1/*
2 * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
3 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
4 *
5 * This code is free software; you can redistribute it and/or modify it
6 * under the terms of the GNU General Public License version 2 only, as
7 * published by the Free Software Foundation. Oracle designates this
8 * particular file as subject to the "Classpath" exception as provided
9 * by Oracle in the LICENSE file that accompanied this code.
10 *
11 * This code is distributed in the hope that it will be useful, but WITHOUT
12 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
13 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
14 * version 2 for more details (a copy is included in the LICENSE file that
15 * accompanied this code).
16 *
17 * You should have received a copy of the GNU General Public License version
18 * 2 along with this work; if not, write to the Free Software Foundation,
19 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
20 *
21 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
22 * or visit www.oracle.com if you need additional information or have any
23 * questions.
24 */
25
26/* tan(x)
27 * Return tangent function of x.
28 *
29 * kernel function:
30 * __kernel_tan ... tangent function on [-pi/4,pi/4]
31 * __ieee754_rem_pio2 ... argument reduction routine
32 *
33 * Method.
34 * Let S,C and T denote the sin, cos and tan respectively on
35 * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
36 * in [-pi/4 , +pi/4], and let n = k mod 4.
37 * We have
38 *
39 * n sin(x) cos(x) tan(x)
40 * ----------------------------------------------------------
41 * 0 S C T
42 * 1 C -S -1/T
43 * 2 -S -C T
44 * 3 -C S -1/T
45 * ----------------------------------------------------------
46 *
47 * Special cases:
48 * Let trig be any of sin, cos, or tan.
49 * trig(+-INF) is NaN, with signals;
50 * trig(NaN) is that NaN;
51 *
52 * Accuracy:
53 * TRIG(x) returns trig(x) nearly rounded
54 */
55
56#include "fdlibm.h"
57
58#ifdef __STDC__
59 double tan(double x)
60#else
61 double tan(x)
62 double x;
63#endif
64{
65 double y[2],z=0.0;
66 int n, ix;
67
68 /* High word of x. */
69 ix = __HI(x);
70
71 /* |x| ~< pi/4 */
72 ix &= 0x7fffffff;
73 if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);
74
75 /* tan(Inf or NaN) is NaN */
76 else if (ix>=0x7ff00000) return x-x; /* NaN */
77
78 /* argument reduction needed */
79 else {
80 n = __ieee754_rem_pio2(x,y);
81 return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even
82 -1 -- n odd */
83 }
84}
85