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* [glibc/maskray/grte] [PATCH 1/7] sin/cos slow paths: avoid slow paths for small inputs
@ 2021-08-28 0:33 Fangrui Song
0 siblings, 0 replies; 4+ messages in thread
From: Fangrui Song @ 2021-08-28 0:33 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] 4+ messages in thread
* [glibc/maskray/grte] [PATCH 1/7] sin/cos slow paths: avoid slow paths for small inputs
@ 2021-08-28 0:29 Fangrui Song
0 siblings, 0 replies; 4+ messages in thread
From: Fangrui Song @ 2021-08-28 0:29 UTC (permalink / raw)
To: glibc-cvs
https://sourceware.org/git/gitweb.cgi?p=glibc.git;h=4c8deb52ffe78160c737fdc23515f4fa3e7e197c
commit 4c8deb52ffe78160c737fdc23515f4fa3e7e197c
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] 4+ messages in thread
* [glibc/maskray/grte] [PATCH 1/7] sin/cos slow paths: avoid slow paths for small inputs
@ 2021-08-27 23:48 Fangrui Song
0 siblings, 0 replies; 4+ messages in thread
From: Fangrui Song @ 2021-08-27 23:48 UTC (permalink / raw)
To: glibc-cvs
https://sourceware.org/git/gitweb.cgi?p=glibc.git;h=0be962b99f11d8528cee7b1944e4eb768d52b8dd
commit 0be962b99f11d8528cee7b1944e4eb768d52b8dd
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] 4+ messages in thread
* [glibc/maskray/grte] [PATCH 1/7] sin/cos slow paths: avoid slow paths for small inputs
@ 2021-08-27 23:46 Fangrui Song
0 siblings, 0 replies; 4+ messages in thread
From: Fangrui Song @ 2021-08-27 23:46 UTC (permalink / raw)
To: glibc-cvs
https://sourceware.org/git/gitweb.cgi?p=glibc.git;h=09a237d066d170dfab2a23390c68bc4a05b78063
commit 09a237d066d170dfab2a23390c68bc4a05b78063
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] 4+ messages in thread
end of thread, other threads:[~2021-08-28 0:33 UTC | newest]
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