softfloat.c

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    z.high = ( zSign<<31 ) + ( zExp<<20 ) + zSig0;
    return z;

}

/*
-------------------------------------------------------------------------------
Takes an abstract floating-point value having sign `zSign', exponent `zExp',
and extended significand formed by the concatenation of `zSig0', `zSig1',
and `zSig2', and returns the proper double-precision floating-point value
corresponding to the abstract input.  Ordinarily, the abstract value is
simply rounded and packed into the double-precision format, with the inexact
exception raised if the abstract input cannot be represented exactly.  If
the abstract value is too large, however, the overflow and inexact
exceptions are raised and an infinity or maximal finite value is returned.
If the abstract value is too small, the input value is rounded to a
subnormal number, and the underflow and inexact exceptions are raised if the
abstract input cannot be represented exactly as a subnormal double-precision
floating-point number.
    The input significand must be normalized or smaller.  If the input
significand is not normalized, `zExp' must be 0; in that case, the result
returned is a subnormal number, and it must not require rounding.  In the
usual case that the input significand is normalized, `zExp' must be 1 less
than the ``true'' floating-point exponent.  The handling of underflow and
overflow follows the IEC/IEEE Standard for Binary Floating-point Arithmetic.
-------------------------------------------------------------------------------
*/
static float64
 roundAndPackFloat64(
     flag zSign, int16 zExp, bits32 zSig0, bits32 zSig1, bits32 zSig2 )
{
    uint8 roundingMode;
    flag roundNearestEven, increment;
    flag isTiny;

    roundingMode = float_rounding_mode;
    roundNearestEven = roundingMode == float_round_nearest_even;
    increment = ( (sbits32) zSig2 ) < 0;
    if ( ! roundNearestEven ) {
        if ( roundingMode == float_round_to_zero ) {
            increment = 0;
        }
        else {
            if ( zSign ) {
                increment = ( roundingMode == float_round_down ) && zSig2;
            }
            else {
                increment = ( roundingMode == float_round_up ) && zSig2;
            }
        }
    }
    if ( 0x7FE - 1 <= ( (bits16) zExp ) ) {
        if (    ( 0x7FE - 1 < zExp )
             || (    ( zExp == 0x7FE - 1 )
                  && eq64( 0x001FFFFF, 0xFFFFFFFF, zSig0, zSig1 )
                  && increment
                )
           ) {
            float_raise( float_flag_overflow | float_flag_inexact );
            if (    ( roundingMode == float_round_to_zero )
                 || ( zSign && ( roundingMode == float_round_up ) )
                 || ( ! zSign && ( roundingMode == float_round_down ) )
               ) {
                return packFloat64( zSign, 0x7FE, 0x000FFFFF, 0xFFFFFFFF );
            }
            return packFloat64( zSign, 0x7FF, 0, 0 );
        }
        if ( zExp < 0 ) {
            isTiny =
                   ( float_detect_tininess == float_tininess_before_rounding )
                || ( zExp < -1 )
                || ! increment
                || lt64( zSig0, zSig1, 0x001FFFFF, 0xFFFFFFFF );
            shiftDown64ExtraJamming(
                zSig0, zSig1, zSig2, - zExp, &zSig0, &zSig1, &zSig2 );
            zExp = 0;
            if ( isTiny && zSig2 ) float_raise( float_flag_underflow );
            if ( roundNearestEven ) {
                increment = ( (sbits32) zSig2 ) < 0;
            }
            else {
                if ( zSign ) {
                    increment = ( roundingMode == float_round_down ) && zSig2;
                }
                else {
                    increment = ( roundingMode == float_round_up ) && zSig2;
                }
            }
        }
    }
    if ( zSig2 ) float_exception_flags |= float_flag_inexact;
    if ( increment ) {
        add64( zSig0, zSig1, 0, 1, &zSig0, &zSig1 );
        zSig1 &= ~ ( ( zSig2 + zSig2 == 0 ) & roundNearestEven );
    }
    if ( ( zSig0 | zSig1 ) == 0 ) zExp = 0;
    return packFloat64( zSign, zExp, zSig0, zSig1 );

}

/*
-------------------------------------------------------------------------------
Takes an abstract floating-point value having sign `zSign', exponent `zExp',
and significand formed by the concatenation of `zSig0' and `zSig1', and
returns the proper double-precision floating-point value corresponding to
the abstract input.  This routine is just like `roundAndPackFloat64' except
that the input significand has fewer bits and does not have to be normalized
in any way.  In all cases, `zExp' must be 1 less than the ``true'' floating-
point exponent.
-------------------------------------------------------------------------------
*/
static float64
 normalizeRoundAndPackFloat64(
     flag zSign, int16 zExp, bits32 zSig0, bits32 zSig1 )
{
    int8 shiftCount;
    bits32 zSig2;

    if ( zSig0 == 0 ) {
        zSig0 = zSig1;
        zSig1 = 0;
        zExp -= 32;
    }
    shiftCount = countLeadingZeros( zSig0 ) - 11;
    if ( 0 <= shiftCount ) {
        zSig2 = 0;
        shortShiftUp64( zSig0, zSig1, shiftCount, &zSig0, &zSig1 );
    }
    else {
        shiftDown64ExtraJamming(
            zSig0, zSig1, 0, - shiftCount, &zSig0, &zSig1, &zSig2 );
    }
    zExp -= shiftCount;
    return roundAndPackFloat64( zSign, zExp, zSig0, zSig1, zSig2 );

}

/*
-------------------------------------------------------------------------------
Returns the result of converting the 32-bit two's complement integer `a' to
the single-precision floating-point format.  The conversion is performed
according to the IEC/IEEE Standard for Binary Floating-point Arithmetic.
-------------------------------------------------------------------------------
*/
float32 int32_to_float32( int32 a )
{
    flag zSign;

    if ( a == 0 ) return 0;
    if ( a == -0x80000000 ) return packFloat32( 1, 0x9E, 0 );
    zSign = ( a < 0 );
    return normalizeRoundAndPackFloat32( zSign, 0x9C, zSign ? - a : a );

}

/*
-------------------------------------------------------------------------------
Returns the result of converting the 32-bit two's complement integer `a' to
the double-precision floating-point format.  The conversion is performed
according to the IEC/IEEE Standard for Binary Floating-point Arithmetic.
-------------------------------------------------------------------------------
*/
float64 int32_to_float64( int32 a )
{
    flag zSign;
    bits32 absA;
    int8 shiftCount;
    bits32 zSig0, zSig1;

    if ( a == 0 ) return packFloat64( 0, 0, 0, 0 );
    zSign = ( a < 0 );
    absA = zSign ? - a : a;
    shiftCount = countLeadingZeros( absA ) - 11;
    if ( 0 <= shiftCount ) {
        zSig0 = absA<<shiftCount;
        zSig1 = 0;
    }
    else {
        shiftDown64( absA, 0, - shiftCount, &zSig0, &zSig1 );
    }
    return packFloat64( zSign, 0x412 - shiftCount, zSig0, zSig1 );

}

/*
-------------------------------------------------------------------------------
Returns the result of converting the single-precision floating-point value
`a' to the 32-bit two's complement integer format.  The conversion is
performed according to the IEC/IEEE Standard for Binary Floating-point
Arithmetic---which means in particular that the conversion is rounded
according to the current rounding mode.  If `a' is a NaN, the largest
positive integer is returned.  If the conversion overflows, the largest
integer with the same sign as `a' is returned.
-------------------------------------------------------------------------------
*/
int32 float32_to_int32( float32 a )
{
    flag aSign;
    int16 aExp, shiftCount;
    bits32 aSig;
    bits32 zExtra;
    int32 z;
    uint8 roundingMode;

    aSig = extractFloat32Frac( a );
    aExp = extractFloat32Exp( a );
    aSign = extractFloat32Sign( a );
    shiftCount = aExp - 0x96;
    if ( 0 <= shiftCount ) {
        if ( 0x9E <= aExp ) {
            if ( a == 0xCF000000 ) return -0x80000000;
            float_raise( float_flag_invalid );
            if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) return 0x7FFFFFFF;
            return -0x80000000;
        }
        z = ( aSig | 0x800000 )<<shiftCount;
        if ( aSign ) z = - z;
    }
    else {
        if ( aExp < 0x7E ) {
            zExtra = aExp | aSig;
            z = 0;
        }
        else {
            aSig |= 0x800000;
            zExtra = aSig<<( shiftCount & 31 );
            z = aSig>>( - shiftCount );
        }
        if ( zExtra ) float_exception_flags |= float_flag_inexact;
        roundingMode = float_rounding_mode;
        if ( roundingMode == float_round_nearest_even ) {
            if ( ( (sbits32) zExtra ) < 0 ) {
                ++z;
                if ( ( zExtra + zExtra ) == 0 ) z &= ~1;
            }
            if ( aSign ) z = - z;
        }
        else {
            zExtra = zExtra != 0;
            if ( aSign ) {
                z += ( roundingMode == float_round_down ) & zExtra;
                z = - z;
            }
            else {
                z += ( roundingMode == float_round_up ) & zExtra;
            }
        }
    }
    return z;

}

/*
-------------------------------------------------------------------------------
Returns the result of converting the single-precision floating-point value
`a' to the 32-bit two's complement integer format.  The conversion is
performed according to the IEC/IEEE Standard for Binary Floating-point
Arithmetic, except that the conversion is always rounded toward zero.  If
`a' is a NaN, the largest positive integer is returned.  If the conversion
overflows, the largest integer with the same sign as `a' is returned.
-------------------------------------------------------------------------------
*/
int32 float32_to_int32_round_to_zero( float32 a )
{
    flag aSign;
    int16 aExp, shiftCount;
    bits32 aSig;
    int32 z;

    aSig = extractFloat32Frac( a );
    aExp = extractFloat32Exp( a );
    aSign = extractFloat32Sign( a );
    shiftCount = aExp - 0x9E;
    if ( 0 <= shiftCount ) {
        if ( a == 0xCF000000 ) return -0x80000000;
        float_raise( float_flag_invalid );
        if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) return 0x7FFFFFFF;
        return -0x80000000;
    }
    else if ( aExp <= 0x7E ) {
        if ( aExp | aSig ) float_exception_flags |= float_flag_inexact;
        return 0;
    }
    aSig = ( aSig | 0x800000 )<<8;
    z = aSig>>( - shiftCount );
    if ( aSig<<( shiftCount & 31 ) ) {
        float_exception_flags |= float_flag_inexact;
    }
    if ( aSign ) z = - z;
    return z;

}

/*
-------------------------------------------------------------------------------
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.
-------------------------------------------------------------------------------
*/
float64 float32_to_float64( float32 a )
{
    flag aSign;
    int16 aExp;
    bits32 aSig;
    bits32 zSig0, zSig1;

    aSig = extractFloat32Frac( a );
    aExp = extractFloat32Exp( a );
    aSign = extractFloat32Sign( a );
    if ( aExp == 0xFF ) {
        if ( aSig ) return float32ToFloat64NaN( a );
        return packFloat64( aSign, 0x7FF, 0, 0 );
    }
    if ( aExp == 0 ) {
        if ( aSig == 0 ) return packFloat64( aSign, 0, 0, 0 );
        normalizeFloat32Subnormal( aSig, &aExp, &aSig );
        --aExp;
    }
    shiftDown64( aSig, 0, 3, &zSig0, &zSig1 );
    return packFloat64( aSign, aExp - 0x7F + 0x3FF, zSig0, zSig1 );

}

/*
-------------------------------------------------------------------------------
Returns the result of converting the double-precision floating-point value
`a' to the 32-bit two's complement integer format.  The conversion is
performed according to the IEC/IEEE Standard for Binary Floating-point
Arithmetic---which means in particular that the conversion is rounded
according to the current rounding mode.  If `a' is a NaN, the largest
positive integer is returned.  If the conversion overflows, the largest
integer with the same sign as `a' is returned.
-------------------------------------------------------------------------------
*/
int32 float64_to_int32( float64 a )
{
    flag aSign;
    int16 aExp, shiftCount;
    bits32 aSig0, aSig1;
    bits32 absZ, zExtra;
    int32 z;
    uint8 roundingMode;

    aSig1 = extractFloat64Frac1( a );
    aSig0 = extractFloat64Frac0( a );
    aExp = extractFloat64Exp( a );
    aSign = extractFloat64Sign( a );
    shiftCount = aExp - 0x413;
    if ( 0 <= shiftCount ) {
        if ( 11 < shiftCount ) {
            if ( ( aExp == 0x7FF ) && ( aSig0 | aSig1 ) ) aSign = 0;
            absZ = 0xC0000000;
        }
        else {
            shortShiftUp64(
                 aSig0 | 0x100000, aSig1, shiftCount, &absZ, &zExtra );
            if ( 0xC0000000 < absZ ) absZ = 0xC0000000;
        }
    }
    else {
        aSig1 = aSig1 != 0;
        if ( aExp < 0x3FE ) {
            zExtra = aExp | aSig0 | aSig1;
            absZ = 0;
        }
        else {
            aSig0 |= 0x100000;
            zExtra = ( aSig0<<( shiftCount & 31 ) ) | aSig1;
            absZ = aSig0>>( - shiftCount );
        }
    }
    roundingMode = float_rounding_mode;
    if ( roundingMode == float_round_nearest_even ) {
        if ( ( (sbits32) zExtra ) < 0 ) {
            ++absZ;
            if ( ( zExtra + zExtra ) == 0 ) absZ &= ~1;
        }
        z = aSign ? - absZ : absZ;
    }
    else {