float32_t i32_to_f32( int32_t a )
{
bool sign;
union ui32_f32 uZ;
uint_fast32_t absA;
sign = (a < 0);
if ( ! (a & 0x7FFFFFFF) ) {
uZ.ui = sign ? packToF32UI( 1, 0x9E, 0 ) : 0;
return uZ.f;
}
absA = sign ? -(uint_fast32_t) a : (uint_fast32_t) a;
return softfloat_normRoundPackToF32( sign, 0x9C, absA );
}
float32_t ui32_to_f32( uint_fast32_t a )
{
union ui32_f32 uZ;
if ( ! a ) {
uZ.ui = 0;
return uZ.f;
}
if ( a & 0x80000000 ) {
return
softfloat_roundPackToF32(
0, 0x9D, softfloat_shortShift32Right1Jam( a ) );
} else {
return softfloat_normRoundPackToF32( 0, 0x9C, a );
}
}
float32_t f32_rem( float32_t a, float32_t b )
{
union ui32_f32 uA;
uint_fast32_t uiA;
bool signA;
int_fast16_t expA;
uint_fast32_t sigA;
union ui32_f32 uB;
uint_fast32_t uiB;
int_fast16_t expB;
uint_fast32_t sigB;
struct exp16_sig32 normExpSig;
uint32_t rem;
int_fast16_t expDiff;
uint32_t q, recip32, altRem, meanRem;
bool signRem;
uint_fast32_t uiZ;
union ui32_f32 uZ;
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
uA.f = a;
uiA = uA.ui;
signA = signF32UI( uiA );
expA = expF32UI( uiA );
sigA = fracF32UI( uiA );
uB.f = b;
uiB = uB.ui;
expB = expF32UI( uiB );
sigB = fracF32UI( uiB );
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
if ( expA == 0xFF ) {
if ( sigA || ((expB == 0xFF) && sigB) ) goto propagateNaN;
goto invalid;
}
if ( expB == 0xFF ) {
if ( sigB ) goto propagateNaN;
return a;
}
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
if ( ! expB ) {
if ( ! sigB ) goto invalid;
normExpSig = softfloat_normSubnormalF32Sig( sigB );
expB = normExpSig.exp;
sigB = normExpSig.sig;
}
if ( ! expA ) {
if ( ! sigA ) return a;
normExpSig = softfloat_normSubnormalF32Sig( sigA );
expA = normExpSig.exp;
sigA = normExpSig.sig;
}
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
rem = sigA | 0x00800000;
sigB |= 0x00800000;
expDiff = expA - expB;
if ( expDiff < 1 ) {
if ( expDiff < -1 ) return a;
sigB <<= 6;
if ( expDiff ) {
rem <<= 5;
q = 0;
} else {
rem <<= 6;
q = (sigB <= rem);
if ( q ) rem -= sigB;
}
} else {
recip32 = softfloat_approxRecip32_1( sigB<<8 );
/*--------------------------------------------------------------------
| Changing the shift of `rem' here requires also changing the initial
| subtraction from `expDiff'.
*--------------------------------------------------------------------*/
rem <<= 7;
expDiff -= 31;
/*--------------------------------------------------------------------
| The scale of `sigB' affects how many bits are obtained during each
| cycle of the loop. Currently this is 29 bits per loop iteration,
| which is believed to be the maximum possible.
*--------------------------------------------------------------------*/
sigB <<= 6;
for (;;) {
q = (rem * (uint_fast64_t) recip32)>>32;
if ( expDiff < 0 ) break;
rem = -(q * (uint32_t) sigB);
expDiff -= 29;
}
/*--------------------------------------------------------------------
| (`expDiff' cannot be less than -30 here.)
*--------------------------------------------------------------------*/
q >>= ~expDiff & 31;
rem = (rem<<(expDiff + 30)) - q * (uint32_t) sigB;
}
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
do {
altRem = rem;
++q;
rem -= sigB;
} while ( ! (rem & 0x80000000) );
meanRem = rem + altRem;
if ( (meanRem & 0x80000000) || (! meanRem && (q & 1)) ) rem = altRem;
signRem = signA;
if ( 0x80000000 <= rem ) {
signRem = ! signRem;
rem = -rem;
}
return softfloat_normRoundPackToF32( signRem, expB, rem );
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
propagateNaN:
uiZ = softfloat_propagateNaNF32UI( uiA, uiB );
goto uiZ;
invalid:
softfloat_raiseFlags( softfloat_flag_invalid );
uiZ = defaultNaNF32UI;
uiZ:
uZ.ui = uiZ;
return uZ.f;
}
float32_t softfloat_subMagsF32( uint_fast32_t uiA, uint_fast32_t uiB )
{
int_fast16_t expA;
uint_fast32_t sigA;
int_fast16_t expB;
uint_fast32_t sigB;
int_fast16_t expDiff;
uint_fast32_t uiZ;
int_fast32_t sigDiff;
bool signZ;
int_fast8_t shiftDist;
int_fast16_t expZ;
uint_fast32_t sigX, sigY;
union ui32_f32 uZ;
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
expA = expF32UI( uiA );
sigA = fracF32UI( uiA );
expB = expF32UI( uiB );
sigB = fracF32UI( uiB );
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
expDiff = expA - expB;
if ( ! expDiff ) {
/*--------------------------------------------------------------------
*--------------------------------------------------------------------*/
if ( expA == 0xFF ) {
if ( sigA | sigB ) goto propagateNaN;
softfloat_raiseFlags( softfloat_flag_invalid );
uiZ = defaultNaNF32UI;
goto uiZ;
}
sigDiff = sigA - sigB;
if ( ! sigDiff ) {
uiZ =
packToF32UI(
(softfloat_roundingMode == softfloat_round_min), 0, 0 );
goto uiZ;
}
if ( expA ) --expA;
signZ = signF32UI( uiA );
if ( sigDiff < 0 ) {
signZ = ! signZ;
sigDiff = -sigDiff;
}
shiftDist = softfloat_countLeadingZeros32( sigDiff ) - 8;
expZ = expA - shiftDist;
if ( expZ < 0 ) {
shiftDist = expA;
expZ = 0;
}
uiZ = packToF32UI( signZ, expZ, sigDiff<<shiftDist );
goto uiZ;
} else {
/*--------------------------------------------------------------------
*--------------------------------------------------------------------*/
signZ = signF32UI( uiA );
sigA <<= 7;
sigB <<= 7;
if ( expDiff < 0 ) {
/*----------------------------------------------------------------
*----------------------------------------------------------------*/
signZ = ! signZ;
if ( expB == 0xFF ) {
if ( sigB ) goto propagateNaN;
uiZ = packToF32UI( signZ, 0xFF, 0 );
goto uiZ;
}
expZ = expB - 1;
sigX = sigB | 0x40000000;
sigY = sigA + (expA ? 0x40000000 : sigA);
expDiff = -expDiff;
} else {
/*----------------------------------------------------------------
*----------------------------------------------------------------*/
if ( expA == 0xFF ) {
if ( sigA ) goto propagateNaN;
uiZ = uiA;
goto uiZ;
}
expZ = expA - 1;
sigX = sigA | 0x40000000;
sigY = sigB + (expB ? 0x40000000 : sigB);
}
return
softfloat_normRoundPackToF32(
signZ, expZ, sigX - softfloat_shiftRightJam32( sigY, expDiff )
);
}
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
propagateNaN:
uiZ = softfloat_propagateNaNF32UI( uiA, uiB );
uiZ:
uZ.ui = uiZ;
return uZ.f;
}
float32_t
softfloat_subMagsF32( uint_fast32_t uiA, uint_fast32_t uiB, bool signZ )
{
int_fast16_t expA;
uint_fast32_t sigA;
int_fast16_t expB;
uint_fast32_t sigB;
int_fast16_t expDiff;
uint_fast32_t uiZ;
int_fast16_t expZ;
uint_fast32_t sigZ;
union ui32_f32 uZ;
expA = expF32UI( uiA );
sigA = fracF32UI( uiA );
expB = expF32UI( uiB );
sigB = fracF32UI( uiB );
expDiff = expA - expB;
sigA <<= 7;
sigB <<= 7;
if ( 0 < expDiff ) goto expABigger;
if ( expDiff < 0 ) goto expBBigger;
if ( expA == 0xFF ) {
if ( sigA | sigB ) goto propagateNaN;
softfloat_raiseFlags( softfloat_flag_invalid );
uiZ = defaultNaNF32UI;
goto uiZ;
}
if ( ! expA ) {
expA = 1;
expB = 1;
}
if ( sigB < sigA ) goto aBigger;
if ( sigA < sigB ) goto bBigger;
uiZ = packToF32UI( softfloat_roundingMode == softfloat_round_min, 0, 0 );
goto uiZ;
expBBigger:
if ( expB == 0xFF ) {
if ( sigB ) goto propagateNaN;
uiZ = packToF32UI( signZ ^ 1, 0xFF, 0 );
goto uiZ;
}
sigA += expA ? 0x40000000 : sigA;
sigA = softfloat_shift32RightJam( sigA, - expDiff );
sigB |= 0x40000000;
bBigger:
signZ ^= 1;
expZ = expB;
sigZ = sigB - sigA;
goto normRoundPack;
expABigger:
if ( expA == 0xFF ) {
if ( sigA ) goto propagateNaN;
uiZ = uiA;
goto uiZ;
}
sigB += expB ? 0x40000000 : sigB;
sigB = softfloat_shift32RightJam( sigB, expDiff );
sigA |= 0x40000000;
aBigger:
expZ = expA;
sigZ = sigA - sigB;
normRoundPack:
return softfloat_normRoundPackToF32( signZ, expZ - 1, sigZ );
propagateNaN:
uiZ = softfloat_propagateNaNF32UI( uiA, uiB );
uiZ:
uZ.ui = uiZ;
return uZ.f;
}
