diff options
Diffstat (limited to 'lib/builtins/divdf3.c')
| -rw-r--r-- | lib/builtins/divdf3.c | 46 |
1 files changed, 23 insertions, 23 deletions
diff --git a/lib/builtins/divdf3.c b/lib/builtins/divdf3.c index 04a4dc5571ca..411c82ebb87a 100644 --- a/lib/builtins/divdf3.c +++ b/lib/builtins/divdf3.c @@ -21,36 +21,36 @@ COMPILER_RT_ABI fp_t __divdf3(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 quotientSign = (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 / infinity = NaN if (bAbs == infRep) return fromRep(qnanRep); // infinity / anything else = +/- infinity else return fromRep(aAbs | quotientSign); } - + // anything else / infinity = +/- 0 if (bAbs == infRep) return fromRep(quotientSign); - + if (!aAbs) { // zero / zero = NaN if (!bAbs) return fromRep(qnanRep); @@ -59,28 +59,28 @@ __divdf3(fp_t a, fp_t b) { } // anything else / zero = +/- infinity if (!bAbs) return fromRep(infRep | quotientSign); - + // 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; int quotientExponent = aExponent - bExponent + scale; - + // Align the significand of b as a Q31 fixed-point number in the range // [1, 2.0) and get a Q32 approximate reciprocal using a small minimax // polynomial approximation: reciprocal = 3/4 + 1/sqrt(2) - b/2. This // is accurate to about 3.5 binary digits. const uint32_t q31b = bSignificand >> 21; uint32_t recip32 = UINT32_C(0x7504f333) - q31b; - + // Now refine the reciprocal estimate using a Newton-Raphson iteration: // // x1 = x0 * (2 - x0 * b) @@ -95,13 +95,13 @@ __divdf3(fp_t a, fp_t b) { recip32 = (uint64_t)recip32 * correction32 >> 31; correction32 = -((uint64_t)recip32 * q31b >> 32); recip32 = (uint64_t)recip32 * correction32 >> 31; - + // recip32 might have overflowed to exactly zero in the preceding // computation if the high word of b is exactly 1.0. This would sabotage // the full-width final stage of the computation that follows, so we adjust // recip32 downward by one bit. recip32--; - + // We need to perform one more iteration to get us to 56 binary digits; // The last iteration needs to happen with extra precision. const uint32_t q63blo = bSignificand << 11; @@ -110,14 +110,14 @@ __divdf3(fp_t a, fp_t b) { uint32_t cHi = correction >> 32; uint32_t cLo = correction; reciprocal = (uint64_t)recip32*cHi + ((uint64_t)recip32*cLo >> 32); - + // We already adjusted the 32-bit estimate, now we need to adjust the final // 64-bit reciprocal estimate downward to ensure that it is strictly smaller // than the infinitely precise exact reciprocal. Because the computation // of the Newton-Raphson step is truncating at every step, this adjustment // is small; most of the work is already done. reciprocal -= 2; - + // The numerical reciprocal is accurate to within 2^-56, lies in the // interval [0.5, 1.0), and is strictly smaller than the true reciprocal // of b. Multiplying a by this reciprocal thus gives a numerical q = a/b @@ -127,12 +127,12 @@ __divdf3(fp_t a, fp_t b) { // 2. q is in the interval [0.5, 2.0) // 3. the error in q is bounded away from 2^-53 (actually, we have a // couple of bits to spare, but this is all we need). - + // We need a 64 x 64 multiply high to compute q, which isn't a basic // operation in C, so we need to be a little bit fussy. rep_t quotient, quotientLo; wideMultiply(aSignificand << 2, reciprocal, "ient, "ientLo); - + // Two cases: quotient is in [0.5, 1.0) or quotient is in [1.0, 2.0). // In either case, we are going to compute a residual of the form // @@ -141,7 +141,7 @@ __divdf3(fp_t a, fp_t b) { // We know from the construction of q that r satisfies: // // 0 <= r < ulp(q)*b - // + // // if r is greater than 1/2 ulp(q)*b, then q rounds up. Otherwise, we // already have the correct result. The exact halfway case cannot occur. // We also take this time to right shift quotient if it falls in the [1,2) @@ -154,20 +154,20 @@ __divdf3(fp_t a, fp_t b) { quotient >>= 1; residual = (aSignificand << 52) - quotient * bSignificand; } - + const int writtenExponent = quotientExponent + exponentBias; - + if (writtenExponent >= maxExponent) { // If we have overflowed the exponent, return infinity. return fromRep(infRep | quotientSign); } - + else if (writtenExponent < 1) { // Flush denormals to zero. In the future, it would be nice to add // code to round them correctly. return fromRep(quotientSign); } - + else { const bool round = (residual << 1) > bSignificand; // Clear the implicit bit |