k_tanf.c revision 152343 
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 lint
16static char rcsid[] = "$FreeBSD: head/lib/msun/src/k_tanf.c 152343 2005-11-12 20:06:04Z bde $";
17#endif
18
19#include "math.h"
20#include "math_private.h"
21
22static const float
23pio4  =  7.8539812565e-01, /* 0x3f490fda */
24pio4lo=  3.7748947079e-08, /* 0x33222168 */
25/* |tan(x)/x - t(x)| < 2**-29.2 (~[-1.73e-09, 1.724e-09]). */
26T[] =  {
27  0xaaaaa3.0p-25,		/* 0.33333310485 */
28  0x888b06.0p-26,		/* 0.13334283238 */
29  0xdc84c8.0p-28,		/* 0.053837567568 */
30  0xb9d8f1.0p-29,		/* 0.022686453536 */
31  0xcfe632.0p-31,		/* 0.0063445800915 */
32  0xeaf97e.0p-31,		/* 0.0071708550677 */
33};
34
35float
36__kernel_tanf(float x, float y, int iy)
37{
38	float z,r,v,w,s;
39	int32_t ix,hx;
40
41	GET_FLOAT_WORD(hx,x);
42	ix = hx&0x7fffffff;
43	if(ix>=0x3f2ca140) { 			/* |x|>=0.67434 */
44	    if(hx<0) {x = -x; y = -y;}
45	    z = pio4-x;
46	    w = pio4lo-y;
47	    x = z+w; y = 0.0;
48	}
49	z	=  x*x;
50	w 	=  z*z;
51    /* Break x^5*(T[1]+x^2*T[2]+...) into
52     *	  x^5*(T[1]+x^4*T[3]+x^8*T[5]) +
53     *	  x^5*(x^2*(T[2]+x^4*T[4]))
54     */
55	r = T[1]+w*(T[3]+w*T[5]);
56	v = z*(T[2]+w*T[4]);
57	s = z*x;
58	r = y + z*(s*(r+v)+y);
59	r += T[0]*s;
60	w = x+r;
61	if(ix>=0x3f2ca140) {
62	    v = (float)iy;
63	    return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r)));
64	}
65	if(iy==1) return w;
66	else {		/* if allow error up to 2 ulp,
67			   simply return -1.0/(x+r) here */
68     /*  compute -1.0/(x+r) accurately */
69	    float a,t;
70	    int32_t i;
71	    z  = w;
72	    GET_FLOAT_WORD(i,z);
73	    SET_FLOAT_WORD(z,i&0xfffff000);
74	    v  = r-(z - x); 	/* z+v = r+x */
75	    t = a  = -(float)1.0/w;	/* a = -1.0/w */
76	    GET_FLOAT_WORD(i,t);
77	    SET_FLOAT_WORD(t,i&0xfffff000);
78	    s  = (float)1.0+t*z;
79	    return t+a*(s+t*v);
80	}
81}
82