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