source: mainline/uspace/lib/softfloat/mul.c@ 1b20da0

/*
 * Copyright (c) 2005 Josef Cejka
 * Copyright (c) 2011 Petr Koupy
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 *
 * - Redistributions of source code must retain the above copyright
 *   notice, this list of conditions and the following disclaimer.
 * - Redistributions in binary form must reproduce the above copyright
 *   notice, this list of conditions and the following disclaimer in the
 *   documentation and/or other materials provided with the distribution.
 * - The name of the author may not be used to endorse or promote products
 *   derived from this software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */

/** @addtogroup softfloat
 * @{
 */
/** @file Multiplication functions.
 */

#include "mul.h"
#include "comparison.h"
#include "common.h"

/** Multiply two single-precision floats.
 *
 * @param a First input operand.
 * @param b Second input operand.
 *
 * @return Result of multiplication.
 *
 */
float32 mul_float32(float32 a, float32 b)
{
        float32 result;
        uint64_t frac1, frac2;
        int32_t exp;
        
        result.parts.sign = a.parts.sign ^ b.parts.sign;
        
        if (is_float32_nan(a) || is_float32_nan(b)) {
                /* TODO: fix SigNaNs */
                if (is_float32_signan(a)) {
                        result.parts.fraction = a.parts.fraction;
                        result.parts.exp = a.parts.exp;
                        return result;
                }
                
                if (is_float32_signan(b)) { /* TODO: fix SigNaN */
                        result.parts.fraction = b.parts.fraction;
                        result.parts.exp = b.parts.exp;
                        return result;
                }
                
                /* set NaN as result */
                result.bin = FLOAT32_NAN;
                return result;
        }
        
        if (is_float32_infinity(a)) {
                if (is_float32_zero(b)) {
                        /* FIXME: zero * infinity */
                        result.bin = FLOAT32_NAN;
                        return result;
                }
                
                result.parts.fraction = a.parts.fraction;
                result.parts.exp = a.parts.exp;
                return result;
        }
        
        if (is_float32_infinity(b)) {
                if (is_float32_zero(a)) {
                        /* FIXME: zero * infinity */
                        result.bin = FLOAT32_NAN;
                        return result;
                }
                
                result.parts.fraction = b.parts.fraction;
                result.parts.exp = b.parts.exp;
                return result;
        }
        
        /* exp is signed so we can easy detect underflow */
        exp = a.parts.exp + b.parts.exp;
        exp -= FLOAT32_BIAS;
        
        if (exp >= FLOAT32_MAX_EXPONENT) {
                /* FIXME: overflow */
                /* set infinity as result */
                result.bin = FLOAT32_INF;
                result.parts.sign = a.parts.sign ^ b.parts.sign;
                return result;
        }
        
        if (exp < 0) {
                /* FIXME: underflow */
                /* return signed zero */
                result.parts.fraction = 0x0;
                result.parts.exp = 0x0;
                return result;
        }
        
        frac1 = a.parts.fraction;
        if (a.parts.exp > 0) {
                frac1 |= FLOAT32_HIDDEN_BIT_MASK;
        } else {
                ++exp;
        }
        
        frac2 = b.parts.fraction;
        
        if (b.parts.exp > 0) {
                frac2 |= FLOAT32_HIDDEN_BIT_MASK;
        } else {
                ++exp;
        }
        
        frac1 <<= 1; /* one bit space for rounding */
        
        frac1 = frac1 * frac2;
        
        /* round and return */
        while ((exp < FLOAT32_MAX_EXPONENT) &&
            (frac1 >= (1 << (FLOAT32_FRACTION_SIZE + 2)))) {
                /* 23 bits of fraction + one more for hidden bit (all shifted 1 bit left) */
                ++exp;
                frac1 >>= 1;
        }
        
        /* rounding */
        /* ++frac1; FIXME: not works - without it is ok */
        frac1 >>= 1; /* shift off rounding space */
        
        if ((exp < FLOAT32_MAX_EXPONENT) &&
            (frac1 >= (1 << (FLOAT32_FRACTION_SIZE + 1)))) {
                ++exp;
                frac1 >>= 1;
        }
        
        if (exp >= FLOAT32_MAX_EXPONENT) {
                /* TODO: fix overflow */
                /* return infinity*/
                result.parts.exp = FLOAT32_MAX_EXPONENT;
                result.parts.fraction = 0x0;
                return result;
        }
        
        exp -= FLOAT32_FRACTION_SIZE;
        
        if (exp <= FLOAT32_FRACTION_SIZE) {
                /* denormalized number */
                frac1 >>= 1; /* denormalize */
                
                while ((frac1 > 0) && (exp < 0)) {
                        frac1 >>= 1;
                        ++exp;
                }
                
                if (frac1 == 0) {
                        /* FIXME : underflow */
                        result.parts.exp = 0;
                        result.parts.fraction = 0;
                        return result;
                }
        }
        
        result.parts.exp = exp;
        result.parts.fraction = frac1 & ((1 << FLOAT32_FRACTION_SIZE) - 1);
        
        return result;
}

/** Multiply two double-precision floats.
 *
 * @param a First input operand.
 * @param b Second input operand.
 *
 * @return Result of multiplication.
 *
 */
float64 mul_float64(float64 a, float64 b)
{
        float64 result;
        uint64_t frac1, frac2;
        int32_t exp;
        
        result.parts.sign = a.parts.sign ^ b.parts.sign;
        
        if (is_float64_nan(a) || is_float64_nan(b)) {
                /* TODO: fix SigNaNs */
                if (is_float64_signan(a)) {
                        result.parts.fraction = a.parts.fraction;
                        result.parts.exp = a.parts.exp;
                        return result;
                }
                if (is_float64_signan(b)) { /* TODO: fix SigNaN */
                        result.parts.fraction = b.parts.fraction;
                        result.parts.exp = b.parts.exp;
                        return result;
                }
                /* set NaN as result */
                result.bin = FLOAT64_NAN;
                return result;
        }
        
        if (is_float64_infinity(a)) {
                if (is_float64_zero(b)) {
                        /* FIXME: zero * infinity */
                        result.bin = FLOAT64_NAN;
                        return result;
                }
                result.parts.fraction = a.parts.fraction;
                result.parts.exp = a.parts.exp;
                return result;
        }
        
        if (is_float64_infinity(b)) {
                if (is_float64_zero(a)) {
                        /* FIXME: zero * infinity */
                        result.bin = FLOAT64_NAN;
                        return result;
                }
                result.parts.fraction = b.parts.fraction;
                result.parts.exp = b.parts.exp;
                return result;
        }
        
        /* exp is signed so we can easy detect underflow */
        exp = a.parts.exp + b.parts.exp - FLOAT64_BIAS;
        
        frac1 = a.parts.fraction;
        
        if (a.parts.exp > 0) {
                frac1 |= FLOAT64_HIDDEN_BIT_MASK;
        } else {
                ++exp;
        }
        
        frac2 = b.parts.fraction;
        
        if (b.parts.exp > 0) {
                frac2 |= FLOAT64_HIDDEN_BIT_MASK;
        } else {
                ++exp;
        }
        
        frac1 <<= (64 - FLOAT64_FRACTION_SIZE - 1);
        frac2 <<= (64 - FLOAT64_FRACTION_SIZE - 2);
        
        mul64(frac1, frac2, &frac1, &frac2);
        
        frac1 |= (frac2 != 0);
        if (frac1 & (0x1ll << 62)) {
                frac1 <<= 1;
                exp--;
        }
        
        result = finish_float64(exp, frac1, result.parts.sign);
        return result;
}

/** Multiply two quadruple-precision floats.
 *
 * @param a First input operand.
 * @param b Second input operand.
 *
 * @return Result of multiplication.
 *
 */
float128 mul_float128(float128 a, float128 b)
{
        float128 result;
        uint64_t frac1_hi, frac1_lo, frac2_hi, frac2_lo, tmp_hi, tmp_lo;
        int32_t exp;
        
        result.parts.sign = a.parts.sign ^ b.parts.sign;
        
        if (is_float128_nan(a) || is_float128_nan(b)) {
                /* TODO: fix SigNaNs */
                if (is_float128_signan(a)) {
                        result.parts.frac_hi = a.parts.frac_hi;
                        result.parts.frac_lo = a.parts.frac_lo;
                        result.parts.exp = a.parts.exp;
                        return result;
                }
                if (is_float128_signan(b)) { /* TODO: fix SigNaN */
                        result.parts.frac_hi = b.parts.frac_hi;
                        result.parts.frac_lo = b.parts.frac_lo;
                        result.parts.exp = b.parts.exp;
                        return result;
                }
                /* set NaN as result */
                result.bin.hi = FLOAT128_NAN_HI;
                result.bin.lo = FLOAT128_NAN_LO;
                return result;
        }
        
        if (is_float128_infinity(a)) {
                if (is_float128_zero(b)) {
                        /* FIXME: zero * infinity */
                        result.bin.hi = FLOAT128_NAN_HI;
                        result.bin.lo = FLOAT128_NAN_LO;
                        return result;
                }
                result.parts.frac_hi = a.parts.frac_hi;
                result.parts.frac_lo = a.parts.frac_lo;
                result.parts.exp = a.parts.exp;
                return result;
        }
        
        if (is_float128_infinity(b)) {
                if (is_float128_zero(a)) {
                        /* FIXME: zero * infinity */
                        result.bin.hi = FLOAT128_NAN_HI;
                        result.bin.lo = FLOAT128_NAN_LO;
                        return result;
                }
                result.parts.frac_hi = b.parts.frac_hi;
                result.parts.frac_lo = b.parts.frac_lo;
                result.parts.exp = b.parts.exp;
                return result;
        }
        
        /* exp is signed so we can easy detect underflow */
        exp = a.parts.exp + b.parts.exp - FLOAT128_BIAS - 1;
        
        frac1_hi = a.parts.frac_hi;
        frac1_lo = a.parts.frac_lo;
        
        if (a.parts.exp > 0) {
                or128(frac1_hi, frac1_lo,
                    FLOAT128_HIDDEN_BIT_MASK_HI, FLOAT128_HIDDEN_BIT_MASK_LO,
                    &frac1_hi, &frac1_lo);
        } else {
                ++exp;
        }
        
        frac2_hi = b.parts.frac_hi;
        frac2_lo = b.parts.frac_lo;
        
        if (b.parts.exp > 0) {
                or128(frac2_hi, frac2_lo,
                    FLOAT128_HIDDEN_BIT_MASK_HI, FLOAT128_HIDDEN_BIT_MASK_LO,
                    &frac2_hi, &frac2_lo);
        } else {
                ++exp;
        }
        
        lshift128(frac2_hi, frac2_lo,
            128 - FLOAT128_FRACTION_SIZE, &frac2_hi, &frac2_lo);
        
        tmp_hi = frac1_hi;
        tmp_lo = frac1_lo;
        mul128(frac1_hi, frac1_lo, frac2_hi, frac2_lo,
            &frac1_hi, &frac1_lo, &frac2_hi, &frac2_lo);
        add128(frac1_hi, frac1_lo, tmp_hi, tmp_lo, &frac1_hi, &frac1_lo);
        frac2_hi |= (frac2_lo != 0x0ll);
        
        if ((FLOAT128_HIDDEN_BIT_MASK_HI << 1) <= frac1_hi) {
                frac2_hi >>= 1;
                if (frac1_lo & 0x1ll) {
                        frac2_hi |= (0x1ull < 64);
                }
                rshift128(frac1_hi, frac1_lo, 1, &frac1_hi, &frac1_lo);
                ++exp;
        }
        
        result = finish_float128(exp, frac1_hi, frac1_lo, result.parts.sign, frac2_hi);
        return result;
}

#ifdef float32_t

float32_t __mulsf3(float32_t a, float32_t b)
{
        float32_u ua;
        ua.val = a;
        
        float32_u ub;
        ub.val = b;
        
        float32_u res;
        res.data = mul_float32(ua.data, ub.data);
        
        return res.val;
}

float32_t __aeabi_fmul(float32_t a, float32_t b)
{
        float32_u ua;
        ua.val = a;
        
        float32_u ub;
        ub.val = b;
        
        float32_u res;
        res.data = mul_float32(ua.data, ub.data);
        
        return res.val;
}

#endif

#ifdef float64_t

float64_t __muldf3(float64_t a, float64_t b)
{
        float64_u ua;
        ua.val = a;
        
        float64_u ub;
        ub.val = b;
        
        float64_u res;
        res.data = mul_float64(ua.data, ub.data);
        
        return res.val;
}

float64_t __aeabi_dmul(float64_t a, float64_t b)
{
        float64_u ua;
        ua.val = a;
        
        float64_u ub;
        ub.val = b;
        
        float64_u res;
        res.data = mul_float64(ua.data, ub.data);
        
        return res.val;
}

#endif

#ifdef float128_t

float128_t __multf3(float128_t a, float128_t b)
{
        float128_u ua;
        ua.val = a;
        
        float128_u ub;
        ub.val = b;
        
        float128_u res;
        res.data = mul_float128(ua.data, ub.data);
        
        return res.val;
}

void _Qp_mul(float128_t *c, float128_t *a, float128_t *b)
{
        *c = __multf3(*a, *b);
}

#endif

/** @}
 */