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