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authorWilco Dijkstra <wdijkstr@arm.com>2018-02-07 12:24:43 +0000
committerWilco Dijkstra <wdijkstr@arm.com>2018-02-07 12:24:43 +0000
commitb7c83ca30ef8e85b6642151d95600a36535f8d97 (patch)
tree96bc33835429ccfe40cd3c257f183b57926ec40c
parent388ff7bd0d57d7061fdd39a2f26f65687e8058da (diff)
downloadglibc-b7c83ca30ef8e85b6642151d95600a36535f8d97.tar.gz
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.
-rw-r--r--ChangeLog7
-rw-r--r--manual/probes.texi17
-rw-r--r--sysdeps/ieee754/dbl-64/e_log.c127
-rw-r--r--sysdeps/ieee754/dbl-64/ulog.h94
4 files changed, 23 insertions, 222 deletions
diff --git a/ChangeLog b/ChangeLog
index 290d474218..d823e3ac3b 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,10 @@
+2018-02-07 Wilco Dijkstra <wdijkstr@arm.com>
+
+ * 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.
+
2018-02-07 Igor Gnatenko <ignatenko@redhat.com>
[BZ #22797]
diff --git a/manual/probes.texi b/manual/probes.texi
index 8ab67562d7..e99b7f3cb4 100644
--- a/manual/probes.texi
+++ b/manual/probes.texi
@@ -288,23 +288,6 @@ input that results in multiple precision computation with precision
and @code{$arg4} is the final accurate value.
@end deftp
-@deftp Probe slowlog (int @var{$arg1}, double @var{$arg2}, double @var{$arg3})
-This probe is triggered when the @code{log} function is called with an
-input that results in multiple precision computation. Argument
-@var{$arg1} is the precision with which the computation succeeded.
-Argument @var{$arg2} is the input and @var{$arg3} is the computed
-output.
-@end deftp
-
-@deftp Probe slowlog_inexact (int @var{$arg1}, double @var{$arg2}, double @var{$arg3})
-This probe is triggered when the @code{log} function is called with an
-input that results in multiple precision computation and none of the
-multiple precision computations result in an accurate result.
-Argument @var{$arg1} is the maximum precision with which computations
-were performed. Argument @var{$arg2} is the input and @var{$arg3} is
-the computed output.
-@end deftp
-
@deftp Probe slowatan2 (int @var{$arg1}, double @var{$arg2}, double @var{$arg3}, double @var{$arg4})
This probe is triggered when the @code{atan2} function is called with
an input that results in multiple precision computation. Argument
diff --git a/sysdeps/ieee754/dbl-64/e_log.c b/sysdeps/ieee754/dbl-64/e_log.c
index 6a18ebb904..2483dd8551 100644
--- a/sysdeps/ieee754/dbl-64/e_log.c
+++ b/sysdeps/ieee754/dbl-64/e_log.c
@@ -23,11 +23,10 @@
/* FUNCTION:ulog */
/* */
/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h ulog.h */
-/* mpexp.c mplog.c mpa.c */
/* ulog.tbl */
/* */
/* An ultimate log routine. Given an IEEE double machine number x */
-/* it computes the correctly rounded (to nearest) value of log(x). */
+/* it computes the rounded (to nearest) value of log(x). */
/* Assumption: Machine arithmetic operations are performed in */
/* round to nearest mode of IEEE 754 standard. */
/* */
@@ -40,34 +39,26 @@
#include "MathLib.h"
#include <math.h>
#include <math_private.h>
-#include <stap-probe.h>
#ifndef SECTION
# define SECTION
#endif
-void __mplog (mp_no *, mp_no *, int);
-
/*********************************************************************/
-/* An ultimate log routine. Given an IEEE double machine number x */
-/* it computes the correctly rounded (to nearest) value of log(x). */
+/* An ultimate log routine. Given an IEEE double machine number x */
+/* it computes the rounded (to nearest) value of log(x). */
/*********************************************************************/
double
SECTION
__ieee754_log (double x)
{
-#define M 4
- static const int pr[M] = { 8, 10, 18, 32 };
- int i, j, n, ux, dx, p;
+ int i, j, n, ux, dx;
double dbl_n, u, p0, q, r0, w, nln2a, luai, lubi, lvaj, lvbj,
- sij, ssij, ttij, A, B, B0, y, y1, y2, polI, polII, sa, sb,
- t1, t2, t7, t8, t, ra, rb, ww,
- a0, aa0, s1, s2, ss2, s3, ss3, a1, aa1, a, aa, b, bb, c;
+ sij, ssij, ttij, A, B, B0, polI, polII, t8, a, aa, b, bb, c;
#ifndef DLA_FMS
- double t3, t4, t5, t6;
+ double t1, t2, t3, t4, t5;
#endif
number num;
- mp_no mpx, mpy, mpy1, mpy2, mperr;
#include "ulog.tbl"
#include "ulog.h"
@@ -101,7 +92,7 @@ __ieee754_log (double x)
if (w == 0.0)
return 0.0;
- /*--- Stage I, the case abs(x-1) < 0.03 */
+ /*--- The case abs(x-1) < 0.03 */
t8 = MHALF * w;
EMULV (t8, w, a, aa, t1, t2, t3, t4, t5);
@@ -118,50 +109,12 @@ __ieee754_log (double x)
polII *= w * w * w;
c = (aa + bb) + polII;
- /* End stage I, case abs(x-1) < 0.03 */
- if ((y = b + (c + b * E2)) == b + (c - b * E2))
- return y;
-
- /*--- Stage II, the case abs(x-1) < 0.03 */
-
- a = d19.d + w * d20.d;
- a = d18.d + w * a;
- a = d17.d + w * a;
- a = d16.d + w * a;
- a = d15.d + w * a;
- a = d14.d + w * a;
- a = d13.d + w * a;
- a = d12.d + w * a;
- a = d11.d + w * a;
-
- EMULV (w, a, s2, ss2, t1, t2, t3, t4, t5);
- ADD2 (d10.d, dd10.d, s2, ss2, s3, ss3, t1, t2);
- MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
- ADD2 (d9.d, dd9.d, s2, ss2, s3, ss3, t1, t2);
- MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
- ADD2 (d8.d, dd8.d, s2, ss2, s3, ss3, t1, t2);
- MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
- ADD2 (d7.d, dd7.d, s2, ss2, s3, ss3, t1, t2);
- MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
- ADD2 (d6.d, dd6.d, s2, ss2, s3, ss3, t1, t2);
- MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
- ADD2 (d5.d, dd5.d, s2, ss2, s3, ss3, t1, t2);
- MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
- ADD2 (d4.d, dd4.d, s2, ss2, s3, ss3, t1, t2);
- MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
- ADD2 (d3.d, dd3.d, s2, ss2, s3, ss3, t1, t2);
- MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
- ADD2 (d2.d, dd2.d, s2, ss2, s3, ss3, t1, t2);
- MUL2 (w, 0, s3, ss3, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
- MUL2 (w, 0, s2, ss2, s3, ss3, t1, t2, t3, t4, t5, t6, t7, t8);
- ADD2 (w, 0, s3, ss3, b, bb, t1, t2);
+ /* Here b contains the high part of the result, and c the low part.
+ Maximum error is b * 2.334e-19, so accuracy is >61 bits.
+ Therefore max ULP error of b + c is ~0.502. */
+ return b + c;
- /* End stage II, case abs(x-1) < 0.03 */
- if ((y = b + (bb + b * E4)) == b + (bb - b * E4))
- return y;
- goto stage_n;
-
- /*--- Stage I, the case abs(x-1) > 0.03 */
+ /*--- The case abs(x-1) > 0.03 */
case_03:
/* Find n,u such that x = u*2**n, 1/sqrt(2) < u < sqrt(2) */
@@ -203,58 +156,10 @@ case_03:
B0 = (((lubi + lvbj) + ssij) + ttij) + dbl_n * LN2B;
B = polI + B0;
- /* End stage I, case abs(x-1) >= 0.03 */
- if ((y = A + (B + E1)) == A + (B - E1))
- return y;
-
-
- /*--- Stage II, the case abs(x-1) > 0.03 */
-
- /* Improve the accuracy of r0 */
- EMULV (p0, r0, sa, sb, t1, t2, t3, t4, t5);
- t = r0 * ((1 - sa) - sb);
- EADD (r0, t, ra, rb);
-
- /* Compute w */
- MUL2 (q, 0, ra, rb, w, ww, t1, t2, t3, t4, t5, t6, t7, t8);
-
- EADD (A, B0, a0, aa0);
-
- /* Evaluate polynomial III */
- s1 = (c3.d + (c4.d + c5.d * w) * w) * w;
- EADD (c2.d, s1, s2, ss2);
- MUL2 (s2, ss2, w, ww, s3, ss3, t1, t2, t3, t4, t5, t6, t7, t8);
- MUL2 (s3, ss3, w, ww, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
- ADD2 (s2, ss2, w, ww, s3, ss3, t1, t2);
- ADD2 (s3, ss3, a0, aa0, a1, aa1, t1, t2);
-
- /* End stage II, case abs(x-1) >= 0.03 */
- if ((y = a1 + (aa1 + E3)) == a1 + (aa1 - E3))
- return y;
-
-
- /* Final stages. Use multi-precision arithmetic. */
-stage_n:
-
- for (i = 0; i < M; i++)
- {
- p = pr[i];
- __dbl_mp (x, &mpx, p);
- __dbl_mp (y, &mpy, p);
- __mplog (&mpx, &mpy, p);
- __dbl_mp (e[i].d, &mperr, p);
- __add (&mpy, &mperr, &mpy1, p);
- __sub (&mpy, &mperr, &mpy2, p);
- __mp_dbl (&mpy1, &y1, p);
- __mp_dbl (&mpy2, &y2, p);
- if (y1 == y2)
- {
- LIBC_PROBE (slowlog, 3, &p, &x, &y1);
- return y1;
- }
- }
- LIBC_PROBE (slowlog_inexact, 3, &p, &x, &y1);
- return y1;
+ /* Here A contains the high part of the result, and B the low part.
+ Maximum abs error is 6.095e-21 and min log (x) is 0.0295 since x > 1.03.
+ Therefore max ULP error of A + B is ~0.502. */
+ return A + B;
}
#ifndef __ieee754_log
diff --git a/sysdeps/ieee754/dbl-64/ulog.h b/sysdeps/ieee754/dbl-64/ulog.h
index 36a31137b7..087b76e2ab 100644
--- a/sysdeps/ieee754/dbl-64/ulog.h
+++ b/sysdeps/ieee754/dbl-64/ulog.h
@@ -42,43 +42,6 @@
/**/ b6 = {{0x3fbc71c5, 0x25db58ac} }, /* 0.111... */
/**/ b7 = {{0xbfb9a4ac, 0x11a2a61c} }, /* -0.100... */
/**/ b8 = {{0x3fb75077, 0x0df2b591} }, /* 0.091... */
- /* polynomial III */
-#if 0
-/**/ c1 = {{0x3ff00000, 0x00000000} }, /* 1 */
-#endif
-/**/ c2 = {{0xbfe00000, 0x00000000} }, /* -1/2 */
-/**/ c3 = {{0x3fd55555, 0x55555555} }, /* 1/3 */
-/**/ c4 = {{0xbfd00000, 0x00000000} }, /* -1/4 */
-/**/ c5 = {{0x3fc99999, 0x9999999a} }, /* 1/5 */
- /* polynomial IV */
-/**/ d2 = {{0xbfe00000, 0x00000000} }, /* -1/2 */
-/**/ dd2 = {{0x00000000, 0x00000000} }, /* -1/2-d2 */
-/**/ d3 = {{0x3fd55555, 0x55555555} }, /* 1/3 */
-/**/ dd3 = {{0x3c755555, 0x55555555} }, /* 1/3-d3 */
-/**/ d4 = {{0xbfd00000, 0x00000000} }, /* -1/4 */
-/**/ dd4 = {{0x00000000, 0x00000000} }, /* -1/4-d4 */
-/**/ d5 = {{0x3fc99999, 0x9999999a} }, /* 1/5 */
-/**/ dd5 = {{0xbc699999, 0x9999999a} }, /* 1/5-d5 */
-/**/ d6 = {{0xbfc55555, 0x55555555} }, /* -1/6 */
-/**/ dd6 = {{0xbc655555, 0x55555555} }, /* -1/6-d6 */
-/**/ d7 = {{0x3fc24924, 0x92492492} }, /* 1/7 */
-/**/ dd7 = {{0x3c624924, 0x92492492} }, /* 1/7-d7 */
-/**/ d8 = {{0xbfc00000, 0x00000000} }, /* -1/8 */
-/**/ dd8 = {{0x00000000, 0x00000000} }, /* -1/8-d8 */
-/**/ d9 = {{0x3fbc71c7, 0x1c71c71c} }, /* 1/9 */
-/**/ dd9 = {{0x3c5c71c7, 0x1c71c71c} }, /* 1/9-d9 */
-/**/ d10 = {{0xbfb99999, 0x9999999a} }, /* -1/10 */
-/**/ dd10 = {{0x3c599999, 0x9999999a} }, /* -1/10-d10 */
-/**/ d11 = {{0x3fb745d1, 0x745d1746} }, /* 1/11 */
-/**/ d12 = {{0xbfb55555, 0x55555555} }, /* -1/12 */
-/**/ d13 = {{0x3fb3b13b, 0x13b13b14} }, /* 1/13 */
-/**/ d14 = {{0xbfb24924, 0x92492492} }, /* -1/14 */
-/**/ d15 = {{0x3fb11111, 0x11111111} }, /* 1/15 */
-/**/ d16 = {{0xbfb00000, 0x00000000} }, /* -1/16 */
-/**/ d17 = {{0x3fae1e1e, 0x1e1e1e1e} }, /* 1/17 */
-/**/ d18 = {{0xbfac71c7, 0x1c71c71c} }, /* -1/18 */
-/**/ d19 = {{0x3faaf286, 0xbca1af28} }, /* 1/19 */
-/**/ d20 = {{0xbfa99999, 0x9999999a} }, /* -1/20 */
/* constants */
/**/ sqrt_2 = {{0x3ff6a09e, 0x667f3bcc} }, /* sqrt(2) */
/**/ h1 = {{0x3fd2e000, 0x00000000} }, /* 151/2**9 */
@@ -87,14 +50,6 @@
/**/ delv = {{0x3ef00000, 0x00000000} }, /* 1/2**16 */
/**/ ln2a = {{0x3fe62e42, 0xfefa3800} }, /* ln(2) 43 bits */
/**/ ln2b = {{0x3d2ef357, 0x93c76730} }, /* ln(2)-ln2a */
-/**/ e1 = {{0x3bbcc868, 0x00000000} }, /* 6.095e-21 */
-/**/ e2 = {{0x3c1138ce, 0x00000000} }, /* 2.334e-19 */
-/**/ e3 = {{0x3aa1565d, 0x00000000} }, /* 2.801e-26 */
-/**/ e4 = {{0x39809d88, 0x00000000} }, /* 1.024e-31 */
-/**/ e[M] ={{{0x37da223a, 0x00000000} }, /* 1.2e-39 */
-/**/ {{0x35c851c4, 0x00000000} }, /* 1.3e-49 */
-/**/ {{0x2ab85e51, 0x00000000} }, /* 6.8e-103 */
-/**/ {{0x17383827, 0x00000000} }},/* 8.1e-197 */
/**/ two54 = {{0x43500000, 0x00000000} }, /* 2**54 */
/**/ u03 = {{0x3f9eb851, 0xeb851eb8} }; /* 0.03 */
@@ -114,43 +69,6 @@
/**/ b6 = {{0x25db58ac, 0x3fbc71c5} }, /* 0.111... */
/**/ b7 = {{0x11a2a61c, 0xbfb9a4ac} }, /* -0.100... */
/**/ b8 = {{0x0df2b591, 0x3fb75077} }, /* 0.091... */
- /* polynomial III */
-#if 0
-/**/ c1 = {{0x00000000, 0x3ff00000} }, /* 1 */
-#endif
-/**/ c2 = {{0x00000000, 0xbfe00000} }, /* -1/2 */
-/**/ c3 = {{0x55555555, 0x3fd55555} }, /* 1/3 */
-/**/ c4 = {{0x00000000, 0xbfd00000} }, /* -1/4 */
-/**/ c5 = {{0x9999999a, 0x3fc99999} }, /* 1/5 */
- /* polynomial IV */
-/**/ d2 = {{0x00000000, 0xbfe00000} }, /* -1/2 */
-/**/ dd2 = {{0x00000000, 0x00000000} }, /* -1/2-d2 */
-/**/ d3 = {{0x55555555, 0x3fd55555} }, /* 1/3 */
-/**/ dd3 = {{0x55555555, 0x3c755555} }, /* 1/3-d3 */
-/**/ d4 = {{0x00000000, 0xbfd00000} }, /* -1/4 */
-/**/ dd4 = {{0x00000000, 0x00000000} }, /* -1/4-d4 */
-/**/ d5 = {{0x9999999a, 0x3fc99999} }, /* 1/5 */
-/**/ dd5 = {{0x9999999a, 0xbc699999} }, /* 1/5-d5 */
-/**/ d6 = {{0x55555555, 0xbfc55555} }, /* -1/6 */
-/**/ dd6 = {{0x55555555, 0xbc655555} }, /* -1/6-d6 */
-/**/ d7 = {{0x92492492, 0x3fc24924} }, /* 1/7 */
-/**/ dd7 = {{0x92492492, 0x3c624924} }, /* 1/7-d7 */
-/**/ d8 = {{0x00000000, 0xbfc00000} }, /* -1/8 */
-/**/ dd8 = {{0x00000000, 0x00000000} }, /* -1/8-d8 */
-/**/ d9 = {{0x1c71c71c, 0x3fbc71c7} }, /* 1/9 */
-/**/ dd9 = {{0x1c71c71c, 0x3c5c71c7} }, /* 1/9-d9 */
-/**/ d10 = {{0x9999999a, 0xbfb99999} }, /* -1/10 */
-/**/ dd10 = {{0x9999999a, 0x3c599999} }, /* -1/10-d10 */
-/**/ d11 = {{0x745d1746, 0x3fb745d1} }, /* 1/11 */
-/**/ d12 = {{0x55555555, 0xbfb55555} }, /* -1/12 */
-/**/ d13 = {{0x13b13b14, 0x3fb3b13b} }, /* 1/13 */
-/**/ d14 = {{0x92492492, 0xbfb24924} }, /* -1/14 */
-/**/ d15 = {{0x11111111, 0x3fb11111} }, /* 1/15 */
-/**/ d16 = {{0x00000000, 0xbfb00000} }, /* -1/16 */
-/**/ d17 = {{0x1e1e1e1e, 0x3fae1e1e} }, /* 1/17 */
-/**/ d18 = {{0x1c71c71c, 0xbfac71c7} }, /* -1/18 */
-/**/ d19 = {{0xbca1af28, 0x3faaf286} }, /* 1/19 */
-/**/ d20 = {{0x9999999a, 0xbfa99999} }, /* -1/20 */
/* constants */
/**/ sqrt_2 = {{0x667f3bcc, 0x3ff6a09e} }, /* sqrt(2) */
/**/ h1 = {{0x00000000, 0x3fd2e000} }, /* 151/2**9 */
@@ -159,14 +77,6 @@
/**/ delv = {{0x00000000, 0x3ef00000} }, /* 1/2**16 */
/**/ ln2a = {{0xfefa3800, 0x3fe62e42} }, /* ln(2) 43 bits */
/**/ 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