softfloat.c

說明FPU的演算法以及浮點運算式中的加減乘除

    }
    return packFloat64( aSign, aExp + 0x380, ( (bits64) aSig )<<29 );

}

#ifdef FLOATX80

/*----------------------------------------------------------------------------
| Returns the result of converting the single-precision floating-point value
| `a' to the extended double-precision floating-point format.  The conversion
| is performed according to the IEC/IEEE Standard for Binary Floating-Point
| Arithmetic.
*----------------------------------------------------------------------------*/

floatx80 float32_to_floatx80( float32 a )
{
    flag aSign;
    int16 aExp;
    bits32 aSig;

    aSig = extractFloat32Frac( a );
    aExp = extractFloat32Exp( a );
    aSign = extractFloat32Sign( a );
    if ( aExp == 0xFF ) {
        if ( aSig ) return commonNaNToFloatx80( float32ToCommonNaN( a ) );
        return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
    }
    if ( aExp == 0 ) {
        if ( aSig == 0 ) return packFloatx80( aSign, 0, 0 );
        normalizeFloat32Subnormal( aSig, &aExp, &aSig );
    }
    aSig |= 0x00800000;
    return packFloatx80( aSign, aExp + 0x3F80, ( (bits64) aSig )<<40 );

}

#endif

#ifdef FLOAT128

/*----------------------------------------------------------------------------
| Returns the result of converting the single-precision floating-point value
| `a' to the double-precision floating-point format.  The conversion is
| performed according to the IEC/IEEE Standard for Binary Floating-Point
| Arithmetic.
*----------------------------------------------------------------------------*/

float128 float32_to_float128( float32 a )
{
    flag aSign;
    int16 aExp;
    bits32 aSig;

    aSig = extractFloat32Frac( a );
    aExp = extractFloat32Exp( a );
    aSign = extractFloat32Sign( a );
    if ( aExp == 0xFF ) {
        if ( aSig ) return commonNaNToFloat128( float32ToCommonNaN( a ) );
        return packFloat128( aSign, 0x7FFF, 0, 0 );
    }
    if ( aExp == 0 ) {
        if ( aSig == 0 ) return packFloat128( aSign, 0, 0, 0 );
        normalizeFloat32Subnormal( aSig, &aExp, &aSig );
        --aExp;
    }
    return packFloat128( aSign, aExp + 0x3F80, ( (bits64) aSig )<<25, 0 );

}

#endif

/*----------------------------------------------------------------------------
| Rounds the single-precision floating-point value `a' to an integer, and
| returns the result as a single-precision floating-point value.  The
| operation is performed according to the IEC/IEEE Standard for Binary
| Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/

float32 float32_round_to_int( float32 a )
{
    flag aSign;
    int16 aExp;
    bits32 lastBitMask, roundBitsMask;
    int8 roundingMode;
    float32 z;

    aExp = extractFloat32Exp( a );
    if ( 0x96 <= aExp ) {
        if ( ( aExp == 0xFF ) && extractFloat32Frac( a ) ) {
            return propagateFloat32NaN( a, a );
        }
        return a;
    }
    if ( aExp <= 0x7E ) {
        if ( (bits32) ( a<<1 ) == 0 ) return a;
        float_exception_flags |= float_flag_inexact;
        aSign = extractFloat32Sign( a );
        switch ( float_rounding_mode ) {
         case float_round_nearest_even:
            if ( ( aExp == 0x7E ) && extractFloat32Frac( a ) ) {
                return packFloat32( aSign, 0x7F, 0 );
            }
            break;
         case float_round_down:
            return aSign ? 0xBF800000 : 0;
         case float_round_up:
            return aSign ? 0x80000000 : 0x3F800000;
        }
        return packFloat32( aSign, 0, 0 );
    }
    lastBitMask = 1;
    lastBitMask <<= 0x96 - aExp;
    roundBitsMask = lastBitMask - 1;
    z = a;
    roundingMode = float_rounding_mode;
    if ( roundingMode == float_round_nearest_even ) {
        z += lastBitMask>>1;
        if ( ( z & roundBitsMask ) == 0 ) z &= ~ lastBitMask;
    }
    else if ( roundingMode != float_round_to_zero ) {
        if ( extractFloat32Sign( z ) ^ ( roundingMode == float_round_up ) ) {
            z += roundBitsMask;
        }
    }
    z &= ~ roundBitsMask;
    if ( z != a ) float_exception_flags |= float_flag_inexact;
    return z;

}

/*----------------------------------------------------------------------------
| Returns the result of adding the absolute values of the single-precision
| floating-point values `a' and `b'.  If `zSign' is 1, the sum is negated
| before being returned.  `zSign' is ignored if the result is a NaN.
| The addition is performed according to the IEC/IEEE Standard for Binary
| Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/

static float32 addFloat32Sigs( float32 a, float32 b, flag zSign )
{
    int16 aExp, bExp, zExp;
    bits32 aSig, bSig, zSig;
    int16 expDiff;

    aSig = extractFloat32Frac( a );
    aExp = extractFloat32Exp( a );
    bSig = extractFloat32Frac( b );
    bExp = extractFloat32Exp( b );
    expDiff = aExp - bExp;
    aSig <<= 6;
    bSig <<= 6;
    if ( 0 < expDiff ) {
        if ( aExp == 0xFF ) {
            if ( aSig ) return propagateFloat32NaN( a, b );
            return a;
        }
        if ( bExp == 0 ) {
            --expDiff;
        }
        else {
            bSig |= 0x20000000;
        }
        shift32RightJamming( bSig, expDiff, &bSig );
        zExp = aExp;
    }
    else if ( expDiff < 0 ) {
        if ( bExp == 0xFF ) {
            if ( bSig ) return propagateFloat32NaN( a, b );
            return packFloat32( zSign, 0xFF, 0 );
        }
        if ( aExp == 0 ) {
            ++expDiff;
        }
        else {
            aSig |= 0x20000000;
        }
        shift32RightJamming( aSig, - expDiff, &aSig );
        zExp = bExp;
    }
    else {
        if ( aExp == 0xFF ) {
            if ( aSig | bSig ) return propagateFloat32NaN( a, b );
            return a;
        }
        if ( aExp == 0 ) return packFloat32( zSign, 0, ( aSig + bSig )>>6 );
        zSig = 0x40000000 + aSig + bSig;
        zExp = aExp;
        goto roundAndPack;
    }
    aSig |= 0x20000000;
    zSig = ( aSig + bSig )<<1;
    --zExp;
    if ( (sbits32) zSig < 0 ) {
        zSig = aSig + bSig;
        ++zExp;
    }
 roundAndPack:
    return roundAndPackFloat32( zSign, zExp, zSig );

}

/*----------------------------------------------------------------------------
| Returns the result of subtracting the absolute values of the single-
| precision floating-point values `a' and `b'.  If `zSign' is 1, the
| difference is negated before being returned.  `zSign' is ignored if the
| result is a NaN.  The subtraction is performed according to the IEC/IEEE
| Standard for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/

static float32 subFloat32Sigs( float32 a, float32 b, flag zSign )
{
    int16 aExp, bExp, zExp;
    bits32 aSig, bSig, zSig;
    int16 expDiff;

    aSig = extractFloat32Frac( a );
    aExp = extractFloat32Exp( a );
    bSig = extractFloat32Frac( b );
    bExp = extractFloat32Exp( b );
    expDiff = aExp - bExp;
    aSig <<= 7;
    bSig <<= 7;
    if ( 0 < expDiff ) goto aExpBigger;
    if ( expDiff < 0 ) goto bExpBigger;
    if ( aExp == 0xFF ) {
        if ( aSig | bSig ) return propagateFloat32NaN( a, b );
        float_raise( float_flag_invalid );
        return float32_default_nan;
    }
    if ( aExp == 0 ) {
        aExp = 1;
        bExp = 1;
    }
    if ( bSig < aSig ) goto aBigger;
    if ( aSig < bSig ) goto bBigger;
    return packFloat32( float_rounding_mode == float_round_down, 0, 0 );
 bExpBigger:
    if ( bExp == 0xFF ) {
        if ( bSig ) return propagateFloat32NaN( a, b );
        return packFloat32( zSign ^ 1, 0xFF, 0 );
    }
    if ( aExp == 0 ) {
        ++expDiff;
    }
    else {
        aSig |= 0x40000000;
    }
    shift32RightJamming( aSig, - expDiff, &aSig );
    bSig |= 0x40000000;
 bBigger:
    zSig = bSig - aSig;
    zExp = bExp;
    zSign ^= 1;
    goto normalizeRoundAndPack;
 aExpBigger:
    if ( aExp == 0xFF ) {
        if ( aSig ) return propagateFloat32NaN( a, b );
        return a;
    }
    if ( bExp == 0 ) {
        --expDiff;
    }
    else {
        bSig |= 0x40000000;
    }
    shift32RightJamming( bSig, expDiff, &bSig );
    aSig |= 0x40000000;
 aBigger:
    zSig = aSig - bSig;
    zExp = aExp;
 normalizeRoundAndPack:
    --zExp;
    return normalizeRoundAndPackFloat32( zSign, zExp, zSig );

}

/*----------------------------------------------------------------------------
| Returns the result of adding the single-precision floating-point values `a'
| and `b'.  The operation is performed according to the IEC/IEEE Standard for
| Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/

float32 float32_add( float32 a, float32 b )
{
    flag aSign, bSign;

    aSign = extractFloat32Sign( a );
    bSign = extractFloat32Sign( b );
    if ( aSign == bSign ) {
        return addFloat32Sigs( a, b, aSign );
    }
    else {
        return subFloat32Sigs( a, b, aSign );
    }

}

/*----------------------------------------------------------------------------
| Returns the result of subtracting the single-precision floating-point values
| `a' and `b'.  The operation is performed according to the IEC/IEEE Standard
| for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/

float32 float32_sub( float32 a, float32 b )
{
    flag aSign, bSign;

    aSign = extractFloat32Sign( a );
    bSign = extractFloat32Sign( b );
    if ( aSign == bSign ) {
        return subFloat32Sigs( a, b, aSign );
    }
    else {
        return addFloat32Sigs( a, b, aSign );
    }

}

/*----------------------------------------------------------------------------
| Returns the result of multiplying the single-precision floating-point values
| `a' and `b'.  The operation is performed according to the IEC/IEEE Standard
| for Binary Floating-Point Arithmetic.
*----------------------------------------------------------------------------*/

float32 float32_mul( float32 a, float32 b )
{
    flag aSign, bSign, zSign;
    int16 aExp, bExp, zExp;
    bits32 aSig, bSig;
    bits64 zSig64;
    bits32 zSig;

    aSig = extractFloat32Frac( a );
    aExp = extractFloat32Exp( a );
    aSign = extractFloat32Sign( a );
    bSig = extractFloat32Frac( b );
    bExp = extractFloat32Exp( b );
    bSign = extractFloat32Sign( b );
    zSign = aSign ^ bSign;
    if ( aExp == 0xFF ) {
        if ( aSig || ( ( bExp == 0xFF ) && bSig ) ) {
            return propagateFloat32NaN( a, b );
        }
        if ( ( bExp | bSig ) == 0 ) {
            float_raise( float_flag_invalid );
            return float32_default_nan;
        }
        return packFloat32( zSign, 0xFF, 0 );
    }
    if ( bExp == 0xFF ) {
        if ( bSig ) return propagateFloat32NaN( a, b );
        if ( ( aExp | aSig ) ==