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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
- Cc: Siddhesh Poyarekar <siddhesh dot poyarekar at linaro dot org>
- Date: Fri, 11 Dec 2015 17:41:50 +0530
- Subject: [PATCH 3/3] Consolidate sincos computation for 2.426265 < |x| < 105414350
- Authentication-results: sourceware.org; auth=none
- References: <1449835910-4651-1-git-send-email-siddhesh dot poyarekar at linaro dot org>
Like the previous change, exploit the fact that computation for sin
and cos is identical except that it is apart by a quadrant.
Siddhesh
* sysdeps/ieee754/dbl-64/s_sin.c [IN_SINCOS]: Avoid defining
sloww, sloww1, sloww2 and csloww2 when included in s_sincos.c.
* sysdeps/ieee754/dbl-64/s_sincos.c (__sin_local, __cos_local):
Move common code...
(do_sincos_1): ... into a new function.
(sincos_sloww, sincos_sloww1, sincos_sloww2): New functions.
(__sincos): Call do_sincos_1.
---
sysdeps/ieee754/dbl-64/s_sin.c | 8 +-
sysdeps/ieee754/dbl-64/s_sincos.c | 343 ++++++++++++++++++++++----------------
2 files changed, 208 insertions(+), 143 deletions(-)
diff --git a/sysdeps/ieee754/dbl-64/s_sin.c b/sysdeps/ieee754/dbl-64/s_sin.c
index a8c5d4a..bc23e84 100644
--- a/sysdeps/ieee754/dbl-64/s_sin.c
+++ b/sysdeps/ieee754/dbl-64/s_sin.c
@@ -135,9 +135,11 @@ double __mpcos (double x, double dx, bool reduce_range);
static double slow (double x);
static double slow1 (double x);
static double slow2 (double x);
+#ifndef IN_SINCOS
static double sloww (double x, double dx, double orig);
static double sloww1 (double x, double dx, double orig, int m);
static double sloww2 (double x, double dx, double orig, int n);
+#endif
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);
@@ -145,7 +147,9 @@ 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);
+#ifndef IN_SINCOS
static double csloww2 (double x, double dx, double orig, int n);
+#endif
/* 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
@@ -818,6 +822,7 @@ slow2 (double x)
return (x > 0) ? __mpsin (x, 0, false) : -__mpsin (-x, 0, false);
}
+#ifndef IN_SINCOS
/***************************************************************************/
/* Routine compute sin(x+dx) (Double-Length number) where x is small enough*/
/* to use Taylor series around zero and (x+dx) */
@@ -946,6 +951,7 @@ sloww2 (double x, double dx, double orig, int n)
return __mpsin (orig, 0, true);
}
+#endif
/***************************************************************************/
/* Routine compute sin(x+dx) or cos(x+dx) (Double-Length number) where x */
@@ -1175,6 +1181,7 @@ csloww1 (double x, double dx, double orig, int m)
}
+#ifndef IN_SINCOS
/***************************************************************************/
/* Routine compute sin(x+dx) (Double-Length number) where x in second or */
/* fourth quarter of unit circle.Routine receive also the original value */
@@ -1207,7 +1214,6 @@ csloww2 (double x, double dx, double orig, int n)
return __mpcos (orig, 0, true);
}
-#ifndef IN_SINCOS
# 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 24dc43c..4d72d2b 100644
--- a/sysdeps/ieee754/dbl-64/s_sincos.c
+++ b/sysdeps/ieee754/dbl-64/s_sincos.c
@@ -33,9 +33,8 @@ 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, eps;
- mynumber u, v;
- int4 m, n;
+ double xx, res, t, cor, y, s, c, sn, ssn, cs, ccs;
+ mynumber u;
double retval = 0;
if (k < 0x3e500000) /* if x->0 =>sin(x)=x */
@@ -74,7 +73,7 @@ __sin_local (double x, int4 k)
} /* else if (k < 0x3feb6000) */
/*----------------------- 0.855469 <|x|<2.426265 ----------------------*/
- else if (k < 0x400368fd)
+ else
{
y = (x > 0) ? hp0 - x : hp0 + x;
@@ -92,72 +91,6 @@ __sin_local (double x, int4 k)
retval = (res == res + 1.020 * cor) ? ((x > 0) ? res : -res) : slow2 (x);
} /* else if (k < 0x400368fd) */
-/*-------------------------- 2.426265<|x|< 105414350 ----------------------*/
- else
- {
- 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;
- }
- } /* else if (k < 0x419921FB ) */
-
return retval;
}
@@ -168,9 +101,9 @@ static double
__always_inline
__cos_local (double x, int4 k)
{
- double y, xx, res, t, cor, xn, a, da, eps;
- mynumber u, v;
- int4 m, n;
+ double y, xx, res, cor, a, da;
+ mynumber u;
+ int m;
double retval = 0;
@@ -187,7 +120,7 @@ __cos_local (double x, int4 k)
retval = (res == res + 1.020 * cor) ? res : cslow2 (x);
} /* else if (k < 0x3feb6000) */
- else if (k < 0x400368fd)
+ else
{ /* 0.855469 <|x|<2.426265 */ ;
y = hp0 - fabs (x);
a = y + hp1;
@@ -221,73 +154,6 @@ __cos_local (double x, int4 k)
} /* else if (k < 0x400368fd) */
-
- 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;
- }
- } /* else if (k < 0x419921FB ) */
-
return retval;
}
@@ -409,6 +275,182 @@ reduce_and_compute_sincos (double x, double *sinxp, double *cosxp)
*cosxp = cosx;
}
+/* Like sloww and csloww, except that it accepts the quadrant and decides to
+ call mpsin or mpcos based on that. */
+static double
+sincos_sloww (double x, double dx, double orig, int4 n)
+{
+ double y, t, res, cor, w[2], a, da, xn;
+ 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;
+ y = (orig - xn * mp1) - xn * mp2;
+ da = xn * pp3;
+ t = y - da;
+ da = (y - t) - da;
+ y = xn * pp4;
+ a = t - y;
+ da = ((t - a) - y) + da;
+
+ if (n & 2)
+ {
+ 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 (n & 1) ? __mpcos (orig, 0, true) : __mpsin (orig, 0, true);
+}
+
+/* Like sloww1 and csloww1, except that it accepts the quadrant and decides to
+ call mpsin or mpcos based on that. */
+static double
+sincos_sloww1 (double x, double dx, double orig, int n)
+{
+ mynumber u;
+ double w[2], y, cor, res, t;
+
+ t = fabs (x);
+ if (x < 0)
+ dx = -dx;
+
+ u.x = big + t;
+ y = t - (u.x - big);
+ res = do_sin_slow (u, y, dx, 3.1e-30 * fabs (orig), &cor);
+
+ if (res == res + cor)
+ return (x > 0) ? res : -res;
+
+ __dubsin (t, 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 (x > 0) ? w[0] : -w[0];
+
+ return (n & 1) ? __mpcos (orig, 0, true) : __mpsin (orig, 0, true);
+}
+
+/* Like sloww2 and csloww2, except that it accepts the quadrant and decides to
+ call mpsin or mpcos based on that. */
+static double
+sincos_sloww2 (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 & 2) ? -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 & 2) ? -w[0] : w[0];
+
+ return (n & 1) ? __mpsin (orig, 0, true) : __mpcos (orig, 0, true);
+}
+
+/* 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)
+{
+ double xx, retval, res, cor, y;
+ mynumber u;
+ int m;
+ double eps = fabs (x) * 1.2e-30;
+
+ switch (n)
+ { /* 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 : sincos_sloww (a, da, x, n);
+ }
+ else
+ {
+ double b = a, db = da;
+ if (a > 0)
+ m = 1;
+ else
+ {
+ m = 0;
+ b = -b;
+ db = -db;
+ }
+ u.x = big + b;
+ y = b - (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)
+ : sincos_sloww1 (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)
+ : sincos_sloww2 (a, da, x, n));
+ break;
+ }
+
+ return retval;
+}
+
void
__sincos (double x, double *sinx, double *cosx)
{
@@ -419,12 +461,29 @@ __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, k);
*cosx = __cos_local (x, k);
return;
}
+ if (k < 0x419921FB)
+ {
+ double t = (x * hpinv + toint);
+ double xn = t - toint;
+ u.x = t;
+ double y = (x - xn * mp1) - xn * mp2;
+ int4 n = u.i[LOW_HALF] & 3;
+ double da = xn * mp3;
+ double a = y - da;
+ da = (y - a) - da;
+
+ *sinx = do_sincos_1 (a, da, x, n);
+ *cosx = do_sincos_1 (a, da, x, (n + 1) & 3);
+
+ return;
+ }
if (k < 0x42F00000)
{
double t = (x * hpinv + toint);
--
2.5.0