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Diffstat (limited to 'compiler-rt/lib/builtins/divdf3.c')
| -rw-r--r-- | compiler-rt/lib/builtins/divdf3.c | 210 |
1 files changed, 210 insertions, 0 deletions
diff --git a/compiler-rt/lib/builtins/divdf3.c b/compiler-rt/lib/builtins/divdf3.c new file mode 100644 index 000000000000..1dea3b534f5a --- /dev/null +++ b/compiler-rt/lib/builtins/divdf3.c @@ -0,0 +1,210 @@ +//===-- lib/divdf3.c - Double-precision division ------------------*- 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 double-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 DOUBLE_PRECISION +#include "fp_lib.h" + +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); + // 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 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; + // 0x7504F333 / 2^32 + 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. + uint32_t correction32; + correction32 = -((uint64_t)recip32 * q31b >> 32); + recip32 = (uint64_t)recip32 * correction32 >> 31; + correction32 = -((uint64_t)recip32 * q31b >> 32); + recip32 = (uint64_t)recip32 * correction32 >> 31; + correction32 = -((uint64_t)recip32 * q31b >> 32); + recip32 = (uint64_t)recip32 * correction32 >> 31; + + // 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. + 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; + uint64_t correction, reciprocal; + correction = -((uint64_t)recip32 * q31b + ((uint64_t)recip32 * q63blo >> 32)); + uint32_t cHi = correction >> 32; + uint32_t cLo = correction; + reciprocal = (uint64_t)recip32 * cHi + ((uint64_t)recip32 * cLo >> 32); + + // 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 + // in Q53 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^-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 + // + // 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; + if (quotient < (implicitBit << 1)) { + residual = (aSignificand << 53) - quotient * bSignificand; + quotientExponent--; + } else { + 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) { + 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 double result = fromRep(absResult | quotientSign); + return result; + } +} + +#if defined(__ARM_EABI__) +#if defined(COMPILER_RT_ARMHF_TARGET) +AEABI_RTABI fp_t __aeabi_ddiv(fp_t a, fp_t b) { return __divdf3(a, b); } +#else +COMPILER_RT_ALIAS(__divdf3, __aeabi_ddiv) +#endif +#endif |