Remove slow paths from log
Remove the slow paths from log. Like several other double precision math functions, log is exactly rounded. This is not required from math functions and causes major overheads as it requires multiple fallbacks using higher precision arithmetic if a result is close to 0.5ULP. Ridiculous slowdowns of up to 100000x have been reported when the highest precision path triggers. Interestingly removing the slow paths makes hardly any difference in practice: the worst case error is still ~0.502ULP, and exp(log(x)) shows identical results before/after on many millions of random cases. All GLIBC math tests pass on AArch64 and x64 with no change in ULP error. A simple test over a few hundred million values shows log is now 18% faster on average. * manual/probes.texi (slowlog): Delete documentation of removed probe. (slowlog_inexact): Likewise * sysdeps/ieee754/dbl-64/e_log.c (__ieee754_log): Remove slow paths. * sysdeps/ieee754/dbl-64/ulog.h: Remove unused declarations.
This commit is contained in:
Wilco Dijkstra
parent
388ff7bd0d
commit
b7c83ca30e
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@ -1,3 +1,10 @@
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2018-02-07 Wilco Dijkstra <wdijkstr@arm.com>
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* manual/probes.texi (slowlog): Delete documentation of removed probe.
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(slowlog_inexact): Likewise
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* sysdeps/ieee754/dbl-64/e_log.c (__ieee754_log): Remove slow paths.
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* sysdeps/ieee754/dbl-64/ulog.h: Remove unused declarations.
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2018-02-07 Igor Gnatenko <ignatenko@redhat.com>
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[BZ #22797]
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@ -288,23 +288,6 @@ input that results in multiple precision computation with precision
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and @code{$arg4} is the final accurate value.
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@end deftp
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@deftp Probe slowlog (int @var{$arg1}, double @var{$arg2}, double @var{$arg3})
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This probe is triggered when the @code{log} function is called with an
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input that results in multiple precision computation. Argument
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@var{$arg1} is the precision with which the computation succeeded.
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Argument @var{$arg2} is the input and @var{$arg3} is the computed
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output.
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@end deftp
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@deftp Probe slowlog_inexact (int @var{$arg1}, double @var{$arg2}, double @var{$arg3})
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This probe is triggered when the @code{log} function is called with an
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input that results in multiple precision computation and none of the
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multiple precision computations result in an accurate result.
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Argument @var{$arg1} is the maximum precision with which computations
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were performed. Argument @var{$arg2} is the input and @var{$arg3} is
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the computed output.
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@end deftp
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@deftp Probe slowatan2 (int @var{$arg1}, double @var{$arg2}, double @var{$arg3}, double @var{$arg4})
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This probe is triggered when the @code{atan2} function is called with
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an input that results in multiple precision computation. Argument
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@ -23,11 +23,10 @@
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/* FUNCTION:ulog */
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/* */
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/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h ulog.h */
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/* mpexp.c mplog.c mpa.c */
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/* ulog.tbl */
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/* */
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/* An ultimate log routine. Given an IEEE double machine number x */
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/* it computes the correctly rounded (to nearest) value of log(x). */
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/* it computes the rounded (to nearest) value of log(x). */
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/* Assumption: Machine arithmetic operations are performed in */
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/* round to nearest mode of IEEE 754 standard. */
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/* */
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@ -40,34 +39,26 @@
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#include "MathLib.h"
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#include <math.h>
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#include <math_private.h>
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#include <stap-probe.h>
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#ifndef SECTION
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# define SECTION
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#endif
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void __mplog (mp_no *, mp_no *, int);
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/*********************************************************************/
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/* An ultimate log routine. Given an IEEE double machine number x */
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/* it computes the correctly rounded (to nearest) value of log(x). */
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/* An ultimate log routine. Given an IEEE double machine number x */
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/* it computes the rounded (to nearest) value of log(x). */
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/*********************************************************************/
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double
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SECTION
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__ieee754_log (double x)
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{
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#define M 4
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static const int pr[M] = { 8, 10, 18, 32 };
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int i, j, n, ux, dx, p;
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int i, j, n, ux, dx;
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double dbl_n, u, p0, q, r0, w, nln2a, luai, lubi, lvaj, lvbj,
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sij, ssij, ttij, A, B, B0, y, y1, y2, polI, polII, sa, sb,
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t1, t2, t7, t8, t, ra, rb, ww,
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a0, aa0, s1, s2, ss2, s3, ss3, a1, aa1, a, aa, b, bb, c;
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sij, ssij, ttij, A, B, B0, polI, polII, t8, a, aa, b, bb, c;
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#ifndef DLA_FMS
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double t3, t4, t5, t6;
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double t1, t2, t3, t4, t5;
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#endif
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number num;
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mp_no mpx, mpy, mpy1, mpy2, mperr;
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#include "ulog.tbl"
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#include "ulog.h"
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@ -101,7 +92,7 @@ __ieee754_log (double x)
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if (w == 0.0)
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return 0.0;
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/*--- Stage I, the case abs(x-1) < 0.03 */
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/*--- The case abs(x-1) < 0.03 */
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t8 = MHALF * w;
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EMULV (t8, w, a, aa, t1, t2, t3, t4, t5);
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@ -118,50 +109,12 @@ __ieee754_log (double x)
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polII *= w * w * w;
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c = (aa + bb) + polII;
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/* End stage I, case abs(x-1) < 0.03 */
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if ((y = b + (c + b * E2)) == b + (c - b * E2))
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return y;
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/* Here b contains the high part of the result, and c the low part.
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Maximum error is b * 2.334e-19, so accuracy is >61 bits.
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Therefore max ULP error of b + c is ~0.502. */
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return b + c;
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/*--- Stage II, the case abs(x-1) < 0.03 */
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a = d19.d + w * d20.d;
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a = d18.d + w * a;
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a = d17.d + w * a;
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a = d16.d + w * a;
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a = d15.d + w * a;
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a = d14.d + w * a;
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a = d13.d + w * a;
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a = d12.d + w * a;
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a = d11.d + w * a;
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EMULV (w, a, s2, ss2, t1, t2, t3, t4, t5);
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ADD2 (d10.d, dd10.d, s2, ss2, s3, ss3, t1, t2);
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MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (d9.d, dd9.d, s2, ss2, s3, ss3, t1, t2);
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MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (d8.d, dd8.d, s2, ss2, s3, ss3, t1, t2);
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MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (d7.d, dd7.d, s2, ss2, s3, ss3, t1, t2);
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MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (d6.d, dd6.d, s2, ss2, s3, ss3, t1, t2);
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MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (d5.d, dd5.d, s2, ss2, s3, ss3, t1, t2);
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MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (d4.d, dd4.d, s2, ss2, s3, ss3, t1, t2);
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MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (d3.d, dd3.d, s2, ss2, s3, ss3, t1, t2);
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MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (d2.d, dd2.d, s2, ss2, s3, ss3, t1, t2);
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MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
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MUL2 (w, 0, s2, ss2, s3, ss3, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (w, 0, s3, ss3, b, bb, t1, t2);
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/* End stage II, case abs(x-1) < 0.03 */
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if ((y = b + (bb + b * E4)) == b + (bb - b * E4))
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return y;
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goto stage_n;
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/*--- Stage I, the case abs(x-1) > 0.03 */
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/*--- The case abs(x-1) > 0.03 */
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case_03:
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/* Find n,u such that x = u*2**n, 1/sqrt(2) < u < sqrt(2) */
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@ -203,58 +156,10 @@ case_03:
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B0 = (((lubi + lvbj) + ssij) + ttij) + dbl_n * LN2B;
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B = polI + B0;
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/* End stage I, case abs(x-1) >= 0.03 */
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if ((y = A + (B + E1)) == A + (B - E1))
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return y;
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/*--- Stage II, the case abs(x-1) > 0.03 */
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/* Improve the accuracy of r0 */
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EMULV (p0, r0, sa, sb, t1, t2, t3, t4, t5);
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t = r0 * ((1 - sa) - sb);
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EADD (r0, t, ra, rb);
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/* Compute w */
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MUL2 (q, 0, ra, rb, w, ww, t1, t2, t3, t4, t5, t6, t7, t8);
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EADD (A, B0, a0, aa0);
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/* Evaluate polynomial III */
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s1 = (c3.d + (c4.d + c5.d * w) * w) * w;
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EADD (c2.d, s1, s2, ss2);
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MUL2 (s2, ss2, w, ww, s3, ss3, t1, t2, t3, t4, t5, t6, t7, t8);
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MUL2 (s3, ss3, w, ww, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
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ADD2 (s2, ss2, w, ww, s3, ss3, t1, t2);
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ADD2 (s3, ss3, a0, aa0, a1, aa1, t1, t2);
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/* End stage II, case abs(x-1) >= 0.03 */
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if ((y = a1 + (aa1 + E3)) == a1 + (aa1 - E3))
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return y;
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/* Final stages. Use multi-precision arithmetic. */
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stage_n:
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for (i = 0; i < M; i++)
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{
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p = pr[i];
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__dbl_mp (x, &mpx, p);
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__dbl_mp (y, &mpy, p);
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__mplog (&mpx, &mpy, p);
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__dbl_mp (e[i].d, &mperr, p);
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__add (&mpy, &mperr, &mpy1, p);
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__sub (&mpy, &mperr, &mpy2, p);
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__mp_dbl (&mpy1, &y1, p);
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__mp_dbl (&mpy2, &y2, p);
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if (y1 == y2)
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{
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LIBC_PROBE (slowlog, 3, &p, &x, &y1);
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return y1;
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}
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}
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LIBC_PROBE (slowlog_inexact, 3, &p, &x, &y1);
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return y1;
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/* Here A contains the high part of the result, and B the low part.
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Maximum abs error is 6.095e-21 and min log (x) is 0.0295 since x > 1.03.
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Therefore max ULP error of A + B is ~0.502. */
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return A + B;
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}
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#ifndef __ieee754_log
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@ -42,43 +42,6 @@
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/**/ b6 = {{0x3fbc71c5, 0x25db58ac} }, /* 0.111... */
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/**/ b7 = {{0xbfb9a4ac, 0x11a2a61c} }, /* -0.100... */
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/**/ b8 = {{0x3fb75077, 0x0df2b591} }, /* 0.091... */
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/* polynomial III */
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#if 0
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/**/ c1 = {{0x3ff00000, 0x00000000} }, /* 1 */
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#endif
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/**/ c2 = {{0xbfe00000, 0x00000000} }, /* -1/2 */
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/**/ c3 = {{0x3fd55555, 0x55555555} }, /* 1/3 */
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/**/ c4 = {{0xbfd00000, 0x00000000} }, /* -1/4 */
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/**/ c5 = {{0x3fc99999, 0x9999999a} }, /* 1/5 */
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/* polynomial IV */
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/**/ d2 = {{0xbfe00000, 0x00000000} }, /* -1/2 */
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/**/ dd2 = {{0x00000000, 0x00000000} }, /* -1/2-d2 */
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/**/ d3 = {{0x3fd55555, 0x55555555} }, /* 1/3 */
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/**/ dd3 = {{0x3c755555, 0x55555555} }, /* 1/3-d3 */
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/**/ d4 = {{0xbfd00000, 0x00000000} }, /* -1/4 */
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/**/ dd4 = {{0x00000000, 0x00000000} }, /* -1/4-d4 */
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/**/ d5 = {{0x3fc99999, 0x9999999a} }, /* 1/5 */
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/**/ dd5 = {{0xbc699999, 0x9999999a} }, /* 1/5-d5 */
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/**/ d6 = {{0xbfc55555, 0x55555555} }, /* -1/6 */
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/**/ dd6 = {{0xbc655555, 0x55555555} }, /* -1/6-d6 */
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/**/ d7 = {{0x3fc24924, 0x92492492} }, /* 1/7 */
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/**/ dd7 = {{0x3c624924, 0x92492492} }, /* 1/7-d7 */
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/**/ d8 = {{0xbfc00000, 0x00000000} }, /* -1/8 */
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/**/ dd8 = {{0x00000000, 0x00000000} }, /* -1/8-d8 */
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/**/ d9 = {{0x3fbc71c7, 0x1c71c71c} }, /* 1/9 */
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/**/ dd9 = {{0x3c5c71c7, 0x1c71c71c} }, /* 1/9-d9 */
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/**/ d10 = {{0xbfb99999, 0x9999999a} }, /* -1/10 */
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/**/ dd10 = {{0x3c599999, 0x9999999a} }, /* -1/10-d10 */
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/**/ d11 = {{0x3fb745d1, 0x745d1746} }, /* 1/11 */
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/**/ d12 = {{0xbfb55555, 0x55555555} }, /* -1/12 */
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/**/ d13 = {{0x3fb3b13b, 0x13b13b14} }, /* 1/13 */
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/**/ d14 = {{0xbfb24924, 0x92492492} }, /* -1/14 */
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/**/ d15 = {{0x3fb11111, 0x11111111} }, /* 1/15 */
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/**/ d16 = {{0xbfb00000, 0x00000000} }, /* -1/16 */
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/**/ d17 = {{0x3fae1e1e, 0x1e1e1e1e} }, /* 1/17 */
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/**/ d18 = {{0xbfac71c7, 0x1c71c71c} }, /* -1/18 */
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/**/ d19 = {{0x3faaf286, 0xbca1af28} }, /* 1/19 */
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/**/ d20 = {{0xbfa99999, 0x9999999a} }, /* -1/20 */
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/* constants */
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/**/ sqrt_2 = {{0x3ff6a09e, 0x667f3bcc} }, /* sqrt(2) */
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/**/ h1 = {{0x3fd2e000, 0x00000000} }, /* 151/2**9 */
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@ -87,14 +50,6 @@
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/**/ delv = {{0x3ef00000, 0x00000000} }, /* 1/2**16 */
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/**/ ln2a = {{0x3fe62e42, 0xfefa3800} }, /* ln(2) 43 bits */
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/**/ ln2b = {{0x3d2ef357, 0x93c76730} }, /* ln(2)-ln2a */
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/**/ e1 = {{0x3bbcc868, 0x00000000} }, /* 6.095e-21 */
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/**/ e2 = {{0x3c1138ce, 0x00000000} }, /* 2.334e-19 */
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/**/ e3 = {{0x3aa1565d, 0x00000000} }, /* 2.801e-26 */
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/**/ e4 = {{0x39809d88, 0x00000000} }, /* 1.024e-31 */
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/**/ e[M] ={{{0x37da223a, 0x00000000} }, /* 1.2e-39 */
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/**/ {{0x35c851c4, 0x00000000} }, /* 1.3e-49 */
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/**/ {{0x2ab85e51, 0x00000000} }, /* 6.8e-103 */
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/**/ {{0x17383827, 0x00000000} }},/* 8.1e-197 */
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/**/ two54 = {{0x43500000, 0x00000000} }, /* 2**54 */
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/**/ u03 = {{0x3f9eb851, 0xeb851eb8} }; /* 0.03 */
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@ -114,43 +69,6 @@
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/**/ b6 = {{0x25db58ac, 0x3fbc71c5} }, /* 0.111... */
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/**/ b7 = {{0x11a2a61c, 0xbfb9a4ac} }, /* -0.100... */
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/**/ b8 = {{0x0df2b591, 0x3fb75077} }, /* 0.091... */
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/* polynomial III */
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#if 0
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/**/ c1 = {{0x00000000, 0x3ff00000} }, /* 1 */
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#endif
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/**/ c2 = {{0x00000000, 0xbfe00000} }, /* -1/2 */
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/**/ c3 = {{0x55555555, 0x3fd55555} }, /* 1/3 */
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/**/ c4 = {{0x00000000, 0xbfd00000} }, /* -1/4 */
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/**/ c5 = {{0x9999999a, 0x3fc99999} }, /* 1/5 */
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/* polynomial IV */
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/**/ d2 = {{0x00000000, 0xbfe00000} }, /* -1/2 */
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/**/ dd2 = {{0x00000000, 0x00000000} }, /* -1/2-d2 */
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/**/ d3 = {{0x55555555, 0x3fd55555} }, /* 1/3 */
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/**/ dd3 = {{0x55555555, 0x3c755555} }, /* 1/3-d3 */
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/**/ d4 = {{0x00000000, 0xbfd00000} }, /* -1/4 */
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/**/ dd4 = {{0x00000000, 0x00000000} }, /* -1/4-d4 */
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/**/ d5 = {{0x9999999a, 0x3fc99999} }, /* 1/5 */
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/**/ dd5 = {{0x9999999a, 0xbc699999} }, /* 1/5-d5 */
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/**/ d6 = {{0x55555555, 0xbfc55555} }, /* -1/6 */
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/**/ dd6 = {{0x55555555, 0xbc655555} }, /* -1/6-d6 */
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/**/ d7 = {{0x92492492, 0x3fc24924} }, /* 1/7 */
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/**/ dd7 = {{0x92492492, 0x3c624924} }, /* 1/7-d7 */
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/**/ d8 = {{0x00000000, 0xbfc00000} }, /* -1/8 */
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/**/ dd8 = {{0x00000000, 0x00000000} }, /* -1/8-d8 */
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/**/ d9 = {{0x1c71c71c, 0x3fbc71c7} }, /* 1/9 */
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/**/ dd9 = {{0x1c71c71c, 0x3c5c71c7} }, /* 1/9-d9 */
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/**/ d10 = {{0x9999999a, 0xbfb99999} }, /* -1/10 */
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/**/ dd10 = {{0x9999999a, 0x3c599999} }, /* -1/10-d10 */
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/**/ d11 = {{0x745d1746, 0x3fb745d1} }, /* 1/11 */
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/**/ d12 = {{0x55555555, 0xbfb55555} }, /* -1/12 */
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/**/ d13 = {{0x13b13b14, 0x3fb3b13b} }, /* 1/13 */
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/**/ d14 = {{0x92492492, 0xbfb24924} }, /* -1/14 */
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/**/ d15 = {{0x11111111, 0x3fb11111} }, /* 1/15 */
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/**/ d16 = {{0x00000000, 0xbfb00000} }, /* -1/16 */
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/**/ d17 = {{0x1e1e1e1e, 0x3fae1e1e} }, /* 1/17 */
|
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/**/ d18 = {{0x1c71c71c, 0xbfac71c7} }, /* -1/18 */
|
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/**/ d19 = {{0xbca1af28, 0x3faaf286} }, /* 1/19 */
|
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/**/ d20 = {{0x9999999a, 0xbfa99999} }, /* -1/20 */
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/* constants */
|
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/**/ sqrt_2 = {{0x667f3bcc, 0x3ff6a09e} }, /* sqrt(2) */
|
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/**/ h1 = {{0x00000000, 0x3fd2e000} }, /* 151/2**9 */
|
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|
|
@ -159,14 +77,6 @@
|
|||
/**/ delv = {{0x00000000, 0x3ef00000} }, /* 1/2**16 */
|
||||
/**/ ln2a = {{0xfefa3800, 0x3fe62e42} }, /* ln(2) 43 bits */
|
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/**/ ln2b = {{0x93c76730, 0x3d2ef357} }, /* ln(2)-ln2a */
|
||||
/**/ e1 = {{0x00000000, 0x3bbcc868} }, /* 6.095e-21 */
|
||||
/**/ e2 = {{0x00000000, 0x3c1138ce} }, /* 2.334e-19 */
|
||||
/**/ e3 = {{0x00000000, 0x3aa1565d} }, /* 2.801e-26 */
|
||||
/**/ e4 = {{0x00000000, 0x39809d88} }, /* 1.024e-31 */
|
||||
/**/ e[M] ={{{0x00000000, 0x37da223a} }, /* 1.2e-39 */
|
||||
/**/ {{0x00000000, 0x35c851c4} }, /* 1.3e-49 */
|
||||
/**/ {{0x00000000, 0x2ab85e51} }, /* 6.8e-103 */
|
||||
/**/ {{0x00000000, 0x17383827} }},/* 8.1e-197 */
|
||||
/**/ two54 = {{0x00000000, 0x43500000} }, /* 2**54 */
|
||||
/**/ u03 = {{0xeb851eb8, 0x3f9eb851} }; /* 0.03 */
|
||||
|
||||
|
|
@ -178,10 +88,6 @@
|
|||
#define DEL_V delv.d
|
||||
#define LN2A ln2a.d
|
||||
#define LN2B ln2b.d
|
||||
#define E1 e1.d
|
||||
#define E2 e2.d
|
||||
#define E3 e3.d
|
||||
#define E4 e4.d
|
||||
#define U03 u03.d
|
||||
|
||||
#endif
|
||||
|
|
|
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Loading…
Reference in New Issue