--- /dev/null
+//===---- lib/fp_mul_impl.inc - floating point multiplication -----*- C -*-===//
+//
+// The LLVM Compiler Infrastructure
+//
+// This file is dual licensed under the MIT and the University of Illinois Open
+// Source Licenses. See LICENSE.TXT for details.
+//
+//===----------------------------------------------------------------------===//
+//
+// 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);
+ }
+
+ // Or in 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;
+
+ // Get the significand of a*b. Before multiplying the significands, shift
+ // one of them left to left-align it in the field. Thus, the product will
+ // have (exponentBits + 2) integral digits, all but two of which must be
+ // zero. Normalizing this result is just a conditional left-shift by one
+ // and bumping the exponent accordingly.
+ rep_t productHi, productLo;
+ wideMultiply(aSignificand, bSignificand << exponentBits,
+ &productHi, &productLo);
+
+ int productExponent = aExponent + bExponent - exponentBias + scale;
+
+ // Normalize the significand, adjust 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) {
+ // Result is denormal before rounding
+ //
+ // If the result is so small that it just underflows to zero, return
+ // a zero of 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 {
+ // Result is normal before rounding; insert the exponent.
+ productHi &= significandMask;
+ productHi |= (rep_t)productExponent << significandBits;
+ }
+
+ // Insert the sign of the result:
+ productHi |= productSign;
+
+ // 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);
+}
//===----------------------------------------------------------------------===//
#define DOUBLE_PRECISION
-#include "fp_lib.h"
+#include "fp_mul_impl.inc"
ARM_EABI_FNALIAS(dmul, muldf3)
-COMPILER_RT_ABI fp_t
-__muldf3(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);
- }
-
- // Or in 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;
-
- // Get the significand of a*b. Before multiplying the significands, shift
- // one of them left to left-align it in the field. Thus, the product will
- // have (exponentBits + 2) integral digits, all but two of which must be
- // zero. Normalizing this result is just a conditional left-shift by one
- // and bumping the exponent accordingly.
- rep_t productHi, productLo;
- wideMultiply(aSignificand, bSignificand << exponentBits,
- &productHi, &productLo);
-
- int productExponent = aExponent + bExponent - exponentBias + scale;
-
- // Normalize the significand, adjust 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) {
- // Result is denormal before rounding
- //
- // If the result is so small that it just underflows to zero, return
- // a zero of 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 = 1U - (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 {
- // Result is normal before rounding; insert the exponent.
- productHi &= significandMask;
- productHi |= (rep_t)productExponent << significandBits;
- }
-
- // Insert the sign of the result:
- productHi |= productSign;
-
- // 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);
+COMPILER_RT_ABI fp_t __muldf3(fp_t a, fp_t b) {
+ return __mulXf3__(a, b);
}
//===----------------------------------------------------------------------===//
#define SINGLE_PRECISION
-#include "fp_lib.h"
+#include "fp_mul_impl.inc"
ARM_EABI_FNALIAS(fmul, mulsf3)
-COMPILER_RT_ABI fp_t
-__mulsf3(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);
- }
-
- // Or in 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;
-
- // Get the significand of a*b. Before multiplying the significands, shift
- // one of them left to left-align it in the field. Thus, the product will
- // have (exponentBits + 2) integral digits, all but two of which must be
- // zero. Normalizing this result is just a conditional left-shift by one
- // and bumping the exponent accordingly.
- rep_t productHi, productLo;
- wideMultiply(aSignificand, bSignificand << exponentBits,
- &productHi, &productLo);
-
- int productExponent = aExponent + bExponent - exponentBias + scale;
-
- // Normalize the significand, adjust 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) {
- // Result is denormal before rounding, the exponent is zero and we
- // need to shift the significand.
- wideRightShiftWithSticky(&productHi, &productLo, 1U - (unsigned)productExponent);
- }
-
- else {
- // Result is normal before rounding; insert the exponent.
- productHi &= significandMask;
- productHi |= (rep_t)productExponent << significandBits;
- }
-
- // Insert the sign of the result:
- productHi |= productSign;
-
- // Final rounding. The final result may overflow to infinity, or underflow
- // to zero, but those are the correct results in those cases.
- if (productLo > signBit) productHi++;
- if (productLo == signBit) productHi += productHi & 1;
- return fromRep(productHi);
+COMPILER_RT_ABI fp_t __mulsf3(fp_t a, fp_t b) {
+ return __mulXf3__(a, b);
}