k_tanf.c revision 152713 
1/* k_tanf.c -- float version of k_tan.c
2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
3 */
4
5/*
6 * ====================================================
7 * Copyright 2004 Sun Microsystems, Inc.  All Rights Reserved.
8 *
9 * Permission to use, copy, modify, and distribute this
10 * software is freely granted, provided that this notice
11 * is preserved.
12 * ====================================================
13 */
14
15#ifndef INLINE_KERNEL_TANF
16#ifndef lint
17static char rcsid[] = "$FreeBSD: head/lib/msun/src/k_tanf.c 152713 2005-11-23 14:27:56Z bde $";
18#endif
19#endif
20
21#include "math.h"
22#include "math_private.h"
23
24static const double
25pio4 = M_PI_4,
26/* |tan(x)/x - t(x)| < 2**-29.1 (~[-1.72e-09, 1.719e-09]). */
27T[] =  {
28  0x1555545f8b54d0.0p-54,	/* 0.333333104424423432022 */
29  0x111160cdc2c9af.0p-55,	/* 0.133342838734802765499 */
30  0x1b9097e5693cd0.0p-57,	/* 0.0538375346701457369036 */
31  0x173b2333895b6f.0p-58,	/* 0.0226865291791357691353 */
32  0x19fcb197e825ab.0p-60,	/* 0.00634450313965243938713 */
33  0x1d5f3701b44a27.0p-60,	/* 0.00717088210082520490646 */
34};
35
36#ifdef INLINE_KERNEL_TANF
37extern inline
38#endif
39float
40__kernel_tandf(double x, int iy)
41{
42	double z,r,v,w,s;
43	int32_t ix,hx;
44
45	GET_FLOAT_WORD(hx,x);
46	ix = hx&0x7fffffff;
47	if(ix>=0x3f2ca140) { 			/* |x|>=0.67434 */
48	    if(hx<0) {x = -x;}
49	    x = pio4-x;
50	}
51	z	=  x*x;
52	w 	=  z*z;
53    /* Break x^5*(T[1]+x^2*T[2]+...) into
54     *	  x^5*(T[1]+x^4*T[3]+x^8*T[5]) +
55     *	  x^5*(x^2*(T[2]+x^4*T[4]))
56     */
57	r = T[1]+w*(T[3]+w*T[5]);
58	v = z*(T[2]+w*T[4]);
59	s = z*x;
60	r = z*s*(r+v);
61	r += T[0]*s;
62	w = x+r;
63	if(ix>=0x3f2ca140) {
64	    v = (double)iy;
65	    return (double)(1-((hx>>30)&2))*(v-2.0*(x-(w*w/(w+v)-r)));
66	}
67	if(iy==1) return w;
68	else return -1.0/w;
69}
70