softfloat.c

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

/*============================================================================

This C source file is part of the SoftFloat IEC/IEEE Floating-point Arithmetic
Package, Release 2b.

Written by John R. Hauser.  This work was made possible in part by the
International Computer Science Institute, located at Suite 600, 1947 Center
Street, Berkeley, California 94704.  Funding was partially provided by the
National Science Foundation under grant MIP-9311980.  The original version
of this code was written as part of a project to build a fixed-point vector
processor in collaboration with the University of California at Berkeley,
overseen by Profs. Nelson Morgan and John Wawrzynek.  More information
is available through the Web page `http://www.cs.berkeley.edu/~jhauser/
arithmetic/SoftFloat.html'.

THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE.  Although reasonable effort has
been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT TIMES
RESULT IN INCORRECT BEHAVIOR.  USE OF THIS SOFTWARE IS RESTRICTED TO PERSONS
AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ALL LOSSES,
COSTS, OR OTHER PROBLEMS THEY INCUR DUE TO THE SOFTWARE, AND WHO FURTHERMORE
EFFECTIVELY INDEMNIFY JOHN HAUSER AND THE INTERNATIONAL COMPUTER SCIENCE
INSTITUTE (possibly via similar legal warning) AGAINST ALL LOSSES, COSTS, OR
OTHER PROBLEMS INCURRED BY THEIR CUSTOMERS AND CLIENTS DUE TO THE SOFTWARE.

Derivative works are acceptable, even for commercial purposes, so long as
(1) the source code for the derivative work includes prominent notice that
the work is derivative, and (2) the source code includes prominent notice with
these four paragraphs for those parts of this code that are retained.

=============================================================================*/

#include "milieu.h"
#include "softfloat.h"

/*----------------------------------------------------------------------------
| Floating-point rounding mode and exception flags.
*----------------------------------------------------------------------------*/
int8 float_rounding_mode = float_round_nearest_even;
int8 float_exception_flags = 0;

/*----------------------------------------------------------------------------
| Primitive arithmetic functions, including multi-word arithmetic, and
| division and square root approximations.  (Can be specialized to target if
| desired.)
*----------------------------------------------------------------------------*/
#include "softfloat-macros"

/*----------------------------------------------------------------------------
| Functions and definitions to determine:  (1) whether tininess for underflow
| is detected before or after rounding by default, (2) what (if anything)
| happens when exceptions are raised, (3) how signaling NaNs are distinguished
| from quiet NaNs, (4) the default generated quiet NaNs, and (4) how NaNs
| are propagated from function inputs to output.  These details are target-
| specific.
*----------------------------------------------------------------------------*/
#include "softfloat-specialize"

/*----------------------------------------------------------------------------
| Returns the fraction bits of the single-precision floating-point value `a'.
*----------------------------------------------------------------------------*/

INLINE bits32 extractFloat32Frac( float32 a )
{

    return a & 0x007FFFFF;

}

/*----------------------------------------------------------------------------
| Returns the exponent bits of the single-precision floating-point value `a'.
*----------------------------------------------------------------------------*/

INLINE int16 extractFloat32Exp( float32 a )
{

    return ( a>>23 ) & 0xFF;

}

/*----------------------------------------------------------------------------
| Returns the sign bit of the single-precision floating-point value `a'.
*----------------------------------------------------------------------------*/

INLINE flag extractFloat32Sign( float32 a )
{

    return a>>31;

}

/*----------------------------------------------------------------------------
| Normalizes the subnormal single-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
 normalizeFloat32Subnormal( bits32 aSig, int16 *zExpPtr, bits32 *zSigPtr )
{
    int8 shiftCount;

    shiftCount = countLeadingZeros32( aSig ) - 8;
    *zSigPtr = aSig<<shiftCount;
    *zExpPtr = 1 - shiftCount;

}

/*----------------------------------------------------------------------------
| Packs the sign `zSign', exponent `zExp', and significand `zSig' into a
| single-precision floating-point value, returning the result.  After being
| shifted into the proper positions, the three fields are simply added
| together to form the result.  This means that any integer portion of `zSig'
| will be added into the exponent.  Since a properly normalized significand
| will have an integer portion equal to 1, the `zExp' input should be 1 less
| than the desired result exponent whenever `zSig' is a complete, normalized
| significand.
*----------------------------------------------------------------------------*/

INLINE float32 packFloat32( flag zSign, int16 zExp, bits32 zSig )
{

    return ( ( (bits32) zSign )<<31 ) + ( ( (bits32) zExp )<<23 ) + zSig;

}

/*----------------------------------------------------------------------------
| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
| and significand `zSig', and returns the proper single-precision floating-
| point value corresponding to the abstract input.  Ordinarily, the abstract
| value is simply rounded and packed into the single-precision format, with
| the inexact exception raised if the abstract input cannot be represented
| exactly.  However, if the abstract value is too large, 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 single-
| precision floating-point number.
|     The input significand `zSig' has its binary point between bits 30
| and 29, which is 7 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 float32 roundAndPackFloat32( flag zSign, int16 zExp, bits32 zSig )
{
    int8 roundingMode;
    flag roundNearestEven;
    int8 roundIncrement, roundBits;
    flag isTiny;

    roundingMode = float_rounding_mode;
    roundNearestEven = roundingMode == float_round_nearest_even;
    roundIncrement = 0x40;
    if ( ! roundNearestEven ) {
        if ( roundingMode == float_round_to_zero ) {
            roundIncrement = 0;
        }
        else {
            roundIncrement = 0x7F;
            if ( zSign ) {
                if ( roundingMode == float_round_up ) roundIncrement = 0;
            }
            else {
                if ( roundingMode == float_round_down ) roundIncrement = 0;
            }
        }
    }
    roundBits = zSig & 0x7F;
    if ( 0xFD <= (bits16) zExp ) {
        if (    ( 0xFD < zExp )
             || (    ( zExp == 0xFD )
                  && ( (sbits32) ( zSig + roundIncrement ) < 0 ) )
           ) {
            float_raise(float_flag_inexact );
            float_raise( float_flag_overflow);			
            return packFloat32( zSign, 0xFF, 0 ) - ( roundIncrement == 0 );
        }
        if ( zExp < 0 ) {
            isTiny =
                   ( float_detect_tininess == float_tininess_before_rounding )
                || ( zExp < -1 )
                || ( zSig + roundIncrement < 0x80000000 );
            shift32RightJamming( zSig, - zExp, &zSig );
            zExp = 0;
            roundBits = zSig & 0x7F;
            if ( isTiny && roundBits ) float_raise( float_flag_underflow );
        }
    }
    if ( roundBits ) float_exception_flags |= float_flag_inexact;
    zSig = ( zSig + roundIncrement )>>7;
    zSig &= ~ ( ( ( roundBits ^ 0x40 ) == 0 ) & roundNearestEven );
    if ( zSig == 0 ) zExp = 0;
    return packFloat32( zSign, zExp, zSig );

}

/*----------------------------------------------------------------------------
| Takes an abstract floating-point value having sign `zSign', exponent `zExp',
| and significand `zSig', and returns the proper single-precision floating-
| point value corresponding to the abstract input.  This routine is just like
| `roundAndPackFloat32' except that `zSig' does not have to be normalized.
| Bit 31 of `zSig' must be zero, and `zExp' must be 1 less than the ``true''
| floating-point exponent.
*----------------------------------------------------------------------------*/

static float32
 normalizeRoundAndPackFloat32( flag zSign, int16 zExp, bits32 zSig )
{
    int8 shiftCount;

    shiftCount = countLeadingZeros32( zSig ) - 1;
    return roundAndPackFloat32( zSign, zExp - shiftCount, zSig<<shiftCount );

}

/*----------------------------------------------------------------------------
| Returns the least-significant 32 fraction bits of the double-precision
| floating-point value `a'.
*----------------------------------------------------------------------------*/

INLINE bits32 extractFloat64Frac1( float64 a )
{

    return a.low;

}

/*----------------------------------------------------------------------------
| Returns the most-significant 20 fraction bits of the double-precision
| floating-point value `a'.
*----------------------------------------------------------------------------*/

INLINE bits32 extractFloat64Frac0( float64 a )
{

    return a.high & 0x000FFFFF;

}

/*----------------------------------------------------------------------------
| Returns the exponent bits of the double-precision floating-point value `a'.
*----------------------------------------------------------------------------*/

INLINE int16 extractFloat64Exp( float64 a )
{

    return ( a.high>>20 ) & 0x7FF;

}

/*----------------------------------------------------------------------------
| Returns the sign bit of the double-precision floating-point value `a'.
*----------------------------------------------------------------------------*/

INLINE flag extractFloat64Sign( float64 a )
{

    return a.high>>31;

}

/*----------------------------------------------------------------------------
| Normalizes the subnormal double-precision floating-point value represented
| by the denormalized significand formed by the concatenation of `aSig0' and
| `aSig1'.  The normalized exponent is stored at the location pointed to by
| `zExpPtr'.  The most significant 21 bits of the normalized significand are
| stored at the location pointed to by `zSig0Ptr', and the least significant
| 32 bits of the normalized significand are stored at the location pointed to
| by `zSig1Ptr'.
*----------------------------------------------------------------------------*/

static void
 normalizeFloat64Subnormal(
     bits32 aSig0,
     bits32 aSig1,
     int16 *zExpPtr,
     bits32 *zSig0Ptr,
     bits32 *zSig1Ptr
 )
{
    int8 shiftCount;

    if ( aSig0 == 0 ) {
        shiftCount = countLeadingZeros32( aSig1 ) - 11;
        if ( shiftCount < 0 ) {
            *zSig0Ptr = aSig1>>( - shiftCount );
            *zSig1Ptr = aSig1<<( shiftCount & 31 );
        }
        else {
            *zSig0Ptr = aSig1<<shiftCount;
            *zSig1Ptr = 0;
        }
        *zExpPtr = - shiftCount - 31;
    }
    else {
        shiftCount = countLeadingZeros32( aSig0 ) - 11;
        shortShift64Left( aSig0, aSig1, shiftCount, zSig0Ptr, zSig1Ptr );
        *zExpPtr = 1 - shiftCount;
    }

}

/*----------------------------------------------------------------------------
| Packs the sign `zSign', the exponent `zExp', and the significand formed by
| the concatenation of `zSig0' and `zSig1' into a double-precision floating-
| point value, returning the result.  After being shifted into the proper
| positions, the three fields `zSign', `zExp', and `zSig0' are simply added
| together to form the most significant 32 bits of the result.  This means
| that any integer portion of `zSig0' will be added into the exponent.  Since
| a properly normalized significand will have an integer portion equal to 1,
| the `zExp' input should be 1 less than the desired result exponent whenever
| `zSig0' and `zSig1' concatenated form a complete, normalized significand.
*----------------------------------------------------------------------------*/

INLINE float64
 packFloat64( flag zSign, int16 zExp, bits32 zSig0, bits32 zSig1 )
{
    float64 z;

    z.low = zSig1;
    z.high = ( ( (bits32) zSign )<<31 ) + ( ( (bits32) 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.
| However, if the abstract value is too large, 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 )
{
    int8 roundingMode;
    flag roundNearestEven, increment, isTiny;