float16_t f16_add( float16_t a, float16_t b )
{
union ui16_f16 uA;
uint_fast16_t uiA;
union ui16_f16 uB;
uint_fast16_t uiB;
#if ! defined INLINE_LEVEL || (INLINE_LEVEL < 1)
float16_t (*magsFuncPtr)( uint_fast16_t, uint_fast16_t );
#endif
uA.f = a;
uiA = uA.ui;
uB.f = b;
uiB = uB.ui;
#if defined INLINE_LEVEL && (1 <= INLINE_LEVEL)
if ( signF16UI( uiA ^ uiB ) ) {
return softfloat_subMagsF16( uiA, uiB );
} else {
return softfloat_addMagsF16( uiA, uiB );
}
#else
magsFuncPtr =
signF16UI( uiA ^ uiB ) ? softfloat_subMagsF16 : softfloat_addMagsF16;
return (*magsFuncPtr)( uiA, uiB );
#endif
}
bool f16_le_quiet( float16_t a, float16_t b )
{
union ui16_f16 uA;
uint_fast16_t uiA;
union ui16_f16 uB;
uint_fast16_t uiB;
bool signA, signB;
uA.f = a;
uiA = uA.ui;
uB.f = b;
uiB = uB.ui;
if ( isNaNF16UI( uiA ) || isNaNF16UI( uiB ) ) {
if (
softfloat_isSigNaNF16UI( uiA ) || softfloat_isSigNaNF16UI( uiB )
) {
softfloat_raiseFlags( softfloat_flag_invalid );
}
return false;
}
signA = signF16UI( uiA );
signB = signF16UI( uiB );
return
(signA != signB) ? signA || ! (uint16_t) ((uiA | uiB)<<1)
: (uiA == uiB) || (signA ^ (uiA < uiB));
}
extFloat80_t f16_to_extF80( float16_t a )
{
union ui16_f16 uA;
uint_fast16_t uiA;
bool sign;
int_fast8_t exp;
uint_fast16_t frac;
struct commonNaN commonNaN;
struct uint128 uiZ;
uint_fast16_t uiZ64;
uint_fast64_t uiZ0;
struct exp8_sig16 normExpSig;
union { struct extFloat80M s; extFloat80_t f; } uZ;
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
uA.f = a;
uiA = uA.ui;
sign = signF16UI( uiA );
exp = expF16UI( uiA );
frac = fracF16UI( uiA );
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
if ( exp == 0x1F ) {
if ( frac ) {
softfloat_f16UIToCommonNaN( uiA, &commonNaN );
uiZ = softfloat_commonNaNToExtF80UI( &commonNaN );
uiZ64 = uiZ.v64;
uiZ0 = uiZ.v0;
} else {
uiZ64 = packToExtF80UI64( sign, 0x7FFF );
uiZ0 = UINT64_C( 0x8000000000000000 );
}
goto uiZ;
}
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
if ( ! exp ) {
if ( ! frac ) {
uiZ64 = packToExtF80UI64( sign, 0 );
uiZ0 = 0;
goto uiZ;
}
normExpSig = softfloat_normSubnormalF16Sig( frac );
exp = normExpSig.exp;
frac = normExpSig.sig;
}
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
uiZ64 = packToExtF80UI64( sign, exp + 0x3FF0 );
uiZ0 = (uint_fast64_t) (frac | 0x0400)<<53;
uiZ:
uZ.s.signExp = uiZ64;
uZ.s.signif = uiZ0;
return uZ.f;
}
float128_t f16_to_f128( float16_t a )
{
union ui16_f16 uA;
uint_fast16_t uiA;
bool sign;
int_fast8_t exp;
uint_fast16_t frac;
struct commonNaN commonNaN;
struct uint128 uiZ;
struct exp8_sig16 normExpSig;
union ui128_f128 uZ;
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
uA.f = a;
uiA = uA.ui;
sign = signF16UI( uiA );
exp = expF16UI( uiA );
frac = fracF16UI( uiA );
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
if ( exp == 0x1F ) {
if ( frac ) {
softfloat_f16UIToCommonNaN( uiA, &commonNaN );
uiZ = softfloat_commonNaNToF128UI( &commonNaN );
} else {
uiZ.v64 = packToF128UI64( sign, 0x7FFF, 0 );
uiZ.v0 = 0;
}
goto uiZ;
}
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
if ( ! exp ) {
if ( ! frac ) {
uiZ.v64 = packToF128UI64( sign, 0, 0 );
uiZ.v0 = 0;
goto uiZ;
}
normExpSig = softfloat_normSubnormalF16Sig( frac );
exp = normExpSig.exp - 1;
frac = normExpSig.sig;
}
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
uiZ.v64 = packToF128UI64( sign, exp + 0x3FF0, (uint_fast64_t) frac<<38 );
uiZ.v0 = 0;
uiZ:
uZ.ui = uiZ;
return uZ.f;
}
float32_t f16_to_f32( float16_t a )
{
union ui16_f16 uA;
uint_fast16_t uiA;
bool sign;
int_fast8_t exp;
uint_fast16_t frac;
struct commonNaN commonNaN;
uint_fast32_t uiZ;
struct exp8_sig16 normExpSig;
union ui32_f32 uZ;
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
uA.f = a;
uiA = uA.ui;
sign = signF16UI( uiA );
exp = expF16UI( uiA );
frac = fracF16UI( uiA );
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
if ( exp == 0x1F ) {
if ( frac ) {
softfloat_f16UIToCommonNaN( uiA, &commonNaN );
uiZ = softfloat_commonNaNToF32UI( &commonNaN );
} else {
uiZ = packToF32UI( sign, 0xFF, 0 );
}
goto uiZ;
}
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
if ( ! exp ) {
if ( ! frac ) {
uiZ = packToF32UI( sign, 0, 0 );
goto uiZ;
}
normExpSig = softfloat_normSubnormalF16Sig( frac );
exp = normExpSig.exp - 1;
frac = normExpSig.sig;
}
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
uiZ = packToF32UI( sign, exp + 0x70, (uint_fast32_t) frac<<13 );
uiZ:
uZ.ui = uiZ;
return uZ.f;
}
int_fast64_t f16_to_i64_r_minMag( float16_t a, bool exact )
{
union ui16_f16 uA;
uint_fast16_t uiA;
int_fast8_t exp;
uint_fast16_t frac;
int_fast8_t shiftDist;
bool sign;
int_fast32_t alignedSig;
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
uA.f = a;
uiA = uA.ui;
exp = expF16UI( uiA );
frac = fracF16UI( uiA );
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
shiftDist = exp - 0x0F;
if ( shiftDist < 0 ) {
if ( exact && (exp | frac) ) {
softfloat_exceptionFlags |= softfloat_flag_inexact;
}
return 0;
}
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
sign = signF16UI( uiA );
if ( exp == 0x1F ) {
softfloat_raiseFlags( softfloat_flag_invalid );
return
(exp == 0x1F) && frac ? i64_fromNaN
: sign ? i64_fromNegOverflow : i64_fromPosOverflow;
}
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
alignedSig = (int_fast32_t) (frac | 0x0400)<<shiftDist;
if ( exact && (alignedSig & 0x3FF) ) {
softfloat_exceptionFlags |= softfloat_flag_inexact;
}
alignedSig >>= 10;
return sign ? -alignedSig : alignedSig;
}
int_fast64_t f16_to_i64( float16_t a, uint_fast8_t roundingMode, bool exact )
{
union ui16_f16 uA;
uint_fast16_t uiA;
bool sign;
int_fast8_t exp;
uint_fast16_t frac;
int_fast32_t sig32;
int_fast8_t shiftDist;
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
uA.f = a;
uiA = uA.ui;
sign = signF16UI( uiA );
exp = expF16UI( uiA );
frac = fracF16UI( uiA );
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
if ( exp == 0x1F ) {
softfloat_raiseFlags( softfloat_flag_invalid );
return
frac ? i64_fromNaN
: sign ? i64_fromNegOverflow : i64_fromPosOverflow;
}
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
sig32 = frac;
if ( exp ) {
sig32 |= 0x0400;
shiftDist = exp - 0x19;
if ( 0 <= shiftDist ) {
sig32 <<= shiftDist;
return sign ? -sig32 : sig32;
}
shiftDist = exp - 0x0D;
if ( 0 < shiftDist ) sig32 <<= shiftDist;
}
return
softfloat_roundPackToI32(
sign, (uint_fast32_t) sig32, roundingMode, exact );
}
float16_t f16_rem( float16_t a, float16_t b )
{
union ui16_f16 uA;
uint_fast16_t uiA;
bool signA;
int_fast8_t expA;
uint_fast16_t sigA;
union ui16_f16 uB;
uint_fast16_t uiB;
int_fast8_t expB;
uint_fast16_t sigB;
struct exp8_sig16 normExpSig;
uint16_t rem;
int_fast8_t expDiff;
uint_fast16_t q;
uint32_t recip32, q32;
uint16_t altRem, meanRem;
bool signRem;
uint_fast16_t uiZ;
union ui16_f16 uZ;
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
uA.f = a;
uiA = uA.ui;
signA = signF16UI( uiA );
expA = expF16UI( uiA );
sigA = fracF16UI( uiA );
uB.f = b;
uiB = uB.ui;
expB = expF16UI( uiB );
sigB = fracF16UI( uiB );
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
if ( expA == 0x1F ) {
if ( sigA || ((expB == 0x1F) && sigB) ) goto propagateNaN;
goto invalid;
}
if ( expB == 0x1F ) {
if ( sigB ) goto propagateNaN;
return a;
}
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
if ( ! expB ) {
if ( ! sigB ) goto invalid;
normExpSig = softfloat_normSubnormalF16Sig( sigB );
expB = normExpSig.exp;
sigB = normExpSig.sig;
}
if ( ! expA ) {
if ( ! sigA ) return a;
normExpSig = softfloat_normSubnormalF16Sig( sigA );
expA = normExpSig.exp;
sigA = normExpSig.sig;
}
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
rem = sigA | 0x0400;
sigB |= 0x0400;
expDiff = expA - expB;
if ( expDiff < 1 ) {
if ( expDiff < -1 ) return a;
sigB <<= 3;
if ( expDiff ) {
rem <<= 2;
q = 0;
} else {
rem <<= 3;
q = (sigB <= rem);
if ( q ) rem -= sigB;
}
} else {
recip32 = softfloat_approxRecip32_1( (uint_fast32_t) sigB<<21 );
/*--------------------------------------------------------------------
| Changing the shift of `rem' here requires also changing the initial
| subtraction from `expDiff'.
*--------------------------------------------------------------------*/
rem <<= 4;
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 <<= 3;
for (;;) {
q32 = (rem * (uint_fast64_t) recip32)>>16;
if ( expDiff < 0 ) break;
rem = -((uint_fast16_t) q32 * sigB);
expDiff -= 29;
}
/*--------------------------------------------------------------------
| (`expDiff' cannot be less than -30 here.)
*--------------------------------------------------------------------*/
q32 >>= ~expDiff & 31;
q = q32;
rem = (rem<<(expDiff + 30)) - q * sigB;
}
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
do {
altRem = rem;
++q;
rem -= sigB;
} while ( ! (rem & 0x8000) );
meanRem = rem + altRem;
if ( (meanRem & 0x8000) || (! meanRem && (q & 1)) ) rem = altRem;
signRem = signA;
if ( 0x8000 <= rem ) {
signRem = ! signRem;
rem = -rem;
}
return softfloat_normRoundPackToF16( signRem, expB, rem );
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
propagateNaN:
uiZ = softfloat_propagateNaNF16UI( uiA, uiB );
goto uiZ;
invalid:
softfloat_raiseFlags( softfloat_flag_invalid );
uiZ = defaultNaNF16UI;
uiZ:
uZ.ui = uiZ;
return uZ.f;
}
float16_t f16_mul( float16_t a, float16_t b )
{
union ui16_f16 uA;
uint_fast16_t uiA;
bool signA;
int_fast8_t expA;
uint_fast16_t sigA;
union ui16_f16 uB;
uint_fast16_t uiB;
bool signB;
int_fast8_t expB;
uint_fast16_t sigB;
bool signZ;
uint_fast16_t magBits;
struct exp8_sig16 normExpSig;
int_fast8_t expZ;
uint_fast32_t sig32Z;
uint_fast16_t sigZ, uiZ;
union ui16_f16 uZ;
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
uA.f = a;
uiA = uA.ui;
signA = signF16UI( uiA );
expA = expF16UI( uiA );
sigA = fracF16UI( uiA );
uB.f = b;
uiB = uB.ui;
signB = signF16UI( uiB );
expB = expF16UI( uiB );
sigB = fracF16UI( uiB );
signZ = signA ^ signB;
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
if ( expA == 0x1F ) {
if ( sigA || ((expB == 0x1F) && sigB) ) goto propagateNaN;
magBits = expB | sigB;
goto infArg;
}
if ( expB == 0x1F ) {
if ( sigB ) goto propagateNaN;
magBits = expA | sigA;
goto infArg;
}
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
if ( ! expA ) {
if ( ! sigA ) goto zero;
normExpSig = softfloat_normSubnormalF16Sig( sigA );
expA = normExpSig.exp;
sigA = normExpSig.sig;
}
if ( ! expB ) {
if ( ! sigB ) goto zero;
normExpSig = softfloat_normSubnormalF16Sig( sigB );
expB = normExpSig.exp;
sigB = normExpSig.sig;
}
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
expZ = expA + expB - 0xF;
sigA = (sigA | 0x0400)<<4;
sigB = (sigB | 0x0400)<<5;
sig32Z = (uint_fast32_t) sigA * sigB;
sigZ = sig32Z>>16;
if ( sig32Z & 0xFFFF ) sigZ |= 1;
if ( sigZ < 0x4000 ) {
--expZ;
sigZ <<= 1;
}
return softfloat_roundPackToF16( signZ, expZ, sigZ );
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
propagateNaN:
uiZ = softfloat_propagateNaNF16UI( uiA, uiB );
goto uiZ;
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
infArg:
if ( ! magBits ) {
softfloat_raiseFlags( softfloat_flag_invalid );
uiZ = defaultNaNF16UI;
} else {
uiZ = packToF16UI( signZ, 0x1F, 0 );
}
goto uiZ;
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
zero:
uiZ = packToF16UI( signZ, 0, 0 );
uiZ:
uZ.ui = uiZ;
return uZ.f;
}
float16_t
softfloat_mulAddF16(
uint_fast16_t uiA, uint_fast16_t uiB, uint_fast16_t uiC, uint_fast8_t op )
{
bool signA;
int_fast8_t expA;
uint_fast16_t sigA;
bool signB;
int_fast8_t expB;
uint_fast16_t sigB;
bool signC;
int_fast8_t expC;
uint_fast16_t sigC;
bool signProd;
uint_fast16_t magBits, uiZ;
struct exp8_sig16 normExpSig;
int_fast8_t expProd;
uint_fast32_t sigProd;
bool signZ;
int_fast8_t expZ;
uint_fast16_t sigZ;
int_fast8_t expDiff;
uint_fast32_t sig32Z, sig32C;
int_fast8_t shiftDist;
union ui16_f16 uZ;
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
signA = signF16UI( uiA );
expA = expF16UI( uiA );
sigA = fracF16UI( uiA );
signB = signF16UI( uiB );
expB = expF16UI( uiB );
sigB = fracF16UI( uiB );
signC = signF16UI( uiC ) ^ (op == softfloat_mulAdd_subC);
expC = expF16UI( uiC );
sigC = fracF16UI( uiC );
signProd = signA ^ signB ^ (op == softfloat_mulAdd_subProd);
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
if ( expA == 0x1F ) {
if ( sigA || ((expB == 0x1F) && sigB) ) goto propagateNaN_ABC;
magBits = expB | sigB;
goto infProdArg;
}
if ( expB == 0x1F ) {
if ( sigB ) goto propagateNaN_ABC;
magBits = expA | sigA;
goto infProdArg;
}
if ( expC == 0x1F ) {
if ( sigC ) {
uiZ = 0;
goto propagateNaN_ZC;
}
uiZ = uiC;
goto uiZ;
}
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
if ( ! expA ) {
if ( ! sigA ) goto zeroProd;
normExpSig = softfloat_normSubnormalF16Sig( sigA );
expA = normExpSig.exp;
sigA = normExpSig.sig;
}
if ( ! expB ) {
if ( ! sigB ) goto zeroProd;
normExpSig = softfloat_normSubnormalF16Sig( sigB );
expB = normExpSig.exp;
sigB = normExpSig.sig;
}
/*------------------------------------------------------------------------
*------------------------------------------------------------------------*/
expProd = expA + expB - 0xE;
sigA = (sigA | 0x0400)<<4;
sigB = (sigB | 0x0400)<<4;
sigProd = (uint_fast32_t) sigA * sigB;
if ( sigProd < 0x20000000 ) {
--expProd;
sigProd <<= 1;
}
signZ = signProd;
if ( ! expC ) {
if ( ! sigC ) {
expZ = expProd - 1;
sigZ = sigProd>>15 | ((sigProd & 0x7FFF) != 0);
goto roundPack;
}
normExpSig = softfloat_normSubnormalF16Sig( sigC );
expC = normExpSig.exp;
sigC = normExpSig.sig;
}
