k_tanf.c revision 152284 
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 152284 2005-11-10 17:43:49Z bde $";
17#endif
18
19#include "math.h"
20#include "math_private.h"
21static const float
22one   =  1.0000000000e+00, /* 0x3f800000 */
23pio4  =  7.8539812565e-01, /* 0x3f490fda */
24pio4lo=  3.7748947079e-08, /* 0x33222168 */
25/* Bounds for tan(x)/x - t(x): ~[-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	GET_FLOAT_WORD(hx,x);
41	ix = hx&0x7fffffff;	/* high word of |x| */
42	if(ix>=0x3f2ca140) { 			/* |x|>=0.6744 */
43	    if(hx<0) {x = -x; y = -y;}
44	    z = pio4-x;
45	    w = pio4lo-y;
46	    x = z+w; y = 0.0;
47	}
48	z	=  x*x;
49	w 	=  z*z;
50    /* Break x^5*(T[1]+x^2*T[2]+...) into
51     *	  x^5*(T[1]+x^4*T[3]+x^8*T[5]) +
52     *	  x^5*(x^2*(T[2]+x^4*T[4]))
53     */
54	r = T[1]+w*(T[3]+w*T[5]);
55	v = z*(T[2]+w*T[4]);
56	s = z*x;
57	r = y + z*(s*(r+v)+y);
58	r += T[0]*s;
59	w = x+r;
60	if(ix>=0x3f2ca140) {
61	    v = (float)iy;
62	    return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r)));
63	}
64	if(iy==1) return w;
65	else {		/* if allow error up to 2 ulp,
66			   simply return -1.0/(x+r) here */
67     /*  compute -1.0/(x+r) accurately */
68	    float a,t;
69	    int32_t i;
70	    z  = w;
71	    GET_FLOAT_WORD(i,z);
72	    SET_FLOAT_WORD(z,i&0xfffff000);
73	    v  = r-(z - x); 	/* z+v = r+x */
74	    t = a  = -(float)1.0/w;	/* a = -1.0/w */
75	    GET_FLOAT_WORD(i,t);
76	    SET_FLOAT_WORD(t,i&0xfffff000);
77	    s  = (float)1.0+t*z;
78	    return t+a*(s+t*v);
79	}
80}
81