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[PATCHv1.1] Consolidate code to compute sin and cos from lookup tables
- From: Siddhesh Poyarekar <siddhesh at redhat dot com>
- To: libc-alpha at sourceware dot org
- Date: Wed, 18 Dec 2013 20:53:08 +0530
- Subject: [PATCHv1.1] Consolidate code to compute sin and cos from lookup tables
- Authentication-results: sourceware.org; auth=none
- References: <20131218122506 dot GL19212 at spoyarek dot pnq dot redhat dot com>
Sorry, I realized that I had not fixed the variable names and style in
the new functions after I had converted them from the macros I had
initially written. Fixed now.
Siddhesh
* sysdeps/ieee754/dbl-64/s_sin.c (do_cos, do_cos_slow, do_sin,
do_sin_slow): New functions.
(__sin, __cos, slow1, slow2, sloww1, sloww2, bsloww1, bsloww2,
cslow2, csloww1, csloww2): Use the new functions.
diff --git a/sysdeps/ieee754/dbl-64/s_sin.c b/sysdeps/ieee754/dbl-64/s_sin.c
index 0033f94..bd2346c 100644
--- a/sysdeps/ieee754/dbl-64/s_sin.c
+++ b/sysdeps/ieee754/dbl-64/s_sin.c
@@ -145,6 +145,102 @@ 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
+ the sin and cos of X (as computed by a variation of the Taylor series) with
+ the values looked up from the sin/cos table to get the result in RES and a
+ correction value in COR. */
+static double
+do_cos (mynumber u, double x, double *corp)
+{
+ double xx, s, sn, ssn, c, cs, ccs, res, cor;
+ xx = x * x;
+ s = x + x * xx * (sn3 + xx * sn5);
+ c = xx * (cs2 + xx * (cs4 + xx * cs6));
+ SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs);
+ cor = (ccs - s * ssn - cs * c) - sn * s;
+ res = cs + cor;
+ cor = (cs - res) + cor;
+ *corp = cor;
+ return res;
+}
+
+/* A more precise variant of DO_COS where the number is partitioned into U, X
+ and DX. EPS is the adjustment to the correction COR. */
+static double
+do_cos_slow (mynumber u, double x, double dx, double eps, double *corp)
+{
+ double xx, y, x1, x2, e1, e2, res, cor;
+ double s, sn, ssn, c, cs, ccs;
+ xx = x * x;
+ s = x * xx * (sn3 + xx * sn5);
+ c = x * dx + xx * (cs2 + xx * (cs4 + xx * cs6));
+ SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs);
+ x1 = (x + t22) - t22;
+ x2 = (x - x1) + dx;
+ e1 = (sn + t22) - t22;
+ e2 = (sn - e1) + ssn;
+ cor = (ccs - cs * c - e1 * x2 - e2 * x) - sn * s;
+ y = cs - e1 * x1;
+ cor = cor + ((cs - y) - e1 * x1);
+ res = y + cor;
+ cor = (y - res) + cor;
+ if (cor > 0)
+ cor = 1.0005 * cor + eps;
+ else
+ cor = 1.0005 * cor - eps;
+ *corp = cor;
+ return res;
+}
+
+/* Given a number partitioned into U and X and DX such that U is an index into
+ the sin/cos table, this macro computes the sine of the number by combining
+ the sin and cos of X (as computed by a variation of the Taylor series) with
+ the values looked up from the sin/cos table to get the result in RES and a
+ correction value in COR. */
+static double
+do_sin (mynumber u, double x, double dx, double *corp)
+{
+ double xx, s, sn, ssn, c, cs, ccs, cor, res;
+ xx = x * x;
+ s = x + (dx + x * xx * (sn3 + xx * sn5));
+ c = x * dx + xx * (cs2 + xx * (cs4 + xx * cs6));
+ SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs);
+ cor = (ssn + s * ccs - sn * c) + cs * s;
+ res = sn + cor;
+ cor = (sn - res) + cor;
+ *corp = cor;
+ return res;
+}
+
+/* A more precise variant of res = do_sin where the number is partitioned into U, X
+ and DX. EPS is the adjustment to the correction COR. */
+static double
+do_sin_slow (mynumber u, double x, double dx, double eps, double *corp)
+{
+ double xx, y, x1, x2, c1, c2, res, cor;
+ double s, sn, ssn, c, cs, ccs;
+ xx = x * x;
+ s = x * xx * (sn3 + xx * sn5);
+ c = xx * (cs2 + xx * (cs4 + xx * cs6));
+ SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs);
+ x1 = (x + t22) - t22;
+ x2 = (x - x1) + dx;
+ c1 = (cs + t22) - t22;
+ c2 = (cs - c1) + ccs;
+ cor = (ssn + s * ccs + cs * s + c2 * x + c1 * x2 - sn * x * dx) - sn * c;
+ y = sn + c1 * x1;
+ cor = cor + ((sn - y) + c1 * x1);
+ res = y + cor;
+ cor = (y - res) + cor;
+ if (cor > 0)
+ cor = 1.0005 * cor + eps;
+ else
+ cor = 1.0005 * cor - eps;
+ *corp = cor;
+ return res;
+}
+
/* Reduce range of X and compute sin of a + da. K is the amount by which to
rotate the quadrants. This allows us to use the same routine to compute cos
by simply rotating the quadrants by 1. */
@@ -244,13 +340,7 @@ __sin (double x)
u.x = big - y;
y = (-hp1) - (y + (u.x - big));
}
- xx = y * y;
- s = y + y * xx * (sn3 + xx * sn5);
- c = xx * (cs2 + xx * (cs4 + xx * cs6));
- SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs);
- cor = (ccs - s * ssn - cs * c) - sn * s;
- res = cs + cor;
- cor = (cs - res) + cor;
+ res = do_cos (u, y, &cor);
retval = (res == res + 1.020 * cor) ? ((m > 0) ? res : -res) : slow2 (x);
} /* else if (k < 0x400368fd) */
@@ -296,13 +386,7 @@ __sin (double x)
}
u.x = big + a;
y = a - (u.x - big);
- xx = y * y;
- s = y + (da + y * xx * (sn3 + xx * sn5));
- c = y * da + xx * (cs2 + xx * (cs4 + xx * cs6));
- SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs);
- cor = (ssn + s * ccs - sn * c) + cs * s;
- res = sn + cor;
- cor = (sn - res) + cor;
+ 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));
@@ -318,13 +402,7 @@ __sin (double x)
}
u.x = big + a;
y = a - (u.x - big) + da;
- xx = y * y;
- SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs);
- s = y + y * xx * (sn3 + xx * sn5);
- c = xx * (cs2 + xx * (cs4 + xx * cs6));
- cor = (ccs - s * ssn - cs * c) - sn * s;
- res = cs + cor;
- cor = (cs - res) + cor;
+ 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));
@@ -382,13 +460,7 @@ __sin (double x)
}
u.x = big + a;
y = a - (u.x - big);
- xx = y * y;
- s = y + (db + y * xx * (sn3 + xx * sn5));
- c = y * db + xx * (cs2 + xx * (cs4 + xx * cs6));
- SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs);
- cor = (ssn + s * ccs - sn * c) + cs * s;
- res = sn + cor;
- cor = (sn - res) + cor;
+ 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));
@@ -404,13 +476,7 @@ __sin (double x)
}
u.x = big + a;
y = a - (u.x - big) + da;
- xx = y * y;
- SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs);
- s = y + y * xx * (sn3 + xx * sn5);
- c = xx * (cs2 + xx * (cs4 + xx * cs6));
- cor = (ccs - s * ssn - cs * c) - sn * s;
- res = cs + cor;
- cor = (cs - res) + cor;
+ 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));
@@ -443,7 +509,7 @@ double
SECTION
__cos (double x)
{
- double y, xx, res, t, cor, s, c, sn, ssn, cs, ccs, xn, a, da, db, eps, xn1,
+ double y, xx, res, t, cor, xn, a, da, db, eps, xn1,
xn2;
mynumber u, v;
int4 k, m, n;
@@ -465,13 +531,7 @@ __cos (double x)
y = ABS (x);
u.x = big + y;
y = y - (u.x - big);
- xx = y * y;
- s = y + y * xx * (sn3 + xx * sn5);
- c = xx * (cs2 + xx * (cs4 + xx * cs6));
- SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs);
- cor = (ccs - s * ssn - cs * c) - sn * s;
- res = cs + cor;
- cor = (cs - res) + cor;
+ res = do_cos (u, y, &cor);
retval = (res == res + 1.020 * cor) ? res : cslow2 (x);
} /* else if (k < 0x3feb6000) */
@@ -501,13 +561,7 @@ __cos (double x)
}
u.x = big + a;
y = a - (u.x - big);
- xx = y * y;
- s = y + (da + y * xx * (sn3 + xx * sn5));
- c = y * da + xx * (cs2 + xx * (cs4 + xx * cs6));
- SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs);
- cor = (ssn + s * ccs - sn * c) + cs * s;
- res = sn + cor;
- cor = (sn - res) + cor;
+ 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));
@@ -558,13 +612,7 @@ __cos (double x)
}
u.x = big + a;
y = a - (u.x - big);
- xx = y * y;
- s = y + (da + y * xx * (sn3 + xx * sn5));
- c = y * da + xx * (cs2 + xx * (cs4 + xx * cs6));
- SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs);
- cor = (ssn + s * ccs - sn * c) + cs * s;
- res = sn + cor;
- cor = (sn - res) + cor;
+ 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));
@@ -580,13 +628,7 @@ __cos (double x)
}
u.x = big + a;
y = a - (u.x - big) + da;
- xx = y * y;
- SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs);
- s = y + y * xx * (sn3 + xx * sn5);
- c = xx * (cs2 + xx * (cs4 + xx * cs6));
- cor = (ccs - s * ssn - cs * c) - sn * s;
- res = cs + cor;
- cor = (cs - res) + cor;
+ 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));
@@ -642,13 +684,7 @@ __cos (double x)
}
u.x = big + a;
y = a - (u.x - big);
- xx = y * y;
- s = y + (db + y * xx * (sn3 + xx * sn5));
- c = y * db + xx * (cs2 + xx * (cs4 + xx * cs6));
- SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs);
- cor = (ssn + s * ccs - sn * c) + cs * s;
- res = sn + cor;
- cor = (sn - res) + cor;
+ 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));
@@ -664,13 +700,7 @@ __cos (double x)
}
u.x = big + a;
y = a - (u.x - big) + da;
- xx = y * y;
- SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs);
- s = y + y * xx * (sn3 + xx * sn5);
- c = xx * (cs2 + xx * (cs4 + xx * cs6));
- cor = (ccs - s * ssn - cs * c) - sn * s;
- res = cs + cor;
- cor = (cs - res) + cor;
+ 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));
@@ -725,24 +755,12 @@ SECTION
slow1 (double x)
{
mynumber u;
- double sn, ssn, cs, ccs, s, c, w[2], y, y1, y2, c1, c2, xx, cor, res;
+ double w[2], y, cor, res;
y = ABS (x);
u.x = big + y;
y = y - (u.x - big);
- xx = y * y;
- s = y * xx * (sn3 + xx * sn5);
- c = xx * (cs2 + xx * (cs4 + xx * cs6));
- SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs);
- y1 = (y + t22) - t22;
- y2 = y - y1;
- c1 = (cs + t22) - t22;
- c2 = (cs - c1) + ccs;
- cor = (ssn + s * ccs + cs * s + c2 * y + c1 * y2) - sn * c;
- y = sn + c1 * y1;
- cor = cor + ((sn - y) + c1 * y1);
- res = y + cor;
- cor = (y - res) + cor;
- if (res == res + 1.0005 * cor)
+ res = do_sin_slow (u, y, 0, 0, &cor);
+ if (res == res + cor)
return (x > 0) ? res : -res;
else
{
@@ -763,7 +781,7 @@ SECTION
slow2 (double x)
{
mynumber u;
- double sn, ssn, cs, ccs, s, c, w[2], y, y1, y2, e1, e2, xx, cor, res, del;
+ double w[2], y, y1, y2, cor, res, del;
y = ABS (x);
y = hp0 - y;
@@ -779,20 +797,8 @@ slow2 (double x)
y = -(y + (u.x - big));
del = -hp1;
}
- xx = y * y;
- s = y * xx * (sn3 + xx * sn5);
- c = y * del + xx * (cs2 + xx * (cs4 + xx * cs6));
- SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs);
- y1 = (y + t22) - t22;
- y2 = (y - y1) + del;
- e1 = (sn + t22) - t22;
- e2 = (sn - e1) + ssn;
- cor = (ccs - cs * c - e1 * y2 - e2 * y) - sn * s;
- y = cs - e1 * y1;
- cor = cor + ((cs - y) - e1 * y1);
- res = y + cor;
- cor = (y - res) + cor;
- if (res == res + 1.0005 * cor)
+ res = do_cos_slow (u, y, del, 0, &cor);
+ if (res == res + cor)
return (x > 0) ? res : -res;
else
{
@@ -884,28 +890,11 @@ SECTION
sloww1 (double x, double dx, double orig, int m)
{
mynumber u;
- double sn, ssn, cs, ccs, s, c, w[2], y, y1, y2, c1, c2, xx, cor, res;
+ double w[2], y, cor, res;
u.x = big + x;
y = x - (u.x - big);
- xx = y * y;
- s = y * xx * (sn3 + xx * sn5);
- c = xx * (cs2 + xx * (cs4 + xx * cs6));
- SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs);
- y1 = (y + t22) - t22;
- y2 = (y - y1) + dx;
- c1 = (cs + t22) - t22;
- c2 = (cs - c1) + ccs;
- cor = (ssn + s * ccs + cs * s + c2 * y + c1 * y2 - sn * y * dx) - sn * c;
- y = sn + c1 * y1;
- cor = cor + ((sn - y) + c1 * y1);
- res = y + cor;
- cor = (y - res) + cor;
-
- if (cor > 0)
- cor = 1.0005 * cor + 3.1e-30 * ABS (orig);
- else
- cor = 1.0005 * cor - 3.1e-30 * ABS (orig);
+ res = do_sin_slow (u, y, dx, 3.1e-30 * ABS (orig), &cor);
if (res == res + cor)
return (m > 0) ? res : -res;
@@ -937,29 +926,11 @@ SECTION
sloww2 (double x, double dx, double orig, int n)
{
mynumber u;
- double sn, ssn, cs, ccs, s, c, w[2], y, y1, y2, e1, e2, xx, cor, res;
+ double w[2], y, cor, res;
u.x = big + x;
y = x - (u.x - big);
- xx = y * y;
- s = y * xx * (sn3 + xx * sn5);
- c = y * dx + xx * (cs2 + xx * (cs4 + xx * cs6));
- SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs);
-
- y1 = (y + t22) - t22;
- y2 = (y - y1) + dx;
- e1 = (sn + t22) - t22;
- e2 = (sn - e1) + ssn;
- cor = (ccs - cs * c - e1 * y2 - e2 * y) - sn * s;
- y = cs - e1 * y1;
- cor = cor + ((cs - y) - e1 * y1);
- res = y + cor;
- cor = (y - res) + cor;
-
- if (cor > 0)
- cor = 1.0005 * cor + 3.1e-30 * ABS (orig);
- else
- cor = 1.0005 * cor - 3.1e-30 * ABS (orig);
+ res = do_cos_slow (u, y, dx, 3.1e-30 * ABS (orig), &cor);
if (res == res + cor)
return (n & 2) ? -res : res;
@@ -1023,26 +994,13 @@ SECTION
bsloww1 (double x, double dx, double orig, int n)
{
mynumber u;
- double sn, ssn, cs, ccs, s, c, w[2], y, y1, y2, c1, c2, xx, cor, res;
+ double w[2], y, cor, res;
y = ABS (x);
u.x = big + y;
y = y - (u.x - big);
dx = (x > 0) ? dx : -dx;
- xx = y * y;
- s = y * xx * (sn3 + xx * sn5);
- c = xx * (cs2 + xx * (cs4 + xx * cs6));
- SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs);
- y1 = (y + t22) - t22;
- y2 = (y - y1) + dx;
- c1 = (cs + t22) - t22;
- c2 = (cs - c1) + ccs;
- cor = (ssn + s * ccs + cs * s + c2 * y + c1 * y2 - sn * y * dx) - sn * c;
- y = sn + c1 * y1;
- cor = cor + ((sn - y) + c1 * y1);
- res = y + cor;
- cor = (y - res) + cor;
- cor = (cor > 0) ? 1.0005 * cor + 1.1e-24 : 1.0005 * cor - 1.1e-24;
+ res = do_sin_slow (u, y, dx, 1.1e-24, &cor);
if (res == res + cor)
return (x > 0) ? res : -res;
else
@@ -1073,27 +1031,13 @@ SECTION
bsloww2 (double x, double dx, double orig, int n)
{
mynumber u;
- double sn, ssn, cs, ccs, s, c, w[2], y, y1, y2, e1, e2, xx, cor, res;
+ double w[2], y, cor, res;
y = ABS (x);
u.x = big + y;
y = y - (u.x - big);
dx = (x > 0) ? dx : -dx;
- xx = y * y;
- s = y * xx * (sn3 + xx * sn5);
- c = y * dx + xx * (cs2 + xx * (cs4 + xx * cs6));
- SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs);
-
- y1 = (y + t22) - t22;
- y2 = (y - y1) + dx;
- e1 = (sn + t22) - t22;
- e2 = (sn - e1) + ssn;
- cor = (ccs - cs * c - e1 * y2 - e2 * y) - sn * s;
- y = cs - e1 * y1;
- cor = cor + ((cs - y) - e1 * y1);
- res = y + cor;
- cor = (y - res) + cor;
- cor = (cor > 0) ? 1.0005 * cor + 1.1e-24 : 1.0005 * cor - 1.1e-24;
+ res = do_cos_slow (u, y, dx, 1.1e-24, &cor);
if (res == res + cor)
return (n & 2) ? -res : res;
else
@@ -1122,25 +1066,13 @@ SECTION
cslow2 (double x)
{
mynumber u;
- double sn, ssn, cs, ccs, s, c, w[2], y, y1, y2, e1, e2, xx, cor, res;
+ double w[2], y, cor, res;
y = ABS (x);
u.x = big + y;
y = y - (u.x - big);
- xx = y * y;
- s = y * xx * (sn3 + xx * sn5);
- c = xx * (cs2 + xx * (cs4 + xx * cs6));
- SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs);
- y1 = (y + t22) - t22;
- y2 = y - y1;
- e1 = (sn + t22) - t22;
- e2 = (sn - e1) + ssn;
- cor = (ccs - cs * c - e1 * y2 - e2 * y) - sn * s;
- y = cs - e1 * y1;
- cor = cor + ((cs - y) - e1 * y1);
- res = y + cor;
- cor = (y - res) + cor;
- if (res == res + 1.0005 * cor)
+ res = do_cos_slow (u, y, 0, 0, &cor);
+ if (res == res + cor)
return res;
else
{
@@ -1235,28 +1167,11 @@ SECTION
csloww1 (double x, double dx, double orig, int m)
{
mynumber u;
- double sn, ssn, cs, ccs, s, c, w[2], y, y1, y2, c1, c2, xx, cor, res;
+ double w[2], y, cor, res;
u.x = big + x;
y = x - (u.x - big);
- xx = y * y;
- s = y * xx * (sn3 + xx * sn5);
- c = xx * (cs2 + xx * (cs4 + xx * cs6));
- SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs);
- y1 = (y + t22) - t22;
- y2 = (y - y1) + dx;
- c1 = (cs + t22) - t22;
- c2 = (cs - c1) + ccs;
- cor = (ssn + s * ccs + cs * s + c2 * y + c1 * y2 - sn * y * dx) - sn * c;
- y = sn + c1 * y1;
- cor = cor + ((sn - y) + c1 * y1);
- res = y + cor;
- cor = (y - res) + cor;
-
- if (cor > 0)
- cor = 1.0005 * cor + 3.1e-30 * ABS (orig);
- else
- cor = 1.0005 * cor - 3.1e-30 * ABS (orig);
+ res = do_sin_slow (u, y, dx, 3.1e-30 * ABS (orig), &cor);
if (res == res + cor)
return (m > 0) ? res : -res;
@@ -1287,29 +1202,11 @@ SECTION
csloww2 (double x, double dx, double orig, int n)
{
mynumber u;
- double sn, ssn, cs, ccs, s, c, w[2], y, y1, y2, e1, e2, xx, cor, res;
+ double w[2], y, cor, res;
u.x = big + x;
y = x - (u.x - big);
- xx = y * y;
- s = y * xx * (sn3 + xx * sn5);
- c = y * dx + xx * (cs2 + xx * (cs4 + xx * cs6));
- SINCOS_TABLE_LOOKUP (u, sn, ssn, cs, ccs);
-
- y1 = (y + t22) - t22;
- y2 = (y - y1) + dx;
- e1 = (sn + t22) - t22;
- e2 = (sn - e1) + ssn;
- cor = (ccs - cs * c - e1 * y2 - e2 * y) - sn * s;
- y = cs - e1 * y1;
- cor = cor + ((cs - y) - e1 * y1);
- res = y + cor;
- cor = (y - res) + cor;
-
- if (cor > 0)
- cor = 1.0005 * cor + 3.1e-30 * ABS (orig);
- else
- cor = 1.0005 * cor - 3.1e-30 * ABS (orig);
+ res = do_cos_slow (u, y, dx, 3.1e-30 * ABS (orig), &cor);
if (res == res + cor)
return (n) ? -res : res;