1*05a0b428SJohn Marino /* k_tanf.c -- float version of k_tan.c
2*05a0b428SJohn Marino * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
3*05a0b428SJohn Marino */
4*05a0b428SJohn Marino
5*05a0b428SJohn Marino /*
6*05a0b428SJohn Marino * ====================================================
7*05a0b428SJohn Marino * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8*05a0b428SJohn Marino *
9*05a0b428SJohn Marino * Developed at SunPro, a Sun Microsystems, Inc. business.
10*05a0b428SJohn Marino * Permission to use, copy, modify, and distribute this
11*05a0b428SJohn Marino * software is freely granted, provided that this notice
12*05a0b428SJohn Marino * is preserved.
13*05a0b428SJohn Marino * ====================================================
14*05a0b428SJohn Marino */
15*05a0b428SJohn Marino
16*05a0b428SJohn Marino #include "math.h"
17*05a0b428SJohn Marino #include "math_private.h"
18*05a0b428SJohn Marino
19*05a0b428SJohn Marino static const float
20*05a0b428SJohn Marino one = 1.0000000000e+00, /* 0x3f800000 */
21*05a0b428SJohn Marino pio4 = 7.8539812565e-01, /* 0x3f490fda */
22*05a0b428SJohn Marino pio4lo= 3.7748947079e-08, /* 0x33222168 */
23*05a0b428SJohn Marino T[] = {
24*05a0b428SJohn Marino 3.3333334327e-01, /* 0x3eaaaaab */
25*05a0b428SJohn Marino 1.3333334029e-01, /* 0x3e088889 */
26*05a0b428SJohn Marino 5.3968254477e-02, /* 0x3d5d0dd1 */
27*05a0b428SJohn Marino 2.1869488060e-02, /* 0x3cb327a4 */
28*05a0b428SJohn Marino 8.8632395491e-03, /* 0x3c11371f */
29*05a0b428SJohn Marino 3.5920790397e-03, /* 0x3b6b6916 */
30*05a0b428SJohn Marino 1.4562094584e-03, /* 0x3abede48 */
31*05a0b428SJohn Marino 5.8804126456e-04, /* 0x3a1a26c8 */
32*05a0b428SJohn Marino 2.4646313977e-04, /* 0x398137b9 */
33*05a0b428SJohn Marino 7.8179444245e-05, /* 0x38a3f445 */
34*05a0b428SJohn Marino 7.1407252108e-05, /* 0x3895c07a */
35*05a0b428SJohn Marino -1.8558637748e-05, /* 0xb79bae5f */
36*05a0b428SJohn Marino 2.5907305826e-05, /* 0x37d95384 */
37*05a0b428SJohn Marino };
38*05a0b428SJohn Marino
39*05a0b428SJohn Marino float
__kernel_tanf(float x,float y,int iy)40*05a0b428SJohn Marino __kernel_tanf(float x, float y, int iy)
41*05a0b428SJohn Marino {
42*05a0b428SJohn Marino float z,r,v,w,s;
43*05a0b428SJohn Marino int32_t ix,hx;
44*05a0b428SJohn Marino GET_FLOAT_WORD(hx,x);
45*05a0b428SJohn Marino ix = hx&0x7fffffff; /* high word of |x| */
46*05a0b428SJohn Marino if(ix<0x31800000) /* x < 2**-28 */
47*05a0b428SJohn Marino {if((int)x==0) { /* generate inexact */
48*05a0b428SJohn Marino if((ix|(iy+1))==0) return one/fabsf(x);
49*05a0b428SJohn Marino else return (iy==1)? x: -one/x;
50*05a0b428SJohn Marino }
51*05a0b428SJohn Marino }
52*05a0b428SJohn Marino if(ix>=0x3f2ca140) { /* |x|>=0.6744 */
53*05a0b428SJohn Marino if(hx<0) {x = -x; y = -y;}
54*05a0b428SJohn Marino z = pio4-x;
55*05a0b428SJohn Marino w = pio4lo-y;
56*05a0b428SJohn Marino x = z+w; y = 0.0;
57*05a0b428SJohn Marino }
58*05a0b428SJohn Marino z = x*x;
59*05a0b428SJohn Marino w = z*z;
60*05a0b428SJohn Marino /* Break x^5*(T[1]+x^2*T[2]+...) into
61*05a0b428SJohn Marino * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
62*05a0b428SJohn Marino * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
63*05a0b428SJohn Marino */
64*05a0b428SJohn Marino r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
65*05a0b428SJohn Marino v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
66*05a0b428SJohn Marino s = z*x;
67*05a0b428SJohn Marino r = y + z*(s*(r+v)+y);
68*05a0b428SJohn Marino r += T[0]*s;
69*05a0b428SJohn Marino w = x+r;
70*05a0b428SJohn Marino if(ix>=0x3f2ca140) {
71*05a0b428SJohn Marino v = (float)iy;
72*05a0b428SJohn Marino return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r)));
73*05a0b428SJohn Marino }
74*05a0b428SJohn Marino if(iy==1) return w;
75*05a0b428SJohn Marino else { /* if allow error up to 2 ulp,
76*05a0b428SJohn Marino simply return -1.0/(x+r) here */
77*05a0b428SJohn Marino /* compute -1.0/(x+r) accurately */
78*05a0b428SJohn Marino float a,t;
79*05a0b428SJohn Marino int32_t i;
80*05a0b428SJohn Marino z = w;
81*05a0b428SJohn Marino GET_FLOAT_WORD(i,z);
82*05a0b428SJohn Marino SET_FLOAT_WORD(z,i&0xfffff000);
83*05a0b428SJohn Marino v = r-(z - x); /* z+v = r+x */
84*05a0b428SJohn Marino t = a = -(float)1.0/w; /* a = -1.0/w */
85*05a0b428SJohn Marino GET_FLOAT_WORD(i,t);
86*05a0b428SJohn Marino SET_FLOAT_WORD(t,i&0xfffff000);
87*05a0b428SJohn Marino s = (float)1.0+t*z;
88*05a0b428SJohn Marino return t+a*(s+t*v);
89*05a0b428SJohn Marino }
90*05a0b428SJohn Marino }
91