[llvm-commits] [compiler-rt] r107579 - /compiler-rt/trunk/lib/divsf3.c
Stephen Canon
scanon at apple.com
Sat Jul 3 23:15:45 PDT 2010
Author: scanon
Date: Sun Jul 4 01:15:44 2010
New Revision: 107579
URL: http://llvm.org/viewvc/llvm-project?rev=107579&view=rev
Log:
Single-precision soft-float division
Added:
compiler-rt/trunk/lib/divsf3.c
Added: compiler-rt/trunk/lib/divsf3.c
URL: http://llvm.org/viewvc/llvm-project/compiler-rt/trunk/lib/divsf3.c?rev=107579&view=auto
==============================================================================
--- compiler-rt/trunk/lib/divsf3.c (added)
+++ compiler-rt/trunk/lib/divsf3.c Sun Jul 4 01:15:44 2010
@@ -0,0 +1,193 @@
+//===-- lib/divsf3.c - Single-precision division ------------------*- C -*-===//
+//
+// The LLVM Compiler Infrastructure
+//
+// This file is distributed under the University of Illinois Open Source
+// License. See LICENSE.TXT for details.
+//
+//===----------------------------------------------------------------------===//
+//
+// 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"
+
+#include <stdio.h>
+
+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);
+ }
+
+ // 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 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, so after three iterations, we have about 28 binary
+ // digits of accuracy.
+ 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;
+
+ // Exhaustive testing shows that the error in reciprocal after three steps
+ // is in the interval [-0x1.f58108p-31, 0x1.d0e48cp-29], in line with our
+ // expectations. We bump the reciprocal by a tiny value to force the error
+ // to be strictly positive (in the range [0x1.4fdfp-37,0x1.287246p-29], to
+ // be specific). This also causes 1/1 to give a sensible approximation
+ // instead of zero (due to overflow).
+ 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);
+ }
+
+ 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
+ return fromRep(absResult | quotientSign);
+ }
+}
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