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authorDimitry Andric <dim@FreeBSD.org>2021-02-16 20:13:02 +0000
committerDimitry Andric <dim@FreeBSD.org>2021-02-16 20:13:02 +0000
commitb60736ec1405bb0a8dd40989f67ef4c93da068ab (patch)
tree5c43fbb7c9fc45f0f87e0e6795a86267dbd12f9d /compiler-rt/lib/builtins/divsf3.c
parentcfca06d7963fa0909f90483b42a6d7d194d01e08 (diff)
downloadsrc-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.c174
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)