public inbox for glibc-cvs@sourceware.org
help / color / mirror / Atom feed
* [glibc/google/grte/v5-2.27/master] [PATCH 1/7] sin/cos slow paths: avoid slow paths for small inputs
@ 2021-07-07 18:54 Stan Shebs
0 siblings, 0 replies; 2+ messages in thread
From: Stan Shebs @ 2021-07-07 18:54 UTC (permalink / raw)
To: glibc-cvs
https://sourceware.org/git/gitweb.cgi?p=glibc.git;h=be9cb9c30f604b7bbede1e9a9da524655cce0255
commit be9cb9c30f604b7bbede1e9a9da524655cce0255
Author: Wilco Dijkstra <wdijkstr@arm.com>
Date: Tue Apr 3 16:24:29 2018 +0100
[PATCH 1/7] sin/cos slow paths: avoid slow paths for small inputs
This series of patches removes the slow patchs from sin, cos and sincos.
Besides greatly simplifying the implementation, the new version is also much
faster for inputs up to PI (41% faster) and for large inputs needing range
reduction (27% faster).
ULP is ~0.55 with no errors found after testing 1.6 billion inputs across most
of the range with mpsin and mpcos. The number of incorrectly rounded results
(ie. ULP >0.5) is at most ~2750 per million inputs between 0.125 and 0.5,
the average is ~850 per million between 0 and PI.
Tested on AArch64 and x86_64 with no regressions.
The first patch removes the slow paths for the cases where the input is small
and doesn't require range reduction. Update ULP tables for sin, cos and sincos
on AArch64 and x86_64.
* sysdeps/aarch64/libm-test-ulps: Update ULP for sin, cos, sincos.
* sysdeps/ieee754/dbl-64/s_sin.c (__sin): Remove slow paths for small
inputs.
(__cos): Likewise.
* sysdeps/x86_64/fpu/libm-test-ulps: Update ULP for sin, cos, sincos.
Diff:
---
sysdeps/aarch64/libm-test-ulps | 6 ++++++
sysdeps/ieee754/dbl-64/s_sin.c | 40 ++++++++++++++-------------------------
sysdeps/x86_64/fpu/libm-test-ulps | 6 ++++++
3 files changed, 26 insertions(+), 26 deletions(-)
diff --git a/sysdeps/aarch64/libm-test-ulps b/sysdeps/aarch64/libm-test-ulps
index 5603f2ea48..d9850c878b 100644
--- a/sysdeps/aarch64/libm-test-ulps
+++ b/sysdeps/aarch64/libm-test-ulps
@@ -1012,7 +1012,9 @@ ildouble: 2
ldouble: 2
Function: "cos":
+double: 1
float: 1
+idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
@@ -1968,7 +1970,9 @@ ildouble: 2
ldouble: 2
Function: "sin":
+double: 1
float: 1
+idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
@@ -1998,7 +2002,9 @@ ildouble: 3
ldouble: 3
Function: "sincos":
+double: 1
float: 1
+idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
diff --git a/sysdeps/ieee754/dbl-64/s_sin.c b/sysdeps/ieee754/dbl-64/s_sin.c
index 8c589cbd4a..0c16b728df 100644
--- a/sysdeps/ieee754/dbl-64/s_sin.c
+++ b/sysdeps/ieee754/dbl-64/s_sin.c
@@ -448,7 +448,7 @@ SECTION
#endif
__sin (double x)
{
- double xx, res, t, cor;
+ double xx, t, cor;
mynumber u;
int4 k, m;
double retval = 0;
@@ -471,26 +471,22 @@ __sin (double x)
xx = x * x;
/* Taylor series. */
t = POLYNOMIAL (xx) * (xx * x);
- res = x + t;
- cor = (x - res) + t;
- retval = (res == res + 1.07 * cor) ? res : slow (x);
+ /* Max ULP of x + t is 0.535. */
+ retval = x + t;
} /* else if (k < 0x3fd00000) */
/*---------------------------- 0.25<|x|< 0.855469---------------------- */
else if (k < 0x3feb6000)
{
- res = do_sin (x, 0, &cor);
- retval = (res == res + 1.096 * cor) ? res : slow1 (x);
- retval = __copysign (retval, x);
+ /* Max ULP is 0.548. */
+ retval = __copysign (do_sin (x, 0, &cor), x);
} /* else if (k < 0x3feb6000) */
/*----------------------- 0.855469 <|x|<2.426265 ----------------------*/
else if (k < 0x400368fd)
{
-
t = hp0 - fabs (x);
- res = do_cos (t, hp1, &cor);
- retval = (res == res + 1.020 * cor) ? res : slow2 (x);
- retval = __copysign (retval, x);
+ /* Max ULP is 0.51. */
+ retval = __copysign (do_cos (t, hp1, &cor), x);
} /* else if (k < 0x400368fd) */
#ifndef IN_SINCOS
@@ -541,7 +537,7 @@ SECTION
#endif
__cos (double x)
{
- double y, xx, res, cor, a, da;
+ double y, xx, cor, a, da;
mynumber u;
int4 k, m;
@@ -561,8 +557,8 @@ __cos (double x)
else if (k < 0x3feb6000)
{ /* 2^-27 < |x| < 0.855469 */
- res = do_cos (x, 0, &cor);
- retval = (res == res + 1.020 * cor) ? res : cslow2 (x);
+ /* Max ULP is 0.51. */
+ retval = do_cos (x, 0, &cor);
} /* else if (k < 0x3feb6000) */
else if (k < 0x400368fd)
@@ -571,20 +567,12 @@ __cos (double x)
a = y + hp1;
da = (y - a) + hp1;
xx = a * a;
+ /* Max ULP is 0.501 if xx < 0.01588 or 0.518 otherwise.
+ Range reduction uses 106 bits here which is sufficient. */
if (xx < 0.01588)
- {
- res = TAYLOR_SIN (xx, a, da, cor);
- cor = 1.02 * cor + __copysign (1.0e-31, cor);
- retval = (res == res + cor) ? res : sloww (a, da, x, true);
- }
+ retval = TAYLOR_SIN (xx, a, da, cor);
else
- {
- res = do_sin (a, da, &cor);
- cor = 1.035 * cor + __copysign (1.0e-31, cor);
- retval = ((res == res + cor) ? __copysign (res, a)
- : sloww1 (a, da, x, true));
- }
-
+ retval = __copysign (do_sin (a, da, &cor), a);
} /* else if (k < 0x400368fd) */
diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps
index 85552bd695..f34e91a477 100644
--- a/sysdeps/x86_64/fpu/libm-test-ulps
+++ b/sysdeps/x86_64/fpu/libm-test-ulps
@@ -1262,7 +1262,9 @@ ildouble: 1
ldouble: 1
Function: "cos":
+double: 1
float128: 1
+idouble: 1
ifloat128: 1
ildouble: 1
ldouble: 1
@@ -2526,7 +2528,9 @@ Function: "pow_vlen8_avx2":
float: 3
Function: "sin":
+double: 1
float128: 1
+idouble: 1
ifloat128: 1
ildouble: 1
ldouble: 1
@@ -2576,7 +2580,9 @@ Function: "sin_vlen8_avx2":
float: 1
Function: "sincos":
+double: 1
float128: 1
+idouble: 1
ifloat128: 1
ildouble: 1
ldouble: 1
^ permalink raw reply [flat|nested] 2+ messages in thread
* [glibc/google/grte/v5-2.27/master] [PATCH 1/7] sin/cos slow paths: avoid slow paths for small inputs
@ 2021-08-28 0:38 Fangrui Song
0 siblings, 0 replies; 2+ messages in thread
From: Fangrui Song @ 2021-08-28 0:38 UTC (permalink / raw)
To: glibc-cvs
https://sourceware.org/git/gitweb.cgi?p=glibc.git;h=bc57e68bbbc6b5290d8944ab8a5cf30a4351beb4
commit bc57e68bbbc6b5290d8944ab8a5cf30a4351beb4
Author: Wilco Dijkstra <wdijkstr@arm.com>
Date: Tue Apr 3 16:24:29 2018 +0100
[PATCH 1/7] sin/cos slow paths: avoid slow paths for small inputs
This series of patches removes the slow patchs from sin, cos and sincos.
Besides greatly simplifying the implementation, the new version is also much
faster for inputs up to PI (41% faster) and for large inputs needing range
reduction (27% faster).
ULP is ~0.55 with no errors found after testing 1.6 billion inputs across most
of the range with mpsin and mpcos. The number of incorrectly rounded results
(ie. ULP >0.5) is at most ~2750 per million inputs between 0.125 and 0.5,
the average is ~850 per million between 0 and PI.
Tested on AArch64 and x86_64 with no regressions.
The first patch removes the slow paths for the cases where the input is small
and doesn't require range reduction. Update ULP tables for sin, cos and sincos
on AArch64 and x86_64.
* sysdeps/aarch64/libm-test-ulps: Update ULP for sin, cos, sincos.
* sysdeps/ieee754/dbl-64/s_sin.c (__sin): Remove slow paths for small
inputs.
(__cos): Likewise.
* sysdeps/x86_64/fpu/libm-test-ulps: Update ULP for sin, cos, sincos.
Diff:
---
sysdeps/aarch64/libm-test-ulps | 6 ++++++
sysdeps/ieee754/dbl-64/s_sin.c | 40 ++++++++++++++-------------------------
sysdeps/x86_64/fpu/libm-test-ulps | 6 ++++++
3 files changed, 26 insertions(+), 26 deletions(-)
diff --git a/sysdeps/aarch64/libm-test-ulps b/sysdeps/aarch64/libm-test-ulps
index 5603f2ea48..d9850c878b 100644
--- a/sysdeps/aarch64/libm-test-ulps
+++ b/sysdeps/aarch64/libm-test-ulps
@@ -1012,7 +1012,9 @@ ildouble: 2
ldouble: 2
Function: "cos":
+double: 1
float: 1
+idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
@@ -1968,7 +1970,9 @@ ildouble: 2
ldouble: 2
Function: "sin":
+double: 1
float: 1
+idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
@@ -1998,7 +2002,9 @@ ildouble: 3
ldouble: 3
Function: "sincos":
+double: 1
float: 1
+idouble: 1
ifloat: 1
ildouble: 1
ldouble: 1
diff --git a/sysdeps/ieee754/dbl-64/s_sin.c b/sysdeps/ieee754/dbl-64/s_sin.c
index 8c589cbd4a..0c16b728df 100644
--- a/sysdeps/ieee754/dbl-64/s_sin.c
+++ b/sysdeps/ieee754/dbl-64/s_sin.c
@@ -448,7 +448,7 @@ SECTION
#endif
__sin (double x)
{
- double xx, res, t, cor;
+ double xx, t, cor;
mynumber u;
int4 k, m;
double retval = 0;
@@ -471,26 +471,22 @@ __sin (double x)
xx = x * x;
/* Taylor series. */
t = POLYNOMIAL (xx) * (xx * x);
- res = x + t;
- cor = (x - res) + t;
- retval = (res == res + 1.07 * cor) ? res : slow (x);
+ /* Max ULP of x + t is 0.535. */
+ retval = x + t;
} /* else if (k < 0x3fd00000) */
/*---------------------------- 0.25<|x|< 0.855469---------------------- */
else if (k < 0x3feb6000)
{
- res = do_sin (x, 0, &cor);
- retval = (res == res + 1.096 * cor) ? res : slow1 (x);
- retval = __copysign (retval, x);
+ /* Max ULP is 0.548. */
+ retval = __copysign (do_sin (x, 0, &cor), x);
} /* else if (k < 0x3feb6000) */
/*----------------------- 0.855469 <|x|<2.426265 ----------------------*/
else if (k < 0x400368fd)
{
-
t = hp0 - fabs (x);
- res = do_cos (t, hp1, &cor);
- retval = (res == res + 1.020 * cor) ? res : slow2 (x);
- retval = __copysign (retval, x);
+ /* Max ULP is 0.51. */
+ retval = __copysign (do_cos (t, hp1, &cor), x);
} /* else if (k < 0x400368fd) */
#ifndef IN_SINCOS
@@ -541,7 +537,7 @@ SECTION
#endif
__cos (double x)
{
- double y, xx, res, cor, a, da;
+ double y, xx, cor, a, da;
mynumber u;
int4 k, m;
@@ -561,8 +557,8 @@ __cos (double x)
else if (k < 0x3feb6000)
{ /* 2^-27 < |x| < 0.855469 */
- res = do_cos (x, 0, &cor);
- retval = (res == res + 1.020 * cor) ? res : cslow2 (x);
+ /* Max ULP is 0.51. */
+ retval = do_cos (x, 0, &cor);
} /* else if (k < 0x3feb6000) */
else if (k < 0x400368fd)
@@ -571,20 +567,12 @@ __cos (double x)
a = y + hp1;
da = (y - a) + hp1;
xx = a * a;
+ /* Max ULP is 0.501 if xx < 0.01588 or 0.518 otherwise.
+ Range reduction uses 106 bits here which is sufficient. */
if (xx < 0.01588)
- {
- res = TAYLOR_SIN (xx, a, da, cor);
- cor = 1.02 * cor + __copysign (1.0e-31, cor);
- retval = (res == res + cor) ? res : sloww (a, da, x, true);
- }
+ retval = TAYLOR_SIN (xx, a, da, cor);
else
- {
- res = do_sin (a, da, &cor);
- cor = 1.035 * cor + __copysign (1.0e-31, cor);
- retval = ((res == res + cor) ? __copysign (res, a)
- : sloww1 (a, da, x, true));
- }
-
+ retval = __copysign (do_sin (a, da, &cor), a);
} /* else if (k < 0x400368fd) */
diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps
index 85552bd695..f34e91a477 100644
--- a/sysdeps/x86_64/fpu/libm-test-ulps
+++ b/sysdeps/x86_64/fpu/libm-test-ulps
@@ -1262,7 +1262,9 @@ ildouble: 1
ldouble: 1
Function: "cos":
+double: 1
float128: 1
+idouble: 1
ifloat128: 1
ildouble: 1
ldouble: 1
@@ -2526,7 +2528,9 @@ Function: "pow_vlen8_avx2":
float: 3
Function: "sin":
+double: 1
float128: 1
+idouble: 1
ifloat128: 1
ildouble: 1
ldouble: 1
@@ -2576,7 +2580,9 @@ Function: "sin_vlen8_avx2":
float: 1
Function: "sincos":
+double: 1
float128: 1
+idouble: 1
ifloat128: 1
ildouble: 1
ldouble: 1
^ permalink raw reply [flat|nested] 2+ messages in thread
end of thread, other threads:[~2021-08-28 0:38 UTC | newest]
Thread overview: 2+ messages (download: mbox.gz / follow: Atom feed)
-- links below jump to the message on this page --
2021-07-07 18:54 [glibc/google/grte/v5-2.27/master] [PATCH 1/7] sin/cos slow paths: avoid slow paths for small inputs Stan Shebs
2021-08-28 0:38 Fangrui Song
This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for read-only IMAP folder(s) and NNTP newsgroup(s).