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[PATCH 3/3] Consolidate sincos computation for 2.426265 < |x| < 105414350
- From: Siddhesh Poyarekar <siddhesh dot poyarekar at linaro dot org>
- To: libc-alpha at sourceware dot org
- Date: Tue, 15 Dec 2015 00:57:15 +0530
- Subject: [PATCH 3/3] Consolidate sincos computation for 2.426265 < |x| < 105414350
- Authentication-results: sourceware.org; auth=none
Like the previous change, exploit the fact that computation for sin
and cos is identical except that it is apart by a quadrant. Also
remove csloww, csloww1 and csloww2 since they can easily be expressed
in terms of sloww, sloww1 and sloww2.
Siddhesh
* sysdeps/ieee754/dbl-64/s_sin.c (csloww, csloww1, csloww2):
Remove functions.
(sloww, sloww1): Accept argument to offset quadrant.
(sloww, sloww1, sloww2): Call __mpsin or __mpcos based on
quadrant.
(__sin, __cos): Consolidate common code into new functions.
(reduce_sincos_1, do_sincos_1): New functions.
* sysdeps/ieee754/dbl-64/s_sincos.c (__sincos): Use them.
---
sysdeps/ieee754/dbl-64/s_sin.c | 392 +++++++++++---------------------------
sysdeps/ieee754/dbl-64/s_sincos.c | 12 +-
2 files changed, 123 insertions(+), 281 deletions(-)
diff --git a/sysdeps/ieee754/dbl-64/s_sin.c b/sysdeps/ieee754/dbl-64/s_sin.c
index 3b26a61..9c57321 100644
--- a/sysdeps/ieee754/dbl-64/s_sin.c
+++ b/sysdeps/ieee754/dbl-64/s_sin.c
@@ -32,9 +32,6 @@
/* bsloww1 */
/* bsloww2 */
/* cslow2 */
-/* csloww */
-/* csloww1 */
-/* csloww2 */
/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h usncs.h */
/* branred.c sincos32.c dosincos.c mpa.c */
/* sincos.tbl */
@@ -135,17 +132,14 @@ double __mpcos (double x, double dx, bool reduce_range);
static double slow (double x);
static double slow1 (double x);
static double slow2 (double x);
-static double sloww (double x, double dx, double orig);
-static double sloww1 (double x, double dx, double orig, int m);
+static double sloww (double x, double dx, double orig, int n);
+static double sloww1 (double x, double dx, double orig, int m, int n);
static double sloww2 (double x, double dx, double orig, int n);
static double bsloww (double x, double dx, double orig, int n);
static double bsloww1 (double x, double dx, double orig, int n);
static double bsloww2 (double x, double dx, double orig, int n);
int __branred (double x, double *a, double *aa);
static double cslow2 (double x);
-static double csloww (double x, double dx, double orig);
-static double csloww1 (double x, double dx, double orig, int m);
-static double csloww2 (double x, double dx, double orig, int n);
/* Given a number partitioned into U and X such that U is an index into the
sin/cos table, this macro computes the cosine of the number by combining
@@ -278,6 +272,91 @@ reduce_and_compute (double x, unsigned int k)
static inline int4
__always_inline
+reduce_sincos_1 (double x, double *a, double *da)
+{
+ mynumber v;
+
+ double t = (x * hpinv + toint);
+ double xn = t - toint;
+ v.x = t;
+ double y = (x - xn * mp1) - xn * mp2;
+ int4 n = v.i[LOW_HALF] & 3;
+ double db = xn * mp3;
+ double b = y - db;
+ db = (y - b) - db;
+
+ *a = b;
+ *da = db;
+
+ return n;
+}
+
+/* Compute sin (A + DA). cos can be computed by shifting the quadrant N
+ clockwise. */
+static double
+__always_inline
+do_sincos_1 (double a, double da, double x, int4 n, int4 k)
+{
+ double xx, retval, res, cor, y;
+ mynumber u;
+ int m;
+ double eps = fabs (x) * 1.2e-30;
+
+ int k1 = (n + k) & 3;
+ switch (k1)
+ { /* quarter of unit circle */
+ case 2:
+ a = -a;
+ da = -da;
+ case 0:
+ xx = a * a;
+ if (xx < 0.01588)
+ {
+ /* Taylor series. */
+ res = TAYLOR_SIN (xx, a, da, cor);
+ cor = (cor > 0) ? 1.02 * cor + eps : 1.02 * cor - eps;
+ retval = (res == res + cor) ? res : sloww (a, da, x, k);
+ }
+ else
+ {
+ if (a > 0)
+ m = 1;
+ else
+ {
+ m = 0;
+ a = -a;
+ da = -da;
+ }
+ u.x = big + a;
+ y = a - (u.x - big);
+ res = do_sin (u, y, da, &cor);
+ cor = (cor > 0) ? 1.035 * cor + eps : 1.035 * cor - eps;
+ retval = ((res == res + cor) ? ((m) ? res : -res)
+ : sloww1 (a, da, x, m, k));
+ }
+ break;
+
+ case 1:
+ case 3:
+ if (a < 0)
+ {
+ a = -a;
+ da = -da;
+ }
+ u.x = big + a;
+ y = a - (u.x - big) + da;
+ res = do_cos (u, y, &cor);
+ cor = (cor > 0) ? 1.025 * cor + eps : 1.025 * cor - eps;
+ retval = ((res == res + cor) ? ((k1 & 2) ? -res : res)
+ : sloww2 (a, da, x, n));
+ break;
+ }
+
+ return retval;
+}
+
+static inline int4
+__always_inline
reduce_sincos_2 (double x, double *a, double *da)
{
mynumber v;
@@ -386,9 +465,9 @@ SECTION
#endif
__sin (double x)
{
- double xx, res, t, cor, y, s, c, sn, ssn, cs, ccs, xn, a, da, eps;
- mynumber u, v;
- int4 k, m, n;
+ double xx, res, t, cor, y, s, c, sn, ssn, cs, ccs;
+ mynumber u;
+ int4 k, m;
double retval = 0;
#ifndef IN_SINCOS
@@ -452,73 +531,15 @@ __sin (double x)
retval = (res == res + 1.020 * cor) ? ((m > 0) ? res : -res) : slow2 (x);
} /* else if (k < 0x400368fd) */
+#ifndef IN_SINCOS
/*-------------------------- 2.426265<|x|< 105414350 ----------------------*/
else if (k < 0x419921FB)
{
- t = (x * hpinv + toint);
- xn = t - toint;
- v.x = t;
- y = (x - xn * mp1) - xn * mp2;
- n = v.i[LOW_HALF] & 3;
- da = xn * mp3;
- a = y - da;
- da = (y - a) - da;
- eps = fabs (x) * 1.2e-30;
-
- switch (n)
- { /* quarter of unit circle */
- case 0:
- case 2:
- xx = a * a;
- if (n)
- {
- a = -a;
- da = -da;
- }
- if (xx < 0.01588)
- {
- /* Taylor series. */
- res = TAYLOR_SIN (xx, a, da, cor);
- cor = (cor > 0) ? 1.02 * cor + eps : 1.02 * cor - eps;
- retval = (res == res + cor) ? res : sloww (a, da, x);
- }
- else
- {
- if (a > 0)
- m = 1;
- else
- {
- m = 0;
- a = -a;
- da = -da;
- }
- u.x = big + a;
- y = a - (u.x - big);
- res = do_sin (u, y, da, &cor);
- cor = (cor > 0) ? 1.035 * cor + eps : 1.035 * cor - eps;
- retval = ((res == res + cor) ? ((m) ? res : -res)
- : sloww1 (a, da, x, m));
- }
- break;
-
- case 1:
- case 3:
- if (a < 0)
- {
- a = -a;
- da = -da;
- }
- u.x = big + a;
- y = a - (u.x - big) + da;
- res = do_cos (u, y, &cor);
- cor = (cor > 0) ? 1.025 * cor + eps : 1.025 * cor - eps;
- retval = ((res == res + cor) ? ((n & 2) ? -res : res)
- : sloww2 (a, da, x, n));
- break;
- }
+ double a, da;
+ int4 n = reduce_sincos_1 (x, &a, &da);
+ retval = do_sincos_1 (a, da, x, n, 0);
} /* else if (k < 0x419921FB ) */
-#ifndef IN_SINCOS
/*---------------------105414350 <|x|< 281474976710656 --------------------*/
else if (k < 0x42F00000)
{
@@ -558,9 +579,9 @@ SECTION
#endif
__cos (double x)
{
- double y, xx, res, t, cor, xn, a, da, eps;
- mynumber u, v;
- int4 k, m, n;
+ double y, xx, res, cor, a, da;
+ mynumber u;
+ int4 k, m;
double retval = 0;
@@ -595,7 +616,7 @@ __cos (double x)
{
res = TAYLOR_SIN (xx, a, da, cor);
cor = (cor > 0) ? 1.02 * cor + 1.0e-31 : 1.02 * cor - 1.0e-31;
- retval = (res == res + cor) ? res : csloww (a, da, x);
+ retval = (res == res + cor) ? res : sloww (a, da, x, 1);
}
else
{
@@ -614,79 +635,20 @@ __cos (double x)
res = do_sin (u, y, da, &cor);
cor = (cor > 0) ? 1.035 * cor + 1.0e-31 : 1.035 * cor - 1.0e-31;
retval = ((res == res + cor) ? ((m) ? res : -res)
- : csloww1 (a, da, x, m));
+ : sloww1 (a, da, x, m, 1));
}
} /* else if (k < 0x400368fd) */
+#ifndef IN_SINCOS
else if (k < 0x419921FB)
{ /* 2.426265<|x|< 105414350 */
- t = (x * hpinv + toint);
- xn = t - toint;
- v.x = t;
- y = (x - xn * mp1) - xn * mp2;
- n = v.i[LOW_HALF] & 3;
- da = xn * mp3;
- a = y - da;
- da = (y - a) - da;
- eps = fabs (x) * 1.2e-30;
-
- switch (n)
- {
- case 1:
- case 3:
- xx = a * a;
- if (n == 1)
- {
- a = -a;
- da = -da;
- }
- if (xx < 0.01588)
- {
- res = TAYLOR_SIN (xx, a, da, cor);
- cor = (cor > 0) ? 1.02 * cor + eps : 1.02 * cor - eps;
- retval = (res == res + cor) ? res : csloww (a, da, x);
- }
- else
- {
- if (a > 0)
- {
- m = 1;
- }
- else
- {
- m = 0;
- a = -a;
- da = -da;
- }
- u.x = big + a;
- y = a - (u.x - big);
- res = do_sin (u, y, da, &cor);
- cor = (cor > 0) ? 1.035 * cor + eps : 1.035 * cor - eps;
- retval = ((res == res + cor) ? ((m) ? res : -res)
- : csloww1 (a, da, x, m));
- }
- break;
-
- case 0:
- case 2:
- if (a < 0)
- {
- a = -a;
- da = -da;
- }
- u.x = big + a;
- y = a - (u.x - big) + da;
- res = do_cos (u, y, &cor);
- cor = (cor > 0) ? 1.025 * cor + eps : 1.025 * cor - eps;
- retval = ((res == res + cor) ? ((n) ? -res : res)
- : csloww2 (a, da, x, n));
- break;
- }
+ double a, da;
+ int4 n = reduce_sincos_1 (x, &a, &da);
+ retval = do_sincos_1 (a, da, x, n, 1);
} /* else if (k < 0x419921FB ) */
-#ifndef IN_SINCOS
else if (k < 0x42F00000)
{
double a, da;
@@ -805,12 +767,13 @@ slow2 (double x)
static double
SECTION
-sloww (double x, double dx, double orig)
+sloww (double x, double dx, double orig, int k)
{
double y, t, res, cor, w[2], a, da, xn;
mynumber v;
int4 n;
res = TAYLOR_SLOW (x, dx, cor);
+
if (cor > 0)
cor = 1.0005 * cor + fabs (orig) * 3.1e-30;
else
@@ -832,14 +795,15 @@ sloww (double x, double dx, double orig)
xn = t - toint;
v.x = t;
y = (orig - xn * mp1) - xn * mp2;
- n = v.i[LOW_HALF] & 3;
+ n = (v.i[LOW_HALF] + k) & 3;
da = xn * pp3;
t = y - da;
da = (y - t) - da;
y = xn * pp4;
a = t - y;
da = ((t - a) - y) + da;
- if (n & 2)
+
+ if (n == 2 || n == 1)
{
a = -a;
da = -da;
@@ -853,7 +817,7 @@ sloww (double x, double dx, double orig)
if (w[0] == w[0] + cor)
return (a > 0) ? w[0] : -w[0];
- return __mpsin (orig, 0, true);
+ return (n & 1) ? __mpcos (orig, 0, true) : __mpsin (orig, 0, true);
}
/***************************************************************************/
@@ -865,7 +829,7 @@ sloww (double x, double dx, double orig)
static double
SECTION
-sloww1 (double x, double dx, double orig, int m)
+sloww1 (double x, double dx, double orig, int m, int k)
{
mynumber u;
double w[2], y, cor, res;
@@ -887,7 +851,7 @@ sloww1 (double x, double dx, double orig, int m)
if (w[0] == w[0] + cor)
return (m > 0) ? w[0] : -w[0];
- return __mpsin (orig, 0, true);
+ return (k == 1) ? __mpcos (orig, 0, true) : __mpsin (orig, 0, true);
}
/***************************************************************************/
@@ -921,7 +885,7 @@ sloww2 (double x, double dx, double orig, int n)
if (w[0] == w[0] + cor)
return (n & 2) ? -w[0] : w[0];
- return __mpsin (orig, 0, true);
+ return (n & 1) ? __mpsin (orig, 0, true) : __mpcos (orig, 0, true);
}
/***************************************************************************/
@@ -1052,138 +1016,6 @@ cslow2 (double x)
return __mpcos (x, 0, false);
}
-/***************************************************************************/
-/* Routine compute cos(x+dx) (Double-Length number) where x is small enough*/
-/* to use Taylor series around zero and (x+dx) .Routine receive also */
-/* (right argument) the original value of x for computing error of */
-/* result.And if result not accurate enough routine calls other routines */
-/***************************************************************************/
-
-
-static double
-SECTION
-csloww (double x, double dx, double orig)
-{
- double y, t, res, cor, w[2], a, da, xn;
- mynumber v;
- int4 n;
-
- /* Taylor series */
- res = TAYLOR_SLOW (x, dx, cor);
-
- if (cor > 0)
- cor = 1.0005 * cor + fabs (orig) * 3.1e-30;
- else
- cor = 1.0005 * cor - fabs (orig) * 3.1e-30;
-
- if (res == res + cor)
- return res;
-
- (x > 0) ? __dubsin (x, dx, w) : __dubsin (-x, -dx, w);
-
- if (w[1] > 0)
- cor = 1.000000001 * w[1] + fabs (orig) * 1.1e-30;
- else
- cor = 1.000000001 * w[1] - fabs (orig) * 1.1e-30;
-
- if (w[0] == w[0] + cor)
- return (x > 0) ? w[0] : -w[0];
-
- t = (orig * hpinv + toint);
- xn = t - toint;
- v.x = t;
- y = (orig - xn * mp1) - xn * mp2;
- n = v.i[LOW_HALF] & 3;
- da = xn * pp3;
- t = y - da;
- da = (y - t) - da;
- y = xn * pp4;
- a = t - y;
- da = ((t - a) - y) + da;
- if (n == 1)
- {
- a = -a;
- da = -da;
- }
- (a > 0) ? __dubsin (a, da, w) : __dubsin (-a, -da, w);
-
- if (w[1] > 0)
- cor = 1.000000001 * w[1] + fabs (orig) * 1.1e-40;
- else
- cor = 1.000000001 * w[1] - fabs (orig) * 1.1e-40;
-
- if (w[0] == w[0] + cor)
- return (a > 0) ? w[0] : -w[0];
-
- return __mpcos (orig, 0, true);
-}
-
-/***************************************************************************/
-/* Routine compute sin(x+dx) (Double-Length number) where x in first or */
-/* third quarter of unit circle.Routine receive also (right argument) the */
-/* original value of x for computing error of result.And if result not */
-/* accurate enough routine calls other routines */
-/***************************************************************************/
-
-static double
-SECTION
-csloww1 (double x, double dx, double orig, int m)
-{
- mynumber u;
- double w[2], y, cor, res;
-
- u.x = big + x;
- y = x - (u.x - big);
- res = do_sin_slow (u, y, dx, 3.1e-30 * fabs (orig), &cor);
-
- if (res == res + cor)
- return (m > 0) ? res : -res;
-
- __dubsin (x, dx, w);
- if (w[1] > 0)
- cor = 1.000000005 * w[1] + 1.1e-30 * fabs (orig);
- else
- cor = 1.000000005 * w[1] - 1.1e-30 * fabs (orig);
-
- if (w[0] == w[0] + cor)
- return (m > 0) ? w[0] : -w[0];
-
- return __mpcos (orig, 0, true);
-}
-
-
-/***************************************************************************/
-/* Routine compute sin(x+dx) (Double-Length number) where x in second or */
-/* fourth quarter of unit circle.Routine receive also the original value */
-/* and quarter(n= 1or 3)of x for computing error of result.And if result not*/
-/* accurate enough routine calls other routines */
-/***************************************************************************/
-
-static double
-SECTION
-csloww2 (double x, double dx, double orig, int n)
-{
- mynumber u;
- double w[2], y, cor, res;
-
- u.x = big + x;
- y = x - (u.x - big);
- res = do_cos_slow (u, y, dx, 3.1e-30 * fabs (orig), &cor);
-
- if (res == res + cor)
- return (n) ? -res : res;
-
- __docos (x, dx, w);
- if (w[1] > 0)
- cor = 1.000000005 * w[1] + 1.1e-30 * fabs (orig);
- else
- cor = 1.000000005 * w[1] - 1.1e-30 * fabs (orig);
- if (w[0] == w[0] + cor)
- return (n) ? -w[0] : w[0];
-
- return __mpcos (orig, 0, true);
-}
-
#ifndef __cos
weak_alias (__cos, cos)
# ifdef NO_LONG_DOUBLE
diff --git a/sysdeps/ieee754/dbl-64/s_sincos.c b/sysdeps/ieee754/dbl-64/s_sincos.c
index 7f78b41..0290004 100644
--- a/sysdeps/ieee754/dbl-64/s_sincos.c
+++ b/sysdeps/ieee754/dbl-64/s_sincos.c
@@ -69,12 +69,22 @@ __sincos (double x, double *sinx, double *cosx)
u.x = x;
k = 0x7fffffff & u.i[HIGH_HALF];
- if (k < 0x419921FB)
+ if (k < 0x400368fd)
{
*sinx = __sin_local (x);
*cosx = __cos_local (x);
return;
}
+ if (k < 0x419921FB)
+ {
+ double a, da;
+ int4 n = reduce_sincos_1 (x, &a, &da);
+
+ *sinx = do_sincos_1 (a, da, x, n, 0);
+ *cosx = do_sincos_1 (a, da, x, n, 1);
+
+ return;
+ }
if (k < 0x42F00000)
{
double a, da;
--
2.5.0