/* * 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 . */ #include "qemu/osdep.h" #include "qemu/int128.h" #include "fpu/softfloat.h" #include "macros.h" #include "conv_emu.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 inline 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 inline 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 inline uint32_t int128_getw0(Int128 x) { return int128_getlo(x); } static inline uint32_t int128_getw1(Int128 x) { return int128_getlo(x) >> 32; } static inline 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 inline 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 inline 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 inline 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; } 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 inline 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 inline 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 inline 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 inline 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 inline 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 inline 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 inline 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 inline 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 inline 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); }