k_tanf.c revision 152647 
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 152647 2005-11-21 04:57:12Z bde $";
18#endif
19#endif
20
21#include "math.h"
22#include "math_private.h"
23
24static const float
25pio4  =  7.8539812565e-01, /* 0x3f490fda */
26pio4lo=  3.7748947079e-08, /* 0x33222168 */
27/* |tan(x)/x - t(x)| < 2**-29.2 (~[-1.73e-09, 1.724e-09]). */
28T[] =  {
29  0xaaaaa3.0p-25,		/* 0.33333310485 */
30  0x888b06.0p-26,		/* 0.13334283238 */
31  0xdc84c8.0p-28,		/* 0.053837567568 */
32  0xb9d8f1.0p-29,		/* 0.022686453536 */
33  0xcfe632.0p-31,		/* 0.0063445800915 */
34  0xeaf97e.0p-31,		/* 0.0071708550677 */
35};
36
37#ifdef INLINE_KERNEL_TANF
38extern inline
39#endif
40float
41__kernel_tanf(float x, float y, int iy)
42{
43	float z,r,v,w,s;
44	int32_t ix,hx;
45
46	GET_FLOAT_WORD(hx,x);
47	ix = hx&0x7fffffff;
48	if(ix>=0x3f2ca140) { 			/* |x|>=0.67434 */
49	    if(hx<0) {x = -x; y = -y;}
50	    z = pio4-x;
51	    w = pio4lo-y;
52	    x = z+w; y = 0.0;
53	}
54	z	=  x*x;
55	w 	=  z*z;
56    /* Break x^5*(T[1]+x^2*T[2]+...) into
57     *	  x^5*(T[1]+x^4*T[3]+x^8*T[5]) +
58     *	  x^5*(x^2*(T[2]+x^4*T[4]))
59     */
60	r = T[1]+w*(T[3]+w*T[5]);
61	v = z*(T[2]+w*T[4]);
62	s = z*x;
63	r = y + z*(s*(r+v)+y);
64	r += T[0]*s;
65	w = x+r;
66	if(ix>=0x3f2ca140) {
67	    v = (float)iy;
68	    return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r)));
69	}
70	if(iy==1) return w;
71	else return -1.0/((double)x+r);
72}
73