k_tanf.c revision 97413 
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 (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8 *
9 * Developed at SunPro, a Sun Microsystems, Inc. business.
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 lint
17static char rcsid[] = "$FreeBSD: head/lib/msun/src/k_tanf.c 97413 2002-05-28 18:15:04Z alfred $";
18#endif
19
20#include "math.h"
21#include "math_private.h"
22static const float
23one   =  1.0000000000e+00, /* 0x3f800000 */
24pio4  =  7.8539812565e-01, /* 0x3f490fda */
25pio4lo=  3.7748947079e-08, /* 0x33222168 */
26T[] =  {
27  3.3333334327e-01, /* 0x3eaaaaab */
28  1.3333334029e-01, /* 0x3e088889 */
29  5.3968254477e-02, /* 0x3d5d0dd1 */
30  2.1869488060e-02, /* 0x3cb327a4 */
31  8.8632395491e-03, /* 0x3c11371f */
32  3.5920790397e-03, /* 0x3b6b6916 */
33  1.4562094584e-03, /* 0x3abede48 */
34  5.8804126456e-04, /* 0x3a1a26c8 */
35  2.4646313977e-04, /* 0x398137b9 */
36  7.8179444245e-05, /* 0x38a3f445 */
37  7.1407252108e-05, /* 0x3895c07a */
38 -1.8558637748e-05, /* 0xb79bae5f */
39  2.5907305826e-05, /* 0x37d95384 */
40};
41
42float
43__kernel_tanf(float x, float y, int iy)
44{
45	float z,r,v,w,s;
46	int32_t ix,hx;
47	GET_FLOAT_WORD(hx,x);
48	ix = hx&0x7fffffff;	/* high word of |x| */
49	if(ix<0x31800000)			/* x < 2**-28 */
50	    {if((int)x==0) {			/* generate inexact */
51		if((ix|(iy+1))==0) return one/fabsf(x);
52		else return (iy==1)? x: -one/x;
53	    }
54	    }
55	if(ix>=0x3f2ca140) { 			/* |x|>=0.6744 */
56	    if(hx<0) {x = -x; y = -y;}
57	    z = pio4-x;
58	    w = pio4lo-y;
59	    x = z+w; y = 0.0;
60	}
61	z	=  x*x;
62	w 	=  z*z;
63    /* Break x^5*(T[1]+x^2*T[2]+...) into
64     *	  x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
65     *	  x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
66     */
67	r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
68	v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
69	s = z*x;
70	r = y + z*(s*(r+v)+y);
71	r += T[0]*s;
72	w = x+r;
73	if(ix>=0x3f2ca140) {
74	    v = (float)iy;
75	    return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r)));
76	}
77	if(iy==1) return w;
78	else {		/* if allow error up to 2 ulp,
79			   simply return -1.0/(x+r) here */
80     /*  compute -1.0/(x+r) accurately */
81	    float a,t;
82	    int32_t i;
83	    z  = w;
84	    GET_FLOAT_WORD(i,z);
85	    SET_FLOAT_WORD(z,i&0xfffff000);
86	    v  = r-(z - x); 	/* z+v = r+x */
87	    t = a  = -(float)1.0/w;	/* a = -1.0/w */
88	    GET_FLOAT_WORD(i,t);
89	    SET_FLOAT_WORD(t,i&0xfffff000);
90	    s  = (float)1.0+t*z;
91	    return t+a*(s+t*v);
92	}
93}
94