k_tanf.c revision 152881 
1/* k_tanf.c -- float version of k_tan.c
2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
3 * Optimized by Bruce D. Evans.
4 */
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#ifndef INLINE_KERNEL_TANDF
17#ifndef lint
18static char rcsid[] = "$FreeBSD: head/lib/msun/src/k_tanf.c 152881 2005-11-28 11:46:20Z bde $";
19#endif
20#endif
21
22#include "math.h"
23#include "math_private.h"
24
25/* |tan(x)/x - t(x)| < 2**-25.5 (~[-2e-08, 2e-08]). */
26static const double
27T[] =  {
28  0x15554d3418c99f.0p-54,	/* 0.333331395030791399758 */
29  0x1112fd38999f72.0p-55,	/* 0.133392002712976742718 */
30  0x1b54c91d865afe.0p-57,	/* 0.0533812378445670393523 */
31  0x191df3908c33ce.0p-58,	/* 0.0245283181166547278873 */
32  0x185dadfcecf44e.0p-61,	/* 0.00297435743359967304927 */
33  0x1362b9bf971bcd.0p-59,	/* 0.00946564784943673166728 */
34};
35
36#ifdef INLINE_KERNEL_TANDF
37extern inline
38#endif
39float
40__kernel_tandf(double x, int iy)
41{
42	double z,r,w,s,t,u;
43
44	z	=  x*x;
45	/*
46	 * Split up the polynomial into small independent terms to give
47	 * opportunities for parallel evaluation.  The chosen splitting is
48	 * micro-optimized for Athlons (XP, X64).  It costs 2 multiplications
49	 * relative to Horner's method on sequential machines.
50	 *
51	 * We add the small terms from lowest degree up for efficiency on
52	 * non-sequential machines (the lowest degree terms tend to be ready
53	 * earlier).  Apart from this, we don't care about order of
54	 * operations, and don't need to to care since we have precision to
55	 * spare.  However, the chosen splitting is good for accuracy too,
56	 * and would give results as accurate as Horner's method if the
57	 * small terms were added from highest degree down.
58	 */
59	r = T[4]+z*T[5];
60	t = T[2]+z*T[3];
61	w = z*z;
62	s = z*x;
63	u = T[0]+z*T[1];
64	r = (x+s*u)+(s*w)*(t+w*r);
65	if(iy==1) return r;
66	else return -1.0/r;
67}
68