softfloat.c

RISC processor ARM-7 emulator

and significand `zSig', 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 `zSig' has its binary point between bits 62
and 61, which is 10 bits to the left of the usual location.  This shifted
significand must be normalized or smaller.  If `zSig' 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 `zSig' 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, bits64 zSig )
{
    int8 roundingMode;
    flag roundNearestEven;
    int16 roundIncrement, roundBits;
    flag isTiny;

    roundingMode = float_rounding_mode;
    roundNearestEven = ( roundingMode == float_round_nearest_even );
    roundIncrement = 0x200;
    if ( ! roundNearestEven ) {
        if ( roundingMode == float_round_to_zero ) {
            roundIncrement = 0;
        }
        else {
            roundIncrement = 0x3FF;
            if ( zSign ) {
                if ( roundingMode == float_round_up ) roundIncrement = 0;
            }
            else {
                if ( roundingMode == float_round_down ) roundIncrement = 0;
            }
        }
    }
    roundBits = zSig & 0x3FF;
    if ( 0x7FD <= (bits16) zExp ) {
        if (    ( 0x7FD < zExp )
             || (    ( zExp == 0x7FD )
                  && ( (sbits64) ( zSig + roundIncrement ) < 0 ) )
           ) {
            //register int lr = __builtin_return_address(0);
            //printk("roundAndPackFloat64 called from 0x%08x\n",lr);
            float_raise( float_flag_overflow | float_flag_inexact );
            return packFloat64( zSign, 0x7FF, 0 ) - ( roundIncrement == 0 );
        }
        if ( zExp < 0 ) {
            isTiny =
                   ( float_detect_tininess == float_tininess_before_rounding )
                || ( zExp < -1 )
                || ( zSig + roundIncrement < LIT64( 0x8000000000000000 ) );
            shift64RightJamming( zSig, - zExp, &zSig );
            zExp = 0;
            roundBits = zSig & 0x3FF;
            if ( isTiny && roundBits ) float_raise( float_flag_underflow );
        }
    }
    if ( roundBits ) float_exception_flags |= float_flag_inexact;
    zSig = ( zSig + roundIncrement )>>10;
    zSig &= ~ ( ( ( roundBits ^ 0x200 ) == 0 ) & roundNearestEven );
    if ( zSig == 0 ) zExp = 0;
    return packFloat64( zSign, zExp, zSig );

}

/*
-------------------------------------------------------------------------------
Takes an abstract floating-point value having sign `zSign', exponent `zExp',
and significand `zSig', and returns the proper double-precision floating-
point value corresponding to the abstract input.  This routine is just like
`roundAndPackFloat64' except that `zSig' 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, bits64 zSig )
{
    int8 shiftCount;

    shiftCount = countLeadingZeros64( zSig ) - 1;
    return roundAndPackFloat64( zSign, zExp - shiftCount, zSig<<shiftCount );

}

#ifdef FLOATX80

/*
-------------------------------------------------------------------------------
Returns the fraction bits of the extended double-precision floating-point
value `a'.
-------------------------------------------------------------------------------
*/
INLINE bits64 extractFloatx80Frac( floatx80 a )
{

    return a.low;

}

/*
-------------------------------------------------------------------------------
Returns the exponent bits of the extended double-precision floating-point
value `a'.
-------------------------------------------------------------------------------
*/
INLINE int32 extractFloatx80Exp( floatx80 a )
{

    return a.high & 0x7FFF;

}

/*
-------------------------------------------------------------------------------
Returns the sign bit of the extended double-precision floating-point value
`a'.
-------------------------------------------------------------------------------
*/
INLINE flag extractFloatx80Sign( floatx80 a )
{

    return a.high>>15;

}

/*
-------------------------------------------------------------------------------
Normalizes the subnormal extended double-precision floating-point value
represented by the denormalized significand `aSig'.  The normalized exponent
and significand are stored at the locations pointed to by `zExpPtr' and
`zSigPtr', respectively.
-------------------------------------------------------------------------------
*/
static void
 normalizeFloatx80Subnormal( bits64 aSig, int32 *zExpPtr, bits64 *zSigPtr )
{
    int8 shiftCount;

    shiftCount = countLeadingZeros64( aSig );
    *zSigPtr = aSig<<shiftCount;
    *zExpPtr = 1 - shiftCount;

}

/*
-------------------------------------------------------------------------------
Packs the sign `zSign', exponent `zExp', and significand `zSig' into an
extended double-precision floating-point value, returning the result.
-------------------------------------------------------------------------------
*/
INLINE floatx80 packFloatx80( flag zSign, int32 zExp, bits64 zSig )
{
    floatx80 z;

    z.low = zSig;
    z.high = ( ( (bits16) zSign )<<15 ) + zExp;
    return z;

}

/*
-------------------------------------------------------------------------------
Takes an abstract floating-point value having sign `zSign', exponent `zExp',
and extended significand formed by the concatenation of `zSig0' and `zSig1',
and returns the proper extended double-precision floating-point value
corresponding to the abstract input.  Ordinarily, the abstract value is
rounded and packed into the extended 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 extended
double-precision floating-point number.
    If `roundingPrecision' is 32 or 64, the result is rounded to the same
number of bits as single or double precision, respectively.  Otherwise, the
result is rounded to the full precision of the extended double-precision
format.
    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.  The
handling of underflow and overflow follows the IEC/IEEE Standard for Binary
Floating-point Arithmetic.
-------------------------------------------------------------------------------
*/
static floatx80
 roundAndPackFloatx80(
     int8 roundingPrecision, flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1
 )
{
    int8 roundingMode;
    flag roundNearestEven, increment, isTiny;
    int64 roundIncrement, roundMask, roundBits;

    roundingMode = float_rounding_mode;
    roundNearestEven = ( roundingMode == float_round_nearest_even );
    if ( roundingPrecision == 80 ) goto precision80;
    if ( roundingPrecision == 64 ) {
        roundIncrement = LIT64( 0x0000000000000400 );
        roundMask = LIT64( 0x00000000000007FF );
    }
    else if ( roundingPrecision == 32 ) {
        roundIncrement = LIT64( 0x0000008000000000 );
        roundMask = LIT64( 0x000000FFFFFFFFFF );
    }
    else {
        goto precision80;
    }
    zSig0 |= ( zSig1 != 0 );
    if ( ! roundNearestEven ) {
        if ( roundingMode == float_round_to_zero ) {
            roundIncrement = 0;
        }
        else {
            roundIncrement = roundMask;
            if ( zSign ) {
                if ( roundingMode == float_round_up ) roundIncrement = 0;
            }
            else {
                if ( roundingMode == float_round_down ) roundIncrement = 0;
            }
        }
    }
    roundBits = zSig0 & roundMask;
    if ( 0x7FFD <= (bits32) ( zExp - 1 ) ) {
        if (    ( 0x7FFE < zExp )
             || ( ( zExp == 0x7FFE ) && ( zSig0 + roundIncrement < zSig0 ) )
           ) {
            goto overflow;
        }
        if ( zExp <= 0 ) {
            isTiny =
                   ( float_detect_tininess == float_tininess_before_rounding )
                || ( zExp < 0 )
                || ( zSig0 <= zSig0 + roundIncrement );
            shift64RightJamming( zSig0, 1 - zExp, &zSig0 );
            zExp = 0;
            roundBits = zSig0 & roundMask;
            if ( isTiny && roundBits ) float_raise( float_flag_underflow );
            if ( roundBits ) float_exception_flags |= float_flag_inexact;
            zSig0 += roundIncrement;
            if ( (sbits64) zSig0 < 0 ) zExp = 1;
            roundIncrement = roundMask + 1;
            if ( roundNearestEven && ( roundBits<<1 == roundIncrement ) ) {
                roundMask |= roundIncrement;
            }
            zSig0 &= ~ roundMask;
            return packFloatx80( zSign, zExp, zSig0 );
        }
    }
    if ( roundBits ) float_exception_flags |= float_flag_inexact;
    zSig0 += roundIncrement;
    if ( zSig0 < roundIncrement ) {
        ++zExp;
        zSig0 = LIT64( 0x8000000000000000 );
    }
    roundIncrement = roundMask + 1;
    if ( roundNearestEven && ( roundBits<<1 == roundIncrement ) ) {
        roundMask |= roundIncrement;
    }
    zSig0 &= ~ roundMask;
    if ( zSig0 == 0 ) zExp = 0;
    return packFloatx80( zSign, zExp, zSig0 );
 precision80:
    increment = ( (sbits64) zSig1 < 0 );
    if ( ! roundNearestEven ) {
        if ( roundingMode == float_round_to_zero ) {
            increment = 0;
        }
        else {
            if ( zSign ) {
                increment = ( roundingMode == float_round_down ) && zSig1;
            }
            else {
                increment = ( roundingMode == float_round_up ) && zSig1;
            }
        }
    }
    if ( 0x7FFD <= (bits32) ( zExp - 1 ) ) {
        if (    ( 0x7FFE < zExp )
             || (    ( zExp == 0x7FFE )
                  && ( zSig0 == LIT64( 0xFFFFFFFFFFFFFFFF ) )
                  && increment
                )
           ) {
            roundMask = 0;
 overflow:
            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 packFloatx80( zSign, 0x7FFE, ~ roundMask );
            }
            return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) );
        }
        if ( zExp <= 0 ) {
            isTiny =
                   ( float_detect_tininess == float_tininess_before_rounding )
                || ( zExp < 0 )
                || ! increment
                || ( zSig0 < LIT64( 0xFFFFFFFFFFFFFFFF ) );
            shift64ExtraRightJamming( zSig0, zSig1, 1 - zExp, &zSig0, &zSig1 );
            zExp = 0;
            if ( isTiny && zSig1 ) float_raise( float_flag_underflow );
            if ( zSig1 ) float_exception_flags |= float_flag_inexact;
            if ( roundNearestEven ) {
                increment = ( (sbits64) zSig1 < 0 );
            }
            else {
                if ( zSign ) {
                    increment = ( roundingMode == float_round_down ) && zSig1;
                }
                else {
                    increment = ( roundingMode == float_round_up ) && zSig1;
                }
            }
            if ( increment ) {
                ++zSig0;
                zSig0 &= ~ ( ( zSig1 + zSig1 == 0 ) & roundNearestEven );
                if ( (sbits64) zSig0 < 0 ) zExp = 1;
            }
            return packFloatx80( zSign, zExp, zSig0 );
        }
    }
    if ( zSig1 ) float_exception_flags |= float_flag_inexact;
    if ( increment ) {
        ++zSig0;
        if ( zSig0 == 0 ) {
            ++zExp;
            zSig0 = LIT64( 0x8000000000000000 );
        }
        else {
            zSig0 &= ~ ( ( zSig1 + zSig1 == 0 ) & roundNearestEven );
        }
    }
    else {
        if ( zSig0 == 0 ) zExp = 0;
    }
    
    return packFloatx80( zSign, zExp, zSig0 );
}

/*
-------------------------------------------------------------------------------
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 extended double-precision floating-point value
corresponding to the abstract input.  This routine is just like
`roundAndPackFloatx80' except that the input significand does not have to be
normalized.
-------------------------------------------------------------------------------
*/
static floatx80
 normalizeRoundAndPackFloatx80(
     int8 roundingPrecision, flag zSign, int32 zExp, bits64 zSig0, bits64 zSig1
 )
{
    int8 shiftCount;