vendor/compiler-rt/compiler-rt-trunk-r366426

1 files changed, 192 insertions, 174 deletions

diff --git a/lib/builtins/divtf3.c b/lib/builtins/divtf3.c
index e81dab826bdd..6e61d2e31b75 100644
--- a/lib/builtins/divtf3.c
+++ b/lib/builtins/divtf3.c
@@ -1,9 +1,8 @@
 //===-- 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.
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
 //
 //===----------------------------------------------------------------------===//
 //
@@ -22,182 +21,201 @@
 #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 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);
     }
 
-    const int writtenExponent = quotientExponent + exponentBias;
+    // anything else / infinity = +/- 0
+    if (bAbs == infRep)
+      return fromRep(quotientSign);
 
-    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.
+    if (!aAbs) {
+      // zero / zero = NaN
+      if (!bAbs)
+        return fromRep(qnanRep);
+      // zero / anything else = +/- zero
+      else
         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;
+    // 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;
+  }
+
+  const int writtenExponent = quotientExponent + exponentBias;
+
+  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 long double result = fromRep(absResult | quotientSign);
+    return result;
+  }
 }
 
 #endif