[llvm-commits] [compiler-rt] r107586 - in /compiler-rt/trunk/lib: divdf3.c divsf3.c fp_lib.h muldf3.c mulsf3.c
Stephen Canon
scanon at apple.com
Sun Jul 4 09:53:39 PDT 2010
Author: scanon
Date: Sun Jul 4 11:53:39 2010
New Revision: 107586
URL: http://llvm.org/viewvc/llvm-project?rev=107586&view=rev
Log:
Initial implementation of double-precision soft-float division, moved a couple utility functions from the multiplications into the utility header
Added:
compiler-rt/trunk/lib/divdf3.c
Modified:
compiler-rt/trunk/lib/divsf3.c
compiler-rt/trunk/lib/fp_lib.h
compiler-rt/trunk/lib/muldf3.c
compiler-rt/trunk/lib/mulsf3.c
Added: compiler-rt/trunk/lib/divdf3.c
URL: http://llvm.org/viewvc/llvm-project/compiler-rt/trunk/lib/divdf3.c?rev=107586&view=auto
==============================================================================
--- compiler-rt/trunk/lib/divdf3.c (added)
+++ compiler-rt/trunk/lib/divdf3.c Sun Jul 4 11:53:39 2010
@@ -0,0 +1,182 @@
+//===-- lib/divdf3.c - Double-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 double-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 DOUBLE_PRECISION
+#include "fp_lib.h"
+
+fp_t __divdf3(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.
+ const uint32_t q31b = bSignificand >> 21;
+ uint32_t recip32 = 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 correction32;
+ correction32 = -((uint64_t)recip32 * q31b >> 32);
+ recip32 = (uint64_t)recip32 * correction32 >> 31;
+ correction32 = -((uint64_t)recip32 * q31b >> 32);
+ recip32 = (uint64_t)recip32 * correction32 >> 31;
+ correction32 = -((uint64_t)recip32 * q31b >> 32);
+ recip32 = (uint64_t)recip32 * correction32 >> 31;
+
+ // recip32 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
+ // recip32 downward by one bit.
+ recip32--;
+
+ // We need to perform one more iteration to get us to 56 binary digits;
+ // The last iteration needs to happen with extra precision.
+ const uint32_t q63blo = bSignificand << 11;
+ uint64_t correction, reciprocal;
+ correction = -((uint64_t)recip32*q31b + ((uint64_t)recip32*q63blo >> 32));
+ uint32_t cHi = correction >> 32;
+ uint32_t cLo = correction;
+ reciprocal = (uint64_t)recip32*cHi + ((uint64_t)recip32*cLo >> 32);
+
+ // We already adjusted the 32-bit estimate, now we need to adjust the final
+ // 64-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^-56, 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 Q53 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^-53 (actually, we have a
+ // couple of bits to spare, but this is all we need).
+
+ // We need a 64 x 64 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;
+ if (quotient < (implicitBit << 1)) {
+ residual = (aSignificand << 53) - quotient * bSignificand;
+ quotientExponent--;
+ } else {
+ quotient >>= 1;
+ residual = (aSignificand << 52) - 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
+ const double result = fromRep(absResult | quotientSign);
+ return result;
+ }
+}
Modified: compiler-rt/trunk/lib/divsf3.c
URL: http://llvm.org/viewvc/llvm-project/compiler-rt/trunk/lib/divsf3.c?rev=107586&r1=107585&r2=107586&view=diff
==============================================================================
--- compiler-rt/trunk/lib/divsf3.c (original)
+++ compiler-rt/trunk/lib/divsf3.c Sun Jul 4 11:53:39 2010
@@ -19,8 +19,6 @@
#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;
@@ -166,28 +164,3 @@
return fromRep(absResult | quotientSign);
}
}
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Modified: compiler-rt/trunk/lib/fp_lib.h
URL: http://llvm.org/viewvc/llvm-project/compiler-rt/trunk/lib/fp_lib.h?rev=107586&r1=107585&r2=107586&view=diff
==============================================================================
--- compiler-rt/trunk/lib/fp_lib.h (original)
+++ compiler-rt/trunk/lib/fp_lib.h Sun Jul 4 11:53:39 2010
@@ -37,6 +37,13 @@
return __builtin_clz(a);
}
+// 32x32 --> 64 bit multiply
+static inline void wideMultiply(rep_t a, rep_t b, rep_t *hi, rep_t *lo) {
+ const uint64_t product = (uint64_t)a*b;
+ *hi = product >> 32;
+ *lo = product;
+}
+
#elif defined DOUBLE_PRECISION
typedef uint64_t rep_t;
@@ -56,6 +63,26 @@
#endif
}
+#define loWord(a) (a & 0xffffffffU)
+#define hiWord(a) (a >> 32)
+
+// 64x64 -> 128 wide multiply for platforms that don't have such an operation;
+// many 64-bit platforms have this operation, but they tend to have hardware
+// floating-point, so we don't bother with a special case for them here.
+static inline void wideMultiply(rep_t a, rep_t b, rep_t *hi, rep_t *lo) {
+ // Each of the component 32x32 -> 64 products
+ const uint64_t plolo = loWord(a) * loWord(b);
+ const uint64_t plohi = loWord(a) * hiWord(b);
+ const uint64_t philo = hiWord(a) * loWord(b);
+ const uint64_t phihi = hiWord(a) * hiWord(b);
+ // Sum terms that contribute to lo in a way that allows us to get the carry
+ const uint64_t r0 = loWord(plolo);
+ const uint64_t r1 = hiWord(plolo) + loWord(plohi) + loWord(philo);
+ *lo = r0 + (r1 << 32);
+ // Sum terms contributing to hi with the carry from lo
+ *hi = hiWord(plohi) + hiWord(philo) + hiWord(r1) + phihi;
+}
+
#else
#error Either SINGLE_PRECISION or DOUBLE_PRECISION must be defined.
#endif
Modified: compiler-rt/trunk/lib/muldf3.c
URL: http://llvm.org/viewvc/llvm-project/compiler-rt/trunk/lib/muldf3.c?rev=107586&r1=107585&r2=107586&view=diff
==============================================================================
--- compiler-rt/trunk/lib/muldf3.c (original)
+++ compiler-rt/trunk/lib/muldf3.c Sun Jul 4 11:53:39 2010
@@ -15,26 +15,6 @@
#define DOUBLE_PRECISION
#include "fp_lib.h"
-#define loWord(a) (a & 0xffffffffU)
-#define hiWord(a) (a >> 32)
-
-// 64x64 -> 128 wide multiply for platforms that don't have such an operation;
-// many 64-bit platforms have this operation, but they tend to have hardware
-// floating-point, so we don't bother with a special case for them here.
-static inline void wideMultiply(rep_t a, rep_t b, rep_t *hi, rep_t *lo) {
- // Each of the component 32x32 -> 64 products
- const uint64_t plolo = loWord(a) * loWord(b);
- const uint64_t plohi = loWord(a) * hiWord(b);
- const uint64_t philo = hiWord(a) * loWord(b);
- const uint64_t phihi = hiWord(a) * hiWord(b);
- // Sum terms that contribute to lo in a way that allows us to get the carry
- const uint64_t r0 = loWord(plolo);
- const uint64_t r1 = hiWord(plolo) + loWord(plohi) + loWord(philo);
- *lo = r0 + (r1 << 32);
- // Sum terms contributing to hi with the carry from lo
- *hi = hiWord(plohi) + hiWord(philo) + hiWord(r1) + phihi;
-}
-
fp_t __muldf3(fp_t a, fp_t b) {
const unsigned int aExponent = toRep(a) >> significandBits & maxExponent;
Modified: compiler-rt/trunk/lib/mulsf3.c
URL: http://llvm.org/viewvc/llvm-project/compiler-rt/trunk/lib/mulsf3.c?rev=107586&r1=107585&r2=107586&view=diff
==============================================================================
--- compiler-rt/trunk/lib/mulsf3.c (original)
+++ compiler-rt/trunk/lib/mulsf3.c Sun Jul 4 11:53:39 2010
@@ -15,13 +15,6 @@
#define SINGLE_PRECISION
#include "fp_lib.h"
-// 32x32 --> 64 bit multiply
-static inline void wideMultiply(rep_t a, rep_t b, rep_t *hi, rep_t *lo) {
- const uint64_t product = (uint64_t)a*b;
- *hi = product >> 32;
- *lo = product;
-}
-
fp_t __mulsf3(fp_t a, fp_t b) {
const unsigned int aExponent = toRep(a) >> significandBits & maxExponent;
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