softfloat.c

<Floating Point Unit Core> fpupack.vhd pre_norm_addsub.vhd addsub_28.vhd post_norm_addsub.

    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 ( 0x7FD <= (bits16) zExp ) {
        if (    ( 0x7FD < zExp )
             || (    ( zExp == 0x7FD )
                  && eq64( 0x001FFFFF, 0xFFFFFFFF, zSig0, zSig1 )
                  && increment
                )
           ) {
            float_raise(float_flag_inexact );
			float_raise( float_flag_overflow);
            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 );
            shift64ExtraRightJamming(
                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 );
    }
    else {
        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 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 = countLeadingZeros32( zSig0 ) - 11;
    if ( 0 <= shiftCount ) {
        zSig2 = 0;
        shortShift64Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 );
    }
    else {
        shift64ExtraRightJamming(
            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 == (sbits32) 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 = countLeadingZeros32( absA ) - 11;
    if ( 0 <= shiftCount ) {
        zSig0 = absA<<shiftCount;
        zSig1 = 0;
    }
    else {
        shift64Right( 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.  Otherwise, 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, aSigExtra;
    int32 z;
    int8 roundingMode;

    aSig = extractFloat32Frac( a );
    aExp = extractFloat32Exp( a );
    aSign = extractFloat32Sign( a );
    shiftCount = aExp - 0x96;
    if ( 0 <= shiftCount ) {
        if ( 0x9E <= aExp ) {
            if ( a != 0xCF000000 ) {
                float_raise( float_flag_invalid );
                if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) {
                    return 0x7FFFFFFF;
                }
            }
            return (sbits32) 0x80000000;
        }
        z = ( aSig | 0x00800000 )<<shiftCount;
        if ( aSign ) z = - z;
    }
    else {
        if ( aExp < 0x7E ) {
            aSigExtra = aExp | aSig;
            z = 0;
        }
        else {
            aSig |= 0x00800000;
            aSigExtra = aSig<<( shiftCount & 31 );
            z = aSig>>( - shiftCount );
        }
        if ( aSigExtra ) float_exception_flags |= float_flag_inexact;
        roundingMode = float_rounding_mode;
        if ( roundingMode == float_round_nearest_even ) {
            if ( (sbits32) aSigExtra < 0 ) {
                ++z;
                if ( (bits32) ( aSigExtra<<1 ) == 0 ) z &= ~1;
            }
            if ( aSign ) z = - z;
        }
        else {
            aSigExtra = ( aSigExtra != 0 );
            if ( aSign ) {
                z += ( roundingMode == float_round_down ) & aSigExtra;
                z = - z;
            }
            else {
                z += ( roundingMode == float_round_up ) & aSigExtra;
            }
        }
    }
    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.  Otherwise, 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 ) {
            float_raise( float_flag_invalid );
            if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) return 0x7FFFFFFF;
        }
        return (sbits32) 0x80000000;
    }
    else if ( aExp <= 0x7E ) {
        if ( aExp | aSig ) float_exception_flags |= float_flag_inexact;
        return 0;
    }
    aSig = ( aSig | 0x00800000 )<<8;
    z = aSig>>( - shiftCount );
    if ( (bits32) ( 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, zSig0, zSig1;

    aSig = extractFloat32Frac( a );
    aExp = extractFloat32Exp( a );
    aSign = extractFloat32Sign( a );
    if ( aExp == 0xFF ) {
        if ( aSig ) return commonNaNToFloat64( float32ToCommonNaN( a ) );
        return packFloat64( aSign, 0x7FF, 0, 0 );
    }
    if ( aExp == 0 ) {
        if ( aSig == 0 ) return packFloat64( aSign, 0, 0, 0 );
        normalizeFloat32Subnormal( aSig, &aExp, &aSig );
        --aExp;
    }
    shift64Right( aSig, 0, 3, &zSig0, &zSig1 );
    return packFloat64( aSign, aExp + 0x380, zSig0, zSig1 );

}

/*----------------------------------------------------------------------------
| 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 )
{