diff options
Diffstat (limited to 'fpu/softfloat.c')
| -rw-r--r-- | fpu/softfloat.c | 427 |
1 files changed, 427 insertions, 0 deletions
diff --git a/fpu/softfloat.c b/fpu/softfloat.c index 3aafa81d58..81a7d1ae09 100644 --- a/fpu/softfloat.c +++ b/fpu/softfloat.c @@ -2118,6 +2118,213 @@ float32 float32_rem( float32 a, float32 b STATUS_PARAM ) } /*---------------------------------------------------------------------------- +| Returns the result of multiplying the single-precision floating-point values +| `a' and `b' then adding 'c', with no intermediate rounding step after the +| multiplication. The operation is performed according to the IEC/IEEE +| Standard for Binary Floating-Point Arithmetic 754-2008. +| The flags argument allows the caller to select negation of the +| addend, the intermediate product, or the final result. (The difference +| between this and having the caller do a separate negation is that negating +| externally will flip the sign bit on NaNs.) +*----------------------------------------------------------------------------*/ + +float32 float32_muladd(float32 a, float32 b, float32 c, int flags STATUS_PARAM) +{ + flag aSign, bSign, cSign, zSign; + int aExp, bExp, cExp, pExp, zExp, expDiff; + uint32_t aSig, bSig, cSig; + flag pInf, pZero, pSign; + uint64_t pSig64, cSig64, zSig64; + uint32_t pSig; + int shiftcount; + flag signflip, infzero; + + a = float32_squash_input_denormal(a STATUS_VAR); + b = float32_squash_input_denormal(b STATUS_VAR); + c = float32_squash_input_denormal(c STATUS_VAR); + aSig = extractFloat32Frac(a); + aExp = extractFloat32Exp(a); + aSign = extractFloat32Sign(a); + bSig = extractFloat32Frac(b); + bExp = extractFloat32Exp(b); + bSign = extractFloat32Sign(b); + cSig = extractFloat32Frac(c); + cExp = extractFloat32Exp(c); + cSign = extractFloat32Sign(c); + + infzero = ((aExp == 0 && aSig == 0 && bExp == 0xff && bSig == 0) || + (aExp == 0xff && aSig == 0 && bExp == 0 && bSig == 0)); + + /* It is implementation-defined whether the cases of (0,inf,qnan) + * and (inf,0,qnan) raise InvalidOperation or not (and what QNaN + * they return if they do), so we have to hand this information + * off to the target-specific pick-a-NaN routine. + */ + if (((aExp == 0xff) && aSig) || + ((bExp == 0xff) && bSig) || + ((cExp == 0xff) && cSig)) { + return propagateFloat32MulAddNaN(a, b, c, infzero STATUS_VAR); + } + + if (infzero) { + float_raise(float_flag_invalid STATUS_VAR); + return float32_default_nan; + } + + if (flags & float_muladd_negate_c) { + cSign ^= 1; + } + + signflip = (flags & float_muladd_negate_result) ? 1 : 0; + + /* Work out the sign and type of the product */ + pSign = aSign ^ bSign; + if (flags & float_muladd_negate_product) { + pSign ^= 1; + } + pInf = (aExp == 0xff) || (bExp == 0xff); + pZero = ((aExp | aSig) == 0) || ((bExp | bSig) == 0); + + if (cExp == 0xff) { + if (pInf && (pSign ^ cSign)) { + /* addition of opposite-signed infinities => InvalidOperation */ + float_raise(float_flag_invalid STATUS_VAR); + return float32_default_nan; + } + /* Otherwise generate an infinity of the same sign */ + return packFloat32(cSign ^ signflip, 0xff, 0); + } + + if (pInf) { + return packFloat32(pSign ^ signflip, 0xff, 0); + } + + if (pZero) { + if (cExp == 0) { + if (cSig == 0) { + /* Adding two exact zeroes */ + if (pSign == cSign) { + zSign = pSign; + } else if (STATUS(float_rounding_mode) == float_round_down) { + zSign = 1; + } else { + zSign = 0; + } + return packFloat32(zSign ^ signflip, 0, 0); + } + /* Exact zero plus a denorm */ + if (STATUS(flush_to_zero)) { + float_raise(float_flag_output_denormal STATUS_VAR); + return packFloat32(cSign ^ signflip, 0, 0); + } + } + /* Zero plus something non-zero : just return the something */ + return c ^ (signflip << 31); + } + + if (aExp == 0) { + normalizeFloat32Subnormal(aSig, &aExp, &aSig); + } + if (bExp == 0) { + normalizeFloat32Subnormal(bSig, &bExp, &bSig); + } + + /* Calculate the actual result a * b + c */ + + /* Multiply first; this is easy. */ + /* NB: we subtract 0x7e where float32_mul() subtracts 0x7f + * because we want the true exponent, not the "one-less-than" + * flavour that roundAndPackFloat32() takes. + */ + pExp = aExp + bExp - 0x7e; + aSig = (aSig | 0x00800000) << 7; + bSig = (bSig | 0x00800000) << 8; + pSig64 = (uint64_t)aSig * bSig; + if ((int64_t)(pSig64 << 1) >= 0) { + pSig64 <<= 1; + pExp--; + } + + zSign = pSign ^ signflip; + + /* Now pSig64 is the significand of the multiply, with the explicit bit in + * position 62. + */ + if (cExp == 0) { + if (!cSig) { + /* Throw out the special case of c being an exact zero now */ + shift64RightJamming(pSig64, 32, &pSig64); + pSig = pSig64; + return roundAndPackFloat32(zSign, pExp - 1, + pSig STATUS_VAR); + } + normalizeFloat32Subnormal(cSig, &cExp, &cSig); + } + + cSig64 = (uint64_t)cSig << (62 - 23); + cSig64 |= LIT64(0x4000000000000000); + expDiff = pExp - cExp; + + if (pSign == cSign) { + /* Addition */ + if (expDiff > 0) { + /* scale c to match p */ + shift64RightJamming(cSig64, expDiff, &cSig64); + zExp = pExp; + } else if (expDiff < 0) { + /* scale p to match c */ + shift64RightJamming(pSig64, -expDiff, &pSig64); + zExp = cExp; + } else { + /* no scaling needed */ + zExp = cExp; + } + /* Add significands and make sure explicit bit ends up in posn 62 */ + zSig64 = pSig64 + cSig64; + if ((int64_t)zSig64 < 0) { + shift64RightJamming(zSig64, 1, &zSig64); + } else { + zExp--; + } + } else { + /* Subtraction */ + if (expDiff > 0) { + shift64RightJamming(cSig64, expDiff, &cSig64); + zSig64 = pSig64 - cSig64; + zExp = pExp; + } else if (expDiff < 0) { + shift64RightJamming(pSig64, -expDiff, &pSig64); + zSig64 = cSig64 - pSig64; + zExp = cExp; + zSign ^= 1; + } else { + zExp = pExp; + if (cSig64 < pSig64) { + zSig64 = pSig64 - cSig64; + } else if (pSig64 < cSig64) { + zSig64 = cSig64 - pSig64; + zSign ^= 1; + } else { + /* Exact zero */ + zSign = signflip; + if (STATUS(float_rounding_mode) == float_round_down) { + zSign ^= 1; + } + return packFloat32(zSign, 0, 0); + } + } + --zExp; + /* Normalize to put the explicit bit back into bit 62. */ + shiftcount = countLeadingZeros64(zSig64) - 1; + zSig64 <<= shiftcount; + zExp -= shiftcount; + } + shift64RightJamming(zSig64, 32, &zSig64); + return roundAndPackFloat32(zSign, zExp, zSig64 STATUS_VAR); +} + + +/*---------------------------------------------------------------------------- | Returns the square root of the single-precision floating-point value `a'. | The operation is performed according to the IEC/IEEE Standard for Binary | Floating-Point Arithmetic. @@ -3465,6 +3672,226 @@ float64 float64_rem( float64 a, float64 b STATUS_PARAM ) } /*---------------------------------------------------------------------------- +| Returns the result of multiplying the double-precision floating-point values +| `a' and `b' then adding 'c', with no intermediate rounding step after the +| multiplication. The operation is performed according to the IEC/IEEE +| Standard for Binary Floating-Point Arithmetic 754-2008. +| The flags argument allows the caller to select negation of the +| addend, the intermediate product, or the final result. (The difference +| between this and having the caller do a separate negation is that negating +| externally will flip the sign bit on NaNs.) +*----------------------------------------------------------------------------*/ + +float64 float64_muladd(float64 a, float64 b, float64 c, int flags STATUS_PARAM) +{ + flag aSign, bSign, cSign, zSign; + int aExp, bExp, cExp, pExp, zExp, expDiff; + uint64_t aSig, bSig, cSig; + flag pInf, pZero, pSign; + uint64_t pSig0, pSig1, cSig0, cSig1, zSig0, zSig1; + int shiftcount; + flag signflip, infzero; + + a = float64_squash_input_denormal(a STATUS_VAR); + b = float64_squash_input_denormal(b STATUS_VAR); + c = float64_squash_input_denormal(c STATUS_VAR); + aSig = extractFloat64Frac(a); + aExp = extractFloat64Exp(a); + aSign = extractFloat64Sign(a); + bSig = extractFloat64Frac(b); + bExp = extractFloat64Exp(b); + bSign = extractFloat64Sign(b); + cSig = extractFloat64Frac(c); + cExp = extractFloat64Exp(c); + cSign = extractFloat64Sign(c); + + infzero = ((aExp == 0 && aSig == 0 && bExp == 0x7ff && bSig == 0) || + (aExp == 0x7ff && aSig == 0 && bExp == 0 && bSig == 0)); + + /* It is implementation-defined whether the cases of (0,inf,qnan) + * and (inf,0,qnan) raise InvalidOperation or not (and what QNaN + * they return if they do), so we have to hand this information + * off to the target-specific pick-a-NaN routine. + */ + if (((aExp == 0x7ff) && aSig) || + ((bExp == 0x7ff) && bSig) || + ((cExp == 0x7ff) && cSig)) { + return propagateFloat64MulAddNaN(a, b, c, infzero STATUS_VAR); + } + + if (infzero) { + float_raise(float_flag_invalid STATUS_VAR); + return float64_default_nan; + } + + if (flags & float_muladd_negate_c) { + cSign ^= 1; + } + + signflip = (flags & float_muladd_negate_result) ? 1 : 0; + + /* Work out the sign and type of the product */ + pSign = aSign ^ bSign; + if (flags & float_muladd_negate_product) { + pSign ^= 1; + } + pInf = (aExp == 0x7ff) || (bExp == 0x7ff); + pZero = ((aExp | aSig) == 0) || ((bExp | bSig) == 0); + + if (cExp == 0x7ff) { + if (pInf && (pSign ^ cSign)) { + /* addition of opposite-signed infinities => InvalidOperation */ + float_raise(float_flag_invalid STATUS_VAR); + return float64_default_nan; + } + /* Otherwise generate an infinity of the same sign */ + return packFloat64(cSign ^ signflip, 0x7ff, 0); + } + + if (pInf) { + return packFloat64(pSign ^ signflip, 0x7ff, 0); + } + + if (pZero) { + if (cExp == 0) { + if (cSig == 0) { + /* Adding two exact zeroes */ + if (pSign == cSign) { + zSign = pSign; + } else if (STATUS(float_rounding_mode) == float_round_down) { + zSign = 1; + } else { + zSign = 0; + } + return packFloat64(zSign ^ signflip, 0, 0); + } + /* Exact zero plus a denorm */ + if (STATUS(flush_to_zero)) { + float_raise(float_flag_output_denormal STATUS_VAR); + return packFloat64(cSign ^ signflip, 0, 0); + } + } + /* Zero plus something non-zero : just return the something */ + return c ^ ((uint64_t)signflip << 63); + } + + if (aExp == 0) { + normalizeFloat64Subnormal(aSig, &aExp, &aSig); + } + if (bExp == 0) { + normalizeFloat64Subnormal(bSig, &bExp, &bSig); + } + + /* Calculate the actual result a * b + c */ + + /* Multiply first; this is easy. */ + /* NB: we subtract 0x3fe where float64_mul() subtracts 0x3ff + * because we want the true exponent, not the "one-less-than" + * flavour that roundAndPackFloat64() takes. + */ + pExp = aExp + bExp - 0x3fe; + aSig = (aSig | LIT64(0x0010000000000000))<<10; + bSig = (bSig | LIT64(0x0010000000000000))<<11; + mul64To128(aSig, bSig, &pSig0, &pSig1); + if ((int64_t)(pSig0 << 1) >= 0) { + shortShift128Left(pSig0, pSig1, 1, &pSig0, &pSig1); + pExp--; + } + + zSign = pSign ^ signflip; + + /* Now [pSig0:pSig1] is the significand of the multiply, with the explicit + * bit in position 126. + */ + if (cExp == 0) { + if (!cSig) { + /* Throw out the special case of c being an exact zero now */ + shift128RightJamming(pSig0, pSig1, 64, &pSig0, &pSig1); + return roundAndPackFloat64(zSign, pExp - 1, + pSig1 STATUS_VAR); + } + normalizeFloat64Subnormal(cSig, &cExp, &cSig); + } + + /* Shift cSig and add the explicit bit so [cSig0:cSig1] is the + * significand of the addend, with the explicit bit in position 126. + */ + cSig0 = cSig << (126 - 64 - 52); + cSig1 = 0; + cSig0 |= LIT64(0x4000000000000000); + expDiff = pExp - cExp; + + if (pSign == cSign) { + /* Addition */ + if (expDiff > 0) { + /* scale c to match p */ + shift128RightJamming(cSig0, cSig1, expDiff, &cSig0, &cSig1); + zExp = pExp; + } else if (expDiff < 0) { + /* scale p to match c */ + shift128RightJamming(pSig0, pSig1, -expDiff, &pSig0, &pSig1); + zExp = cExp; + } else { + /* no scaling needed */ + zExp = cExp; + } + /* Add significands and make sure explicit bit ends up in posn 126 */ + add128(pSig0, pSig1, cSig0, cSig1, &zSig0, &zSig1); + if ((int64_t)zSig0 < 0) { + shift128RightJamming(zSig0, zSig1, 1, &zSig0, &zSig1); + } else { + zExp--; + } + shift128RightJamming(zSig0, zSig1, 64, &zSig0, &zSig1); + return roundAndPackFloat64(zSign, zExp, zSig1 STATUS_VAR); + } else { + /* Subtraction */ + if (expDiff > 0) { + shift128RightJamming(cSig0, cSig1, expDiff, &cSig0, &cSig1); + sub128(pSig0, pSig1, cSig0, cSig1, &zSig0, &zSig1); + zExp = pExp; + } else if (expDiff < 0) { + shift128RightJamming(pSig0, pSig1, -expDiff, &pSig0, &pSig1); + sub128(cSig0, cSig1, pSig0, pSig1, &zSig0, &zSig1); + zExp = cExp; + zSign ^= 1; + } else { + zExp = pExp; + if (lt128(cSig0, cSig1, pSig0, pSig1)) { + sub128(pSig0, pSig1, cSig0, cSig1, &zSig0, &zSig1); + } else if (lt128(pSig0, pSig1, cSig0, cSig1)) { + sub128(cSig0, cSig1, pSig0, pSig1, &zSig0, &zSig1); + zSign ^= 1; + } else { + /* Exact zero */ + zSign = signflip; + if (STATUS(float_rounding_mode) == float_round_down) { + zSign ^= 1; + } + return packFloat64(zSign, 0, 0); + } + } + --zExp; + /* Do the equivalent of normalizeRoundAndPackFloat64() but + * starting with the significand in a pair of uint64_t. + */ + if (zSig0) { + shiftcount = countLeadingZeros64(zSig0) - 1; + shortShift128Left(zSig0, zSig1, shiftcount, &zSig0, &zSig1); + if (zSig1) { + zSig0 |= 1; + } + zExp -= shiftcount; + } else { + shiftcount = countLeadingZeros64(zSig1) - 1; + zSig0 = zSig1 << shiftcount; + zExp -= (shiftcount + 64); + } + return roundAndPackFloat64(zSign, zExp, zSig0 STATUS_VAR); + } +} + +/*---------------------------------------------------------------------------- | Returns the square root of the double-precision floating-point value `a'. | The operation is performed according to the IEC/IEEE Standard for Binary | Floating-Point Arithmetic. |