703 lines
20 KiB
C
703 lines
20 KiB
C
/*
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* Copyright(c) 2019-2021 Qualcomm Innovation Center, Inc. All Rights Reserved.
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 2 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, see <http://www.gnu.org/licenses/>.
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*/
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#include "qemu/osdep.h"
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#include "qemu/int128.h"
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#include "fpu/softfloat.h"
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#include "macros.h"
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#include "fma_emu.h"
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#define DF_INF_EXP 0x7ff
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#define DF_BIAS 1023
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#define DF_MANTBITS 52
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#define DF_NAN 0xffffffffffffffffULL
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#define DF_INF 0x7ff0000000000000ULL
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#define DF_MINUS_INF 0xfff0000000000000ULL
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#define DF_MAXF 0x7fefffffffffffffULL
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#define DF_MINUS_MAXF 0xffefffffffffffffULL
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#define SF_INF_EXP 0xff
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#define SF_BIAS 127
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#define SF_MANTBITS 23
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#define SF_INF 0x7f800000
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#define SF_MINUS_INF 0xff800000
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#define SF_MAXF 0x7f7fffff
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#define SF_MINUS_MAXF 0xff7fffff
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#define HF_INF_EXP 0x1f
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#define HF_BIAS 15
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#define WAY_BIG_EXP 4096
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typedef union {
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double f;
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uint64_t i;
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struct {
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uint64_t mant:52;
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uint64_t exp:11;
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uint64_t sign:1;
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};
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} Double;
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typedef union {
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float f;
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uint32_t i;
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struct {
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uint32_t mant:23;
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uint32_t exp:8;
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uint32_t sign:1;
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};
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} Float;
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static uint64_t float64_getmant(float64 f64)
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{
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Double a = { .i = f64 };
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if (float64_is_normal(f64)) {
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return a.mant | 1ULL << 52;
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}
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if (float64_is_zero(f64)) {
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return 0;
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}
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if (float64_is_denormal(f64)) {
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return a.mant;
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}
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return ~0ULL;
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}
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int32_t float64_getexp(float64 f64)
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{
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Double a = { .i = f64 };
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if (float64_is_normal(f64)) {
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return a.exp;
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}
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if (float64_is_denormal(f64)) {
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return a.exp + 1;
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}
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return -1;
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}
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static uint64_t float32_getmant(float32 f32)
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{
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Float a = { .i = f32 };
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if (float32_is_normal(f32)) {
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return a.mant | 1ULL << 23;
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}
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if (float32_is_zero(f32)) {
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return 0;
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}
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if (float32_is_denormal(f32)) {
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return a.mant;
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}
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return ~0ULL;
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}
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int32_t float32_getexp(float32 f32)
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{
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Float a = { .i = f32 };
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if (float32_is_normal(f32)) {
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return a.exp;
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}
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if (float32_is_denormal(f32)) {
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return a.exp + 1;
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}
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return -1;
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}
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static uint32_t int128_getw0(Int128 x)
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{
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return int128_getlo(x);
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}
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static uint32_t int128_getw1(Int128 x)
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{
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return int128_getlo(x) >> 32;
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}
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static Int128 int128_mul_6464(uint64_t ai, uint64_t bi)
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{
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Int128 a, b;
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uint64_t pp0, pp1a, pp1b, pp1s, pp2;
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a = int128_make64(ai);
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b = int128_make64(bi);
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pp0 = (uint64_t)int128_getw0(a) * (uint64_t)int128_getw0(b);
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pp1a = (uint64_t)int128_getw1(a) * (uint64_t)int128_getw0(b);
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pp1b = (uint64_t)int128_getw1(b) * (uint64_t)int128_getw0(a);
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pp2 = (uint64_t)int128_getw1(a) * (uint64_t)int128_getw1(b);
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pp1s = pp1a + pp1b;
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if ((pp1s < pp1a) || (pp1s < pp1b)) {
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pp2 += (1ULL << 32);
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}
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uint64_t ret_low = pp0 + (pp1s << 32);
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if ((ret_low < pp0) || (ret_low < (pp1s << 32))) {
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pp2 += 1;
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}
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return int128_make128(ret_low, pp2 + (pp1s >> 32));
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}
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static Int128 int128_sub_borrow(Int128 a, Int128 b, int borrow)
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{
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Int128 ret = int128_sub(a, b);
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if (borrow != 0) {
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ret = int128_sub(ret, int128_one());
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}
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return ret;
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}
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typedef struct {
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Int128 mant;
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int32_t exp;
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uint8_t sign;
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uint8_t guard;
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uint8_t round;
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uint8_t sticky;
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} Accum;
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static void accum_init(Accum *p)
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{
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p->mant = int128_zero();
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p->exp = 0;
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p->sign = 0;
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p->guard = 0;
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p->round = 0;
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p->sticky = 0;
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}
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static Accum accum_norm_left(Accum a)
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{
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a.exp--;
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a.mant = int128_lshift(a.mant, 1);
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a.mant = int128_or(a.mant, int128_make64(a.guard));
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a.guard = a.round;
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a.round = a.sticky;
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return a;
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}
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/* This function is marked inline for performance reasons */
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static inline Accum accum_norm_right(Accum a, int amt)
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{
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if (amt > 130) {
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a.sticky |=
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a.round | a.guard | int128_nz(a.mant);
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a.guard = a.round = 0;
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a.mant = int128_zero();
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a.exp += amt;
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return a;
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}
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while (amt >= 64) {
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a.sticky |= a.round | a.guard | (int128_getlo(a.mant) != 0);
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a.guard = (int128_getlo(a.mant) >> 63) & 1;
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a.round = (int128_getlo(a.mant) >> 62) & 1;
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a.mant = int128_make64(int128_gethi(a.mant));
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a.exp += 64;
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amt -= 64;
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}
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while (amt > 0) {
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a.exp++;
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a.sticky |= a.round;
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a.round = a.guard;
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a.guard = int128_getlo(a.mant) & 1;
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a.mant = int128_rshift(a.mant, 1);
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amt--;
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}
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return a;
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}
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/*
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* On the add/sub, we need to be able to shift out lots of bits, but need a
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* sticky bit for what was shifted out, I think.
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*/
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static Accum accum_add(Accum a, Accum b);
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static Accum accum_sub(Accum a, Accum b, int negate)
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{
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Accum ret;
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accum_init(&ret);
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int borrow;
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if (a.sign != b.sign) {
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b.sign = !b.sign;
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return accum_add(a, b);
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}
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if (b.exp > a.exp) {
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/* small - big == - (big - small) */
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return accum_sub(b, a, !negate);
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}
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if ((b.exp == a.exp) && (int128_gt(b.mant, a.mant))) {
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/* small - big == - (big - small) */
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return accum_sub(b, a, !negate);
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}
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while (a.exp > b.exp) {
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/* Try to normalize exponents: shrink a exponent and grow mantissa */
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if (int128_gethi(a.mant) & (1ULL << 62)) {
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/* Can't grow a any more */
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break;
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} else {
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a = accum_norm_left(a);
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}
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}
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while (a.exp > b.exp) {
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/* Try to normalize exponents: grow b exponent and shrink mantissa */
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/* Keep around shifted out bits... we might need those later */
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b = accum_norm_right(b, a.exp - b.exp);
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}
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if ((int128_gt(b.mant, a.mant))) {
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return accum_sub(b, a, !negate);
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}
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/* OK, now things should be normalized! */
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ret.sign = a.sign;
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ret.exp = a.exp;
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assert(!int128_gt(b.mant, a.mant));
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borrow = (b.round << 2) | (b.guard << 1) | b.sticky;
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ret.mant = int128_sub_borrow(a.mant, b.mant, (borrow != 0));
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borrow = 0 - borrow;
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ret.guard = (borrow >> 2) & 1;
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ret.round = (borrow >> 1) & 1;
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ret.sticky = (borrow >> 0) & 1;
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if (negate) {
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ret.sign = !ret.sign;
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}
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return ret;
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}
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static Accum accum_add(Accum a, Accum b)
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{
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Accum ret;
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accum_init(&ret);
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if (a.sign != b.sign) {
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b.sign = !b.sign;
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return accum_sub(a, b, 0);
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}
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if (b.exp > a.exp) {
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/* small + big == (big + small) */
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return accum_add(b, a);
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}
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if ((b.exp == a.exp) && int128_gt(b.mant, a.mant)) {
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/* small + big == (big + small) */
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return accum_add(b, a);
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}
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while (a.exp > b.exp) {
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/* Try to normalize exponents: shrink a exponent and grow mantissa */
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if (int128_gethi(a.mant) & (1ULL << 62)) {
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/* Can't grow a any more */
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break;
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} else {
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a = accum_norm_left(a);
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}
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}
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while (a.exp > b.exp) {
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/* Try to normalize exponents: grow b exponent and shrink mantissa */
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/* Keep around shifted out bits... we might need those later */
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b = accum_norm_right(b, a.exp - b.exp);
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}
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/* OK, now things should be normalized! */
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if (int128_gt(b.mant, a.mant)) {
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return accum_add(b, a);
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};
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ret.sign = a.sign;
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ret.exp = a.exp;
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assert(!int128_gt(b.mant, a.mant));
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ret.mant = int128_add(a.mant, b.mant);
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ret.guard = b.guard;
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ret.round = b.round;
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ret.sticky = b.sticky;
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return ret;
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}
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/* Return an infinity with requested sign */
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static float64 infinite_float64(uint8_t sign)
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{
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if (sign) {
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return make_float64(DF_MINUS_INF);
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} else {
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return make_float64(DF_INF);
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}
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}
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/* Return a maximum finite value with requested sign */
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static float64 maxfinite_float64(uint8_t sign)
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{
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if (sign) {
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return make_float64(DF_MINUS_MAXF);
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} else {
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return make_float64(DF_MAXF);
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}
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}
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/* Return a zero value with requested sign */
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static float64 zero_float64(uint8_t sign)
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{
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if (sign) {
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return make_float64(0x8000000000000000);
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} else {
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return float64_zero;
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}
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}
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/* Return an infinity with the requested sign */
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float32 infinite_float32(uint8_t sign)
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{
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if (sign) {
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return make_float32(SF_MINUS_INF);
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} else {
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return make_float32(SF_INF);
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}
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}
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/* Return a maximum finite value with the requested sign */
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static float32 maxfinite_float32(uint8_t sign)
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{
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if (sign) {
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return make_float32(SF_MINUS_MAXF);
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} else {
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return make_float32(SF_MAXF);
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}
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}
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/* Return a zero value with requested sign */
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static float32 zero_float32(uint8_t sign)
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{
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if (sign) {
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return make_float32(0x80000000);
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} else {
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return float32_zero;
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}
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}
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#define GEN_XF_ROUND(SUFFIX, MANTBITS, INF_EXP, INTERNAL_TYPE) \
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static SUFFIX accum_round_##SUFFIX(Accum a, float_status * fp_status) \
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{ \
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if ((int128_gethi(a.mant) == 0) && (int128_getlo(a.mant) == 0) \
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&& ((a.guard | a.round | a.sticky) == 0)) { \
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/* result zero */ \
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switch (fp_status->float_rounding_mode) { \
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case float_round_down: \
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return zero_##SUFFIX(1); \
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default: \
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return zero_##SUFFIX(0); \
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} \
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} \
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/* Normalize right */ \
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/* We want MANTBITS bits of mantissa plus the leading one. */ \
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/* That means that we want MANTBITS+1 bits, or 0x000000000000FF_FFFF */ \
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/* So we need to normalize right while the high word is non-zero and \
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* while the low word is nonzero when masked with 0xffe0_0000_0000_0000 */ \
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while ((int128_gethi(a.mant) != 0) || \
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((int128_getlo(a.mant) >> (MANTBITS + 1)) != 0)) { \
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a = accum_norm_right(a, 1); \
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} \
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/* \
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* OK, now normalize left \
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* We want to normalize left until we have a leading one in bit 24 \
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* Theoretically, we only need to shift a maximum of one to the left if we \
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* shifted out lots of bits from B, or if we had no shift / 1 shift sticky \
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* shoudl be 0 \
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*/ \
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while ((int128_getlo(a.mant) & (1ULL << MANTBITS)) == 0) { \
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a = accum_norm_left(a); \
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} \
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/* \
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* OK, now we might need to denormalize because of potential underflow. \
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* We need to do this before rounding, and rounding might make us normal \
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* again \
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*/ \
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while (a.exp <= 0) { \
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a = accum_norm_right(a, 1 - a.exp); \
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/* \
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* Do we have underflow? \
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* That's when we get an inexact answer because we ran out of bits \
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* in a denormal. \
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*/ \
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if (a.guard || a.round || a.sticky) { \
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float_raise(float_flag_underflow, fp_status); \
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} \
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} \
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/* OK, we're relatively canonical... now we need to round */ \
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if (a.guard || a.round || a.sticky) { \
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float_raise(float_flag_inexact, fp_status); \
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switch (fp_status->float_rounding_mode) { \
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case float_round_to_zero: \
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/* Chop and we're done */ \
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break; \
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case float_round_up: \
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if (a.sign == 0) { \
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a.mant = int128_add(a.mant, int128_one()); \
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} \
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break; \
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case float_round_down: \
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if (a.sign != 0) { \
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a.mant = int128_add(a.mant, int128_one()); \
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} \
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break; \
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default: \
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if (a.round || a.sticky) { \
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/* round up if guard is 1, down if guard is zero */ \
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a.mant = int128_add(a.mant, int128_make64(a.guard)); \
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} else if (a.guard) { \
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/* exactly .5, round up if odd */ \
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a.mant = int128_add(a.mant, int128_and(a.mant, int128_one())); \
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} \
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break; \
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} \
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} \
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/* \
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* OK, now we might have carried all the way up. \
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* So we might need to shr once \
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* at least we know that the lsb should be zero if we rounded and \
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* got a carry out... \
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*/ \
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if ((int128_getlo(a.mant) >> (MANTBITS + 1)) != 0) { \
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a = accum_norm_right(a, 1); \
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} \
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/* Overflow? */ \
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if (a.exp >= INF_EXP) { \
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/* Yep, inf result */ \
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float_raise(float_flag_overflow, fp_status); \
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float_raise(float_flag_inexact, fp_status); \
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switch (fp_status->float_rounding_mode) { \
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case float_round_to_zero: \
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return maxfinite_##SUFFIX(a.sign); \
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case float_round_up: \
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if (a.sign == 0) { \
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return infinite_##SUFFIX(a.sign); \
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} else { \
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return maxfinite_##SUFFIX(a.sign); \
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} \
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case float_round_down: \
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if (a.sign != 0) { \
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return infinite_##SUFFIX(a.sign); \
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} else { \
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return maxfinite_##SUFFIX(a.sign); \
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} \
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default: \
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return infinite_##SUFFIX(a.sign); \
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} \
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} \
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/* Underflow? */ \
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if (int128_getlo(a.mant) & (1ULL << MANTBITS)) { \
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/* Leading one means: No, we're normal. So, we should be done... */ \
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INTERNAL_TYPE ret; \
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ret.i = 0; \
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ret.sign = a.sign; \
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ret.exp = a.exp; \
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ret.mant = int128_getlo(a.mant); \
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return ret.i; \
|
|
} \
|
|
assert(a.exp == 1); \
|
|
INTERNAL_TYPE ret; \
|
|
ret.i = 0; \
|
|
ret.sign = a.sign; \
|
|
ret.exp = 0; \
|
|
ret.mant = int128_getlo(a.mant); \
|
|
return ret.i; \
|
|
}
|
|
|
|
GEN_XF_ROUND(float64, DF_MANTBITS, DF_INF_EXP, Double)
|
|
GEN_XF_ROUND(float32, SF_MANTBITS, SF_INF_EXP, Float)
|
|
|
|
static bool is_inf_prod(float64 a, float64 b)
|
|
{
|
|
return ((float64_is_infinity(a) && float64_is_infinity(b)) ||
|
|
(float64_is_infinity(a) && is_finite(b) && (!float64_is_zero(b))) ||
|
|
(float64_is_infinity(b) && is_finite(a) && (!float64_is_zero(a))));
|
|
}
|
|
|
|
static float64 special_fma(float64 a, float64 b, float64 c,
|
|
float_status *fp_status)
|
|
{
|
|
float64 ret = make_float64(0);
|
|
|
|
/*
|
|
* If A multiplied by B is an exact infinity and C is also an infinity
|
|
* but with the opposite sign, FMA returns NaN and raises invalid.
|
|
*/
|
|
uint8_t a_sign = float64_is_neg(a);
|
|
uint8_t b_sign = float64_is_neg(b);
|
|
uint8_t c_sign = float64_is_neg(c);
|
|
if (is_inf_prod(a, b) && float64_is_infinity(c)) {
|
|
if ((a_sign ^ b_sign) != c_sign) {
|
|
ret = make_float64(DF_NAN);
|
|
float_raise(float_flag_invalid, fp_status);
|
|
return ret;
|
|
}
|
|
}
|
|
if ((float64_is_infinity(a) && float64_is_zero(b)) ||
|
|
(float64_is_zero(a) && float64_is_infinity(b))) {
|
|
ret = make_float64(DF_NAN);
|
|
float_raise(float_flag_invalid, fp_status);
|
|
return ret;
|
|
}
|
|
/*
|
|
* If none of the above checks are true and C is a NaN,
|
|
* a NaN shall be returned
|
|
* If A or B are NaN, a NAN shall be returned.
|
|
*/
|
|
if (float64_is_any_nan(a) ||
|
|
float64_is_any_nan(b) ||
|
|
float64_is_any_nan(c)) {
|
|
if (float64_is_any_nan(a) && (fGETBIT(51, a) == 0)) {
|
|
float_raise(float_flag_invalid, fp_status);
|
|
}
|
|
if (float64_is_any_nan(b) && (fGETBIT(51, b) == 0)) {
|
|
float_raise(float_flag_invalid, fp_status);
|
|
}
|
|
if (float64_is_any_nan(c) && (fGETBIT(51, c) == 0)) {
|
|
float_raise(float_flag_invalid, fp_status);
|
|
}
|
|
ret = make_float64(DF_NAN);
|
|
return ret;
|
|
}
|
|
/*
|
|
* We have checked for adding opposite-signed infinities.
|
|
* Other infinities return infinity with the correct sign
|
|
*/
|
|
if (float64_is_infinity(c)) {
|
|
ret = infinite_float64(c_sign);
|
|
return ret;
|
|
}
|
|
if (float64_is_infinity(a) || float64_is_infinity(b)) {
|
|
ret = infinite_float64(a_sign ^ b_sign);
|
|
return ret;
|
|
}
|
|
g_assert_not_reached();
|
|
}
|
|
|
|
static float32 special_fmaf(float32 a, float32 b, float32 c,
|
|
float_status *fp_status)
|
|
{
|
|
float64 aa, bb, cc;
|
|
aa = float32_to_float64(a, fp_status);
|
|
bb = float32_to_float64(b, fp_status);
|
|
cc = float32_to_float64(c, fp_status);
|
|
return float64_to_float32(special_fma(aa, bb, cc, fp_status), fp_status);
|
|
}
|
|
|
|
float32 internal_fmafx(float32 a, float32 b, float32 c, int scale,
|
|
float_status *fp_status)
|
|
{
|
|
Accum prod;
|
|
Accum acc;
|
|
Accum result;
|
|
accum_init(&prod);
|
|
accum_init(&acc);
|
|
accum_init(&result);
|
|
|
|
uint8_t a_sign = float32_is_neg(a);
|
|
uint8_t b_sign = float32_is_neg(b);
|
|
uint8_t c_sign = float32_is_neg(c);
|
|
if (float32_is_infinity(a) ||
|
|
float32_is_infinity(b) ||
|
|
float32_is_infinity(c)) {
|
|
return special_fmaf(a, b, c, fp_status);
|
|
}
|
|
if (float32_is_any_nan(a) ||
|
|
float32_is_any_nan(b) ||
|
|
float32_is_any_nan(c)) {
|
|
return special_fmaf(a, b, c, fp_status);
|
|
}
|
|
if ((scale == 0) && (float32_is_zero(a) || float32_is_zero(b))) {
|
|
float32 tmp = float32_mul(a, b, fp_status);
|
|
tmp = float32_add(tmp, c, fp_status);
|
|
return tmp;
|
|
}
|
|
|
|
/* (a * 2**b) * (c * 2**d) == a*c * 2**(b+d) */
|
|
prod.mant = int128_mul_6464(float32_getmant(a), float32_getmant(b));
|
|
|
|
/*
|
|
* Note: extracting the mantissa into an int is multiplying by
|
|
* 2**23, so adjust here
|
|
*/
|
|
prod.exp = float32_getexp(a) + float32_getexp(b) - SF_BIAS - 23;
|
|
prod.sign = a_sign ^ b_sign;
|
|
if (float32_is_zero(a) || float32_is_zero(b)) {
|
|
prod.exp = -2 * WAY_BIG_EXP;
|
|
}
|
|
if ((scale > 0) && float32_is_denormal(c)) {
|
|
acc.mant = int128_mul_6464(0, 0);
|
|
acc.exp = -WAY_BIG_EXP;
|
|
acc.sign = c_sign;
|
|
acc.sticky = 1;
|
|
result = accum_add(prod, acc);
|
|
} else if (!float32_is_zero(c)) {
|
|
acc.mant = int128_mul_6464(float32_getmant(c), 1);
|
|
acc.exp = float32_getexp(c);
|
|
acc.sign = c_sign;
|
|
result = accum_add(prod, acc);
|
|
} else {
|
|
result = prod;
|
|
}
|
|
result.exp += scale;
|
|
return accum_round_float32(result, fp_status);
|
|
}
|
|
|
|
float32 internal_mpyf(float32 a, float32 b, float_status *fp_status)
|
|
{
|
|
if (float32_is_zero(a) || float32_is_zero(b)) {
|
|
return float32_mul(a, b, fp_status);
|
|
}
|
|
return internal_fmafx(a, b, float32_zero, 0, fp_status);
|
|
}
|
|
|
|
float64 internal_mpyhh(float64 a, float64 b,
|
|
unsigned long long int accumulated,
|
|
float_status *fp_status)
|
|
{
|
|
Accum x;
|
|
unsigned long long int prod;
|
|
unsigned int sticky;
|
|
uint8_t a_sign, b_sign;
|
|
|
|
sticky = accumulated & 1;
|
|
accumulated >>= 1;
|
|
accum_init(&x);
|
|
if (float64_is_zero(a) ||
|
|
float64_is_any_nan(a) ||
|
|
float64_is_infinity(a)) {
|
|
return float64_mul(a, b, fp_status);
|
|
}
|
|
if (float64_is_zero(b) ||
|
|
float64_is_any_nan(b) ||
|
|
float64_is_infinity(b)) {
|
|
return float64_mul(a, b, fp_status);
|
|
}
|
|
x.mant = int128_mul_6464(accumulated, 1);
|
|
x.sticky = sticky;
|
|
prod = fGETUWORD(1, float64_getmant(a)) * fGETUWORD(1, float64_getmant(b));
|
|
x.mant = int128_add(x.mant, int128_mul_6464(prod, 0x100000000ULL));
|
|
x.exp = float64_getexp(a) + float64_getexp(b) - DF_BIAS - 20;
|
|
if (!float64_is_normal(a) || !float64_is_normal(b)) {
|
|
/* crush to inexact zero */
|
|
x.sticky = 1;
|
|
x.exp = -4096;
|
|
}
|
|
a_sign = float64_is_neg(a);
|
|
b_sign = float64_is_neg(b);
|
|
x.sign = a_sign ^ b_sign;
|
|
return accum_round_float64(x, fp_status);
|
|
}
|