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author | Dimitry Andric <dim@FreeBSD.org> | 2021-02-16 20:13:02 +0000 |
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committer | Dimitry Andric <dim@FreeBSD.org> | 2021-02-16 20:13:02 +0000 |
commit | b60736ec1405bb0a8dd40989f67ef4c93da068ab (patch) | |
tree | 5c43fbb7c9fc45f0f87e0e6795a86267dbd12f9d /compiler-rt/lib/builtins/divsf3.c | |
parent | cfca06d7963fa0909f90483b42a6d7d194d01e08 (diff) | |
download | src-b60736ec1405bb0a8dd40989f67ef4c93da068ab.tar.gz src-b60736ec1405bb0a8dd40989f67ef4c93da068ab.zip |
Vendor import of llvm-project main 8e464dd76bef, the last commit beforevendor/llvm-project/llvmorg-12-init-17869-g8e464dd76bef
the upstream release/12.x branch was created.
Diffstat (limited to 'compiler-rt/lib/builtins/divsf3.c')
-rw-r--r-- | compiler-rt/lib/builtins/divsf3.c | 174 |
1 files changed, 5 insertions, 169 deletions
diff --git a/compiler-rt/lib/builtins/divsf3.c b/compiler-rt/lib/builtins/divsf3.c index 593f93b45ac2..5744c015240b 100644 --- a/compiler-rt/lib/builtins/divsf3.c +++ b/compiler-rt/lib/builtins/divsf3.c @@ -9,181 +9,17 @@ // 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" - -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); - } - - // 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; - // 0x7504F333 / 2^32 + 1 = 3/4 + 1/sqrt(2) - - // 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. - 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; - - // Adust the final 32-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^-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); - } +#define NUMBER_OF_HALF_ITERATIONS 0 +#define NUMBER_OF_FULL_ITERATIONS 3 +#define USE_NATIVE_FULL_ITERATIONS - 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); - } +#include "fp_div_impl.inc" - 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); - } -} +COMPILER_RT_ABI fp_t __divsf3(fp_t a, fp_t b) { return __divXf3__(a, b); } #if defined(__ARM_EABI__) #if defined(COMPILER_RT_ARMHF_TARGET) |