Index: fusl/src/math/__cos.c |
diff --git a/fusl/src/math/__cos.c b/fusl/src/math/__cos.c |
new file mode 100644 |
index 0000000000000000000000000000000000000000..46cefb38134398a4e0e7b40621eb6ea6e514ca38 |
--- /dev/null |
+++ b/fusl/src/math/__cos.c |
@@ -0,0 +1,71 @@ |
+/* origin: FreeBSD /usr/src/lib/msun/src/k_cos.c */ |
+/* |
+ * ==================================================== |
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
+ * |
+ * Developed at SunSoft, a Sun Microsystems, Inc. business. |
+ * Permission to use, copy, modify, and distribute this |
+ * software is freely granted, provided that this notice |
+ * is preserved. |
+ * ==================================================== |
+ */ |
+/* |
+ * __cos( x, y ) |
+ * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164 |
+ * Input x is assumed to be bounded by ~pi/4 in magnitude. |
+ * Input y is the tail of x. |
+ * |
+ * Algorithm |
+ * 1. Since cos(-x) = cos(x), we need only to consider positive x. |
+ * 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0. |
+ * 3. cos(x) is approximated by a polynomial of degree 14 on |
+ * [0,pi/4] |
+ * 4 14 |
+ * cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x |
+ * where the remez error is |
+ * |
+ * | 2 4 6 8 10 12 14 | -58 |
+ * |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2 |
+ * | | |
+ * |
+ * 4 6 8 10 12 14 |
+ * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then |
+ * cos(x) ~ 1 - x*x/2 + r |
+ * since cos(x+y) ~ cos(x) - sin(x)*y |
+ * ~ cos(x) - x*y, |
+ * a correction term is necessary in cos(x) and hence |
+ * cos(x+y) = 1 - (x*x/2 - (r - x*y)) |
+ * For better accuracy, rearrange to |
+ * cos(x+y) ~ w + (tmp + (r-x*y)) |
+ * where w = 1 - x*x/2 and tmp is a tiny correction term |
+ * (1 - x*x/2 == w + tmp exactly in infinite precision). |
+ * The exactness of w + tmp in infinite precision depends on w |
+ * and tmp having the same precision as x. If they have extra |
+ * precision due to compiler bugs, then the extra precision is |
+ * only good provided it is retained in all terms of the final |
+ * expression for cos(). Retention happens in all cases tested |
+ * under FreeBSD, so don't pessimize things by forcibly clipping |
+ * any extra precision in w. |
+ */ |
+ |
+#include "libm.h" |
+ |
+static const double |
+C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */ |
+C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */ |
+C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */ |
+C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */ |
+C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */ |
+C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */ |
+ |
+double __cos(double x, double y) |
+{ |
+ double_t hz,z,r,w; |
+ |
+ z = x*x; |
+ w = z*z; |
+ r = z*(C1+z*(C2+z*C3)) + w*w*(C4+z*(C5+z*C6)); |
+ hz = 0.5*z; |
+ w = 1.0-hz; |
+ return w + (((1.0-w)-hz) + (z*r-x*y)); |
+} |