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