struct uint192 softfloat_mul128By64To192( uint64_t a64, uint64_t a0, uint64_t b ) { struct uint128 p0, p64; struct uint192 z; p0 = softfloat_mul64To128( a0, b ); z.v0 = p0.v0; p64 = softfloat_mul64To128( a64, b ); z.v64 = p64.v0 + p0.v64; z.v128 = p64.v64 + ( z.v64 < p64.v0 ); return z; }
struct uint256 softfloat_mul128To256( uint64_t a64, uint64_t a0, uint64_t b64, uint64_t b0 ) { struct uint128 p0, p64, p128; struct uint256 z; p0 = softfloat_mul64To128( a0, b0 ); z.v0 = p0.v0; p64 = softfloat_mul64To128( a64, b0 ); z.v64 = p64.v0 + p0.v64; z.v128 = p64.v64 + ( z.v64 < p64.v0 ); p128 = softfloat_mul64To128( a64, b64 ); z.v128 += p128.v0; z.v192 = p128.v64 + ( z.v128 < p128.v0 ); p64 = softfloat_mul64To128( a0, b64 ); z.v64 += p64.v0; p64.v64 += ( z.v64 < p64.v0 ); z.v128 += p64.v64; z.v192 += ( z.v128 < p64.v64 ); return z; }
void softfloat_mul128To256M( uint64_t a64, uint64_t a0, uint64_t b64, uint64_t b0, uint64_t *zPtr ) { struct uint128 p0, p64, p128; uint_fast64_t z64, z128, z192; p0 = softfloat_mul64To128( a0, b0 ); zPtr[indexWord( 4, 0 )] = p0.v0; p64 = softfloat_mul64To128( a64, b0 ); z64 = p64.v0 + p0.v64; z128 = p64.v64 + (z64 < p64.v0); p128 = softfloat_mul64To128( a64, b64 ); z128 += p128.v0; z192 = p128.v64 + (z128 < p128.v0); p64 = softfloat_mul64To128( a0, b64 ); z64 += p64.v0; zPtr[indexWord( 4, 1 )] = z64; p64.v64 += (z64 < p64.v0); z128 += p64.v64; zPtr[indexWord( 4, 2 )] = z128; zPtr[indexWord( 4, 3 )] = z192 + (z128 < p64.v64); }
extFloat80_t extF80_mul( extFloat80_t a, extFloat80_t b ) { union { struct extFloat80M s; extFloat80_t f; } uA; uint_fast16_t uiA64; uint_fast64_t uiA0; bool signA; int_fast32_t expA; uint_fast64_t sigA; union { struct extFloat80M s; extFloat80_t f; } uB; uint_fast16_t uiB64; uint_fast64_t uiB0; bool signB; int_fast32_t expB; uint_fast64_t sigB; bool signZ; uint_fast64_t magBits; struct exp32_sig64 normExpSig; int_fast32_t expZ; struct uint128 sig128Z, uiZ; uint_fast16_t uiZ64; uint_fast64_t uiZ0; union { struct extFloat80M s; extFloat80_t f; } uZ; /*------------------------------------------------------------------------ *------------------------------------------------------------------------*/ uA.f = a; uiA64 = uA.s.signExp; uiA0 = uA.s.signif; signA = signExtF80UI64( uiA64 ); expA = expExtF80UI64( uiA64 ); sigA = uiA0; uB.f = b; uiB64 = uB.s.signExp; uiB0 = uB.s.signif; signB = signExtF80UI64( uiB64 ); expB = expExtF80UI64( uiB64 ); sigB = uiB0; signZ = signA ^ signB; /*------------------------------------------------------------------------ *------------------------------------------------------------------------*/ if ( expA == 0x7FFF ) { if ( (sigA & UINT64_C( 0x7FFFFFFFFFFFFFFF )) || ((expB == 0x7FFF) && (sigB & UINT64_C( 0x7FFFFFFFFFFFFFFF ))) ) { goto propagateNaN; } magBits = expB | sigB; goto infArg; } if ( expB == 0x7FFF ) { if ( sigB & UINT64_C( 0x7FFFFFFFFFFFFFFF ) ) goto propagateNaN; magBits = expA | sigA; goto infArg; } /*------------------------------------------------------------------------ *------------------------------------------------------------------------*/ if ( ! expA ) expA = 1; if ( ! (sigA & UINT64_C( 0x8000000000000000 )) ) { if ( ! sigA ) goto zero; normExpSig = softfloat_normSubnormalExtF80Sig( sigA ); expA += normExpSig.exp; sigA = normExpSig.sig; } if ( ! expB ) expB = 1; if ( ! (sigB & UINT64_C( 0x8000000000000000 )) ) { if ( ! sigB ) goto zero; normExpSig = softfloat_normSubnormalExtF80Sig( sigB ); expB += normExpSig.exp; sigB = normExpSig.sig; } /*------------------------------------------------------------------------ *------------------------------------------------------------------------*/ expZ = expA + expB - 0x3FFE; sig128Z = softfloat_mul64To128( sigA, sigB ); if ( sig128Z.v64 < UINT64_C( 0x8000000000000000 ) ) { --expZ; sig128Z = softfloat_add128( sig128Z.v64, sig128Z.v0, sig128Z.v64, sig128Z.v0 ); } return softfloat_roundPackToExtF80( signZ, expZ, sig128Z.v64, sig128Z.v0, extF80_roundingPrecision ); /*------------------------------------------------------------------------ *------------------------------------------------------------------------*/ propagateNaN: uiZ = softfloat_propagateNaNExtF80UI( uiA64, uiA0, uiB64, uiB0 ); uiZ64 = uiZ.v64; uiZ0 = uiZ.v0; goto uiZ; /*------------------------------------------------------------------------ *------------------------------------------------------------------------*/ infArg: if ( ! magBits ) { softfloat_raiseFlags( softfloat_flag_invalid ); uiZ64 = defaultNaNExtF80UI64; uiZ0 = defaultNaNExtF80UI0; } else { uiZ64 = packToExtF80UI64( signZ, 0x7FFF ); uiZ0 = UINT64_C( 0x8000000000000000 ); } goto uiZ; /*------------------------------------------------------------------------ *------------------------------------------------------------------------*/ zero: uiZ64 = packToExtF80UI64( signZ, 0 ); uiZ0 = 0; uiZ: uZ.s.signExp = uiZ64; uZ.s.signif = uiZ0; return uZ.f; }
float64_t softfloat_mulAddF64( uint_fast64_t uiA, uint_fast64_t uiB, uint_fast64_t uiC, uint_fast8_t op ) { bool signA; int_fast16_t expA; uint_fast64_t sigA; bool signB; int_fast16_t expB; uint_fast64_t sigB; bool signC; int_fast16_t expC; uint_fast64_t sigC; bool signZ; uint_fast64_t magBits, uiZ; struct exp16_sig64 normExpSig; int_fast16_t expZ; struct uint128 sig128Z; uint_fast64_t sigZ; int_fast16_t expDiff; struct uint128 sig128C; int_fast8_t shiftCount; union ui64_f64 uZ; /*------------------------------------------------------------------------ *------------------------------------------------------------------------*/ signA = signF64UI( uiA ); expA = expF64UI( uiA ); sigA = fracF64UI( uiA ); signB = signF64UI( uiB ); expB = expF64UI( uiB ); sigB = fracF64UI( uiB ); signC = signF64UI( uiC ) ^ (op == softfloat_mulAdd_subC); expC = expF64UI( uiC ); sigC = fracF64UI( uiC ); signZ = signA ^ signB ^ (op == softfloat_mulAdd_subProd); /*------------------------------------------------------------------------ *------------------------------------------------------------------------*/ if ( expA == 0x7FF ) { if ( sigA || ((expB == 0x7FF) && sigB) ) goto propagateNaN_ABC; magBits = expB | sigB; goto infProdArg; } if ( expB == 0x7FF ) { if ( sigB ) goto propagateNaN_ABC; magBits = expA | sigA; goto infProdArg; } if ( expC == 0x7FF ) { if ( sigC ) { uiZ = 0; goto propagateNaN_ZC; } uiZ = uiC; goto uiZ; } /*------------------------------------------------------------------------ *------------------------------------------------------------------------*/ if ( ! expA ) { if ( ! sigA ) goto zeroProd; normExpSig = softfloat_normSubnormalF64Sig( sigA ); expA = normExpSig.exp; sigA = normExpSig.sig; } if ( ! expB ) { if ( ! sigB ) goto zeroProd; normExpSig = softfloat_normSubnormalF64Sig( sigB ); expB = normExpSig.exp; sigB = normExpSig.sig; } /*------------------------------------------------------------------------ *------------------------------------------------------------------------*/ expZ = expA + expB - 0x3FE; sigA = (sigA | UINT64_C( 0x0010000000000000 ))<<10; sigB = (sigB | UINT64_C( 0x0010000000000000 ))<<10; sig128Z = softfloat_mul64To128( sigA, sigB ); if ( sig128Z.v64 < UINT64_C( 0x2000000000000000 ) ) { --expZ; sig128Z = softfloat_add128( sig128Z.v64, sig128Z.v0, sig128Z.v64, sig128Z.v0 ); } if ( ! expC ) { if ( ! sigC ) { --expZ; sigZ = sig128Z.v64<<1 | (sig128Z.v0 != 0); goto roundPack; } normExpSig = softfloat_normSubnormalF64Sig( sigC ); expC = normExpSig.exp; sigC = normExpSig.sig; } sigC = (sigC | UINT64_C( 0x0010000000000000 ))<<9; /*------------------------------------------------------------------------ *------------------------------------------------------------------------*/ expDiff = expZ - expC; if ( expDiff < 0 ) { expZ = expC; if ( (signZ == signC) || (expDiff < -1) ) { sig128Z.v64 = softfloat_shiftRightJam64( sig128Z.v64, -expDiff ); } else { sig128Z = softfloat_shortShiftRightJam128( sig128Z.v64, sig128Z.v0, 1 ); } } else if ( expDiff ) { sig128C = softfloat_shiftRightJam128( sigC, 0, expDiff ); } /*------------------------------------------------------------------------ *------------------------------------------------------------------------*/ if ( signZ == signC ) { /*-------------------------------------------------------------------- *--------------------------------------------------------------------*/ if ( expDiff <= 0 ) { sigZ = (sigC + sig128Z.v64) | (sig128Z.v0 != 0); } else { sig128Z = softfloat_add128( sig128Z.v64, sig128Z.v0, sig128C.v64, sig128C.v0 ); sigZ = sig128Z.v64 | (sig128Z.v0 != 0); } if ( sigZ < UINT64_C( 0x4000000000000000 ) ) { --expZ; sigZ <<= 1; } } else { /*-------------------------------------------------------------------- *--------------------------------------------------------------------*/ if ( expDiff < 0 ) { signZ = signC; sig128Z = softfloat_sub128( sigC, 0, sig128Z.v64, sig128Z.v0 ); } else if ( ! expDiff ) { sig128Z.v64 = sig128Z.v64 - sigC; if ( ! (sig128Z.v64 | sig128Z.v0) ) goto completeCancellation; if ( sig128Z.v64 & UINT64_C( 0x8000000000000000 ) ) { signZ ^= 1; sig128Z = softfloat_sub128( 0, 0, sig128Z.v64, sig128Z.v0 ); } } else { sig128Z = softfloat_sub128( sig128Z.v64, sig128Z.v0, sig128C.v64, sig128C.v0 ); } /*-------------------------------------------------------------------- *--------------------------------------------------------------------*/ if ( ! sig128Z.v64 ) { expZ -= 64; sig128Z.v64 = sig128Z.v0; sig128Z.v0 = 0; } shiftCount = softfloat_countLeadingZeros64( sig128Z.v64 ) - 1; expZ -= shiftCount; if ( shiftCount < 0 ) { sigZ = softfloat_shortShiftRightJam64( sig128Z.v64, -shiftCount ); } else { sig128Z = softfloat_shortShiftLeft128( sig128Z.v64, sig128Z.v0, shiftCount ); sigZ = sig128Z.v64; } sigZ |= (sig128Z.v0 != 0); } roundPack: return softfloat_roundPackToF64( signZ, expZ, sigZ ); /*------------------------------------------------------------------------ *------------------------------------------------------------------------*/ propagateNaN_ABC: uiZ = softfloat_propagateNaNF64UI( uiA, uiB ); goto propagateNaN_ZC; /*------------------------------------------------------------------------ *------------------------------------------------------------------------*/ infProdArg: if ( magBits ) { uiZ = packToF64UI( signZ, 0x7FF, 0 ); if ( expC != 0x7FF ) goto uiZ; if ( sigC ) goto propagateNaN_ZC; if ( signZ == signC ) goto uiZ; } invalid: softfloat_raiseFlags( softfloat_flag_invalid ); uiZ = defaultNaNF64UI; propagateNaN_ZC: uiZ = softfloat_propagateNaNF64UI( uiZ, uiC ); goto uiZ; /*------------------------------------------------------------------------ *------------------------------------------------------------------------*/ zeroProd: uiZ = uiC; if ( ! (expC | sigC) && (signZ != signC) ) { completeCancellation: uiZ = packToF64UI( softfloat_roundingMode == softfloat_round_min, 0, 0 ); } uiZ: uZ.ui = uiZ; return uZ.f; }
float64_t f64_mul( float64_t a, float64_t b ) { union ui64_f64 uA; uint_fast64_t uiA; bool signA; int_fast16_t expA; uint_fast64_t sigA; union ui64_f64 uB; uint_fast64_t uiB; bool signB; int_fast16_t expB; uint_fast64_t sigB; bool signZ; uint_fast64_t magBits; struct exp16_sig64 normExpSig; int_fast16_t expZ; #ifdef SOFTFLOAT_FAST_INT64 struct uint128 sig128Z; #else uint32_t sig128Z[4]; #endif uint_fast64_t sigZ, uiZ; union ui64_f64 uZ; /*------------------------------------------------------------------------ *------------------------------------------------------------------------*/ uA.f = a; uiA = uA.ui; signA = signF64UI( uiA ); expA = expF64UI( uiA ); sigA = fracF64UI( uiA ); uB.f = b; uiB = uB.ui; signB = signF64UI( uiB ); expB = expF64UI( uiB ); sigB = fracF64UI( uiB ); signZ = signA ^ signB; /*------------------------------------------------------------------------ *------------------------------------------------------------------------*/ if ( expA == 0x7FF ) { if ( sigA || ((expB == 0x7FF) && sigB) ) goto propagateNaN; magBits = expB | sigB; goto infArg; } if ( expB == 0x7FF ) { if ( sigB ) goto propagateNaN; magBits = expA | sigA; goto infArg; } /*------------------------------------------------------------------------ *------------------------------------------------------------------------*/ if ( ! expA ) { if ( ! sigA ) goto zero; normExpSig = softfloat_normSubnormalF64Sig( sigA ); expA = normExpSig.exp; sigA = normExpSig.sig; } if ( ! expB ) { if ( ! sigB ) goto zero; normExpSig = softfloat_normSubnormalF64Sig( sigB ); expB = normExpSig.exp; sigB = normExpSig.sig; } /*------------------------------------------------------------------------ *------------------------------------------------------------------------*/ expZ = expA + expB - 0x3FF; sigA = (sigA | UINT64_C( 0x0010000000000000 ))<<10; sigB = (sigB | UINT64_C( 0x0010000000000000 ))<<11; #ifdef SOFTFLOAT_FAST_INT64 sig128Z = softfloat_mul64To128( sigA, sigB ); sigZ = sig128Z.v64 | (sig128Z.v0 != 0); #else softfloat_mul64To128M( sigA, sigB, sig128Z ); sigZ = (uint64_t) sig128Z[indexWord( 4, 3 )]<<32 | sig128Z[indexWord( 4, 2 )]; if ( sig128Z[indexWord( 4, 1 )] || sig128Z[indexWord( 4, 0 )] ) sigZ |= 1; #endif if ( sigZ < UINT64_C( 0x4000000000000000 ) ) { --expZ; sigZ <<= 1; } return softfloat_roundPackToF64( signZ, expZ, sigZ ); /*------------------------------------------------------------------------ *------------------------------------------------------------------------*/ propagateNaN: uiZ = softfloat_propagateNaNF64UI( uiA, uiB ); goto uiZ; /*------------------------------------------------------------------------ *------------------------------------------------------------------------*/ infArg: if ( ! magBits ) { softfloat_raiseFlags( softfloat_flag_invalid ); uiZ = defaultNaNF64UI; } else { uiZ = packToF64UI( signZ, 0x7FF, 0 ); } goto uiZ; /*------------------------------------------------------------------------ *------------------------------------------------------------------------*/ zero: uiZ = packToF64UI( signZ, 0, 0 ); uiZ: uZ.ui = uiZ; return uZ.f; }
float64_t f64_mul( float64_t a, float64_t b ) { union ui64_f64 uA; uint_fast64_t uiA; bool signA; int_fast16_t expA; uint_fast64_t sigA; union ui64_f64 uB; uint_fast64_t uiB; bool signB; int_fast16_t expB; uint_fast64_t sigB; bool signZ; uint_fast64_t magBits; struct exp16_sig64 normExpSig; int_fast16_t expZ; struct uint128 sigZ128; uint_fast64_t sigZ, uiZ; union ui64_f64 uZ; uA.f = a; uiA = uA.ui; signA = signF64UI( uiA ); expA = expF64UI( uiA ); sigA = fracF64UI( uiA ); uB.f = b; uiB = uB.ui; signB = signF64UI( uiB ); expB = expF64UI( uiB ); sigB = fracF64UI( uiB ); signZ = signA ^ signB; if ( expA == 0x7FF ) { if ( sigA || ( ( expB == 0x7FF ) && sigB ) ) goto propagateNaN; magBits = expB | sigB; goto infArg; } if ( expB == 0x7FF ) { if ( sigB ) goto propagateNaN; magBits = expA | sigA; goto infArg; } if ( ! expA ) { if ( ! sigA ) goto zero; normExpSig = softfloat_normSubnormalF64Sig( sigA ); expA = normExpSig.exp; sigA = normExpSig.sig; } if ( ! expB ) { if ( ! sigB ) goto zero; normExpSig = softfloat_normSubnormalF64Sig( sigB ); expB = normExpSig.exp; sigB = normExpSig.sig; } expZ = expA + expB - 0x3FF; sigA = ( sigA | UINT64_C( 0x0010000000000000 ) )<<10; sigB = ( sigB | UINT64_C( 0x0010000000000000 ) )<<11; sigZ128 = softfloat_mul64To128( sigA, sigB ); sigZ = sigZ128.v64 | ( sigZ128.v0 != 0 ); if ( sigZ < UINT64_C( 0x4000000000000000 ) ) { --expZ; sigZ <<= 1; } return softfloat_roundPackToF64( signZ, expZ, sigZ ); propagateNaN: uiZ = softfloat_propagateNaNF64UI( uiA, uiB ); goto uiZ; infArg: if ( ! magBits ) { softfloat_raiseFlags( softfloat_flag_invalid ); uiZ = defaultNaNF64UI; } else { uiZ = packToF64UI( signZ, 0x7FF, 0 ); } goto uiZ; zero: uiZ = packToF64UI( signZ, 0, 0 ); uiZ: uZ.ui = uiZ; return uZ.f; }