1 /* kf_tan.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 "fdlibm.h"
17 static const float one = 1.0000000000e+00, /* 0x3f800000 */
18 pio4 = 7.8539812565e-01, /* 0x3f490fda */
19 pio4lo = 3.7748947079e-08, /* 0x33222168 */
20 T[] = {
21 3.3333334327e-01, /* 0x3eaaaaab */
22 1.3333334029e-01, /* 0x3e088889 */
23 5.3968254477e-02, /* 0x3d5d0dd1 */
24 2.1869488060e-02, /* 0x3cb327a4 */
25 8.8632395491e-03, /* 0x3c11371f */
26 3.5920790397e-03, /* 0x3b6b6916 */
27 1.4562094584e-03, /* 0x3abede48 */
28 5.8804126456e-04, /* 0x3a1a26c8 */
29 2.4646313977e-04, /* 0x398137b9 */
30 7.8179444245e-05, /* 0x38a3f445 */
31 7.1407252108e-05, /* 0x3895c07a */
32 -1.8558637748e-05, /* 0xb79bae5f */
33 2.5907305826e-05, /* 0x37d95384 */
34 };
35
36 float
__kernel_tanf(float x,float y,int iy)37 __kernel_tanf(float x, float y, int iy)
38 {
39 float z, r, v, w, s;
40 __int32_t ix, hx;
41 GET_FLOAT_WORD(hx, x);
42 ix = hx & 0x7fffffff; /* high word of |x| */
43 if (ix < 0x31800000) /* x < 2**-28 */
44 {
45 if ((int)x == 0) { /* generate inexact */
46 if ((ix | (iy + 1)) == 0)
47 return one / fabsf(x);
48 else
49 return (iy == 1) ? x : -one / x;
50 }
51 }
52 if (ix >= 0x3f2ca140) { /* |x|>=0.6744 */
53 if (hx < 0) {
54 x = -x;
55 y = -y;
56 }
57 z = pio4 - x;
58 w = pio4lo - y;
59 x = z + w;
60 y = 0.0;
61 }
62 z = x * x;
63 w = z * z;
64 /* Break x^5*(T[1]+x^2*T[2]+...) into
65 * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
66 * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
67 */
68 r = T[1] + w * (T[3] + w * (T[5] + w * (T[7] + w * (T[9] + w * T[11]))));
69 v = z *
70 (T[2] + w * (T[4] + w * (T[6] + w * (T[8] + w * (T[10] + w * T[12])))));
71 s = z * x;
72 r = y + z * (s * (r + v) + y);
73 r += T[0] * s;
74 w = x + r;
75 if (ix >= 0x3f2ca140) {
76 v = (float)iy;
77 return (float)(1 - ((hx >> 30) & 2)) *
78 (v - (float)2.0 * (x - (w * w / (w + v) - r)));
79 }
80 if (iy == 1)
81 return w;
82 else { /* if allow error up to 2 ulp,
83 simply return -1.0/(x+r) here */
84 /* compute -1.0/(x+r) accurately */
85 float a, t;
86 __int32_t i;
87 z = w;
88 GET_FLOAT_WORD(i, z);
89 SET_FLOAT_WORD(z, i & 0xfffff000);
90 v = r - (z - x); /* z+v = r+x */
91 t = a = -(float)1.0 / w; /* a = -1.0/w */
92 GET_FLOAT_WORD(i, t);
93 SET_FLOAT_WORD(t, i & 0xfffff000);
94 s = (float)1.0 + t * z;
95 return t + a * (s + t * v);
96 }
97 }
98
