mul.c

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/*
 * Copyright (c) 2005 Josef Cejka
 * 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.
 */

#include <sftypes.h>
#include <mul.h>
#include <comparison.h>
#include <common.h>

float32 mulFloat32(float32 a, float32 b)
{
        float32 result;
        uint64_t frac1, frac2;
        int32_t exp;

        result.parts.sign = a.parts.sign ^ b.parts.sign;
        
        if (isFloat32NaN(a) || isFloat32NaN(b) ) {
                /* TODO: fix SigNaNs */
                if (isFloat32SigNaN(a)) {
                        result.parts.fraction = a.parts.fraction;
                        result.parts.exp = a.parts.exp;
                        return result;
                };
                if (isFloat32SigNaN(b)) { /* TODO: fix SigNaN */
                        result.parts.fraction = b.parts.fraction;
                        result.parts.exp = b.parts.exp;
                        return result;
                };
                /* set NaN as result */
                result.binary = FLOAT32_NAN;
                return result;
        };
                
        if (isFloat32Infinity(a)) { 
                if (isFloat32Zero(b)) {
                        /* FIXME: zero * infinity */
                        result.binary = FLOAT32_NAN;
                        return result;
                }
                result.parts.fraction = a.parts.fraction;
                result.parts.exp = a.parts.exp;
                return result;
        }

        if (isFloat32Infinity(b)) { 
                if (isFloat32Zero(a)) {
                        /* FIXME: zero * infinity */
                        result.binary = 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.binary = 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;  
        
}

float64 mulFloat64(float64 a, float64 b)
{
        float64 result;
        uint64_t frac1, frac2;
        int32_t exp;

        result.parts.sign = a.parts.sign ^ b.parts.sign;
        
        if (isFloat64NaN(a) || isFloat64NaN(b) ) {
                /* TODO: fix SigNaNs */
                if (isFloat64SigNaN(a)) {
                        result.parts.fraction = a.parts.fraction;
                        result.parts.exp = a.parts.exp;
                        return result;
                };
                if (isFloat64SigNaN(b)) { /* TODO: fix SigNaN */
                        result.parts.fraction = b.parts.fraction;
                        result.parts.exp = b.parts.exp;
                        return result;
                };
                /* set NaN as result */
                result.binary = FLOAT64_NAN;
                return result;
        };
                
        if (isFloat64Infinity(a)) { 
                if (isFloat64Zero(b)) {
                        /* FIXME: zero * infinity */
                        result.binary = FLOAT64_NAN;
                        return result;
                }
                result.parts.fraction = a.parts.fraction;
                result.parts.exp = a.parts.exp;
                return result;
        }

        if (isFloat64Infinity(b)) { 
                if (isFloat64Zero(a)) {
                        /* FIXME: zero * infinity */
                        result.binary = 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);

        mul64integers(frac1, frac2, &frac1, &frac2);

        frac2 |= (frac1 != 0);
        if (frac2 & (0x1ll << 62)) {
                frac2 <<= 1;
                exp--;
        }

        result = finishFloat64(exp, frac2, result.parts.sign);
        return result;
}

void mul64integers(uint64_t a,uint64_t b, uint64_t *lo, uint64_t *hi)
{
        uint64_t low, high, middle1, middle2;
        uint32_t alow, blow;

        alow = a & 0xFFFFFFFF;
        blow = b & 0xFFFFFFFF;
        
        a >>= 32;
        b >>= 32;
        
        low = ((uint64_t)alow) * blow;
        middle1 = a * blow;
        middle2 = alow * b;
        high = a * b;

        middle1 += middle2;
        high += (((uint64_t)(middle1 < middle2)) << 32) + (middle1 >> 32);
        middle1 <<= 32;
        low += middle1;
        high += (low < middle1);
        *lo = low;
        *hi = high;
        
        return;
}

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