qemu/target/hexagon/fma_emu.c

/*
 *  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);
}