| /* |
| * QEMU float support |
| * |
| * The code in this source file is derived from release 2a of the SoftFloat |
| * IEC/IEEE Floating-point Arithmetic Package. Those parts of the code (and |
| * some later contributions) are provided under that license, as detailed below. |
| * It has subsequently been modified by contributors to the QEMU Project, |
| * so some portions are provided under: |
| * the SoftFloat-2a license |
| * the BSD license |
| * GPL-v2-or-later |
| * |
| * Any future contributions to this file after December 1st 2014 will be |
| * taken to be licensed under the Softfloat-2a license unless specifically |
| * indicated otherwise. |
| */ |
| |
| /* |
| =============================================================================== |
| This C source file is part of the SoftFloat IEC/IEEE Floating-point |
| Arithmetic Package, Release 2a. |
| |
| Written by John R. Hauser. This work was made possible in part by the |
| International Computer Science Institute, located at Suite 600, 1947 Center |
| Street, Berkeley, California 94704. Funding was partially provided by the |
| National Science Foundation under grant MIP-9311980. The original version |
| of this code was written as part of a project to build a fixed-point vector |
| processor in collaboration with the University of California at Berkeley, |
| overseen by Profs. Nelson Morgan and John Wawrzynek. More information |
| is available through the Web page `http://HTTP.CS.Berkeley.EDU/~jhauser/ |
| arithmetic/SoftFloat.html'. |
| |
| THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort |
| has been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT |
| TIMES RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO |
| PERSONS AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ANY |
| AND ALL LOSSES, COSTS, OR OTHER PROBLEMS ARISING FROM ITS USE. |
| |
| Derivative works are acceptable, even for commercial purposes, so long as |
| (1) they include prominent notice that the work is derivative, and (2) they |
| include prominent notice akin to these four paragraphs for those parts of |
| this code that are retained. |
| |
| =============================================================================== |
| */ |
| |
| /* BSD licensing: |
| * Copyright (c) 2006, Fabrice Bellard |
| * All rights reserved. |
| * |
| * Redistribution and use in source and binary forms, with or without |
| * modification, are permitted provided that the following conditions are met: |
| * |
| * 1. Redistributions of source code must retain the above copyright notice, |
| * this list of conditions and the following disclaimer. |
| * |
| * 2. Redistributions in binary form must reproduce the above copyright notice, |
| * this list of conditions and the following disclaimer in the documentation |
| * and/or other materials provided with the distribution. |
| * |
| * 3. Neither the name of the copyright holder nor the names of its contributors |
| * may be used to endorse or promote products derived from this software without |
| * specific prior written permission. |
| * |
| * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" |
| * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
| * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE |
| * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR |
| * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF |
| * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS |
| * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN |
| * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
| * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF |
| * THE POSSIBILITY OF SUCH DAMAGE. |
| */ |
| |
| /* Portions of this work are licensed under the terms of the GNU GPL, |
| * version 2 or later. See the COPYING file in the top-level directory. |
| */ |
| |
| /* softfloat (and in particular the code in softfloat-specialize.h) is |
| * target-dependent and needs the TARGET_* macros. |
| */ |
| #include "qemu/osdep.h" |
| #include <math.h> |
| #include "qemu/bitops.h" |
| #include "fpu/softfloat.h" |
| |
| /* We only need stdlib for abort() */ |
| |
| /*---------------------------------------------------------------------------- |
| | Primitive arithmetic functions, including multi-word arithmetic, and |
| | division and square root approximations. (Can be specialized to target if |
| | desired.) |
| *----------------------------------------------------------------------------*/ |
| #include "fpu/softfloat-macros.h" |
| |
| /* |
| * Hardfloat |
| * |
| * Fast emulation of guest FP instructions is challenging for two reasons. |
| * First, FP instruction semantics are similar but not identical, particularly |
| * when handling NaNs. Second, emulating at reasonable speed the guest FP |
| * exception flags is not trivial: reading the host's flags register with a |
| * feclearexcept & fetestexcept pair is slow [slightly slower than soft-fp], |
| * and trapping on every FP exception is not fast nor pleasant to work with. |
| * |
| * We address these challenges by leveraging the host FPU for a subset of the |
| * operations. To do this we expand on the idea presented in this paper: |
| * |
| * Guo, Yu-Chuan, et al. "Translating the ARM Neon and VFP instructions in a |
| * binary translator." Software: Practice and Experience 46.12 (2016):1591-1615. |
| * |
| * The idea is thus to leverage the host FPU to (1) compute FP operations |
| * and (2) identify whether FP exceptions occurred while avoiding |
| * expensive exception flag register accesses. |
| * |
| * An important optimization shown in the paper is that given that exception |
| * flags are rarely cleared by the guest, we can avoid recomputing some flags. |
| * This is particularly useful for the inexact flag, which is very frequently |
| * raised in floating-point workloads. |
| * |
| * We optimize the code further by deferring to soft-fp whenever FP exception |
| * detection might get hairy. Two examples: (1) when at least one operand is |
| * denormal/inf/NaN; (2) when operands are not guaranteed to lead to a 0 result |
| * and the result is < the minimum normal. |
| */ |
| #define GEN_INPUT_FLUSH__NOCHECK(name, soft_t) \ |
| static inline void name(soft_t *a, float_status *s) \ |
| { \ |
| if (unlikely(soft_t ## _is_denormal(*a))) { \ |
| *a = soft_t ## _set_sign(soft_t ## _zero, \ |
| soft_t ## _is_neg(*a)); \ |
| float_raise(float_flag_input_denormal, s); \ |
| } \ |
| } |
| |
| GEN_INPUT_FLUSH__NOCHECK(float32_input_flush__nocheck, float32) |
| GEN_INPUT_FLUSH__NOCHECK(float64_input_flush__nocheck, float64) |
| #undef GEN_INPUT_FLUSH__NOCHECK |
| |
| #define GEN_INPUT_FLUSH1(name, soft_t) \ |
| static inline void name(soft_t *a, float_status *s) \ |
| { \ |
| if (likely(!s->flush_inputs_to_zero)) { \ |
| return; \ |
| } \ |
| soft_t ## _input_flush__nocheck(a, s); \ |
| } |
| |
| GEN_INPUT_FLUSH1(float32_input_flush1, float32) |
| GEN_INPUT_FLUSH1(float64_input_flush1, float64) |
| #undef GEN_INPUT_FLUSH1 |
| |
| #define GEN_INPUT_FLUSH2(name, soft_t) \ |
| static inline void name(soft_t *a, soft_t *b, float_status *s) \ |
| { \ |
| if (likely(!s->flush_inputs_to_zero)) { \ |
| return; \ |
| } \ |
| soft_t ## _input_flush__nocheck(a, s); \ |
| soft_t ## _input_flush__nocheck(b, s); \ |
| } |
| |
| GEN_INPUT_FLUSH2(float32_input_flush2, float32) |
| GEN_INPUT_FLUSH2(float64_input_flush2, float64) |
| #undef GEN_INPUT_FLUSH2 |
| |
| #define GEN_INPUT_FLUSH3(name, soft_t) \ |
| static inline void name(soft_t *a, soft_t *b, soft_t *c, float_status *s) \ |
| { \ |
| if (likely(!s->flush_inputs_to_zero)) { \ |
| return; \ |
| } \ |
| soft_t ## _input_flush__nocheck(a, s); \ |
| soft_t ## _input_flush__nocheck(b, s); \ |
| soft_t ## _input_flush__nocheck(c, s); \ |
| } |
| |
| GEN_INPUT_FLUSH3(float32_input_flush3, float32) |
| GEN_INPUT_FLUSH3(float64_input_flush3, float64) |
| #undef GEN_INPUT_FLUSH3 |
| |
| /* |
| * Choose whether to use fpclassify or float32/64_* primitives in the generated |
| * hardfloat functions. Each combination of number of inputs and float size |
| * gets its own value. |
| */ |
| #if defined(__x86_64__) |
| # define QEMU_HARDFLOAT_1F32_USE_FP 0 |
| # define QEMU_HARDFLOAT_1F64_USE_FP 1 |
| # define QEMU_HARDFLOAT_2F32_USE_FP 0 |
| # define QEMU_HARDFLOAT_2F64_USE_FP 1 |
| # define QEMU_HARDFLOAT_3F32_USE_FP 0 |
| # define QEMU_HARDFLOAT_3F64_USE_FP 1 |
| #else |
| # define QEMU_HARDFLOAT_1F32_USE_FP 0 |
| # define QEMU_HARDFLOAT_1F64_USE_FP 0 |
| # define QEMU_HARDFLOAT_2F32_USE_FP 0 |
| # define QEMU_HARDFLOAT_2F64_USE_FP 0 |
| # define QEMU_HARDFLOAT_3F32_USE_FP 0 |
| # define QEMU_HARDFLOAT_3F64_USE_FP 0 |
| #endif |
| |
| /* |
| * QEMU_HARDFLOAT_USE_ISINF chooses whether to use isinf() over |
| * float{32,64}_is_infinity when !USE_FP. |
| * On x86_64/aarch64, using the former over the latter can yield a ~6% speedup. |
| * On power64 however, using isinf() reduces fp-bench performance by up to 50%. |
| */ |
| #if defined(__x86_64__) || defined(__aarch64__) |
| # define QEMU_HARDFLOAT_USE_ISINF 1 |
| #else |
| # define QEMU_HARDFLOAT_USE_ISINF 0 |
| #endif |
| |
| /* |
| * Some targets clear the FP flags before most FP operations. This prevents |
| * the use of hardfloat, since hardfloat relies on the inexact flag being |
| * already set. |
| */ |
| #if defined(TARGET_PPC) || defined(__FAST_MATH__) |
| # if defined(__FAST_MATH__) |
| # warning disabling hardfloat due to -ffast-math: hardfloat requires an exact \ |
| IEEE implementation |
| # endif |
| # define QEMU_NO_HARDFLOAT 1 |
| # define QEMU_SOFTFLOAT_ATTR QEMU_FLATTEN |
| #else |
| # define QEMU_NO_HARDFLOAT 0 |
| # define QEMU_SOFTFLOAT_ATTR QEMU_FLATTEN __attribute__((noinline)) |
| #endif |
| |
| static inline bool can_use_fpu(const float_status *s) |
| { |
| if (QEMU_NO_HARDFLOAT) { |
| return false; |
| } |
| return likely(s->float_exception_flags & float_flag_inexact && |
| s->float_rounding_mode == float_round_nearest_even); |
| } |
| |
| /* |
| * Hardfloat generation functions. Each operation can have two flavors: |
| * either using softfloat primitives (e.g. float32_is_zero_or_normal) for |
| * most condition checks, or native ones (e.g. fpclassify). |
| * |
| * The flavor is chosen by the callers. Instead of using macros, we rely on the |
| * compiler to propagate constants and inline everything into the callers. |
| * |
| * We only generate functions for operations with two inputs, since only |
| * these are common enough to justify consolidating them into common code. |
| */ |
| |
| typedef union { |
| float32 s; |
| float h; |
| } union_float32; |
| |
| typedef union { |
| float64 s; |
| double h; |
| } union_float64; |
| |
| typedef bool (*f32_check_fn)(union_float32 a, union_float32 b); |
| typedef bool (*f64_check_fn)(union_float64 a, union_float64 b); |
| |
| typedef float32 (*soft_f32_op2_fn)(float32 a, float32 b, float_status *s); |
| typedef float64 (*soft_f64_op2_fn)(float64 a, float64 b, float_status *s); |
| typedef float (*hard_f32_op2_fn)(float a, float b); |
| typedef double (*hard_f64_op2_fn)(double a, double b); |
| |
| /* 2-input is-zero-or-normal */ |
| static inline bool f32_is_zon2(union_float32 a, union_float32 b) |
| { |
| if (QEMU_HARDFLOAT_2F32_USE_FP) { |
| /* |
| * Not using a temp variable for consecutive fpclassify calls ends up |
| * generating faster code. |
| */ |
| return (fpclassify(a.h) == FP_NORMAL || fpclassify(a.h) == FP_ZERO) && |
| (fpclassify(b.h) == FP_NORMAL || fpclassify(b.h) == FP_ZERO); |
| } |
| return float32_is_zero_or_normal(a.s) && |
| float32_is_zero_or_normal(b.s); |
| } |
| |
| static inline bool f64_is_zon2(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 || fpclassify(b.h) == FP_ZERO); |
| } |
| return float64_is_zero_or_normal(a.s) && |
| float64_is_zero_or_normal(b.s); |
| } |
| |
| /* 3-input is-zero-or-normal */ |
| static inline |
| bool f32_is_zon3(union_float32 a, union_float32 b, union_float32 c) |
| { |
| if (QEMU_HARDFLOAT_3F32_USE_FP) { |
| return (fpclassify(a.h) == FP_NORMAL || fpclassify(a.h) == FP_ZERO) && |
| (fpclassify(b.h) == FP_NORMAL || fpclassify(b.h) == FP_ZERO) && |
| (fpclassify(c.h) == FP_NORMAL || fpclassify(c.h) == FP_ZERO); |
| } |
| return float32_is_zero_or_normal(a.s) && |
| float32_is_zero_or_normal(b.s) && |
| float32_is_zero_or_normal(c.s); |
| } |
| |
| static inline |
| bool f64_is_zon3(union_float64 a, union_float64 b, union_float64 c) |
| { |
| if (QEMU_HARDFLOAT_3F64_USE_FP) { |
| return (fpclassify(a.h) == FP_NORMAL || fpclassify(a.h) == FP_ZERO) && |
| (fpclassify(b.h) == FP_NORMAL || fpclassify(b.h) == FP_ZERO) && |
| (fpclassify(c.h) == FP_NORMAL || fpclassify(c.h) == FP_ZERO); |
| } |
| return float64_is_zero_or_normal(a.s) && |
| float64_is_zero_or_normal(b.s) && |
| float64_is_zero_or_normal(c.s); |
| } |
| |
| static inline bool f32_is_inf(union_float32 a) |
| { |
| if (QEMU_HARDFLOAT_USE_ISINF) { |
| 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 |
| 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; |
| |
| ua.s = xa; |
| ub.s = xb; |
| |
| if (unlikely(!can_use_fpu(s))) { |
| goto soft; |
| } |
| |
| float32_input_flush2(&ua.s, &ub.s, s); |
| if (unlikely(!pre(ua, ub))) { |
| goto soft; |
| } |
| |
| ur.h = hard(ua.h, ub.h); |
| if (unlikely(f32_is_inf(ur))) { |
| float_raise(float_flag_overflow, s); |
| } 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))) { |
| float_raise(float_flag_overflow, s); |
| } else if (unlikely(fabs(ur.h) <= DBL_MIN) && post(ua, ub)) { |
| goto soft; |
| } |
| return ur.s; |
| |
| soft: |
| return soft(ua.s, ub.s, s); |
| } |
| |
| /* |
| * 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; |
| |
| #define float_cmask(bit) (1u << (bit)) |
| |
| enum { |
| float_cmask_zero = float_cmask(float_class_zero), |
| float_cmask_normal = float_cmask(float_class_normal), |
| float_cmask_inf = float_cmask(float_class_inf), |
| float_cmask_qnan = float_cmask(float_class_qnan), |
| float_cmask_snan = float_cmask(float_class_snan), |
| |
| float_cmask_infzero = float_cmask_zero | float_cmask_inf, |
| float_cmask_anynan = float_cmask_qnan | float_cmask_snan, |
| }; |
| |
| /* Flags for parts_minmax. */ |
| enum { |
| /* Set for minimum; clear for maximum. */ |
| minmax_ismin = 1, |
| /* Set for the IEEE 754-2008 minNum() and maxNum() operations. */ |
| minmax_isnum = 2, |
| /* Set for the IEEE 754-2008 minNumMag() and minNumMag() operations. */ |
| minmax_ismag = 4, |
| /* |
| * Set for the IEEE 754-2019 minimumNumber() and maximumNumber() |
| * operations. |
| */ |
| minmax_isnumber = 8, |
| }; |
| |
| /* Simple helpers for checking if, or what kind of, NaN we have */ |
| static inline __attribute__((unused)) bool is_nan(FloatClass c) |
| { |
| return unlikely(c >= float_class_qnan); |
| } |
| |
| static inline __attribute__((unused)) bool is_snan(FloatClass c) |
| { |
| return c == float_class_snan; |
| } |
| |
| static inline __attribute__((unused)) 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. |
| * |
| * The fraction words are stored in big-endian word ordering, |
| * so that truncation from a larger format to a smaller format |
| * can be done simply by ignoring subsequent elements. |
| */ |
| |
| typedef struct { |
| FloatClass cls; |
| bool sign; |
| int32_t exp; |
| union { |
| /* Routines that know the structure may reference the singular name. */ |
| uint64_t frac; |
| /* |
| * Routines expanded with multiple structures reference "hi" and "lo" |
| * depending on the operation. In FloatParts64, "hi" and "lo" are |
| * both the same word and aliased here. |
| */ |
| uint64_t frac_hi; |
| uint64_t frac_lo; |
| }; |
| } FloatParts64; |
| |
| typedef struct { |
| FloatClass cls; |
| bool sign; |
| int32_t exp; |
| uint64_t frac_hi; |
| uint64_t frac_lo; |
| } FloatParts128; |
| |
| typedef struct { |
| FloatClass cls; |
| bool sign; |
| int32_t exp; |
| uint64_t frac_hi; |
| uint64_t frac_hm; /* high-middle */ |
| uint64_t frac_lm; /* low-middle */ |
| uint64_t frac_lo; |
| } FloatParts256; |
| |
| /* These apply to the most significant word of each FloatPartsN. */ |
| #define DECOMPOSED_BINARY_POINT 63 |
| #define DECOMPOSED_IMPLICIT_BIT (1ull << DECOMPOSED_BINARY_POINT) |
| |
| /* 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 |
| * round_mask: bits below lsb which must be rounded |
| * 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; |
| bool arm_althp; |
| uint64_t round_mask; |
| } FloatFmt; |
| |
| /* Expand fields based on the size of exponent and fraction */ |
| #define FLOAT_PARAMS_(E) \ |
| .exp_size = E, \ |
| .exp_bias = ((1 << E) - 1) >> 1, \ |
| .exp_max = (1 << E) - 1 |
| |
| #define FLOAT_PARAMS(E, F) \ |
| FLOAT_PARAMS_(E), \ |
| .frac_size = F, \ |
| .frac_shift = (-F - 1) & 63, \ |
| .round_mask = (1ull << ((-F - 1) & 63)) - 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 bfloat16_params = { |
| FLOAT_PARAMS(8, 7) |
| }; |
| |
| static const FloatFmt float32_params = { |
| FLOAT_PARAMS(8, 23) |
| }; |
| |
| static const FloatFmt float64_params = { |
| FLOAT_PARAMS(11, 52) |
| }; |
| |
| static const FloatFmt float128_params = { |
| FLOAT_PARAMS(15, 112) |
| }; |
| |
| #define FLOATX80_PARAMS(R) \ |
| FLOAT_PARAMS_(15), \ |
| .frac_size = R == 64 ? 63 : R, \ |
| .frac_shift = 0, \ |
| .round_mask = R == 64 ? -1 : (1ull << ((-R - 1) & 63)) - 1 |
| |
| static const FloatFmt floatx80_params[3] = { |
| [floatx80_precision_s] = { FLOATX80_PARAMS(23) }, |
| [floatx80_precision_d] = { FLOATX80_PARAMS(52) }, |
| [floatx80_precision_x] = { FLOATX80_PARAMS(64) }, |
| }; |
| |
| /* Unpack a float to parts, but do not canonicalize. */ |
| static void unpack_raw64(FloatParts64 *r, const FloatFmt *fmt, uint64_t raw) |
| { |
| const int f_size = fmt->frac_size; |
| const int e_size = fmt->exp_size; |
| |
| *r = (FloatParts64) { |
| .cls = float_class_unclassified, |
| .sign = extract64(raw, f_size + e_size, 1), |
| .exp = extract64(raw, f_size, e_size), |
| .frac = extract64(raw, 0, f_size) |
| }; |
| } |
| |
| static inline void float16_unpack_raw(FloatParts64 *p, float16 f) |
| { |
| unpack_raw64(p, &float16_params, f); |
| } |
| |
| static inline void bfloat16_unpack_raw(FloatParts64 *p, bfloat16 f) |
| { |
| unpack_raw64(p, &bfloat16_params, f); |
| } |
| |
| static inline void float32_unpack_raw(FloatParts64 *p, float32 f) |
| { |
| unpack_raw64(p, &float32_params, f); |
| } |
| |
| static inline void float64_unpack_raw(FloatParts64 *p, float64 f) |
| { |
| unpack_raw64(p, &float64_params, f); |
| } |
| |
| static void floatx80_unpack_raw(FloatParts128 *p, floatx80 f) |
| { |
| *p = (FloatParts128) { |
| .cls = float_class_unclassified, |
| .sign = extract32(f.high, 15, 1), |
| .exp = extract32(f.high, 0, 15), |
| .frac_hi = f.low |
| }; |
| } |
| |
| static void float128_unpack_raw(FloatParts128 *p, float128 f) |
| { |
| const int f_size = float128_params.frac_size - 64; |
| const int e_size = float128_params.exp_size; |
| |
| *p = (FloatParts128) { |
| .cls = float_class_unclassified, |
| .sign = extract64(f.high, f_size + e_size, 1), |
| .exp = extract64(f.high, f_size, e_size), |
| .frac_hi = extract64(f.high, 0, f_size), |
| .frac_lo = f.low, |
| }; |
| } |
| |
| /* Pack a float from parts, but do not canonicalize. */ |
| static uint64_t pack_raw64(const FloatParts64 *p, const FloatFmt *fmt) |
| { |
| const int f_size = fmt->frac_size; |
| const int e_size = fmt->exp_size; |
| uint64_t ret; |
| |
| ret = (uint64_t)p->sign << (f_size + e_size); |
| ret = deposit64(ret, f_size, e_size, p->exp); |
| ret = deposit64(ret, 0, f_size, p->frac); |
| return ret; |
| } |
| |
| static inline float16 float16_pack_raw(const FloatParts64 *p) |
| { |
| return make_float16(pack_raw64(p, &float16_params)); |
| } |
| |
| static inline bfloat16 bfloat16_pack_raw(const FloatParts64 *p) |
| { |
| return pack_raw64(p, &bfloat16_params); |
| } |
| |
| static inline float32 float32_pack_raw(const FloatParts64 *p) |
| { |
| return make_float32(pack_raw64(p, &float32_params)); |
| } |
| |
| static inline float64 float64_pack_raw(const FloatParts64 *p) |
| { |
| return make_float64(pack_raw64(p, &float64_params)); |
| } |
| |
| static float128 float128_pack_raw(const FloatParts128 *p) |
| { |
| const int f_size = float128_params.frac_size - 64; |
| const int e_size = float128_params.exp_size; |
| uint64_t hi; |
| |
| hi = (uint64_t)p->sign << (f_size + e_size); |
| hi = deposit64(hi, f_size, e_size, p->exp); |
| hi = deposit64(hi, 0, f_size, p->frac_hi); |
| return make_float128(hi, p->frac_lo); |
| } |
| |
| /*---------------------------------------------------------------------------- |
| | 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.c.inc" |
| |
| #define PARTS_GENERIC_64_128(NAME, P) \ |
| _Generic((P), FloatParts64 *: parts64_##NAME, \ |
| FloatParts128 *: parts128_##NAME) |
| |
| #define PARTS_GENERIC_64_128_256(NAME, P) \ |
| _Generic((P), FloatParts64 *: parts64_##NAME, \ |
| FloatParts128 *: parts128_##NAME, \ |
| FloatParts256 *: parts256_##NAME) |
| |
| #define parts_default_nan(P, S) PARTS_GENERIC_64_128(default_nan, P)(P, S) |
| #define parts_silence_nan(P, S) PARTS_GENERIC_64_128(silence_nan, P)(P, S) |
| |
| static void parts64_return_nan(FloatParts64 *a, float_status *s); |
| static void parts128_return_nan(FloatParts128 *a, float_status *s); |
| |
| #define parts_return_nan(P, S) PARTS_GENERIC_64_128(return_nan, P)(P, S) |
| |
| static FloatParts64 *parts64_pick_nan(FloatParts64 *a, FloatParts64 *b, |
| float_status *s); |
| static FloatParts128 *parts128_pick_nan(FloatParts128 *a, FloatParts128 *b, |
| float_status *s); |
| |
| #define parts_pick_nan(A, B, S) PARTS_GENERIC_64_128(pick_nan, A)(A, B, S) |
| |
| static FloatParts64 *parts64_pick_nan_muladd(FloatParts64 *a, FloatParts64 *b, |
| FloatParts64 *c, float_status *s, |
| int ab_mask, int abc_mask); |
| static FloatParts128 *parts128_pick_nan_muladd(FloatParts128 *a, |
| FloatParts128 *b, |
| FloatParts128 *c, |
| float_status *s, |
| int ab_mask, int abc_mask); |
| |
| #define parts_pick_nan_muladd(A, B, C, S, ABM, ABCM) \ |
| PARTS_GENERIC_64_128(pick_nan_muladd, A)(A, B, C, S, ABM, ABCM) |
| |
| static void parts64_canonicalize(FloatParts64 *p, float_status *status, |
| const FloatFmt *fmt); |
| static void parts128_canonicalize(FloatParts128 *p, float_status *status, |
| const FloatFmt *fmt); |
| |
| #define parts_canonicalize(A, S, F) \ |
| PARTS_GENERIC_64_128(canonicalize, A)(A, S, F) |
| |
| static void parts64_uncanon_normal(FloatParts64 *p, float_status *status, |
| const FloatFmt *fmt); |
| static void parts128_uncanon_normal(FloatParts128 *p, float_status *status, |
| const FloatFmt *fmt); |
| |
| #define parts_uncanon_normal(A, S, F) \ |
| PARTS_GENERIC_64_128(uncanon_normal, A)(A, S, F) |
| |
| static void parts64_uncanon(FloatParts64 *p, float_status *status, |
| const FloatFmt *fmt); |
| static void parts128_uncanon(FloatParts128 *p, float_status *status, |
| const FloatFmt *fmt); |
| |
| #define parts_uncanon(A, S, F) \ |
| PARTS_GENERIC_64_128(uncanon, A)(A, S, F) |
| |
| static void parts64_add_normal(FloatParts64 *a, FloatParts64 *b); |
| static void parts128_add_normal(FloatParts128 *a, FloatParts128 *b); |
| static void parts256_add_normal(FloatParts256 *a, FloatParts256 *b); |
| |
| #define parts_add_normal(A, B) \ |
| PARTS_GENERIC_64_128_256(add_normal, A)(A, B) |
| |
| static bool parts64_sub_normal(FloatParts64 *a, FloatParts64 *b); |
| static bool parts128_sub_normal(FloatParts128 *a, FloatParts128 *b); |
| static bool parts256_sub_normal(FloatParts256 *a, FloatParts256 *b); |
| |
| #define parts_sub_normal(A, B) \ |
| PARTS_GENERIC_64_128_256(sub_normal, A)(A, B) |
| |
| static FloatParts64 *parts64_addsub(FloatParts64 *a, FloatParts64 *b, |
| float_status *s, bool subtract); |
| static FloatParts128 *parts128_addsub(FloatParts128 *a, FloatParts128 *b, |
| float_status *s, bool subtract); |
| |
| #define parts_addsub(A, B, S, Z) \ |
| PARTS_GENERIC_64_128(addsub, A)(A, B, S, Z) |
| |
| static FloatParts64 *parts64_mul(FloatParts64 *a, FloatParts64 *b, |
| float_status *s); |
| static FloatParts128 *parts128_mul(FloatParts128 *a, FloatParts128 *b, |
| float_status *s); |
| |
| #define parts_mul(A, B, S) \ |
| PARTS_GENERIC_64_128(mul, A)(A, B, S) |
| |
| static FloatParts64 *parts64_muladd(FloatParts64 *a, FloatParts64 *b, |
| FloatParts64 *c, int flags, |
| float_status *s); |
| static FloatParts128 *parts128_muladd(FloatParts128 *a, FloatParts128 *b, |
| FloatParts128 *c, int flags, |
| float_status *s); |
| |
| #define parts_muladd(A, B, C, Z, S) \ |
| PARTS_GENERIC_64_128(muladd, A)(A, B, C, Z, S) |
| |
| static FloatParts64 *parts64_div(FloatParts64 *a, FloatParts64 *b, |
| float_status *s); |
| static FloatParts128 *parts128_div(FloatParts128 *a, FloatParts128 *b, |
| float_status *s); |
| |
| #define parts_div(A, B, S) \ |
| PARTS_GENERIC_64_128(div, A)(A, B, S) |
| |
| static FloatParts64 *parts64_modrem(FloatParts64 *a, FloatParts64 *b, |
| uint64_t *mod_quot, float_status *s); |
| static FloatParts128 *parts128_modrem(FloatParts128 *a, FloatParts128 *b, |
| uint64_t *mod_quot, float_status *s); |
| |
| #define parts_modrem(A, B, Q, S) \ |
| PARTS_GENERIC_64_128(modrem, A)(A, B, Q, S) |
| |
| static void parts64_sqrt(FloatParts64 *a, float_status *s, const FloatFmt *f); |
| static void parts128_sqrt(FloatParts128 *a, float_status *s, const FloatFmt *f); |
| |
| #define parts_sqrt(A, S, F) \ |
| PARTS_GENERIC_64_128(sqrt, A)(A, S, F) |
| |
| static bool parts64_round_to_int_normal(FloatParts64 *a, FloatRoundMode rm, |
| int scale, int frac_size); |
| static bool parts128_round_to_int_normal(FloatParts128 *a, FloatRoundMode r, |
| int scale, int frac_size); |
| |
| #define parts_round_to_int_normal(A, R, C, F) \ |
| PARTS_GENERIC_64_128(round_to_int_normal, A)(A, R, C, F) |
| |
| static void parts64_round_to_int(FloatParts64 *a, FloatRoundMode rm, |
| int scale, float_status *s, |
| const FloatFmt *fmt); |
| static void parts128_round_to_int(FloatParts128 *a, FloatRoundMode r, |
| int scale, float_status *s, |
| const FloatFmt *fmt); |
| |
| #define parts_round_to_int(A, R, C, S, F) \ |
| PARTS_GENERIC_64_128(round_to_int, A)(A, R, C, S, F) |
| |
| static int64_t parts64_float_to_sint(FloatParts64 *p, FloatRoundMode rmode, |
| int scale, int64_t min, int64_t max, |
| float_status *s); |
| static int64_t parts128_float_to_sint(FloatParts128 *p, FloatRoundMode rmode, |
| int scale, int64_t min, int64_t max, |
| float_status *s); |
| |
| #define parts_float_to_sint(P, R, Z, MN, MX, S) \ |
| PARTS_GENERIC_64_128(float_to_sint, P)(P, R, Z, MN, MX, S) |
| |
| static uint64_t parts64_float_to_uint(FloatParts64 *p, FloatRoundMode rmode, |
| int scale, uint64_t max, |
| float_status *s); |
| static uint64_t parts128_float_to_uint(FloatParts128 *p, FloatRoundMode rmode, |
| int scale, uint64_t max, |
| float_status *s); |
| |
| #define parts_float_to_uint(P, R, Z, M, S) \ |
| PARTS_GENERIC_64_128(float_to_uint, P)(P, R, Z, M, S) |
| |
| static void parts64_sint_to_float(FloatParts64 *p, int64_t a, |
| int scale, float_status *s); |
| static void parts128_sint_to_float(FloatParts128 *p, int64_t a, |
| int scale, float_status *s); |
| |
| #define parts_sint_to_float(P, I, Z, S) \ |
| PARTS_GENERIC_64_128(sint_to_float, P)(P, I, Z, S) |
| |
| static void parts64_uint_to_float(FloatParts64 *p, uint64_t a, |
| int scale, float_status *s); |
| static void parts128_uint_to_float(FloatParts128 *p, uint64_t a, |
| int scale, float_status *s); |
| |
| #define parts_uint_to_float(P, I, Z, S) \ |
| PARTS_GENERIC_64_128(uint_to_float, P)(P, I, Z, S) |
| |
| static FloatParts64 *parts64_minmax(FloatParts64 *a, FloatParts64 *b, |
| float_status *s, int flags); |
| static FloatParts128 *parts128_minmax(FloatParts128 *a, FloatParts128 *b, |
| float_status *s, int flags); |
| |
| #define parts_minmax(A, B, S, F) \ |
| PARTS_GENERIC_64_128(minmax, A)(A, B, S, F) |
| |
| static int parts64_compare(FloatParts64 *a, FloatParts64 *b, |
| float_status *s, bool q); |
| static int parts128_compare(FloatParts128 *a, FloatParts128 *b, |
| float_status *s, bool q); |
| |
| #define parts_compare(A, B, S, Q) \ |
| PARTS_GENERIC_64_128(compare, A)(A, B, S, Q) |
| |
| static void parts64_scalbn(FloatParts64 *a, int n, float_status *s); |
| static void parts128_scalbn(FloatParts128 *a, int n, float_status *s); |
| |
| #define parts_scalbn(A, N, S) \ |
| PARTS_GENERIC_64_128(scalbn, A)(A, N, S) |
| |
| static void parts64_log2(FloatParts64 *a, float_status *s, const FloatFmt *f); |
| static void parts128_log2(FloatParts128 *a, float_status *s, const FloatFmt *f); |
| |
| #define parts_log2(A, S, F) \ |
| PARTS_GENERIC_64_128(log2, A)(A, S, F) |
| |
| /* |
| * Helper functions for softfloat-parts.c.inc, per-size operations. |
| */ |
| |
| #define FRAC_GENERIC_64_128(NAME, P) \ |
| _Generic((P), FloatParts64 *: frac64_##NAME, \ |
| FloatParts128 *: frac128_##NAME) |
| |
| #define FRAC_GENERIC_64_128_256(NAME, P) \ |
| _Generic((P), FloatParts64 *: frac64_##NAME, \ |
| FloatParts128 *: frac128_##NAME, \ |
| FloatParts256 *: frac256_##NAME) |
| |
| static bool frac64_add(FloatParts64 *r, FloatParts64 *a, FloatParts64 *b) |
| { |
| return uadd64_overflow(a->frac, b->frac, &r->frac); |
| } |
| |
| static bool frac128_add(FloatParts128 *r, FloatParts128 *a, FloatParts128 *b) |
| { |
| bool c = 0; |
| r->frac_lo = uadd64_carry(a->frac_lo, b->frac_lo, &c); |
| r->frac_hi = uadd64_carry(a->frac_hi, b->frac_hi, &c); |
| return c; |
| } |
| |
| static bool frac256_add(FloatParts256 *r, FloatParts256 *a, FloatParts256 *b) |
| { |
| bool c = 0; |
| r->frac_lo = uadd64_carry(a->frac_lo, b->frac_lo, &c); |
| r->frac_lm = uadd64_carry(a->frac_lm, b->frac_lm, &c); |
| r->frac_hm = uadd64_carry(a->frac_hm, b->frac_hm, &c); |
| r->frac_hi = uadd64_carry(a->frac_hi, b->frac_hi, &c); |
| return c; |
| } |
| |
| #define frac_add(R, A, B) FRAC_GENERIC_64_128_256(add, R)(R, A, B) |
| |
| static bool frac64_addi(FloatParts64 *r, FloatParts64 *a, uint64_t c) |
| { |
| return uadd64_overflow(a->frac, c, &r->frac); |
| } |
| |
| static bool frac128_addi(FloatParts128 *r, FloatParts128 *a, uint64_t c) |
| { |
| c = uadd64_overflow(a->frac_lo, c, &r->frac_lo); |
| return uadd64_overflow(a->frac_hi, c, &r->frac_hi); |
| } |
| |
| #define frac_addi(R, A, C) FRAC_GENERIC_64_128(addi, R)(R, A, C) |
| |
| static void frac64_allones(FloatParts64 *a) |
| { |
| a->frac = -1; |
| } |
| |
| static void frac128_allones(FloatParts128 *a) |
| { |
| a->frac_hi = a->frac_lo = -1; |
| } |
| |
| #define frac_allones(A) FRAC_GENERIC_64_128(allones, A)(A) |
| |
| static int frac64_cmp(FloatParts64 *a, FloatParts64 *b) |
| { |
| return a->frac == b->frac ? 0 : a->frac < b->frac ? -1 : 1; |
| } |
| |
| static int frac128_cmp(FloatParts128 *a, FloatParts128 *b) |
| { |
| uint64_t ta = a->frac_hi, tb = b->frac_hi; |
| if (ta == tb) { |
| ta = a->frac_lo, tb = b->frac_lo; |
| if (ta == tb) { |
| return 0; |
| } |
| } |
| return ta < tb ? -1 : 1; |
| } |
| |
| #define frac_cmp(A, B) FRAC_GENERIC_64_128(cmp, A)(A, B) |
| |
| static void frac64_clear(FloatParts64 *a) |
| { |
| a->frac = 0; |
| } |
| |
| static void frac128_clear(FloatParts128 *a) |
| { |
| a->frac_hi = a->frac_lo = 0; |
| } |
| |
| #define frac_clear(A) FRAC_GENERIC_64_128(clear, A)(A) |
| |
| static bool frac64_div(FloatParts64 *a, FloatParts64 *b) |
| { |
| uint64_t n1, n0, r, q; |
| bool ret; |
| |
| /* |
| * 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 return true to |
| * 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, which is already true. |
| */ |
| ret = a->frac < b->frac; |
| if (ret) { |
| n0 = a->frac; |
| n1 = 0; |
| } else { |
| n0 = a->frac >> 1; |
| n1 = a->frac << 63; |
| } |
| q = udiv_qrnnd(&r, n0, n1, b->frac); |
| |
| /* Set lsb if there is a remainder, to set inexact. */ |
| a->frac = q | (r != 0); |
| |
| return ret; |
| } |
| |
| static bool frac128_div(FloatParts128 *a, FloatParts128 *b) |
| { |
| uint64_t q0, q1, a0, a1, b0, b1; |
| uint64_t r0, r1, r2, r3, t0, t1, t2, t3; |
| bool ret = false; |
| |
| a0 = a->frac_hi, a1 = a->frac_lo; |
| b0 = b->frac_hi, b1 = b->frac_lo; |
| |
| ret = lt128(a0, a1, b0, b1); |
| if (!ret) { |
| a1 = shr_double(a0, a1, 1); |
| a0 = a0 >> 1; |
| } |
| |
| /* Use 128/64 -> 64 division as estimate for 192/128 -> 128 division. */ |
| q0 = estimateDiv128To64(a0, a1, b0); |
| |
| /* |
| * Estimate is high because B1 was not included (unless B1 == 0). |
| * Reduce quotient and increase remainder until remainder is non-negative. |
| * This loop will execute 0 to 2 times. |
| */ |
| mul128By64To192(b0, b1, q0, &t0, &t1, &t2); |
| sub192(a0, a1, 0, t0, t1, t2, &r0, &r1, &r2); |
| while (r0 != 0) { |
| q0--; |
| add192(r0, r1, r2, 0, b0, b1, &r0, &r1, &r2); |
| } |
| |
| /* Repeat using the remainder, producing a second word of quotient. */ |
| q1 = estimateDiv128To64(r1, r2, b0); |
| mul128By64To192(b0, b1, q1, &t1, &t2, &t3); |
| sub192(r1, r2, 0, t1, t2, t3, &r1, &r2, &r3); |
| while (r1 != 0) { |
| q1--; |
| add192(r1, r2, r3, 0, b0, b1, &r1, &r2, &r3); |
| } |
| |
| /* Any remainder indicates inexact; set sticky bit. */ |
| q1 |= (r2 | r3) != 0; |
| |
| a->frac_hi = q0; |
| a->frac_lo = q1; |
| return ret; |
| } |
| |
| #define frac_div(A, B) FRAC_GENERIC_64_128(div, A)(A, B) |
| |
| static bool frac64_eqz(FloatParts64 *a) |
| { |
| return a->frac == 0; |
| } |
| |
| static bool frac128_eqz(FloatParts128 *a) |
| { |
| return (a->frac_hi | a->frac_lo) == 0; |
| } |
| |
| #define frac_eqz(A) FRAC_GENERIC_64_128(eqz, A)(A) |
| |
| static void frac64_mulw(FloatParts128 *r, FloatParts64 *a, FloatParts64 *b) |
| { |
| mulu64(&r->frac_lo, &r->frac_hi, a->frac, b->frac); |
| } |
| |
| static void frac128_mulw(FloatParts256 *r, FloatParts128 *a, FloatParts128 *b) |
| { |
| mul128To256(a->frac_hi, a->frac_lo, b->frac_hi, b->frac_lo, |
| &r->frac_hi, &r->frac_hm, &r->frac_lm, &r->frac_lo); |
| } |
| |
| #define frac_mulw(R, A, B) FRAC_GENERIC_64_128(mulw, A)(R, A, B) |
| |
| static void frac64_neg(FloatParts64 *a) |
| { |
| a->frac = -a->frac; |
| } |
| |
| static void frac128_neg(FloatParts128 *a) |
| { |
| bool c = 0; |
| a->frac_lo = usub64_borrow(0, a->frac_lo, &c); |
| a->frac_hi = usub64_borrow(0, a->frac_hi, &c); |
| } |
| |
| static void frac256_neg(FloatParts256 *a) |
| { |
| bool c = 0; |
| a->frac_lo = usub64_borrow(0, a->frac_lo, &c); |
| a->frac_lm = usub64_borrow(0, a->frac_lm, &c); |
| a->frac_hm = usub64_borrow(0, a->frac_hm, &c); |
| a->frac_hi = usub64_borrow(0, a->frac_hi, &c); |
| } |
| |
| #define frac_neg(A) FRAC_GENERIC_64_128_256(neg, A)(A) |
| |
| static int frac64_normalize(FloatParts64 *a) |
| { |
| if (a->frac) { |
| int shift = clz64(a->frac); |
| a->frac <<= shift; |
| return shift; |
| } |
| return 64; |
| } |
| |
| static int frac128_normalize(FloatParts128 *a) |
| { |
| if (a->frac_hi) { |
| int shl = clz64(a->frac_hi); |
| a->frac_hi = shl_double(a->frac_hi, a->frac_lo, shl); |
| a->frac_lo <<= shl; |
| return shl; |
| } else if (a->frac_lo) { |
| int shl = clz64(a->frac_lo); |
| a->frac_hi = a->frac_lo << shl; |
| a->frac_lo = 0; |
| return shl + 64; |
| } |
| return 128; |
| } |
| |
| static int frac256_normalize(FloatParts256 *a) |
| { |
| uint64_t a0 = a->frac_hi, a1 = a->frac_hm; |
| uint64_t a2 = a->frac_lm, a3 = a->frac_lo; |
| int ret, shl; |
| |
| if (likely(a0)) { |
| shl = clz64(a0); |
| if (shl == 0) { |
| return 0; |
| } |
| ret = shl; |
| } else { |
| if (a1) { |
| ret = 64; |
| a0 = a1, a1 = a2, a2 = a3, a3 = 0; |
| } else if (a2) { |
| ret = 128; |
| a0 = a2, a1 = a3, a2 = 0, a3 = 0; |
| } else if (a3) { |
| ret = 192; |
| a0 = a3, a1 = 0, a2 = 0, a3 = 0; |
| } else { |
| ret = 256; |
| a0 = 0, a1 = 0, a2 = 0, a3 = 0; |
| goto done; |
| } |
| shl = clz64(a0); |
| if (shl == 0) { |
| goto done; |
| } |
| ret += shl; |
| } |
| |
| a0 = shl_double(a0, a1, shl); |
| a1 = shl_double(a1, a2, shl); |
| a2 = shl_double(a2, a3, shl); |
| a3 <<= shl; |
| |
| done: |
| a->frac_hi = a0; |
| a->frac_hm = a1; |
| a->frac_lm = a2; |
| a->frac_lo = a3; |
| return ret; |
| } |
| |
| #define frac_normalize(A) FRAC_GENERIC_64_128_256(normalize, A)(A) |
| |
| static void frac64_modrem(FloatParts64 *a, FloatParts64 *b, uint64_t *mod_quot) |
| { |
| uint64_t a0, a1, b0, t0, t1, q, quot; |
| int exp_diff = a->exp - b->exp; |
| int shift; |
| |
| a0 = a->frac; |
| a1 = 0; |
| |
| if (exp_diff < -1) { |
| if (mod_quot) { |
| *mod_quot = 0; |
| } |
| return; |
| } |
| if (exp_diff == -1) { |
| a0 >>= 1; |
| exp_diff = 0; |
| } |
| |
| b0 = b->frac; |
| quot = q = b0 <= a0; |
| if (q) { |
| a0 -= b0; |
| } |
| |
| exp_diff -= 64; |
| while (exp_diff > 0) { |
| q = estimateDiv128To64(a0, a1, b0); |
| q = q > 2 ? q - 2 : 0; |
| mul64To128(b0, q, &t0, &t1); |
| sub128(a0, a1, t0, t1, &a0, &a1); |
| shortShift128Left(a0, a1, 62, &a0, &a1); |
| exp_diff -= 62; |
| quot = (quot << 62) + q; |
| } |
| |
| exp_diff += 64; |
| if (exp_diff > 0) { |
| q = estimateDiv128To64(a0, a1, b0); |
| q = q > 2 ? (q - 2) >> (64 - exp_diff) : 0; |
| mul64To128(b0, q << (64 - exp_diff), &t0, &t1); |
| sub128(a0, a1, t0, t1, &a0, &a1); |
| shortShift128Left(0, b0, 64 - exp_diff, &t0, &t1); |
| while (le128(t0, t1, a0, a1)) { |
| ++q; |
| sub128(a0, a1, t0, t1, &a0, &a1); |
| } |
| quot = (exp_diff < 64 ? quot << exp_diff : 0) + q; |
| } else { |
| t0 = b0; |
| t1 = 0; |
| } |
| |
| if (mod_quot) { |
| *mod_quot = quot; |
| } else { |
| sub128(t0, t1, a0, a1, &t0, &t1); |
| if (lt128(t0, t1, a0, a1) || |
| (eq128(t0, t1, a0, a1) && (q & 1))) { |
| a0 = t0; |
| a1 = t1; |
| a->sign = !a->sign; |
| } |
| } |
| |
| if (likely(a0)) { |
| shift = clz64(a0); |
| shortShift128Left(a0, a1, shift, &a0, &a1); |
| } else if (likely(a1)) { |
| shift = clz64(a1); |
| a0 = a1 << shift; |
| a1 = 0; |
| shift += 64; |
| } else { |
| a->cls = float_class_zero; |
| return; |
| } |
| |
| a->exp = b->exp + exp_diff - shift; |
| a->frac = a0 | (a1 != 0); |
| } |
| |
| static void frac128_modrem(FloatParts128 *a, FloatParts128 *b, |
| uint64_t *mod_quot) |
| { |
| uint64_t a0, a1, a2, b0, b1, t0, t1, t2, q, quot; |
| int exp_diff = a->exp - b->exp; |
| int shift; |
| |
| a0 = a->frac_hi; |
| a1 = a->frac_lo; |
| a2 = 0; |
| |
| if (exp_diff < -1) { |
| if (mod_quot) { |
| *mod_quot = 0; |
| } |
| return; |
| } |
| if (exp_diff == -1) { |
| shift128Right(a0, a1, 1, &a0, &a1); |
| exp_diff = 0; |
| } |
| |
| b0 = b->frac_hi; |
| b1 = b->frac_lo; |
| |
| quot = q = le128(b0, b1, a0, a1); |
| if (q) { |
| sub128(a0, a1, b0, b1, &a0, &a1); |
| } |
| |
| exp_diff -= 64; |
| while (exp_diff > 0) { |
| q = estimateDiv128To64(a0, a1, b0); |
| q = q > 4 ? q - 4 : 0; |
| mul128By64To192(b0, b1, q, &t0, &t1, &t2); |
| sub192(a0, a1, a2, t0, t1, t2, &a0, &a1, &a2); |
| shortShift192Left(a0, a1, a2, 61, &a0, &a1, &a2); |
| exp_diff -= 61; |
| quot = (quot << 61) + q; |
| } |
| |
| exp_diff += 64; |
| if (exp_diff > 0) { |
| q = estimateDiv128To64(a0, a1, b0); |
| q = q > 4 ? (q - 4) >> (64 - exp_diff) : 0; |
| mul128By64To192(b0, b1, q << (64 - exp_diff), &t0, &t1, &t2); |
| sub192(a0, a1, a2, t0, t1, t2, &a0, &a1, &a2); |
| shortShift192Left(0, b0, b1, 64 - exp_diff, &t0, &t1, &t2); |
| while (le192(t0, t1, t2, a0, a1, a2)) { |
| ++q; |
| sub192(a0, a1, a2, t0, t1, t2, &a0, &a1, &a2); |
| } |
| quot = (exp_diff < 64 ? quot << exp_diff : 0) + q; |
| } else { |
| t0 = b0; |
| t1 = b1; |
| t2 = 0; |
| } |
| |
| if (mod_quot) { |
| *mod_quot = quot; |
| } else { |
| sub192(t0, t1, t2, a0, a1, a2, &t0, &t1, &t2); |
| if (lt192(t0, t1, t2, a0, a1, a2) || |
| (eq192(t0, t1, t2, a0, a1, a2) && (q & 1))) { |
| a0 = t0; |
| a1 = t1; |
| a2 = t2; |
| a->sign = !a->sign; |
| } |
| } |
| |
| if (likely(a0)) { |
| shift = clz64(a0); |
| shortShift192Left(a0, a1, a2, shift, &a0, &a1, &a2); |
| } else if (likely(a1)) { |
| shift = clz64(a1); |
| shortShift128Left(a1, a2, shift, &a0, &a1); |
| a2 = 0; |
| shift += 64; |
| } else if (likely(a2)) { |
| shift = clz64(a2); |
| a0 = a2 << shift; |
| a1 = a2 = 0; |
| shift += 128; |
| } else { |
| a->cls = float_class_zero; |
| return; |
| } |
| |
| a->exp = b->exp + exp_diff - shift; |
| a->frac_hi = a0; |
| a->frac_lo = a1 | (a2 != 0); |
| } |
| |
| #define frac_modrem(A, B, Q) FRAC_GENERIC_64_128(modrem, A)(A, B, Q) |
| |
| static void frac64_shl(FloatParts64 *a, int c) |
| { |
| a->frac <<= c; |
| } |
| |
| static void frac128_shl(FloatParts128 *a, int c) |
| { |
| uint64_t a0 = a->frac_hi, a1 = a->frac_lo; |
| |
| if (c & 64) { |
| a0 = a1, a1 = 0; |
| } |
| |
| c &= 63; |
| if (c) { |
| a0 = shl_double(a0, a1, c); |
| a1 = a1 << c; |
| } |
| |
| a->frac_hi = a0; |
| a->frac_lo = a1; |
| } |
| |
| #define frac_shl(A, C) FRAC_GENERIC_64_128(shl, A)(A, C) |
| |
| static void frac64_shr(FloatParts64 *a, int c) |
| { |
| a->frac >>= c; |
| } |
| |
| static void frac128_shr(FloatParts128 *a, int c) |
| { |
| uint64_t a0 = a->frac_hi, a1 = a->frac_lo; |
| |
| if (c & 64) { |
| a1 = a0, a0 = 0; |
| } |
| |
| c &= 63; |
| if (c) { |
| a1 = shr_double(a0, a1, c); |
| a0 = a0 >> c; |
| } |
| |
| a->frac_hi = a0; |
| a->frac_lo = a1; |
| } |
| |
| #define frac_shr(A, C) FRAC_GENERIC_64_128(shr, A)(A, C) |
| |
| static void frac64_shrjam(FloatParts64 *a, int c) |
| { |
| uint64_t a0 = a->frac; |
| |
| if (likely(c != 0)) { |
| if (likely(c < 64)) { |
| a0 = (a0 >> c) | (shr_double(a0, 0, c) != 0); |
| } else { |
| a0 = a0 != 0; |
| } |
| a->frac = a0; |
| } |
| } |
| |
| static void frac128_shrjam(FloatParts128 *a, int c) |
| { |
| uint64_t a0 = a->frac_hi, a1 = a->frac_lo; |
| uint64_t sticky = 0; |
| |
| if (unlikely(c == 0)) { |
| return; |
| } else if (likely(c < 64)) { |
| /* nothing */ |
| } else if (likely(c < 128)) { |
| sticky = a1; |
| a1 = a0; |
| a0 = 0; |
| c &= 63; |
| if (c == 0) { |
| goto done; |
| } |
| } else { |
| sticky = a0 | a1; |
| a0 = a1 = 0; |
| goto done; |
| } |
| |
| sticky |= shr_double(a1, 0, c); |
| a1 = shr_double(a0, a1, c); |
| a0 = a0 >> c; |
| |
| done: |
| a->frac_lo = a1 | (sticky != 0); |
| a->frac_hi = a0; |
| } |
| |
| static void frac256_shrjam(FloatParts256 *a, int c) |
| { |
| uint64_t a0 = a->frac_hi, a1 = a->frac_hm; |
| uint64_t a2 = a->frac_lm, a3 = a->frac_lo; |
| uint64_t sticky = 0; |
| |
| if (unlikely(c == 0)) { |
| return; |
| } else if (likely(c < 64)) { |
| /* nothing */ |
| } else if (likely(c < 256)) { |
| if (unlikely(c & 128)) { |
| sticky |= a2 | a3; |
| a3 = a1, a2 = a0, a1 = 0, a0 = 0; |
| } |
| if (unlikely(c & 64)) { |
| sticky |= a3; |
| a3 = a2, a2 = a1, a1 = a0, a0 = 0; |
| } |
| c &= 63; |
| if (c == 0) { |
| goto done; |
| } |
| } else { |
| sticky = a0 | a1 | a2 | a3; |
| a0 = a1 = a2 = a3 = 0; |
| goto done; |
| } |
| |
| sticky |= shr_double(a3, 0, c); |
| a3 = shr_double(a2, a3, c); |
| a2 = shr_double(a1, a2, c); |
| a1 = shr_double(a0, a1, c); |
| a0 = a0 >> c; |
| |
| done: |
| a->frac_lo = a3 | (sticky != 0); |
| a->frac_lm = a2; |
| a->frac_hm = a1; |
| a->frac_hi = a0; |
| } |
| |
| #define frac_shrjam(A, C) FRAC_GENERIC_64_128_256(shrjam, A)(A, C) |
| |
| static bool frac64_sub(FloatParts64 *r, FloatParts64 *a, FloatParts64 *b) |
| { |
| return usub64_overflow(a->frac, b->frac, &r->frac); |
| } |
| |
| static bool frac128_sub(FloatParts128 *r, FloatParts128 *a, FloatParts128 *b) |
| { |
| bool c = 0; |
| r->frac_lo = usub64_borrow(a->frac_lo, b->frac_lo, &c); |
| r->frac_hi = usub64_borrow(a->frac_hi, b->frac_hi, &c); |
| return c; |
| } |
| |
| static bool frac256_sub(FloatParts256 *r, FloatParts256 *a, FloatParts256 *b) |
| { |
| bool c = 0; |
| r->frac_lo = usub64_borrow(a->frac_lo, b->frac_lo, &c); |
| r->frac_lm = usub64_borrow(a->frac_lm, b->frac_lm, &c); |
| r->frac_hm = usub64_borrow(a->frac_hm, b->frac_hm, &c); |
| r->frac_hi = usub64_borrow(a->frac_hi, b->frac_hi, &c); |
| return c; |
| } |
| |
| #define frac_sub(R, A, B) FRAC_GENERIC_64_128_256(sub, R)(R, A, B) |
| |
| static void frac64_truncjam(FloatParts64 *r, FloatParts128 *a) |
| { |
| r->frac = a->frac_hi | (a->frac_lo != 0); |
| } |
| |
| static void frac128_truncjam(FloatParts128 *r, FloatParts256 *a) |
| { |
| r->frac_hi = a->frac_hi; |
| r->frac_lo = a->frac_hm | ((a->frac_lm | a->frac_lo) != 0); |
| } |
| |
| #define frac_truncjam(R, A) FRAC_GENERIC_64_128(truncjam, R)(R, A) |
| |
| static void frac64_widen(FloatParts128 *r, FloatParts64 *a) |
| { |
| r->frac_hi = a->frac; |
| r->frac_lo = 0; |
| } |
| |
| static void frac128_widen(FloatParts256 *r, FloatParts128 *a) |
| { |
| r->frac_hi = a->frac_hi; |
| r->frac_hm = a->frac_lo; |
| r->frac_lm = 0; |
| r->frac_lo = 0; |
| } |
| |
| #define frac_widen(A, B) FRAC_GENERIC_64_128(widen, B)(A, B) |
| |
| /* |
| * Reciprocal sqrt table. 1 bit of exponent, 6-bits of mantessa. |
| * From https://git.musl-libc.org/cgit/musl/tree/src/math/sqrt_data.c |
| * and thus MIT licenced. |
| */ |
| static const uint16_t rsqrt_tab[128] = { |
| 0xb451, 0xb2f0, 0xb196, 0xb044, 0xaef9, 0xadb6, 0xac79, 0xab43, |
| 0xaa14, 0xa8eb, 0xa7c8, 0xa6aa, 0xa592, 0xa480, 0xa373, 0xa26b, |
| 0xa168, 0xa06a, 0x9f70, 0x9e7b, 0x9d8a, 0x9c9d, 0x9bb5, 0x9ad1, |
| 0x99f0, 0x9913, 0x983a, 0x9765, 0x9693, 0x95c4, 0x94f8, 0x9430, |
| 0x936b, 0x92a9, 0x91ea, 0x912e, 0x9075, 0x8fbe, 0x8f0a, 0x8e59, |
| 0x8daa, 0x8cfe, 0x8c54, 0x8bac, 0x8b07, 0x8a64, 0x89c4, 0x8925, |
| 0x8889, 0x87ee, 0x8756, 0x86c0, 0x862b, 0x8599, 0x8508, 0x8479, |
| 0x83ec, 0x8361, 0x82d8, 0x8250, 0x81c9, 0x8145, 0x80c2, 0x8040, |
| 0xff02, 0xfd0e, 0xfb25, 0xf947, 0xf773, 0xf5aa, 0xf3ea, 0xf234, |
| 0xf087, 0xeee3, 0xed47, 0xebb3, 0xea27, 0xe8a3, 0xe727, 0xe5b2, |
| 0xe443, 0xe2dc, 0xe17a, 0xe020, 0xdecb, 0xdd7d, 0xdc34, 0xdaf1, |
| 0xd9b3, 0xd87b, 0xd748, 0xd61a, 0xd4f1, 0xd3cd, 0xd2ad, 0xd192, |
| 0xd07b, 0xcf69, 0xce5b, 0xcd51, 0xcc4a, 0xcb48, 0xca4a, 0xc94f, |
| 0xc858, 0xc764, 0xc674, 0xc587, 0xc49d, 0xc3b7, 0xc2d4, 0xc1f4, |
| 0xc116, 0xc03c, 0xbf65, 0xbe90, 0xbdbe, 0xbcef, 0xbc23, 0xbb59, |
| 0xba91, 0xb9cc, 0xb90a, 0xb84a, 0xb78c, 0xb6d0, 0xb617, 0xb560, |
| }; |
| |
| #define partsN(NAME) glue(glue(glue(parts,N),_),NAME) |
| #define FloatPartsN glue(FloatParts,N) |
| #define FloatPartsW glue(FloatParts,W) |
| |
| #define N 64 |
| #define W 128 |
| |
| #include "softfloat-parts-addsub.c.inc" |
| #include "softfloat-parts.c.inc" |
| |
| #undef N |
| #undef W |
| #define N 128 |
| #define W 256 |
| |
| #include "softfloat-parts-addsub.c.inc" |
| #include "softfloat-parts.c.inc" |
| |
| #undef N |
| #undef W |
| #define N 256 |
| |
| #include "softfloat-parts-addsub.c.inc" |
| |
| #undef N |
| #undef W |
| #undef partsN |
| #undef FloatPartsN |
| #undef FloatPartsW |
| |
| /* |
| * Pack/unpack routines with a specific FloatFmt. |
| */ |
| |
| static void float16a_unpack_canonical(FloatParts64 *p, float16 f, |
| float_status *s, const FloatFmt *params) |
| { |
| float16_unpack_raw(p, f); |
| parts_canonicalize(p, s, params); |
| } |
| |
| static void float16_unpack_canonical(FloatParts64 *p, float16 f, |
| float_status *s) |
| { |
| float16a_unpack_canonical(p, f, s, &float16_params); |
| } |
| |
| static void bfloat16_unpack_canonical(FloatParts64 *p, bfloat16 f, |
| float_status *s) |
| { |
| bfloat16_unpack_raw(p, f); |
| parts_canonicalize(p, s, &bfloat16_params); |
| } |
| |
| static float16 float16a_round_pack_canonical(FloatParts64 *p, |
| float_status *s, |
| const FloatFmt *params) |
| { |
| parts_uncanon(p, s, params); |
| return float16_pack_raw(p); |
| } |
| |
| static float16 float16_round_pack_canonical(FloatParts64 *p, |
| float_status *s) |
| { |
| return float16a_round_pack_canonical(p, s, &float16_params); |
| } |
| |
| static bfloat16 bfloat16_round_pack_canonical(FloatParts64 *p, |
| float_status *s) |
| { |
| parts_uncanon(p, s, &bfloat16_params); |
| return bfloat16_pack_raw(p); |
| } |
| |
| static void float32_unpack_canonical(FloatParts64 *p, float32 f, |
| float_status *s) |
| { |
| float32_unpack_raw(p, f); |
| parts_canonicalize(p, s, &float32_params); |
| } |
| |
| static float32 float32_round_pack_canonical(FloatParts64 *p, |
| float_status *s) |
| { |
| parts_uncanon(p, s, &float32_params); |
| return float32_pack_raw(p); |
| } |
| |
| static void float64_unpack_canonical(FloatParts64 *p, float64 f, |
| float_status *s) |
| { |
| float64_unpack_raw(p, f); |
| parts_canonicalize(p, s, &float64_params); |
| } |
| |
| static float64 float64_round_pack_canonical(FloatParts64 *p, |
| float_status *s) |
| { |
| parts_uncanon(p, s, &float64_params); |
| return float64_pack_raw(p); |
| } |
| |
| static float64 float64r32_round_pack_canonical(FloatParts64 *p, |
| float_status *s) |
| { |
| parts_uncanon(p, s, &float32_params); |
| |
| /* |
| * In parts_uncanon, we placed the fraction for float32 at the lsb. |
| * We need to adjust the fraction higher so that the least N bits are |
| * zero, and the fraction is adjacent to the float64 implicit bit. |
| */ |
| switch (p->cls) { |
| case float_class_normal: |
| if (unlikely(p->exp == 0)) { |
| /* |
| * The result is denormal for float32, but can be represented |
| * in normalized form for float64. Adjust, per canonicalize. |
| */ |
| int shift = frac_normalize(p); |
| p->exp = (float32_params.frac_shift - |
| float32_params.exp_bias - shift + 1 + |
| float64_params.exp_bias); |
| frac_shr(p, float64_params.frac_shift); |
| } else { |
| frac_shl(p, float32_params.frac_shift - float64_params.frac_shift); |
| p->exp += float64_params.exp_bias - float32_params.exp_bias; |
| } |
| break; |
| case float_class_snan: |
| case float_class_qnan: |
| frac_shl(p, float32_params.frac_shift - float64_params.frac_shift); |
| p->exp = float64_params.exp_max; |
| break; |
| case float_class_inf: |
| p->exp = float64_params.exp_max; |
| break; |
| case float_class_zero: |
| break; |
| default: |
| g_assert_not_reached(); |
| } |
| |
| return float64_pack_raw(p); |
| } |
| |
| static void float128_unpack_canonical(FloatParts128 *p, float128 f, |
| float_status *s) |
| { |
| float128_unpack_raw(p, f); |
| parts_canonicalize(p, s, &float128_params); |
| } |
| |
| static float128 float128_round_pack_canonical(FloatParts128 *p, |
| float_status *s) |
| { |
| parts_uncanon(p, s, &float128_params); |
| return float128_pack_raw(p); |
| } |
| |
| /* Returns false if the encoding is invalid. */ |
| static bool floatx80_unpack_canonical(FloatParts128 *p, floatx80 f, |
| float_status *s) |
| { |
| /* Ensure rounding precision is set before beginning. */ |
| switch (s->floatx80_rounding_precision) { |
| case floatx80_precision_x: |
| case floatx80_precision_d: |
| case floatx80_precision_s: |
| break; |
| default: |
| g_assert_not_reached(); |
| } |
| |
| if (unlikely(floatx80_invalid_encoding(f))) { |
| float_raise(float_flag_invalid, s); |
| return false; |
| } |
| |
| floatx80_unpack_raw(p, f); |
| |
| if (likely(p->exp != floatx80_params[floatx80_precision_x].exp_max)) { |
| parts_canonicalize(p, s, &floatx80_params[floatx80_precision_x]); |
| } else { |
| /* The explicit integer bit is ignored, after invalid checks. */ |
| p->frac_hi &= MAKE_64BIT_MASK(0, 63); |
| p->cls = (p->frac_hi == 0 ? float_class_inf |
| : parts_is_snan_frac(p->frac_hi, s) |
| ? float_class_snan : float_class_qnan); |
| } |
| return true; |
| } |
| |
| static floatx80 floatx80_round_pack_canonical(FloatParts128 *p, |
| float_status *s) |
| { |
| const FloatFmt *fmt = &floatx80_params[s->floatx80_rounding_precision]; |
| uint64_t frac; |
| int exp; |
| |
| switch (p->cls) { |
| case float_class_normal: |
| if (s->floatx80_rounding_precision == floatx80_precision_x) { |
| parts_uncanon_normal(p, s, fmt); |
| frac = p->frac_hi; |
| exp = p->exp; |
| } else { |
| FloatParts64 p64; |
| |
| p64.sign = p->sign; |
| p64.exp = p->exp; |
| frac_truncjam(&p64, p); |
| parts_uncanon_normal(&p64, s, fmt); |
| frac = p64.frac; |
| exp = p64.exp; |
| } |
| if (exp != fmt->exp_max) { |
| break; |
| } |
| /* rounded to inf -- fall through to set frac correctly */ |
| |
| case float_class_inf: |
| /* x86 and m68k differ in the setting of the integer bit. */ |
| frac = floatx80_infinity_low; |
| exp = fmt->exp_max; |
| break; |
| |
| case float_class_zero: |
| frac = 0; |
| exp = 0; |
| break; |
| |
| case float_class_snan: |
| case float_class_qnan: |
| /* NaNs have the integer bit set. */ |
| frac = p->frac_hi | (1ull << 63); |
| exp = fmt->exp_max; |
| break; |
| |
| default: |
| g_assert_not_reached(); |
| } |
| |
| return packFloatx80(p->sign, exp, frac); |
| } |
| |
| /* |
| * Addition and subtraction |
| */ |
| |
| static float16 QEMU_FLATTEN |
| float16_addsub(float16 a, float16 b, float_status *status, bool subtract) |
| { |
| FloatParts64 pa, pb, *pr; |
| |
| float16_unpack_canonical(&pa, a, status); |
| float16_unpack_canonical(&pb, b, status); |
| pr = parts_addsub(&pa, &pb, status, subtract); |
| |
| return float16_round_pack_canonical(pr, status); |
| } |
| |
| float16 float16_add(float16 a, float16 b, float_status *status) |
| { |
| return float16_addsub(a, b, status, false); |
| } |
| |
| float16 float16_sub(float16 a, float16 b, float_status *status) |
| { |
| return float16_addsub(a, b, status, true); |
| } |
| |
| static float32 QEMU_SOFTFLOAT_ATTR |
| soft_f32_addsub(float32 a, float32 b, float_status *status, bool subtract) |
| { |
| FloatParts64 pa, pb, *pr; |
| |
| float32_unpack_canonical(&pa, a, status); |
| float32_unpack_canonical(&pb, b, status); |
| pr = parts_addsub(&pa, &pb, status, subtract); |
| |
| return float32_round_pack_canonical(pr, status); |
| } |
| |
| static float32 soft_f32_add(float32 a, float32 b, float_status *status) |
| { |
| return soft_f32_addsub(a, b, status, false); |
| } |
| |
| static float32 soft_f32_sub(float32 a, float32 b, float_status *status) |
| { |
| return soft_f32_addsub(a, b, status, true); |
| } |
| |
| static float64 QEMU_SOFTFLOAT_ATTR |
| soft_f64_addsub(float64 a, float64 b, float_status *status, bool subtract) |
| { |
| FloatParts64 pa, pb, *pr; |
| |
| float64_unpack_canonical(&pa, a, status); |
| float64_unpack_canonical(&pb, b, status); |
| pr = parts_addsub(&pa, &pb, status, subtract); |
| |
| return float64_round_pack_canonical(pr, status); |
| } |
| |
| static float64 soft_f64_add(float64 a, float64 b, float_status *status) |
| { |
| return soft_f64_addsub(a, b, status, false); |
| } |
| |
| static float64 soft_f64_sub(float64 a, float64 b, float_status *status) |
| { |
| return soft_f64_addsub(a, b, status, true); |
| } |
| |
| 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); |
| } |
| |
| static float64 float64r32_addsub(float64 a, float64 b, float_status *status, |
| bool subtract) |
| { |
| FloatParts64 pa, pb, *pr; |
| |
| float64_unpack_canonical(&pa, a, status); |
| float64_unpack_canonical(&pb, b, status); |
| pr = parts_addsub(&pa, &pb, status, subtract); |
| |
| return float64r32_round_pack_canonical(pr, status); |
| } |
| |
| float64 float64r32_add(float64 a, float64 b, float_status *status) |
| { |
| return float64r32_addsub(a, b, status, false); |
| } |
| |
| float64 float64r32_sub(float64 a, float64 b, float_status *status) |
| { |
| return float64r32_addsub(a, b, status, true); |
| } |
| |
| static bfloat16 QEMU_FLATTEN |
| bfloat16_addsub(bfloat16 a, bfloat16 b, float_status *status, bool subtract) |
| { |
| FloatParts64 pa, pb, *pr; |
| |
| bfloat16_unpack_canonical(&pa, a, status); |
| bfloat16_unpack_canonical(&pb, b, status); |
| pr = parts_addsub(&pa, &pb, status, subtract); |
| |
| return bfloat16_round_pack_canonical(pr, status); |
| } |
| |
| bfloat16 bfloat16_add(bfloat16 a, bfloat16 b, float_status *status) |
| { |
| return bfloat16_addsub(a, b, status, false); |
| } |
| |
| bfloat16 bfloat16_sub(bfloat16 a, bfloat16 b, float_status *status) |
| { |
| return bfloat16_addsub(a, b, status, true); |
| } |
| |
| static float128 QEMU_FLATTEN |
| float128_addsub(float128 a, float128 b, float_status *status, bool subtract) |
| { |
| FloatParts128 pa, pb, *pr; |
| |
| float128_unpack_canonical(&pa, a, status); |
| float128_unpack_canonical(&pb, b, status); |
| pr = parts_addsub(&pa, &pb, status, subtract); |
| |
| return float128_round_pack_canonical(pr, status); |
| } |
| |
| float128 float128_add(float128 a, float128 b, float_status *status) |
| { |
| return float128_addsub(a, b, status, false); |
| } |
| |
| float128 float128_sub(float128 a, float128 b, float_status *status) |
| { |
| return float128_addsub(a, b, status, true); |
| } |
| |
| static floatx80 QEMU_FLATTEN |
| floatx80_addsub(floatx80 a, floatx80 b, float_status *status, bool subtract) |
| { |
| FloatParts128 pa, pb, *pr; |
| |
| if (!floatx80_unpack_canonical(&pa, a, status) || |
| !floatx80_unpack_canonical(&pb, b, status)) { |
| return floatx80_default_nan(status); |
| } |
| |
| pr = parts_addsub(&pa, &pb, status, subtract); |
| return floatx80_round_pack_canonical(pr, status); |
| } |
| |
| floatx80 floatx80_add(floatx80 a, floatx80 b, float_status *status) |
| { |
| return floatx80_addsub(a, b, status, false); |
| } |
| |
| floatx80 floatx80_sub(floatx80 a, floatx80 b, float_status *status) |
| { |
| return floatx80_addsub(a, b, status, true); |
| } |
| |
| /* |
| * Multiplication |
| */ |
| |
| float16 QEMU_FLATTEN float16_mul(float16 a, float16 b, float_status *status) |
| { |
| FloatParts64 pa, pb, *pr; |
| |
| float16_unpack_canonical(&pa, a, status); |
| float16_unpack_canonical(&pb, b, status); |
| pr = parts_mul(&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) |
| { |
| FloatParts64 pa, pb, *pr; |
| |
| float32_unpack_canonical(&pa, a, status); |
| float32_unpack_canonical(&pb, b, status); |
| pr = parts_mul(&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) |
| { |
| FloatParts64 pa, pb, *pr; |
| |
| float64_unpack_canonical(&pa, a, status); |
| float64_unpack_canonical(&pb, b, status); |
| pr = parts_mul(&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); |
| } |
| |
| float64 float64r32_mul(float64 a, float64 b, float_status *status) |
| { |
| FloatParts64 pa, pb, *pr; |
| |
| float64_unpack_canonical(&pa, a, status); |
| float64_unpack_canonical(&pb, b, status); |
| pr = parts_mul(&pa, &pb, status); |
| |
| return float64r32_round_pack_canonical(pr, status); |
| } |
| |
| bfloat16 QEMU_FLATTEN |
| bfloat16_mul(bfloat16 a, bfloat16 b, float_status *status) |
| { |
| FloatParts64 pa, pb, *pr; |
| |
| bfloat16_unpack_canonical(&pa, a, status); |
| bfloat16_unpack_canonical(&pb, b, status); |
| pr = parts_mul(&pa, &pb, status); |
| |
| return bfloat16_round_pack_canonical(pr, status); |
| } |
| |
| float128 QEMU_FLATTEN |
| float128_mul(float128 a, float128 b, float_status *status) |
| { |
| FloatParts128 pa, pb, *pr; |
| |
| float128_unpack_canonical(&pa, a, status); |
| float128_unpack_canonical(&pb, b, status); |
| pr = parts_mul(&pa, &pb, status); |
| |
| return float128_round_pack_canonical(pr, status); |
| } |
| |
| floatx80 QEMU_FLATTEN |
| floatx80_mul(floatx80 a, floatx80 b, float_status *status) |
| { |
| FloatParts128 pa, pb, *pr; |
| |
| if (!floatx80_unpack_canonical(&pa, a, status) || |
| !floatx80_unpack_canonical(&pb, b, status)) { |
| return floatx80_default_nan(status); |
| } |
| |
| pr = parts_mul(&pa, &pb, status); |
| return floatx80_round_pack_canonical(pr, status); |
| } |
| |
| /* |
| * Fused multiply-add |
| */ |
| |
| float16 QEMU_FLATTEN float16_muladd(float16 a, float16 b, float16 c, |
| int flags, float_status *status) |
| { |
| FloatParts64 pa, pb, pc, *pr; |
| |
| float16_unpack_canonical(&pa, a, status); |
| float16_unpack_canonical(&pb, b, status); |
| float16_unpack_canonical(&pc, c, status); |
| pr = parts_muladd(&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) |
| { |
| FloatParts64 pa, pb, pc, *pr; |
| |
| float32_unpack_canonical(&pa, a, status); |
| float32_unpack_canonical(&pb, b, status); |
| float32_unpack_canonical(&pc, c, status); |
| pr = parts_muladd(&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) |
| { |
| FloatParts64 pa, pb, pc, *pr; |
| |
| float64_unpack_canonical(&pa, a, status); |
| float64_unpack_canonical(&pb, b, status); |
| float64_unpack_canonical(&pc, c, status); |
| pr = parts_muladd(&pa, &pb, &pc, flags, status); |
| |
| return float64_round_pack_canonical(pr, status); |
| } |
| |
| static bool force_soft_fma; |
| |
| 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; |
| } |
| |
| if (unlikely(force_soft_fma)) { |
| 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 { |
| union_float32 ua_orig = ua; |
| union_float32 uc_orig = uc; |
| |
| 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))) { |
| float_raise(float_flag_overflow, s); |
| } else if (unlikely(fabsf(ur.h) <= FLT_MIN)) { |
| ua = ua_orig; |
| uc = uc_orig; |
| 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; |
| } |
| |
| if (unlikely(force_soft_fma)) { |
| 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 { |
| union_float64 ua_orig = ua; |
| union_float64 uc_orig = uc; |
| |
| 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))) { |
| float_raise(float_flag_overflow, s); |
| } else if (unlikely(fabs(ur.h) <= FLT_MIN)) { |
| ua = ua_orig; |
| uc = uc_orig; |
| 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); |
| } |
| |
| float64 float64r32_muladd(float64 a, float64 b, float64 c, |
| int flags, float_status *status) |
| { |
| FloatParts64 pa, pb, pc, *pr; |
| |
| float64_unpack_canonical(&pa, a, status); |
| float64_unpack_canonical(&pb, b, status); |
| float64_unpack_canonical(&pc, c, status); |
| pr = parts_muladd(&pa, &pb, &pc, flags, status); |
| |
| return float64r32_round_pack_canonical(pr, status); |
| } |
| |
| bfloat16 QEMU_FLATTEN bfloat16_muladd(bfloat16 a, bfloat16 b, bfloat16 c, |
| int flags, float_status *status) |
| { |
| FloatParts64 pa, pb, pc, *pr; |
| |
| bfloat16_unpack_canonical(&pa, a, status); |
| bfloat16_unpack_canonical(&pb, b, status); |
| bfloat16_unpack_canonical(&pc, c, status); |
| pr = parts_muladd(&pa, &pb, &pc, flags, status); |
| |
| return bfloat16_round_pack_canonical(pr, status); |
| } |
| |
| float128 QEMU_FLATTEN float128_muladd(float128 a, float128 b, float128 c, |
| int flags, float_status *status) |
| { |
| FloatParts128 pa, pb, pc, *pr; |
| |
| float128_unpack_canonical(&pa, a, status); |
| float128_unpack_canonical(&pb, b, status); |
| float128_unpack_canonical(&pc, c, status); |
| pr = parts_muladd(&pa, &pb, &pc, flags, status); |
| |
| return float128_round_pack_canonical(pr, status); |
| } |
| |
| /* |
| * Division |
| */ |
| |
| float16 float16_div(float16 a, float16 b, float_status *status) |
| { |
| FloatParts64 pa, pb, *pr; |
| |
| float16_unpack_canonical(&pa, a, status); |
| float16_unpack_canonical(&pb, b, status); |
| pr = parts_div(&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) |
| { |
| FloatParts64 pa, pb, *pr; |
| |
| float32_unpack_canonical(&pa, a, status); |
| float32_unpack_canonical(&pb, b, status); |
| pr = parts_div(&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) |
| { |
| FloatParts64 pa, pb, *pr; |
| |
| float64_unpack_canonical(&pa, a, status); |
| float64_unpack_canonical(&pb, b, status); |
| pr = parts_div(&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); |
| } |
| |
| float64 float64r32_div(float64 a, float64 b, float_status *status) |
| { |
| FloatParts64 pa, pb, *pr; |
| |
| float64_unpack_canonical(&pa, a, status); |
| float64_unpack_canonical(&pb, b, status); |
| pr = parts_div(&pa, &pb, status); |
| |
| return float64r32_round_pack_canonical(pr, status); |
| } |
| |
| bfloat16 QEMU_FLATTEN |
| bfloat16_div(bfloat16 a, bfloat16 b, float_status *status) |
| { |
| FloatParts64 pa, pb, *pr; |
| |
| bfloat16_unpack_canonical(&pa, a, status); |
| bfloat16_unpack_canonical(&pb, b, status); |
| pr = parts_div(&pa, &pb, status); |
| |
| return bfloat16_round_pack_canonical(pr, status); |
| } |
| |
| float128 QEMU_FLATTEN |
| float128_div(float128 a, float128 b, float_status *status) |
| { |
| FloatParts128 pa, pb, *pr; |
| |
| float128_unpack_canonical(&pa, a, status); |
| float128_unpack_canonical(&pb, b, status); |
| pr = parts_div(&pa, &pb, status); |
| |
| return float128_round_pack_canonical(pr, status); |
| } |
| |
| floatx80 floatx80_div(floatx80 a, floatx80 b, float_status *status) |
| { |
| FloatParts128 pa, pb, *pr; |
| |
| if (!floatx80_unpack_canonical(&pa, a, status) || |
| !floatx80_unpack_canonical(&pb, b, status)) { |
| return floatx80_default_nan(status); |
| } |
| |
| pr = parts_div(&pa, &pb, status); |
| return floatx80_round_pack_canonical(pr, status); |
| } |
| |
| /* |
| * Remainder |
| */ |
| |
| float32 float32_rem(float32 a, float32 b, float_status *status) |
| { |
| FloatParts64 pa, pb, *pr; |
| |
| float32_unpack_canonical(&pa, a, status); |
| float32_unpack_canonical(&pb, b, status); |
| pr = parts_modrem(&pa, &pb, NULL, status); |
| |
| return float32_round_pack_canonical(pr, status); |
| } |
| |
| float64 float64_rem(float64 a, float64 b, float_status *status) |
| { |
| FloatParts64 pa, pb, *pr; |
| |
| float64_unpack_canonical(&pa, a, status); |
| float64_unpack_canonical(&pb, b, status); |
| pr = parts_modrem(&pa, &pb, NULL, status); |
| |
| return float64_round_pack_canonical(pr, status); |
| } |
| |
| float128 float128_rem(float128 a, float128 b, float_status *status) |
| { |
| FloatParts128 pa, pb, *pr; |
| |
| float128_unpack_canonical(&pa, a, status); |
| float128_unpack_canonical(&pb, b, status); |
| pr = parts_modrem(&pa, &pb, NULL, status); |
| |
| return float128_round_pack_canonical(pr, status); |
| } |
| |
| /* |
| * Returns the remainder of the extended double-precision floating-point value |
| * `a' with respect to the corresponding value `b'. |
| * If 'mod' is false, the operation is performed according to the IEC/IEEE |
| * Standard for Binary Floating-Point Arithmetic. If 'mod' is true, return |
| * the remainder based on truncating the quotient toward zero instead and |
| * *quotient is set to the low 64 bits of the absolute value of the integer |
| * quotient. |
| */ |
| floatx80 floatx80_modrem(floatx80 a, floatx80 b, bool mod, |
| uint64_t *quotient, float_status *status) |
| { |
| FloatParts128 pa, pb, *pr; |
| |
| *quotient = 0; |
| if (!floatx80_unpack_canonical(&pa, a, status) || |
| !floatx80_unpack_canonical(&pb, b, status)) { |
| return floatx80_default_nan(status); |
| } |
| pr = parts_modrem(&pa, &pb, mod ? quotient : NULL, status); |
| |
| return floatx80_round_pack_canonical(pr, status); |
| } |
| |
| floatx80 floatx80_rem(floatx80 a, floatx80 b, float_status *status) |
| { |
| uint64_t quotient; |
| return floatx80_modrem(a, b, false, "ient, status); |
| } |
| |
| floatx80 floatx80_mod(floatx80 a, floatx80 b, float_status *status) |
| { |
| uint64_t quotient; |
| return floatx80_modrem(a, b, true, "ient, status); |
| } |
| |
| /* |
| * 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. |
| * |
| * Usually this only needs to take care of raising invalid exceptions |
| * and handling the conversion on NaNs. |
| */ |
| |
| static void parts_float_to_ahp(FloatParts64 *a, float_status *s) |
| { |
| switch (a->cls) { |
| case float_class_snan: |
| float_raise(float_flag_invalid_snan, s); |
| /* fall through */ |
| case float_class_qnan: |
| /* |
| * There is no NaN in the destination format. Raise Invalid |
| * and return a zero with the sign of the input NaN. |
| */ |
| float_raise(float_flag_invalid, s); |
| a->cls = float_class_zero; |
| break; |
| |
| case float_class_inf: |
| /* |
| * There is no Inf in the destination format. Raise Invalid |
| * and return the maximum normal with the correct sign. |
| */ |
| float_raise(float_flag_invalid, s); |
| a->cls = float_class_normal; |
| a->exp = float16_params_ahp.exp_max; |
| a->frac = MAKE_64BIT_MASK(float16_params_ahp.frac_shift, |
| float16_params_ahp.frac_size + 1); |
| break; |
| |
| case float_class_normal: |
| case float_class_zero: |
| break; |
| |
| default: |
| g_assert_not_reached(); |
| } |
| } |
| |
| static void parts64_float_to_float(FloatParts64 *a, float_status *s) |
| { |
| if (is_nan(a->cls)) { |
| parts_return_nan(a, s); |
| } |
| } |
| |
| static void parts128_float_to_float(FloatParts128 *a, float_status *s) |
| { |
| if (is_nan(a->cls)) { |
| parts_return_nan(a, s); |
| } |
| } |
| |
| #define parts_float_to_float(P, S) \ |
| PARTS_GENERIC_64_128(float_to_float, P)(P, S) |
| |
| static void parts_float_to_float_narrow(FloatParts64 *a, FloatParts128 *b, |
| float_status *s) |
| { |
| a->cls = b->cls; |
| a->sign = b->sign; |
| a->exp = b->exp; |
| |
| if (a->cls == float_class_normal) { |
| frac_truncjam(a, b); |
| } else if (is_nan(a->cls)) { |
| /* Discard the low bits of the NaN. */ |
| a->frac = b->frac_hi; |
| parts_return_nan(a, s); |
| } |
| } |
| |
| static void parts_float_to_float_widen(FloatParts128 *a, FloatParts64 *b, |
| float_status *s) |
| { |
| a->cls = b->cls; |
| a->sign = b->sign; |
| a->exp = b->exp; |
| frac_widen(a, b); |
| |
| if (is_nan(a->cls)) { |
| parts_return_nan(a, s); |
| } |
| } |
| |
| float32 float16_to_float32(float16 a, bool ieee, float_status *s) |
| { |
| const FloatFmt *fmt16 = ieee ? &float16_params : &float16_params_ahp; |
| FloatParts64 p; |
| |
| float16a_unpack_canonical(&p, a, s, fmt16); |
| parts_float_to_float(&p, s); |
| return float32_round_pack_canonical(&p, s); |
| } |
| |
| float64 float16_to_float64(float16 a, bool ieee, float_status *s) |
| { |
| const FloatFmt *fmt16 = ieee ? &float16_params : &float16_params_ahp; |
| FloatParts64 p; |
| |
| float16a_unpack_canonical(&p, a, s, fmt16); |
| parts_float_to_float(&p, s); |
| return float64_round_pack_canonical(&p, s); |
| } |
| |
| float16 float32_to_float16(float32 a, bool ieee, float_status *s) |
| { |
| FloatParts64 p; |
| const FloatFmt *fmt; |
| |
| float32_unpack_canonical(&p, a, s); |
| if (ieee) { |
| parts_float_to_float(&p, s); |
| fmt = &float16_params; |
| } else { |
| parts_float_to_ahp(&p, s); |
| fmt = &float16_params_ahp; |
| } |
| return float16a_round_pack_canonical(&p, s, fmt); |
| } |
| |
| static float64 QEMU_SOFTFLOAT_ATTR |
| soft_float32_to_float64(float32 a, float_status *s) |
| { |
| FloatParts64 p; |
| |
| float32_unpack_canonical(&p, a, s); |
| parts_float_to_float(&p, s); |
| return float64_round_pack_canonical(&p, s); |
| } |
| |
| float64 float32_to_float64(float32 a, float_status *s) |
| { |
| if (likely(float32_is_normal(a))) { |
| /* Widening conversion can never produce inexact results. */ |
| union_float32 uf; |
| union_float64 ud; |
| uf.s = a; |
| ud.h = uf.h; |
| return ud.s; |
| } else if (float32_is_zero(a)) { |
| return float64_set_sign(float64_zero, float32_is_neg(a)); |
| } else { |
| return soft_float32_to_float64(a, s); |
| } |
| } |
| |
| float16 float64_to_float16(float64 a, bool ieee, float_status *s) |
| { |
| FloatParts64 p; |
| const FloatFmt *fmt; |
| |
| float64_unpack_canonical(&p, a, s); |
| if (ieee) { |
| parts_float_to_float(&p, s); |
| fmt = &float16_params; |
| } else { |
| parts_float_to_ahp(&p, s); |
| fmt = &float16_params_ahp; |
| } |
| return float16a_round_pack_canonical(&p, s, fmt); |
| } |
| |
| float32 float64_to_float32(float64 a, float_status *s) |
| { |
| FloatParts64 p; |
| |
| float64_unpack_canonical(&p, a, s); |
| parts_float_to_float(&p, s); |
| return float32_round_pack_canonical(&p, s); |
| } |
| |
| float32 bfloat16_to_float32(bfloat16 a, float_status *s) |
| { |
| FloatParts64 p; |
| |
| bfloat16_unpack_canonical(&p, a, s); |
| parts_float_to_float(&p, s); |
| return float32_round_pack_canonical(&p, s); |
| } |
| |
| float64 bfloat16_to_float64(bfloat16 a, float_status *s) |
| { |
| FloatParts64 p; |
| |
| bfloat16_unpack_canonical(&p, a, s); |
| parts_float_to_float(&p, s); |
| return float64_round_pack_canonical(&p, s); |
| } |
| |
| bfloat16 float32_to_bfloat16(float32 a, float_status *s) |
| { |
| FloatParts64 p; |
| |
| float32_unpack_canonical(&p, a, s); |
| parts_float_to_float(&p, s); |
| return bfloat16_round_pack_canonical(&p, s); |
| } |
| |
| bfloat16 float64_to_bfloat16(float64 a, float_status *s) |
| { |
| FloatParts64 p; |
| |
| float64_unpack_canonical(&p, a, s); |
| parts_float_to_float(&p, s); |
| return bfloat16_round_pack_canonical(&p, s); |
| } |
| |
| float32 float128_to_float32(float128 a, float_status *s) |
| { |
| FloatParts64 p64; |
| FloatParts128 p128; |
| |
| float128_unpack_canonical(&p128, a, s); |
| parts_float_to_float_narrow(&p64, &p128, s); |
| return float32_round_pack_canonical(&p64, s); |
| } |
| |
| float64 float128_to_float64(float128 a, float_status *s) |
| { |
| FloatParts64 p64; |
| FloatParts128 p128; |
| |
| float128_unpack_canonical(&p128, a, s); |
| parts_float_to_float_narrow(&p64, &p128, s); |
| return float64_round_pack_canonical(&p64, s); |
| } |
| |
| float128 float32_to_float128(float32 a, float_status *s) |
| { |
| FloatParts64 p64; |
| FloatParts128 p128; |
| |
| float32_unpack_canonical(&p64, a, s); |
| parts_float_to_float_widen(&p128, &p64, s); |
| return float128_round_pack_canonical(&p128, s); |
| } |
| |
| float128 float64_to_float128(float64 a, float_status *s) |
| { |
| FloatParts64 p64; |
| FloatParts128 p128; |
| |
| float64_unpack_canonical(&p64, a, s); |
| parts_float_to_float_widen(&p128, &p64, s); |
| return float128_round_pack_canonical(&p128, s); |
| } |
| |
| float32 floatx80_to_float32(floatx80 a, float_status *s) |
| { |
| FloatParts64 p64; |
| FloatParts128 p128; |
| |
| if (floatx80_unpack_canonical(&p128, a, s)) { |
| parts_float_to_float_narrow(&p64, &p128, s); |
| } else { |
| parts_default_nan(&p64, s); |
| } |
| return float32_round_pack_canonical(&p64, s); |
| } |
| |
| float64 floatx80_to_float64(floatx80 a, float_status *s) |
| { |
| FloatParts64 p64; |
| FloatParts128 p128; |
| |
| if (floatx80_unpack_canonical(&p128, a, s)) { |
| parts_float_to_float_narrow(&p64, &p128, s); |
| } else { |
| parts_default_nan(&p64, s); |
| } |
| return float64_round_pack_canonical(&p64, s); |
| } |
| |
| float128 floatx80_to_float128(floatx80 a, float_status *s) |
| { |
| FloatParts128 p; |
| |
| if (floatx80_unpack_canonical(&p, a, s)) { |
| parts_float_to_float(&p, s); |
| } else { |
| parts_default_nan(&p, s); |
| } |
| return float128_round_pack_canonical(&p, s); |
| } |
| |
| floatx80 float32_to_floatx80(float32 a, float_status *s) |
| { |
| FloatParts64 p64; |
| FloatParts128 p128; |
| |
| float32_unpack_canonical(&p64, a, s); |
| parts_float_to_float_widen(&p128, &p64, s); |
| return floatx80_round_pack_canonical(&p128, s); |
| } |
| |
| floatx80 float64_to_floatx80(float64 a, float_status *s) |
| { |
| FloatParts64 p64; |
| FloatParts128 p128; |
| |
| float64_unpack_canonical(&p64, a, s); |
| parts_float_to_float_widen(&p128, &p64, s); |
| return floatx80_round_pack_canonical(&p128, s); |
| } |
| |
| floatx80 float128_to_floatx80(float128 a, float_status *s) |
| { |
| FloatParts128 p; |
| |
| float128_unpack_canonical(&p, a, s); |
| parts_float_to_float(&p, s); |
| return floatx80_round_pack_canonical(&p, s); |
| } |
| |
| /* |
| * Round to integral value |
| */ |
| |
| float16 float16_round_to_int(float16 a, float_status *s) |
| { |
| FloatParts64 p; |
| |
| float16_unpack_canonical(&p, a, s); |
| parts_round_to_int(&p, s->float_rounding_mode, 0, s, &float16_params); |
| return float16_round_pack_canonical(&p, s); |
| } |
| |
| float32 float32_round_to_int(float32 a, float_status *s) |
| { |
| FloatParts64 p; |
| |
| float32_unpack_canonical(&p, a, s); |
| parts_round_to_int(&p, s->float_rounding_mode, 0, s, &float32_params); |
| return float32_round_pack_canonical(&p, s); |
| } |
| |
| float64 float64_round_to_int(float64 a, float_status *s) |
| { |
| FloatParts64 p; |
| |
| float64_unpack_canonical(&p, a, s); |
| parts_round_to_int(&p, s->float_rounding_mode, 0, s, &float64_params); |
| return float64_round_pack_canonical(&p, s); |
| } |
| |
| bfloat16 bfloat16_round_to_int(bfloat16 a, float_status *s) |
| { |
| FloatParts64 p; |
| |
| bfloat16_unpack_canonical(&p, a, s); |
| parts_round_to_int(&p, s->float_rounding_mode, 0, s, &bfloat16_params); |
| return bfloat16_round_pack_canonical(&p, s); |
| } |
| |
| float128 float128_round_to_int(float128 a, float_status *s) |
| { |
| FloatParts128 p; |
| |
| float128_unpack_canonical(&p, a, s); |
| parts_round_to_int(&p, s->float_rounding_mode, 0, s, &float128_params); |
| return float128_round_pack_canonical(&p, s); |
| } |
| |
| floatx80 floatx80_round_to_int(floatx80 a, float_status *status) |
| { |
| FloatParts128 p; |
| |
| if (!floatx80_unpack_canonical(&p, a, status)) { |
| return floatx80_default_nan(status); |
| } |
| |
| parts_round_to_int(&p, status->float_rounding_mode, 0, status, |
| &floatx80_params[status->floatx80_rounding_precision]); |
| return floatx80_round_pack_canonical(&p, status); |
| } |
| |
| /* |
| * Floating-point to signed integer conversions |
| */ |
| |
| int8_t float16_to_int8_scalbn(float16 a, FloatRoundMode rmode, int scale, |
| float_status *s) |
| { |
| FloatParts64 p; |
| |
| float16_unpack_canonical(&p, a, s); |
| return parts_float_to_sint(&p, rmode, scale, INT8_MIN, INT8_MAX, s); |
| } |
| |
| int16_t float16_to_int16_scalbn(float16 a, FloatRoundMode rmode, int scale, |
| float_status *s) |
| { |
| FloatParts64 p; |
| |
| float16_unpack_canonical(&p, a, s); |
| return parts_float_to_sint(&p, rmode, scale, INT16_MIN, INT16_MAX, s); |
| } |
| |
| int32_t float16_to_int32_scalbn(float16 a, FloatRoundMode rmode, int scale, |
| float_status *s) |
| { |
| FloatParts64 p; |
| |
| float16_unpack_canonical(&p, a, s); |
| return parts_float_to_sint(&p, rmode, scale, INT32_MIN, INT32_MAX, s); |
| } |
| |
| int64_t float16_to_int64_scalbn(float16 a, FloatRoundMode rmode, int scale, |
| float_status *s) |
| { |
| FloatParts64 p; |
| |
| float16_unpack_canonical(&p, a, s); |
| return parts_float_to_sint(&p, rmode, scale, INT64_MIN, INT64_MAX, s); |
| } |
| |
| int16_t float32_to_int16_scalbn(float32 a, FloatRoundMode rmode, int scale, |
| float_status *s) |
| { |
| FloatParts64 p; |
| |
| float32_unpack_canonical(&p, a, s); |
| return parts_float_to_sint(&p, rmode, scale, INT16_MIN, INT16_MAX, s); |
| } |
| |
| int32_t float32_to_int32_scalbn(float32 a, FloatRoundMode rmode, int scale, |
| float_status *s) |
| { |
| FloatParts64 p; |
| |
| float32_unpack_canonical(&p, a, s); |
| return parts_float_to_sint(&p, rmode, scale, INT32_MIN, INT32_MAX, s); |
| } |
| |
| int64_t float32_to_int64_scalbn(float32 a, FloatRoundMode rmode, int scale, |
| float_status *s) |
| { |
| FloatParts64 p; |
| |
| float32_unpack_canonical(&p, a, s); |
| return parts_float_to_sint(&p, rmode, scale, INT64_MIN, INT64_MAX, s); |
| } |
| |
| int16_t float64_to_int16_scalbn(float64 a, FloatRoundMode rmode, int scale, |
| float_status *s) |
| { |
| FloatParts64 p; |
| |
| float64_unpack_canonical(&p, a, s); |
| return parts_float_to_sint(&p, rmode, scale, INT16_MIN, INT16_MAX, s); |
| } |
| |
| int32_t float64_to_int32_scalbn(float64 a, FloatRoundMode rmode, int scale, |
| float_status *s) |
| { |
| FloatParts64 p; |
| |
| float64_unpack_canonical(&p, a, s); |
| return parts_float_to_sint(&p, rmode, scale, INT32_MIN, INT32_MAX, s); |
| } |
| |
| int64_t float64_to_int64_scalbn(float64 a, FloatRoundMode rmode, int scale, |
| float_status *s) |
| { |
| FloatParts64 p; |
| |
| float64_unpack_canonical(&p, a, s); |
| return parts_float_to_sint(&p, rmode, scale, INT64_MIN, INT64_MAX, s); |
| } |
| |
| int16_t bfloat16_to_int16_scalbn(bfloat16 a, FloatRoundMode rmode, int scale, |
| float_status *s) |
| { |
| FloatParts64 p; |
| |
| bfloat16_unpack_canonical(&p, a, s); |
| return parts_float_to_sint(&p, rmode, scale, INT16_MIN, INT16_MAX, s); |
| } |
| |
| int32_t bfloat16_to_int32_scalbn(bfloat16 a, FloatRoundMode rmode, int scale, |
| float_status *s) |
| { |
| FloatParts64 p; |
| |
| bfloat16_unpack_canonical(&p, a, s); |
| return parts_float_to_sint(&p, rmode, scale, INT32_MIN, INT32_MAX, s); |
| } |
| |
| int64_t bfloat16_to_int64_scalbn(bfloat16 a, FloatRoundMode rmode, int scale, |
| float_status *s) |
| { |
| FloatParts64 p; |
| |
| bfloat16_unpack_canonical(&p, a, s); |
| return parts_float_to_sint(&p, rmode, scale, INT64_MIN, INT64_MAX, s); |
| } |
| |
| static int32_t float128_to_int32_scalbn(float128 a, FloatRoundMode rmode, |
| int scale, float_status *s) |
| { |
| FloatParts128 p; |
| |
| float128_unpack_canonical(&p, a, s); |
| return parts_float_to_sint(&p, rmode, scale, INT32_MIN, INT32_MAX, s); |
| } |
| |
| static int64_t float128_to_int64_scalbn(float128 a, FloatRoundMode rmode, |
| int scale, float_status *s) |
| { |
| FloatParts128 p; |
| |
| float128_unpack_canonical(&p, a, s); |
| return parts_float_to_sint(&p, rmode, scale, INT64_MIN, INT64_MAX, s); |
| } |
| |
| static int32_t floatx80_to_int32_scalbn(floatx80 a, FloatRoundMode rmode, |
| int scale, float_status *s) |
| { |
| FloatParts128 p; |
| |
| if (!floatx80_unpack_canonical(&p, a, s)) { |
| parts_default_nan(&p, s); |
| } |
| return parts_float_to_sint(&p, rmode, scale, INT32_MIN, INT32_MAX, s); |
| } |
| |
| static int64_t floatx80_to_int64_scalbn(floatx80 a, FloatRoundMode rmode, |
| int scale, float_status *s) |
| { |
| FloatParts128 p; |
| |
| if (!floatx80_unpack_canonical(&p, a, s)) { |
| parts_default_nan(&p, s); |
| } |
| return parts_float_to_sint(&p, rmode, scale, INT64_MIN, INT64_MAX, s); |
| } |
| |
| int8_t float16_to_int8(float16 a, float_status *s) |
| { |
| return float16_to_int8_scalbn(a, s->float_rounding_mode, 0, 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); |
| } |
| |
| int32_t float128_to_int32(float128 a, float_status *s) |
| { |
| return float128_to_int32_scalbn(a, s->float_rounding_mode, 0, s); |
| } |
| |
| int64_t float128_to_int64(float128 a, float_status *s) |
| { |
| return float128_to_int64_scalbn(a, s->float_rounding_mode, 0, s); |
| } |
| |
| int32_t floatx80_to_int32(floatx80 a, float_status *s) |
| { |
| return floatx80_to_int32_scalbn(a, s->float_rounding_mode, 0, s); |
| } |
| |
| int64_t floatx80_to_int64(floatx80 a, float_status *s) |
| { |
| return floatx80_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); |
| } |
| |
| int32_t float128_to_int32_round_to_zero(float128 a, float_status *s) |
| { |
| return float128_to_int32_scalbn(a, float_round_to_zero, 0, s); |
| } |
| |
| int64_t float128_to_int64_round_to_zero(float128 a, float_status *s) |
| { |
| return float128_to_int64_scalbn(a, float_round_to_zero, 0, s); |
| } |
| |
| int32_t floatx80_to_int32_round_to_zero(floatx80 a, float_status *s) |
| { |
| return floatx80_to_int32_scalbn(a, float_round_to_zero, 0, s); |
| } |
| |
| int64_t floatx80_to_int64_round_to_zero(floatx80 a, float_status *s) |
| { |
| return floatx80_to_int64_scalbn(a, float_round_to_zero, 0, s); |
| } |
| |
| int16_t bfloat16_to_int16(bfloat16 a, float_status *s) |
| { |
| return bfloat16_to_int16_scalbn(a, s->float_rounding_mode, 0, s); |
| } |
| |
| int32_t bfloat16_to_int32(bfloat16 a, float_status *s) |
| { |
| return bfloat16_to_int32_scalbn(a, s->float_rounding_mode, 0, s); |
| } |
| |
| int64_t bfloat16_to_int64(bfloat16 a, float_status *s) |
| { |
| return bfloat16_to_int64_scalbn(a, s->float_rounding_mode, 0, s); |
| } |
| |
| int16_t bfloat16_to_int16_round_to_zero(bfloat16 a, float_status *s) |
| { |
| return bfloat16_to_int16_scalbn(a, float_round_to_zero, 0, s); |
| } |
| |
| int32_t bfloat16_to_int32_round_to_zero(bfloat16 a, float_status *s) |
| { |
| return bfloat16_to_int32_scalbn(a, float_round_to_zero, 0, s); |
| } |
| |
| int64_t bfloat16_to_int64_round_to_zero(bfloat16 a, float_status *s) |
| { |
| return bfloat16_to_int64_scalbn(a, float_round_to_zero, 0, s); |
| } |
| |
| /* |
| * Floating-point to unsigned integer conversions |
| */ |
| |
| uint8_t float16_to_uint8_scalbn(float16 a, FloatRoundMode rmode, int scale, |
| float_status *s) |
| { |
| FloatParts64 p; |
| |
| float16_unpack_canonical(&p, a, s); |
| return parts_float_to_uint(&p, rmode, scale, UINT8_MAX, s); |
| } |
| |
| uint16_t float16_to_uint16_scalbn(float16 a, FloatRoundMode rmode, int scale, |
| float_status *s) |
| { |
| FloatParts64 p; |
| |
| float16_unpack_canonical(&p, a, s); |
| return parts_float_to_uint(&p, rmode, scale, UINT16_MAX, s); |
| } |
| |
| uint32_t float16_to_uint32_scalbn(float16 a, FloatRoundMode rmode, int scale, |
| float_status *s) |
| { |
| FloatParts64 p; |
| |
| float16_unpack_canonical(&p, a, s); |
| return parts_float_to_uint(&p, rmode, scale, UINT32_MAX, s); |
| } |
| |
| uint64_t float16_to_uint64_scalbn(float16 a, FloatRoundMode rmode, int scale, |
| float_status *s) |
| { |
| FloatParts64 p; |
| |
| float16_unpack_canonical(&p, a, s); |
| return parts_float_to_uint(&p, rmode, scale, UINT64_MAX, s); |
| } |
| |
| uint16_t float32_to_uint16_scalbn(float32 a, FloatRoundMode rmode, int scale, |
| float_status *s) |
| { |
| FloatParts64 p; |
| |
| float32_unpack_canonical(&p, a, s); |
| return parts_float_to_uint(&p, rmode, scale, UINT16_MAX, s); |
| } |
| |
| uint32_t float32_to_uint32_scalbn(float32 a, FloatRoundMode rmode, int scale, |
| float_status *s) |
| { |
| FloatParts64 p; |
| |
| float32_unpack_canonical(&p, a, s); |
| return parts_float_to_uint(&p, rmode, scale, UINT32_MAX, s); |
| } |
| |
| uint64_t float32_to_uint64_scalbn(float32 a, FloatRoundMode rmode, int scale, |
| float_status *s) |
| { |
| FloatParts64 p; |
| |
| float32_unpack_canonical(&p, a, s); |
| return parts_float_to_uint(&p, rmode, scale, UINT64_MAX, s); |
| } |
| |
| uint16_t float64_to_uint16_scalbn(float64 a, FloatRoundMode rmode, int scale, |
| float_status *s) |
| { |
| FloatParts64 p; |
| |
| float64_unpack_canonical(&p, a, s); |
| return parts_float_to_uint(&p, rmode, scale, UINT16_MAX, s); |
| } |
| |
| uint32_t float64_to_uint32_scalbn(float64 a, FloatRoundMode rmode, int scale, |
| float_status *s) |
| { |
| FloatParts64 p; |
| |
| float64_unpack_canonical(&p, a, s); |
| return parts_float_to_uint(&p, rmode, scale, UINT32_MAX, s); |
| } |
| |
| uint64_t float64_to_uint64_scalbn(float64 a, FloatRoundMode rmode, int scale, |
| float_status *s) |
| { |
| FloatParts64 p; |
| |
| float64_unpack_canonical(&p, a, s); |
| return parts_float_to_uint(&p, rmode, scale, UINT64_MAX, s); |
| } |
| |
| uint16_t bfloat16_to_uint16_scalbn(bfloat16 a, FloatRoundMode rmode, |
| int scale, float_status *s) |
| { |
| FloatParts64 p; |
| |
| bfloat16_unpack_canonical(&p, a, s); |
| return parts_float_to_uint(&p, rmode, scale, UINT16_MAX, s); |
| } |
| |
| uint32_t bfloat16_to_uint32_scalbn(bfloat16 a, FloatRoundMode rmode, |
| int scale, float_status *s) |
| { |
| FloatParts64 p; |
| |
| bfloat16_unpack_canonical(&p, a, s); |
| return parts_float_to_uint(&p, rmode, scale, UINT32_MAX, s); |
| } |
| |
| uint64_t bfloat16_to_uint64_scalbn(bfloat16 a, FloatRoundMode rmode, |
| int scale, float_status *s) |
| { |
| FloatParts64 p; |
| |
| bfloat16_unpack_canonical(&p, a, s); |
| return parts_float_to_uint(&p, rmode, scale, UINT64_MAX, s); |
| } |
| |
| static uint32_t float128_to_uint32_scalbn(float128 a, FloatRoundMode rmode, |
| int scale, float_status *s) |
| { |
| FloatParts128 p; |
| |
| float128_unpack_canonical(&p, a, s); |
| return parts_float_to_uint(&p, rmode, scale, UINT32_MAX, s); |
| } |
| |
| static uint64_t float128_to_uint64_scalbn(float128 a, FloatRoundMode rmode, |
| int scale, float_status *s) |
| { |
| FloatParts128 p; |
| |
| float128_unpack_canonical(&p, a, s); |
| return parts_float_to_uint(&p, rmode, scale, UINT64_MAX, s); |
| } |
| |
| uint8_t float16_to_uint8(float16 a, float_status *s) |
| { |
| return float16_to_uint8_scalbn(a, s->float_rounding_mode, 0, 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); |
| } |
| |
| uint32_t float128_to_uint32(float128 a, float_status *s) |
| { |
| return float128_to_uint32_scalbn(a, s->float_rounding_mode, 0, s); |
| } |
| |
| uint64_t float128_to_uint64(float128 a, float_status *s) |
| { |
| return float128_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); |
| } |
| |
| uint32_t float128_to_uint32_round_to_zero(float128 a, float_status *s) |
| { |
| return float128_to_uint32_scalbn(a, float_round_to_zero, 0, s); |
| } |
| |
| uint64_t float128_to_uint64_round_to_zero(float128 a, float_status *s) |
| { |
| return float128_to_uint64_scalbn(a, float_round_to_zero, 0, s); |
| } |
| |
| uint16_t bfloat16_to_uint16(bfloat16 a, float_status *s) |
| { |
| return bfloat16_to_uint16_scalbn(a, s->float_rounding_mode, 0, s); |
| } |
| |
| uint32_t bfloat16_to_uint32(bfloat16 a, float_status *s) |
| { |
| return bfloat16_to_uint32_scalbn(a, s->float_rounding_mode, 0, s); |
| } |
| |
| uint64_t bfloat16_to_uint64(bfloat16 a, float_status *s) |
| { |
| return bfloat16_to_uint64_scalbn(a, s->float_rounding_mode, 0, s); |
| } |
| |
| uint16_t bfloat16_to_uint16_round_to_zero(bfloat16 a, float_status *s) |
| { |
| return bfloat16_to_uint16_scalbn(a, float_round_to_zero, 0, s); |
| } |
| |
| uint32_t bfloat16_to_uint32_round_to_zero(bfloat16 a, float_status *s) |
| { |
| return bfloat16_to_uint32_scalbn(a, float_round_to_zero, 0, s); |
| } |
| |
| uint64_t bfloat16_to_uint64_round_to_zero(bfloat16 a, float_status *s) |
| { |
| return bfloat16_to_uint64_scalbn(a, float_round_to_zero, 0, s); |
| } |
| |
| /* |
| * Signed integer to floating-point conversions |
| */ |
| |
| float16 int64_to_float16_scalbn(int64_t a, int scale, float_status *status) |
| { |
| FloatParts64 p; |
| |
| parts_sint_to_float(&p, a, scale, status); |
| return float16_round_pack_canonical(&p, 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); |
| } |
| |
| float16 int8_to_float16(int8_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) |
| { |
| FloatParts64 p; |
| |
| /* Without scaling, there are no overflow concerns. */ |
| if (likely(scale == 0) && can_use_fpu(status)) { |
| union_float32 ur; |
| ur.h = a; |
| return ur.s; |
| } |
| |
| parts64_sint_to_float(&p, a, scale, status); |
| return float32_round_pack_canonical(&p, 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) |
| { |
| FloatParts64 p; |
| |
| /* Without scaling, there are no overflow concerns. */ |
| if (likely(scale == 0) && can_use_fpu(status)) { |
| union_float64 ur; |
| ur.h = a; |
| return ur.s; |
| } |
| |
| parts_sint_to_float(&p, a, scale, status); |
| return float64_round_pack_canonical(&p, 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); |
| } |
| |
| bfloat16 int64_to_bfloat16_scalbn(int64_t a, int scale, float_status *status) |
| { |
| FloatParts64 p; |
| |
| parts_sint_to_float(&p, a, scale, status); |
| return bfloat16_round_pack_canonical(&p, status); |
| } |
| |
| bfloat16 int32_to_bfloat16_scalbn(int32_t a, int scale, float_status *status) |
| { |
| return int64_to_bfloat16_scalbn(a, scale, status); |
| } |
| |
| bfloat16 int16_to_bfloat16_scalbn(int16_t a, int scale, float_status *status) |
| { |
| return int64_to_bfloat16_scalbn(a, scale, status); |
| } |
| |
| bfloat16 int64_to_bfloat16(int64_t a, float_status *status) |
| { |
| return int64_to_bfloat16_scalbn(a, 0, status); |
| } |
| |
| bfloat16 int32_to_bfloat16(int32_t a, float_status *status) |
| { |
| return int64_to_bfloat16_scalbn(a, 0, status); |
| } |
| |
| bfloat16 int16_to_bfloat16(int16_t a, float_status *status) |
| { |
| return int64_to_bfloat16_scalbn(a, 0, status); |
| } |
| |
| float128 int64_to_float128(int64_t a, float_status *status) |
| { |
| FloatParts128 p; |
| |
| parts_sint_to_float(&p, a, 0, status); |
| return float128_round_pack_canonical(&p, status); |
| } |
| |
| float128 int32_to_float128(int32_t a, float_status *status) |
| { |
| return int64_to_float128(a, status); |
| } |
| |
| floatx80 int64_to_floatx80(int64_t a, float_status *status) |
| { |
| FloatParts128 p; |
| |
| parts_sint_to_float(&p, a, 0, status); |
| return floatx80_round_pack_canonical(&p, status); |
| } |
| |
| floatx80 int32_to_floatx80(int32_t a, float_status *status) |
| { |
| return int64_to_floatx80(a, status); |
| } |
| |
| /* |
| * Unsigned Integer to floating-point conversions |
| */ |
| |
| float16 uint64_to_float16_scalbn(uint64_t a, int scale, float_status *status) |
| { |
| FloatParts64 p; |
| |
| parts_uint_to_float(&p, a, scale, status); |
| return float16_round_pack_canonical(&p, 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); |
| } |
| |
| float16 uint8_to_float16(uint8_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) |
| { |
| FloatParts64 p; |
| |
| /* Without scaling, there are no overflow concerns. */ |
| if (likely(scale == 0) && can_use_fpu(status)) { |
| union_float32 ur; |
| ur.h = a; |
| return ur.s; |
| } |
| |
| parts_uint_to_float(&p, a, scale, status); |
| return float32_round_pack_canonical(&p, 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) |
| { |
| FloatParts64 p; |
| |
| /* Without scaling, there are no overflow concerns. */ |
| if (likely(scale == 0) && can_use_fpu(status)) { |
| union_float64 ur; |
| ur.h = a; |
| return ur.s; |
| } |
| |
| parts_uint_to_float(&p, a, scale, status); |
| return float64_round_pack_canonical(&p, 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); |
| } |
| |
| bfloat16 uint64_to_bfloat16_scalbn(uint64_t a, int scale, float_status *status) |
| { |
| FloatParts64 p; |
| |
| parts_uint_to_float(&p, a, scale, status); |
| return bfloat16_round_pack_canonical(&p, status); |
| } |
| |
| bfloat16 uint32_to_bfloat16_scalbn(uint32_t a, int scale, float_status *status) |
| { |
| return uint64_to_bfloat16_scalbn(a, scale, status); |
| } |
| |
| bfloat16 uint16_to_bfloat16_scalbn(uint16_t a, int scale, float_status *status) |
| { |
| return uint64_to_bfloat16_scalbn(a, scale, status); |
| } |
| |
| bfloat16 uint64_to_bfloat16(uint64_t a, float_status *status) |
| { |
| return uint64_to_bfloat16_scalbn(a, 0, status); |
| } |
| |
| bfloat16 uint32_to_bfloat16(uint32_t a, float_status *status) |
| { |
| return uint64_to_bfloat16_scalbn(a, 0, status); |
| } |
| |
| bfloat16 uint16_to_bfloat16(uint16_t a, float_status *status) |
| { |
| return uint64_to_bfloat16_scalbn(a, 0, status); |
| } |
| |
| float128 uint64_to_float128(uint64_t a, float_status *status) |
| { |
| FloatParts128 p; |
| |
| parts_uint_to_float(&p, a, 0, status); |
| return float128_round_pack_canonical(&p, status); |
| } |
| |
| /* |
| * Minimum and maximum |
| */ |
| |
| static float16 float16_minmax(float16 a, float16 b, float_status *s, int flags) |
| { |
| FloatParts64 pa, pb, *pr; |
| |
| float16_unpack_canonical(&pa, a, s); |
| float16_unpack_canonical(&pb, b, s); |
| pr = parts_minmax(&pa, &pb, s, flags); |
| |
| return float16_round_pack_canonical(pr, s); |
| } |
| |
| static bfloat16 bfloat16_minmax(bfloat16 a, bfloat16 b, |
| float_status *s, int flags) |
| { |
| FloatParts64 pa, pb, *pr; |
| |
| bfloat16_unpack_canonical(&pa, a, s); |
| bfloat16_unpack_canonical(&pb, b, s); |
| pr = parts_minmax(&pa, &pb, s, flags); |
| |
| return bfloat16_round_pack_canonical(pr, s); |
| } |
| |
| static float32 float32_minmax(float32 a, float32 b, float_status *s, int flags) |
| { |
| FloatParts64 pa, pb, *pr; |
| |
| float32_unpack_canonical(&pa, a, s); |
| float32_unpack_canonical(&pb, b, s); |
| pr = parts_minmax(&pa, &pb, s, flags); |
| |
| return float32_round_pack_canonical(pr, s); |
| } |
| |
| static float64 float64_minmax(float64 a, float64 b, float_status *s, int flags) |
| { |
| FloatParts64 pa, pb, *pr; |
| |
| float64_unpack_canonical(&pa, a, s); |
| float64_unpack_canonical(&pb, b, s); |
| pr = parts_minmax(&pa, &pb, s, flags); |
| |
| return float64_round_pack_canonical(pr, s); |
| } |
| |
| static float128 float128_minmax(float128 a, float128 b, |
| float_status *s, int flags) |
| { |
| FloatParts128 pa, pb, *pr; |
| |
| float128_unpack_canonical(&pa, a, s); |
| float128_unpack_canonical(&pb, b, s); |
| pr = parts_minmax(&pa, &pb, s, flags); |
| |
| return float128_round_pack_canonical(pr, s); |
| } |
| |
| #define MINMAX_1(type, name, flags) \ |
| type type##_##name(type a, type b, float_status *s) \ |
| { return type##_minmax(a, b, s, flags); } |
| |
| #define MINMAX_2(type) \ |
| MINMAX_1(type, max, 0) \ |
| MINMAX_1(type, maxnum, minmax_isnum) \ |
| MINMAX_1(type, maxnummag, minmax_isnum | minmax_ismag) \ |
| MINMAX_1(type, maximum_number, minmax_isnumber) \ |
| MINMAX_1(type, min, minmax_ismin) \ |
| MINMAX_1(type, minnum, minmax_ismin | minmax_isnum) \ |
| MINMAX_1(type, minnummag, minmax_ismin | minmax_isnum | minmax_ismag) \ |
| MINMAX_1(type, minimum_number, minmax_ismin | minmax_isnumber) \ |
| |
| MINMAX_2(float16) |
| MINMAX_2(bfloat16) |
| MINMAX_2(float32) |
| MINMAX_2(float64) |
| MINMAX_2(float128) |
| |
| #undef MINMAX_1 |
| #undef MINMAX_2 |
| |
| /* |
| * Floating point compare |
| */ |
| |
| static FloatRelation QEMU_FLATTEN |
| float16_do_compare(float16 a, float16 b, float_status *s, bool is_quiet) |
| { |
| FloatParts64 pa, pb; |
| |
| float16_unpack_canonical(&pa, a, s); |
| float16_unpack_canonical(&pb, b, s); |
| return parts_compare(&pa, &pb, s, is_quiet); |
| } |
| |
| FloatRelation float16_compare(float16 a, float16 b, float_status *s) |
| { |
| return float16_do_compare(a, b, s, false); |
| } |
| |
| FloatRelation float16_compare_quiet(float16 a, float16 b, float_status *s) |
| { |
| return float16_do_compare(a, b, s, true); |
| } |
| |
| static FloatRelation QEMU_SOFTFLOAT_ATTR |
| float32_do_compare(float32 a, float32 b, float_status *s, bool is_quiet) |
| { |
| FloatParts64 pa, pb; |
| |
| float32_unpack_canonical(&pa, a, s); |
| float32_unpack_canonical(&pb, b, s); |
| return parts_compare(&pa, &pb, s, is_quiet); |
| } |
| |
| static FloatRelation QEMU_FLATTEN |
| float32_hs_compare(float32 xa, float32 xb, float_status *s, bool is_quiet) |
| { |
| 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 float32_do_compare(ua.s, ub.s, s, is_quiet); |
| } |
| |
| FloatRelation float32_compare(float32 a, float32 b, float_status *s) |
| { |
| return float32_hs_compare(a, b, s, false); |
| } |
| |
| FloatRelation float32_compare_quiet(float32 a, float32 b, float_status *s) |
| { |
| return float32_hs_compare(a, b, s, true); |
| } |
| |
| static FloatRelation QEMU_SOFTFLOAT_ATTR |
| float64_do_compare(float64 a, float64 b, float_status *s, bool is_quiet) |
| { |
| FloatParts64 pa, pb; |
| |
| float64_unpack_canonical(&pa, a, s); |
| float64_unpack_canonical(&pb, b, s); |
| return parts_compare(&pa, &pb, s, is_quiet); |
| } |
| |
| static FloatRelation QEMU_FLATTEN |
| float64_hs_compare(float64 xa, float64 xb, float_status *s, bool is_quiet) |
| { |
| 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 float64_do_compare(ua.s, ub.s, s, is_quiet); |
| } |
| |
| FloatRelation float64_compare(float64 a, float64 b, float_status *s) |
| { |
| return float64_hs_compare(a, b, s, false); |
| } |
| |
| FloatRelation float64_compare_quiet(float64 a, float64 b, float_status *s) |
| { |
| return float64_hs_compare(a, b, s, true); |
| } |
| |
| static FloatRelation QEMU_FLATTEN |
| bfloat16_do_compare(bfloat16 a, bfloat16 b, float_status *s, bool is_quiet) |
| { |
| FloatParts64 pa, pb; |
| |
| bfloat16_unpack_canonical(&pa, a, s); |
| bfloat16_unpack_canonical(&pb, b, s); |
| return parts_compare(&pa, &pb, s, is_quiet); |
| } |
| |
| FloatRelation bfloat16_compare(bfloat16 a, bfloat16 b, float_status *s) |
| { |
| return bfloat16_do_compare(a, b, s, false); |
| } |
| |
| FloatRelation bfloat16_compare_quiet(bfloat16 a, bfloat16 b, float_status *s) |
| { |
| return bfloat16_do_compare(a, b, s, true); |
| } |
| |
| static FloatRelation QEMU_FLATTEN |
| float128_do_compare(float128 a, float128 b, float_status *s, bool is_quiet) |
| { |
| FloatParts128 pa, pb; |
| |
| float128_unpack_canonical(&pa, a, s); |
| float128_unpack_canonical(&pb, b, s); |
| return parts_compare(&pa, &pb, s, is_quiet); |
| } |
| |
| FloatRelation float128_compare(float128 a, float128 b, float_status *s) |
| { |
| return float128_do_compare(a, b, s, false); |
| } |
| |
| FloatRelation float128_compare_quiet(float128 a, float128 b, float_status *s) |
| { |
| return float128_do_compare(a, b, s, true); |
| } |
| |
| static FloatRelation QEMU_FLATTEN |
| floatx80_do_compare(floatx80 a, floatx80 b, float_status *s, bool is_quiet) |
| { |
| FloatParts128 pa, pb; |
| |
| if (!floatx80_unpack_canonical(&pa, a, s) || |
| !floatx80_unpack_canonical(&pb, b, s)) { |
| return float_relation_unordered; |
| } |
| return parts_compare(&pa, &pb, s, is_quiet); |
| } |
| |
| FloatRelation floatx80_compare(floatx80 a, floatx80 b, float_status *s) |
| { |
| return floatx80_do_compare(a, b, s, false); |
| } |
| |
| FloatRelation floatx80_compare_quiet(floatx80 a, floatx80 b, float_status *s) |
| { |
| return floatx80_do_compare(a, b, s, true); |
| } |
| |
| /* |
| * Scale by 2**N |
| */ |
| |
| float16 float16_scalbn(float16 a, int n, float_status *status) |
| { |
| FloatParts64 p; |
| |
| float16_unpack_canonical(&p, a, status); |
| parts_scalbn(&p, n, status); |
| return float16_round_pack_canonical(&p, status); |
| } |
| |
| float32 float32_scalbn(float32 a, int n, float_status *status) |
| { |
| FloatParts64 p; |
| |
| float32_unpack_canonical(&p, a, status); |
| parts_scalbn(&p, n, status); |
| return float32_round_pack_canonical(&p, status); |
| } |
| |
| float64 float64_scalbn(float64 a, int n, float_status *status) |
| { |
| FloatParts64 p; |
| |
| float64_unpack_canonical(&p, a, status); |
| parts_scalbn(&p, n, status); |
| return float64_round_pack_canonical(&p, status); |
| } |
| |
| bfloat16 bfloat16_scalbn(bfloat16 a, int n, float_status *status) |
| { |
| FloatParts64 p; |
| |
| bfloat16_unpack_canonical(&p, a, status); |
| parts_scalbn(&p, n, status); |
| return bfloat16_round_pack_canonical(&p, status); |
| } |
| |
| float128 float128_scalbn(float128 a, int n, float_status *status) |
| { |
| FloatParts128 p; |
| |
| float128_unpack_canonical(&p, a, status); |
| parts_scalbn(&p, n, status); |
| return float128_round_pack_canonical(&p, status); |
| } |
| |
| floatx80 floatx80_scalbn(floatx80 a, int n, float_status *status) |
| { |
| FloatParts128 p; |
| |
| if (!floatx80_unpack_canonical(&p, a, status)) { |
| return floatx80_default_nan(status); |
| } |
| parts_scalbn(&p, n, status); |
| return floatx80_round_pack_canonical(&p, status); |
| } |
| |
| /* |
| * Square Root |
| */ |
| |
| float16 QEMU_FLATTEN float16_sqrt(float16 a, float_status *status) |
| { |
| FloatParts64 p; |
| |
| float16_unpack_canonical(&p, a, status); |
| parts_sqrt(&p, status, &float16_params); |
| return float16_round_pack_canonical(&p, status); |
| } |
| |
| static float32 QEMU_SOFTFLOAT_ATTR |
| soft_f32_sqrt(float32 a, float_status *status) |
| { |
| FloatParts64 p; |
| |
| float32_unpack_canonical(&p, a, status); |
| parts_sqrt(&p, status, &float32_params); |
| return float32_round_pack_canonical(&p, status); |
| } |
| |
| static float64 QEMU_SOFTFLOAT_ATTR |
| soft_f64_sqrt(float64 a, float_status *status) |
| { |
| FloatParts64 p; |
| |
| float64_unpack_canonical(&p, a, status); |
| parts_sqrt(&p, status, &float64_params); |
| return float64_round_pack_canonical(&p, 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); |
| } |
| |
| float64 float64r32_sqrt(float64 a, float_status *status) |
| { |
| FloatParts64 p; |
| |
| float64_unpack_canonical(&p, a, status); |
| parts_sqrt(&p, status, &float64_params); |
| return float64r32_round_pack_canonical(&p, status); |
| } |
| |
| bfloat16 QEMU_FLATTEN bfloat16_sqrt(bfloat16 a, float_status *status) |
| { |
| FloatParts64 p; |
| |
| bfloat16_unpack_canonical(&p, a, status); |
| parts_sqrt(&p, status, &bfloat16_params); |
| return bfloat16_round_pack_canonical(&p, status); |
| } |
| |
| float128 QEMU_FLATTEN float128_sqrt(float128 a, float_status *status) |
| { |
| FloatParts128 p; |
| |
| float128_unpack_canonical(&p, a, status); |
| parts_sqrt(&p, status, &float128_params); |
| return float128_round_pack_canonical(&p, status); |
| } |
| |
| floatx80 floatx80_sqrt(floatx80 a, float_status *s) |
| { |
| FloatParts128 p; |
| |
| if (!floatx80_unpack_canonical(&p, a, s)) { |
| return floatx80_default_nan(s); |
| } |
| parts_sqrt(&p, s, &floatx80_params[s->floatx80_rounding_precision]); |
| return floatx80_round_pack_canonical(&p, s); |
| } |
| |
| /* |
| * log2 |
| */ |
| float32 float32_log2(float32 a, float_status *status) |
| { |
| FloatParts64 p; |
| |
| float32_unpack_canonical(&p, a, status); |
| parts_log2(&p, status, &float32_params); |
| return float32_round_pack_canonical(&p, status); |
| } |
| |
| float64 float64_log2(float64 a, float_status *status) |
| { |
| FloatParts64 p; |
| |
| float64_unpack_canonical(&p, a, status); |
| parts_log2(&p, status, &float64_params); |
| return float64_round_pack_canonical(&p, status); |
| } |
| |
| /*---------------------------------------------------------------------------- |
| | The pattern for a default generated NaN. |
| *----------------------------------------------------------------------------*/ |
| |
| float16 float16_default_nan(float_status *status) |
| { |
| FloatParts64 p; |
| |
| parts_default_nan(&p, status); |
| p.frac >>= float16_params.frac_shift; |
| return float16_pack_raw(&p); |
| } |
| |
| float32 float32_default_nan(float_status *status) |
| { |
| FloatParts64 p; |
| |
| parts_default_nan(&p, status); |
| p.frac >>= float32_params.frac_shift; |
| return float32_pack_raw(&p); |
| } |
| |
| float64 float64_default_nan(float_status *status) |
| { |
| FloatParts64 p; |
| |
| parts_default_nan(&p, status); |
| p.frac >>= float64_params.frac_shift; |
| return float64_pack_raw(&p); |
| } |
| |
| float128 float128_default_nan(float_status *status) |
| { |
| FloatParts128 p; |
| |
| parts_default_nan(&p, status); |
| frac_shr(&p, float128_params.frac_shift); |
| return float128_pack_raw(&p); |
| } |
| |
| bfloat16 bfloat16_default_nan(float_status *status) |
| { |
| FloatParts64 p; |
| |
| parts_default_nan(&p, status); |
| p.frac >>= bfloat16_params.frac_shift; |
| return bfloat16_pack_raw(&p); |
| } |
| |
| /*---------------------------------------------------------------------------- |
| | Returns a quiet NaN from a signalling NaN for the floating point value `a'. |
| *----------------------------------------------------------------------------*/ |
| |
| float16 float16_silence_nan(float16 a, float_status *status) |
| { |
| FloatParts64 p; |
| |
| float16_unpack_raw(&p, a); |
| p.frac <<= float16_params.frac_shift; |
| 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) |
| { |
| FloatParts64 p; |
| |
| float32_unpack_raw(&p, a); |
| p.frac <<= float32_params.frac_shift; |
| 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) |
| { |
| FloatParts64 p; |
| |
| float64_unpack_raw(&p, a); |
| p.frac <<= float64_params.frac_shift; |
| parts_silence_nan(&p, status); |
| p.frac >>= float64_params.frac_shift; |
| return float64_pack_raw(&p); |
| } |
| |
| bfloat16 bfloat16_silence_nan(bfloat16 a, float_status *status) |
| { |
| FloatParts64 p; |
| |
| bfloat16_unpack_raw(&p, a); |
| p.frac <<= bfloat16_params.frac_shift; |
| parts_silence_nan(&p, status); |
| p.frac >>= bfloat16_params.frac_shift; |
| return bfloat16_pack_raw(&p); |
| } |
| |
| float128 float128_silence_nan(float128 a, float_status *status) |
| { |
| FloatParts128 p; |
| |
| float128_unpack_raw(&p, a); |
| frac_shl(&p, float128_params.frac_shift); |
| parts_silence_nan(&p, status); |
| frac_shr(&p, float128_params.frac_shift); |
| return float128_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(FloatParts64 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) { |
| FloatParts64 p; |
| |
| float16_unpack_raw(&p, 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) { |
| FloatParts64 p; |
| |
| float32_unpack_raw(&p, 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) { |
| FloatParts64 p; |
| |
| float64_unpack_raw(&p, a); |
| if (parts_squash_denormal(p, status)) { |
| return float64_set_sign(float64_zero, p.sign); |
| } |
| } |
| return a; |
| } |
| |
| bfloat16 bfloat16_squash_input_denormal(bfloat16 a, float_status *status) |
| { |
| if (status->flush_inputs_to_zero) { |
| FloatParts64 p; |
| |
| bfloat16_unpack_raw(&p, a); |
| if (parts_squash_denormal(p, status)) { |
| return bfloat16_set_sign(bfloat16_zero, p.sign); |
| } |
| } |
| return a; |
| } |
| |
| /*---------------------------------------------------------------------------- |
| | 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 floatx80_precision_s or floatx80_precision_d, |
| | 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(FloatX80RoundPrec roundingPrecision, bool zSign, |
| int32_t zExp, uint64_t zSig0, uint64_t zSig1, |
| float_status *status) |
| { |
| FloatRoundMode roundingMode; |
| bool roundNearestEven, increment, isTiny; |
| int64_t roundIncrement, roundMask, roundBits; |
| |
| roundingMode = status->float_rounding_mode; |
| roundNearestEven = ( roundingMode == float_round_nearest_even ); |
| switch (roundingPrecision) { |
| case floatx80_precision_x: |
| goto precision80; |
| case floatx80_precision_d: |
| roundIncrement = UINT64_C(0x0000000000000400); |
| roundMask = UINT64_C(0x00000000000007FF); |
| break; |
| case floatx80_precision_s: |
| roundIncrement = UINT64_C(0x0000008000000000); |
| roundMask = UINT64_C(0x000000FFFFFFFFFF); |
| break; |
| default: |
| g_assert_not_reached(); |
| } |
| 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) { |
| float_raise(float_flag_inexact, status); |
| } |
| 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) { |
| float_raise(float_flag_inexact, status); |
| } |
| 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) { |
| float_raise(float_flag_inexact, status); |
| } |
| 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; |
| if (!(zSig1 << 1) && roundNearestEven) { |
| zSig0 &= ~1; |
| } |
| if ( (int64_t) zSig0 < 0 ) zExp = 1; |
| } |
| return packFloatx80( zSign, zExp, zSig0 ); |
| } |
| } |
| if (zSig1) { |
| float_raise(float_flag_inexact, status); |
| } |
| if ( increment ) { |
| ++zSig0; |
| if ( zSig0 == 0 ) { |
| ++zExp; |
| zSig0 = UINT64_C(0x8000000000000000); |
| } |
| else { |
| if (!(zSig1 << 1) && roundNearestEven) { |
| zSig0 &= ~1; |
| } |
| } |
| } |
| 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(FloatX80RoundPrec 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 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) |
| { |
| FloatParts64 xp, xnp, tp, rp; |
| int i; |
| |
| float32_unpack_canonical(&xp, a, status); |
| if (unlikely(xp.cls != float_class_normal)) { |
| switch (xp.cls) { |
| case float_class_snan: |
| case float_class_qnan: |
| parts_return_nan(&xp, status); |
| return float32_round_pack_canonical(&xp, status); |
| case float_class_inf: |
| return xp.sign ? float32_zero : a; |
| case float_class_zero: |
| return float32_one; |
| default: |
| break; |
| } |
| g_assert_not_reached(); |
| } |
| |
| float_raise(float_flag_inexact, status); |
| |
| float64_unpack_canonical(&tp, float64_ln2, status); |
| xp = *parts_mul(&xp, &tp, status); |
| xnp = xp; |
| |
| float64_unpack_canonical(&rp, float64_one, status); |
| for (i = 0 ; i < 15 ; i++) { |
| float64_unpack_canonical(&tp, float32_exp2_coefficients[i], status); |
| rp = *parts_muladd(&tp, &xp, &rp, 0, status); |
| xnp = *parts_mul(&xnp, &xp, status); |
| } |
| |
| return float32_round_pack_canonical(&rp, status); |
| } |
| |
| /*---------------------------------------------------------------------------- |
| | 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) |
| { |
| FloatParts128 p; |
| |
| if (!floatx80_unpack_canonical(&p, a, status)) { |
| return floatx80_default_nan(status); |
| } |
| return floatx80_round_pack_canonical(&p, status); |
| } |
| |
| static void __attribute__((constructor)) softfloat_init(void) |
| { |
| union_float64 ua, ub, uc, ur; |
| |
| if (QEMU_NO_HARDFLOAT) { |
| return; |
| } |
| /* |
| * Test that the host's FMA is not obviously broken. For example, |
| * glibc < 2.23 can perform an incorrect FMA on certain hosts; see |
| * https://sourceware.org/bugzilla/show_bug.cgi?id=13304 |
| */ |
| ua.s = 0x0020000000000001ULL; |
| ub.s = 0x3ca0000000000000ULL; |
| uc.s = 0x0020000000000000ULL; |
| ur.h = fma(ua.h, ub.h, uc.h); |
| if (ur.s != 0x0020000000000001ULL) { |
| force_soft_fma = true; |
| } |
| } |
