[COMPILER-RT] Implement __divtf3

[koviankevin]

Summary

Implement __divtf3, which performs long double division

[koviankevin]

add test

[koviankevin]

Use CRT_HAS_128BIT and modify the codes according to gribozavr's comments

[koviankevin]

introduce CRT_LDBL_128BIT

[koviankevin]

modify by gribozavr's comment and use COMPILER_RT_ABI

[koviankevin]

use UINT64_C and drop le64

[joerg]

lib/builtins/divtf3.c

82 ↗

(On Diff #9735)

Do we really need the full 64bit constant here?

[koviankevin]

lib/builtins/divtf3.c

82 ↗

(On Diff #9735)

Yes, we need the upper 64-bit of recip64 * q63b
If we use 32-bit constant only, the carry may be dropped, and the result will be incorrect

[joerg]

Closed by commit rL209886 (authored by @joerg).

[joerg]

Please drop me a patch for CREDITS.TXT BTW.

lib/builtins/divtf3.c

82 ↗

(On Diff #9735)

Sure, I mean: isn't it enough to use the highest 8bit of the constant? recip64 is only accurate to 3.5bit anyway (see comment), so anything more shouldn't matter?

[koviankevin]

Sorry for leaving this hanging so long.
I just refered the double-pecision version(i.e, divdf3) to write this function
Since it used 32-bit instead of the highest 8-bit in divdf3, I used 64-bit constant here.

compiler-rt/trunk/lib/builtins/divtf3.c

+//===-- 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, &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;
+    }
+
+    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

compiler-rt/trunk/test/builtins/Unit/divtf3_test.c

+//===--------------- 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;
+}