[compiler-rt] r209886 - Implement __divtf3 for IEEE quad precision.
Joerg Sonnenberger
joerg at bec.de
Fri May 30 04:08:19 PDT 2014
Author: joerg
Date: Fri May 30 06:08:18 2014
New Revision: 209886
URL: http://llvm.org/viewvc/llvm-project?rev=209886&view=rev
Log:
Implement __divtf3 for IEEE quad precision.
Patch by: GuanHong Liu
Differential Revision: http://reviews.llvm.org/D2800
Added:
compiler-rt/trunk/lib/builtins/divtf3.c
compiler-rt/trunk/test/builtins/Unit/divtf3_test.c
Added: compiler-rt/trunk/lib/builtins/divtf3.c
URL: http://llvm.org/viewvc/llvm-project/compiler-rt/trunk/lib/builtins/divtf3.c?rev=209886&view=auto
==============================================================================
--- compiler-rt/trunk/lib/builtins/divtf3.c (added)
+++ compiler-rt/trunk/lib/builtins/divtf3.c Fri May 30 06:08:18 2014
@@ -0,0 +1,203 @@
+//===-- lib/divtf3.c - Quad-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 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);
+ }
+
+ // 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 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;
+
+ // recip64 might have overflowed to exactly zero in the preceeding
+ // computation if the high word of b is exactly 1.0. This would sabotage
+ // the full-width final stage of the computation that follows, so we adjust
+ // recip64 downward 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);
+
+ // We already adjusted the 64-bit estimate, now we need to 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, "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;
+ 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;
+ }
+
+ 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
+ const long double result = fromRep(absResult | quotientSign);
+ return result;
+ }
+}
+
+#endif
Added: compiler-rt/trunk/test/builtins/Unit/divtf3_test.c
URL: http://llvm.org/viewvc/llvm-project/compiler-rt/trunk/test/builtins/Unit/divtf3_test.c?rev=209886&view=auto
==============================================================================
--- compiler-rt/trunk/test/builtins/Unit/divtf3_test.c (added)
+++ compiler-rt/trunk/test/builtins/Unit/divtf3_test.c Fri May 30 06:08:18 2014
@@ -0,0 +1,94 @@
+//===--------------- divtf3_test.c - Test __divtf3 ------------------------===//
+//
+// 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 tests __divtf3 for the compiler_rt library.
+//
+//===----------------------------------------------------------------------===//
+
+#include <stdio.h>
+
+#if __LDBL_MANT_DIG__ == 113
+
+#include "fp_test.h"
+
+// Returns: a / b
+long double __divtf3(long double a, long double b);
+
+int test__divtf3(long double a, long double b,
+ uint64_t expectedHi, uint64_t expectedLo)
+{
+ long double x = __divtf3(a, b);
+ int ret = compareResultLD(x, expectedHi, expectedLo);
+
+ if (ret){
+ printf("error in test__divtf3(%.20Lf, %.20Lf) = %.20Lf, "
+ "expected %.20Lf\n", a, b, x,
+ fromRep128(expectedHi, expectedLo));
+ }
+ return ret;
+}
+
+char assumption_1[sizeof(long double) * CHAR_BIT == 128] = {0};
+
+#endif
+
+int main()
+{
+#if __LDBL_MANT_DIG__ == 113
+ // qNaN / any = qNaN
+ if (test__divtf3(makeQNaN128(),
+ 0x1.23456789abcdefp+5L,
+ UINT64_C(0x7fff800000000000),
+ UINT64_C(0x0)))
+ return 1;
+ // NaN / any = NaN
+ if (test__divtf3(makeNaN128(UINT64_C(0x800030000000)),
+ 0x1.23456789abcdefp+5L,
+ UINT64_C(0x7fff800000000000),
+ UINT64_C(0x0)))
+ return 1;
+ // inf / any = inf
+ if (test__divtf3(makeInf128(),
+ 0x1.23456789abcdefp+5L,
+ UINT64_C(0x7fff000000000000),
+ UINT64_C(0x0)))
+ return 1;
+ // any / any
+ if (test__divtf3(0x1.a23b45362464523375893ab4cdefp+5L,
+ 0x1.eedcbaba3a94546558237654321fp-1L,
+ UINT64_C(0x4004b0b72924d407),
+ UINT64_C(0x0717e84356c6eba2)))
+ return 1;
+ if (test__divtf3(0x1.a2b34c56d745382f9abf2c3dfeffp-50L,
+ 0x1.ed2c3ba15935332532287654321fp-9L,
+ UINT64_C(0x3fd5b2af3f828c9b),
+ UINT64_C(0x40e51f64cde8b1f2)))
+ return 15;
+ if (test__divtf3(0x1.2345f6aaaa786555f42432abcdefp+456L,
+ 0x1.edacbba9874f765463544dd3621fp+6400L,
+ UINT64_C(0x28c62e15dc464466),
+ UINT64_C(0xb5a07586348557ac)))
+ return 1;
+ if (test__divtf3(0x1.2d3456f789ba6322bc665544edefp-234L,
+ 0x1.eddcdba39f3c8b7a36564354321fp-4455L,
+ UINT64_C(0x507b38442b539266),
+ UINT64_C(0x22ce0f1d024e1252)))
+ return 1;
+ if (test__divtf3(0x1.2345f6b77b7a8953365433abcdefp+234L,
+ 0x1.edcba987d6bb3aa467754354321fp-4055L,
+ UINT64_C(0x50bf2e02f0798d36),
+ UINT64_C(0x5e6fcb6b60044078)))
+ return 1;
+
+#else
+ printf("skipped\n");
+
+#endif
+ return 0;
+}
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