FloatFmt float16_params = {
|
|
FLOAT_PARAMS(5, 10)
|
|
};
|
|
|
|
static const FloatFmt float16_params_ahp = {
|
|
FLOAT_PARAMS(5, 10),
|
|
.arm_althp = true
|
|
};
|
|
|
|
static const FloatFmt float32_params = {
|
|
FLOAT_PARAMS(8, 23)
|
|
};
|
|
|
|
static const FloatFmt float64_params = {
|
|
FLOAT_PARAMS(11, 52)
|
|
};
|
|
|
|
/* Unpack a float to parts, but do not canonicalize. */
|
|
static inline FloatParts unpack_raw(FloatFmt fmt, uint64_t raw)
|
|
{
|
|
const int sign_pos = fmt.frac_size + fmt.exp_size;
|
|
FloatParts result;
|
|
result.cls = float_class_unclassified;
|
|
result.sign = extract64(raw, sign_pos, 1);
|
|
result.exp = extract64(raw, fmt.frac_size, fmt.exp_size);
|
|
result.frac = extract64(raw, 0, fmt.frac_size);
|
|
|
|
return result;
|
|
}
|
|
|
|
static inline FloatParts float16_unpack_raw(float16 f)
|
|
{
|
|
return unpack_raw(float16_params, f);
|
|
}
|
|
|
|
static inline FloatParts float32_unpack_raw(float32 f)
|
|
{
|
|
return unpack_raw(float32_params, f);
|
|
}
|
|
|
|
static inline FloatParts float64_unpack_raw(float64 f)
|
|
{
|
|
return unpack_raw(float64_params, f);
|
|
}
|
|
|
|
/* Pack a float from parts, but do not canonicalize. */
|
|
static inline uint64_t pack_raw(FloatFmt fmt, FloatParts p)
|
|
{
|
|
const int sign_pos = fmt.frac_size + fmt.exp_size;
|
|
uint64_t ret = deposit64(p.frac, fmt.frac_size, fmt.exp_size, p.exp);
|
|
return deposit64(ret, sign_pos, 1, p.sign);
|
|
}
|
|
|
|
static inline float16 float16_pack_raw(FloatParts p)
|
|
{
|
|
return make_float16(pack_raw(float16_params, p));
|
|
}
|
|
|
|
static inline float32 float32_pack_raw(FloatParts p)
|
|
{
|
|
return make_float32(pack_raw(float32_params, p));
|
|
}
|
|
|
|
static inline float64 float64_pack_raw(FloatParts p)
|
|
{
|
|
return make_float64(pack_raw(float64_params, p));
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Functions and definitions to determine: (1) whether tininess for underflow
|
|
| is detected before or after rounding by default, (2) what (if anything)
|
|
| happens when exceptions are raised, (3) how signaling NaNs are distinguished
|
|
| from quiet NaNs, (4) the default generated quiet NaNs, and (5) how NaNs
|
|
| are propagated from function inputs to output. These details are target-
|
|
| specific.
|
|
*----------------------------------------------------------------------------*/
|
|
#include "softfloat-specialize.inc.c"
|
|
|
|
/* Canonicalize EXP and FRAC, setting CLS. */
|
|
static FloatParts sf_canonicalize(FloatParts part, const FloatFmt *parm,
|
|
float_status *status)
|
|
{
|
|
if (part.exp == parm->exp_max && !parm->arm_althp) {
|
|
if (part.frac == 0) {
|
|
part.cls = float_class_inf;
|
|
} else {
|
|
part.frac <<= parm->frac_shift;
|
|
part.cls = (parts_is_snan_frac(part.frac, status)
|
|
? float_class_snan : float_class_qnan);
|
|
}
|
|
} else if (part.exp == 0) {
|
|
if (likely(part.frac == 0)) {
|
|
part.cls = float_class_zero;
|
|
} else if (status->flush_inputs_to_zero) {
|
|
float_raise(float_flag_input_denormal, status);
|
|
part.cls = float_class_zero;
|
|
part.frac = 0;
|
|
} else {
|
|
int shift = clz64(part.frac) - 1;
|
|
part.cls = float_class_normal;
|
|
part.exp = parm->frac_shift - parm->exp_bias - shift + 1;
|
|
part.frac <<= shift;
|
|
}
|
|
} else {
|
|
part.cls = float_class_normal;
|
|
part.exp -= parm->exp_bias;
|
|
part.frac = DECOMPOSED_IMPLICIT_BIT + (part.frac << parm->frac_shift);
|
|
}
|
|
return part;
|
|
}
|
|
|
|
/* Round and uncanonicalize a floating-point number by parts. There
|
|
* are FRAC_SHIFT bits that may require rounding at the bottom of the
|
|
* fraction; these bits will be removed. The exponent will be biased
|
|
* by EXP_BIAS and must be bounded by [EXP_MAX-1, 0].
|
|
*/
|
|
|
|
static FloatParts round_canonical(FloatParts p, float_status *s,
|
|
const FloatFmt *parm)
|
|
{
|
|
const uint64_t frac_lsb = parm->frac_lsb;
|
|
const uint64_t frac_lsbm1 = parm->frac_lsbm1;
|
|
const uint64_t round_mask = parm->round_mask;
|
|
const uint64_t roundeven_mask = parm->roundeven_mask;
|
|
const int exp_max = parm->exp_max;
|
|
const int frac_shift = parm->frac_shift;
|
|
uint64_t frac, inc;
|
|
int exp, flags = 0;
|
|
bool overflow_norm;
|
|
|
|
frac = p.frac;
|
|
exp = p.exp;
|
|
|
|
switch (p.cls) {
|
|
case float_class_normal:
|
|
switch (s->float_rounding_mode) {
|
|
case float_round_nearest_even:
|
|
overflow_norm = false;
|
|
inc = ((frac & roundeven_mask) != frac_lsbm1 ? frac_lsbm1 : 0);
|
|
break;
|
|
case float_round_ties_away:
|
|
overflow_norm = false;
|
|
inc = frac_lsbm1;
|
|
break;
|
|
case float_round_to_zero:
|
|
overflow_norm = true;
|
|
inc = 0;
|
|
break;
|
|
case float_round_up:
|
|
inc = p.sign ? 0 : round_mask;
|
|
overflow_norm = p.sign;
|
|
break;
|
|
case float_round_down:
|
|
inc = p.sign ? round_mask : 0;
|
|
overflow_norm = !p.sign;
|
|
break;
|
|
case float_round_to_odd:
|
|
overflow_norm = true;
|
|
inc = frac & frac_lsb ? 0 : round_mask;
|
|
break;
|
|
default:
|
|
g_assert_not_reached();
|
|
}
|
|
|
|
exp += parm->exp_bias;
|
|
if (likely(exp > 0)) {
|
|
if (frac & round_mask) {
|
|
flags |= float_flag_inexact;
|
|
frac += inc;
|
|
if (frac & DECOMPOSED_OVERFLOW_BIT) {
|
|
frac >>= 1;
|
|
exp++;
|
|
}
|
|
}
|
|
frac >>= frac_shift;
|
|
|
|
if (parm->arm_althp) {
|
|
/* ARM Alt HP eschews Inf and NaN for a wider exponent. */
|
|
if (unlikely(exp > exp_max)) {
|
|
/* Overflow. Return the maximum normal. */
|
|
flags = float_flag_invalid;
|
|
exp = exp_max;
|
|
frac = -1;
|
|
}
|
|
} else if (unlikely(exp >= exp_max)) {
|
|
flags |= float_flag_overflow | float_flag_inexact;
|
|
if (overflow_norm) {
|
|
exp = exp_max - 1;
|
|
frac = -1;
|
|
} else {
|
|
p.cls = float_class_inf;
|
|
goto do_inf;
|
|
}
|
|
}
|
|
} else if (s->flush_to_zero) {
|
|
flags |= float_flag_output_denormal;
|
|
p.cls = float_class_zero;
|
|
goto do_zero;
|
|
} else {
|
|
bool is_tiny = s->tininess_before_rounding
|
|
|| (exp < 0)
|
|
|| !((frac + inc) & DECOMPOSED_OVERFLOW_BIT);
|
|
|
|
shift64RightJamming(frac, 1 - exp, &frac);
|
|
if (frac & round_mask) {
|
|
/* Need to recompute round-to-even. */
|
|
switch (s->float_rounding_mode) {
|
|
case float_round_nearest_even:
|
|
inc = ((frac & roundeven_mask) != frac_lsbm1
|
|
? frac_lsbm1 : 0);
|
|
break;
|
|
case float_round_to_odd:
|
|
inc = frac & frac_lsb ? 0 : round_mask;
|
|
break;
|
|
default:
|
|
break;
|
|
}
|
|
flags |= float_flag_inexact;
|
|
frac += inc;
|
|
}
|
|
|
|
exp = (frac & DECOMPOSED_IMPLICIT_BIT ? 1 : 0);
|
|
frac >>= frac_shift;
|
|
|
|
if (is_tiny && (flags & float_flag_inexact)) {
|
|
flags |= float_flag_underflow;
|
|
}
|
|
if (exp == 0 && frac == 0) {
|
|
p.cls = float_class_zero;
|
|
}
|
|
}
|
|
break;
|
|
|
|
case float_class_zero:
|
|
do_zero:
|
|
exp = 0;
|
|
frac = 0;
|
|
break;
|
|
|
|
case float_class_inf:
|
|
do_inf:
|
|
assert(!parm->arm_althp);
|
|
exp = exp_max;
|
|
frac = 0;
|
|
break;
|
|
|
|
case float_class_qnan:
|
|
case float_class_snan:
|
|
assert(!parm->arm_althp);
|
|
exp = exp_max;
|
|
frac >>= parm->frac_shift;
|
|
break;
|
|
|
|
default:
|
|
g_assert_not_reached();
|
|
}
|
|
|
|
float_raise(flags, s);
|
|
p.exp = exp;
|
|
p.frac = frac;
|
|
return p;
|
|
}
|
|
|
|
/* Explicit FloatFmt version */
|
|
static FloatParts float16a_unpack_canonical(float16 f, float_status *s,
|
|
const FloatFmt *params)
|
|
{
|
|
return sf_canonicalize(float16_unpack_raw(f), params, s);
|
|
}
|
|
|
|
static FloatParts float16_unpack_canonical(float16 f, float_status *s)
|
|
{
|
|
return float16a_unpack_canonical(f, s, &float16_params);
|
|
}
|
|
|
|
static float16 float16a_round_pack_canonical(FloatParts p, float_status *s,
|
|
const FloatFmt *params)
|
|
{
|
|
return float16_pack_raw(round_canonical(p, s, params));
|
|
}
|
|
|
|
static float16 float16_round_pack_canonical(FloatParts p, float_status *s)
|
|
{
|
|
return float16a_round_pack_canonical(p, s, &float16_params);
|
|
}
|
|
|
|
static FloatParts float32_unpack_canonical(float32 f, float_status *s)
|
|
{
|
|
return sf_canonicalize(float32_unpack_raw(f), &float32_params, s);
|
|
}
|
|
|
|
static float32 float32_round_pack_canonical(FloatParts p, float_status *s)
|
|
{
|
|
return float32_pack_raw(round_canonical(p, s, &float32_params));
|
|
}
|
|
|
|
static FloatParts float64_unpack_canonical(float64 f, float_status *s)
|
|
{
|
|
return sf_canonicalize(float64_unpack_raw(f), &float64_params, s);
|
|
}
|
|
|
|
static float64 float64_round_pack_canonical(FloatParts p, float_status *s)
|
|
{
|
|
return float64_pack_raw(round_canonical(p, s, &float64_params));
|
|
}
|
|
|
|
static FloatParts return_nan(FloatParts a, float_status *s)
|
|
{
|
|
switch (a.cls) {
|
|
case float_class_snan:
|
|
s->float_exception_flags |= float_flag_invalid;
|
|
a = parts_silence_nan(a, s);
|
|
/* fall through */
|
|
case float_class_qnan:
|
|
if (s->default_nan_mode) {
|
|
return parts_default_nan(s);
|
|
}
|
|
break;
|
|
|
|
default:
|
|
g_assert_not_reached();
|
|
}
|
|
return a;
|
|
}
|
|
|
|
static FloatParts pick_nan(FloatParts a, FloatParts b, float_status *s)
|
|
{
|
|
if (is_snan(a.cls) || is_snan(b.cls)) {
|
|
s->float_exception_flags |= float_flag_invalid;
|
|
}
|
|
|
|
if (s->default_nan_mode) {
|
|
return parts_default_nan(s);
|
|
} else {
|
|
if (pickNaN(a.cls, b.cls,
|
|
a.frac > b.frac ||
|
|
(a.frac == b.frac && a.sign < b.sign))) {
|
|
a = b;
|
|
}
|
|
if (is_snan(a.cls)) {
|
|
return parts_silence_nan(a, s);
|
|
}
|
|
}
|
|
return a;
|
|
}
|
|
|
|
static FloatParts pick_nan_muladd(FloatParts a, FloatParts b, FloatParts c,
|
|
bool inf_zero, float_status *s)
|
|
{
|
|
int which;
|
|
|
|
if (is_snan(a.cls) || is_snan(b.cls) || is_snan(c.cls)) {
|
|
s->float_exception_flags |= float_flag_invalid;
|
|
}
|
|
|
|
which = pickNaNMulAdd(a.cls, b.cls, c.cls, inf_zero, s);
|
|
|
|
if (s->default_nan_mode) {
|
|
/* Note that this check is after pickNaNMulAdd so that function
|
|
* has an opportunity to set the Invalid flag.
|
|
*/
|
|
which = 3;
|
|
}
|
|
|
|
switch (which) {
|
|
case 0:
|
|
break;
|
|
case 1:
|
|
a = b;
|
|
break;
|
|
case 2:
|
|
a = c;
|
|
break;
|
|
case 3:
|
|
return parts_default_nan(s);
|
|
default:
|
|
g_assert_not_reached();
|
|
}
|
|
|
|
if (is_snan(a.cls)) {
|
|
return parts_silence_nan(a, s);
|
|
}
|
|
return a;
|
|
}
|
|
|
|
/*
|
|
* Returns the result of adding or subtracting the values of the
|
|
* floating-point values `a' and `b'. The operation is performed
|
|
* according to the IEC/IEEE Standard for Binary Floating-Point
|
|
* Arithmetic.
|
|
*/
|
|
|
|
static FloatParts addsub_floats(FloatParts a, FloatParts b, bool subtract,
|
|
float_status *s)
|
|
{
|
|
bool a_sign = a.sign;
|
|
bool b_sign = b.sign ^ subtract;
|
|
|
|
if (a_sign != b_sign) {
|
|
/* Subtraction */
|
|
|
|
if (a.cls == float_class_normal && b.cls == float_class_normal) {
|
|
if (a.exp > b.exp || (a.exp == b.exp && a.frac >= b.frac)) {
|
|
shift64RightJamming(b.frac, a.exp - b.exp, &b.frac);
|
|
a.frac = a.frac - b.frac;
|
|
} else {
|
|
shift64RightJamming(a.frac, b.exp - a.exp, &a.frac);
|
|
a.frac = b.frac - a.frac;
|
|
a.exp = b.exp;
|
|
a_sign ^= 1;
|
|
}
|
|
|
|
if (a.frac == 0) {
|
|
a.cls = float_class_zero;
|
|
a.sign = s->float_rounding_mode == float_round_down;
|
|
} else {
|
|
int shift = clz64(a.frac) - 1;
|
|
a.frac = a.frac << shift;
|
|
a.exp = a.exp - shift;
|
|
a.sign = a_sign;
|
|
}
|
|
return a;
|
|
}
|
|
if (is_nan(a.cls) || is_nan(b.cls)) {
|
|
return pick_nan(a, b, s);
|
|
}
|
|
if (a.cls == float_class_inf) {
|
|
if (b.cls == float_class_inf) {
|
|
float_raise(float_flag_invalid, s);
|
|
return parts_default_nan(s);
|
|
}
|
|
return a;
|
|
}
|
|
if (a.cls == float_class_zero && b.cls == float_class_zero) {
|
|
a.sign = s->float_rounding_mode == float_round_down;
|
|
return a;
|
|
}
|
|
if (a.cls == float_class_zero || b.cls == float_class_inf) {
|
|
b.sign = a_sign ^ 1;
|
|
return b;
|
|
}
|
|
if (b.cls == float_class_zero) {
|
|
return a;
|
|
}
|
|
} else {
|
|
/* Addition */
|
|
if (a.cls == float_class_normal && b.cls == float_class_normal) {
|
|
if (a.exp > b.exp) {
|
|
shift64RightJamming(b.frac, a.exp - b.exp, &b.frac);
|
|
} else if (a.exp < b.exp) {
|
|
shift64RightJamming(a.frac, b.exp - a.exp, &a.frac);
|
|
a.exp = b.exp;
|
|
}
|
|
a.frac += b.frac;
|
|
if (a.frac & DECOMPOSED_OVERFLOW_BIT) {
|
|
shift64RightJamming(a.frac, 1, &a.frac);
|
|
a.exp += 1;
|
|
}
|
|
return a;
|
|
}
|
|
if (is_nan(a.cls) || is_nan(b.cls)) {
|
|
return pick_nan(a, b, s);
|
|
}
|
|
if (a.cls == float_class_inf || b.cls == float_class_zero) {
|
|
return a;
|
|
}
|
|
if (b.cls == float_class_inf || a.cls == float_class_zero) {
|
|
b.sign = b_sign;
|
|
return b;
|
|
}
|
|
}
|
|
g_assert_not_reached();
|
|
}
|
|
|
|
/*
|
|
* Returns the result of adding or subtracting the floating-point
|
|
* values `a' and `b'. The operation is performed according to the
|
|
* IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
|
*/
|
|
|
|
float16 QEMU_FLATTEN float16_add(float16 a, float16 b, float_status *status)
|
|
{
|
|
FloatParts pa = float16_unpack_canonical(a, status);
|
|
FloatParts pb = float16_unpack_canonical(b, status);
|
|
FloatParts pr = addsub_floats(pa, pb, false, status);
|
|
|
|
return float16_round_pack_canonical(pr, status);
|
|
}
|
|
|
|
float16 QEMU_FLATTEN float16_sub(float16 a, float16 b, float_status *status)
|
|
{
|
|
FloatParts pa = float16_unpack_canonical(a, status);
|
|
FloatParts pb = float16_unpack_canonical(b, status);
|
|
FloatParts pr = addsub_floats(pa, pb, true, status);
|
|
|
|
return float16_round_pack_canonical(pr, status);
|
|
}
|
|
|
|
static float32 QEMU_SOFTFLOAT_ATTR
|
|
soft_f32_addsub(float32 a, float32 b, bool subtract, float_status *status)
|
|
{
|
|
FloatParts pa = float32_unpack_canonical(a, status);
|
|
FloatParts pb = float32_unpack_canonical(b, status);
|
|
FloatParts pr = addsub_floats(pa, pb, subtract, status);
|
|
|
|
return float32_round_pack_canonical(pr, status);
|
|
}
|
|
|
|
static inline float32 soft_f32_add(float32 a, float32 b, float_status *status)
|
|
{
|
|
return soft_f32_addsub(a, b, false, status);
|
|
}
|
|
|
|
static inline float32 soft_f32_sub(float32 a, float32 b, float_status *status)
|
|
{
|
|
return soft_f32_addsub(a, b, true, status);
|
|
}
|
|
|
|
static float64 QEMU_SOFTFLOAT_ATTR
|
|
soft_f64_addsub(float64 a, float64 b, bool subtract, float_status *status)
|
|
{
|
|
FloatParts pa = float64_unpack_canonical(a, status);
|
|
FloatParts pb = float64_unpack_canonical(b, status);
|
|
FloatParts pr = addsub_floats(pa, pb, subtract, status);
|
|
|
|
return float64_round_pack_canonical(pr, status);
|
|
}
|
|
|
|
static inline float64 soft_f64_add(float64 a, float64 b, float_status *status)
|
|
{
|
|
return soft_f64_addsub(a, b, false, status);
|
|
}
|
|
|
|
static inline float64 soft_f64_sub(float64 a, float64 b, float_status *status)
|
|
{
|
|
return soft_f64_addsub(a, b, true, status);
|
|
}
|
|
|
|
static float hard_f32_add(float a, float b)
|
|
{
|
|
return a + b;
|
|
}
|
|
|
|
static float hard_f32_sub(float a, float b)
|
|
{
|
|
return a - b;
|
|
}
|
|
|
|
static double hard_f64_add(double a, double b)
|
|
{
|
|
return a + b;
|
|
}
|
|
|
|
static double hard_f64_sub(double a, double b)
|
|
{
|
|
return a - b;
|
|
}
|
|
|
|
static bool f32_addsubmul_post(union_float32 a, union_float32 b)
|
|
{
|
|
if (QEMU_HARDFLOAT_2F32_USE_FP) {
|
|
return !(fpclassify(a.h) == FP_ZERO && fpclassify(b.h) == FP_ZERO);
|
|
}
|
|
return !(float32_is_zero(a.s) && float32_is_zero(b.s));
|
|
}
|
|
|
|
static bool f64_addsubmul_post(union_float64 a, union_float64 b)
|
|
{
|
|
if (QEMU_HARDFLOAT_2F64_USE_FP) {
|
|
return !(fpclassify(a.h) == FP_ZERO && fpclassify(b.h) == FP_ZERO);
|
|
} else {
|
|
return !(float64_is_zero(a.s) && float64_is_zero(b.s));
|
|
}
|
|
}
|
|
|
|
static float32 float32_addsub(float32 a, float32 b, float_status *s,
|
|
hard_f32_op2_fn hard, soft_f32_op2_fn soft)
|
|
{
|
|
return float32_gen2(a, b, s, hard, soft,
|
|
f32_is_zon2, f32_addsubmul_post);
|
|
}
|
|
|
|
static float64 float64_addsub(float64 a, float64 b, float_status *s,
|
|
hard_f64_op2_fn hard, soft_f64_op2_fn soft)
|
|
{
|
|
return float64_gen2(a, b, s, hard, soft,
|
|
f64_is_zon2, f64_addsubmul_post);
|
|
}
|
|
|
|
float32 QEMU_FLATTEN
|
|
float32_add(float32 a, float32 b, float_status *s)
|
|
{
|
|
return float32_addsub(a, b, s, hard_f32_add, soft_f32_add);
|
|
}
|
|
|
|
float32 QEMU_FLATTEN
|
|
float32_sub(float32 a, float32 b, float_status *s)
|
|
{
|
|
return float32_addsub(a, b, s, hard_f32_sub, soft_f32_sub);
|
|
}
|
|
|
|
float64 QEMU_FLATTEN
|
|
float64_add(float64 a, float64 b, float_status *s)
|
|
{
|
|
return float64_addsub(a, b, s, hard_f64_add, soft_f64_add);
|
|
}
|
|
|
|
float64 QEMU_FLATTEN
|
|
float64_sub(float64 a, float64 b, float_status *s)
|
|
{
|
|
return float64_addsub(a, b, s, hard_f64_sub, soft_f64_sub);
|
|
}
|
|
|
|
/*
|
|
* Returns the result of multiplying the floating-point values `a' and
|
|
* `b'. The operation is performed according to the IEC/IEEE Standard
|
|
* for Binary Floating-Point Arithmetic.
|
|
*/
|
|
|
|
static FloatParts mul_floats(FloatParts a, FloatParts b, float_status *s)
|
|
{
|
|
bool sign = a.sign ^ b.sign;
|
|
|
|
if (a.cls == float_class_normal && b.cls == float_class_normal) {
|
|
uint64_t hi, lo;
|
|
int exp = a.exp + b.exp;
|
|
|
|
mul64To128(a.frac, b.frac, &hi, &lo);
|
|
shift128RightJamming(hi, lo, DECOMPOSED_BINARY_POINT, &hi, &lo);
|
|
if (lo & DECOMPOSED_OVERFLOW_BIT) {
|
|
shift64RightJamming(lo, 1, &lo);
|
|
exp += 1;
|
|
}
|
|
|
|
/* Re-use a */
|
|
a.exp = exp;
|
|
a.sign = sign;
|
|
a.frac = lo;
|
|
return a;
|
|
}
|
|
/* handle all the NaN cases */
|
|
if (is_nan(a.cls) || is_nan(b.cls)) {
|
|
return pick_nan(a, b, s);
|
|
}
|
|
/* Inf * Zero == NaN */
|
|
if ((a.cls == float_class_inf && b.cls == float_class_zero) ||
|
|
(a.cls == float_class_zero && b.cls == float_class_inf)) {
|
|
s->float_exception_flags |= float_flag_invalid;
|
|
return parts_default_nan(s);
|
|
}
|
|
/* Multiply by 0 or Inf */
|
|
if (a.cls == float_class_inf || a.cls == float_class_zero) {
|
|
a.sign = sign;
|
|
return a;
|
|
}
|
|
if (b.cls == float_class_inf || b.cls == float_class_zero) {
|
|
b.sign = sign;
|
|
return b;
|
|
}
|
|
g_assert_not_reached();
|
|
}
|
|
|
|
float16 QEMU_FLATTEN float16_mul(float16 a, float16 b, float_status *status)
|
|
{
|
|
FloatParts pa = float16_unpack_canonical(a, status);
|
|
FloatParts pb = float16_unpack_canonical(b, status);
|
|
FloatParts pr = mul_floats(pa, pb, status);
|
|
|
|
return float16_round_pack_canonical(pr, status);
|
|
}
|
|
|
|
static float32 QEMU_SOFTFLOAT_ATTR
|
|
soft_f32_mul(float32 a, float32 b, float_status *status)
|
|
{
|
|
FloatParts pa = float32_unpack_canonical(a, status);
|
|
FloatParts pb = float32_unpack_canonical(b, status);
|
|
FloatParts pr = mul_floats(pa, pb, status);
|
|
|
|
return float32_round_pack_canonical(pr, status);
|
|
}
|
|
|
|
static float64 QEMU_SOFTFLOAT_ATTR
|
|
soft_f64_mul(float64 a, float64 b, float_status *status)
|
|
{
|
|
FloatParts pa = float64_unpack_canonical(a, status);
|
|
FloatParts pb = float64_unpack_canonical(b, status);
|
|
FloatParts pr = mul_floats(pa, pb, status);
|
|
|
|
return float64_round_pack_canonical(pr, status);
|
|
}
|
|
|
|
static float hard_f32_mul(float a, float b)
|
|
{
|
|
return a * b;
|
|
}
|
|
|
|
static double hard_f64_mul(double a, double b)
|
|
{
|
|
return a * b;
|
|
}
|
|
|
|
float32 QEMU_FLATTEN
|
|
float32_mul(float32 a, float32 b, float_status *s)
|
|
{
|
|
return float32_gen2(a, b, s, hard_f32_mul, soft_f32_mul,
|
|
f32_is_zon2, f32_addsubmul_post);
|
|
}
|
|
|
|
float64 QEMU_FLATTEN
|
|
float64_mul(float64 a, float64 b, float_status *s)
|
|
{
|
|
return float64_gen2(a, b, s, hard_f64_mul, soft_f64_mul,
|
|
f64_is_zon2, f64_addsubmul_post);
|
|
}
|
|
|
|
/*
|
|
* Returns the result of multiplying the floating-point values `a' and
|
|
* `b' then adding 'c', with no intermediate rounding step after the
|
|
* multiplication. The operation is performed according to the
|
|
* IEC/IEEE Standard for Binary Floating-Point Arithmetic 754-2008.
|
|
* The flags argument allows the caller to select negation of the
|
|
* addend, the intermediate product, or the final result. (The
|
|
* difference between this and having the caller do a separate
|
|
* negation is that negating externally will flip the sign bit on
|
|
* NaNs.)
|
|
*/
|
|
|
|
static FloatParts muladd_floats(FloatParts a, FloatParts b, FloatParts c,
|
|
int flags, float_status *s)
|
|
{
|
|
bool inf_zero = ((1 << a.cls) | (1 << b.cls)) ==
|
|
((1 << float_class_inf) | (1 << float_class_zero));
|
|
bool p_sign;
|
|
bool sign_flip = flags & float_muladd_negate_result;
|
|
FloatClass p_class;
|
|
uint64_t hi, lo;
|
|
int p_exp;
|
|
|
|
/* It is implementation-defined whether the cases of (0,inf,qnan)
|
|
* and (inf,0,qnan) raise InvalidOperation or not (and what QNaN
|
|
* they return if they do), so we have to hand this information
|
|
* off to the target-specific pick-a-NaN routine.
|
|
*/
|
|
if (is_nan(a.cls) || is_nan(b.cls) || is_nan(c.cls)) {
|
|
return pick_nan_muladd(a, b, c, inf_zero, s);
|
|
}
|
|
|
|
if (inf_zero) {
|
|
s->float_exception_flags |= float_flag_invalid;
|
|
return parts_default_nan(s);
|
|
}
|
|
|
|
if (flags & float_muladd_negate_c) {
|
|
c.sign ^= 1;
|
|
}
|
|
|
|
p_sign = a.sign ^ b.sign;
|
|
|
|
if (flags & float_muladd_negate_product) {
|
|
p_sign ^= 1;
|
|
}
|
|
|
|
if (a.cls == float_class_inf || b.cls == float_class_inf) {
|
|
p_class = float_class_inf;
|
|
} else if (a.cls == float_class_zero || b.cls == float_class_zero) {
|
|
p_class = float_class_zero;
|
|
} else {
|
|
p_class = float_class_normal;
|
|
}
|
|
|
|
if (c.cls == float_class_inf) {
|
|
if (p_class == float_class_inf && p_sign != c.sign) {
|
|
s->float_exception_flags |= float_flag_invalid;
|
|
return parts_default_nan(s);
|
|
} else {
|
|
a.cls = float_class_inf;
|
|
a.sign = c.sign ^ sign_flip;
|
|
return a;
|
|
}
|
|
}
|
|
|
|
if (p_class == float_class_inf) {
|
|
a.cls = float_class_inf;
|
|
a.sign = p_sign ^ sign_flip;
|
|
return a;
|
|
}
|
|
|
|
if (p_class == float_class_zero) {
|
|
if (c.cls == float_class_zero) {
|
|
if (p_sign != c.sign) {
|
|
p_sign = s->float_rounding_mode == float_round_down;
|
|
}
|
|
c.sign = p_sign;
|
|
} else if (flags & float_muladd_halve_result) {
|
|
c.exp -= 1;
|
|
}
|
|
c.sign ^= sign_flip;
|
|
return c;
|
|
}
|
|
|
|
/* a & b should be normals now... */
|
|
assert(a.cls == float_class_normal &&
|
|
b.cls == float_class_normal);
|
|
|
|
p_exp = a.exp + b.exp;
|
|
|
|
/* Multiply of 2 62-bit numbers produces a (2*62) == 124-bit
|
|
* result.
|
|
*/
|
|
mul64To128(a.frac, b.frac, &hi, &lo);
|
|
/* binary point now at bit 124 */
|
|
|
|
/* check for overflow */
|
|
if (hi & (1ULL << (DECOMPOSED_BINARY_POINT * 2 + 1 - 64))) {
|
|
shift128RightJamming(hi, lo, 1, &hi, &lo);
|
|
p_exp += 1;
|
|
}
|
|
|
|
/* + add/sub */
|
|
if (c.cls == float_class_zero) {
|
|
/* move binary point back to 62 */
|
|
shift128RightJamming(hi, lo, DECOMPOSED_BINARY_POINT, &hi, &lo);
|
|
} else {
|
|
int exp_diff = p_exp - c.exp;
|
|
if (p_sign == c.sign) {
|
|
/* Addition */
|
|
if (exp_diff <= 0) {
|
|
shift128RightJamming(hi, lo,
|
|
DECOMPOSED_BINARY_POINT - exp_diff,
|
|
&hi, &lo);
|
|
lo += c.frac;
|
|
p_exp = c.exp;
|
|
} else {
|
|
uint64_t c_hi, c_lo;
|
|
/* shift c to the same binary point as the product (124) */
|
|
c_hi = c.frac >> 2;
|
|
c_lo = 0;
|
|
shift128RightJamming(c_hi, c_lo,
|
|
exp_diff,
|
|
&c_hi, &c_lo);
|
|
add128(hi, lo, c_hi, c_lo, &hi, &lo);
|
|
/* move binary point back to 62 */
|
|
shift128RightJamming(hi, lo, DECOMPOSED_BINARY_POINT, &hi, &lo);
|
|
}
|
|
|
|
if (lo & DECOMPOSED_OVERFLOW_BIT) {
|
|
shift64RightJamming(lo, 1, &lo);
|
|
p_exp += 1;
|
|
}
|
|
|
|
} else {
|
|
/* Subtraction */
|
|
uint64_t c_hi, c_lo;
|
|
/* make C binary point match product at bit 124 */
|
|
c_hi = c.frac >> 2;
|
|
c_lo = 0;
|
|
|
|
if (exp_diff <= 0) {
|
|
shift128RightJamming(hi, lo, -exp_diff, &hi, &lo);
|
|
if (exp_diff == 0
|
|
&&
|
|
(hi > c_hi || (hi == c_hi && lo >= c_lo))) {
|
|
sub128(hi, lo, c_hi, c_lo, &hi, &lo);
|
|
} else {
|
|
sub128(c_hi, c_lo, hi, lo, &hi, &lo);
|
|
p_sign ^= 1;
|
|
p_exp = c.exp;
|
|
}
|
|
} else {
|
|
shift128RightJamming(c_hi, c_lo,
|
|
exp_diff,
|
|
&c_hi, &c_lo);
|
|
sub128(hi, lo, c_hi, c_lo, &hi, &lo);
|
|
}
|
|
|
|
if (hi == 0 && lo == 0) {
|
|
a.cls = float_class_zero;
|
|
a.sign = s->float_rounding_mode == float_round_down;
|
|
a.sign ^= sign_flip;
|
|
return a;
|
|
} else {
|
|
int shift;
|
|
if (hi != 0) {
|
|
shift = clz64(hi);
|
|
} else {
|
|
shift = clz64(lo) + 64;
|
|
}
|
|
/* Normalizing to a binary point of 124 is the
|
|
correct adjust for the exponent. However since we're
|
|
shifting, we might as well put the binary point back
|
|
at 62 where we really want it. Therefore shift as
|
|
if we're leaving 1 bit at the top of the word, but
|
|
adjust the exponent as if we're leaving 3 bits. */
|
|
shift -= 1;
|
|
if (shift >= 64) {
|
|
lo = lo << (shift - 64);
|
|
} else {
|
|
hi = (hi << shift) | (lo >> (64 - shift));
|
|
lo = hi | ((lo << shift) != 0);
|
|
}
|
|
p_exp -= shift - 2;
|
|
}
|
|
}
|
|
}
|
|
|
|
if (flags & float_muladd_halve_result) {
|
|
p_exp -= 1;
|
|
}
|
|
|
|
/* finally prepare our result */
|
|
a.cls = float_class_normal;
|
|
a.sign = p_sign ^ sign_flip;
|
|
a.exp = p_exp;
|
|
a.frac = lo;
|
|
|
|
return a;
|
|
}
|
|
|
|
float16 QEMU_FLATTEN float16_muladd(float16 a, float16 b, float16 c,
|
|
int flags, float_status *status)
|
|
{
|
|
FloatParts pa = float16_unpack_canonical(a, status);
|
|
FloatParts pb = float16_unpack_canonical(b, status);
|
|
FloatParts pc = float16_unpack_canonical(c, status);
|
|
FloatParts pr = muladd_floats(pa, pb, pc, flags, status);
|
|
|
|
return float16_round_pack_canonical(pr, status);
|
|
}
|
|
|
|
static float32 QEMU_SOFTFLOAT_ATTR
|
|
soft_f32_muladd(float32 a, float32 b, float32 c, int flags,
|
|
float_status *status)
|
|
{
|
|
FloatParts pa = float32_unpack_canonical(a, status);
|
|
FloatParts pb = float32_unpack_canonical(b, status);
|
|
FloatParts pc = float32_unpack_canonical(c, status);
|
|
FloatParts pr = muladd_floats(pa, pb, pc, flags, status);
|
|
|
|
return float32_round_pack_canonical(pr, status);
|
|
}
|
|
|
|
static float64 QEMU_SOFTFLOAT_ATTR
|
|
soft_f64_muladd(float64 a, float64 b, float64 c, int flags,
|
|
float_status *status)
|
|
{
|
|
FloatParts pa = float64_unpack_canonical(a, status);
|
|
FloatParts pb = float64_unpack_canonical(b, status);
|
|
FloatParts pc = float64_unpack_canonical(c, status);
|
|
FloatParts pr = muladd_floats(pa, pb, pc, flags, status);
|
|
|
|
return float64_round_pack_canonical(pr, status);
|
|
}
|
|
|
|
float32 QEMU_FLATTEN
|
|
float32_muladd(float32 xa, float32 xb, float32 xc, int flags, float_status *s)
|
|
{
|
|
union_float32 ua, ub, uc, ur;
|
|
|
|
ua.s = xa;
|
|
ub.s = xb;
|
|
uc.s = xc;
|
|
|
|
if (unlikely(!can_use_fpu(s))) {
|
|
goto soft;
|
|
}
|
|
if (unlikely(flags & float_muladd_halve_result)) {
|
|
goto soft;
|
|
}
|
|
|
|
float32_input_flush3(&ua.s, &ub.s, &uc.s, s);
|
|
if (unlikely(!f32_is_zon3(ua, ub, uc))) {
|
|
goto soft;
|
|
}
|
|
/*
|
|
* When (a || b) == 0, there's no need to check for under/over flow,
|
|
* since we know the addend is (normal || 0) and the product is 0.
|
|
*/
|
|
if (float32_is_zero(ua.s) || float32_is_zero(ub.s)) {
|
|
union_float32 up;
|
|
bool prod_sign;
|
|
|
|
prod_sign = float32_is_neg(ua.s) ^ float32_is_neg(ub.s);
|
|
prod_sign ^= !!(flags & float_muladd_negate_product);
|
|
up.s = float32_set_sign(float32_zero, prod_sign);
|
|
|
|
if (flags & float_muladd_negate_c) {
|
|
uc.h = -uc.h;
|
|
}
|
|
ur.h = up.h + uc.h;
|
|
} else {
|
|
if (flags & float_muladd_negate_product) {
|
|
ua.h = -ua.h;
|
|
}
|
|
if (flags & float_muladd_negate_c) {
|
|
uc.h = -uc.h;
|
|
}
|
|
|
|
ur.h = fmaf(ua.h, ub.h, uc.h);
|
|
|
|
if (unlikely(f32_is_inf(ur))) {
|
|
s->float_exception_flags |= float_flag_overflow;
|
|
} else if (unlikely(fabsf(ur.h) <= FLT_MIN)) {
|
|
goto soft;
|
|
}
|
|
}
|
|
if (flags & float_muladd_negate_result) {
|
|
return float32_chs(ur.s);
|
|
}
|
|
return ur.s;
|
|
|
|
soft:
|
|
return soft_f32_muladd(ua.s, ub.s, uc.s, flags, s);
|
|
}
|
|
|
|
float64 QEMU_FLATTEN
|
|
float64_muladd(float64 xa, float64 xb, float64 xc, int flags, float_status *s)
|
|
{
|
|
union_float64 ua, ub, uc, ur;
|
|
|
|
ua.s = xa;
|
|
ub.s = xb;
|
|
uc.s = xc;
|
|
|
|
if (unlikely(!can_use_fpu(s))) {
|
|
goto soft;
|
|
}
|
|
if (unlikely(flags & float_muladd_halve_result)) {
|
|
goto soft;
|
|
}
|
|
|
|
float64_input_flush3(&ua.s, &ub.s, &uc.s, s);
|
|
if (unlikely(!f64_is_zon3(ua, ub, uc))) {
|
|
goto soft;
|
|
}
|
|
/*
|
|
* When (a || b) == 0, there's no need to check for under/over flow,
|
|
* since we know the addend is (normal || 0) and the product is 0.
|
|
*/
|
|
if (float64_is_zero(ua.s) || float64_is_zero(ub.s)) {
|
|
union_float64 up;
|
|
bool prod_sign;
|
|
|
|
prod_sign = float64_is_neg(ua.s) ^ float64_is_neg(ub.s);
|
|
prod_sign ^= !!(flags & float_muladd_negate_product);
|
|
up.s = float64_set_sign(float64_zero, prod_sign);
|
|
|
|
if (flags & float_muladd_negate_c) {
|
|
uc.h = -uc.h;
|
|
}
|
|
ur.h = up.h + uc.h;
|
|
} else {
|
|
if (flags & float_muladd_negate_product) {
|
|
ua.h = -ua.h;
|
|
}
|
|
if (flags & float_muladd_negate_c) {
|
|
uc.h = -uc.h;
|
|
}
|
|
|
|
ur.h = fma(ua.h, ub.h, uc.h);
|
|
|
|
if (unlikely(f64_is_inf(ur))) {
|
|
s->float_exception_flags |= float_flag_overflow;
|
|
} else if (unlikely(fabs(ur.h) <= FLT_MIN)) {
|
|
goto soft;
|
|
}
|
|
}
|
|
if (flags & float_muladd_negate_result) {
|
|
return float64_chs(ur.s);
|
|
}
|
|
return ur.s;
|
|
|
|
soft:
|
|
return soft_f64_muladd(ua.s, ub.s, uc.s, flags, s);
|
|
}
|
|
|
|
/*
|
|
* Returns the result of dividing the floating-point value `a' by the
|
|
* corresponding value `b'. The operation is performed according to
|
|
* the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
|
*/
|
|
|
|
static FloatParts div_floats(FloatParts a, FloatParts b, float_status *s)
|
|
{
|
|
bool sign = a.sign ^ b.sign;
|
|
|
|
if (a.cls == float_class_normal && b.cls == float_class_normal) {
|
|
uint64_t n0, n1, q, r;
|
|
int exp = a.exp - b.exp;
|
|
|
|
/*
|
|
* We want a 2*N / N-bit division to produce exactly an N-bit
|
|
* result, so that we do not lose any precision and so that we
|
|
* do not have to renormalize afterward. If A.frac < B.frac,
|
|
* then division would produce an (N-1)-bit result; shift A left
|
|
* by one to produce the an N-bit result, and decrement the
|
|
* exponent to match.
|
|
*
|
|
* The udiv_qrnnd algorithm that we're using requires normalization,
|
|
* i.e. the msb of the denominator must be set. Since we know that
|
|
* DECOMPOSED_BINARY_POINT is msb-1, the inputs must be shifted left
|
|
* by one (more), and the remainder must be shifted right by one.
|
|
*/
|
|
if (a.frac < b.frac) {
|
|
exp -= 1;
|
|
shift128Left(0, a.frac, DECOMPOSED_BINARY_POINT + 2, &n1, &n0);
|
|
} else {
|
|
shift128Left(0, a.frac, DECOMPOSED_BINARY_POINT + 1, &n1, &n0);
|
|
}
|
|
q = udiv_qrnnd(&r, n1, n0, b.frac << 1);
|
|
|
|
/*
|
|
* Set lsb if there is a remainder, to set inexact.
|
|
* As mentioned above, to find the actual value of the remainder we
|
|
* would need to shift right, but (1) we are only concerned about
|
|
* non-zero-ness, and (2) the remainder will always be even because
|
|
* both inputs to the division primitive are even.
|
|
*/
|
|
a.frac = q | (r != 0);
|
|
a.sign = sign;
|
|
a.exp = exp;
|
|
return a;
|
|
}
|
|
/* handle all the NaN cases */
|
|
if (is_nan(a.cls) || is_nan(b.cls)) {
|
|
return pick_nan(a, b, s);
|
|
}
|
|
/* 0/0 or Inf/Inf */
|
|
if (a.cls == b.cls
|
|
&&
|
|
(a.cls == float_class_inf || a.cls == float_class_zero)) {
|
|
s->float_exception_flags |= float_flag_invalid;
|
|
return parts_default_nan(s);
|
|
}
|
|
/* Inf / x or 0 / x */
|
|
if (a.cls == float_class_inf || a.cls == float_class_zero) {
|
|
a.sign = sign;
|
|
return a;
|
|
}
|
|
/* Div 0 => Inf */
|
|
if (b.cls == float_class_zero) {
|
|
s->float_exception_flags |= float_flag_divbyzero;
|
|
a.cls = float_class_inf;
|
|
a.sign = sign;
|
|
return a;
|
|
}
|
|
/* Div by Inf */
|
|
if (b.cls == float_class_inf) {
|
|
a.cls = float_class_zero;
|
|
a.sign = sign;
|
|
return a;
|
|
}
|
|
g_assert_not_reached();
|
|
}
|
|
|
|
float16 float16_div(float16 a, float16 b, float_status *status)
|
|
{
|
|
FloatParts pa = float16_unpack_canonical(a, status);
|
|
FloatParts pb = float16_unpack_canonical(b, status);
|
|
FloatParts pr = div_floats(pa, pb, status);
|
|
|
|
return float16_round_pack_canonical(pr, status);
|
|
}
|
|
|
|
static float32 QEMU_SOFTFLOAT_ATTR
|
|
soft_f32_div(float32 a, float32 b, float_status *status)
|
|
{
|
|
FloatParts pa = float32_unpack_canonical(a, status);
|
|
FloatParts pb = float32_unpack_canonical(b, status);
|
|
FloatParts pr = div_floats(pa, pb, status);
|
|
|
|
return float32_round_pack_canonical(pr, status);
|
|
}
|
|
|
|
static float64 QEMU_SOFTFLOAT_ATTR
|
|
soft_f64_div(float64 a, float64 b, float_status *status)
|
|
{
|
|
FloatParts pa = float64_unpack_canonical(a, status);
|
|
FloatParts pb = float64_unpack_canonical(b, status);
|
|
FloatParts pr = div_floats(pa, pb, status);
|
|
|
|
return float64_round_pack_canonical(pr, status);
|
|
}
|
|
|
|
static float hard_f32_div(float a, float b)
|
|
{
|
|
return a / b;
|
|
}
|
|
|
|
static double hard_f64_div(double a, double b)
|
|
{
|
|
return a / b;
|
|
}
|
|
|
|
static bool f32_div_pre(union_float32 a, union_float32 b)
|
|
{
|
|
if (QEMU_HARDFLOAT_2F32_USE_FP) {
|
|
return (fpclassify(a.h) == FP_NORMAL || fpclassify(a.h) == FP_ZERO) &&
|
|
fpclassify(b.h) == FP_NORMAL;
|
|
}
|
|
return float32_is_zero_or_normal(a.s) && float32_is_normal(b.s);
|
|
}
|
|
|
|
static bool f64_div_pre(union_float64 a, union_float64 b)
|
|
{
|
|
if (QEMU_HARDFLOAT_2F64_USE_FP) {
|
|
return (fpclassify(a.h) == FP_NORMAL || fpclassify(a.h) == FP_ZERO) &&
|
|
fpclassify(b.h) == FP_NORMAL;
|
|
}
|
|
return float64_is_zero_or_normal(a.s) && float64_is_normal(b.s);
|
|
}
|
|
|
|
static bool f32_div_post(union_float32 a, union_float32 b)
|
|
{
|
|
if (QEMU_HARDFLOAT_2F32_USE_FP) {
|
|
return fpclassify(a.h) != FP_ZERO;
|
|
}
|
|
return !float32_is_zero(a.s);
|
|
}
|
|
|
|
static bool f64_div_post(union_float64 a, union_float64 b)
|
|
{
|
|
if (QEMU_HARDFLOAT_2F64_USE_FP) {
|
|
return fpclassify(a.h) != FP_ZERO;
|
|
}
|
|
return !float64_is_zero(a.s);
|
|
}
|
|
|
|
float32 QEMU_FLATTEN
|
|
float32_div(float32 a, float32 b, float_status *s)
|
|
{
|
|
return float32_gen2(a, b, s, hard_f32_div, soft_f32_div,
|
|
f32_div_pre, f32_div_post);
|
|
}
|
|
|
|
float64 QEMU_FLATTEN
|
|
float64_div(float64 a, float64 b, float_status *s)
|
|
{
|
|
return float64_gen2(a, b, s, hard_f64_div, soft_f64_div,
|
|
f64_div_pre, f64_div_post);
|
|
}
|
|
|
|
/*
|
|
* Float to Float conversions
|
|
*
|
|
* Returns the result of converting one float format to another. The
|
|
* conversion is performed according to the IEC/IEEE Standard for
|
|
* Binary Floating-Point Arithmetic.
|
|
*
|
|
* The float_to_float helper only needs to take care of raising
|
|
* invalid exceptions and handling the conversion on NaNs.
|
|
*/
|
|
|
|
static FloatParts float_to_float(FloatParts a, const FloatFmt *dstf,
|
|
float_status *s)
|
|
{
|
|
if (dstf->arm_althp) {
|
|
switch (a.cls) {
|
|
case float_class_qnan:
|
|
case float_class_snan:
|
|
/* There is no NaN in the destination format. Raise Invalid
|
|
* and return a zero with the sign of the input NaN.
|
|
*/
|
|
s->float_exception_flags |= float_flag_invalid;
|
|
a.cls = float_class_zero;
|
|
a.frac = 0;
|
|
a.exp = 0;
|
|
break;
|
|
|
|
case float_class_inf:
|
|
/* There is no Inf in the destination format. Raise Invalid
|
|
* and return the maximum normal with the correct sign.
|
|
*/
|
|
s->float_exception_flags |= float_flag_invalid;
|
|
a.cls = float_class_normal;
|
|
a.exp = dstf->exp_max;
|
|
a.frac = ((1ull << dstf->frac_size) - 1) << dstf->frac_shift;
|
|
break;
|
|
|
|
default:
|
|
break;
|
|
}
|
|
} else if (is_nan(a.cls)) {
|
|
if (is_snan(a.cls)) {
|
|
s->float_exception_flags |= float_flag_invalid;
|
|
a = parts_silence_nan(a, s);
|
|
}
|
|
if (s->default_nan_mode) {
|
|
return parts_default_nan(s);
|
|
}
|
|
}
|
|
return a;
|
|
}
|
|
|
|
float32 float16_to_float32(float16 a, bool ieee, float_status *s)
|
|
{
|
|
const FloatFmt *fmt16 = ieee ? &float16_params : &float16_params_ahp;
|
|
FloatParts p = float16a_unpack_canonical(a, s, fmt16);
|
|
FloatParts pr = float_to_float(p, &float32_params, s);
|
|
return float32_round_pack_canonical(pr, s);
|
|
}
|
|
|
|
float64 float16_to_float64(float16 a, bool ieee, float_status *s)
|
|
{
|
|
const FloatFmt *fmt16 = ieee ? &float16_params : &float16_params_ahp;
|
|
FloatParts p = float16a_unpack_canonical(a, s, fmt16);
|
|
FloatParts pr = float_to_float(p, &float64_params, s);
|
|
return float64_round_pack_canonical(pr, s);
|
|
}
|
|
|
|
float16 float32_to_float16(float32 a, bool ieee, float_status *s)
|
|
{
|
|
const FloatFmt *fmt16 = ieee ? &float16_params : &float16_params_ahp;
|
|
FloatParts p = float32_unpack_canonical(a, s);
|
|
FloatParts pr = float_to_float(p, fmt16, s);
|
|
return float16a_round_pack_canonical(pr, s, fmt16);
|
|
}
|
|
|
|
float64 float32_to_float64(float32 a, float_status *s)
|
|
{
|
|
FloatParts p = float32_unpack_canonical(a, s);
|
|
FloatParts pr = float_to_float(p, &float64_params, s);
|
|
return float64_round_pack_canonical(pr, s);
|
|
}
|
|
|
|
float16 float64_to_float16(float64 a, bool ieee, float_status *s)
|
|
{
|
|
const FloatFmt *fmt16 = ieee ? &float16_params : &float16_params_ahp;
|
|
FloatParts p = float64_unpack_canonical(a, s);
|
|
FloatParts pr = float_to_float(p, fmt16, s);
|
|
return float16a_round_pack_canonical(pr, s, fmt16);
|
|
}
|
|
|
|
float32 float64_to_float32(float64 a, float_status *s)
|
|
{
|
|
FloatParts p = float64_unpack_canonical(a, s);
|
|
FloatParts pr = float_to_float(p, &float32_params, s);
|
|
return float32_round_pack_canonical(pr, s);
|
|
}
|
|
|
|
/*
|
|
* Rounds the floating-point value `a' to an integer, and returns the
|
|
* result as a floating-point value. The operation is performed
|
|
* according to the IEC/IEEE Standard for Binary Floating-Point
|
|
* Arithmetic.
|
|
*/
|
|
|
|
static FloatParts round_to_int(FloatParts a, FloatRoundMode rmode,
|
|
int scale, float_status *s)
|
|
{
|
|
switch (a.cls) {
|
|
case float_class_qnan:
|
|
case float_class_snan:
|
|
return return_nan(a, s);
|
|
|
|
case float_class_zero:
|
|
case float_class_inf:
|
|
/* already "integral" */
|
|
break;
|
|
|
|
case float_class_normal:
|
|
scale = MIN(MAX(scale, -0x10000), 0x10000);
|
|
a.exp += scale;
|
|
|
|
if (a.exp >= DECOMPOSED_BINARY_POINT) {
|
|
/* already integral */
|
|
break;
|
|
}
|
|
if (a.exp < 0) {
|
|
bool one;
|
|
/* all fractional */
|
|
s->float_exception_flags |= float_flag_inexact;
|
|
switch (rmode) {
|
|
case float_round_nearest_even:
|
|
one = a.exp == -1 && a.frac > DECOMPOSED_IMPLICIT_BIT;
|
|
break;
|
|
case float_round_ties_away:
|
|
one = a.exp == -1 && a.frac >= DECOMPOSED_IMPLICIT_BIT;
|
|
break;
|
|
case float_round_to_zero:
|
|
one = false;
|
|
break;
|
|
case float_round_up:
|
|
one = !a.sign;
|
|
break;
|
|
case float_round_down:
|
|
one = a.sign;
|
|
break;
|
|
case float_round_to_odd:
|
|
one = true;
|
|
break;
|
|
default:
|
|
g_assert_not_reached();
|
|
}
|
|
|
|
if (one) {
|
|
a.frac = DECOMPOSED_IMPLICIT_BIT;
|
|
a.exp = 0;
|
|
} else {
|
|
a.cls = float_class_zero;
|
|
}
|
|
} else {
|
|
uint64_t frac_lsb = DECOMPOSED_IMPLICIT_BIT >> a.exp;
|
|
uint64_t frac_lsbm1 = frac_lsb >> 1;
|
|
uint64_t rnd_even_mask = (frac_lsb - 1) | frac_lsb;
|
|
uint64_t rnd_mask = rnd_even_mask >> 1;
|
|
uint64_t inc;
|
|
|
|
switch (rmode) {
|
|
case float_round_nearest_even:
|
|
inc = ((a.frac & rnd_even_mask) != frac_lsbm1 ? frac_lsbm1 : 0);
|
|
break;
|
|
case float_round_ties_away:
|
|
inc = frac_lsbm1;
|
|
break;
|
|
case float_round_to_zero:
|
|
inc = 0;
|
|
break;
|
|
case float_round_up:
|
|
inc = a.sign ? 0 : rnd_mask;
|
|
break;
|
|
case float_round_down:
|
|
inc = a.sign ? rnd_mask : 0;
|
|
break;
|
|
case float_round_to_odd:
|
|
inc = a.frac & frac_lsb ? 0 : rnd_mask;
|
|
break;
|
|
default:
|
|
g_assert_not_reached();
|
|
}
|
|
|
|
if (a.frac & rnd_mask) {
|
|
s->float_exception_flags |= float_flag_inexact;
|
|
a.frac += inc;
|
|
a.frac &= ~rnd_mask;
|
|
if (a.frac & DECOMPOSED_OVERFLOW_BIT) {
|
|
a.frac >>= 1;
|
|
a.exp++;
|
|
}
|
|
}
|
|
}
|
|
break;
|
|
default:
|
|
g_assert_not_reached();
|
|
}
|
|
return a;
|
|
}
|
|
|
|
float16 float16_round_to_int(float16 a, float_status *s)
|
|
{
|
|
FloatParts pa = float16_unpack_canonical(a, s);
|
|
FloatParts pr = round_to_int(pa, s->float_rounding_mode, 0, s);
|
|
return float16_round_pack_canonical(pr, s);
|
|
}
|
|
|
|
float32 float32_round_to_int(float32 a, float_status *s)
|
|
{
|
|
FloatParts pa = float32_unpack_canonical(a, s);
|
|
FloatParts pr = round_to_int(pa, s->float_rounding_mode, 0, s);
|
|
return float32_round_pack_canonical(pr, s);
|
|
}
|
|
|
|
float64 float64_round_to_int(float64 a, float_status *s)
|
|
{
|
|
FloatParts pa = float64_unpack_canonical(a, s);
|
|
FloatParts pr = round_to_int(pa, s->float_rounding_mode, 0, s);
|
|
return float64_round_pack_canonical(pr, s);
|
|
}
|
|
|
|
/*
|
|
* Returns the result of converting the floating-point value `a' to
|
|
* the two's complement integer format. The conversion is performed
|
|
* according to the IEC/IEEE Standard for Binary Floating-Point
|
|
* Arithmetic---which means in particular that the conversion is
|
|
* rounded according to the current rounding mode. If `a' is a NaN,
|
|
* the largest positive integer is returned. Otherwise, if the
|
|
* conversion overflows, the largest integer with the same sign as `a'
|
|
* is returned.
|
|
*/
|
|
|
|
static int64_t round_to_int_and_pack(FloatParts in, FloatRoundMode rmode,
|
|
int scale, int64_t min, int64_t max,
|
|
float_status *s)
|
|
{
|
|
uint64_t r;
|
|
int orig_flags = get_float_exception_flags(s);
|
|
FloatParts p = round_to_int(in, rmode, scale, s);
|
|
|
|
switch (p.cls) {
|
|
case float_class_snan:
|
|
case float_class_qnan:
|
|
s->float_exception_flags = orig_flags | float_flag_invalid;
|
|
return max;
|
|
case float_class_inf:
|
|
s->float_exception_flags = orig_flags | float_flag_invalid;
|
|
return p.sign ? min : max;
|
|
case float_class_zero:
|
|
return 0;
|
|
case float_class_normal:
|
|
if (p.exp < DECOMPOSED_BINARY_POINT) {
|
|
r = p.frac >> (DECOMPOSED_BINARY_POINT - p.exp);
|
|
} else if (p.exp - DECOMPOSED_BINARY_POINT < 2) {
|
|
r = p.frac << (p.exp - DECOMPOSED_BINARY_POINT);
|
|
} else {
|
|
r = UINT64_MAX;
|
|
}
|
|
if (p.sign) {
|
|
if (r <= -(uint64_t) min) {
|
|
return -r;
|
|
} else {
|
|
s->float_exception_flags = orig_flags | float_flag_invalid;
|
|
return min;
|
|
}
|
|
} else {
|
|
if (r <= max) {
|
|
return r;
|
|
} else {
|
|
s->float_exception_flags = orig_flags | float_flag_invalid;
|
|
return max;
|
|
}
|
|
}
|
|
default:
|
|
g_assert_not_reached();
|
|
}
|
|
}
|
|
|
|
int16_t float16_to_int16_scalbn(float16 a, FloatRoundMode rmode, int scale,
|
|
float_status *s)
|
|
{
|
|
return round_to_int_and_pack(float16_unpack_canonical(a, s),
|
|
rmode, scale, INT16_MIN, INT16_MAX, s);
|
|
}
|
|
|
|
int32_t float16_to_int32_scalbn(float16 a, FloatRoundMode rmode, int scale,
|
|
float_status *s)
|
|
{
|
|
return round_to_int_and_pack(float16_unpack_canonical(a, s),
|
|
rmode, scale, INT32_MIN, INT32_MAX, s);
|
|
}
|
|
|
|
int64_t float16_to_int64_scalbn(float16 a, FloatRoundMode rmode, int scale,
|
|
float_status *s)
|
|
{
|
|
return round_to_int_and_pack(float16_unpack_canonical(a, s),
|
|
rmode, scale, INT64_MIN, INT64_MAX, s);
|
|
}
|
|
|
|
int16_t float32_to_int16_scalbn(float32 a, FloatRoundMode rmode, int scale,
|
|
float_status *s)
|
|
{
|
|
return round_to_int_and_pack(float32_unpack_canonical(a, s),
|
|
rmode, scale, INT16_MIN, INT16_MAX, s);
|
|
}
|
|
|
|
int32_t float32_to_int32_scalbn(float32 a, FloatRoundMode rmode, int scale,
|
|
float_status *s)
|
|
{
|
|
return round_to_int_and_pack(float32_unpack_canonical(a, s),
|
|
rmode, scale, INT32_MIN, INT32_MAX, s);
|
|
}
|
|
|
|
int64_t float32_to_int64_scalbn(float32 a, FloatRoundMode rmode, int scale,
|
|
float_status *s)
|
|
{
|
|
return round_to_int_and_pack(float32_unpack_canonical(a, s),
|
|
rmode, scale, INT64_MIN, INT64_MAX, s);
|
|
}
|
|
|
|
int16_t float64_to_int16_scalbn(float64 a, FloatRoundMode rmode, int scale,
|
|
float_status *s)
|
|
{
|
|
return round_to_int_and_pack(float64_unpack_canonical(a, s),
|
|
rmode, scale, INT16_MIN, INT16_MAX, s);
|
|
}
|
|
|
|
int32_t float64_to_int32_scalbn(float64 a, FloatRoundMode rmode, int scale,
|
|
float_status *s)
|
|
{
|
|
return round_to_int_and_pack(float64_unpack_canonical(a, s),
|
|
rmode, scale, INT32_MIN, INT32_MAX, s);
|
|
}
|
|
|
|
int64_t float64_to_int64_scalbn(float64 a, FloatRoundMode rmode, int scale,
|
|
float_status *s)
|
|
{
|
|
return round_to_int_and_pack(float64_unpack_canonical(a, s),
|
|
rmode, scale, INT64_MIN, INT64_MAX, s);
|
|
}
|
|
|
|
int16_t float16_to_int16(float16 a, float_status *s)
|
|
{
|
|
return float16_to_int16_scalbn(a, s->float_rounding_mode, 0, s);
|
|
}
|
|
|
|
int32_t float16_to_int32(float16 a, float_status *s)
|
|
{
|
|
return float16_to_int32_scalbn(a, s->float_rounding_mode, 0, s);
|
|
}
|
|
|
|
int64_t float16_to_int64(float16 a, float_status *s)
|
|
{
|
|
return float16_to_int64_scalbn(a, s->float_rounding_mode, 0, s);
|
|
}
|
|
|
|
int16_t float32_to_int16(float32 a, float_status *s)
|
|
{
|
|
return float32_to_int16_scalbn(a, s->float_rounding_mode, 0, s);
|
|
}
|
|
|
|
int32_t float32_to_int32(float32 a, float_status *s)
|
|
{
|
|
return float32_to_int32_scalbn(a, s->float_rounding_mode, 0, s);
|
|
}
|
|
|
|
int64_t float32_to_int64(float32 a, float_status *s)
|
|
{
|
|
return float32_to_int64_scalbn(a, s->float_rounding_mode, 0, s);
|
|
}
|
|
|
|
int16_t float64_to_int16(float64 a, float_status *s)
|
|
{
|
|
return float64_to_int16_scalbn(a, s->float_rounding_mode, 0, s);
|
|
}
|
|
|
|
int32_t float64_to_int32(float64 a, float_status *s)
|
|
{
|
|
return float64_to_int32_scalbn(a, s->float_rounding_mode, 0, s);
|
|
}
|
|
|
|
int64_t float64_to_int64(float64 a, float_status *s)
|
|
{
|
|
return float64_to_int64_scalbn(a, s->float_rounding_mode, 0, s);
|
|
}
|
|
|
|
int16_t float16_to_int16_round_to_zero(float16 a, float_status *s)
|
|
{
|
|
return float16_to_int16_scalbn(a, float_round_to_zero, 0, s);
|
|
}
|
|
|
|
int32_t float16_to_int32_round_to_zero(float16 a, float_status *s)
|
|
{
|
|
return float16_to_int32_scalbn(a, float_round_to_zero, 0, s);
|
|
}
|
|
|
|
int64_t float16_to_int64_round_to_zero(float16 a, float_status *s)
|
|
{
|
|
return float16_to_int64_scalbn(a, float_round_to_zero, 0, s);
|
|
}
|
|
|
|
int16_t float32_to_int16_round_to_zero(float32 a, float_status *s)
|
|
{
|
|
return float32_to_int16_scalbn(a, float_round_to_zero, 0, s);
|
|
}
|
|
|
|
int32_t float32_to_int32_round_to_zero(float32 a, float_status *s)
|
|
{
|
|
return float32_to_int32_scalbn(a, float_round_to_zero, 0, s);
|
|
}
|
|
|
|
int64_t float32_to_int64_round_to_zero(float32 a, float_status *s)
|
|
{
|
|
return float32_to_int64_scalbn(a, float_round_to_zero, 0, s);
|
|
}
|
|
|
|
int16_t float64_to_int16_round_to_zero(float64 a, float_status *s)
|
|
{
|
|
return float64_to_int16_scalbn(a, float_round_to_zero, 0, s);
|
|
}
|
|
|
|
int32_t float64_to_int32_round_to_zero(float64 a, float_status *s)
|
|
{
|
|
return float64_to_int32_scalbn(a, float_round_to_zero, 0, s);
|
|
}
|
|
|
|
int64_t float64_to_int64_round_to_zero(float64 a, float_status *s)
|
|
{
|
|
return float64_to_int64_scalbn(a, float_round_to_zero, 0, s);
|
|
}
|
|
|
|
/*
|
|
* Returns the result of converting the floating-point value `a' to
|
|
* the unsigned integer format. The conversion is performed according
|
|
* to the IEC/IEEE Standard for Binary Floating-Point
|
|
* Arithmetic---which means in particular that the conversion is
|
|
* rounded according to the current rounding mode. If `a' is a NaN,
|
|
* the largest unsigned integer is returned. Otherwise, if the
|
|
* conversion overflows, the largest unsigned integer is returned. If
|
|
* the 'a' is negative, the result is rounded and zero is returned;
|
|
* values that do not round to zero will raise the inexact exception
|
|
* flag.
|
|
*/
|
|
|
|
static uint64_t round_to_uint_and_pack(FloatParts in, FloatRoundMode rmode,
|
|
int scale, uint64_t max,
|
|
float_status *s)
|
|
{
|
|
int orig_flags = get_float_exception_flags(s);
|
|
FloatParts p = round_to_int(in, rmode, scale, s);
|
|
uint64_t r;
|
|
|
|
switch (p.cls) {
|
|
case float_class_snan:
|
|
case float_class_qnan:
|
|
s->float_exception_flags = orig_flags | float_flag_invalid;
|
|
return max;
|
|
case float_class_inf:
|
|
s->float_exception_flags = orig_flags | float_flag_invalid;
|
|
return p.sign ? 0 : max;
|
|
case float_class_zero:
|
|
return 0;
|
|
case float_class_normal:
|
|
if (p.sign) {
|
|
s->float_exception_flags = orig_flags | float_flag_invalid;
|
|
return 0;
|
|
}
|
|
|
|
if (p.exp < DECOMPOSED_BINARY_POINT) {
|
|
r = p.frac >> (DECOMPOSED_BINARY_POINT - p.exp);
|
|
} else if (p.exp - DECOMPOSED_BINARY_POINT < 2) {
|
|
r = p.frac << (p.exp - DECOMPOSED_BINARY_POINT);
|
|
} else {
|
|
s->float_exception_flags = orig_flags | float_flag_invalid;
|
|
return max;
|
|
}
|
|
|
|
/* For uint64 this will never trip, but if p.exp is too large
|
|
* to shift a decomposed fraction we shall have exited via the
|
|
* 3rd leg above.
|
|
*/
|
|
if (r > max) {
|
|
s->float_exception_flags = orig_flags | float_flag_invalid;
|
|
return max;
|
|
}
|
|
return r;
|
|
default:
|
|
g_assert_not_reached();
|
|
}
|
|
}
|
|
|
|
uint16_t float16_to_uint16_scalbn(float16 a, FloatRoundMode rmode, int scale,
|
|
float_status *s)
|
|
{
|
|
return round_to_uint_and_pack(float16_unpack_canonical(a, s),
|
|
rmode, scale, UINT16_MAX, s);
|
|
}
|
|
|
|
uint32_t float16_to_uint32_scalbn(float16 a, FloatRoundMode rmode, int scale,
|
|
float_status *s)
|
|
{
|
|
return round_to_uint_and_pack(float16_unpack_canonical(a, s),
|
|
rmode, scale, UINT32_MAX, s);
|
|
}
|
|
|
|
uint64_t float16_to_uint64_scalbn(float16 a, FloatRoundMode rmode, int scale,
|
|
float_status *s)
|
|
{
|
|
return round_to_uint_and_pack(float16_unpack_canonical(a, s),
|
|
rmode, scale, UINT64_MAX, s);
|
|
}
|
|
|
|
uint16_t float32_to_uint16_scalbn(float32 a, FloatRoundMode rmode, int scale,
|
|
float_status *s)
|
|
{
|
|
return round_to_uint_and_pack(float32_unpack_canonical(a, s),
|
|
rmode, scale, UINT16_MAX, s);
|
|
}
|
|
|
|
uint32_t float32_to_uint32_scalbn(float32 a, FloatRoundMode rmode, int scale,
|
|
float_status *s)
|
|
{
|
|
return round_to_uint_and_pack(float32_unpack_canonical(a, s),
|
|
rmode, scale, UINT32_MAX, s);
|
|
}
|
|
|
|
uint64_t float32_to_uint64_scalbn(float32 a, FloatRoundMode rmode, int scale,
|
|
float_status *s)
|
|
{
|
|
return round_to_uint_and_pack(float32_unpack_canonical(a, s),
|
|
rmode, scale, UINT64_MAX, s);
|
|
}
|
|
|
|
uint16_t float64_to_uint16_scalbn(float64 a, FloatRoundMode rmode, int scale,
|
|
float_status *s)
|
|
{
|
|
return round_to_uint_and_pack(float64_unpack_canonical(a, s),
|
|
rmode, scale, UINT16_MAX, s);
|
|
}
|
|
|
|
uint32_t float64_to_uint32_scalbn(float64 a, FloatRoundMode rmode, int scale,
|
|
float_status *s)
|
|
{
|
|
return round_to_uint_and_pack(float64_unpack_canonical(a, s),
|
|
rmode, scale, UINT32_MAX, s);
|
|
}
|
|
|
|
uint64_t float64_to_uint64_scalbn(float64 a, FloatRoundMode rmode, int scale,
|
|
float_status *s)
|
|
{
|
|
return round_to_uint_and_pack(float64_unpack_canonical(a, s),
|
|
rmode, scale, UINT64_MAX, s);
|
|
}
|
|
|
|
uint16_t float16_to_uint16(float16 a, float_status *s)
|
|
{
|
|
return float16_to_uint16_scalbn(a, s->float_rounding_mode, 0, s);
|
|
}
|
|
|
|
uint32_t float16_to_uint32(float16 a, float_status *s)
|
|
{
|
|
return float16_to_uint32_scalbn(a, s->float_rounding_mode, 0, s);
|
|
}
|
|
|
|
uint64_t float16_to_uint64(float16 a, float_status *s)
|
|
{
|
|
return float16_to_uint64_scalbn(a, s->float_rounding_mode, 0, s);
|
|
}
|
|
|
|
uint16_t float32_to_uint16(float32 a, float_status *s)
|
|
{
|
|
return float32_to_uint16_scalbn(a, s->float_rounding_mode, 0, s);
|
|
}
|
|
|
|
uint32_t float32_to_uint32(float32 a, float_status *s)
|
|
{
|
|
return float32_to_uint32_scalbn(a, s->float_rounding_mode, 0, s);
|
|
}
|
|
|
|
uint64_t float32_to_uint64(float32 a, float_status *s)
|
|
{
|
|
return float32_to_uint64_scalbn(a, s->float_rounding_mode, 0, s);
|
|
}
|
|
|
|
uint16_t float64_to_uint16(float64 a, float_status *s)
|
|
{
|
|
return float64_to_uint16_scalbn(a, s->float_rounding_mode, 0, s);
|
|
}
|
|
|
|
uint32_t float64_to_uint32(float64 a, float_status *s)
|
|
{
|
|
return float64_to_uint32_scalbn(a, s->float_rounding_mode, 0, s);
|
|
}
|
|
|
|
uint64_t float64_to_uint64(float64 a, float_status *s)
|
|
{
|
|
return float64_to_uint64_scalbn(a, s->float_rounding_mode, 0, s);
|
|
}
|
|
|
|
uint16_t float16_to_uint16_round_to_zero(float16 a, float_status *s)
|
|
{
|
|
return float16_to_uint16_scalbn(a, float_round_to_zero, 0, s);
|
|
}
|
|
|
|
uint32_t float16_to_uint32_round_to_zero(float16 a, float_status *s)
|
|
{
|
|
return float16_to_uint32_scalbn(a, float_round_to_zero, 0, s);
|
|
}
|
|
|
|
uint64_t float16_to_uint64_round_to_zero(float16 a, float_status *s)
|
|
{
|
|
return float16_to_uint64_scalbn(a, float_round_to_zero, 0, s);
|
|
}
|
|
|
|
uint16_t float32_to_uint16_round_to_zero(float32 a, float_status *s)
|
|
{
|
|
return float32_to_uint16_scalbn(a, float_round_to_zero, 0, s);
|
|
}
|
|
|
|
uint32_t float32_to_uint32_round_to_zero(float32 a, float_status *s)
|
|
{
|
|
return float32_to_uint32_scalbn(a, float_round_to_zero, 0, s);
|
|
}
|
|
|
|
uint64_t float32_to_uint64_round_to_zero(float32 a, float_status *s)
|
|
{
|
|
return float32_to_uint64_scalbn(a, float_round_to_zero, 0, s);
|
|
}
|
|
|
|
uint16_t float64_to_uint16_round_to_zero(float64 a, float_status *s)
|
|
{
|
|
return float64_to_uint16_scalbn(a, float_round_to_zero, 0, s);
|
|
}
|
|
|
|
uint32_t float64_to_uint32_round_to_zero(float64 a, float_status *s)
|
|
{
|
|
return float64_to_uint32_scalbn(a, float_round_to_zero, 0, s);
|
|
}
|
|
|
|
uint64_t float64_to_uint64_round_to_zero(float64 a, float_status *s)
|
|
{
|
|
return float64_to_uint64_scalbn(a, float_round_to_zero, 0, s);
|
|
}
|
|
|
|
/*
|
|
* Integer to float conversions
|
|
*
|
|
* Returns the result of converting the two's complement integer `a'
|
|
* to the floating-point format. The conversion is performed according
|
|
* to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
|
*/
|
|
|
|
static FloatParts int_to_float(int64_t a, int scale, float_status *status)
|
|
{
|
|
FloatParts r = { .sign = false };
|
|
|
|
if (a == 0) {
|
|
r.cls = float_class_zero;
|
|
} else {
|
|
uint64_t f = a;
|
|
int shift;
|
|
|
|
r.cls = float_class_normal;
|
|
if (a < 0) {
|
|
f = -f;
|
|
r.sign = true;
|
|
}
|
|
shift = clz64(f) - 1;
|
|
scale = MIN(MAX(scale, -0x10000), 0x10000);
|
|
|
|
r.exp = DECOMPOSED_BINARY_POINT - shift + scale;
|
|
r.frac = (shift < 0 ? DECOMPOSED_IMPLICIT_BIT : f << shift);
|
|
}
|
|
|
|
return r;
|
|
}
|
|
|
|
float16 int64_to_float16_scalbn(int64_t a, int scale, float_status *status)
|
|
{
|
|
FloatParts pa = int_to_float(a, scale, status);
|
|
return float16_round_pack_canonical(pa, status);
|
|
}
|
|
|
|
float16 int32_to_float16_scalbn(int32_t a, int scale, float_status *status)
|
|
{
|
|
return int64_to_float16_scalbn(a, scale, status);
|
|
}
|
|
|
|
float16 int16_to_float16_scalbn(int16_t a, int scale, float_status *status)
|
|
{
|
|
return int64_to_float16_scalbn(a, scale, status);
|
|
}
|
|
|
|
float16 int64_to_float16(int64_t a, float_status *status)
|
|
{
|
|
return int64_to_float16_scalbn(a, 0, status);
|
|
}
|
|
|
|
float16 int32_to_float16(int32_t a, float_status *status)
|
|
{
|
|
return int64_to_float16_scalbn(a, 0, status);
|
|
}
|
|
|
|
float16 int16_to_float16(int16_t a, float_status *status)
|
|
{
|
|
return int64_to_float16_scalbn(a, 0, status);
|
|
}
|
|
|
|
float32 int64_to_float32_scalbn(int64_t a, int scale, float_status *status)
|
|
{
|
|
FloatParts pa = int_to_float(a, scale, status);
|
|
return float32_round_pack_canonical(pa, status);
|
|
}
|
|
|
|
float32 int32_to_float32_scalbn(int32_t a, int scale, float_status *status)
|
|
{
|
|
return int64_to_float32_scalbn(a, scale, status);
|
|
}
|
|
|
|
float32 int16_to_float32_scalbn(int16_t a, int scale, float_status *status)
|
|
{
|
|
return int64_to_float32_scalbn(a, scale, status);
|
|
}
|
|
|
|
float32 int64_to_float32(int64_t a, float_status *status)
|
|
{
|
|
return int64_to_float32_scalbn(a, 0, status);
|
|
}
|
|
|
|
float32 int32_to_float32(int32_t a, float_status *status)
|
|
{
|
|
return int64_to_float32_scalbn(a, 0, status);
|
|
}
|
|
|
|
float32 int16_to_float32(int16_t a, float_status *status)
|
|
{
|
|
return int64_to_float32_scalbn(a, 0, status);
|
|
}
|
|
|
|
float64 int64_to_float64_scalbn(int64_t a, int scale, float_status *status)
|
|
{
|
|
FloatParts pa = int_to_float(a, scale, status);
|
|
return float64_round_pack_canonical(pa, status);
|
|
}
|
|
|
|
float64 int32_to_float64_scalbn(int32_t a, int scale, float_status *status)
|
|
{
|
|
return int64_to_float64_scalbn(a, scale, status);
|
|
}
|
|
|
|
float64 int16_to_float64_scalbn(int16_t a, int scale, float_status *status)
|
|
{
|
|
return int64_to_float64_scalbn(a, scale, status);
|
|
}
|
|
|
|
float64 int64_to_float64(int64_t a, float_status *status)
|
|
{
|
|
return int64_to_float64_scalbn(a, 0, status);
|
|
}
|
|
|
|
float64 int32_to_float64(int32_t a, float_status *status)
|
|
{
|
|
return int64_to_float64_scalbn(a, 0, status);
|
|
}
|
|
|
|
float64 int16_to_float64(int16_t a, float_status *status)
|
|
{
|
|
return int64_to_float64_scalbn(a, 0, status);
|
|
}
|
|
|
|
|
|
/*
|
|
* Unsigned Integer to float conversions
|
|
*
|
|
* Returns the result of converting the unsigned integer `a' to the
|
|
* floating-point format. The conversion is performed according to the
|
|
* IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
|
*/
|
|
|
|
static FloatParts uint_to_float(uint64_t a, int scale, float_status *status)
|
|
{
|
|
FloatParts r = { .sign = false };
|
|
|
|
if (a == 0) {
|
|
r.cls = float_class_zero;
|
|
} else {
|
|
scale = MIN(MAX(scale, -0x10000), 0x10000);
|
|
r.cls = float_class_normal;
|
|
if ((int64_t)a < 0) {
|
|
r.exp = DECOMPOSED_BINARY_POINT + 1 + scale;
|
|
shift64RightJamming(a, 1, &a);
|
|
r.frac = a;
|
|
} else {
|
|
int shift = clz64(a) - 1;
|
|
r.exp = DECOMPOSED_BINARY_POINT - shift + scale;
|
|
r.frac = a << shift;
|
|
}
|
|
}
|
|
|
|
return r;
|
|
}
|
|
|
|
float16 uint64_to_float16_scalbn(uint64_t a, int scale, float_status *status)
|
|
{
|
|
FloatParts pa = uint_to_float(a, scale, status);
|
|
return float16_round_pack_canonical(pa, status);
|
|
}
|
|
|
|
float16 uint32_to_float16_scalbn(uint32_t a, int scale, float_status *status)
|
|
{
|
|
return uint64_to_float16_scalbn(a, scale, status);
|
|
}
|
|
|
|
float16 uint16_to_float16_scalbn(uint16_t a, int scale, float_status *status)
|
|
{
|
|
return uint64_to_float16_scalbn(a, scale, status);
|
|
}
|
|
|
|
float16 uint64_to_float16(uint64_t a, float_status *status)
|
|
{
|
|
return uint64_to_float16_scalbn(a, 0, status);
|
|
}
|
|
|
|
float16 uint32_to_float16(uint32_t a, float_status *status)
|
|
{
|
|
return uint64_to_float16_scalbn(a, 0, status);
|
|
}
|
|
|
|
float16 uint16_to_float16(uint16_t a, float_status *status)
|
|
{
|
|
return uint64_to_float16_scalbn(a, 0, status);
|
|
}
|
|
|
|
float32 uint64_to_float32_scalbn(uint64_t a, int scale, float_status *status)
|
|
{
|
|
FloatParts pa = uint_to_float(a, scale, status);
|
|
return float32_round_pack_canonical(pa, status);
|
|
}
|
|
|
|
float32 uint32_to_float32_scalbn(uint32_t a, int scale, float_status *status)
|
|
{
|
|
return uint64_to_float32_scalbn(a, scale, status);
|
|
}
|
|
|
|
float32 uint16_to_float32_scalbn(uint16_t a, int scale, float_status *status)
|
|
{
|
|
return uint64_to_float32_scalbn(a, scale, status);
|
|
}
|
|
|
|
float32 uint64_to_float32(uint64_t a, float_status *status)
|
|
{
|
|
return uint64_to_float32_scalbn(a, 0, status);
|
|
}
|
|
|
|
float32 uint32_to_float32(uint32_t a, float_status *status)
|
|
{
|
|
return uint64_to_float32_scalbn(a, 0, status);
|
|
}
|
|
|
|
float32 uint16_to_float32(uint16_t a, float_status *status)
|
|
{
|
|
return uint64_to_float32_scalbn(a, 0, status);
|
|
}
|
|
|
|
float64 uint64_to_float64_scalbn(uint64_t a, int scale, float_status *status)
|
|
{
|
|
FloatParts pa = uint_to_float(a, scale, status);
|
|
return float64_round_pack_canonical(pa, status);
|
|
}
|
|
|
|
float64 uint32_to_float64_scalbn(uint32_t a, int scale, float_status *status)
|
|
{
|
|
return uint64_to_float64_scalbn(a, scale, status);
|
|
}
|
|
|
|
float64 uint16_to_float64_scalbn(uint16_t a, int scale, float_status *status)
|
|
{
|
|
return uint64_to_float64_scalbn(a, scale, status);
|
|
}
|
|
|
|
float64 uint64_to_float64(uint64_t a, float_status *status)
|
|
{
|
|
return uint64_to_float64_scalbn(a, 0, status);
|
|
}
|
|
|
|
float64 uint32_to_float64(uint32_t a, float_status *status)
|
|
{
|
|
return uint64_to_float64_scalbn(a, 0, status);
|
|
}
|
|
|
|
float64 uint16_to_float64(uint16_t a, float_status *status)
|
|
{
|
|
return uint64_to_float64_scalbn(a, 0, status);
|
|
}
|
|
|
|
/* Float Min/Max */
|
|
/* min() and max() functions. These can't be implemented as
|
|
* 'compare and pick one input' because that would mishandle
|
|
* NaNs and +0 vs -0.
|
|
*
|
|
* minnum() and maxnum() functions. These are similar to the min()
|
|
* and max() functions but if one of the arguments is a QNaN and
|
|
* the other is numerical then the numerical argument is returned.
|
|
* SNaNs will get quietened before being returned.
|
|
* minnum() and maxnum correspond to the IEEE 754-2008 minNum()
|
|
* and maxNum() operations. min() and max() are the typical min/max
|
|
* semantics provided by many CPUs which predate that specification.
|
|
*
|
|
* minnummag() and maxnummag() functions correspond to minNumMag()
|
|
* and minNumMag() from the IEEE-754 2008.
|
|
*/
|
|
static FloatParts minmax_floats(FloatParts a, FloatParts b, bool ismin,
|
|
bool ieee, bool ismag, float_status *s)
|
|
{
|
|
if (unlikely(is_nan(a.cls) || is_nan(b.cls))) {
|
|
if (ieee) {
|
|
/* Takes two 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.
|
|
*/
|
|
if (is_snan(a.cls) || is_snan(b.cls)) {
|
|
return pick_nan(a, b, s);
|
|
} else if (is_nan(a.cls) && !is_nan(b.cls)) {
|
|
return b;
|
|
} else if (is_nan(b.cls) && !is_nan(a.cls)) {
|
|
return a;
|
|
}
|
|
}
|
|
return pick_nan(a, b, s);
|
|
} else {
|
|
int a_exp, b_exp;
|
|
|
|
switch (a.cls) {
|
|
case float_class_normal:
|
|
a_exp = a.exp;
|
|
break;
|
|
case float_class_inf:
|
|
a_exp = INT_MAX;
|
|
break;
|
|
case float_class_zero:
|
|
a_exp = INT_MIN;
|
|
break;
|
|
default:
|
|
g_assert_not_reached();
|
|
break;
|
|
}
|
|
switch (b.cls) {
|
|
case float_class_normal:
|
|
b_exp = b.exp;
|
|
break;
|
|
case float_class_inf:
|
|
b_exp = INT_MAX;
|
|
break;
|
|
case float_class_zero:
|
|
b_exp = INT_MIN;
|
|
break;
|
|
default:
|
|
g_assert_not_reached();
|
|
break;
|
|
}
|
|
|
|
if (ismag && (a_exp != b_exp || a.frac != b.frac)) {
|
|
bool a_less = a_exp < b_exp;
|
|
if (a_exp == b_exp) {
|
|
a_less = a.frac < b.frac;
|
|
}
|
|
return a_less ^ ismin ? b : a;
|
|
}
|
|
|
|
if (a.sign == b.sign) {
|
|
bool a_less = a_exp < b_exp;
|
|
if (a_exp == b_exp) {
|
|
a_less = a.frac < b.frac;
|
|
}
|
|
return a.sign ^ a_less ^ ismin ? b : a;
|
|
} else {
|
|
return a.sign ^ ismin ? b : a;
|
|
}
|
|
}
|
|
}
|
|
|
|
#define MINMAX(sz, name, ismin, isiee, ismag) \
|
|
float ## sz float ## sz ## _ ## name(float ## sz a, float ## sz b, \
|
|
float_status *s) \
|
|
{ \
|
|
FloatParts pa = float ## sz ## _unpack_canonical(a, s); \
|
|
FloatParts pb = float ## sz ## _unpack_canonical(b, s); \
|
|
FloatParts pr = minmax_floats(pa, pb, ismin, isiee, ismag, s); \
|
|
\
|
|
return float ## sz ## _round_pack_canonical(pr, s); \
|
|
}
|
|
|
|
MINMAX(16, min, true, false, false)
|
|
MINMAX(16, minnum, true, true, false)
|
|
MINMAX(16, minnummag, true, true, true)
|
|
MINMAX(16, max, false, false, false)
|
|
MINMAX(16, maxnum, false, true, false)
|
|
MINMAX(16, maxnummag, false, true, true)
|
|
|
|
MINMAX(32, min, true, false, false)
|
|
MINMAX(32, minnum, true, true, false)
|
|
MINMAX(32, minnummag, true, true, true)
|
|
MINMAX(32, max, false, false, false)
|
|
MINMAX(32, maxnum, false, true, false)
|
|
MINMAX(32, maxnummag, false, true, true)
|
|
|
|
MINMAX(64, min, true, false, false)
|
|
MINMAX(64, minnum, true, true, false)
|
|
MINMAX(64, minnummag, true, true, true)
|
|
MINMAX(64, max, false, false, false)
|
|
MINMAX(64, maxnum, false, true, false)
|
|
MINMAX(64, maxnummag, false, true, true)
|
|
|
|
#undef MINMAX
|
|
|
|
/* Floating point compare */
|
|
static FloatRelation compare_floats(FloatParts a, FloatParts b, bool is_quiet,
|
|
float_status *s)
|
|
{
|
|
if (is_nan(a.cls) || is_nan(b.cls)) {
|
|
if (!is_quiet ||
|
|
a.cls == float_class_snan ||
|
|
b.cls == float_class_snan) {
|
|
s->float_exception_flags |= float_flag_invalid;
|
|
}
|
|
return float_relation_unordered;
|
|
}
|
|
|
|
if (a.cls == float_class_zero) {
|
|
if (b.cls == float_class_zero) {
|
|
return float_relation_equal;
|
|
}
|
|
return b.sign ? float_relation_greater : float_relation_less;
|
|
} else if (b.cls == float_class_zero) {
|
|
return a.sign ? float_relation_less : float_relation_greater;
|
|
}
|
|
|
|
/* The only really important thing about infinity is its sign. If
|
|
* both are infinities the sign marks the smallest of the two.
|
|
*/
|
|
if (a.cls == float_class_inf) {
|
|
if ((b.cls == float_class_inf) && (a.sign == b.sign)) {
|
|
return float_relation_equal;
|
|
}
|
|
return a.sign ? float_relation_less : float_relation_greater;
|
|
} else if (b.cls == float_class_inf) {
|
|
return b.sign ? float_relation_greater : float_relation_less;
|
|
}
|
|
|
|
if (a.sign != b.sign) {
|
|
return a.sign ? float_relation_less : float_relation_greater;
|
|
}
|
|
|
|
if (a.exp == b.exp) {
|
|
if (a.frac == b.frac) {
|
|
return float_relation_equal;
|
|
}
|
|
if (a.sign) {
|
|
return a.frac > b.frac ?
|
|
float_relation_less : float_relation_greater;
|
|
} else {
|
|
return a.frac > b.frac ?
|
|
float_relation_greater : float_relation_less;
|
|
}
|
|
} else {
|
|
if (a.sign) {
|
|
return a.exp > b.exp ? float_relation_less : float_relation_greater;
|
|
} else {
|
|
return a.exp > b.exp ? float_relation_greater : float_relation_less;
|
|
}
|
|
}
|
|
}
|
|
|
|
#define COMPARE(name, attr, sz) \
|
|
static int attr \
|
|
name(float ## sz a, float ## sz b, bool is_quiet, float_status *s) \
|
|
{ \
|
|
FloatParts pa = float ## sz ## _unpack_canonical(a, s); \
|
|
FloatParts pb = float ## sz ## _unpack_canonical(b, s); \
|
|
return compare_floats(pa, pb, is_quiet, s); \
|
|
}
|
|
|
|
COMPARE(soft_f16_compare, QEMU_FLATTEN, 16)
|
|
COMPARE(soft_f32_compare, QEMU_SOFTFLOAT_ATTR, 32)
|
|
COMPARE(soft_f64_compare, QEMU_SOFTFLOAT_ATTR, 64)
|
|
|
|
#undef COMPARE
|
|
|
|
FloatRelation float16_compare(float16 a, float16 b, float_status *s)
|
|
{
|
|
return soft_f16_compare(a, b, false, s);
|
|
}
|
|
|
|
FloatRelation float16_compare_quiet(float16 a, float16 b, float_status *s)
|
|
{
|
|
return soft_f16_compare(a, b, true, s);
|
|
}
|
|
|
|
static FloatRelation QEMU_FLATTEN
|
|
f32_compare(float32 xa, float32 xb, bool is_quiet, float_status *s)
|
|
{
|
|
union_float32 ua, ub;
|
|
|
|
ua.s = xa;
|
|
ub.s = xb;
|
|
|
|
if (QEMU_NO_HARDFLOAT) {
|
|
goto soft;
|
|
}
|
|
|
|
float32_input_flush2(&ua.s, &ub.s, s);
|
|
if (isgreaterequal(ua.h, ub.h)) {
|
|
if (isgreater(ua.h, ub.h)) {
|
|
return float_relation_greater;
|
|
}
|
|
return float_relation_equal;
|
|
}
|
|
if (likely(isless(ua.h, ub.h))) {
|
|
return float_relation_less;
|
|
}
|
|
/* The only condition remaining is unordered.
|
|
* Fall through to set flags.
|
|
*/
|
|
soft:
|
|
return soft_f32_compare(ua.s, ub.s, is_quiet, s);
|
|
}
|
|
|
|
FloatRelation float32_compare(float32 a, float32 b, float_status *s)
|
|
{
|
|
return f32_compare(a, b, false, s);
|
|
}
|
|
|
|
FloatRelation float32_compare_quiet(float32 a, float32 b, float_status *s)
|
|
{
|
|
return f32_compare(a, b, true, s);
|
|
}
|
|
|
|
static FloatRelation QEMU_FLATTEN
|
|
f64_compare(float64 xa, float64 xb, bool is_quiet, float_status *s)
|
|
{
|
|
union_float64 ua, ub;
|
|
|
|
ua.s = xa;
|
|
ub.s = xb;
|
|
|
|
if (QEMU_NO_HARDFLOAT) {
|
|
goto soft;
|
|
}
|
|
|
|
float64_input_flush2(&ua.s, &ub.s, s);
|
|
if (isgreaterequal(ua.h, ub.h)) {
|
|
if (isgreater(ua.h, ub.h)) {
|
|
return float_relation_greater;
|
|
}
|
|
return float_relation_equal;
|
|
}
|
|
if (likely(isless(ua.h, ub.h))) {
|
|
return float_relation_less;
|
|
}
|
|
/* The only condition remaining is unordered.
|
|
* Fall through to set flags.
|
|
*/
|
|
soft:
|
|
return soft_f64_compare(ua.s, ub.s, is_quiet, s);
|
|
}
|
|
|
|
FloatRelation float64_compare(float64 a, float64 b, float_status *s)
|
|
{
|
|
return f64_compare(a, b, false, s);
|
|
}
|
|
|
|
FloatRelation float64_compare_quiet(float64 a, float64 b, float_status *s)
|
|
{
|
|
return f64_compare(a, b, true, s);
|
|
}
|
|
|
|
/* Multiply A by 2 raised to the power N. */
|
|
static FloatParts scalbn_decomposed(FloatParts a, int n, float_status *s)
|
|
{
|
|
if (unlikely(is_nan(a.cls))) {
|
|
return return_nan(a, s);
|
|
}
|
|
if (a.cls == float_class_normal) {
|
|
/* The largest float type (even though not supported by FloatParts)
|
|
* is float128, which has a 15 bit exponent. Bounding N to 16 bits
|
|
* still allows rounding to infinity, without allowing overflow
|
|
* within the int32_t that backs FloatParts.exp.
|
|
*/
|
|
n = MIN(MAX(n, -0x10000), 0x10000);
|
|
a.exp += n;
|
|
}
|
|
return a;
|
|
}
|
|
|
|
float16 float16_scalbn(float16 a, int n, float_status *status)
|
|
{
|
|
FloatParts pa = float16_unpack_canonical(a, status);
|
|
FloatParts pr = scalbn_decomposed(pa, n, status);
|
|
return float16_round_pack_canonical(pr, status);
|
|
}
|
|
|
|
float32 float32_scalbn(float32 a, int n, float_status *status)
|
|
{
|
|
FloatParts pa = float32_unpack_canonical(a, status);
|
|
FloatParts pr = scalbn_decomposed(pa, n, status);
|
|
return float32_round_pack_canonical(pr, status);
|
|
}
|
|
|
|
float64 float64_scalbn(float64 a, int n, float_status *status)
|
|
{
|
|
FloatParts pa = float64_unpack_canonical(a, status);
|
|
FloatParts pr = scalbn_decomposed(pa, n, status);
|
|
return float64_round_pack_canonical(pr, status);
|
|
}
|
|
|
|
/*
|
|
* Square Root
|
|
*
|
|
* The old softfloat code did an approximation step before zeroing in
|
|
* on the final result. However for simpleness we just compute the
|
|
* square root by iterating down from the implicit bit to enough extra
|
|
* bits to ensure we get a correctly rounded result.
|
|
*
|
|
* This does mean however the calculation is slower than before,
|
|
* especially for 64 bit floats.
|
|
*/
|
|
|
|
static FloatParts sqrt_float(FloatParts a, float_status *s, const FloatFmt *p)
|
|
{
|
|
uint64_t a_frac, r_frac, s_frac;
|
|
int bit, last_bit;
|
|
|
|
if (is_nan(a.cls)) {
|
|
return return_nan(a, s);
|
|
}
|
|
if (a.cls == float_class_zero) {
|
|
return a; /* sqrt(+-0) = +-0 */
|
|
}
|
|
if (a.sign) {
|
|
s->float_exception_flags |= float_flag_invalid;
|
|
return parts_default_nan(s);
|
|
}
|
|
if (a.cls == float_class_inf) {
|
|
return a; /* sqrt(+inf) = +inf */
|
|
}
|
|
|
|
assert(a.cls == float_class_normal);
|
|
|
|
/* We need two overflow bits at the top. Adding room for that is a
|
|
* right shift. If the exponent is odd, we can discard the low bit
|
|
* by multiplying the fraction by 2; that's a left shift. Combine
|
|
* those and we shift right if the exponent is even.
|
|
*/
|
|
a_frac = a.frac;
|
|
if (!(a.exp & 1)) {
|
|
a_frac >>= 1;
|
|
}
|
|
a.exp >>= 1;
|
|
|
|
/* Bit-by-bit computation of sqrt. */
|
|
r_frac = 0;
|
|
s_frac = 0;
|
|
|
|
/* Iterate from implicit bit down to the 3 extra bits to compute a
|
|
* properly rounded result. Remember we've inserted one more bit
|
|
* at the top, so these positions are one less.
|
|
*/
|
|
bit = DECOMPOSED_BINARY_POINT - 1;
|
|
last_bit = MAX(p->frac_shift - 4, 0);
|
|
do {
|
|
uint64_t q = 1ULL << bit;
|
|
uint64_t t_frac = s_frac + q;
|
|
if (t_frac <= a_frac) {
|
|
s_frac = t_frac + q;
|
|
a_frac -= t_frac;
|
|
r_frac += q;
|
|
}
|
|
a_frac <<= 1;
|
|
} while (--bit >= last_bit);
|
|
|
|
/* Undo the right shift done above. If there is any remaining
|
|
* fraction, the result is inexact. Set the sticky bit.
|
|
*/
|
|
a.frac = (r_frac << 1) + (a_frac != 0);
|
|
|
|
return a;
|
|
}
|
|
|
|
float16 QEMU_FLATTEN float16_sqrt(float16 a, float_status *status)
|
|
{
|
|
FloatParts pa = float16_unpack_canonical(a, status);
|
|
FloatParts pr = sqrt_float(pa, status, &float16_params);
|
|
return float16_round_pack_canonical(pr, status);
|
|
}
|
|
|
|
static float32 QEMU_SOFTFLOAT_ATTR
|
|
soft_f32_sqrt(float32 a, float_status *status)
|
|
{
|
|
FloatParts pa = float32_unpack_canonical(a, status);
|
|
FloatParts pr = sqrt_float(pa, status, &float32_params);
|
|
return float32_round_pack_canonical(pr, status);
|
|
}
|
|
|
|
static float64 QEMU_SOFTFLOAT_ATTR
|
|
soft_f64_sqrt(float64 a, float_status *status)
|
|
{
|
|
FloatParts pa = float64_unpack_canonical(a, status);
|
|
FloatParts pr = sqrt_float(pa, status, &float64_params);
|
|
return float64_round_pack_canonical(pr, status);
|
|
}
|
|
|
|
float32 QEMU_FLATTEN float32_sqrt(float32 xa, float_status *s)
|
|
{
|
|
union_float32 ua, ur;
|
|
|
|
ua.s = xa;
|
|
if (unlikely(!can_use_fpu(s))) {
|
|
goto soft;
|
|
}
|
|
|
|
float32_input_flush1(&ua.s, s);
|
|
if (QEMU_HARDFLOAT_1F32_USE_FP) {
|
|
if (unlikely(!(fpclassify(ua.h) == FP_NORMAL ||
|
|
fpclassify(ua.h) == FP_ZERO) ||
|
|
signbit(ua.h))) {
|
|
goto soft;
|
|
}
|
|
} else if (unlikely(!float32_is_zero_or_normal(ua.s) ||
|
|
float32_is_neg(ua.s))) {
|
|
goto soft;
|
|
}
|
|
ur.h = sqrtf(ua.h);
|
|
return ur.s;
|
|
|
|
soft:
|
|
return soft_f32_sqrt(ua.s, s);
|
|
}
|
|
|
|
float64 QEMU_FLATTEN float64_sqrt(float64 xa, float_status *s)
|
|
{
|
|
union_float64 ua, ur;
|
|
|
|
ua.s = xa;
|
|
if (unlikely(!can_use_fpu(s))) {
|
|
goto soft;
|
|
}
|
|
|
|
float64_input_flush1(&ua.s, s);
|
|
if (QEMU_HARDFLOAT_1F64_USE_FP) {
|
|
if (unlikely(!(fpclassify(ua.h) == FP_NORMAL ||
|
|
fpclassify(ua.h) == FP_ZERO) ||
|
|
signbit(ua.h))) {
|
|
goto soft;
|
|
}
|
|
} else if (unlikely(!float64_is_zero_or_normal(ua.s) ||
|
|
float64_is_neg(ua.s))) {
|
|
goto soft;
|
|
}
|
|
ur.h = sqrt(ua.h);
|
|
return ur.s;
|
|
|
|
soft:
|
|
return soft_f64_sqrt(ua.s, s);
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| The pattern for a default generated NaN.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
float16 float16_default_nan(float_status *status)
|
|
{
|
|
FloatParts p = parts_default_nan(status);
|
|
p.frac >>= float16_params.frac_shift;
|
|
return float16_pack_raw(p);
|
|
}
|
|
|
|
float32 float32_default_nan(float_status *status)
|
|
{
|
|
FloatParts p = parts_default_nan(status);
|
|
p.frac >>= float32_params.frac_shift;
|
|
return float32_pack_raw(p);
|
|
}
|
|
|
|
float64 float64_default_nan(float_status *status)
|
|
{
|
|
FloatParts p = parts_default_nan(status);
|
|
p.frac >>= float64_params.frac_shift;
|
|
return float64_pack_raw(p);
|
|
}
|
|
|
|
float128 float128_default_nan(float_status *status)
|
|
{
|
|
FloatParts p = parts_default_nan(status);
|
|
float128 r;
|
|
|
|
/* Extrapolate from the choices made by parts_default_nan to fill
|
|
* in the quad-floating format. If the low bit is set, assume we
|
|
* want to set all non-snan bits.
|
|
*/
|
|
r.low = -(p.frac & 1);
|
|
r.high = p.frac >> (DECOMPOSED_BINARY_POINT - 48);
|
|
r.high |= UINT64_C(0x7FFF000000000000);
|
|
r.high |= (uint64_t)p.sign << 63;
|
|
|
|
return r;
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns a quiet NaN from a signalling NaN for the floating point value `a'.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
float16 float16_silence_nan(float16 a, float_status *status)
|
|
{
|
|
FloatParts p = float16_unpack_raw(a);
|
|
p.frac <<= float16_params.frac_shift;
|
|
p = parts_silence_nan(p, status);
|
|
p.frac >>= float16_params.frac_shift;
|
|
return float16_pack_raw(p);
|
|
}
|
|
|
|
float32 float32_silence_nan(float32 a, float_status *status)
|
|
{
|
|
FloatParts p = float32_unpack_raw(a);
|
|
p.frac <<= float32_params.frac_shift;
|
|
p = parts_silence_nan(p, status);
|
|
p.frac >>= float32_params.frac_shift;
|
|
return float32_pack_raw(p);
|
|
}
|
|
|
|
float64 float64_silence_nan(float64 a, float_status *status)
|
|
{
|
|
FloatParts p = float64_unpack_raw(a);
|
|
p.frac <<= float64_params.frac_shift;
|
|
p = parts_silence_nan(p, status);
|
|
p.frac >>= float64_params.frac_shift;
|
|
return float64_pack_raw(p);
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| If `a' is denormal and we are in flush-to-zero mode then set the
|
|
| input-denormal exception and return zero. Otherwise just return the value.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
static bool parts_squash_denormal(FloatParts p, float_status *status)
|
|
{
|
|
if (p.exp == 0 && p.frac != 0) {
|
|
float_raise(float_flag_input_denormal, status);
|
|
return true;
|
|
}
|
|
|
|
return false;
|
|
}
|
|
|
|
float16 float16_squash_input_denormal(float16 a, float_status *status)
|
|
{
|
|
if (status->flush_inputs_to_zero) {
|
|
FloatParts p = float16_unpack_raw(a);
|
|
if (parts_squash_denormal(p, status)) {
|
|
return float16_set_sign(float16_zero, p.sign);
|
|
}
|
|
}
|
|
return a;
|
|
}
|
|
|
|
float32 float32_squash_input_denormal(float32 a, float_status *status)
|
|
{
|
|
if (status->flush_inputs_to_zero) {
|
|
FloatParts p = float32_unpack_raw(a);
|
|
if (parts_squash_denormal(p, status)) {
|
|
return float32_set_sign(float32_zero, p.sign);
|
|
}
|
|
}
|
|
return a;
|
|
}
|
|
|
|
float64 float64_squash_input_denormal(float64 a, float_status *status)
|
|
{
|
|
if (status->flush_inputs_to_zero) {
|
|
FloatParts p = float64_unpack_raw(a);
|
|
if (parts_squash_denormal(p, status)) {
|
|
return float64_set_sign(float64_zero, p.sign);
|
|
}
|
|
}
|
|
return a;
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Takes a 64-bit fixed-point value `absZ' with binary point between bits 6
|
|
| and 7, and returns the properly rounded 32-bit integer corresponding to the
|
|
| input. If `zSign' is 1, the input is negated before being converted to an
|
|
| integer. Bit 63 of `absZ' must be zero. Ordinarily, the fixed-point input
|
|
| is simply rounded to an integer, with the inexact exception raised if the
|
|
| input cannot be represented exactly as an integer. However, if the fixed-
|
|
| point input is too large, the invalid exception is raised and the largest
|
|
| positive or negative integer is returned.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
static int32_t roundAndPackInt32(bool zSign, uint64_t absZ,
|
|
float_status *status)
|
|
{
|
|
int8_t roundingMode;
|
|
bool roundNearestEven;
|
|
int8_t roundIncrement, roundBits;
|
|
int32_t z;
|
|
|
|
roundingMode = status->float_rounding_mode;
|
|
roundNearestEven = ( roundingMode == float_round_nearest_even );
|
|
switch (roundingMode) {
|
|
case float_round_nearest_even:
|
|
case float_round_ties_away:
|
|
roundIncrement = 0x40;
|
|
break;
|
|
case float_round_to_zero:
|
|
roundIncrement = 0;
|
|
break;
|
|
case float_round_up:
|
|
roundIncrement = zSign ? 0 : 0x7f;
|
|
break;
|
|
case float_round_down:
|
|
roundIncrement = zSign ? 0x7f : 0;
|
|
break;
|
|
case float_round_to_odd:
|
|
roundIncrement = absZ & 0x80 ? 0 : 0x7f;
|
|
break;
|
|
default:
|
|
abort();
|
|
}
|
|
roundBits = absZ & 0x7F;
|
|
absZ = ( absZ + roundIncrement )>>7;
|
|
absZ &= ~ ( ( ( roundBits ^ 0x40 ) == 0 ) & roundNearestEven );
|
|
z = absZ;
|
|
if ( zSign ) z = - z;
|
|
if ( ( absZ>>32 ) || ( z && ( ( z < 0 ) ^ zSign ) ) ) {
|
|
float_raise(float_flag_invalid, status);
|
|
return zSign ? INT32_MIN : INT32_MAX;
|
|
}
|
|
if (roundBits) {
|
|
status->float_exception_flags |= float_flag_inexact;
|
|
}
|
|
return z;
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Takes the 128-bit fixed-point value formed by concatenating `absZ0' and
|
|
| `absZ1', with binary point between bits 63 and 64 (between the input words),
|
|
| and returns the properly rounded 64-bit integer corresponding to the input.
|
|
| If `zSign' is 1, the input is negated before being converted to an integer.
|
|
| Ordinarily, the fixed-point input is simply rounded to an integer, with
|
|
| the inexact exception raised if the input cannot be represented exactly as
|
|
| an integer. However, if the fixed-point input is too large, the invalid
|
|
| exception is raised and the largest positive or negative integer is
|
|
| returned.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
static int64_t roundAndPackInt64(bool zSign, uint64_t absZ0, uint64_t absZ1,
|
|
float_status *status)
|
|
{
|
|
int8_t roundingMode;
|
|
bool roundNearestEven, increment;
|
|
int64_t z;
|
|
|
|
roundingMode = status->float_rounding_mode;
|
|
roundNearestEven = ( roundingMode == float_round_nearest_even );
|
|
switch (roundingMode) {
|
|
case float_round_nearest_even:
|
|
case float_round_ties_away:
|
|
increment = ((int64_t) absZ1 < 0);
|
|
break;
|
|
case float_round_to_zero:
|
|
increment = 0;
|
|
break;
|
|
case float_round_up:
|
|
increment = !zSign && absZ1;
|
|
break;
|
|
case float_round_down:
|
|
increment = zSign && absZ1;
|
|
break;
|
|
case float_round_to_odd:
|
|
increment = !(absZ0 & 1) && absZ1;
|
|
break;
|
|
default:
|
|
abort();
|
|
}
|
|
if ( increment ) {
|
|
++absZ0;
|
|
if ( absZ0 == 0 ) goto overflow;
|
|
absZ0 &= ~ ( ( (uint64_t) ( absZ1<<1 ) == 0 ) & roundNearestEven );
|
|
}
|
|
z = absZ0;
|
|
if ( zSign ) z = - z;
|
|
if ( z && ( ( z < 0 ) ^ zSign ) ) {
|
|
overflow:
|
|
float_raise(float_flag_invalid, status);
|
|
return zSign ? INT64_MIN : INT64_MAX;
|
|
}
|
|
if (absZ1) {
|
|
status->float_exception_flags |= float_flag_inexact;
|
|
}
|
|
return z;
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Takes the 128-bit fixed-point value formed by concatenating `absZ0' and
|
|
| `absZ1', with binary point between bits 63 and 64 (between the input words),
|
|
| and returns the properly rounded 64-bit unsigned integer corresponding to the
|
|
| input. Ordinarily, the fixed-point input is simply rounded to an integer,
|
|
| with the inexact exception raised if the input cannot be represented exactly
|
|
| as an integer. However, if the fixed-point input is too large, the invalid
|
|
| exception is raised and the largest unsigned integer is returned.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
static int64_t roundAndPackUint64(bool zSign, uint64_t absZ0,
|
|
uint64_t absZ1, float_status *status)
|
|
{
|
|
int8_t roundingMode;
|
|
bool roundNearestEven, increment;
|
|
|
|
roundingMode = status->float_rounding_mode;
|
|
roundNearestEven = (roundingMode == float_round_nearest_even);
|
|
switch (roundingMode) {
|
|
case float_round_nearest_even:
|
|
case float_round_ties_away:
|
|
increment = ((int64_t)absZ1 < 0);
|
|
break;
|
|
case float_round_to_zero:
|
|
increment = 0;
|
|
break;
|
|
case float_round_up:
|
|
increment = !zSign && absZ1;
|
|
break;
|
|
case float_round_down:
|
|
increment = zSign && absZ1;
|
|
break;
|
|
case float_round_to_odd:
|
|
increment = !(absZ0 & 1) && absZ1;
|
|
break;
|
|
default:
|
|
abort();
|
|
}
|
|
if (increment) {
|
|
++absZ0;
|
|
if (absZ0 == 0) {
|
|
float_raise(float_flag_invalid, status);
|
|
return UINT64_MAX;
|
|
}
|
|
absZ0 &= ~(((uint64_t)(absZ1<<1) == 0) & roundNearestEven);
|
|
}
|
|
|
|
if (zSign && absZ0) {
|
|
float_raise(float_flag_invalid, status);
|
|
return 0;
|
|
}
|
|
|
|
if (absZ1) {
|
|
status->float_exception_flags |= float_flag_inexact;
|
|
}
|
|
return absZ0;
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Normalizes the subnormal single-precision floating-point value represented
|
|
| by the denormalized significand `aSig'. The normalized exponent and
|
|
| significand are stored at the locations pointed to by `zExpPtr' and
|
|
| `zSigPtr', respectively.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
static void
|
|
normalizeFloat32Subnormal(uint32_t aSig, int *zExpPtr, uint32_t *zSigPtr)
|
|
{
|
|
int8_t shiftCount;
|
|
|
|
shiftCount = clz32(aSig) - 8;
|
|
*zSigPtr = aSig<<shiftCount;
|
|
*zExpPtr = 1 - shiftCount;
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
|
|
| and significand `zSig', and returns the proper single-precision floating-
|
|
| point value corresponding to the abstract input. Ordinarily, the abstract
|
|
| value is simply rounded and packed into the single-precision format, with
|
|
| the inexact exception raised if the abstract input cannot be represented
|
|
| exactly. However, if the abstract value is too large, the overflow and
|
|
| inexact exceptions are raised and an infinity or maximal finite value is
|
|
| returned. If the abstract value is too small, the input value is rounded to
|
|
| a subnormal number, and the underflow and inexact exceptions are raised if
|
|
| the abstract input cannot be represented exactly as a subnormal single-
|
|
| precision floating-point number.
|
|
| The input significand `zSig' has its binary point between bits 30
|
|
| and 29, which is 7 bits to the left of the usual location. This shifted
|
|
| significand must be normalized or smaller. If `zSig' is not normalized,
|
|
| `zExp' must be 0; in that case, the result returned is a subnormal number,
|
|
| and it must not require rounding. In the usual case that `zSig' is
|
|
| normalized, `zExp' must be 1 less than the ``true'' floating-point exponent.
|
|
| The handling of underflow and overflow follows the IEC/IEEE Standard for
|
|
| Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
static float32 roundAndPackFloat32(bool zSign, int zExp, uint32_t zSig,
|
|
float_status *status)
|
|
{
|
|
int8_t roundingMode;
|
|
bool roundNearestEven;
|
|
int8_t roundIncrement, roundBits;
|
|
bool isTiny;
|
|
|
|
roundingMode = status->float_rounding_mode;
|
|
roundNearestEven = ( roundingMode == float_round_nearest_even );
|
|
switch (roundingMode) {
|
|
case float_round_nearest_even:
|
|
case float_round_ties_away:
|
|
roundIncrement = 0x40;
|
|
break;
|
|
case float_round_to_zero:
|
|
roundIncrement = 0;
|
|
break;
|
|
case float_round_up:
|
|
roundIncrement = zSign ? 0 : 0x7f;
|
|
break;
|
|
case float_round_down:
|
|
roundIncrement = zSign ? 0x7f : 0;
|
|
break;
|
|
case float_round_to_odd:
|
|
roundIncrement = zSig & 0x80 ? 0 : 0x7f;
|
|
break;
|
|
default:
|
|
abort();
|
|
break;
|
|
}
|
|
roundBits = zSig & 0x7F;
|
|
if ( 0xFD <= (uint16_t) zExp ) {
|
|
if ( ( 0xFD < zExp )
|
|
|| ( ( zExp == 0xFD )
|
|
&& ( (int32_t) ( zSig + roundIncrement ) < 0 ) )
|
|
) {
|
|
bool overflow_to_inf = roundingMode != float_round_to_odd &&
|
|
roundIncrement != 0;
|
|
float_raise(float_flag_overflow | float_flag_inexact, status);
|
|
return packFloat32(zSign, 0xFF, -!overflow_to_inf);
|
|
}
|
|
if ( zExp < 0 ) {
|
|
if (status->flush_to_zero) {
|
|
float_raise(float_flag_output_denormal, status);
|
|
return packFloat32(zSign, 0, 0);
|
|
}
|
|
isTiny = status->tininess_before_rounding
|
|
|| (zExp < -1)
|
|
|| (zSig + roundIncrement < 0x80000000);
|
|
shift32RightJamming( zSig, - zExp, &zSig );
|
|
zExp = 0;
|
|
roundBits = zSig & 0x7F;
|
|
if (isTiny && roundBits) {
|
|
float_raise(float_flag_underflow, status);
|
|
}
|
|
if (roundingMode == float_round_to_odd) {
|
|
/*
|
|
* For round-to-odd case, the roundIncrement depends on
|
|
* zSig which just changed.
|
|
*/
|
|
roundIncrement = zSig & 0x80 ? 0 : 0x7f;
|
|
}
|
|
}
|
|
}
|
|
if (roundBits) {
|
|
status->float_exception_flags |= float_flag_inexact;
|
|
}
|
|
zSig = ( zSig + roundIncrement )>>7;
|
|
zSig &= ~ ( ( ( roundBits ^ 0x40 ) == 0 ) & roundNearestEven );
|
|
if ( zSig == 0 ) zExp = 0;
|
|
return packFloat32( zSign, zExp, zSig );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
|
|
| and significand `zSig', and returns the proper single-precision floating-
|
|
| point value corresponding to the abstract input. This routine is just like
|
|
| `roundAndPackFloat32' except that `zSig' does not have to be normalized.
|
|
| Bit 31 of `zSig' must be zero, and `zExp' must be 1 less than the ``true''
|
|
| floating-point exponent.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
static float32
|
|
normalizeRoundAndPackFloat32(bool zSign, int zExp, uint32_t zSig,
|
|
float_status *status)
|
|
{
|
|
int8_t shiftCount;
|
|
|
|
shiftCount = clz32(zSig) - 1;
|
|
return roundAndPackFloat32(zSign, zExp - shiftCount, zSig<<shiftCount,
|
|
status);
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Normalizes the subnormal double-precision floating-point value represented
|
|
| by the denormalized significand `aSig'. The normalized exponent and
|
|
| significand are stored at the locations pointed to by `zExpPtr' and
|
|
| `zSigPtr', respectively.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
static void
|
|
normalizeFloat64Subnormal(uint64_t aSig, int *zExpPtr, uint64_t *zSigPtr)
|
|
{
|
|
int8_t shiftCount;
|
|
|
|
shiftCount = clz64(aSig) - 11;
|
|
*zSigPtr = aSig<<shiftCount;
|
|
*zExpPtr = 1 - shiftCount;
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Packs the sign `zSign', exponent `zExp', and significand `zSig' into a
|
|
| double-precision floating-point value, returning the result. After being
|
|
| shifted into the proper positions, the three fields are simply added
|
|
| together to form the result. This means that any integer portion of `zSig'
|
|
| will be added into the exponent. Since a properly normalized significand
|
|
| will have an integer portion equal to 1, the `zExp' input should be 1 less
|
|
| than the desired result exponent whenever `zSig' is a complete, normalized
|
|
| significand.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
static inline float64 packFloat64(bool zSign, int zExp, uint64_t zSig)
|
|
{
|
|
|
|
return make_float64(
|
|
( ( (uint64_t) zSign )<<63 ) + ( ( (uint64_t) zExp )<<52 ) + zSig);
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
|
|
| and significand `zSig', and returns the proper double-precision floating-
|
|
| point value corresponding to the abstract input. Ordinarily, the abstract
|
|
| value is simply rounded and packed into the double-precision format, with
|
|
| the inexact exception raised if the abstract input cannot be represented
|
|
| exactly. However, if the abstract value is too large, the overflow and
|
|
| inexact exceptions are raised and an infinity or maximal finite value is
|
|
| returned. If the abstract value is too small, the input value is rounded to
|
|
| a subnormal number, and the underflow and inexact exceptions are raised if
|
|
| the abstract input cannot be represented exactly as a subnormal double-
|
|
| precision floating-point number.
|
|
| The input significand `zSig' has its binary point between bits 62
|
|
| and 61, which is 10 bits to the left of the usual location. This shifted
|
|
| significand must be normalized or smaller. If `zSig' is not normalized,
|
|
| `zExp' must be 0; in that case, the result returned is a subnormal number,
|
|
| and it must not require rounding. In the usual case that `zSig' is
|
|
| normalized, `zExp' must be 1 less than the ``true'' floating-point exponent.
|
|
| The handling of underflow and overflow follows the IEC/IEEE Standard for
|
|
| Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
static float64 roundAndPackFloat64(bool zSign, int zExp, uint64_t zSig,
|
|
float_status *status)
|
|
{
|
|
int8_t roundingMode;
|
|
bool roundNearestEven;
|
|
int roundIncrement, roundBits;
|
|
bool isTiny;
|
|
|
|
roundingMode = status->float_rounding_mode;
|
|
roundNearestEven = ( roundingMode == float_round_nearest_even );
|
|
switch (roundingMode) {
|
|
case float_round_nearest_even:
|
|
case float_round_ties_away:
|
|
roundIncrement = 0x200;
|
|
break;
|
|
case float_round_to_zero:
|
|
roundIncrement = 0;
|
|
break;
|
|
case float_round_up:
|
|
roundIncrement = zSign ? 0 : 0x3ff;
|
|
break;
|
|
case float_round_down:
|
|
roundIncrement = zSign ? 0x3ff : 0;
|
|
break;
|
|
case float_round_to_odd:
|
|
roundIncrement = (zSig & 0x400) ? 0 : 0x3ff;
|
|
break;
|
|
default:
|
|
abort();
|
|
}
|
|
roundBits = zSig & 0x3FF;
|
|
if ( 0x7FD <= (uint16_t) zExp ) {
|
|
if ( ( 0x7FD < zExp )
|
|
|| ( ( zExp == 0x7FD )
|
|
&& ( (int64_t) ( zSig + roundIncrement ) < 0 ) )
|
|
) {
|
|
bool overflow_to_inf = roundingMode != float_round_to_odd &&
|
|
roundIncrement != 0;
|
|
float_raise(float_flag_overflow | float_flag_inexact, status);
|
|
return packFloat64(zSign, 0x7FF, -(!overflow_to_inf));
|
|
}
|
|
if ( zExp < 0 ) {
|
|
if (status->flush_to_zero) {
|
|
float_raise(float_flag_output_denormal, status);
|
|
return packFloat64(zSign, 0, 0);
|
|
}
|
|
isTiny = status->tininess_before_rounding
|
|
|| (zExp < -1)
|
|
|| (zSig + roundIncrement < UINT64_C(0x8000000000000000));
|
|
shift64RightJamming( zSig, - zExp, &zSig );
|
|
zExp = 0;
|
|
roundBits = zSig & 0x3FF;
|
|
if (isTiny && roundBits) {
|
|
float_raise(float_flag_underflow, status);
|
|
}
|
|
if (roundingMode == float_round_to_odd) {
|
|
/*
|
|
* For round-to-odd case, the roundIncrement depends on
|
|
* zSig which just changed.
|
|
*/
|
|
roundIncrement = (zSig & 0x400) ? 0 : 0x3ff;
|
|
}
|
|
}
|
|
}
|
|
if (roundBits) {
|
|
status->float_exception_flags |= float_flag_inexact;
|
|
}
|
|
zSig = ( zSig + roundIncrement )>>10;
|
|
zSig &= ~ ( ( ( roundBits ^ 0x200 ) == 0 ) & roundNearestEven );
|
|
if ( zSig == 0 ) zExp = 0;
|
|
return packFloat64( zSign, zExp, zSig );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
|
|
| and significand `zSig', and returns the proper double-precision floating-
|
|
| point value corresponding to the abstract input. This routine is just like
|
|
| `roundAndPackFloat64' except that `zSig' does not have to be normalized.
|
|
| Bit 63 of `zSig' must be zero, and `zExp' must be 1 less than the ``true''
|
|
| floating-point exponent.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
static float64
|
|
normalizeRoundAndPackFloat64(bool zSign, int zExp, uint64_t zSig,
|
|
float_status *status)
|
|
{
|
|
int8_t shiftCount;
|
|
|
|
shiftCount = clz64(zSig) - 1;
|
|
return roundAndPackFloat64(zSign, zExp - shiftCount, zSig<<shiftCount,
|
|
status);
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| 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)
|
|
{
|
|
int8_t shiftCount;
|
|
|
|
shiftCount = clz64(aSig);
|
|
*zSigPtr = aSig<<shiftCount;
|
|
*zExpPtr = 1 - shiftCount;
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| 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, bool zSign,
|
|
int32_t zExp, uint64_t zSig0, uint64_t zSig1,
|
|
float_status *status)
|
|
{
|
|
int8_t roundingMode;
|
|
bool roundNearestEven, increment, isTiny;
|
|
int64_t roundIncrement, roundMask, roundBits;
|
|
|
|
roundingMode = status->float_rounding_mode;
|
|
roundNearestEven = ( roundingMode == float_round_nearest_even );
|
|
if ( roundingPrecision == 80 ) goto precision80;
|
|
if ( roundingPrecision == 64 ) {
|
|
roundIncrement = UINT64_C(0x0000000000000400);
|
|
roundMask = UINT64_C(0x00000000000007FF);
|
|
}
|
|
else if ( roundingPrecision == 32 ) {
|
|
roundIncrement = UINT64_C(0x0000008000000000);
|
|
roundMask = UINT64_C(0x000000FFFFFFFFFF);
|
|
}
|
|
else {
|
|
goto precision80;
|
|
}
|
|
zSig0 |= ( zSig1 != 0 );
|
|
switch (roundingMode) {
|
|
case float_round_nearest_even:
|
|
case float_round_ties_away:
|
|
break;
|
|
case float_round_to_zero:
|
|
roundIncrement = 0;
|
|
break;
|
|
case float_round_up:
|
|
roundIncrement = zSign ? 0 : roundMask;
|
|
break;
|
|
case float_round_down:
|
|
roundIncrement = zSign ? roundMask : 0;
|
|
break;
|
|
default:
|
|
abort();
|
|
}
|
|
roundBits = zSig0 & roundMask;
|
|
if ( 0x7FFD <= (uint32_t) ( zExp - 1 ) ) {
|
|
if ( ( 0x7FFE < zExp )
|
|
|| ( ( zExp == 0x7FFE ) && ( zSig0 + roundIncrement < zSig0 ) )
|
|
) {
|
|
goto overflow;
|
|
}
|
|
if ( zExp <= 0 ) {
|
|
if (status->flush_to_zero) {
|
|
float_raise(float_flag_output_denormal, status);
|
|
return packFloatx80(zSign, 0, 0);
|
|
}
|
|
isTiny = status->tininess_before_rounding
|
|
|| (zExp < 0 )
|
|
|| (zSig0 <= zSig0 + roundIncrement);
|
|
shift64RightJamming( zSig0, 1 - zExp, &zSig0 );
|
|
zExp = 0;
|
|
roundBits = zSig0 & roundMask;
|
|
if (isTiny && roundBits) {
|
|
float_raise(float_flag_underflow, status);
|
|
}
|
|
if (roundBits) {
|
|
status->float_exception_flags |= float_flag_inexact;
|
|
}
|
|
zSig0 += roundIncrement;
|
|
if ( (int64_t) zSig0 < 0 ) zExp = 1;
|
|
roundIncrement = roundMask + 1;
|
|
if ( roundNearestEven && ( roundBits<<1 == roundIncrement ) ) {
|
|
roundMask |= roundIncrement;
|
|
}
|
|
zSig0 &= ~ roundMask;
|
|
return packFloatx80( zSign, zExp, zSig0 );
|
|
}
|
|
}
|
|
if (roundBits) {
|
|
status->float_exception_flags |= float_flag_inexact;
|
|
}
|
|
zSig0 += roundIncrement;
|
|
if ( zSig0 < roundIncrement ) {
|
|
++zExp;
|
|
zSig0 = UINT64_C(0x8000000000000000);
|
|
}
|
|
roundIncrement = roundMask + 1;
|
|
if ( roundNearestEven && ( roundBits<<1 == roundIncrement ) ) {
|
|
roundMask |= roundIncrement;
|
|
}
|
|
zSig0 &= ~ roundMask;
|
|
if ( zSig0 == 0 ) zExp = 0;
|
|
return packFloatx80( zSign, zExp, zSig0 );
|
|
precision80:
|
|
switch (roundingMode) {
|
|
case float_round_nearest_even:
|
|
case float_round_ties_away:
|
|
increment = ((int64_t)zSig1 < 0);
|
|
break;
|
|
case float_round_to_zero:
|
|
increment = 0;
|
|
break;
|
|
case float_round_up:
|
|
increment = !zSign && zSig1;
|
|
break;
|
|
case float_round_down:
|
|
increment = zSign && zSig1;
|
|
break;
|
|
default:
|
|
abort();
|
|
}
|
|
if ( 0x7FFD <= (uint32_t) ( zExp - 1 ) ) {
|
|
if ( ( 0x7FFE < zExp )
|
|
|| ( ( zExp == 0x7FFE )
|
|
&& ( zSig0 == UINT64_C(0xFFFFFFFFFFFFFFFF) )
|
|
&& increment
|
|
)
|
|
) {
|
|
roundMask = 0;
|
|
overflow:
|
|
float_raise(float_flag_overflow | float_flag_inexact, status);
|
|
if ( ( roundingMode == float_round_to_zero )
|
|
|| ( zSign && ( roundingMode == float_round_up ) )
|
|
|| ( ! zSign && ( roundingMode == float_round_down ) )
|
|
) {
|
|
return packFloatx80( zSign, 0x7FFE, ~ roundMask );
|
|
}
|
|
return packFloatx80(zSign,
|
|
floatx80_infinity_high,
|
|
floatx80_infinity_low);
|
|
}
|
|
if ( zExp <= 0 ) {
|
|
isTiny = status->tininess_before_rounding
|
|
|| (zExp < 0)
|
|
|| !increment
|
|
|| (zSig0 < UINT64_C(0xFFFFFFFFFFFFFFFF));
|
|
shift64ExtraRightJamming( zSig0, zSig1, 1 - zExp, &zSig0, &zSig1 );
|
|
zExp = 0;
|
|
if (isTiny && zSig1) {
|
|
float_raise(float_flag_underflow, status);
|
|
}
|
|
if (zSig1) {
|
|
status->float_exception_flags |= float_flag_inexact;
|
|
}
|
|
switch (roundingMode) {
|
|
case float_round_nearest_even:
|
|
case float_round_ties_away:
|
|
increment = ((int64_t)zSig1 < 0);
|
|
break;
|
|
case float_round_to_zero:
|
|
increment = 0;
|
|
break;
|
|
case float_round_up:
|
|
increment = !zSign && zSig1;
|
|
break;
|
|
case float_round_down:
|
|
increment = zSign && zSig1;
|
|
break;
|
|
default:
|
|
abort();
|
|
}
|
|
if ( increment ) {
|
|
++zSig0;
|
|
zSig0 &=
|
|
~ ( ( (uint64_t) ( zSig1<<1 ) == 0 ) & roundNearestEven );
|
|
if ( (int64_t) zSig0 < 0 ) zExp = 1;
|
|
}
|
|
return packFloatx80( zSign, zExp, zSig0 );
|
|
}
|
|
}
|
|
if (zSig1) {
|
|
status->float_exception_flags |= float_flag_inexact;
|
|
}
|
|
if ( increment ) {
|
|
++zSig0;
|
|
if ( zSig0 == 0 ) {
|
|
++zExp;
|
|
zSig0 = UINT64_C(0x8000000000000000);
|
|
}
|
|
else {
|
|
zSig0 &= ~ ( ( (uint64_t) ( zSig1<<1 ) == 0 ) & roundNearestEven );
|
|
}
|
|
}
|
|
else {
|
|
if ( zSig0 == 0 ) zExp = 0;
|
|
}
|
|
return packFloatx80( zSign, zExp, zSig0 );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Takes an abstract floating-point value having sign `zSign', exponent
|
|
| `zExp', and significand formed by the concatenation of `zSig0' and `zSig1',
|
|
| and returns the proper extended double-precision floating-point value
|
|
| corresponding to the abstract input. This routine is just like
|
|
| `roundAndPackFloatx80' except that the input significand does not have to be
|
|
| normalized.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
floatx80 normalizeRoundAndPackFloatx80(int8_t roundingPrecision,
|
|
bool zSign, int32_t zExp,
|
|
uint64_t zSig0, uint64_t zSig1,
|
|
float_status *status)
|
|
{
|
|
int8_t shiftCount;
|
|
|
|
if ( zSig0 == 0 ) {
|
|
zSig0 = zSig1;
|
|
zSig1 = 0;
|
|
zExp -= 64;
|
|
}
|
|
shiftCount = clz64(zSig0);
|
|
shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 );
|
|
zExp -= shiftCount;
|
|
return roundAndPackFloatx80(roundingPrecision, zSign, zExp,
|
|
zSig0, zSig1, status);
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the least-significant 64 fraction bits of the quadruple-precision
|
|
| floating-point value `a'.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
static inline uint64_t extractFloat128Frac1( float128 a )
|
|
{
|
|
|
|
return a.low;
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the most-significant 48 fraction bits of the quadruple-precision
|
|
| floating-point value `a'.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
static inline uint64_t extractFloat128Frac0( float128 a )
|
|
{
|
|
|
|
return a.high & UINT64_C(0x0000FFFFFFFFFFFF);
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the exponent bits of the quadruple-precision floating-point value
|
|
| `a'.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
static inline int32_t extractFloat128Exp( float128 a )
|
|
{
|
|
|
|
return ( a.high>>48 ) & 0x7FFF;
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the sign bit of the quadruple-precision floating-point value `a'.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
static inline bool extractFloat128Sign( float128 a )
|
|
{
|
|
return a.high >> 63;
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Normalizes the subnormal quadruple-precision floating-point value
|
|
| represented by the denormalized significand formed by the concatenation of
|
|
| `aSig0' and `aSig1'. The normalized exponent is stored at the location
|
|
| pointed to by `zExpPtr'. The most significant 49 bits of the normalized
|
|
| significand are stored at the location pointed to by `zSig0Ptr', and the
|
|
| least significant 64 bits of the normalized significand are stored at the
|
|
| location pointed to by `zSig1Ptr'.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
static void
|
|
normalizeFloat128Subnormal(
|
|
uint64_t aSig0,
|
|
uint64_t aSig1,
|
|
int32_t *zExpPtr,
|
|
uint64_t *zSig0Ptr,
|
|
uint64_t *zSig1Ptr
|
|
)
|
|
{
|
|
int8_t shiftCount;
|
|
|
|
if ( aSig0 == 0 ) {
|
|
shiftCount = clz64(aSig1) - 15;
|
|
if ( shiftCount < 0 ) {
|
|
*zSig0Ptr = aSig1>>( - shiftCount );
|
|
*zSig1Ptr = aSig1<<( shiftCount & 63 );
|
|
}
|
|
else {
|
|
*zSig0Ptr = aSig1<<shiftCount;
|
|
*zSig1Ptr = 0;
|
|
}
|
|
*zExpPtr = - shiftCount - 63;
|
|
}
|
|
else {
|
|
shiftCount = clz64(aSig0) - 15;
|
|
shortShift128Left( aSig0, aSig1, shiftCount, zSig0Ptr, zSig1Ptr );
|
|
*zExpPtr = 1 - shiftCount;
|
|
}
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Packs the sign `zSign', the exponent `zExp', and the significand formed
|
|
| by the concatenation of `zSig0' and `zSig1' into a quadruple-precision
|
|
| floating-point value, returning the result. After being shifted into the
|
|
| proper positions, the three fields `zSign', `zExp', and `zSig0' are simply
|
|
| added together to form the most significant 32 bits of the result. This
|
|
| means that any integer portion of `zSig0' will be added into the exponent.
|
|
| Since a properly normalized significand will have an integer portion equal
|
|
| to 1, the `zExp' input should be 1 less than the desired result exponent
|
|
| whenever `zSig0' and `zSig1' concatenated form a complete, normalized
|
|
| significand.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
static inline float128
|
|
packFloat128(bool zSign, int32_t zExp, uint64_t zSig0, uint64_t zSig1)
|
|
{
|
|
float128 z;
|
|
|
|
z.low = zSig1;
|
|
z.high = ((uint64_t)zSign << 63) + ((uint64_t)zExp << 48) + zSig0;
|
|
return z;
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
|
|
| and extended significand formed by the concatenation of `zSig0', `zSig1',
|
|
| and `zSig2', and returns the proper quadruple-precision floating-point value
|
|
| corresponding to the abstract input. Ordinarily, the abstract value is
|
|
| simply rounded and packed into the quadruple-precision format, with the
|
|
| inexact exception raised if the abstract input cannot be represented
|
|
| exactly. However, if the abstract value is too large, the overflow and
|
|
| inexact exceptions are raised and an infinity or maximal finite value is
|
|
| returned. If the abstract value is too small, the input value is rounded to
|
|
| a subnormal number, and the underflow and inexact exceptions are raised if
|
|
| the abstract input cannot be represented exactly as a subnormal quadruple-
|
|
| precision floating-point number.
|
|
| The input significand must be normalized or smaller. If the input
|
|
| significand is not normalized, `zExp' must be 0; in that case, the result
|
|
| returned is a subnormal number, and it must not require rounding. In the
|
|
| usual case that the input significand is normalized, `zExp' must be 1 less
|
|
| than the ``true'' floating-point exponent. The handling of underflow and
|
|
| overflow follows the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
static float128 roundAndPackFloat128(bool zSign, int32_t zExp,
|
|
uint64_t zSig0, uint64_t zSig1,
|
|
uint64_t zSig2, float_status *status)
|
|
{
|
|
int8_t roundingMode;
|
|
bool roundNearestEven, increment, isTiny;
|
|
|
|
roundingMode = status->float_rounding_mode;
|
|
roundNearestEven = ( roundingMode == float_round_nearest_even );
|
|
switch (roundingMode) {
|
|
case float_round_nearest_even:
|
|
case float_round_ties_away:
|
|
increment = ((int64_t)zSig2 < 0);
|
|
break;
|
|
case float_round_to_zero:
|
|
increment = 0;
|
|
break;
|
|
case float_round_up:
|
|
increment = !zSign && zSig2;
|
|
break;
|
|
case float_round_down:
|
|
increment = zSign && zSig2;
|
|
break;
|
|
case float_round_to_odd:
|
|
increment = !(zSig1 & 0x1) && zSig2;
|
|
break;
|
|
default:
|
|
abort();
|
|
}
|
|
if ( 0x7FFD <= (uint32_t) zExp ) {
|
|
if ( ( 0x7FFD < zExp )
|
|
|| ( ( zExp == 0x7FFD )
|
|
&& eq128(
|
|
UINT64_C(0x0001FFFFFFFFFFFF),
|
|
UINT64_C(0xFFFFFFFFFFFFFFFF),
|
|
zSig0,
|
|
zSig1
|
|
)
|
|
&& increment
|
|
)
|
|
) {
|
|
float_raise(float_flag_overflow | float_flag_inexact, status);
|
|
if ( ( roundingMode == float_round_to_zero )
|
|
|| ( zSign && ( roundingMode == float_round_up ) )
|
|
|| ( ! zSign && ( roundingMode == float_round_down ) )
|
|
|| (roundingMode == float_round_to_odd)
|
|
) {
|
|
return
|
|
packFloat128(
|
|
zSign,
|
|
0x7FFE,
|
|
UINT64_C(0x0000FFFFFFFFFFFF),
|
|
UINT64_C(0xFFFFFFFFFFFFFFFF)
|
|
);
|
|
}
|
|
return packFloat128( zSign, 0x7FFF, 0, 0 );
|
|
}
|
|
if ( zExp < 0 ) {
|
|
if (status->flush_to_zero) {
|
|
float_raise(float_flag_output_denormal, status);
|
|
return packFloat128(zSign, 0, 0, 0);
|
|
}
|
|
isTiny = status->tininess_before_rounding
|
|
|| (zExp < -1)
|
|
|| !increment
|
|
|| lt128(zSig0, zSig1,
|
|
UINT64_C(0x0001FFFFFFFFFFFF),
|
|
UINT64_C(0xFFFFFFFFFFFFFFFF));
|
|
shift128ExtraRightJamming(
|
|
zSig0, zSig1, zSig2, - zExp, &zSig0, &zSig1, &zSig2 );
|
|
zExp = 0;
|
|
if (isTiny && zSig2) {
|
|
float_raise(float_flag_underflow, status);
|
|
}
|
|
switch (roundingMode) {
|
|
case float_round_nearest_even:
|
|
case float_round_ties_away:
|
|
increment = ((int64_t)zSig2 < 0);
|
|
break;
|
|
case float_round_to_zero:
|
|
increment = 0;
|
|
break;
|
|
case float_round_up:
|
|
increment = !zSign && zSig2;
|
|
break;
|
|
case float_round_down:
|
|
increment = zSign && zSig2;
|
|
break;
|
|
case float_round_to_odd:
|
|
increment = !(zSig1 & 0x1) && zSig2;
|
|
break;
|
|
default:
|
|
abort();
|
|
}
|
|
}
|
|
}
|
|
if (zSig2) {
|
|
status->float_exception_flags |= float_flag_inexact;
|
|
}
|
|
if ( increment ) {
|
|
add128( zSig0, zSig1, 0, 1, &zSig0, &zSig1 );
|
|
zSig1 &= ~ ( ( zSig2 + zSig2 == 0 ) & roundNearestEven );
|
|
}
|
|
else {
|
|
if ( ( zSig0 | zSig1 ) == 0 ) zExp = 0;
|
|
}
|
|
return packFloat128( zSign, zExp, zSig0, zSig1 );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
|
|
| and significand formed by the concatenation of `zSig0' and `zSig1', and
|
|
| returns the proper quadruple-precision floating-point value corresponding
|
|
| to the abstract input. This routine is just like `roundAndPackFloat128'
|
|
| except that the input significand has fewer bits and does not have to be
|
|
| normalized. In all cases, `zExp' must be 1 less than the ``true'' floating-
|
|
| point exponent.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
static float128 normalizeRoundAndPackFloat128(bool zSign, int32_t zExp,
|
|
uint64_t zSig0, uint64_t zSig1,
|
|
float_status *status)
|
|
{
|
|
int8_t shiftCount;
|
|
uint64_t zSig2;
|
|
|
|
if ( zSig0 == 0 ) {
|
|
zSig0 = zSig1;
|
|
zSig1 = 0;
|
|
zExp -= 64;
|
|
}
|
|
shiftCount = clz64(zSig0) - 15;
|
|
if ( 0 <= shiftCount ) {
|
|
zSig2 = 0;
|
|
shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 );
|
|
}
|
|
else {
|
|
shift128ExtraRightJamming(
|
|
zSig0, zSig1, 0, - shiftCount, &zSig0, &zSig1, &zSig2 );
|
|
}
|
|
zExp -= shiftCount;
|
|
return roundAndPackFloat128(zSign, zExp, zSig0, zSig1, zSig2, status);
|
|
|
|
}
|
|
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of converting the 32-bit two's complement integer `a'
|
|
| to the extended double-precision floating-point format. The conversion
|
|
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
|
| Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
floatx80 int32_to_floatx80(int32_t a, float_status *status)
|
|
{
|
|
bool zSign;
|
|
uint32_t absA;
|
|
int8_t shiftCount;
|
|
uint64_t zSig;
|
|
|
|
if ( a == 0 ) return packFloatx80( 0, 0, 0 );
|
|
zSign = ( a < 0 );
|
|
absA = zSign ? - a : a;
|
|
shiftCount = clz32(absA) + 32;
|
|
zSig = absA;
|
|
return packFloatx80( zSign, 0x403E - shiftCount, zSig<<shiftCount );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of converting the 32-bit two's complement integer `a' to
|
|
| the quadruple-precision floating-point format. The conversion is performed
|
|
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
float128 int32_to_float128(int32_t a, float_status *status)
|
|
{
|
|
bool zSign;
|
|
uint32_t absA;
|
|
int8_t shiftCount;
|
|
uint64_t zSig0;
|
|
|
|
if ( a == 0 ) return packFloat128( 0, 0, 0, 0 );
|
|
zSign = ( a < 0 );
|
|
absA = zSign ? - a : a;
|
|
shiftCount = clz32(absA) + 17;
|
|
zSig0 = absA;
|
|
return packFloat128( zSign, 0x402E - shiftCount, zSig0<<shiftCount, 0 );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of converting the 64-bit two's complement integer `a'
|
|
| to the extended double-precision floating-point format. The conversion
|
|
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
|
| Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
floatx80 int64_to_floatx80(int64_t a, float_status *status)
|
|
{
|
|
bool zSign;
|
|
uint64_t absA;
|
|
int8_t shiftCount;
|
|
|
|
if ( a == 0 ) return packFloatx80( 0, 0, 0 );
|
|
zSign = ( a < 0 );
|
|
absA = zSign ? - a : a;
|
|
shiftCount = clz64(absA);
|
|
return packFloatx80( zSign, 0x403E - shiftCount, absA<<shiftCount );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of converting the 64-bit two's complement integer `a' to
|
|
| the quadruple-precision floating-point format. The conversion is performed
|
|
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
float128 int64_to_float128(int64_t a, float_status *status)
|
|
{
|
|
bool zSign;
|
|
uint64_t absA;
|
|
int8_t shiftCount;
|
|
int32_t zExp;
|
|
uint64_t zSig0, zSig1;
|
|
|
|
if ( a == 0 ) return packFloat128( 0, 0, 0, 0 );
|
|
zSign = ( a < 0 );
|
|
absA = zSign ? - a : a;
|
|
shiftCount = clz64(absA) + 49;
|
|
zExp = 0x406E - shiftCount;
|
|
if ( 64 <= shiftCount ) {
|
|
zSig1 = 0;
|
|
zSig0 = absA;
|
|
shiftCount -= 64;
|
|
}
|
|
else {
|
|
zSig1 = absA;
|
|
zSig0 = 0;
|
|
}
|
|
shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 );
|
|
return packFloat128( zSign, zExp, zSig0, zSig1 );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of converting the 64-bit unsigned integer `a'
|
|
| to the quadruple-precision floating-point format. The conversion is performed
|
|
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
float128 uint64_to_float128(uint64_t a, float_status *status)
|
|
{
|
|
if (a == 0) {
|
|
float128 zero = {0};
|
|
return zero;
|
|
}
|
|
return normalizeRoundAndPackFloat128(0, 0x406E, 0, a, status);
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of converting the single-precision floating-point value
|
|
| `a' to the extended double-precision floating-point format. The conversion
|
|
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
|
| Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
floatx80 float32_to_floatx80(float32 a, float_status *status)
|
|
{
|
|
bool aSign;
|
|
int aExp;
|
|
uint32_t aSig;
|
|
|
|
a = float32_squash_input_denormal(a, status);
|
|
aSig = extractFloat32Frac( a );
|
|
aExp = extractFloat32Exp( a );
|
|
aSign = extractFloat32Sign( a );
|
|
if ( aExp == 0xFF ) {
|
|
if (aSig) {
|
|
floatx80 res = commonNaNToFloatx80(float32ToCommonNaN(a, status),
|
|
status);
|
|
return floatx80_silence_nan(res, status);
|
|
}
|
|
return packFloatx80(aSign,
|
|
floatx80_infinity_high,
|
|
floatx80_infinity_low);
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( aSig == 0 ) return packFloatx80( aSign, 0, 0 );
|
|
normalizeFloat32Subnormal( aSig, &aExp, &aSig );
|
|
}
|
|
aSig |= 0x00800000;
|
|
return packFloatx80( aSign, aExp + 0x3F80, ( (uint64_t) aSig )<<40 );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of converting the single-precision floating-point value
|
|
| `a' to the double-precision floating-point format. The conversion is
|
|
| performed according to the IEC/IEEE Standard for Binary Floating-Point
|
|
| Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
float128 float32_to_float128(float32 a, float_status *status)
|
|
{
|
|
bool aSign;
|
|
int aExp;
|
|
uint32_t aSig;
|
|
|
|
a = float32_squash_input_denormal(a, status);
|
|
aSig = extractFloat32Frac( a );
|
|
aExp = extractFloat32Exp( a );
|
|
aSign = extractFloat32Sign( a );
|
|
if ( aExp == 0xFF ) {
|
|
if (aSig) {
|
|
return commonNaNToFloat128(float32ToCommonNaN(a, status), status);
|
|
}
|
|
return packFloat128( aSign, 0x7FFF, 0, 0 );
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( aSig == 0 ) return packFloat128( aSign, 0, 0, 0 );
|
|
normalizeFloat32Subnormal( aSig, &aExp, &aSig );
|
|
--aExp;
|
|
}
|
|
return packFloat128( aSign, aExp + 0x3F80, ( (uint64_t) aSig )<<25, 0 );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the remainder of the single-precision floating-point value `a'
|
|
| with respect to the corresponding value `b'. The operation is performed
|
|
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
float32 float32_rem(float32 a, float32 b, float_status *status)
|
|
{
|
|
bool aSign, zSign;
|
|
int aExp, bExp, expDiff;
|
|
uint32_t aSig, bSig;
|
|
uint32_t q;
|
|
uint64_t aSig64, bSig64, q64;
|
|
uint32_t alternateASig;
|
|
int32_t sigMean;
|
|
a = float32_squash_input_denormal(a, status);
|
|
b = float32_squash_input_denormal(b, status);
|
|
|
|
aSig = extractFloat32Frac( a );
|
|
aExp = extractFloat32Exp( a );
|
|
aSign = extractFloat32Sign( a );
|
|
bSig = extractFloat32Frac( b );
|
|
bExp = extractFloat32Exp( b );
|
|
if ( aExp == 0xFF ) {
|
|
if ( aSig || ( ( bExp == 0xFF ) && bSig ) ) {
|
|
return propagateFloat32NaN(a, b, status);
|
|
}
|
|
float_raise(float_flag_invalid, status);
|
|
return float32_default_nan(status);
|
|
}
|
|
if ( bExp == 0xFF ) {
|
|
if (bSig) {
|
|
return propagateFloat32NaN(a, b, status);
|
|
}
|
|
return a;
|
|
}
|
|
if ( bExp == 0 ) {
|
|
if ( bSig == 0 ) {
|
|
float_raise(float_flag_invalid, status);
|
|
return float32_default_nan(status);
|
|
}
|
|
normalizeFloat32Subnormal( bSig, &bExp, &bSig );
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( aSig == 0 ) return a;
|
|
normalizeFloat32Subnormal( aSig, &aExp, &aSig );
|
|
}
|
|
expDiff = aExp - bExp;
|
|
aSig |= 0x00800000;
|
|
bSig |= 0x00800000;
|
|
if ( expDiff < 32 ) {
|
|
aSig <<= 8;
|
|
bSig <<= 8;
|
|
if ( expDiff < 0 ) {
|
|
if ( expDiff < -1 ) return a;
|
|
aSig >>= 1;
|
|
}
|
|
q = ( bSig <= aSig );
|
|
if ( q ) aSig -= bSig;
|
|
if ( 0 < expDiff ) {
|
|
q = ( ( (uint64_t) aSig )<<32 ) / bSig;
|
|
q >>= 32 - expDiff;
|
|
bSig >>= 2;
|
|
aSig = ( ( aSig>>1 )<<( expDiff - 1 ) ) - bSig * q;
|
|
}
|
|
else {
|
|
aSig >>= 2;
|
|
bSig >>= 2;
|
|
}
|
|
}
|
|
else {
|
|
if ( bSig <= aSig ) aSig -= bSig;
|
|
aSig64 = ( (uint64_t) aSig )<<40;
|
|
bSig64 = ( (uint64_t) bSig )<<40;
|
|
expDiff -= 64;
|
|
while ( 0 < expDiff ) {
|
|
q64 = estimateDiv128To64( aSig64, 0, bSig64 );
|
|
q64 = ( 2 < q64 ) ? q64 - 2 : 0;
|
|
aSig64 = - ( ( bSig * q64 )<<38 );
|
|
expDiff -= 62;
|
|
}
|
|
expDiff += 64;
|
|
q64 = estimateDiv128To64( aSig64, 0, bSig64 );
|
|
q64 = ( 2 < q64 ) ? q64 - 2 : 0;
|
|
q = q64>>( 64 - expDiff );
|
|
bSig <<= 6;
|
|
aSig = ( ( aSig64>>33 )<<( expDiff - 1 ) ) - bSig * q;
|
|
}
|
|
do {
|
|
alternateASig = aSig;
|
|
++q;
|
|
aSig -= bSig;
|
|
} while ( 0 <= (int32_t) aSig );
|
|
sigMean = aSig + alternateASig;
|
|
if ( ( sigMean < 0 ) || ( ( sigMean == 0 ) && ( q & 1 ) ) ) {
|
|
aSig = alternateASig;
|
|
}
|
|
zSign = ( (int32_t) aSig < 0 );
|
|
if ( zSign ) aSig = - aSig;
|
|
return normalizeRoundAndPackFloat32(aSign ^ zSign, bExp, aSig, status);
|
|
}
|
|
|
|
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the binary exponential of the single-precision floating-point value
|
|
| `a'. The operation is performed according to the IEC/IEEE Standard for
|
|
| Binary Floating-Point Arithmetic.
|
|
|
|
|
| Uses the following identities:
|
|
|
|
|
| 1. -------------------------------------------------------------------------
|
|
| x x*ln(2)
|
|
| 2 = e
|
|
|
|
|
| 2. -------------------------------------------------------------------------
|
|
| 2 3 4 5 n
|
|
| x x x x x x x
|
|
| e = 1 + --- + --- + --- + --- + --- + ... + --- + ...
|
|
| 1! 2! 3! 4! 5! n!
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
static const float64 float32_exp2_coefficients[15] =
|
|
{
|
|
const_float64( 0x3ff0000000000000ll ), /* 1 */
|
|
const_float64( 0x3fe0000000000000ll ), /* 2 */
|
|
const_float64( 0x3fc5555555555555ll ), /* 3 */
|
|
const_float64( 0x3fa5555555555555ll ), /* 4 */
|
|
const_float64( 0x3f81111111111111ll ), /* 5 */
|
|
const_float64( 0x3f56c16c16c16c17ll ), /* 6 */
|
|
const_float64( 0x3f2a01a01a01a01all ), /* 7 */
|
|
const_float64( 0x3efa01a01a01a01all ), /* 8 */
|
|
const_float64( 0x3ec71de3a556c734ll ), /* 9 */
|
|
const_float64( 0x3e927e4fb7789f5cll ), /* 10 */
|
|
const_float64( 0x3e5ae64567f544e4ll ), /* 11 */
|
|
const_float64( 0x3e21eed8eff8d898ll ), /* 12 */
|
|
const_float64( 0x3de6124613a86d09ll ), /* 13 */
|
|
const_float64( 0x3da93974a8c07c9dll ), /* 14 */
|
|
const_float64( 0x3d6ae7f3e733b81fll ), /* 15 */
|
|
};
|
|
|
|
float32 float32_exp2(float32 a, float_status *status)
|
|
{
|
|
bool aSign;
|
|
int aExp;
|
|
uint32_t aSig;
|
|
float64 r, x, xn;
|
|
int i;
|
|
a = float32_squash_input_denormal(a, status);
|
|
|
|
aSig = extractFloat32Frac( a );
|
|
aExp = extractFloat32Exp( a );
|
|
aSign = extractFloat32Sign( a );
|
|
|
|
if ( aExp == 0xFF) {
|
|
if (aSig) {
|
|
return propagateFloat32NaN(a, float32_zero, status);
|
|
}
|
|
return (aSign) ? float32_zero : a;
|
|
}
|
|
if (aExp == 0) {
|
|
if (aSig == 0) return float32_one;
|
|
}
|
|
|
|
float_raise(float_flag_inexact, status);
|
|
|
|
/* ******************************* */
|
|
/* using float64 for approximation */
|
|
/* ******************************* */
|
|
x = float32_to_float64(a, status);
|
|
x = float64_mul(x, float64_ln2, status);
|
|
|
|
xn = x;
|
|
r = float64_one;
|
|
for (i = 0 ; i < 15 ; i++) {
|
|
float64 f;
|
|
|
|
f = float64_mul(xn, float32_exp2_coefficients[i], status);
|
|
r = float64_add(r, f, status);
|
|
|
|
xn = float64_mul(xn, x, status);
|
|
}
|
|
|
|
return float64_to_float32(r, status);
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the binary log of the single-precision floating-point value `a'.
|
|
| The operation is performed according to the IEC/IEEE Standard for Binary
|
|
| Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
float32 float32_log2(float32 a, float_status *status)
|
|
{
|
|
bool aSign, zSign;
|
|
int aExp;
|
|
uint32_t aSig, zSig, i;
|
|
|
|
a = float32_squash_input_denormal(a, status);
|
|
aSig = extractFloat32Frac( a );
|
|
aExp = extractFloat32Exp( a );
|
|
aSign = extractFloat32Sign( a );
|
|
|
|
if ( aExp == 0 ) {
|
|
if ( aSig == 0 ) return packFloat32( 1, 0xFF, 0 );
|
|
normalizeFloat32Subnormal( aSig, &aExp, &aSig );
|
|
}
|
|
if ( aSign ) {
|
|
float_raise(float_flag_invalid, status);
|
|
return float32_default_nan(status);
|
|
}
|
|
if ( aExp == 0xFF ) {
|
|
if (aSig) {
|
|
return propagateFloat32NaN(a, float32_zero, status);
|
|
}
|
|
return a;
|
|
}
|
|
|
|
aExp -= 0x7F;
|
|
aSig |= 0x00800000;
|
|
zSign = aExp < 0;
|
|
zSig = aExp << 23;
|
|
|
|
for (i = 1 << 22; i > 0; i >>= 1) {
|
|
aSig = ( (uint64_t)aSig * aSig ) >> 23;
|
|
if ( aSig & 0x01000000 ) {
|
|
aSig >>= 1;
|
|
zSig |= i;
|
|
}
|
|
}
|
|
|
|
if ( zSign )
|
|
zSig = -zSig;
|
|
|
|
return normalizeRoundAndPackFloat32(zSign, 0x85, zSig, status);
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of converting the double-precision floating-point value
|
|
| `a' to the extended double-precision floating-point format. The conversion
|
|
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
|
| Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
floatx80 float64_to_floatx80(float64 a, float_status *status)
|
|
{
|
|
bool aSign;
|
|
int aExp;
|
|
uint64_t aSig;
|
|
|
|
a = float64_squash_input_denormal(a, status);
|
|
aSig = extractFloat64Frac( a );
|
|
aExp = extractFloat64Exp( a );
|
|
aSign = extractFloat64Sign( a );
|
|
if ( aExp == 0x7FF ) {
|
|
if (aSig) {
|
|
floatx80 res = commonNaNToFloatx80(float64ToCommonNaN(a, status),
|
|
status);
|
|
return floatx80_silence_nan(res, status);
|
|
}
|
|
return packFloatx80(aSign,
|
|
floatx80_infinity_high,
|
|
floatx80_infinity_low);
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( aSig == 0 ) return packFloatx80( aSign, 0, 0 );
|
|
normalizeFloat64Subnormal( aSig, &aExp, &aSig );
|
|
}
|
|
return
|
|
packFloatx80(
|
|
aSign, aExp + 0x3C00, (aSig | UINT64_C(0x0010000000000000)) << 11);
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of converting the double-precision floating-point value
|
|
| `a' to the quadruple-precision floating-point format. The conversion is
|
|
| performed according to the IEC/IEEE Standard for Binary Floating-Point
|
|
| Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
float128 float64_to_float128(float64 a, float_status *status)
|
|
{
|
|
bool aSign;
|
|
int aExp;
|
|
uint64_t aSig, zSig0, zSig1;
|
|
|
|
a = float64_squash_input_denormal(a, status);
|
|
aSig = extractFloat64Frac( a );
|
|
aExp = extractFloat64Exp( a );
|
|
aSign = extractFloat64Sign( a );
|
|
if ( aExp == 0x7FF ) {
|
|
if (aSig) {
|
|
return commonNaNToFloat128(float64ToCommonNaN(a, status), status);
|
|
}
|
|
return packFloat128( aSign, 0x7FFF, 0, 0 );
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( aSig == 0 ) return packFloat128( aSign, 0, 0, 0 );
|
|
normalizeFloat64Subnormal( aSig, &aExp, &aSig );
|
|
--aExp;
|
|
}
|
|
shift128Right( aSig, 0, 4, &zSig0, &zSig1 );
|
|
return packFloat128( aSign, aExp + 0x3C00, zSig0, zSig1 );
|
|
|
|
}
|
|
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the remainder of the double-precision floating-point value `a'
|
|
| with respect to the corresponding value `b'. The operation is performed
|
|
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
float64 float64_rem(float64 a, float64 b, float_status *status)
|
|
{
|
|
bool aSign, zSign;
|
|
int aExp, bExp, expDiff;
|
|
uint64_t aSig, bSig;
|
|
uint64_t q, alternateASig;
|
|
int64_t sigMean;
|
|
|
|
a = float64_squash_input_denormal(a, status);
|
|
b = float64_squash_input_denormal(b, status);
|
|
aSig = extractFloat64Frac( a );
|
|
aExp = extractFloat64Exp( a );
|
|
aSign = extractFloat64Sign( a );
|
|
bSig = extractFloat64Frac( b );
|
|
bExp = extractFloat64Exp( b );
|
|
if ( aExp == 0x7FF ) {
|
|
if ( aSig || ( ( bExp == 0x7FF ) && bSig ) ) {
|
|
return propagateFloat64NaN(a, b, status);
|
|
}
|
|
float_raise(float_flag_invalid, status);
|
|
return float64_default_nan(status);
|
|
}
|
|
if ( bExp == 0x7FF ) {
|
|
if (bSig) {
|
|
return propagateFloat64NaN(a, b, status);
|
|
}
|
|
return a;
|
|
}
|
|
if ( bExp == 0 ) {
|
|
if ( bSig == 0 ) {
|
|
float_raise(float_flag_invalid, status);
|
|
return float64_default_nan(status);
|
|
}
|
|
normalizeFloat64Subnormal( bSig, &bExp, &bSig );
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( aSig == 0 ) return a;
|
|
normalizeFloat64Subnormal( aSig, &aExp, &aSig );
|
|
}
|
|
expDiff = aExp - bExp;
|
|
aSig = (aSig | UINT64_C(0x0010000000000000)) << 11;
|
|
bSig = (bSig | UINT64_C(0x0010000000000000)) << 11;
|
|
if ( expDiff < 0 ) {
|
|
if ( expDiff < -1 ) return a;
|
|
aSig >>= 1;
|
|
}
|
|
q = ( bSig <= aSig );
|
|
if ( q ) aSig -= bSig;
|
|
expDiff -= 64;
|
|
while ( 0 < expDiff ) {
|
|
q = estimateDiv128To64( aSig, 0, bSig );
|
|
q = ( 2 < q ) ? q - 2 : 0;
|
|
aSig = - ( ( bSig>>2 ) * q );
|
|
expDiff -= 62;
|
|
}
|
|
expDiff += 64;
|
|
if ( 0 < expDiff ) {
|
|
q = estimateDiv128To64( aSig, 0, bSig );
|
|
q = ( 2 < q ) ? q - 2 : 0;
|
|
q >>= 64 - expDiff;
|
|
bSig >>= 2;
|
|
aSig = ( ( aSig>>1 )<<( expDiff - 1 ) ) - bSig * q;
|
|
}
|
|
else {
|
|
aSig >>= 2;
|
|
bSig >>= 2;
|
|
}
|
|
do {
|
|
alternateASig = aSig;
|
|
++q;
|
|
aSig -= bSig;
|
|
} while ( 0 <= (int64_t) aSig );
|
|
sigMean = aSig + alternateASig;
|
|
if ( ( sigMean < 0 ) || ( ( sigMean == 0 ) && ( q & 1 ) ) ) {
|
|
aSig = alternateASig;
|
|
}
|
|
zSign = ( (int64_t) aSig < 0 );
|
|
if ( zSign ) aSig = - aSig;
|
|
return normalizeRoundAndPackFloat64(aSign ^ zSign, bExp, aSig, status);
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the binary log of the double-precision floating-point value `a'.
|
|
| The operation is performed according to the IEC/IEEE Standard for Binary
|
|
| Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
float64 float64_log2(float64 a, float_status *status)
|
|
{
|
|
bool aSign, zSign;
|
|
int aExp;
|
|
uint64_t aSig, aSig0, aSig1, zSig, i;
|
|
a = float64_squash_input_denormal(a, status);
|
|
|
|
aSig = extractFloat64Frac( a );
|
|
aExp = extractFloat64Exp( a );
|
|
aSign = extractFloat64Sign( a );
|
|
|
|
if ( aExp == 0 ) {
|
|
if ( aSig == 0 ) return packFloat64( 1, 0x7FF, 0 );
|
|
normalizeFloat64Subnormal( aSig, &aExp, &aSig );
|
|
}
|
|
if ( aSign ) {
|
|
float_raise(float_flag_invalid, status);
|
|
return float64_default_nan(status);
|
|
}
|
|
if ( aExp == 0x7FF ) {
|
|
if (aSig) {
|
|
return propagateFloat64NaN(a, float64_zero, status);
|
|
}
|
|
return a;
|
|
}
|
|
|
|
aExp -= 0x3FF;
|
|
aSig |= UINT64_C(0x0010000000000000);
|
|
zSign = aExp < 0;
|
|
zSig = (uint64_t)aExp << 52;
|
|
for (i = 1LL << 51; i > 0; i >>= 1) {
|
|
mul64To128( aSig, aSig, &aSig0, &aSig1 );
|
|
aSig = ( aSig0 << 12 ) | ( aSig1 >> 52 );
|
|
if ( aSig & UINT64_C(0x0020000000000000) ) {
|
|
aSig >>= 1;
|
|
zSig |= i;
|
|
}
|
|
}
|
|
|
|
if ( zSign )
|
|
zSig = -zSig;
|
|
return normalizeRoundAndPackFloat64(zSign, 0x408, zSig, status);
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of converting the extended double-precision floating-
|
|
| point value `a' to the 32-bit two's complement integer format. The
|
|
| conversion is performed according to the IEC/IEEE Standard for Binary
|
|
| Floating-Point Arithmetic---which means in particular that the conversion
|
|
| is rounded according to the current rounding mode. If `a' is a NaN, the
|
|
| largest positive integer is returned. Otherwise, if the conversion
|
|
| overflows, the largest integer with the same sign as `a' is returned.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
int32_t floatx80_to_int32(floatx80 a, float_status *status)
|
|
{
|
|
bool aSign;
|
|
int32_t aExp, shiftCount;
|
|
uint64_t aSig;
|
|
|
|
if (floatx80_invalid_encoding(a)) {
|
|
float_raise(float_flag_invalid, status);
|
|
return (int32_t)(1U << 31);
|
|
}
|
|
aSig = extractFloatx80Frac( a );
|
|
aExp = extractFloatx80Exp( a );
|
|
aSign = extractFloatx80Sign( a );
|
|
if ( ( aExp == 0x7FFF ) && (uint64_t) ( aSig<<1 ) ) aSign = 0;
|
|
shiftCount = 0x4037 - aExp;
|
|
if ( shiftCount <= 0 ) shiftCount = 1;
|
|
shift64RightJamming( aSig, shiftCount, &aSig );
|
|
return roundAndPackInt32(aSign, aSig, status);
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of converting the extended double-precision floating-
|
|
| point value `a' to the 32-bit two's complement integer format. The
|
|
| conversion is performed according to the IEC/IEEE Standard for Binary
|
|
| Floating-Point Arithmetic, except that the conversion is always rounded
|
|
| toward zero. If `a' is a NaN, the largest positive integer is returned.
|
|
| Otherwise, if the conversion overflows, the largest integer with the same
|
|
| sign as `a' is returned.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
int32_t floatx80_to_int32_round_to_zero(floatx80 a, float_status *status)
|
|
{
|
|
bool aSign;
|
|
int32_t aExp, shiftCount;
|
|
uint64_t aSig, savedASig;
|
|
int32_t z;
|
|
|
|
if (floatx80_invalid_encoding(a)) {
|
|
float_raise(float_flag_invalid, status);
|
|
return (int32_t)(1U << 31);
|
|
}
|
|
aSig = extractFloatx80Frac( a );
|
|
aExp = extractFloatx80Exp( a );
|
|
aSign = extractFloatx80Sign( a );
|
|
if ( 0x401E < aExp ) {
|
|
if ( ( aExp == 0x7FFF ) && (uint64_t) ( aSig<<1 ) ) aSign = 0;
|
|
goto invalid;
|
|
}
|
|
else if ( aExp < 0x3FFF ) {
|
|
if (aExp || aSig) {
|
|
status->float_exception_flags |= float_flag_inexact;
|
|
}
|
|
return 0;
|
|
}
|
|
shiftCount = 0x403E - aExp;
|
|
savedASig = aSig;
|
|
aSig >>= shiftCount;
|
|
z = aSig;
|
|
if ( aSign ) z = - z;
|
|
if ( ( z < 0 ) ^ aSign ) {
|
|
invalid:
|
|
float_raise(float_flag_invalid, status);
|
|
return aSign ? (int32_t) 0x80000000 : 0x7FFFFFFF;
|
|
}
|
|
if ( ( aSig<<shiftCount ) != savedASig ) {
|
|
status->float_exception_flags |= float_flag_inexact;
|
|
}
|
|
return z;
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of converting the extended double-precision floating-
|
|
| point value `a' to the 64-bit two's complement integer format. The
|
|
| conversion is performed according to the IEC/IEEE Standard for Binary
|
|
| Floating-Point Arithmetic---which means in particular that the conversion
|
|
| is rounded according to the current rounding mode. If `a' is a NaN,
|
|
| the largest positive integer is returned. Otherwise, if the conversion
|
|
| overflows, the largest integer with the same sign as `a' is returned.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
int64_t floatx80_to_int64(floatx80 a, float_status *status)
|
|
{
|
|
bool aSign;
|
|
int32_t aExp, shiftCount;
|
|
uint64_t aSig, aSigExtra;
|
|
|
|
if (floatx80_invalid_encoding(a)) {
|
|
float_raise(float_flag_invalid, status);
|
|
return 1ULL << 63;
|
|
}
|
|
aSig = extractFloatx80Frac( a );
|
|
aExp = extractFloatx80Exp( a );
|
|
aSign = extractFloatx80Sign( a );
|
|
shiftCount = 0x403E - aExp;
|
|
if ( shiftCount <= 0 ) {
|
|
if ( shiftCount ) {
|
|
float_raise(float_flag_invalid, status);
|
|
if (!aSign || floatx80_is_any_nan(a)) {
|
|
return INT64_MAX;
|
|
}
|
|
return INT64_MIN;
|
|
}
|
|
aSigExtra = 0;
|
|
}
|
|
else {
|
|
shift64ExtraRightJamming( aSig, 0, shiftCount, &aSig, &aSigExtra );
|
|
}
|
|
return roundAndPackInt64(aSign, aSig, aSigExtra, status);
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of converting the extended double-precision floating-
|
|
| point value `a' to the 64-bit two's complement integer format. The
|
|
| conversion is performed according to the IEC/IEEE Standard for Binary
|
|
| Floating-Point Arithmetic, except that the conversion is always rounded
|
|
| toward zero. If `a' is a NaN, the largest positive integer is returned.
|
|
| Otherwise, if the conversion overflows, the largest integer with the same
|
|
| sign as `a' is returned.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
int64_t floatx80_to_int64_round_to_zero(floatx80 a, float_status *status)
|
|
{
|
|
bool aSign;
|
|
int32_t aExp, shiftCount;
|
|
uint64_t aSig;
|
|
int64_t z;
|
|
|
|
if (floatx80_invalid_encoding(a)) {
|
|
float_raise(float_flag_invalid, status);
|
|
return 1ULL << 63;
|
|
}
|
|
aSig = extractFloatx80Frac( a );
|
|
aExp = extractFloatx80Exp( a );
|
|
aSign = extractFloatx80Sign( a );
|
|
shiftCount = aExp - 0x403E;
|
|
if ( 0 <= shiftCount ) {
|
|
aSig &= UINT64_C(0x7FFFFFFFFFFFFFFF);
|
|
if ( ( a.high != 0xC03E ) || aSig ) {
|
|
float_raise(float_flag_invalid, status);
|
|
if ( ! aSign || ( ( aExp == 0x7FFF ) && aSig ) ) {
|
|
return INT64_MAX;
|
|
}
|
|
}
|
|
return INT64_MIN;
|
|
}
|
|
else if ( aExp < 0x3FFF ) {
|
|
if (aExp | aSig) {
|
|
status->float_exception_flags |= float_flag_inexact;
|
|
}
|
|
return 0;
|
|
}
|
|
z = aSig>>( - shiftCount );
|
|
if ( (uint64_t) ( aSig<<( shiftCount & 63 ) ) ) {
|
|
status->float_exception_flags |= float_flag_inexact;
|
|
}
|
|
if ( aSign ) z = - z;
|
|
return z;
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of converting the extended double-precision floating-
|
|
| point value `a' to the single-precision floating-point format. The
|
|
| conversion is performed according to the IEC/IEEE Standard for Binary
|
|
| Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
float32 floatx80_to_float32(floatx80 a, float_status *status)
|
|
{
|
|
bool aSign;
|
|
int32_t aExp;
|
|
uint64_t aSig;
|
|
|
|
if (floatx80_invalid_encoding(a)) {
|
|
float_raise(float_flag_invalid, status);
|
|
return float32_default_nan(status);
|
|
}
|
|
aSig = extractFloatx80Frac( a );
|
|
aExp = extractFloatx80Exp( a );
|
|
aSign = extractFloatx80Sign( a );
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( (uint64_t) ( aSig<<1 ) ) {
|
|
float32 res = commonNaNToFloat32(floatx80ToCommonNaN(a, status),
|
|
status);
|
|
return float32_silence_nan(res, status);
|
|
}
|
|
return packFloat32( aSign, 0xFF, 0 );
|
|
}
|
|
shift64RightJamming( aSig, 33, &aSig );
|
|
if ( aExp || aSig ) aExp -= 0x3F81;
|
|
return roundAndPackFloat32(aSign, aExp, aSig, status);
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of converting the extended double-precision floating-
|
|
| point value `a' to the double-precision floating-point format. The
|
|
| conversion is performed according to the IEC/IEEE Standard for Binary
|
|
| Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
float64 floatx80_to_float64(floatx80 a, float_status *status)
|
|
{
|
|
bool aSign;
|
|
int32_t aExp;
|
|
uint64_t aSig, zSig;
|
|
|
|
if (floatx80_invalid_encoding(a)) {
|
|
float_raise(float_flag_invalid, status);
|
|
return float64_default_nan(status);
|
|
}
|
|
aSig = extractFloatx80Frac( a );
|
|
aExp = extractFloatx80Exp( a );
|
|
aSign = extractFloatx80Sign( a );
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( (uint64_t) ( aSig<<1 ) ) {
|
|
float64 res = commonNaNToFloat64(floatx80ToCommonNaN(a, status),
|
|
status);
|
|
return float64_silence_nan(res, status);
|
|
}
|
|
return packFloat64( aSign, 0x7FF, 0 );
|
|
}
|
|
shift64RightJamming( aSig, 1, &zSig );
|
|
if ( aExp || aSig ) aExp -= 0x3C01;
|
|
return roundAndPackFloat64(aSign, aExp, zSig, status);
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of converting the extended double-precision floating-
|
|
| point value `a' to the quadruple-precision floating-point format. The
|
|
| conversion is performed according to the IEC/IEEE Standard for Binary
|
|
| Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
float128 floatx80_to_float128(floatx80 a, float_status *status)
|
|
{
|
|
bool aSign;
|
|
int aExp;
|
|
uint64_t aSig, zSig0, zSig1;
|
|
|
|
if (floatx80_invalid_encoding(a)) {
|
|
float_raise(float_flag_invalid, status);
|
|
return float128_default_nan(status);
|
|
}
|
|
aSig = extractFloatx80Frac( a );
|
|
aExp = extractFloatx80Exp( a );
|
|
aSign = extractFloatx80Sign( a );
|
|
if ( ( aExp == 0x7FFF ) && (uint64_t) ( aSig<<1 ) ) {
|
|
float128 res = commonNaNToFloat128(floatx80ToCommonNaN(a, status),
|
|
status);
|
|
return float128_silence_nan(res, status);
|
|
}
|
|
shift128Right( aSig<<1, 0, 16, &zSig0, &zSig1 );
|
|
return packFloat128( aSign, aExp, zSig0, zSig1 );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Rounds the extended double-precision floating-point value `a'
|
|
| to the precision provided by floatx80_rounding_precision and returns the
|
|
| result as an extended double-precision floating-point value.
|
|
| The operation is performed according to the IEC/IEEE Standard for Binary
|
|
| Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
floatx80 floatx80_round(floatx80 a, float_status *status)
|
|
{
|
|
return roundAndPackFloatx80(status->floatx80_rounding_precision,
|
|
extractFloatx80Sign(a),
|
|
extractFloatx80Exp(a),
|
|
extractFloatx80Frac(a), 0, status);
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Rounds the extended double-precision floating-point value `a' to an integer,
|
|
| and returns the result as an extended quadruple-precision floating-point
|
|
| value. The operation is performed according to the IEC/IEEE Standard for
|
|
| Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
floatx80 floatx80_round_to_int(floatx80 a, float_status *status)
|
|
{
|
|
bool aSign;
|
|
int32_t aExp;
|
|
uint64_t lastBitMask, roundBitsMask;
|
|
floatx80 z;
|
|
|
|
if (floatx80_invalid_encoding(a)) {
|
|
float_raise(float_flag_invalid, status);
|
|
return floatx80_default_nan(status);
|
|
}
|
|
aExp = extractFloatx80Exp( a );
|
|
if ( 0x403E <= aExp ) {
|
|
if ( ( aExp == 0x7FFF ) && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) {
|
|
return propagateFloatx80NaN(a, a, status);
|
|
}
|
|
return a;
|
|
}
|
|
if ( aExp < 0x3FFF ) {
|
|
if ( ( aExp == 0 )
|
|
&& ( (uint64_t) ( extractFloatx80Frac( a ) ) == 0 ) ) {
|
|
return a;
|
|
}
|
|
status->float_exception_flags |= float_flag_inexact;
|
|
aSign = extractFloatx80Sign( a );
|
|
switch (status->float_rounding_mode) {
|
|
case float_round_nearest_even:
|
|
if ( ( aExp == 0x3FFE ) && (uint64_t) ( extractFloatx80Frac( a )<<1 )
|
|
) {
|
|
return
|
|
packFloatx80( aSign, 0x3FFF, UINT64_C(0x8000000000000000));
|
|
}
|
|
break;
|
|
case float_round_ties_away:
|
|
if (aExp == 0x3FFE) {
|
|
return packFloatx80(aSign, 0x3FFF, UINT64_C(0x8000000000000000));
|
|
}
|
|
break;
|
|
case float_round_down:
|
|
return
|
|
aSign ?
|
|
packFloatx80( 1, 0x3FFF, UINT64_C(0x8000000000000000))
|
|
: packFloatx80( 0, 0, 0 );
|
|
case float_round_up:
|
|
return
|
|
aSign ? packFloatx80( 1, 0, 0 )
|
|
: packFloatx80( 0, 0x3FFF, UINT64_C(0x8000000000000000));
|
|
|
|
case float_round_to_zero:
|
|
break;
|
|
default:
|
|
g_assert_not_reached();
|
|
}
|
|
return packFloatx80( aSign, 0, 0 );
|
|
}
|
|
lastBitMask = 1;
|
|
lastBitMask <<= 0x403E - aExp;
|
|
roundBitsMask = lastBitMask - 1;
|
|
z = a;
|
|
switch (status->float_rounding_mode) {
|
|
case float_round_nearest_even:
|
|
z.low += lastBitMask>>1;
|
|
if ((z.low & roundBitsMask) == 0) {
|
|
z.low &= ~lastBitMask;
|
|
}
|
|
break;
|
|
case float_round_ties_away:
|
|
z.low += lastBitMask >> 1;
|
|
break;
|
|
case float_round_to_zero:
|
|
break;
|
|
case float_round_up:
|
|
if (!extractFloatx80Sign(z)) {
|
|
z.low += roundBitsMask;
|
|
}
|
|
break;
|
|
case float_round_down:
|
|
if (extractFloatx80Sign(z)) {
|
|
z.low += roundBitsMask;
|
|
}
|
|
break;
|
|
default:
|
|
abort();
|
|
}
|
|
z.low &= ~ roundBitsMask;
|
|
if ( z.low == 0 ) {
|
|
++z.high;
|
|
z.low = UINT64_C(0x8000000000000000);
|
|
}
|
|
if (z.low != a.low) {
|
|
status->float_exception_flags |= float_flag_inexact;
|
|
}
|
|
return z;
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of adding the absolute values of the extended double-
|
|
| precision floating-point values `a' and `b'. If `zSign' is 1, the sum is
|
|
| negated before being returned. `zSign' is ignored if the result is a NaN.
|
|
| The addition is performed according to the IEC/IEEE Standard for Binary
|
|
| Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
static floatx80 addFloatx80Sigs(floatx80 a, floatx80 b, bool zSign,
|
|
float_status *status)
|
|
{
|
|
int32_t aExp, bExp, zExp;
|
|
uint64_t aSig, bSig, zSig0, zSig1;
|
|
int32_t expDiff;
|
|
|
|
aSig = extractFloatx80Frac( a );
|
|
aExp = extractFloatx80Exp( a );
|
|
bSig = extractFloatx80Frac( b );
|
|
bExp = extractFloatx80Exp( b );
|
|
expDiff = aExp - bExp;
|
|
if ( 0 < expDiff ) {
|
|
if ( aExp == 0x7FFF ) {
|
|
if ((uint64_t)(aSig << 1)) {
|
|
return propagateFloatx80NaN(a, b, status);
|
|
}
|
|
return a;
|
|
}
|
|
if ( bExp == 0 ) --expDiff;
|
|
shift64ExtraRightJamming( bSig, 0, expDiff, &bSig, &zSig1 );
|
|
zExp = aExp;
|
|
}
|
|
else if ( expDiff < 0 ) {
|
|
if ( bExp == 0x7FFF ) {
|
|
if ((uint64_t)(bSig << 1)) {
|
|
return propagateFloatx80NaN(a, b, status);
|
|
}
|
|
return packFloatx80(zSign,
|
|
floatx80_infinity_high,
|
|
floatx80_infinity_low);
|
|
}
|
|
if ( aExp == 0 ) ++expDiff;
|
|
shift64ExtraRightJamming( aSig, 0, - expDiff, &aSig, &zSig1 );
|
|
zExp = bExp;
|
|
}
|
|
else {
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( (uint64_t) ( ( aSig | bSig )<<1 ) ) {
|
|
return propagateFloatx80NaN(a, b, status);
|
|
}
|
|
return a;
|
|
}
|
|
zSig1 = 0;
|
|
zSig0 = aSig + bSig;
|
|
if ( aExp == 0 ) {
|
|
if ((aSig | bSig) & UINT64_C(0x8000000000000000) && zSig0 < aSig) {
|
|
/* At least one of the values is a pseudo-denormal,
|
|
* and there is a carry out of the result. */
|
|
zExp = 1;
|
|
goto shiftRight1;
|
|
}
|
|
if (zSig0 == 0) {
|
|
return packFloatx80(zSign, 0, 0);
|
|
}
|
|
normalizeFloatx80Subnormal( zSig0, &zExp, &zSig0 );
|
|
goto roundAndPack;
|
|
}
|
|
zExp = aExp;
|
|
goto shiftRight1;
|
|
}
|
|
zSig0 = aSig + bSig;
|
|
if ( (int64_t) zSig0 < 0 ) goto roundAndPack;
|
|
shiftRight1:
|
|
shift64ExtraRightJamming( zSig0, zSig1, 1, &zSig0, &zSig1 );
|
|
zSig0 |= UINT64_C(0x8000000000000000);
|
|
++zExp;
|
|
roundAndPack:
|
|
return roundAndPackFloatx80(status->floatx80_rounding_precision,
|
|
zSign, zExp, zSig0, zSig1, status);
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of subtracting the absolute values of the extended
|
|
| double-precision floating-point values `a' and `b'. If `zSign' is 1, the
|
|
| difference is negated before being returned. `zSign' is ignored if the
|
|
| result is a NaN. The subtraction is performed according to the IEC/IEEE
|
|
| Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
static floatx80 subFloatx80Sigs(floatx80 a, floatx80 b, bool zSign,
|
|
float_status *status)
|
|
{
|
|
int32_t aExp, bExp, zExp;
|
|
uint64_t aSig, bSig, zSig0, zSig1;
|
|
int32_t expDiff;
|
|
|
|
aSig = extractFloatx80Frac( a );
|
|
aExp = extractFloatx80Exp( a );
|
|
bSig = extractFloatx80Frac( b );
|
|
bExp = extractFloatx80Exp( b );
|
|
expDiff = aExp - bExp;
|
|
if ( 0 < expDiff ) goto aExpBigger;
|
|
if ( expDiff < 0 ) goto bExpBigger;
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( (uint64_t) ( ( aSig | bSig )<<1 ) ) {
|
|
return propagateFloatx80NaN(a, b, status);
|
|
}
|
|
float_raise(float_flag_invalid, status);
|
|
return floatx80_default_nan(status);
|
|
}
|
|
if ( aExp == 0 ) {
|
|
aExp = 1;
|
|
bExp = 1;
|
|
}
|
|
zSig1 = 0;
|
|
if ( bSig < aSig ) goto aBigger;
|
|
if ( aSig < bSig ) goto bBigger;
|
|
return packFloatx80(status->float_rounding_mode == float_round_down, 0, 0);
|
|
bExpBigger:
|
|
if ( bExp == 0x7FFF ) {
|
|
if ((uint64_t)(bSig << 1)) {
|
|
return propagateFloatx80NaN(a, b, status);
|
|
}
|
|
return packFloatx80(zSign ^ 1, floatx80_infinity_high,
|
|
floatx80_infinity_low);
|
|
}
|
|
if ( aExp == 0 ) ++expDiff;
|
|
shift128RightJamming( aSig, 0, - expDiff, &aSig, &zSig1 );
|
|
bBigger:
|
|
sub128( bSig, 0, aSig, zSig1, &zSig0, &zSig1 );
|
|
zExp = bExp;
|
|
zSign ^= 1;
|
|
goto normalizeRoundAndPack;
|
|
aExpBigger:
|
|
if ( aExp == 0x7FFF ) {
|
|
if ((uint64_t)(aSig << 1)) {
|
|
return propagateFloatx80NaN(a, b, status);
|
|
}
|
|
return a;
|
|
}
|
|
if ( bExp == 0 ) --expDiff;
|
|
shift128RightJamming( bSig, 0, expDiff, &bSig, &zSig1 );
|
|
aBigger:
|
|
sub128( aSig, 0, bSig, zSig1, &zSig0, &zSig1 );
|
|
zExp = aExp;
|
|
normalizeRoundAndPack:
|
|
return normalizeRoundAndPackFloatx80(status->floatx80_rounding_precision,
|
|
zSign, zExp, zSig0, zSig1, status);
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of adding the extended double-precision floating-point
|
|
| values `a' and `b'. The operation is performed according to the IEC/IEEE
|
|
| Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
floatx80 floatx80_add(floatx80 a, floatx80 b, float_status *status)
|
|
{
|
|
bool aSign, bSign;
|
|
|
|
if (floatx80_invalid_encoding(a) || floatx80_invalid_encoding(b)) {
|
|
float_raise(float_flag_invalid, status);
|
|
return floatx80_default_nan(status);
|
|
}
|
|
aSign = extractFloatx80Sign( a );
|
|
bSign = extractFloatx80Sign( b );
|
|
if ( aSign == bSign ) {
|
|
return addFloatx80Sigs(a, b, aSign, status);
|
|
}
|
|
else {
|
|
return subFloatx80Sigs(a, b, aSign, status);
|
|
}
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of subtracting the extended double-precision floating-
|
|
| point values `a' and `b'. The operation is performed according to the
|
|
| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
floatx80 floatx80_sub(floatx80 a, floatx80 b, float_status *status)
|
|
{
|
|
bool aSign, bSign;
|
|
|
|
if (floatx80_invalid_encoding(a) || floatx80_invalid_encoding(b)) {
|
|
float_raise(float_flag_invalid, status);
|
|
return floatx80_default_nan(status);
|
|
}
|
|
aSign = extractFloatx80Sign( a );
|
|
bSign = extractFloatx80Sign( b );
|
|
if ( aSign == bSign ) {
|
|
return subFloatx80Sigs(a, b, aSign, status);
|
|
}
|
|
else {
|
|
return addFloatx80Sigs(a, b, aSign, status);
|
|
}
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of multiplying the extended double-precision floating-
|
|
| point values `a' and `b'. The operation is performed according to the
|
|
| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
floatx80 floatx80_mul(floatx80 a, floatx80 b, float_status *status)
|
|
{
|
|
bool aSign, bSign, zSign;
|
|
int32_t aExp, bExp, zExp;
|
|
uint64_t aSig, bSig, zSig0, zSig1;
|
|
|
|
if (floatx80_invalid_encoding(a) || floatx80_invalid_encoding(b)) {
|
|
float_raise(float_flag_invalid, status);
|
|
return floatx80_default_nan(status);
|
|
}
|
|
aSig = extractFloatx80Frac( a );
|
|
aExp = extractFloatx80Exp( a );
|
|
aSign = extractFloatx80Sign( a );
|
|
bSig = extractFloatx80Frac( b );
|
|
bExp = extractFloatx80Exp( b );
|
|
bSign = extractFloatx80Sign( b );
|
|
zSign = aSign ^ bSign;
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( (uint64_t) ( aSig<<1 )
|
|
|| ( ( bExp == 0x7FFF ) && (uint64_t) ( bSig<<1 ) ) ) {
|
|
return propagateFloatx80NaN(a, b, status);
|
|
}
|
|
if ( ( bExp | bSig ) == 0 ) goto invalid;
|
|
return packFloatx80(zSign, floatx80_infinity_high,
|
|
floatx80_infinity_low);
|
|
}
|
|
if ( bExp == 0x7FFF ) {
|
|
if ((uint64_t)(bSig << 1)) {
|
|
return propagateFloatx80NaN(a, b, status);
|
|
}
|
|
if ( ( aExp | aSig ) == 0 ) {
|
|
invalid:
|
|
float_raise(float_flag_invalid, status);
|
|
return floatx80_default_nan(status);
|
|
}
|
|
return packFloatx80(zSign, floatx80_infinity_high,
|
|
floatx80_infinity_low);
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( aSig == 0 ) return packFloatx80( zSign, 0, 0 );
|
|
normalizeFloatx80Subnormal( aSig, &aExp, &aSig );
|
|
}
|
|
if ( bExp == 0 ) {
|
|
if ( bSig == 0 ) return packFloatx80( zSign, 0, 0 );
|
|
normalizeFloatx80Subnormal( bSig, &bExp, &bSig );
|
|
}
|
|
zExp = aExp + bExp - 0x3FFE;
|
|
mul64To128( aSig, bSig, &zSig0, &zSig1 );
|
|
if ( 0 < (int64_t) zSig0 ) {
|
|
shortShift128Left( zSig0, zSig1, 1, &zSig0, &zSig1 );
|
|
--zExp;
|
|
}
|
|
return roundAndPackFloatx80(status->floatx80_rounding_precision,
|
|
zSign, zExp, zSig0, zSig1, status);
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of dividing the extended double-precision floating-point
|
|
| value `a' by the corresponding value `b'. The operation is performed
|
|
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
floatx80 floatx80_div(floatx80 a, floatx80 b, float_status *status)
|
|
{
|
|
bool aSign, bSign, zSign;
|
|
int32_t aExp, bExp, zExp;
|
|
uint64_t aSig, bSig, zSig0, zSig1;
|
|
uint64_t rem0, rem1, rem2, term0, term1, term2;
|
|
|
|
if (floatx80_invalid_encoding(a) || floatx80_invalid_encoding(b)) {
|
|
float_raise(float_flag_invalid, status);
|
|
return floatx80_default_nan(status);
|
|
}
|
|
aSig = extractFloatx80Frac( a );
|
|
aExp = extractFloatx80Exp( a );
|
|
aSign = extractFloatx80Sign( a );
|
|
bSig = extractFloatx80Frac( b );
|
|
bExp = extractFloatx80Exp( b );
|
|
bSign = extractFloatx80Sign( b );
|
|
zSign = aSign ^ bSign;
|
|
if ( aExp == 0x7FFF ) {
|
|
if ((uint64_t)(aSig << 1)) {
|
|
return propagateFloatx80NaN(a, b, status);
|
|
}
|
|
if ( bExp == 0x7FFF ) {
|
|
if ((uint64_t)(bSig << 1)) {
|
|
return propagateFloatx80NaN(a, b, status);
|
|
}
|
|
goto invalid;
|
|
}
|
|
return packFloatx80(zSign, floatx80_infinity_high,
|
|
floatx80_infinity_low);
|
|
}
|
|
if ( bExp == 0x7FFF ) {
|
|
if ((uint64_t)(bSig << 1)) {
|
|
return propagateFloatx80NaN(a, b, status);
|
|
}
|
|
return packFloatx80( zSign, 0, 0 );
|
|
}
|
|
if ( bExp == 0 ) {
|
|
if ( bSig == 0 ) {
|
|
if ( ( aExp | aSig ) == 0 ) {
|
|
invalid:
|
|
float_raise(float_flag_invalid, status);
|
|
return floatx80_default_nan(status);
|
|
}
|
|
float_raise(float_flag_divbyzero, status);
|
|
return packFloatx80(zSign, floatx80_infinity_high,
|
|
floatx80_infinity_low);
|
|
}
|
|
normalizeFloatx80Subnormal( bSig, &bExp, &bSig );
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( aSig == 0 ) return packFloatx80( zSign, 0, 0 );
|
|
normalizeFloatx80Subnormal( aSig, &aExp, &aSig );
|
|
}
|
|
zExp = aExp - bExp + 0x3FFE;
|
|
rem1 = 0;
|
|
if ( bSig <= aSig ) {
|
|
shift128Right( aSig, 0, 1, &aSig, &rem1 );
|
|
++zExp;
|
|
}
|
|
zSig0 = estimateDiv128To64( aSig, rem1, bSig );
|
|
mul64To128( bSig, zSig0, &term0, &term1 );
|
|
sub128( aSig, rem1, term0, term1, &rem0, &rem1 );
|
|
while ( (int64_t) rem0 < 0 ) {
|
|
--zSig0;
|
|
add128( rem0, rem1, 0, bSig, &rem0, &rem1 );
|
|
}
|
|
zSig1 = estimateDiv128To64( rem1, 0, bSig );
|
|
if ( (uint64_t) ( zSig1<<1 ) <= 8 ) {
|
|
mul64To128( bSig, zSig1, &term1, &term2 );
|
|
sub128( rem1, 0, term1, term2, &rem1, &rem2 );
|
|
while ( (int64_t) rem1 < 0 ) {
|
|
--zSig1;
|
|
add128( rem1, rem2, 0, bSig, &rem1, &rem2 );
|
|
}
|
|
zSig1 |= ( ( rem1 | rem2 ) != 0 );
|
|
}
|
|
return roundAndPackFloatx80(status->floatx80_rounding_precision,
|
|
zSign, zExp, zSig0, zSig1, status);
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the remainder of the extended double-precision floating-point value
|
|
| `a' with respect to the corresponding value `b'. The operation is performed
|
|
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
floatx80 floatx80_rem(floatx80 a, floatx80 b, float_status *status)
|
|
{
|
|
bool aSign, zSign;
|
|
int32_t aExp, bExp, expDiff;
|
|
uint64_t aSig0, aSig1, bSig;
|
|
uint64_t q, term0, term1, alternateASig0, alternateASig1;
|
|
|
|
if (floatx80_invalid_encoding(a) || floatx80_invalid_encoding(b)) {
|
|
float_raise(float_flag_invalid, status);
|
|
return floatx80_default_nan(status);
|
|
}
|
|
aSig0 = extractFloatx80Frac( a );
|
|
aExp = extractFloatx80Exp( a );
|
|
aSign = extractFloatx80Sign( a );
|
|
bSig = extractFloatx80Frac( b );
|
|
bExp = extractFloatx80Exp( b );
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( (uint64_t) ( aSig0<<1 )
|
|
|| ( ( bExp == 0x7FFF ) && (uint64_t) ( bSig<<1 ) ) ) {
|
|
return propagateFloatx80NaN(a, b, status);
|
|
}
|
|
goto invalid;
|
|
}
|
|
if ( bExp == 0x7FFF ) {
|
|
if ((uint64_t)(bSig << 1)) {
|
|
return propagateFloatx80NaN(a, b, status);
|
|
}
|
|
return a;
|
|
}
|
|
if ( bExp == 0 ) {
|
|
if ( bSig == 0 ) {
|
|
invalid:
|
|
float_raise(float_flag_invalid, status);
|
|
return floatx80_default_nan(status);
|
|
}
|
|
normalizeFloatx80Subnormal( bSig, &bExp, &bSig );
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( (uint64_t) ( aSig0<<1 ) == 0 ) return a;
|
|
normalizeFloatx80Subnormal( aSig0, &aExp, &aSig0 );
|
|
}
|
|
bSig |= UINT64_C(0x8000000000000000);
|
|
zSign = aSign;
|
|
expDiff = aExp - bExp;
|
|
aSig1 = 0;
|
|
if ( expDiff < 0 ) {
|
|
if ( expDiff < -1 ) return a;
|
|
shift128Right( aSig0, 0, 1, &aSig0, &aSig1 );
|
|
expDiff = 0;
|
|
}
|
|
q = ( bSig <= aSig0 );
|
|
if ( q ) aSig0 -= bSig;
|
|
expDiff -= 64;
|
|
while ( 0 < expDiff ) {
|
|
q = estimateDiv128To64( aSig0, aSig1, bSig );
|
|
q = ( 2 < q ) ? q - 2 : 0;
|
|
mul64To128( bSig, q, &term0, &term1 );
|
|
sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 );
|
|
shortShift128Left( aSig0, aSig1, 62, &aSig0, &aSig1 );
|
|
expDiff -= 62;
|
|
}
|
|
expDiff += 64;
|
|
if ( 0 < expDiff ) {
|
|
q = estimateDiv128To64( aSig0, aSig1, bSig );
|
|
q = ( 2 < q ) ? q - 2 : 0;
|
|
q >>= 64 - expDiff;
|
|
mul64To128( bSig, q<<( 64 - expDiff ), &term0, &term1 );
|
|
sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 );
|
|
shortShift128Left( 0, bSig, 64 - expDiff, &term0, &term1 );
|
|
while ( le128( term0, term1, aSig0, aSig1 ) ) {
|
|
++q;
|
|
sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 );
|
|
}
|
|
}
|
|
else {
|
|
term1 = 0;
|
|
term0 = bSig;
|
|
}
|
|
sub128( term0, term1, aSig0, aSig1, &alternateASig0, &alternateASig1 );
|
|
if ( lt128( alternateASig0, alternateASig1, aSig0, aSig1 )
|
|
|| ( eq128( alternateASig0, alternateASig1, aSig0, aSig1 )
|
|
&& ( q & 1 ) )
|
|
) {
|
|
aSig0 = alternateASig0;
|
|
aSig1 = alternateASig1;
|
|
zSign = ! zSign;
|
|
}
|
|
return
|
|
normalizeRoundAndPackFloatx80(
|
|
80, zSign, bExp + expDiff, aSig0, aSig1, status);
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the square root of the extended double-precision floating-point
|
|
| value `a'. The operation is performed according to the IEC/IEEE Standard
|
|
| for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
floatx80 floatx80_sqrt(floatx80 a, float_status *status)
|
|
{
|
|
bool aSign;
|
|
int32_t aExp, zExp;
|
|
uint64_t aSig0, aSig1, zSig0, zSig1, doubleZSig0;
|
|
uint64_t rem0, rem1, rem2, rem3, term0, term1, term2, term3;
|
|
|
|
if (floatx80_invalid_encoding(a)) {
|
|
float_raise(float_flag_invalid, status);
|
|
return floatx80_default_nan(status);
|
|
}
|
|
aSig0 = extractFloatx80Frac( a );
|
|
aExp = extractFloatx80Exp( a );
|
|
aSign = extractFloatx80Sign( a );
|
|
if ( aExp == 0x7FFF ) {
|
|
if ((uint64_t)(aSig0 << 1)) {
|
|
return propagateFloatx80NaN(a, a, status);
|
|
}
|
|
if ( ! aSign ) return a;
|
|
goto invalid;
|
|
}
|
|
if ( aSign ) {
|
|
if ( ( aExp | aSig0 ) == 0 ) return a;
|
|
invalid:
|
|
float_raise(float_flag_invalid, status);
|
|
return floatx80_default_nan(status);
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( aSig0 == 0 ) return packFloatx80( 0, 0, 0 );
|
|
normalizeFloatx80Subnormal( aSig0, &aExp, &aSig0 );
|
|
}
|
|
zExp = ( ( aExp - 0x3FFF )>>1 ) + 0x3FFF;
|
|
zSig0 = estimateSqrt32( aExp, aSig0>>32 );
|
|
shift128Right( aSig0, 0, 2 + ( aExp & 1 ), &aSig0, &aSig1 );
|
|
zSig0 = estimateDiv128To64( aSig0, aSig1, zSig0<<32 ) + ( zSig0<<30 );
|
|
doubleZSig0 = zSig0<<1;
|
|
mul64To128( zSig0, zSig0, &term0, &term1 );
|
|
sub128( aSig0, aSig1, term0, term1, &rem0, &rem1 );
|
|
while ( (int64_t) rem0 < 0 ) {
|
|
--zSig0;
|
|
doubleZSig0 -= 2;
|
|
add128( rem0, rem1, zSig0>>63, doubleZSig0 | 1, &rem0, &rem1 );
|
|
}
|
|
zSig1 = estimateDiv128To64( rem1, 0, doubleZSig0 );
|
|
if ( ( zSig1 & UINT64_C(0x3FFFFFFFFFFFFFFF) ) <= 5 ) {
|
|
if ( zSig1 == 0 ) zSig1 = 1;
|
|
mul64To128( doubleZSig0, zSig1, &term1, &term2 );
|
|
sub128( rem1, 0, term1, term2, &rem1, &rem2 );
|
|
mul64To128( zSig1, zSig1, &term2, &term3 );
|
|
sub192( rem1, rem2, 0, 0, term2, term3, &rem1, &rem2, &rem3 );
|
|
while ( (int64_t) rem1 < 0 ) {
|
|
--zSig1;
|
|
shortShift128Left( 0, zSig1, 1, &term2, &term3 );
|
|
term3 |= 1;
|
|
term2 |= doubleZSig0;
|
|
add192( rem1, rem2, rem3, 0, term2, term3, &rem1, &rem2, &rem3 );
|
|
}
|
|
zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 );
|
|
}
|
|
shortShift128Left( 0, zSig1, 1, &zSig0, &zSig1 );
|
|
zSig0 |= doubleZSig0;
|
|
return roundAndPackFloatx80(status->floatx80_rounding_precision,
|
|
0, zExp, zSig0, zSig1, status);
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns 1 if the extended double-precision floating-point value `a' is equal
|
|
| to the corresponding value `b', and 0 otherwise. The invalid exception is
|
|
| raised if either operand is a NaN. Otherwise, the comparison is performed
|
|
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
int floatx80_eq(floatx80 a, floatx80 b, float_status *status)
|
|
{
|
|
|
|
if (floatx80_invalid_encoding(a) || floatx80_invalid_encoding(b)
|
|
|| (extractFloatx80Exp(a) == 0x7FFF
|
|
&& (uint64_t) (extractFloatx80Frac(a) << 1))
|
|
|| (extractFloatx80Exp(b) == 0x7FFF
|
|
&& (uint64_t) (extractFloatx80Frac(b) << 1))
|
|
) {
|
|
float_raise(float_flag_invalid, status);
|
|
return 0;
|
|
}
|
|
return
|
|
( a.low == b.low )
|
|
&& ( ( a.high == b.high )
|
|
|| ( ( a.low == 0 )
|
|
&& ( (uint16_t) ( ( a.high | b.high )<<1 ) == 0 ) )
|
|
);
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns 1 if the extended double-precision floating-point value `a' is
|
|
| less than or equal to the corresponding value `b', and 0 otherwise. The
|
|
| invalid exception is raised if either operand is a NaN. The comparison is
|
|
| performed according to the IEC/IEEE Standard for Binary Floating-Point
|
|
| Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
int floatx80_le(floatx80 a, floatx80 b, float_status *status)
|
|
{
|
|
bool aSign, bSign;
|
|
|
|
if (floatx80_invalid_encoding(a) || floatx80_invalid_encoding(b)
|
|
|| (extractFloatx80Exp(a) == 0x7FFF
|
|
&& (uint64_t) (extractFloatx80Frac(a) << 1))
|
|
|| (extractFloatx80Exp(b) == 0x7FFF
|
|
&& (uint64_t) (extractFloatx80Frac(b) << 1))
|
|
) {
|
|
float_raise(float_flag_invalid, status);
|
|
return 0;
|
|
}
|
|
aSign = extractFloatx80Sign( a );
|
|
bSign = extractFloatx80Sign( b );
|
|
if ( aSign != bSign ) {
|
|
return
|
|
aSign
|
|
|| ( ( ( (uint16_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
|
|
== 0 );
|
|
}
|
|
return
|
|
aSign ? le128( b.high, b.low, a.high, a.low )
|
|
: le128( a.high, a.low, b.high, b.low );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns 1 if the extended double-precision floating-point value `a' is
|
|
| less than the corresponding value `b', and 0 otherwise. The invalid
|
|
| exception is raised if either operand is a NaN. The comparison is performed
|
|
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
int floatx80_lt(floatx80 a, floatx80 b, float_status *status)
|
|
{
|
|
bool aSign, bSign;
|
|
|
|
if (floatx80_invalid_encoding(a) || floatx80_invalid_encoding(b)
|
|
|| (extractFloatx80Exp(a) == 0x7FFF
|
|
&& (uint64_t) (extractFloatx80Frac(a) << 1))
|
|
|| (extractFloatx80Exp(b) == 0x7FFF
|
|
&& (uint64_t) (extractFloatx80Frac(b) << 1))
|
|
) {
|
|
float_raise(float_flag_invalid, status);
|
|
return 0;
|
|
}
|
|
aSign = extractFloatx80Sign( a );
|
|
bSign = extractFloatx80Sign( b );
|
|
if ( aSign != bSign ) {
|
|
return
|
|
aSign
|
|
&& ( ( ( (uint16_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
|
|
!= 0 );
|
|
}
|
|
return
|
|
aSign ? lt128( b.high, b.low, a.high, a.low )
|
|
: lt128( a.high, a.low, b.high, b.low );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns 1 if the extended double-precision floating-point values `a' and `b'
|
|
| cannot be compared, and 0 otherwise. The invalid exception is raised if
|
|
| either operand is a NaN. The comparison is performed according to the
|
|
| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
int floatx80_unordered(floatx80 a, floatx80 b, float_status *status)
|
|
{
|
|
if (floatx80_invalid_encoding(a) || floatx80_invalid_encoding(b)
|
|
|| (extractFloatx80Exp(a) == 0x7FFF
|
|
&& (uint64_t) (extractFloatx80Frac(a) << 1))
|
|
|| (extractFloatx80Exp(b) == 0x7FFF
|
|
&& (uint64_t) (extractFloatx80Frac(b) << 1))
|
|
) {
|
|
float_raise(float_flag_invalid, status);
|
|
return 1;
|
|
}
|
|
return 0;
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns 1 if the extended double-precision floating-point value `a' is
|
|
| equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not
|
|
| cause an exception. The comparison is performed according to the IEC/IEEE
|
|
| Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
int floatx80_eq_quiet(floatx80 a, floatx80 b, float_status *status)
|
|
{
|
|
|
|
if (floatx80_invalid_encoding(a) || floatx80_invalid_encoding(b)) {
|
|
float_raise(float_flag_invalid, status);
|
|
return 0;
|
|
}
|
|
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
|
|
&& (uint64_t) ( extractFloatx80Frac( a )<<1 ) )
|
|
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
|
|
&& (uint64_t) ( extractFloatx80Frac( b )<<1 ) )
|
|
) {
|
|
if (floatx80_is_signaling_nan(a, status)
|
|
|| floatx80_is_signaling_nan(b, status)) {
|
|
float_raise(float_flag_invalid, status);
|
|
}
|
|
return 0;
|
|
}
|
|
return
|
|
( a.low == b.low )
|
|
&& ( ( a.high == b.high )
|
|
|| ( ( a.low == 0 )
|
|
&& ( (uint16_t) ( ( a.high | b.high )<<1 ) == 0 ) )
|
|
);
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns 1 if the extended double-precision floating-point value `a' is less
|
|
| than or equal to the corresponding value `b', and 0 otherwise. Quiet NaNs
|
|
| do not cause an exception. Otherwise, the comparison is performed according
|
|
| to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
int floatx80_le_quiet(floatx80 a, floatx80 b, float_status *status)
|
|
{
|
|
bool aSign, bSign;
|
|
|
|
if (floatx80_invalid_encoding(a) || floatx80_invalid_encoding(b)) {
|
|
float_raise(float_flag_invalid, status);
|
|
return 0;
|
|
}
|
|
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
|
|
&& (uint64_t) ( extractFloatx80Frac( a )<<1 ) )
|
|
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
|
|
&& (uint64_t) ( extractFloatx80Frac( b )<<1 ) )
|
|
) {
|
|
if (floatx80_is_signaling_nan(a, status)
|
|
|| floatx80_is_signaling_nan(b, status)) {
|
|
float_raise(float_flag_invalid, status);
|
|
}
|
|
return 0;
|
|
}
|
|
aSign = extractFloatx80Sign( a );
|
|
bSign = extractFloatx80Sign( b );
|
|
if ( aSign != bSign ) {
|
|
return
|
|
aSign
|
|
|| ( ( ( (uint16_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
|
|
== 0 );
|
|
}
|
|
return
|
|
aSign ? le128( b.high, b.low, a.high, a.low )
|
|
: le128( a.high, a.low, b.high, b.low );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns 1 if the extended double-precision floating-point value `a' is less
|
|
| than the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause
|
|
| an exception. Otherwise, the comparison is performed according to the
|
|
| IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
int floatx80_lt_quiet(floatx80 a, floatx80 b, float_status *status)
|
|
{
|
|
bool aSign, bSign;
|
|
|
|
if (floatx80_invalid_encoding(a) || floatx80_invalid_encoding(b)) {
|
|
float_raise(float_flag_invalid, status);
|
|
return 0;
|
|
}
|
|
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
|
|
&& (uint64_t) ( extractFloatx80Frac( a )<<1 ) )
|
|
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
|
|
&& (uint64_t) ( extractFloatx80Frac( b )<<1 ) )
|
|
) {
|
|
if (floatx80_is_signaling_nan(a, status)
|
|
|| floatx80_is_signaling_nan(b, status)) {
|
|
float_raise(float_flag_invalid, status);
|
|
}
|
|
return 0;
|
|
}
|
|
aSign = extractFloatx80Sign( a );
|
|
bSign = extractFloatx80Sign( b );
|
|
if ( aSign != bSign ) {
|
|
return
|
|
aSign
|
|
&& ( ( ( (uint16_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low )
|
|
!= 0 );
|
|
}
|
|
return
|
|
aSign ? lt128( b.high, b.low, a.high, a.low )
|
|
: lt128( a.high, a.low, b.high, b.low );
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns 1 if the extended double-precision floating-point values `a' and `b'
|
|
| cannot be compared, and 0 otherwise. Quiet NaNs do not cause an exception.
|
|
| The comparison is performed according to the IEC/IEEE Standard for Binary
|
|
| Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
int floatx80_unordered_quiet(floatx80 a, floatx80 b, float_status *status)
|
|
{
|
|
if (floatx80_invalid_encoding(a) || floatx80_invalid_encoding(b)) {
|
|
float_raise(float_flag_invalid, status);
|
|
return 1;
|
|
}
|
|
if ( ( ( extractFloatx80Exp( a ) == 0x7FFF )
|
|
&& (uint64_t) ( extractFloatx80Frac( a )<<1 ) )
|
|
|| ( ( extractFloatx80Exp( b ) == 0x7FFF )
|
|
&& (uint64_t) ( extractFloatx80Frac( b )<<1 ) )
|
|
) {
|
|
if (floatx80_is_signaling_nan(a, status)
|
|
|| floatx80_is_signaling_nan(b, status)) {
|
|
float_raise(float_flag_invalid, status);
|
|
}
|
|
return 1;
|
|
}
|
|
return 0;
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of converting the quadruple-precision floating-point
|
|
| value `a' to the 32-bit two's complement integer format. The conversion
|
|
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
|
| Arithmetic---which means in particular that the conversion is rounded
|
|
| according to the current rounding mode. If `a' is a NaN, the largest
|
|
| positive integer is returned. Otherwise, if the conversion overflows, the
|
|
| largest integer with the same sign as `a' is returned.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
int32_t float128_to_int32(float128 a, float_status *status)
|
|
{
|
|
bool aSign;
|
|
int32_t aExp, shiftCount;
|
|
uint64_t aSig0, aSig1;
|
|
|
|
aSig1 = extractFloat128Frac1( a );
|
|
aSig0 = extractFloat128Frac0( a );
|
|
aExp = extractFloat128Exp( a );
|
|
aSign = extractFloat128Sign( a );
|
|
if ( ( aExp == 0x7FFF ) && ( aSig0 | aSig1 ) ) aSign = 0;
|
|
if ( aExp ) aSig0 |= UINT64_C(0x0001000000000000);
|
|
aSig0 |= ( aSig1 != 0 );
|
|
shiftCount = 0x4028 - aExp;
|
|
if ( 0 < shiftCount ) shift64RightJamming( aSig0, shiftCount, &aSig0 );
|
|
return roundAndPackInt32(aSign, aSig0, status);
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of converting the quadruple-precision floating-point
|
|
| value `a' to the 32-bit two's complement integer format. The conversion
|
|
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
|
| Arithmetic, except that the conversion is always rounded toward zero. If
|
|
| `a' is a NaN, the largest positive integer is returned. Otherwise, if the
|
|
| conversion overflows, the largest integer with the same sign as `a' is
|
|
| returned.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
int32_t float128_to_int32_round_to_zero(float128 a, float_status *status)
|
|
{
|
|
bool aSign;
|
|
int32_t aExp, shiftCount;
|
|
uint64_t aSig0, aSig1, savedASig;
|
|
int32_t z;
|
|
|
|
aSig1 = extractFloat128Frac1( a );
|
|
aSig0 = extractFloat128Frac0( a );
|
|
aExp = extractFloat128Exp( a );
|
|
aSign = extractFloat128Sign( a );
|
|
aSig0 |= ( aSig1 != 0 );
|
|
if ( 0x401E < aExp ) {
|
|
if ( ( aExp == 0x7FFF ) && aSig0 ) aSign = 0;
|
|
goto invalid;
|
|
}
|
|
else if ( aExp < 0x3FFF ) {
|
|
if (aExp || aSig0) {
|
|
status->float_exception_flags |= float_flag_inexact;
|
|
}
|
|
return 0;
|
|
}
|
|
aSig0 |= UINT64_C(0x0001000000000000);
|
|
shiftCount = 0x402F - aExp;
|
|
savedASig = aSig0;
|
|
aSig0 >>= shiftCount;
|
|
z = aSig0;
|
|
if ( aSign ) z = - z;
|
|
if ( ( z < 0 ) ^ aSign ) {
|
|
invalid:
|
|
float_raise(float_flag_invalid, status);
|
|
return aSign ? INT32_MIN : INT32_MAX;
|
|
}
|
|
if ( ( aSig0<<shiftCount ) != savedASig ) {
|
|
status->float_exception_flags |= float_flag_inexact;
|
|
}
|
|
return z;
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of converting the quadruple-precision floating-point
|
|
| value `a' to the 64-bit two's complement integer format. The conversion
|
|
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
|
| Arithmetic---which means in particular that the conversion is rounded
|
|
| according to the current rounding mode. If `a' is a NaN, the largest
|
|
| positive integer is returned. Otherwise, if the conversion overflows, the
|
|
| largest integer with the same sign as `a' is returned.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
int64_t float128_to_int64(float128 a, float_status *status)
|
|
{
|
|
bool aSign;
|
|
int32_t aExp, shiftCount;
|
|
uint64_t aSig0, aSig1;
|
|
|
|
aSig1 = extractFloat128Frac1( a );
|
|
aSig0 = extractFloat128Frac0( a );
|
|
aExp = extractFloat128Exp( a );
|
|
aSign = extractFloat128Sign( a );
|
|
if ( aExp ) aSig0 |= UINT64_C(0x0001000000000000);
|
|
shiftCount = 0x402F - aExp;
|
|
if ( shiftCount <= 0 ) {
|
|
if ( 0x403E < aExp ) {
|
|
float_raise(float_flag_invalid, status);
|
|
if ( ! aSign
|
|
|| ( ( aExp == 0x7FFF )
|
|
&& ( aSig1 || ( aSig0 != UINT64_C(0x0001000000000000) ) )
|
|
)
|
|
) {
|
|
return INT64_MAX;
|
|
}
|
|
return INT64_MIN;
|
|
}
|
|
shortShift128Left( aSig0, aSig1, - shiftCount, &aSig0, &aSig1 );
|
|
}
|
|
else {
|
|
shift64ExtraRightJamming( aSig0, aSig1, shiftCount, &aSig0, &aSig1 );
|
|
}
|
|
return roundAndPackInt64(aSign, aSig0, aSig1, status);
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of converting the quadruple-precision floating-point
|
|
| value `a' to the 64-bit two's complement integer format. The conversion
|
|
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
|
| Arithmetic, except that the conversion is always rounded toward zero.
|
|
| If `a' is a NaN, the largest positive integer is returned. Otherwise, if
|
|
| the conversion overflows, the largest integer with the same sign as `a' is
|
|
| returned.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
int64_t float128_to_int64_round_to_zero(float128 a, float_status *status)
|
|
{
|
|
bool aSign;
|
|
int32_t aExp, shiftCount;
|
|
uint64_t aSig0, aSig1;
|
|
int64_t z;
|
|
|
|
aSig1 = extractFloat128Frac1( a );
|
|
aSig0 = extractFloat128Frac0( a );
|
|
aExp = extractFloat128Exp( a );
|
|
aSign = extractFloat128Sign( a );
|
|
if ( aExp ) aSig0 |= UINT64_C(0x0001000000000000);
|
|
shiftCount = aExp - 0x402F;
|
|
if ( 0 < shiftCount ) {
|
|
if ( 0x403E <= aExp ) {
|
|
aSig0 &= UINT64_C(0x0000FFFFFFFFFFFF);
|
|
if ( ( a.high == UINT64_C(0xC03E000000000000) )
|
|
&& ( aSig1 < UINT64_C(0x0002000000000000) ) ) {
|
|
if (aSig1) {
|
|
status->float_exception_flags |= float_flag_inexact;
|
|
}
|
|
}
|
|
else {
|
|
float_raise(float_flag_invalid, status);
|
|
if ( ! aSign || ( ( aExp == 0x7FFF ) && ( aSig0 | aSig1 ) ) ) {
|
|
return INT64_MAX;
|
|
}
|
|
}
|
|
return INT64_MIN;
|
|
}
|
|
z = ( aSig0<<shiftCount ) | ( aSig1>>( ( - shiftCount ) & 63 ) );
|
|
if ( (uint64_t) ( aSig1<<shiftCount ) ) {
|
|
status->float_exception_flags |= float_flag_inexact;
|
|
}
|
|
}
|
|
else {
|
|
if ( aExp < 0x3FFF ) {
|
|
if ( aExp | aSig0 | aSig1 ) {
|
|
status->float_exception_flags |= float_flag_inexact;
|
|
}
|
|
return 0;
|
|
}
|
|
z = aSig0>>( - shiftCount );
|
|
if ( aSig1
|
|
|| ( shiftCount && (uint64_t) ( aSig0<<( shiftCount & 63 ) ) ) ) {
|
|
status->float_exception_flags |= float_flag_inexact;
|
|
}
|
|
}
|
|
if ( aSign ) z = - z;
|
|
return z;
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of converting the quadruple-precision floating-point value
|
|
| `a' to the 64-bit unsigned integer format. The conversion is
|
|
| performed according to the IEC/IEEE Standard for Binary Floating-Point
|
|
| Arithmetic---which means in particular that the conversion is rounded
|
|
| according to the current rounding mode. If `a' is a NaN, the largest
|
|
| positive integer is returned. If the conversion overflows, the
|
|
| largest unsigned integer is returned. If 'a' is negative, the value is
|
|
| rounded and zero is returned; negative values that do not round to zero
|
|
| will raise the inexact exception.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
uint64_t float128_to_uint64(float128 a, float_status *status)
|
|
{
|
|
bool aSign;
|
|
int aExp;
|
|
int shiftCount;
|
|
uint64_t aSig0, aSig1;
|
|
|
|
aSig0 = extractFloat128Frac0(a);
|
|
aSig1 = extractFloat128Frac1(a);
|
|
aExp = extractFloat128Exp(a);
|
|
aSign = extractFloat128Sign(a);
|
|
if (aSign && (aExp > 0x3FFE)) {
|
|
float_raise(float_flag_invalid, status);
|
|
if (float128_is_any_nan(a)) {
|
|
return UINT64_MAX;
|
|
} else {
|
|
return 0;
|
|
}
|
|
}
|
|
if (aExp) {
|
|
aSig0 |= UINT64_C(0x0001000000000000);
|
|
}
|
|
shiftCount = 0x402F - aExp;
|
|
if (shiftCount <= 0) {
|
|
if (0x403E < aExp) {
|
|
float_raise(float_flag_invalid, status);
|
|
return UINT64_MAX;
|
|
}
|
|
shortShift128Left(aSig0, aSig1, -shiftCount, &aSig0, &aSig1);
|
|
} else {
|
|
shift64ExtraRightJamming(aSig0, aSig1, shiftCount, &aSig0, &aSig1);
|
|
}
|
|
return roundAndPackUint64(aSign, aSig0, aSig1, status);
|
|
}
|
|
|
|
uint64_t float128_to_uint64_round_to_zero(float128 a, float_status *status)
|
|
{
|
|
uint64_t v;
|
|
signed char current_rounding_mode = status->float_rounding_mode;
|
|
|
|
set_float_rounding_mode(float_round_to_zero, status);
|
|
v = float128_to_uint64(a, status);
|
|
set_float_rounding_mode(current_rounding_mode, status);
|
|
|
|
return v;
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of converting the quadruple-precision floating-point
|
|
| value `a' to the 32-bit unsigned integer format. The conversion
|
|
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
|
| Arithmetic except that the conversion is always rounded toward zero.
|
|
| If `a' is a NaN, the largest positive integer is returned. Otherwise,
|
|
| if the conversion overflows, the largest unsigned integer is returned.
|
|
| If 'a' is negative, the value is rounded and zero is returned; negative
|
|
| values that do not round to zero will raise the inexact exception.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
uint32_t float128_to_uint32_round_to_zero(float128 a, float_status *status)
|
|
{
|
|
uint64_t v;
|
|
uint32_t res;
|
|
int old_exc_flags = get_float_exception_flags(status);
|
|
|
|
v = float128_to_uint64_round_to_zero(a, status);
|
|
if (v > 0xffffffff) {
|
|
res = 0xffffffff;
|
|
} else {
|
|
return v;
|
|
}
|
|
set_float_exception_flags(old_exc_flags, status);
|
|
float_raise(float_flag_invalid, status);
|
|
return res;
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of converting the quadruple-precision floating-point value
|
|
| `a' to the 32-bit unsigned integer format. The conversion is
|
|
| performed according to the IEC/IEEE Standard for Binary Floating-Point
|
|
| Arithmetic---which means in particular that the conversion is rounded
|
|
| according to the current rounding mode. If `a' is a NaN, the largest
|
|
| positive integer is returned. If the conversion overflows, the
|
|
| largest unsigned integer is returned. If 'a' is negative, the value is
|
|
| rounded and zero is returned; negative values that do not round to zero
|
|
| will raise the inexact exception.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
uint32_t float128_to_uint32(float128 a, float_status *status)
|
|
{
|
|
uint64_t v;
|
|
uint32_t res;
|
|
int old_exc_flags = get_float_exception_flags(status);
|
|
|
|
v = float128_to_uint64(a, status);
|
|
if (v > 0xffffffff) {
|
|
res = 0xffffffff;
|
|
} else {
|
|
return v;
|
|
}
|
|
set_float_exception_flags(old_exc_flags, status);
|
|
float_raise(float_flag_invalid, status);
|
|
return res;
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of converting the quadruple-precision floating-point
|
|
| value `a' to the single-precision floating-point format. The conversion
|
|
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
|
| Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
float32 float128_to_float32(float128 a, float_status *status)
|
|
{
|
|
bool aSign;
|
|
int32_t aExp;
|
|
uint64_t aSig0, aSig1;
|
|
uint32_t zSig;
|
|
|
|
aSig1 = extractFloat128Frac1( a );
|
|
aSig0 = extractFloat128Frac0( a );
|
|
aExp = extractFloat128Exp( a );
|
|
aSign = extractFloat128Sign( a );
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( aSig0 | aSig1 ) {
|
|
return commonNaNToFloat32(float128ToCommonNaN(a, status), status);
|
|
}
|
|
return packFloat32( aSign, 0xFF, 0 );
|
|
}
|
|
aSig0 |= ( aSig1 != 0 );
|
|
shift64RightJamming( aSig0, 18, &aSig0 );
|
|
zSig = aSig0;
|
|
if ( aExp || zSig ) {
|
|
zSig |= 0x40000000;
|
|
aExp -= 0x3F81;
|
|
}
|
|
return roundAndPackFloat32(aSign, aExp, zSig, status);
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of converting the quadruple-precision floating-point
|
|
| value `a' to the double-precision floating-point format. The conversion
|
|
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
|
|
| Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
float64 float128_to_float64(float128 a, float_status *status)
|
|
{
|
|
bool aSign;
|
|
int32_t aExp;
|
|
uint64_t aSig0, aSig1;
|
|
|
|
aSig1 = extractFloat128Frac1( a );
|
|
aSig0 = extractFloat128Frac0( a );
|
|
aExp = extractFloat128Exp( a );
|
|
aSign = extractFloat128Sign( a );
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( aSig0 | aSig1 ) {
|
|
return commonNaNToFloat64(float128ToCommonNaN(a, status), status);
|
|
}
|
|
return packFloat64( aSign, 0x7FF, 0 );
|
|
}
|
|
shortShift128Left( aSig0, aSig1, 14, &aSig0, &aSig1 );
|
|
aSig0 |= ( aSig1 != 0 );
|
|
if ( aExp || aSig0 ) {
|
|
aSig0 |= UINT64_C(0x4000000000000000);
|
|
aExp -= 0x3C01;
|
|
}
|
|
return roundAndPackFloat64(aSign, aExp, aSig0, status);
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of converting the quadruple-precision floating-point
|
|
| value `a' to the extended double-precision floating-point format. The
|
|
| conversion is performed according to the IEC/IEEE Standard for Binary
|
|
| Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
floatx80 float128_to_floatx80(float128 a, float_status *status)
|
|
{
|
|
bool aSign;
|
|
int32_t aExp;
|
|
uint64_t aSig0, aSig1;
|
|
|
|
aSig1 = extractFloat128Frac1( a );
|
|
aSig0 = extractFloat128Frac0( a );
|
|
aExp = extractFloat128Exp( a );
|
|
aSign = extractFloat128Sign( a );
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( aSig0 | aSig1 ) {
|
|
floatx80 res = commonNaNToFloatx80(float128ToCommonNaN(a, status),
|
|
status);
|
|
return floatx80_silence_nan(res, status);
|
|
}
|
|
return packFloatx80(aSign, floatx80_infinity_high,
|
|
floatx80_infinity_low);
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( ( aSig0 | aSig1 ) == 0 ) return packFloatx80( aSign, 0, 0 );
|
|
normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 );
|
|
}
|
|
else {
|
|
aSig0 |= UINT64_C(0x0001000000000000);
|
|
}
|
|
shortShift128Left( aSig0, aSig1, 15, &aSig0, &aSig1 );
|
|
return roundAndPackFloatx80(80, aSign, aExp, aSig0, aSig1, status);
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Rounds the quadruple-precision floating-point value `a' to an integer, and
|
|
| returns the result as a quadruple-precision floating-point value. The
|
|
| operation is performed according to the IEC/IEEE Standard for Binary
|
|
| Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
float128 float128_round_to_int(float128 a, float_status *status)
|
|
{
|
|
bool aSign;
|
|
int32_t aExp;
|
|
uint64_t lastBitMask, roundBitsMask;
|
|
float128 z;
|
|
|
|
aExp = extractFloat128Exp( a );
|
|
if ( 0x402F <= aExp ) {
|
|
if ( 0x406F <= aExp ) {
|
|
if ( ( aExp == 0x7FFF )
|
|
&& ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) )
|
|
) {
|
|
return propagateFloat128NaN(a, a, status);
|
|
}
|
|
return a;
|
|
}
|
|
lastBitMask = 1;
|
|
lastBitMask = ( lastBitMask<<( 0x406E - aExp ) )<<1;
|
|
roundBitsMask = lastBitMask - 1;
|
|
z = a;
|
|
switch (status->float_rounding_mode) {
|
|
case float_round_nearest_even:
|
|
if ( lastBitMask ) {
|
|
add128( z.high, z.low, 0, lastBitMask>>1, &z.high, &z.low );
|
|
if ( ( z.low & roundBitsMask ) == 0 ) z.low &= ~ lastBitMask;
|
|
}
|
|
else {
|
|
if ( (int64_t) z.low < 0 ) {
|
|
++z.high;
|
|
if ( (uint64_t) ( z.low<<1 ) == 0 ) z.high &= ~1;
|
|
}
|
|
}
|
|
break;
|
|
case float_round_ties_away:
|
|
if (lastBitMask) {
|
|
add128(z.high, z.low, 0, lastBitMask >> 1, &z.high, &z.low);
|
|
} else {
|
|
if ((int64_t) z.low < 0) {
|
|
++z.high;
|
|
}
|
|
}
|
|
break;
|
|
case float_round_to_zero:
|
|
break;
|
|
case float_round_up:
|
|
if (!extractFloat128Sign(z)) {
|
|
add128(z.high, z.low, 0, roundBitsMask, &z.high, &z.low);
|
|
}
|
|
break;
|
|
case float_round_down:
|
|
if (extractFloat128Sign(z)) {
|
|
add128(z.high, z.low, 0, roundBitsMask, &z.high, &z.low);
|
|
}
|
|
break;
|
|
case float_round_to_odd:
|
|
/*
|
|
* Note that if lastBitMask == 0, the last bit is the lsb
|
|
* of high, and roundBitsMask == -1.
|
|
*/
|
|
if ((lastBitMask ? z.low & lastBitMask : z.high & 1) == 0) {
|
|
add128(z.high, z.low, 0, roundBitsMask, &z.high, &z.low);
|
|
}
|
|
break;
|
|
default:
|
|
abort();
|
|
}
|
|
z.low &= ~ roundBitsMask;
|
|
}
|
|
else {
|
|
if ( aExp < 0x3FFF ) {
|
|
if ( ( ( (uint64_t) ( a.high<<1 ) ) | a.low ) == 0 ) return a;
|
|
status->float_exception_flags |= float_flag_inexact;
|
|
aSign = extractFloat128Sign( a );
|
|
switch (status->float_rounding_mode) {
|
|
case float_round_nearest_even:
|
|
if ( ( aExp == 0x3FFE )
|
|
&& ( extractFloat128Frac0( a )
|
|
| extractFloat128Frac1( a ) )
|
|
) {
|
|
return packFloat128( aSign, 0x3FFF, 0, 0 );
|
|
}
|
|
break;
|
|
case float_round_ties_away:
|
|
if (aExp == 0x3FFE) {
|
|
return packFloat128(aSign, 0x3FFF, 0, 0);
|
|
}
|
|
break;
|
|
case float_round_down:
|
|
return
|
|
aSign ? packFloat128( 1, 0x3FFF, 0, 0 )
|
|
: packFloat128( 0, 0, 0, 0 );
|
|
case float_round_up:
|
|
return
|
|
aSign ? packFloat128( 1, 0, 0, 0 )
|
|
: packFloat128( 0, 0x3FFF, 0, 0 );
|
|
|
|
case float_round_to_odd:
|
|
return packFloat128(aSign, 0x3FFF, 0, 0);
|
|
|
|
case float_round_to_zero:
|
|
break;
|
|
}
|
|
return packFloat128( aSign, 0, 0, 0 );
|
|
}
|
|
lastBitMask = 1;
|
|
lastBitMask <<= 0x402F - aExp;
|
|
roundBitsMask = lastBitMask - 1;
|
|
z.low = 0;
|
|
z.high = a.high;
|
|
switch (status->float_rounding_mode) {
|
|
case float_round_nearest_even:
|
|
z.high += lastBitMask>>1;
|
|
if ( ( ( z.high & roundBitsMask ) | a.low ) == 0 ) {
|
|
z.high &= ~ lastBitMask;
|
|
}
|
|
break;
|
|
case float_round_ties_away:
|
|
z.high += lastBitMask>>1;
|
|
break;
|
|
case float_round_to_zero:
|
|
break;
|
|
case float_round_up:
|
|
if (!extractFloat128Sign(z)) {
|
|
z.high |= ( a.low != 0 );
|
|
z.high += roundBitsMask;
|
|
}
|
|
break;
|
|
case float_round_down:
|
|
if (extractFloat128Sign(z)) {
|
|
z.high |= (a.low != 0);
|
|
z.high += roundBitsMask;
|
|
}
|
|
break;
|
|
case float_round_to_odd:
|
|
if ((z.high & lastBitMask) == 0) {
|
|
z.high |= (a.low != 0);
|
|
z.high += roundBitsMask;
|
|
}
|
|
break;
|
|
default:
|
|
abort();
|
|
}
|
|
z.high &= ~ roundBitsMask;
|
|
}
|
|
if ( ( z.low != a.low ) || ( z.high != a.high ) ) {
|
|
status->float_exception_flags |= float_flag_inexact;
|
|
}
|
|
return z;
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of adding the absolute values of the quadruple-precision
|
|
| floating-point values `a' and `b'. If `zSign' is 1, the sum is negated
|
|
| before being returned. `zSign' is ignored if the result is a NaN.
|
|
| The addition is performed according to the IEC/IEEE Standard for Binary
|
|
| Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
static float128 addFloat128Sigs(float128 a, float128 b, bool zSign,
|
|
float_status *status)
|
|
{
|
|
int32_t aExp, bExp, zExp;
|
|
uint64_t aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2;
|
|
int32_t expDiff;
|
|
|
|
aSig1 = extractFloat128Frac1( a );
|
|
aSig0 = extractFloat128Frac0( a );
|
|
aExp = extractFloat128Exp( a );
|
|
bSig1 = extractFloat128Frac1( b );
|
|
bSig0 = extractFloat128Frac0( b );
|
|
bExp = extractFloat128Exp( b );
|
|
expDiff = aExp - bExp;
|
|
if ( 0 < expDiff ) {
|
|
if ( aExp == 0x7FFF ) {
|
|
if (aSig0 | aSig1) {
|
|
return propagateFloat128NaN(a, b, status);
|
|
}
|
|
return a;
|
|
}
|
|
if ( bExp == 0 ) {
|
|
--expDiff;
|
|
}
|
|
else {
|
|
bSig0 |= UINT64_C(0x0001000000000000);
|
|
}
|
|
shift128ExtraRightJamming(
|
|
bSig0, bSig1, 0, expDiff, &bSig0, &bSig1, &zSig2 );
|
|
zExp = aExp;
|
|
}
|
|
else if ( expDiff < 0 ) {
|
|
if ( bExp == 0x7FFF ) {
|
|
if (bSig0 | bSig1) {
|
|
return propagateFloat128NaN(a, b, status);
|
|
}
|
|
return packFloat128( zSign, 0x7FFF, 0, 0 );
|
|
}
|
|
if ( aExp == 0 ) {
|
|
++expDiff;
|
|
}
|
|
else {
|
|
aSig0 |= UINT64_C(0x0001000000000000);
|
|
}
|
|
shift128ExtraRightJamming(
|
|
aSig0, aSig1, 0, - expDiff, &aSig0, &aSig1, &zSig2 );
|
|
zExp = bExp;
|
|
}
|
|
else {
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( aSig0 | aSig1 | bSig0 | bSig1 ) {
|
|
return propagateFloat128NaN(a, b, status);
|
|
}
|
|
return a;
|
|
}
|
|
add128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 );
|
|
if ( aExp == 0 ) {
|
|
if (status->flush_to_zero) {
|
|
if (zSig0 | zSig1) {
|
|
float_raise(float_flag_output_denormal, status);
|
|
}
|
|
return packFloat128(zSign, 0, 0, 0);
|
|
}
|
|
return packFloat128( zSign, 0, zSig0, zSig1 );
|
|
}
|
|
zSig2 = 0;
|
|
zSig0 |= UINT64_C(0x0002000000000000);
|
|
zExp = aExp;
|
|
goto shiftRight1;
|
|
}
|
|
aSig0 |= UINT64_C(0x0001000000000000);
|
|
add128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 );
|
|
--zExp;
|
|
if ( zSig0 < UINT64_C(0x0002000000000000) ) goto roundAndPack;
|
|
++zExp;
|
|
shiftRight1:
|
|
shift128ExtraRightJamming(
|
|
zSig0, zSig1, zSig2, 1, &zSig0, &zSig1, &zSig2 );
|
|
roundAndPack:
|
|
return roundAndPackFloat128(zSign, zExp, zSig0, zSig1, zSig2, status);
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of subtracting the absolute values of the quadruple-
|
|
| precision floating-point values `a' and `b'. If `zSign' is 1, the
|
|
| difference is negated before being returned. `zSign' is ignored if the
|
|
| result is a NaN. The subtraction is performed according to the IEC/IEEE
|
|
| Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
static float128 subFloat128Sigs(float128 a, float128 b, bool zSign,
|
|
float_status *status)
|
|
{
|
|
int32_t aExp, bExp, zExp;
|
|
uint64_t aSig0, aSig1, bSig0, bSig1, zSig0, zSig1;
|
|
int32_t expDiff;
|
|
|
|
aSig1 = extractFloat128Frac1( a );
|
|
aSig0 = extractFloat128Frac0( a );
|
|
aExp = extractFloat128Exp( a );
|
|
bSig1 = extractFloat128Frac1( b );
|
|
bSig0 = extractFloat128Frac0( b );
|
|
bExp = extractFloat128Exp( b );
|
|
expDiff = aExp - bExp;
|
|
shortShift128Left( aSig0, aSig1, 14, &aSig0, &aSig1 );
|
|
shortShift128Left( bSig0, bSig1, 14, &bSig0, &bSig1 );
|
|
if ( 0 < expDiff ) goto aExpBigger;
|
|
if ( expDiff < 0 ) goto bExpBigger;
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( aSig0 | aSig1 | bSig0 | bSig1 ) {
|
|
return propagateFloat128NaN(a, b, status);
|
|
}
|
|
float_raise(float_flag_invalid, status);
|
|
return float128_default_nan(status);
|
|
}
|
|
if ( aExp == 0 ) {
|
|
aExp = 1;
|
|
bExp = 1;
|
|
}
|
|
if ( bSig0 < aSig0 ) goto aBigger;
|
|
if ( aSig0 < bSig0 ) goto bBigger;
|
|
if ( bSig1 < aSig1 ) goto aBigger;
|
|
if ( aSig1 < bSig1 ) goto bBigger;
|
|
return packFloat128(status->float_rounding_mode == float_round_down,
|
|
0, 0, 0);
|
|
bExpBigger:
|
|
if ( bExp == 0x7FFF ) {
|
|
if (bSig0 | bSig1) {
|
|
return propagateFloat128NaN(a, b, status);
|
|
}
|
|
return packFloat128( zSign ^ 1, 0x7FFF, 0, 0 );
|
|
}
|
|
if ( aExp == 0 ) {
|
|
++expDiff;
|
|
}
|
|
else {
|
|
aSig0 |= UINT64_C(0x4000000000000000);
|
|
}
|
|
shift128RightJamming( aSig0, aSig1, - expDiff, &aSig0, &aSig1 );
|
|
bSig0 |= UINT64_C(0x4000000000000000);
|
|
bBigger:
|
|
sub128( bSig0, bSig1, aSig0, aSig1, &zSig0, &zSig1 );
|
|
zExp = bExp;
|
|
zSign ^= 1;
|
|
goto normalizeRoundAndPack;
|
|
aExpBigger:
|
|
if ( aExp == 0x7FFF ) {
|
|
if (aSig0 | aSig1) {
|
|
return propagateFloat128NaN(a, b, status);
|
|
}
|
|
return a;
|
|
}
|
|
if ( bExp == 0 ) {
|
|
--expDiff;
|
|
}
|
|
else {
|
|
bSig0 |= UINT64_C(0x4000000000000000);
|
|
}
|
|
shift128RightJamming( bSig0, bSig1, expDiff, &bSig0, &bSig1 );
|
|
aSig0 |= UINT64_C(0x4000000000000000);
|
|
aBigger:
|
|
sub128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 );
|
|
zExp = aExp;
|
|
normalizeRoundAndPack:
|
|
--zExp;
|
|
return normalizeRoundAndPackFloat128(zSign, zExp - 14, zSig0, zSig1,
|
|
status);
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of adding the quadruple-precision floating-point values
|
|
| `a' and `b'. The operation is performed according to the IEC/IEEE Standard
|
|
| for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
float128 float128_add(float128 a, float128 b, float_status *status)
|
|
{
|
|
bool aSign, bSign;
|
|
|
|
aSign = extractFloat128Sign( a );
|
|
bSign = extractFloat128Sign( b );
|
|
if ( aSign == bSign ) {
|
|
return addFloat128Sigs(a, b, aSign, status);
|
|
}
|
|
else {
|
|
return subFloat128Sigs(a, b, aSign, status);
|
|
}
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of subtracting the quadruple-precision floating-point
|
|
| values `a' and `b'. The operation is performed according to the IEC/IEEE
|
|
| Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
float128 float128_sub(float128 a, float128 b, float_status *status)
|
|
{
|
|
bool aSign, bSign;
|
|
|
|
aSign = extractFloat128Sign( a );
|
|
bSign = extractFloat128Sign( b );
|
|
if ( aSign == bSign ) {
|
|
return subFloat128Sigs(a, b, aSign, status);
|
|
}
|
|
else {
|
|
return addFloat128Sigs(a, b, aSign, status);
|
|
}
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of multiplying the quadruple-precision floating-point
|
|
| values `a' and `b'. The operation is performed according to the IEC/IEEE
|
|
| Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
float128 float128_mul(float128 a, float128 b, float_status *status)
|
|
{
|
|
bool aSign, bSign, zSign;
|
|
int32_t aExp, bExp, zExp;
|
|
uint64_t aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2, zSig3;
|
|
|
|
aSig1 = extractFloat128Frac1( a );
|
|
aSig0 = extractFloat128Frac0( a );
|
|
aExp = extractFloat128Exp( a );
|
|
aSign = extractFloat128Sign( a );
|
|
bSig1 = extractFloat128Frac1( b );
|
|
bSig0 = extractFloat128Frac0( b );
|
|
bExp = extractFloat128Exp( b );
|
|
bSign = extractFloat128Sign( b );
|
|
zSign = aSign ^ bSign;
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( ( aSig0 | aSig1 )
|
|
|| ( ( bExp == 0x7FFF ) && ( bSig0 | bSig1 ) ) ) {
|
|
return propagateFloat128NaN(a, b, status);
|
|
}
|
|
if ( ( bExp | bSig0 | bSig1 ) == 0 ) goto invalid;
|
|
return packFloat128( zSign, 0x7FFF, 0, 0 );
|
|
}
|
|
if ( bExp == 0x7FFF ) {
|
|
if (bSig0 | bSig1) {
|
|
return propagateFloat128NaN(a, b, status);
|
|
}
|
|
if ( ( aExp | aSig0 | aSig1 ) == 0 ) {
|
|
invalid:
|
|
float_raise(float_flag_invalid, status);
|
|
return float128_default_nan(status);
|
|
}
|
|
return packFloat128( zSign, 0x7FFF, 0, 0 );
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 );
|
|
normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 );
|
|
}
|
|
if ( bExp == 0 ) {
|
|
if ( ( bSig0 | bSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 );
|
|
normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 );
|
|
}
|
|
zExp = aExp + bExp - 0x4000;
|
|
aSig0 |= UINT64_C(0x0001000000000000);
|
|
shortShift128Left( bSig0, bSig1, 16, &bSig0, &bSig1 );
|
|
mul128To256( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1, &zSig2, &zSig3 );
|
|
add128( zSig0, zSig1, aSig0, aSig1, &zSig0, &zSig1 );
|
|
zSig2 |= ( zSig3 != 0 );
|
|
if (UINT64_C( 0x0002000000000000) <= zSig0 ) {
|
|
shift128ExtraRightJamming(
|
|
zSig0, zSig1, zSig2, 1, &zSig0, &zSig1, &zSig2 );
|
|
++zExp;
|
|
}
|
|
return roundAndPackFloat128(zSign, zExp, zSig0, zSig1, zSig2, status);
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the result of dividing the quadruple-precision floating-point value
|
|
| `a' by the corresponding value `b'. The operation is performed according to
|
|
| the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
float128 float128_div(float128 a, float128 b, float_status *status)
|
|
{
|
|
bool aSign, bSign, zSign;
|
|
int32_t aExp, bExp, zExp;
|
|
uint64_t aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2;
|
|
uint64_t rem0, rem1, rem2, rem3, term0, term1, term2, term3;
|
|
|
|
aSig1 = extractFloat128Frac1( a );
|
|
aSig0 = extractFloat128Frac0( a );
|
|
aExp = extractFloat128Exp( a );
|
|
aSign = extractFloat128Sign( a );
|
|
bSig1 = extractFloat128Frac1( b );
|
|
bSig0 = extractFloat128Frac0( b );
|
|
bExp = extractFloat128Exp( b );
|
|
bSign = extractFloat128Sign( b );
|
|
zSign = aSign ^ bSign;
|
|
if ( aExp == 0x7FFF ) {
|
|
if (aSig0 | aSig1) {
|
|
return propagateFloat128NaN(a, b, status);
|
|
}
|
|
if ( bExp == 0x7FFF ) {
|
|
if (bSig0 | bSig1) {
|
|
return propagateFloat128NaN(a, b, status);
|
|
}
|
|
goto invalid;
|
|
}
|
|
return packFloat128( zSign, 0x7FFF, 0, 0 );
|
|
}
|
|
if ( bExp == 0x7FFF ) {
|
|
if (bSig0 | bSig1) {
|
|
return propagateFloat128NaN(a, b, status);
|
|
}
|
|
return packFloat128( zSign, 0, 0, 0 );
|
|
}
|
|
if ( bExp == 0 ) {
|
|
if ( ( bSig0 | bSig1 ) == 0 ) {
|
|
if ( ( aExp | aSig0 | aSig1 ) == 0 ) {
|
|
invalid:
|
|
float_raise(float_flag_invalid, status);
|
|
return float128_default_nan(status);
|
|
}
|
|
float_raise(float_flag_divbyzero, status);
|
|
return packFloat128( zSign, 0x7FFF, 0, 0 );
|
|
}
|
|
normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 );
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 );
|
|
normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 );
|
|
}
|
|
zExp = aExp - bExp + 0x3FFD;
|
|
shortShift128Left(
|
|
aSig0 | UINT64_C(0x0001000000000000), aSig1, 15, &aSig0, &aSig1 );
|
|
shortShift128Left(
|
|
bSig0 | UINT64_C(0x0001000000000000), bSig1, 15, &bSig0, &bSig1 );
|
|
if ( le128( bSig0, bSig1, aSig0, aSig1 ) ) {
|
|
shift128Right( aSig0, aSig1, 1, &aSig0, &aSig1 );
|
|
++zExp;
|
|
}
|
|
zSig0 = estimateDiv128To64( aSig0, aSig1, bSig0 );
|
|
mul128By64To192( bSig0, bSig1, zSig0, &term0, &term1, &term2 );
|
|
sub192( aSig0, aSig1, 0, term0, term1, term2, &rem0, &rem1, &rem2 );
|
|
while ( (int64_t) rem0 < 0 ) {
|
|
--zSig0;
|
|
add192( rem0, rem1, rem2, 0, bSig0, bSig1, &rem0, &rem1, &rem2 );
|
|
}
|
|
zSig1 = estimateDiv128To64( rem1, rem2, bSig0 );
|
|
if ( ( zSig1 & 0x3FFF ) <= 4 ) {
|
|
mul128By64To192( bSig0, bSig1, zSig1, &term1, &term2, &term3 );
|
|
sub192( rem1, rem2, 0, term1, term2, term3, &rem1, &rem2, &rem3 );
|
|
while ( (int64_t) rem1 < 0 ) {
|
|
--zSig1;
|
|
add192( rem1, rem2, rem3, 0, bSig0, bSig1, &rem1, &rem2, &rem3 );
|
|
}
|
|
zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 );
|
|
}
|
|
shift128ExtraRightJamming( zSig0, zSig1, 0, 15, &zSig0, &zSig1, &zSig2 );
|
|
return roundAndPackFloat128(zSign, zExp, zSig0, zSig1, zSig2, status);
|
|
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the remainder of the quadruple-precision floating-point value `a'
|
|
| with respect to the corresponding value `b'. The operation is performed
|
|
| according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
float128 float128_rem(float128 a, float128 b, float_status *status)
|
|
{
|
|
bool aSign, zSign;
|
|
int32_t aExp, bExp, expDiff;
|
|
uint64_t aSig0, aSig1, bSig0, bSig1, q, term0, term1, term2;
|
|
uint64_t allZero, alternateASig0, alternateASig1, sigMean1;
|
|
int64_t sigMean0;
|
|
|
|
aSig1 = extractFloat128Frac1( a );
|
|
aSig0 = extractFloat128Frac0( a );
|
|
aExp = extractFloat128Exp( a );
|
|
aSign = extractFloat128Sign( a );
|
|
bSig1 = extractFloat128Frac1( b );
|
|
bSig0 = extractFloat128Frac0( b );
|
|
bExp = extractFloat128Exp( b );
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( ( aSig0 | aSig1 )
|
|
|| ( ( bExp == 0x7FFF ) && ( bSig0 | bSig1 ) ) ) {
|
|
return propagateFloat128NaN(a, b, status);
|
|
}
|
|
goto invalid;
|
|
}
|
|
if ( bExp == 0x7FFF ) {
|
|
if (bSig0 | bSig1) {
|
|
return propagateFloat128NaN(a, b, status);
|
|
}
|
|
return a;
|
|
}
|
|
if ( bExp == 0 ) {
|
|
if ( ( bSig0 | bSig1 ) == 0 ) {
|
|
invalid:
|
|
float_raise(float_flag_invalid, status);
|
|
return float128_default_nan(status);
|
|
}
|
|
normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 );
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( ( aSig0 | aSig1 ) == 0 ) return a;
|
|
normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 );
|
|
}
|
|
expDiff = aExp - bExp;
|
|
if ( expDiff < -1 ) return a;
|
|
shortShift128Left(
|
|
aSig0 | UINT64_C(0x0001000000000000),
|
|
aSig1,
|
|
15 - ( expDiff < 0 ),
|
|
&aSig0,
|
|
&aSig1
|
|
);
|
|
shortShift128Left(
|
|
bSig0 | UINT64_C(0x0001000000000000), bSig1, 15, &bSig0, &bSig1 );
|
|
q = le128( bSig0, bSig1, aSig0, aSig1 );
|
|
if ( q ) sub128( aSig0, aSig1, bSig0, bSig1, &aSig0, &aSig1 );
|
|
expDiff -= 64;
|
|
while ( 0 < expDiff ) {
|
|
q = estimateDiv128To64( aSig0, aSig1, bSig0 );
|
|
q = ( 4 < q ) ? q - 4 : 0;
|
|
mul128By64To192( bSig0, bSig1, q, &term0, &term1, &term2 );
|
|
shortShift192Left( term0, term1, term2, 61, &term1, &term2, &allZero );
|
|
shortShift128Left( aSig0, aSig1, 61, &aSig0, &allZero );
|
|
sub128( aSig0, 0, term1, term2, &aSig0, &aSig1 );
|
|
expDiff -= 61;
|
|
}
|
|
if ( -64 < expDiff ) {
|
|
q = estimateDiv128To64( aSig0, aSig1, bSig0 );
|
|
q = ( 4 < q ) ? q - 4 : 0;
|
|
q >>= - expDiff;
|
|
shift128Right( bSig0, bSig1, 12, &bSig0, &bSig1 );
|
|
expDiff += 52;
|
|
if ( expDiff < 0 ) {
|
|
shift128Right( aSig0, aSig1, - expDiff, &aSig0, &aSig1 );
|
|
}
|
|
else {
|
|
shortShift128Left( aSig0, aSig1, expDiff, &aSig0, &aSig1 );
|
|
}
|
|
mul128By64To192( bSig0, bSig1, q, &term0, &term1, &term2 );
|
|
sub128( aSig0, aSig1, term1, term2, &aSig0, &aSig1 );
|
|
}
|
|
else {
|
|
shift128Right( aSig0, aSig1, 12, &aSig0, &aSig1 );
|
|
shift128Right( bSig0, bSig1, 12, &bSig0, &bSig1 );
|
|
}
|
|
do {
|
|
alternateASig0 = aSig0;
|
|
alternateASig1 = aSig1;
|
|
++q;
|
|
sub128( aSig0, aSig1, bSig0, bSig1, &aSig0, &aSig1 );
|
|
} while ( 0 <= (int64_t) aSig0 );
|
|
add128(
|
|
aSig0, aSig1, alternateASig0, alternateASig1, (uint64_t *)&sigMean0, &sigMean1 );
|
|
if ( ( sigMean0 < 0 )
|
|
|| ( ( ( sigMean0 | sigMean1 ) == 0 ) && ( q & 1 ) ) ) {
|
|
aSig0 = alternateASig0;
|
|
aSig1 = alternateASig1;
|
|
}
|
|
zSign = ( (int64_t) aSig0 < 0 );
|
|
if ( zSign ) sub128( 0, 0, aSig0, aSig1, &aSig0, &aSig1 );
|
|
return normalizeRoundAndPackFloat128(aSign ^ zSign, bExp - 4, aSig0, aSig1,
|
|
status);
|
|
}
|
|
|
|
/*----------------------------------------------------------------------------
|
|
| Returns the square root of the quadruple-precision floating-point value `a'.
|
|
| The operation is performed according to the IEC/IEEE Standard for Binary
|
|
| Floating-Point Arithmetic.
|
|
*----------------------------------------------------------------------------*/
|
|
|
|
float128 float128_sqrt(float128 a, float_status *status)
|
|
{
|
|
bool aSign;
|
|
int32_t aExp, zExp;
|
|
uint64_t aSig0, aSig1, zSig0, zSig1, zSig2, doubleZSig0;
|
|
uint64_t rem0, rem1, rem2, rem3, term0, term1, term2, term3;
|
|
|
|
aSig1 = extractFloat128Frac1( a );
|
|
aSig0 = extractFloat128Frac0( a );
|
|
aExp = extractFloat128Exp( a );
|
|
aSign = extractFloat128Sign( a );
|
|
if ( aExp == 0x7FFF ) {
|
|
if (aSig0 | aSig1) {
|
|
return propagateFloat128NaN(a, a, status);
|
|
}
|
|
if ( ! aSign ) return a;
|
|
goto invalid;
|
|
}
|
|
if ( aSign ) {
|
|
if ( ( aExp | aSig0 | aSig1 ) == 0 ) return a;
|
|
invalid:
|
|
float_raise(float_flag_invalid, status);
|
|
return float128_default_nan(status);
|
|
}
|
|
if ( aExp == 0 ) {
|
|
if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( 0, 0, 0, 0 );
|
|
normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 );
|
|
}
|
|
zExp = ( ( aExp - 0x3FFF )>>1 ) + 0x3FFE;
|
|
aSig0 |= UINT64_C(0x0001000000000000);
|
|
zSig0 = estimateSqrt32( aExp, aSig0>>17 );
|
|
shortShift128Left( aSig0, aSig1, 13 - ( aExp & 1 ), &aSig0, &aSig1 );
|
|
zSig0 = estimateDiv128To64( aSig0, aSig1, zSig0<<32 ) + ( zSig0<<30 );
|
|
doubleZSig0 = zSig0<<1;
|
|
mul64To128( zSig0, zSig0, &term0, &term1 );
|
|
sub128( aSig0, aSig1, term0, term1, &rem0, &rem1 );
|
|
while ( (int64_t) rem0 < 0 ) {
|
|
--zSig0;
|
|
doubleZSig0 -= 2;
|
|
add128( rem0, rem1, zSig0>>63, doubleZSig0 | 1, &rem0, &rem1 );
|
|
}
|
|
zSig1 = estimateDiv128To64( rem1, 0, doubleZSig0 );
|
|
if ( ( zSig1 & 0x1FFF ) <= 5 ) {
|
|
if ( zSig1 == 0 ) zSig1 = 1;
|
|
mul64To128( doubleZSig0, zSig1, &term1, &term2 );
|
|
sub128( rem1, 0, term1, term2, &rem1, &rem2 );
|
|
mul64To128( zSig1, zSig1, &term2, &term3 );
|
|
sub192( rem1, rem2, 0, 0, term2, term3, &rem1, &rem2, &rem3 );
|
|
while ( (int64_t) rem1 < 0 ) {
|
|
--zSig1;
|
|
shortShift128Left( 0, zSig1, 1, &term2, &term3 );
|
|
term3 |= 1;
|
|
term2 |= doubleZSig0;
|
|
add192( rem1, rem2, rem3, 0, term2, term3, &rem1, &rem2, &rem3 );
|
|
}
|
|
zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 );
|
|
}
|
|
shift128ExtraRightJamming( zSig0, zSig1, 0, 14, &zSig0, &zSig1, &zSig2 );
|
|
return roundAndPackFloat128(0, zExp, zSig0, zSig1, zSig2, status);
|
|
|
|
}
|
|
|
|
static inline FloatRelation
|
|
floatx80_compare_internal(floatx80 a, floatx80 b, bool is_quiet,
|
|
float_status *status)
|
|
{
|
|
bool aSign, bSign;
|
|
|
|
if (floatx80_invalid_encoding(a) || floatx80_invalid_encoding(b)) {
|
|
float_raise(float_flag_invalid, status);
|
|
return float_relation_unordered;
|
|
}
|
|
if (( ( extractFloatx80Exp( a ) == 0x7fff ) &&
|
|
( extractFloatx80Frac( a )<<1 ) ) ||
|
|
( ( extractFloatx80Exp( b ) == 0x7fff ) &&
|
|
( extractFloatx80Frac( b )<<1 ) )) {
|
|
if (!is_quiet ||
|
|
floatx80_is_signaling_nan(a, status) ||
|
|
floatx80_is_signaling_nan(b, status)) {
|
|
float_raise(float_flag_invalid, status);
|
|
}
|
|
return float_relation_unordered;
|
|
}
|
|
aSign = extractFloatx80Sign( a );
|
|
bSign = extractFloatx80Sign( b );
|
|
if ( aSign != bSign ) {
|
|
|
|
if ( ( ( (uint16_t) ( ( a.high | b.high ) << 1 ) ) == 0) &&
|
|
( ( a.low | b.low ) == 0 ) ) {
|
|
/* zero case */
|
|
return float_relation_equal;
|
|
} else {
|
|
return 1 - (2 * aSign);
|
|
}
|
|
} else {
|
|
/* Normalize pseudo-denormals before comparison. */
|
|
if ((a.high & 0x7fff) == 0 && a.low & UINT64_C(0x8000000000000000)) {
|
|
++a.high;
|
|
}
|
|
if ((b.high & 0x7fff) == 0 && b.low & UINT64_C(0x8000000000000000)) {
|
|
++b.high;
|
|
}
|
|
if (a.low == b.low && a.high == b.high) {
|
|
return float_relation_equal;
|
|
} else {
|
|
return 1 - 2 * (aSign ^ ( lt128( a.high, a.low, b.high, b.low ) ));
|
|
}
|
|
}
|
|
}
|
|
|
|
FloatRelation floatx80_compare(floatx80 a, floatx80 b, float_status *status)
|
|
{
|
|
return floatx80_compare_internal(a, b, 0, status);
|
|
}
|
|
|
|
FloatRelation floatx80_compare_quiet(floatx80 a, floatx80 b, float_status *status)
|
|
{
|
|
return floatx80_compare_internal(a, b, 1, status);
|
|
}
|
|
|
|
static inline FloatRelation
|
|
float128_compare_internal(float128 a, float128 b, bool is_quiet,
|
|
float_status *status)
|
|
{
|
|
bool aSign, bSign;
|
|
|
|
if (( ( extractFloat128Exp( a ) == 0x7fff ) &&
|
|
( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) ||
|
|
( ( extractFloat128Exp( b ) == 0x7fff ) &&
|
|
( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) )) {
|
|
if (!is_quiet ||
|
|
float128_is_signaling_nan(a, status) ||
|
|
float128_is_signaling_nan(b, status)) {
|
|
float_raise(float_flag_invalid, status);
|
|
}
|
|
return float_relation_unordered;
|
|
}
|
|
aSign = extractFloat128Sign( a );
|
|
bSign = extractFloat128Sign( b );
|
|
if ( aSign != bSign ) {
|
|
if ( ( ( ( a.high | b.high )<<1 ) | a.low | b.low ) == 0 ) {
|
|
/* zero case */
|
|
return float_relation_equal;
|
|
} else {
|
|
return 1 - (2 * aSign);
|
|
}
|
|
} else {
|
|
if (a.low == b.low && a.high == b.high) {
|
|
return float_relation_equal;
|
|
} else {
|
|
return 1 - 2 * (aSign ^ ( lt128( a.high, a.low, b.high, b.low ) ));
|
|
}
|
|
}
|
|
}
|
|
|
|
FloatRelation float128_compare(float128 a, float128 b, float_status *status)
|
|
{
|
|
return float128_compare_internal(a, b, 0, status);
|
|
}
|
|
|
|
FloatRelation float128_compare_quiet(float128 a, float128 b,
|
|
float_status *status)
|
|
{
|
|
return float128_compare_internal(a, b, 1, status);
|
|
}
|
|
|
|
floatx80 floatx80_scalbn(floatx80 a, int n, float_status *status)
|
|
{
|
|
bool aSign;
|
|
int32_t aExp;
|
|
uint64_t aSig;
|
|
|
|
if (floatx80_invalid_encoding(a)) {
|
|
float_raise(float_flag_invalid, status);
|
|
return floatx80_default_nan(status);
|
|
}
|
|
aSig = extractFloatx80Frac( a );
|
|
aExp = extractFloatx80Exp( a );
|
|
aSign = extractFloatx80Sign( a );
|
|
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( aSig<<1 ) {
|
|
return propagateFloatx80NaN(a, a, status);
|
|
}
|
|
return a;
|
|
}
|
|
|
|
if (aExp == 0) {
|
|
if (aSig == 0) {
|
|
return a;
|
|
}
|
|
aExp++;
|
|
}
|
|
|
|
if (n > 0x10000) {
|
|
n = 0x10000;
|
|
} else if (n < -0x10000) {
|
|
n = -0x10000;
|
|
}
|
|
|
|
aExp += n;
|
|
return normalizeRoundAndPackFloatx80(status->floatx80_rounding_precision,
|
|
aSign, aExp, aSig, 0, status);
|
|
}
|
|
|
|
float128 float128_scalbn(float128 a, int n, float_status *status)
|
|
{
|
|
bool aSign;
|
|
int32_t aExp;
|
|
uint64_t aSig0, aSig1;
|
|
|
|
aSig1 = extractFloat128Frac1( a );
|
|
aSig0 = extractFloat128Frac0( a );
|
|
aExp = extractFloat128Exp( a );
|
|
aSign = extractFloat128Sign( a );
|
|
if ( aExp == 0x7FFF ) {
|
|
if ( aSig0 | aSig1 ) {
|
|
return propagateFloat128NaN(a, a, status);
|
|
}
|
|
return a;
|
|
}
|
|
if (aExp != 0) {
|
|
aSig0 |= UINT64_C(0x0001000000000000);
|
|
} else if (aSig0 == 0 && aSig1 == 0) {
|
|
return a;
|
|
} else {
|
|
aExp++;
|
|
}
|
|
|
|
if (n > 0x10000) {
|
|
n = 0x10000;
|
|
} else if (n < -0x10000) {
|
|
n = -0x10000;
|
|
}
|
|
|
|
aExp += n - 1;
|
|
return normalizeRoundAndPackFloat128( aSign, aExp, aSig0, aSig1
|
|
, status);
|
|
|
|
}
|