/*** CHECK COMMENTS ***/

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

This C source fragment is part of the SoftFloat IEC/IEEE Floating-point
Arithmetic Package, Release 1a.

Written by John R. Hauser.  This work was made possible by the International
Computer Science Institute, located at Suite 600, 1947 Center Street,
Berkeley, California 94704.  Funding was provided in part 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/
softfloat.html'.

THIS PACKAGE IS DISTRIBUTED AS IS, FOR FREE.  Although reasonable effort has
been made to avoid it, THIS PACKAGE MAY CONTAIN FAULTS THAT WILL AT TIMES
RESULT IN INCORRECT BEHAVIOR.  USE OF THIS PACKAGE IS RESTRICTED TO PERSONS
AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ANY AND ALL
LOSSES, COSTS, OR OTHER PROBLEMS ARISING FROM ITS USE.

Derivative works are acceptable, even for commercial purposes, so long as
(1) they include prominent notice that the work is derivative, and (2) they
include prominent notice akin to these three paragraphs for those parts of
this code that are retained.

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

/*
-------------------------------------------------------------------------------
Underflow tininess-detection mode.  (Statically initialized to default
value.  The declaration in `softfloat.h' must match the `int8' type here.)
-------------------------------------------------------------------------------
*/
int8 float_detect_tininess = float_tininess_after_rounding;

/*
-------------------------------------------------------------------------------
Raises the exceptions specified by `flags'.  Floating-point traps can be
defined here if desired.  It is currently not possible for such a trap to
substitute a result value.  If traps are not implemented, this routine
should be simply `float_exception_flags |= flags;'.
-------------------------------------------------------------------------------
*/
void float_raise( int8 flags )
{

    float_exception_flags |= flags;

}

/*
-------------------------------------------------------------------------------
-------------------------------------------------------------------------------
*/
typedef struct {
    flag sign;
    bits64 high, low;
} commonNaNT;

/*
-------------------------------------------------------------------------------
The pattern for a default generated single-precision NaN.
-------------------------------------------------------------------------------
*/
#define float32_default_nan 0xFFC00000

/*
-------------------------------------------------------------------------------
-------------------------------------------------------------------------------
*/
flag float32_is_nan( float32 a )
{

    return ( 0xFF000000 < (bits32) ( a<<1 ) );

}

/*
-------------------------------------------------------------------------------
Returns true if the single-precision floating-point value `a' is a signaling
NaN; otherwise returns false.
-------------------------------------------------------------------------------
*/
flag float32_is_signaling_nan( float32 a )
{

    return ( ( ( a>>22 ) & 0x1FF ) == 0x1FE ) && ( a & 0x003FFFFF );

}

/*
-------------------------------------------------------------------------------
-------------------------------------------------------------------------------
*/
static commonNaNT float32ToCommonNaN( float32 a )
{
    commonNaNT z;

    if ( float32_is_signaling_nan( a ) ) float_raise( float_flag_invalid );
    z.sign = a>>31;
    z.low = 0;
    z.high = ( (bits64) a )<<41;
    return z;

}

/*
-------------------------------------------------------------------------------
-------------------------------------------------------------------------------
*/
static float32 commonNaNToFloat32( commonNaNT a )
{

    return ( ( (bits32) a.sign )<<31 ) | 0x7FC00000 | ( a.high>>41 );

}

/*
-------------------------------------------------------------------------------
Takes two single-precision floating-point values `a' and `b', one of which
is a NaN, and returns the appropriate NaN result.  If either `a' or `b' is a
signaling NaN, the invalid exception is raised.
-------------------------------------------------------------------------------
*/
static float32 propagateFloat32NaN( float32 a, float32 b )
{
    flag aIsNaN, aIsSignalingNaN, bIsNaN, bIsSignalingNaN;

    aIsNaN = float32_is_nan( a );
    aIsSignalingNaN = float32_is_signaling_nan( a );
    bIsNaN = float32_is_nan( b );
    bIsSignalingNaN = float32_is_signaling_nan( b );
    a |= 0x00400000;
    b |= 0x00400000;
    if ( aIsSignalingNaN | bIsSignalingNaN ) float_raise( float_flag_invalid );
    if ( aIsSignalingNaN ) {
        if ( bIsSignalingNaN ) goto returnLargerSignificand;
        return bIsNaN ? b : a;
    }
    else if ( aIsNaN ) {
        if ( bIsSignalingNaN | ! bIsNaN ) return a;
 returnLargerSignificand:
        if ( (bits32) ( a<<1 ) < (bits32) ( b<<1 ) ) return b;
        if ( (bits32) ( b<<1 ) < (bits32) ( a<<1 ) ) return a;
        return ( a < b ) ? a : b;
    }
    else {
        return b;
    }

}

/*
-------------------------------------------------------------------------------
The pattern for a default generated double-precision NaN.
-------------------------------------------------------------------------------
*/
#define float64_default_nan LIT64( 0xFFF8000000000000 )

/*
-------------------------------------------------------------------------------
-------------------------------------------------------------------------------
*/
flag float64_is_nan( float64 a )
{

    return ( LIT64( 0xFFE0000000000000 ) < (bits64) ( a<<1 ) );

}

/*
-------------------------------------------------------------------------------
Returns true if the double-precision floating-point value `a' is a signaling
NaN; otherwise returns false.
-------------------------------------------------------------------------------
*/
flag float64_is_signaling_nan( float64 a )
{

    return
           ( ( ( a>>51 ) & 0xFFF ) == 0xFFE )
        && ( a & LIT64( 0x0007FFFFFFFFFFFF ) );

}

/*
-------------------------------------------------------------------------------
-------------------------------------------------------------------------------
*/
static commonNaNT float64ToCommonNaN( float64 a )
{
    commonNaNT z;

    if ( float64_is_signaling_nan( a ) ) float_raise( float_flag_invalid );
    z.sign = a>>63;
    z.low = 0;
    z.high = a<<12;
    return z;

}

/*
-------------------------------------------------------------------------------
-------------------------------------------------------------------------------
*/
static float64 commonNaNToFloat64( commonNaNT a )
{

    return
          ( ( (bits64) a.sign )<<63 )
        | LIT64( 0x7FF8000000000000 )
        | ( a.high>>12 );

}

/*
-------------------------------------------------------------------------------
Takes two double-precision floating-point values `a' and `b', one of which
is a NaN, and returns the appropriate NaN result.  If either `a' or `b' is a
signaling NaN, the invalid exception is raised.
-------------------------------------------------------------------------------
*/
static float64 propagateFloat64NaN( float64 a, float64 b )
{
    flag aIsNaN, aIsSignalingNaN, bIsNaN, bIsSignalingNaN;

    aIsNaN = float64_is_nan( a );
    aIsSignalingNaN = float64_is_signaling_nan( a );
    bIsNaN = float64_is_nan( b );
    bIsSignalingNaN = float64_is_signaling_nan( b );
    a |= LIT64( 0x0008000000000000 );
    b |= LIT64( 0x0008000000000000 );
    if ( aIsSignalingNaN | bIsSignalingNaN ) float_raise( float_flag_invalid );
    if ( aIsSignalingNaN ) {
        if ( bIsSignalingNaN ) goto returnLargerSignificand;
        return bIsNaN ? b : a;
    }
    else if ( aIsNaN ) {
        if ( bIsSignalingNaN | ! bIsNaN ) return a;
 returnLargerSignificand:
        if ( (bits64) ( a<<1 ) < (bits64) ( b<<1 ) ) return b;
        if ( (bits64) ( b<<1 ) < (bits64) ( a<<1 ) ) return a;
        return ( a < b ) ? a : b;
    }
    else {
        return b;
    }

}

#ifdef FLOATX80

/*
-------------------------------------------------------------------------------
The pattern for a default generated extended double-precision NaN.  The
`high' and `low' values hold the most- and least-significant bits,
respectively.
-------------------------------------------------------------------------------
*/
#define floatx80_default_nan_high 0xFFFF
#define floatx80_default_nan_low  LIT64( 0xC000000000000000 )

/*
-------------------------------------------------------------------------------
-------------------------------------------------------------------------------
*/
flag floatx80_is_nan( floatx80 a )
{

    return ( ( a.high & 0x7FFF ) == 0x7FFF ) && (bits64) ( a.low<<1 );

}

/*
-------------------------------------------------------------------------------
Returns true if the extended double-precision floating-point value `a' is a
signaling NaN; otherwise returns false.
-------------------------------------------------------------------------------
*/
flag floatx80_is_signaling_nan( floatx80 a )
{
    bits64 aLow;

    aLow = a.low & ~ LIT64( 0x4000000000000000 );
    return
           ( ( a.high & 0x7FFF ) == 0x7FFF )
        && (bits64) ( aLow<<1 )
        && ( a.low == aLow );

}

/*
-------------------------------------------------------------------------------
-------------------------------------------------------------------------------
*/
static commonNaNT floatx80ToCommonNaN( floatx80 a )
{
    commonNaNT z;

    if ( floatx80_is_signaling_nan( a ) ) float_raise( float_flag_invalid );
    z.sign = a.high>>15;
    z.low = 0;
    z.high = a.low<<1;
    return z;

}

/*
-------------------------------------------------------------------------------
-------------------------------------------------------------------------------
*/
static floatx80 commonNaNToFloatx80( commonNaNT a )
{
    floatx80 z;

    z.low = LIT64( 0xC000000000000000 ) | ( a.high>>1 );
    z.high = ( ( (bits16) a.sign )<<15 ) | 0x7FFF;
    return z;

}

/*
-------------------------------------------------------------------------------
Takes two extended double-precision floating-point values `a' and `b', one
of which is a NaN, and returns the appropriate NaN result.  If either `a' or
`b' is a signaling NaN, the invalid exception is raised.
-------------------------------------------------------------------------------
*/
static floatx80 propagateFloatx80NaN( floatx80 a, floatx80 b )
{
    flag aIsNaN, aIsSignalingNaN, bIsNaN, bIsSignalingNaN;

    aIsNaN = floatx80_is_nan( a );
    aIsSignalingNaN = floatx80_is_signaling_nan( a );
    bIsNaN = floatx80_is_nan( b );
    bIsSignalingNaN = floatx80_is_signaling_nan( b );
    a.low |= LIT64( 0xC000000000000000 );
    b.low |= LIT64( 0xC000000000000000 );
    if ( aIsSignalingNaN | bIsSignalingNaN ) float_raise( float_flag_invalid );
    if ( aIsSignalingNaN ) {
        if ( bIsSignalingNaN ) goto returnLargerSignificand;
        return bIsNaN ? b : a;
    }
    else if ( aIsNaN ) {
        if ( bIsSignalingNaN | ! bIsNaN ) return a;
 returnLargerSignificand:
        if ( a.low < b.low ) return b;
        if ( b.low < a.low ) return a;
        return ( a.high < b.high ) ? a : b;
    }
    else {
        return b;
    }

}

#endif

#ifdef FLOAT128

/*
-------------------------------------------------------------------------------
The pattern for a default generated quadruple-precision NaN.  The `high' and
`low' values hold the most- and least-significant bits, respectively.
-------------------------------------------------------------------------------
*/
#define float128_default_nan_high LIT64( 0xFFFF800000000000 )
#define float128_default_nan_low  LIT64( 0x0000000000000000 )

/*
-------------------------------------------------------------------------------
-------------------------------------------------------------------------------
*/
flag float128_is_nan( float128 a )
{

    return
           ( LIT64( 0xFFFE000000000000 ) <= (bits64) ( a.high<<1 ) )
        && ( a.low || ( a.high & LIT64( 0x0000FFFFFFFFFFFF ) ) );

}

/*
-------------------------------------------------------------------------------
Returns true if the quadruple-precision floating-point value `a' is a
signaling NaN; otherwise returns false.
-------------------------------------------------------------------------------
*/
flag float128_is_signaling_nan( float128 a )
{

    return
           ( ( ( a.high>>47 ) & 0xFFFF ) == 0xFFFE )
        && ( a.low || ( a.high & LIT64( 0x00007FFFFFFFFFFF ) ) );

}

/*
-------------------------------------------------------------------------------
-------------------------------------------------------------------------------
*/
static commonNaNT float128ToCommonNaN( float128 a )
{
    commonNaNT z;

    if ( float128_is_signaling_nan( a ) ) float_raise( float_flag_invalid );
    z.sign = a.high>>63;
    shortShift128Left( a.high, a.low, 16, &z.high, &z.low );
    return z;

}

/*
-------------------------------------------------------------------------------
-------------------------------------------------------------------------------
*/
static float128 commonNaNToFloat128( commonNaNT a )
{
    float128 z;

    shift128Right( a.high, a.low, 16, &z.high, &z.low );
    z.high |= ( ( (bits64) a.sign )<<63 ) | LIT64( 0x7FFF800000000000 );
    return z;

}

/*
-------------------------------------------------------------------------------
Takes two quadruple-precision floating-point values `a' and `b', one of
which is a NaN, and returns the appropriate NaN result.  If either `a' or
`b' is a signaling NaN, the invalid exception is raised.
-------------------------------------------------------------------------------
*/
static float128 propagateFloat128NaN( float128 a, float128 b )
{
    flag aIsNaN, aIsSignalingNaN, bIsNaN, bIsSignalingNaN;

    aIsNaN = float128_is_nan( a );
    aIsSignalingNaN = float128_is_signaling_nan( a );
    bIsNaN = float128_is_nan( b );
    bIsSignalingNaN = float128_is_signaling_nan( b );
    a.high |= LIT64( 0x0000800000000000 );
    b.high |= LIT64( 0x0000800000000000 );
    if ( aIsSignalingNaN | bIsSignalingNaN ) float_raise( float_flag_invalid );
    if ( aIsSignalingNaN ) {
        if ( bIsSignalingNaN ) goto returnLargerSignificand;
        return bIsNaN ? b : a;
    }
    else if ( aIsNaN ) {
        if ( bIsSignalingNaN | ! bIsNaN ) return a;
 returnLargerSignificand:
        if ( lt128( a.high<<1, a.low, b.high<<1, b.low ) ) return b;
        if ( lt128( b.high<<1, b.low, a.high<<1, a.low ) ) return a;
        return ( a.high < b.high ) ? a : b;
    }
    else {
        return b;
    }

}

#endif