1 /* origin: FreeBSD /usr/src/lib/msun/src/k_tanf.c */
2 /*
3 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
4 * Optimized by Bruce D. Evans.
5 */
6 /*
7 * ====================================================
8 * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved.
9 *
10 * Permission to use, copy, modify, and distribute this
11 * software is freely granted, provided that this notice
12 * is preserved.
13 * ====================================================
14 */
15 16 #include "libm.h"
17 18 /* |tan(x)/x - t(x)| < 2**-25.5 (~[-2e-08, 2e-08]). */
19 static const double T[] = {
20 0x15554d3418c99f.0p-54, /* 0.333331395030791399758 */
21 0x1112fd38999f72.0p-55, /* 0.133392002712976742718 */
22 0x1b54c91d865afe.0p-57, /* 0.0533812378445670393523 */
23 0x191df3908c33ce.0p-58, /* 0.0245283181166547278873 */
24 0x185dadfcecf44e.0p-61, /* 0.00297435743359967304927 */
25 0x1362b9bf971bcd.0p-59, /* 0.00946564784943673166728 */
26 };
27 28 float __tandf(double x, int odd)
29 {
30 double_t z,r,w,s,t,u;
31 32 z = x*x;
33 /*
34 * Split up the polynomial into small independent terms to give
35 * opportunities for parallel evaluation. The chosen splitting is
36 * micro-optimized for Athlons (XP, X64). It costs 2 multiplications
37 * relative to Horner's method on sequential machines.
38 *
39 * We add the small terms from lowest degree up for efficiency on
40 * non-sequential machines (the lowest degree terms tend to be ready
41 * earlier). Apart from this, we don't care about order of
42 * operations, and don't need to to care since we have precision to
43 * spare. However, the chosen splitting is good for accuracy too,
44 * and would give results as accurate as Horner's method if the
45 * small terms were added from highest degree down.
46 */
47 r = T[4] + z*T[5];
48 t = T[2] + z*T[3];
49 w = z*z;
50 s = z*x;
51 u = T[0] + z*T[1];
52 r = (x + s*u) + (s*w)*(t + w*r);
53 return odd ? -1.0/r : r;
54 }
55