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Use fabs(x) instead of branching on signedness of input to sin and cos
The sin and cos code is inconsistent about its use of fabs to get the absolute value of X where in some places it conditionalizes the code while in others it uses fabs. fabs seems to be a better candidate in most cases because it avoids a branch. Similarly there is an attempt to make it easier for the compiler to emit conditional assignment instructions (like fcsel on aarch64) where it can, by isolating conditional assignment constructs from the rest of the expression. A further benefit of this change is to identify common constructs across functions and consolidate them in future patches. * sysdeps/ieee754/dbl-64/s_sin.c (do_cos_slow): Use ternary instead of if/else. (do_sin_slow): Likewise. (do_sincos_1): Use fabs instead of if/else. (do_sincos_2): Likewise. (__sin): Likewise. (__cos): Likewise. (slow2): Likewise. (sloww): Likewise. (sloww1): Likewise. Drop argument M. (sloww2): Use fabs instead of if/else. (bsloww): Likewise. (bsloww1): Likewise. (bsloww2): Likewise.
This commit is contained in:
Siddhesh Poyarekar
parent
1a822c6184
commit
9d84d0e51d
15
ChangeLog
15
ChangeLog
@ -1,5 +1,20 @@
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2016-08-30 Siddhesh Poyarekar <siddhesh@sourceware.org>
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* sysdeps/ieee754/dbl-64/s_sin.c (do_cos_slow): Use ternary
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instead of if/else.
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(do_sin_slow): Likewise.
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(do_sincos_1): Use fabs instead of if/else.
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(do_sincos_2): Likewise.
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(__sin): Likewise.
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(__cos): Likewise.
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(slow2): Likewise.
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(sloww): Likewise.
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(sloww1): Likewise. Drop argument M.
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(sloww2): Use fabs instead of if/else.
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(bsloww): Likewise.
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(bsloww1): Likewise.
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(bsloww2): Likewise.
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* sysdeps/ieee754/dbl-64/s_sin.c (reduce_and_compute): Add
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fall through comment.
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(do_sincos_1): Likewise.
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@ -133,7 +133,7 @@ static double slow (double x);
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static double slow1 (double x);
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static double slow2 (double x);
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static double sloww (double x, double dx, double orig, int n);
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static double sloww1 (double x, double dx, double orig, int m, int n);
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static double sloww1 (double x, double dx, double orig, int n);
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static double sloww2 (double x, double dx, double orig, int n);
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static double bsloww (double x, double dx, double orig, int n);
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static double bsloww1 (double x, double dx, double orig, int n);
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@ -181,10 +181,7 @@ do_cos_slow (mynumber u, double x, double dx, double eps, double *corp)
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cor = cor + ((cs - y) - e1 * x1);
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res = y + cor;
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cor = (y - res) + cor;
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if (cor > 0)
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cor = 1.0005 * cor + eps;
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else
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cor = 1.0005 * cor - eps;
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cor = 1.0005 * cor + ((cor > 0) ? eps : -eps);
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*corp = cor;
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return res;
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}
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@ -229,10 +226,7 @@ do_sin_slow (mynumber u, double x, double dx, double eps, double *corp)
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cor = cor + ((sn - y) + c1 * x1);
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res = y + cor;
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cor = (y - res) + cor;
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if (cor > 0)
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cor = 1.0005 * cor + eps;
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else
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cor = 1.0005 * cor - eps;
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cor = 1.0005 * cor + ((cor > 0) ? eps : -eps);
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*corp = cor;
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return res;
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}
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@ -297,7 +291,6 @@ do_sincos_1 (double a, double da, double x, int4 n, int4 k)
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{
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double xx, retval, res, cor, y;
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mynumber u;
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int m;
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double eps = fabs (x) * 1.2e-30;
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int k1 = (n + k) & 3;
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@ -318,37 +311,28 @@ do_sincos_1 (double a, double da, double x, int4 n, int4 k)
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}
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else
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{
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if (a > 0)
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m = 1;
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else
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{
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m = 0;
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a = -a;
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da = -da;
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}
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u.x = big + a;
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y = a - (u.x - big);
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res = do_sin (u, y, da, &cor);
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double db = (a > 0 ? da : -da);
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u.x = big + fabs (a);
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y = fabs (a) - (u.x - big);
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res = do_sin (u, y, db, &cor);
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cor = (cor > 0) ? 1.035 * cor + eps : 1.035 * cor - eps;
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retval = ((res == res + cor) ? ((m) ? res : -res)
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: sloww1 (a, da, x, m, k));
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retval = ((res == res + cor) ? ((a > 0) ? res : -res)
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: sloww1 (a, da, x, k));
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}
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break;
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case 1:
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case 3:
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if (a < 0)
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{
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a = -a;
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da = -da;
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double db = (a > 0 ? da : -da);
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u.x = big + fabs (a);
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y = fabs (a) - (u.x - big) + db;
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res = do_cos (u, y, &cor);
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cor = (cor > 0) ? 1.025 * cor + eps : 1.025 * cor - eps;
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retval = ((res == res + cor) ? ((k1 & 2) ? -res : res)
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: sloww2 (a, da, x, n));
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break;
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}
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u.x = big + a;
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y = a - (u.x - big) + da;
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res = do_cos (u, y, &cor);
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cor = (cor > 0) ? 1.025 * cor + eps : 1.025 * cor - eps;
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retval = ((res == res + cor) ? ((k1 & 2) ? -res : res)
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: sloww2 (a, da, x, n));
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break;
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}
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return retval;
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@ -410,43 +394,28 @@ do_sincos_2 (double a, double da, double x, int4 n, int4 k)
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}
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else
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{
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double t, db, y;
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int m;
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if (a > 0)
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{
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m = 1;
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t = a;
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db = da;
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}
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else
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{
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m = 0;
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t = -a;
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db = -da;
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}
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u.x = big + t;
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y = t - (u.x - big);
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double db = (a > 0 ? da : -da);
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u.x = big + fabs (a);
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double y = fabs (a) - (u.x - big);
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res = do_sin (u, y, db, &cor);
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cor = (cor > 0) ? 1.035 * cor + eps : 1.035 * cor - eps;
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retval = ((res == res + cor) ? ((m) ? res : -res)
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retval = ((res == res + cor) ? ((a > 0) ? res : -res)
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: bsloww1 (a, da, x, n));
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}
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break;
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case 1:
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case 3:
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if (a < 0)
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{
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a = -a;
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da = -da;
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double db = (a > 0 ? da : -da);
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u.x = big + fabs (a);
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double y = fabs (a) - (u.x - big) + db;
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res = do_cos (u, y, &cor);
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cor = (cor > 0) ? 1.025 * cor + eps : 1.025 * cor - eps;
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retval = ((res == res + cor) ? ((n & 2) ? -res : res)
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: bsloww2 (a, da, x, n));
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break;
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}
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u.x = big + a;
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double y = a - (u.x - big) + da;
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res = do_cos (u, y, &cor);
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cor = (cor > 0) ? 1.025 * cor + eps : 1.025 * cor - eps;
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retval = ((res == res + cor) ? ((n & 2) ? -res : res)
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: bsloww2 (a, da, x, n));
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break;
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}
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return retval;
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@ -494,8 +463,10 @@ __sin (double x)
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/*---------------------------- 0.25<|x|< 0.855469---------------------- */
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else if (k < 0x3feb6000)
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{
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u.x = (m > 0) ? big + x : big - x;
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y = (m > 0) ? x - (u.x - big) : x + (u.x - big);
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u.x = big + fabs (x);
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y = fabs (x) - (u.x - big);
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y = (x > 0 ? y : -y);
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xx = y * y;
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s = y + y * xx * (sn3 + xx * sn5);
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c = xx * (cs2 + xx * (cs4 + xx * cs6));
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@ -515,17 +486,11 @@ __sin (double x)
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else if (k < 0x400368fd)
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{
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y = (m > 0) ? hp0 - x : hp0 + x;
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if (y >= 0)
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{
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u.x = big + y;
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y = (y - (u.x - big)) + hp1;
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}
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else
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{
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u.x = big - y;
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y = (-hp1) - (y + (u.x - big));
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}
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t = hp0 - fabs (x);
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u.x = big + fabs (t);
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y = fabs (t) - (u.x - big);
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y = ((t >= 0) ? hp1 : -hp1) + y;
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res = do_cos (u, y, &cor);
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retval = (res == res + 1.020 * cor) ? ((m > 0) ? res : -res) : slow2 (x);
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} /* else if (k < 0x400368fd) */
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@ -619,22 +584,13 @@ __cos (double x)
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}
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else
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{
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if (a > 0)
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{
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m = 1;
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}
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else
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{
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m = 0;
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a = -a;
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da = -da;
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}
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u.x = big + a;
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y = a - (u.x - big);
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res = do_sin (u, y, da, &cor);
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double db = (a > 0 ? da : -da);
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u.x = big + fabs (a);
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y = fabs (a) - (u.x - big);
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res = do_sin (u, y, db, &cor);
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cor = (cor > 0) ? 1.035 * cor + 1.0e-31 : 1.035 * cor - 1.0e-31;
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retval = ((res == res + cor) ? ((m) ? res : -res)
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: sloww1 (a, da, x, m, 1));
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retval = ((res == res + cor) ? ((a > 0) ? res : -res)
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: sloww1 (a, da, x, 1));
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}
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} /* else if (k < 0x400368fd) */
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@ -728,20 +684,11 @@ slow2 (double x)
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mynumber u;
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double w[2], y, y1, y2, cor, res, del;
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y = fabs (x);
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y = hp0 - y;
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if (y >= 0)
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{
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u.x = big + y;
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y = y - (u.x - big);
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del = hp1;
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}
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else
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{
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u.x = big - y;
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y = -(y + (u.x - big));
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del = -hp1;
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}
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double t = hp0 - fabs (x);
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u.x = big + fabs (t);
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y = fabs (t) - (u.x - big);
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del = (t >= 0) ? hp1 : -hp1;
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res = do_cos_slow (u, y, del, 0, &cor);
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if (res == res + cor)
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return (x > 0) ? res : -res;
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@ -773,19 +720,18 @@ sloww (double x, double dx, double orig, int k)
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int4 n;
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res = TAYLOR_SLOW (x, dx, cor);
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if (cor > 0)
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cor = 1.0005 * cor + fabs (orig) * 3.1e-30;
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else
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cor = 1.0005 * cor - fabs (orig) * 3.1e-30;
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double eps = fabs (orig) * 3.1e-30;
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cor = 1.0005 * cor + ((cor > 0) ? eps : -eps);
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if (res == res + cor)
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return res;
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(x > 0) ? __dubsin (x, dx, w) : __dubsin (-x, -dx, w);
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if (w[1] > 0)
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cor = 1.000000001 * w[1] + fabs (orig) * 1.1e-30;
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else
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cor = 1.000000001 * w[1] - fabs (orig) * 1.1e-30;
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a = fabs (x);
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da = (x > 0) ? dx : -dx;
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__dubsin (a, da, w);
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eps = fabs (orig) * 1.1e-30;
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cor = 1.000000001 * w[1] + ((w[1] > 0) ? eps : -eps);
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if (w[0] == w[0] + cor)
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return (x > 0) ? w[0] : -w[0];
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@ -807,11 +753,11 @@ sloww (double x, double dx, double orig, int k)
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a = -a;
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da = -da;
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}
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(a > 0) ? __dubsin (a, da, w) : __dubsin (-a, -da, w);
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if (w[1] > 0)
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cor = 1.000000001 * w[1] + fabs (orig) * 1.1e-40;
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else
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cor = 1.000000001 * w[1] - fabs (orig) * 1.1e-40;
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x = fabs (a);
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dx = (a > 0) ? da : -da;
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__dubsin (x, dx, w);
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eps = fabs (orig) * 1.1e-40;
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cor = 1.000000001 * w[1] + ((w[1] > 0) ? eps : -eps);
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if (w[0] == w[0] + cor)
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return (a > 0) ? w[0] : -w[0];
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@ -828,27 +774,26 @@ sloww (double x, double dx, double orig, int k)
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static double
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SECTION
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sloww1 (double x, double dx, double orig, int m, int k)
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sloww1 (double x, double dx, double orig, int k)
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{
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mynumber u;
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double w[2], y, cor, res;
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u.x = big + x;
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y = x - (u.x - big);
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u.x = big + fabs (x);
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y = fabs (x) - (u.x - big);
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dx = (x > 0 ? dx : -dx);
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res = do_sin_slow (u, y, dx, 3.1e-30 * fabs (orig), &cor);
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if (res == res + cor)
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return (m > 0) ? res : -res;
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return (x > 0) ? res : -res;
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__dubsin (x, dx, w);
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__dubsin (fabs (x), dx, w);
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if (w[1] > 0)
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cor = 1.000000005 * w[1] + 1.1e-30 * fabs (orig);
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else
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cor = 1.000000005 * w[1] - 1.1e-30 * fabs (orig);
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double eps = 1.1e-30 * fabs (orig);
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cor = 1.000000005 * w[1] + ((w[1] > 0) ? eps : -eps);
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if (w[0] == w[0] + cor)
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return (m > 0) ? w[0] : -w[0];
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return (x > 0) ? w[0] : -w[0];
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return (k == 1) ? __mpcos (orig, 0, true) : __mpsin (orig, 0, true);
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}
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@ -867,19 +812,18 @@ sloww2 (double x, double dx, double orig, int n)
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mynumber u;
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double w[2], y, cor, res;
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u.x = big + x;
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y = x - (u.x - big);
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u.x = big + fabs (x);
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y = fabs (x) - (u.x - big);
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dx = (x > 0 ? dx : -dx);
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res = do_cos_slow (u, y, dx, 3.1e-30 * fabs (orig), &cor);
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if (res == res + cor)
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return (n & 2) ? -res : res;
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__docos (x, dx, w);
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__docos (fabs (x), dx, w);
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if (w[1] > 0)
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cor = 1.000000005 * w[1] + 1.1e-30 * fabs (orig);
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else
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cor = 1.000000005 * w[1] - 1.1e-30 * fabs (orig);
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double eps = 1.1e-30 * fabs (orig);
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cor = 1.000000005 * w[1] + ((w[1] > 0) ? eps : -eps);
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if (w[0] == w[0] + cor)
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return (n & 2) ? -w[0] : w[0];
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@ -899,18 +843,17 @@ static double
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SECTION
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bsloww (double x, double dx, double orig, int n)
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{
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double res, cor, w[2];
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double res, cor, w[2], a, da;
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res = TAYLOR_SLOW (x, dx, cor);
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cor = (cor > 0) ? 1.0005 * cor + 1.1e-24 : 1.0005 * cor - 1.1e-24;
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cor = 1.0005 * cor + ((cor > 0) ? 1.1e-24 : -1.1e-24);
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if (res == res + cor)
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return res;
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(x > 0) ? __dubsin (x, dx, w) : __dubsin (-x, -dx, w);
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if (w[1] > 0)
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cor = 1.000000001 * w[1] + 1.1e-24;
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else
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cor = 1.000000001 * w[1] - 1.1e-24;
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a = fabs (x);
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da = (x > 0) ? dx : -dx;
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__dubsin (a, da, w);
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cor = 1.000000001 * w[1] + ((w[1] > 0) ? 1.1e-24 : -1.1e-24);
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if (w[0] == w[0] + cor)
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return (x > 0) ? w[0] : -w[0];
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@ -942,10 +885,7 @@ bsloww1 (double x, double dx, double orig, int n)
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__dubsin (fabs (x), dx, w);
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if (w[1] > 0)
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cor = 1.000000005 * w[1] + 1.1e-24;
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else
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cor = 1.000000005 * w[1] - 1.1e-24;
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cor = 1.000000005 * w[1] + ((w[1] > 0) ? 1.1e-24 : -1.1e-24);
|
||||
|
||||
if (w[0] == w[0] + cor)
|
||||
return (x > 0) ? w[0] : -w[0];
|
||||
@ -977,10 +917,7 @@ bsloww2 (double x, double dx, double orig, int n)
|
||||
|
||||
__docos (fabs (x), dx, w);
|
||||
|
||||
if (w[1] > 0)
|
||||
cor = 1.000000005 * w[1] + 1.1e-24;
|
||||
else
|
||||
cor = 1.000000005 * w[1] - 1.1e-24;
|
||||
cor = 1.000000005 * w[1] + ((w[1] > 0) ? 1.1e-24 : -1.1e-24);
|
||||
|
||||
if (w[0] == w[0] + cor)
|
||||
return (n & 2) ? -w[0] : w[0];
|
||||
|
||||
Loading…
Reference in New Issue
Block a user