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softfloat: Implement fused multiply-add
Implement fused multiply-add as a softfloat primitive. This implements "a+b*c" as a single step without any intermediate rounding; it is specified in IEEE 754-2008 and implemented in a number of CPUs. Signed-off-by: Peter Maydell <peter.maydell@linaro.org>
This commit is contained in:
Peter Maydell
parent
b8b8ea05c4
commit
369be8f618
3 changed files with 619 additions and 0 deletions
427
fpu/softfloat.c
427
fpu/softfloat.c
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@ -2117,6 +2117,213 @@ float32 float32_rem( float32 a, float32 b STATUS_PARAM )
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}
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/*----------------------------------------------------------------------------
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| Returns the result of multiplying the single-precision floating-point values
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| `a' and `b' then adding 'c', with no intermediate rounding step after the
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| multiplication. The operation is performed according to the IEC/IEEE
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| Standard for Binary Floating-Point Arithmetic 754-2008.
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| The flags argument allows the caller to select negation of the
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| addend, the intermediate product, or the final result. (The difference
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| between this and having the caller do a separate negation is that negating
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| externally will flip the sign bit on NaNs.)
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*----------------------------------------------------------------------------*/
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float32 float32_muladd(float32 a, float32 b, float32 c, int flags STATUS_PARAM)
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{
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flag aSign, bSign, cSign, zSign;
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int aExp, bExp, cExp, pExp, zExp, expDiff;
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uint32_t aSig, bSig, cSig;
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flag pInf, pZero, pSign;
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uint64_t pSig64, cSig64, zSig64;
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uint32_t pSig;
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int shiftcount;
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flag signflip, infzero;
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a = float32_squash_input_denormal(a STATUS_VAR);
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b = float32_squash_input_denormal(b STATUS_VAR);
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c = float32_squash_input_denormal(c STATUS_VAR);
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aSig = extractFloat32Frac(a);
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aExp = extractFloat32Exp(a);
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aSign = extractFloat32Sign(a);
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bSig = extractFloat32Frac(b);
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bExp = extractFloat32Exp(b);
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bSign = extractFloat32Sign(b);
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cSig = extractFloat32Frac(c);
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cExp = extractFloat32Exp(c);
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cSign = extractFloat32Sign(c);
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infzero = ((aExp == 0 && aSig == 0 && bExp == 0xff && bSig == 0) ||
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(aExp == 0xff && aSig == 0 && bExp == 0 && bSig == 0));
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/* It is implementation-defined whether the cases of (0,inf,qnan)
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* and (inf,0,qnan) raise InvalidOperation or not (and what QNaN
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* they return if they do), so we have to hand this information
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* off to the target-specific pick-a-NaN routine.
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*/
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if (((aExp == 0xff) && aSig) ||
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((bExp == 0xff) && bSig) ||
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((cExp == 0xff) && cSig)) {
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return propagateFloat32MulAddNaN(a, b, c, infzero STATUS_VAR);
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}
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if (infzero) {
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float_raise(float_flag_invalid STATUS_VAR);
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return float32_default_nan;
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}
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if (flags & float_muladd_negate_c) {
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cSign ^= 1;
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}
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signflip = (flags & float_muladd_negate_result) ? 1 : 0;
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/* Work out the sign and type of the product */
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pSign = aSign ^ bSign;
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if (flags & float_muladd_negate_product) {
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pSign ^= 1;
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}
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pInf = (aExp == 0xff) || (bExp == 0xff);
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pZero = ((aExp | aSig) == 0) || ((bExp | bSig) == 0);
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if (cExp == 0xff) {
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if (pInf && (pSign ^ cSign)) {
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/* addition of opposite-signed infinities => InvalidOperation */
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float_raise(float_flag_invalid STATUS_VAR);
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return float32_default_nan;
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}
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/* Otherwise generate an infinity of the same sign */
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return packFloat32(cSign ^ signflip, 0xff, 0);
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}
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if (pInf) {
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return packFloat32(pSign ^ signflip, 0xff, 0);
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}
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if (pZero) {
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if (cExp == 0) {
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if (cSig == 0) {
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/* Adding two exact zeroes */
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if (pSign == cSign) {
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zSign = pSign;
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} else if (STATUS(float_rounding_mode) == float_round_down) {
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zSign = 1;
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} else {
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zSign = 0;
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}
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return packFloat32(zSign ^ signflip, 0, 0);
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}
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/* Exact zero plus a denorm */
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if (STATUS(flush_to_zero)) {
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float_raise(float_flag_output_denormal STATUS_VAR);
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return packFloat32(cSign ^ signflip, 0, 0);
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}
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}
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/* Zero plus something non-zero : just return the something */
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return c ^ (signflip << 31);
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}
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if (aExp == 0) {
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normalizeFloat32Subnormal(aSig, &aExp, &aSig);
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}
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if (bExp == 0) {
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normalizeFloat32Subnormal(bSig, &bExp, &bSig);
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}
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/* Calculate the actual result a * b + c */
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/* Multiply first; this is easy. */
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/* NB: we subtract 0x7e where float32_mul() subtracts 0x7f
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* because we want the true exponent, not the "one-less-than"
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* flavour that roundAndPackFloat32() takes.
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*/
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pExp = aExp + bExp - 0x7e;
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aSig = (aSig | 0x00800000) << 7;
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bSig = (bSig | 0x00800000) << 8;
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pSig64 = (uint64_t)aSig * bSig;
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if ((int64_t)(pSig64 << 1) >= 0) {
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pSig64 <<= 1;
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pExp--;
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}
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zSign = pSign ^ signflip;
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/* Now pSig64 is the significand of the multiply, with the explicit bit in
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* position 62.
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*/
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if (cExp == 0) {
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if (!cSig) {
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/* Throw out the special case of c being an exact zero now */
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shift64RightJamming(pSig64, 32, &pSig64);
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pSig = pSig64;
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return roundAndPackFloat32(zSign, pExp - 1,
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pSig STATUS_VAR);
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}
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normalizeFloat32Subnormal(cSig, &cExp, &cSig);
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}
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cSig64 = (uint64_t)cSig << (62 - 23);
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cSig64 |= LIT64(0x4000000000000000);
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expDiff = pExp - cExp;
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if (pSign == cSign) {
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/* Addition */
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if (expDiff > 0) {
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/* scale c to match p */
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shift64RightJamming(cSig64, expDiff, &cSig64);
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zExp = pExp;
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} else if (expDiff < 0) {
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/* scale p to match c */
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shift64RightJamming(pSig64, -expDiff, &pSig64);
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zExp = cExp;
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} else {
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/* no scaling needed */
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zExp = cExp;
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}
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/* Add significands and make sure explicit bit ends up in posn 62 */
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zSig64 = pSig64 + cSig64;
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if ((int64_t)zSig64 < 0) {
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shift64RightJamming(zSig64, 1, &zSig64);
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} else {
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zExp--;
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}
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} else {
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/* Subtraction */
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if (expDiff > 0) {
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shift64RightJamming(cSig64, expDiff, &cSig64);
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zSig64 = pSig64 - cSig64;
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zExp = pExp;
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} else if (expDiff < 0) {
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shift64RightJamming(pSig64, -expDiff, &pSig64);
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zSig64 = cSig64 - pSig64;
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zExp = cExp;
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zSign ^= 1;
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} else {
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zExp = pExp;
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if (cSig64 < pSig64) {
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zSig64 = pSig64 - cSig64;
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} else if (pSig64 < cSig64) {
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zSig64 = cSig64 - pSig64;
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zSign ^= 1;
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} else {
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/* Exact zero */
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zSign = signflip;
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if (STATUS(float_rounding_mode) == float_round_down) {
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zSign ^= 1;
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}
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return packFloat32(zSign, 0, 0);
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}
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}
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--zExp;
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/* Normalize to put the explicit bit back into bit 62. */
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shiftcount = countLeadingZeros64(zSig64) - 1;
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zSig64 <<= shiftcount;
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zExp -= shiftcount;
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}
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shift64RightJamming(zSig64, 32, &zSig64);
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return roundAndPackFloat32(zSign, zExp, zSig64 STATUS_VAR);
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}
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/*----------------------------------------------------------------------------
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| Returns the square root of the single-precision floating-point value `a'.
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| The operation is performed according to the IEC/IEEE Standard for Binary
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@ -3464,6 +3671,226 @@ float64 float64_rem( float64 a, float64 b STATUS_PARAM )
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}
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/*----------------------------------------------------------------------------
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| Returns the result of multiplying the double-precision floating-point values
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| `a' and `b' then adding 'c', with no intermediate rounding step after the
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| multiplication. The operation is performed according to the IEC/IEEE
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| Standard for Binary Floating-Point Arithmetic 754-2008.
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| The flags argument allows the caller to select negation of the
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| addend, the intermediate product, or the final result. (The difference
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| between this and having the caller do a separate negation is that negating
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| externally will flip the sign bit on NaNs.)
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*----------------------------------------------------------------------------*/
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float64 float64_muladd(float64 a, float64 b, float64 c, int flags STATUS_PARAM)
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{
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flag aSign, bSign, cSign, zSign;
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int aExp, bExp, cExp, pExp, zExp, expDiff;
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uint64_t aSig, bSig, cSig;
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flag pInf, pZero, pSign;
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uint64_t pSig0, pSig1, cSig0, cSig1, zSig0, zSig1;
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int shiftcount;
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flag signflip, infzero;
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a = float64_squash_input_denormal(a STATUS_VAR);
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b = float64_squash_input_denormal(b STATUS_VAR);
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c = float64_squash_input_denormal(c STATUS_VAR);
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aSig = extractFloat64Frac(a);
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aExp = extractFloat64Exp(a);
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aSign = extractFloat64Sign(a);
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bSig = extractFloat64Frac(b);
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bExp = extractFloat64Exp(b);
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bSign = extractFloat64Sign(b);
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cSig = extractFloat64Frac(c);
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cExp = extractFloat64Exp(c);
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cSign = extractFloat64Sign(c);
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infzero = ((aExp == 0 && aSig == 0 && bExp == 0x7ff && bSig == 0) ||
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(aExp == 0x7ff && aSig == 0 && bExp == 0 && bSig == 0));
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/* It is implementation-defined whether the cases of (0,inf,qnan)
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* and (inf,0,qnan) raise InvalidOperation or not (and what QNaN
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* they return if they do), so we have to hand this information
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* off to the target-specific pick-a-NaN routine.
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*/
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if (((aExp == 0x7ff) && aSig) ||
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((bExp == 0x7ff) && bSig) ||
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((cExp == 0x7ff) && cSig)) {
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return propagateFloat64MulAddNaN(a, b, c, infzero STATUS_VAR);
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}
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if (infzero) {
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float_raise(float_flag_invalid STATUS_VAR);
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return float64_default_nan;
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}
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if (flags & float_muladd_negate_c) {
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cSign ^= 1;
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}
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signflip = (flags & float_muladd_negate_result) ? 1 : 0;
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/* Work out the sign and type of the product */
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pSign = aSign ^ bSign;
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if (flags & float_muladd_negate_product) {
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pSign ^= 1;
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}
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pInf = (aExp == 0x7ff) || (bExp == 0x7ff);
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pZero = ((aExp | aSig) == 0) || ((bExp | bSig) == 0);
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if (cExp == 0x7ff) {
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if (pInf && (pSign ^ cSign)) {
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/* addition of opposite-signed infinities => InvalidOperation */
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float_raise(float_flag_invalid STATUS_VAR);
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return float64_default_nan;
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}
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/* Otherwise generate an infinity of the same sign */
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return packFloat64(cSign ^ signflip, 0x7ff, 0);
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}
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if (pInf) {
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return packFloat64(pSign ^ signflip, 0x7ff, 0);
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}
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if (pZero) {
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if (cExp == 0) {
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if (cSig == 0) {
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/* Adding two exact zeroes */
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if (pSign == cSign) {
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zSign = pSign;
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} else if (STATUS(float_rounding_mode) == float_round_down) {
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zSign = 1;
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} else {
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zSign = 0;
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}
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return packFloat64(zSign ^ signflip, 0, 0);
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}
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/* Exact zero plus a denorm */
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if (STATUS(flush_to_zero)) {
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float_raise(float_flag_output_denormal STATUS_VAR);
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return packFloat64(cSign ^ signflip, 0, 0);
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}
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}
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/* Zero plus something non-zero : just return the something */
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return c ^ ((uint64_t)signflip << 63);
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}
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if (aExp == 0) {
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normalizeFloat64Subnormal(aSig, &aExp, &aSig);
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}
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if (bExp == 0) {
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normalizeFloat64Subnormal(bSig, &bExp, &bSig);
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}
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/* Calculate the actual result a * b + c */
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/* Multiply first; this is easy. */
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/* NB: we subtract 0x3fe where float64_mul() subtracts 0x3ff
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* because we want the true exponent, not the "one-less-than"
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* flavour that roundAndPackFloat64() takes.
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*/
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pExp = aExp + bExp - 0x3fe;
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aSig = (aSig | LIT64(0x0010000000000000))<<10;
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bSig = (bSig | LIT64(0x0010000000000000))<<11;
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mul64To128(aSig, bSig, &pSig0, &pSig1);
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if ((int64_t)(pSig0 << 1) >= 0) {
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shortShift128Left(pSig0, pSig1, 1, &pSig0, &pSig1);
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pExp--;
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}
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zSign = pSign ^ signflip;
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/* Now [pSig0:pSig1] is the significand of the multiply, with the explicit
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* bit in position 126.
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*/
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if (cExp == 0) {
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if (!cSig) {
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/* Throw out the special case of c being an exact zero now */
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shift128RightJamming(pSig0, pSig1, 64, &pSig0, &pSig1);
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return roundAndPackFloat64(zSign, pExp - 1,
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pSig1 STATUS_VAR);
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}
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normalizeFloat64Subnormal(cSig, &cExp, &cSig);
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}
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/* Shift cSig and add the explicit bit so [cSig0:cSig1] is the
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* significand of the addend, with the explicit bit in position 126.
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*/
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cSig0 = cSig << (126 - 64 - 52);
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cSig1 = 0;
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cSig0 |= LIT64(0x4000000000000000);
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expDiff = pExp - cExp;
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if (pSign == cSign) {
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/* Addition */
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if (expDiff > 0) {
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/* scale c to match p */
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shift128RightJamming(cSig0, cSig1, expDiff, &cSig0, &cSig1);
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zExp = pExp;
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} else if (expDiff < 0) {
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/* scale p to match c */
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shift128RightJamming(pSig0, pSig1, -expDiff, &pSig0, &pSig1);
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zExp = cExp;
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} else {
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/* no scaling needed */
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zExp = cExp;
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}
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/* Add significands and make sure explicit bit ends up in posn 126 */
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add128(pSig0, pSig1, cSig0, cSig1, &zSig0, &zSig1);
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if ((int64_t)zSig0 < 0) {
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shift128RightJamming(zSig0, zSig1, 1, &zSig0, &zSig1);
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} else {
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zExp--;
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}
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shift128RightJamming(zSig0, zSig1, 64, &zSig0, &zSig1);
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return roundAndPackFloat64(zSign, zExp, zSig1 STATUS_VAR);
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} else {
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/* Subtraction */
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if (expDiff > 0) {
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shift128RightJamming(cSig0, cSig1, expDiff, &cSig0, &cSig1);
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sub128(pSig0, pSig1, cSig0, cSig1, &zSig0, &zSig1);
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zExp = pExp;
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} else if (expDiff < 0) {
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shift128RightJamming(pSig0, pSig1, -expDiff, &pSig0, &pSig1);
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sub128(cSig0, cSig1, pSig0, pSig1, &zSig0, &zSig1);
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zExp = cExp;
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zSign ^= 1;
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} else {
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zExp = pExp;
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if (lt128(cSig0, cSig1, pSig0, pSig1)) {
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sub128(pSig0, pSig1, cSig0, cSig1, &zSig0, &zSig1);
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} else if (lt128(pSig0, pSig1, cSig0, cSig1)) {
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sub128(cSig0, cSig1, pSig0, pSig1, &zSig0, &zSig1);
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zSign ^= 1;
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} else {
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/* Exact zero */
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zSign = signflip;
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if (STATUS(float_rounding_mode) == float_round_down) {
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zSign ^= 1;
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}
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return packFloat64(zSign, 0, 0);
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}
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}
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--zExp;
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/* Do the equivalent of normalizeRoundAndPackFloat64() but
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* starting with the significand in a pair of uint64_t.
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*/
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if (zSig0) {
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shiftcount = countLeadingZeros64(zSig0) - 1;
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shortShift128Left(zSig0, zSig1, shiftcount, &zSig0, &zSig1);
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if (zSig1) {
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zSig0 |= 1;
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}
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zExp -= shiftcount;
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} else {
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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
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue