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authorDimitry Andric <dim@FreeBSD.org>2021-06-13 19:31:46 +0000
committerDimitry Andric <dim@FreeBSD.org>2021-06-13 19:37:19 +0000
commite8d8bef961a50d4dc22501cde4fb9fb0be1b2532 (patch)
tree94f04805f47bb7c59ae29690d8952b6074fff602 /contrib/llvm-project/compiler-rt/lib/builtins/divtf3.c
parentbb130ff39747b94592cb26d71b7cb097b9a4ea6b (diff)
parentb60736ec1405bb0a8dd40989f67ef4c93da068ab (diff)
Diffstat (limited to 'contrib/llvm-project/compiler-rt/lib/builtins/divtf3.c')
-rw-r--r--contrib/llvm-project/compiler-rt/lib/builtins/divtf3.c203
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, &quotient, &quotientLo);
-
- // 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