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author | Anton Samokhvalov <pg83@yandex.ru> | 2022-02-10 16:45:17 +0300 |
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committer | Daniil Cherednik <dcherednik@yandex-team.ru> | 2022-02-10 16:45:17 +0300 |
commit | d3a398281c6fd1d3672036cb2d63f842d2cb28c5 (patch) | |
tree | dd4bd3ca0f36b817e96812825ffaf10d645803f2 /contrib/libs/cxxsupp/builtins/divsf3.c | |
parent | 72cb13b4aff9bc9cf22e49251bc8fd143f82538f (diff) | |
download | ydb-d3a398281c6fd1d3672036cb2d63f842d2cb28c5.tar.gz |
Restoring authorship annotation for Anton Samokhvalov <pg83@yandex.ru>. Commit 2 of 2.
Diffstat (limited to 'contrib/libs/cxxsupp/builtins/divsf3.c')
-rw-r--r-- | contrib/libs/cxxsupp/builtins/divsf3.c | 336 |
1 files changed, 168 insertions, 168 deletions
diff --git a/contrib/libs/cxxsupp/builtins/divsf3.c b/contrib/libs/cxxsupp/builtins/divsf3.c index d88b3048c7..de2e376125 100644 --- a/contrib/libs/cxxsupp/builtins/divsf3.c +++ b/contrib/libs/cxxsupp/builtins/divsf3.c @@ -1,169 +1,169 @@ -//===-- lib/divsf3.c - Single-precision division ------------------*- 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 single-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 SINGLE_PRECISION -#include "fp_lib.h" - -ARM_EABI_FNALIAS(fdiv, divsf3) - -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); - // 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); - } - - // 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: +//===-- lib/divsf3.c - Single-precision division ------------------*- 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 single-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 SINGLE_PRECISION +#include "fp_lib.h" + +ARM_EABI_FNALIAS(fdiv, divsf3) + +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); + // 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); + } + + // 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) + // + // This doubles the number of correct binary digits in the approximation + // with each iteration, so after three iterations, we have about 28 binary + // digits of accuracy. + uint32_t correction; + correction = -((uint64_t)reciprocal * q31b >> 32); + reciprocal = (uint64_t)reciprocal * correction >> 31; + correction = -((uint64_t)reciprocal * q31b >> 32); + 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 + // to be strictly positive (in the range [0x1.4fdfp-37,0x1.287246p-29], to + // 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 + // gives a numerical q = a/b in Q24 with the following properties: + // + // 1. q < a/b + // 2. q is in the interval [0x1.000000eep-1, 0x1.fffffffcp0) + // 3. the error in q is at most 2^-24 + 2^-27 -- the 2^24 term comes + // 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 + 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 + // + // r = a - q*b + // + // We know from the construction of q that r satisfies: + // + // 0 <= r < ulp(q)*b // - // x1 = x0 * (2 - x0 * b) - // - // This doubles the number of correct binary digits in the approximation - // with each iteration, so after three iterations, we have about 28 binary - // digits of accuracy. - uint32_t correction; - correction = -((uint64_t)reciprocal * q31b >> 32); - reciprocal = (uint64_t)reciprocal * correction >> 31; - correction = -((uint64_t)reciprocal * q31b >> 32); - 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 - // to be strictly positive (in the range [0x1.4fdfp-37,0x1.287246p-29], to - // 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 - // gives a numerical q = a/b in Q24 with the following properties: - // - // 1. q < a/b - // 2. q is in the interval [0x1.000000eep-1, 0x1.fffffffcp0) - // 3. the error in q is at most 2^-24 + 2^-27 -- the 2^24 term comes - // 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 - 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 - // - // 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 << 24) - quotient * bSignificand; - quotientExponent--; - } else { - quotient >>= 1; - residual = (aSignificand << 23) - 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 - rep_t absResult = quotient & significandMask; - // Insert the exponent - absResult |= (rep_t)writtenExponent << significandBits; - // Round - absResult += round; - // Insert the sign and return - return fromRep(absResult | quotientSign); - } -} + // 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 << 24) - quotient * bSignificand; + quotientExponent--; + } else { + quotient >>= 1; + residual = (aSignificand << 23) - 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 + rep_t absResult = quotient & significandMask; + // Insert the exponent + absResult |= (rep_t)writtenExponent << significandBits; + // Round + absResult += round; + // Insert the sign and return + return fromRep(absResult | quotientSign); + } +} |