diff options
Diffstat (limited to 'lib/libcompiler_rt/divsf3.c')
| -rw-r--r-- | lib/libcompiler_rt/divsf3.c | 40 |
1 files changed, 20 insertions, 20 deletions
diff --git a/lib/libcompiler_rt/divsf3.c b/lib/libcompiler_rt/divsf3.c index 65294d70fc6..a74917fd1de 100644 --- a/lib/libcompiler_rt/divsf3.c +++ b/lib/libcompiler_rt/divsf3.c @@ -21,36 +21,36 @@ COMPILER_RT_ABI fp_t __divsf3(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 @@ __divsf3(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. uint32_t q31b = bSignificand << 8; uint32_t reciprocal = UINT32_C(0x7504f333) - q31b; - + // Now refine the reciprocal estimate using a Newton-Raphson iteration: // // x1 = x0 * (2 - x0 * b) @@ -95,7 +95,7 @@ __divsf3(fp_t a, fp_t b) { reciprocal = (uint64_t)reciprocal * correction >> 31; correction = -((uint64_t)reciprocal * q31b >> 32); reciprocal = (uint64_t)reciprocal * correction >> 31; - + // Exhaustive testing shows that the error in reciprocal after three steps // is in the interval [-0x1.f58108p-31, 0x1.d0e48cp-29], in line with our // expectations. We bump the reciprocal by a tiny value to force the error @@ -103,7 +103,7 @@ __divsf3(fp_t a, fp_t b) { // be specific). This also causes 1/1 to give a sensible approximation // instead of zero (due to overflow). reciprocal -= 2; - + // The numerical reciprocal is accurate to within 2^-28, lies in the // interval [0x1.000000eep-1, 0x1.fffffffcp-1], and is strictly smaller // than the true reciprocal of b. Multiplying a by this reciprocal thus @@ -115,9 +115,9 @@ __divsf3(fp_t a, fp_t b) { // from the fact that we truncate the product, and the 2^27 term // is the error in the reciprocal of b scaled by the maximum // possible value of a. As a consequence of this error bound, - // either q or nextafter(q) is the correctly rounded + // either q or nextafter(q) is the correctly rounded rep_t quotient = (uint64_t)reciprocal*(aSignificand << 1) >> 32; - + // 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 // @@ -126,7 +126,7 @@ __divsf3(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) @@ -141,18 +141,18 @@ __divsf3(fp_t a, fp_t b) { } 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 |