k_tanf.c revision 22993 
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[] = "$Id$";
18#endif
19
20#include "math.h"
21#include "math_private.h"
22#ifdef __STDC__
23static const float
24#else
25static float
26#endif
27one   =  1.0000000000e+00, /* 0x3f800000 */
28pio4  =  7.8539812565e-01, /* 0x3f490fda */
29pio4lo=  3.7748947079e-08, /* 0x33222168 */
30T[] =  {
31  3.3333334327e-01, /* 0x3eaaaaab */
32  1.3333334029e-01, /* 0x3e088889 */
33  5.3968254477e-02, /* 0x3d5d0dd1 */
34  2.1869488060e-02, /* 0x3cb327a4 */
35  8.8632395491e-03, /* 0x3c11371f */
36  3.5920790397e-03, /* 0x3b6b6916 */
37  1.4562094584e-03, /* 0x3abede48 */
38  5.8804126456e-04, /* 0x3a1a26c8 */
39  2.4646313977e-04, /* 0x398137b9 */
40  7.8179444245e-05, /* 0x38a3f445 */
41  7.1407252108e-05, /* 0x3895c07a */
42 -1.8558637748e-05, /* 0xb79bae5f */
43  2.5907305826e-05, /* 0x37d95384 */
44};
45
46#ifdef __STDC__
47	float __kernel_tanf(float x, float y, int iy)
48#else
49	float __kernel_tanf(x, y, iy)
50	float x,y; int iy;
51#endif
52{
53	float z,r,v,w,s;
54	int32_t ix,hx;
55	GET_FLOAT_WORD(hx,x);
56	ix = hx&0x7fffffff;	/* high word of |x| */
57	if(ix<0x31800000)			/* x < 2**-28 */
58	    {if((int)x==0) {			/* generate inexact */
59		if((ix|(iy+1))==0) return one/fabsf(x);
60		else return (iy==1)? x: -one/x;
61	    }
62	    }
63	if(ix>=0x3f2ca140) { 			/* |x|>=0.6744 */
64	    if(hx<0) {x = -x; y = -y;}
65	    z = pio4-x;
66	    w = pio4lo-y;
67	    x = z+w; y = 0.0;
68	}
69	z	=  x*x;
70	w 	=  z*z;
71    /* Break x^5*(T[1]+x^2*T[2]+...) into
72     *	  x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
73     *	  x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
74     */
75	r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
76	v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
77	s = z*x;
78	r = y + z*(s*(r+v)+y);
79	r += T[0]*s;
80	w = x+r;
81	if(ix>=0x3f2ca140) {
82	    v = (float)iy;
83	    return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r)));
84	}
85	if(iy==1) return w;
86	else {		/* if allow error up to 2 ulp,
87			   simply return -1.0/(x+r) here */
88     /*  compute -1.0/(x+r) accurately */
89	    float a,t;
90	    int32_t i;
91	    z  = w;
92	    GET_FLOAT_WORD(i,z);
93	    SET_FLOAT_WORD(z,i&0xfffff000);
94	    v  = r-(z - x); 	/* z+v = r+x */
95	    t = a  = -(float)1.0/w;	/* a = -1.0/w */
96	    GET_FLOAT_WORD(i,t);
97	    SET_FLOAT_WORD(t,i&0xfffff000);
98	    s  = (float)1.0+t*z;
99	    return t+a*(s+t*v);
100	}
101}
102