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[PATCH 2/3] Consolidate sin and cos code for 105414350 <|x|< 281474976710656
- From: Siddhesh Poyarekar <siddhesh dot poyarekar at linaro dot org>
- To: libc-alpha at sourceware dot org
- Cc: Siddhesh Poyarekar <siddhesh dot poyarekar at linaro dot org>
- Date: Fri, 11 Dec 2015 17:41:49 +0530
- Subject: [PATCH 2/3] Consolidate sin and cos code for 105414350 <|x|< 281474976710656
- Authentication-results: sourceware.org; auth=none
- References: <1449835910-4651-1-git-send-email-siddhesh dot poyarekar at linaro dot org>
The sin and cos computation for this range of input is identical
except for a difference in quadrants by 1. Exploit that fact and the
common argument reduction to reduce computations for sincos.
Siddhesh
* sysdeps/ieee754/dbl-64/s_sincos.c (__sin_local, __cos_local):
Move common code...
(do_sincos_2): ... a new function.
(__sincos): Call do_sincos_2 for sin as well as cos.
---
sysdeps/ieee754/dbl-64/s_sincos.c | 231 ++++++++++++++------------------------
1 file changed, 84 insertions(+), 147 deletions(-)
diff --git a/sysdeps/ieee754/dbl-64/s_sincos.c b/sysdeps/ieee754/dbl-64/s_sincos.c
index 078d65d..24dc43c 100644
--- a/sysdeps/ieee754/dbl-64/s_sincos.c
+++ b/sysdeps/ieee754/dbl-64/s_sincos.c
@@ -33,8 +33,7 @@ static double
__always_inline
__sin_local (double x, int4 k)
{
- double xx, res, t, cor, y, s, c, sn, ssn, cs, ccs, xn, a, da, db, eps, xn1,
- xn2;
+ double xx, res, t, cor, y, s, c, sn, ssn, cs, ccs, xn, a, da, eps;
mynumber u, v;
int4 m, n;
double retval = 0;
@@ -94,7 +93,7 @@ __sin_local (double x, int4 k)
} /* else if (k < 0x400368fd) */
/*-------------------------- 2.426265<|x|< 105414350 ----------------------*/
- else if (k < 0x419921FB)
+ else
{
t = (x * hpinv + toint);
xn = t - toint;
@@ -159,82 +158,6 @@ __sin_local (double x, int4 k)
}
} /* else if (k < 0x419921FB ) */
-/*---------------------105414350 <|x|< 281474976710656 --------------------*/
- else
- {
- t = (x * hpinv + toint);
- xn = t - toint;
- v.x = t;
- xn1 = (xn + 8.0e22) - 8.0e22;
- xn2 = xn - xn1;
- y = ((((x - xn1 * mp1) - xn1 * mp2) - xn2 * mp1) - xn2 * mp2);
- n = v.i[LOW_HALF] & 3;
- da = xn1 * pp3;
- t = y - da;
- da = (y - t) - da;
- da = (da - xn2 * pp3) - xn * pp4;
- a = t + da;
- da = (t - a) + da;
- eps = 1.0e-24;
-
- switch (n)
- {
- 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 : bsloww (a, da, x, n);
- }
- else
- {
- double t;
- if (a > 0)
- {
- m = 1;
- t = a;
- db = da;
- }
- else
- {
- m = 0;
- t = -a;
- db = -da;
- }
- u.x = big + t;
- y = t - (u.x - big);
- res = do_sin (u, y, db, &cor);
- cor = (cor > 0) ? 1.035 * cor + eps : 1.035 * cor - eps;
- retval = ((res == res + cor) ? ((m) ? res : -res)
- : bsloww1 (a, da, x, n));
- }
- 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)
- : bsloww2 (a, da, x, n));
- break;
- }
- } /* else if (k < 0x42F00000 ) */
-
return retval;
}
@@ -245,8 +168,7 @@ static double
__always_inline
__cos_local (double x, int4 k)
{
- double y, xx, res, t, cor, xn, a, da, db, eps, xn1,
- xn2;
+ double y, xx, res, t, cor, xn, a, da, eps;
mynumber u, v;
int4 m, n;
@@ -366,79 +288,75 @@ __cos_local (double x, int4 k)
}
} /* else if (k < 0x419921FB ) */
- else
+ return retval;
+}
+
+/* Compute sin (A + DA). cos can be computed by shifting the quadrant N
+ clockwise. */
+static double
+__always_inline
+do_sincos_2 (double a, double da, double x, unsigned int n)
+{
+ double res, retval, cor, xx;
+ mynumber u;
+
+ double eps = 1.0e-24;
+
+ switch (n)
{
- t = (x * hpinv + toint);
- xn = t - toint;
- v.x = t;
- xn1 = (xn + 8.0e22) - 8.0e22;
- xn2 = xn - xn1;
- y = ((((x - xn1 * mp1) - xn1 * mp2) - xn2 * mp1) - xn2 * mp2);
- n = v.i[LOW_HALF] & 3;
- da = xn1 * pp3;
- t = y - da;
- da = (y - t) - da;
- da = (da - xn2 * pp3) - xn * pp4;
- a = t + da;
- da = (t - a) + da;
- eps = 1.0e-24;
-
- switch (n)
+ case 2:
+ a = -a;
+ da = -da;
+ /* Fall through. */
+ case 0:
+ xx = a * a;
+ if (xx < 0.01588)
{
- case 1:
- case 3:
- xx = a * a;
- if (n == 1)
- {
- 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 : bsloww (a, da, x, n);
+ }
+ else
+ {
+ double t, db, y;
+ int m;
+ if (a > 0)
{
- res = TAYLOR_SIN (xx, a, da, cor);
- cor = (cor > 0) ? 1.02 * cor + eps : 1.02 * cor - eps;
- retval = (res == res + cor) ? res : bsloww (a, da, x, n);
+ m = 1;
+ t = a;
+ db = da;
}
else
{
- double t;
- if (a > 0)
- {
- m = 1;
- t = a;
- db = da;
- }
- else
- {
- m = 0;
- t = -a;
- db = -da;
- }
- u.x = big + t;
- y = t - (u.x - big);
- res = do_sin (u, y, db, &cor);
- cor = (cor > 0) ? 1.035 * cor + eps : 1.035 * cor - eps;
- retval = ((res == res + cor) ? ((m) ? res : -res)
- : bsloww1 (a, da, x, n));
+ m = 0;
+ t = -a;
+ db = -da;
}
- break;
+ u.x = big + t;
+ y = t - (u.x - big);
+ res = do_sin (u, y, db, &cor);
+ cor = (cor > 0) ? 1.035 * cor + eps : 1.035 * cor - eps;
+ retval = ((res == res + cor) ? ((m) ? res : -res)
+ : bsloww1 (a, da, x, n));
+ }
+ 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)
- : bsloww2 (a, da, x, n));
- break;
+ case 1:
+ case 3:
+ if (a < 0)
+ {
+ a = -a;
+ da = -da;
}
- } /* else if (k < 0x42F00000 ) */
+ u.x = big + a;
+ double 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)
+ : bsloww2 (a, da, x, n));
+ break;
+ }
return retval;
}
@@ -501,13 +419,32 @@ __sincos (double x, double *sinx, double *cosx)
u.x = x;
k = 0x7fffffff & u.i[HIGH_HALF];
-
- if (k < 0x42F00000)
+ if (k < 0x419921FB)
{
*sinx = __sin_local (x, k);
*cosx = __cos_local (x, k);
return;
}
+ if (k < 0x42F00000)
+ {
+ double t = (x * hpinv + toint);
+ double xn = t - toint;
+ u.x = t;
+ double xn1 = (xn + 8.0e22) - 8.0e22;
+ double xn2 = xn - xn1;
+ double y = ((((x - xn1 * mp1) - xn1 * mp2) - xn2 * mp1) - xn2 * mp2);
+ int4 n = u.i[LOW_HALF] & 3;
+ double da = xn1 * pp3;
+ t = y - da;
+ da = (y - t) - da;
+ da = (da - xn2 * pp3) - xn * pp4;
+ double a = t + da;
+ da = (t - a) + da;
+
+ *sinx = do_sincos_2 (a, da, x, n);
+ *cosx = do_sincos_2 (a, da, x, (n + 1) & 3);
+ return;
+ }
if (k < 0x7ff00000)
{
reduce_and_compute_sincos (x, sinx, cosx);
--
2.5.0