diff options
author | Dimitry Andric <dim@FreeBSD.org> | 2021-06-13 19:31:46 +0000 |
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committer | Dimitry Andric <dim@FreeBSD.org> | 2021-06-13 19:37:19 +0000 |
commit | e8d8bef961a50d4dc22501cde4fb9fb0be1b2532 (patch) | |
tree | 94f04805f47bb7c59ae29690d8952b6074fff602 /contrib/llvm-project/compiler-rt/lib/builtins/divtf3.c | |
parent | bb130ff39747b94592cb26d71b7cb097b9a4ea6b (diff) | |
parent | b60736ec1405bb0a8dd40989f67ef4c93da068ab (diff) |
Diffstat (limited to 'contrib/llvm-project/compiler-rt/lib/builtins/divtf3.c')
-rw-r--r-- | contrib/llvm-project/compiler-rt/lib/builtins/divtf3.c | 203 |
1 files changed, 4 insertions, 199 deletions
diff --git a/contrib/llvm-project/compiler-rt/lib/builtins/divtf3.c b/contrib/llvm-project/compiler-rt/lib/builtins/divtf3.c index ce462d4d46c1..5bcc9a8e4aa1 100644 --- a/contrib/llvm-project/compiler-rt/lib/builtins/divtf3.c +++ b/contrib/llvm-project/compiler-rt/lib/builtins/divtf3.c @@ -9,213 +9,18 @@ // This file implements quad-precision soft-float division // with the IEEE-754 default rounding (to nearest, ties to even). // -// For simplicity, this implementation currently flushes denormals to zero. -// It should be a fairly straightforward exercise to implement gradual -// underflow with correct rounding. -// //===----------------------------------------------------------------------===// #define QUAD_PRECISION #include "fp_lib.h" #if defined(CRT_HAS_128BIT) && defined(CRT_LDBL_128BIT) -COMPILER_RT_ABI fp_t __divtf3(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); - // zero / anything else = +/- zero - else - return fromRep(quotientSign); - } - // 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); - } - - // 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; - int quotientExponent = aExponent - bExponent + scale; - - // Align the significand of b as a Q63 fixed-point number in the range - // [1, 2.0) and get a Q64 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 uint64_t q63b = bSignificand >> 49; - uint64_t recip64 = UINT64_C(0x7504f333F9DE6484) - q63b; - // 0x7504f333F9DE6484 / 2^64 + 1 = 3/4 + 1/sqrt(2) - - // Now refine the reciprocal estimate using a Newton-Raphson iteration: - // - // x1 = x0 * (2 - x0 * b) - // - // This doubles the number of correct binary digits in the approximation - // with each iteration. - uint64_t correction64; - correction64 = -((rep_t)recip64 * q63b >> 64); - recip64 = (rep_t)recip64 * correction64 >> 63; - correction64 = -((rep_t)recip64 * q63b >> 64); - recip64 = (rep_t)recip64 * correction64 >> 63; - correction64 = -((rep_t)recip64 * q63b >> 64); - recip64 = (rep_t)recip64 * correction64 >> 63; - correction64 = -((rep_t)recip64 * q63b >> 64); - recip64 = (rep_t)recip64 * correction64 >> 63; - correction64 = -((rep_t)recip64 * q63b >> 64); - recip64 = (rep_t)recip64 * correction64 >> 63; - - // The reciprocal may have overflowed to zero if the upper half of b is - // exactly 1.0. This would sabatoge the full-width final stage of the - // computation that follows, so we adjust the reciprocal down by one bit. - recip64--; - - // We need to perform one more iteration to get us to 112 binary digits; - // The last iteration needs to happen with extra precision. - const uint64_t q127blo = bSignificand << 15; - rep_t correction, reciprocal; - - // NOTE: This operation is equivalent to __multi3, which is not implemented - // in some architechure - rep_t r64q63, r64q127, r64cH, r64cL, dummy; - wideMultiply((rep_t)recip64, (rep_t)q63b, &dummy, &r64q63); - wideMultiply((rep_t)recip64, (rep_t)q127blo, &dummy, &r64q127); - - correction = -(r64q63 + (r64q127 >> 64)); - - uint64_t cHi = correction >> 64; - uint64_t cLo = correction; - - wideMultiply((rep_t)recip64, (rep_t)cHi, &dummy, &r64cH); - wideMultiply((rep_t)recip64, (rep_t)cLo, &dummy, &r64cL); - - reciprocal = r64cH + (r64cL >> 64); - - // Adjust the final 128-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^-112, 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 - // in Q127 with the following properties: - // - // 1. q < a/b - // 2. q is in the interval [0.5, 2.0) - // 3. The error in q is bounded away from 2^-113 (actually, we have a - // couple of bits to spare, but this is all we need). - - // We need a 128 x 128 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 - // - // r = a - q*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) - // range and adjust the exponent accordingly. - rep_t residual; - rep_t qb; - if (quotient < (implicitBit << 1)) { - wideMultiply(quotient, bSignificand, &dummy, &qb); - residual = (aSignificand << 113) - qb; - quotientExponent--; - } else { - quotient >>= 1; - wideMultiply(quotient, bSignificand, &dummy, &qb); - residual = (aSignificand << 112) - qb; - } +#define NUMBER_OF_HALF_ITERATIONS 4 +#define NUMBER_OF_FULL_ITERATIONS 1 - const int writtenExponent = quotientExponent + exponentBias; +#include "fp_div_impl.inc" - if (writtenExponent >= maxExponent) { - // If we have overflowed the exponent, return infinity. - return fromRep(infRep | quotientSign); - } else if (writtenExponent < 1) { - if (writtenExponent == 0) { - // Check whether the rounded result is normal. - const bool round = (residual << 1) > bSignificand; - // Clear the implicit bit. - rep_t absResult = quotient & significandMask; - // Round. - absResult += round; - if (absResult & ~significandMask) { - // The rounded result is normal; return it. - return fromRep(absResult | quotientSign); - } - } - // 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. - rep_t absResult = quotient & significandMask; - // Insert the exponent. - absResult |= (rep_t)writtenExponent << significandBits; - // Round. - absResult += round; - // Insert the sign and return. - const fp_t result = fromRep(absResult | quotientSign); - return result; - } -} +COMPILER_RT_ABI fp_t __divtf3(fp_t a, fp_t b) { return __divXf3__(a, b); } #endif |