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+//===---- lib/fp_mul_impl.inc - floating point multiplication -----*- C -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+//
+// This file implements soft-float multiplication with the IEEE-754 default
+// rounding (to nearest, ties to even).
+//
+//===----------------------------------------------------------------------===//
+
+#include "fp_lib.h"
+
+static __inline fp_t __mulXf3__(fp_t a, fp_t b) {
+ const unsigned int aExponent = toRep(a) >> significandBits & maxExponent;
+ const unsigned int bExponent = toRep(b) >> significandBits & maxExponent;
+ const rep_t productSign = (toRep(a) ^ toRep(b)) & signBit;
+
+ rep_t aSignificand = toRep(a) & significandMask;
+ rep_t bSignificand = toRep(b) & significandMask;
+ int scale = 0;
+
+ // Detect if a or b is zero, denormal, infinity, or NaN.
+ if (aExponent - 1U >= maxExponent - 1U ||
+ bExponent - 1U >= maxExponent - 1U) {
+
+ const rep_t aAbs = toRep(a) & absMask;
+ const rep_t bAbs = toRep(b) & absMask;
+
+ // NaN * anything = qNaN
+ if (aAbs > infRep)
+ return fromRep(toRep(a) | quietBit);
+ // anything * NaN = qNaN
+ if (bAbs > infRep)
+ return fromRep(toRep(b) | quietBit);
+
+ if (aAbs == infRep) {
+ // infinity * non-zero = +/- infinity
+ if (bAbs)
+ return fromRep(aAbs | productSign);
+ // infinity * zero = NaN
+ else
+ return fromRep(qnanRep);
+ }
+
+ if (bAbs == infRep) {
+ // non-zero * infinity = +/- infinity
+ if (aAbs)
+ return fromRep(bAbs | productSign);
+ // zero * infinity = NaN
+ else
+ return fromRep(qnanRep);
+ }
+
+ // zero * anything = +/- zero
+ if (!aAbs)
+ return fromRep(productSign);
+ // anything * zero = +/- zero
+ if (!bAbs)
+ return fromRep(productSign);
+
+ // One or both of a or b is denormal. The other (if applicable) is a
+ // normal number. Renormalize one or both of a and b, and set scale to
+ // include the necessary exponent adjustment.
+ if (aAbs < implicitBit)
+ scale += normalize(&aSignificand);
+ if (bAbs < implicitBit)
+ scale += normalize(&bSignificand);
+ }
+
+ // Set the implicit significand bit. If we fell through from the
+ // denormal path it was already set by normalize( ), but setting it twice
+ // won't hurt anything.
+ aSignificand |= implicitBit;
+ bSignificand |= implicitBit;
+
+ // Perform a basic multiplication on the significands. One of them must be
+ // shifted beforehand to be aligned with the exponent.
+ rep_t productHi, productLo;
+ wideMultiply(aSignificand, bSignificand << exponentBits, &productHi,
+ &productLo);
+
+ int productExponent = aExponent + bExponent - exponentBias + scale;
+
+ // Normalize the significand and adjust the exponent if needed.
+ if (productHi & implicitBit)
+ productExponent++;
+ else
+ wideLeftShift(&productHi, &productLo, 1);
+
+ // If we have overflowed the type, return +/- infinity.
+ if (productExponent >= maxExponent)
+ return fromRep(infRep | productSign);
+
+ if (productExponent <= 0) {
+ // The result is denormal before rounding.
+ //
+ // If the result is so small that it just underflows to zero, return
+ // zero with the appropriate sign. Mathematically, there is no need to
+ // handle this case separately, but we make it a special case to
+ // simplify the shift logic.
+ const unsigned int shift = REP_C(1) - (unsigned int)productExponent;
+ if (shift >= typeWidth)
+ return fromRep(productSign);
+
+ // Otherwise, shift the significand of the result so that the round
+ // bit is the high bit of productLo.
+ wideRightShiftWithSticky(&productHi, &productLo, shift);
+ } else {
+ // The result is normal before rounding. Insert the exponent.
+ productHi &= significandMask;
+ productHi |= (rep_t)productExponent << significandBits;
+ }
+
+ // Insert the sign of the result.
+ productHi |= productSign;
+
+ // Perform the final rounding. The final result may overflow to infinity,
+ // or underflow to zero, but those are the correct results in those cases.
+ // We use the default IEEE-754 round-to-nearest, ties-to-even rounding mode.
+ if (productLo > signBit)
+ productHi++;
+ if (productLo == signBit)
+ productHi += productHi & 1;
+ return fromRep(productHi);
+}