1 /* @(#)s_tan.c 5.1 93/09/24 */
2 /*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
9 * is preserved.
10 * ====================================================
11 */
12
13 /* tan(x)
14 * Return tangent function of x.
15 *
16 * kernel function:
17 * __kernel_tan ... tangent function on [-pi/4,pi/4]
18 * __ieee754_rem_pio2 ... argument reduction routine
19 *
20 * Method.
21 * Let S,C and T denote the sin, cos and tan respectively on
22 * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
23 * in [-pi/4 , +pi/4], and let n = k mod 4.
24 * We have
25 *
26 * n sin(x) cos(x) tan(x)
27 * ----------------------------------------------------------
28 * 0 S C T
29 * 1 C -S -1/T
30 * 2 -S -C T
31 * 3 -C S -1/T
32 * ----------------------------------------------------------
33 *
34 * Special cases:
35 * Let trig be any of sin, cos, or tan.
36 * trig(+-INF) is NaN, with signals;
37 * trig(NaN) is that NaN;
38 *
39 * Accuracy:
40 * TRIG(x) returns trig(x) nearly rounded
41 */
42
43 #include <float.h>
44 #include <math.h>
45
46 #include "math_private.h"
47
48 double
tan(double x)49 tan(double x)
50 {
51 double y[2],z=0.0;
52 int32_t n, ix;
53
54 /* High word of x. */
55 GET_HIGH_WORD(ix,x);
56
57 /* |x| ~< pi/4 */
58 ix &= 0x7fffffff;
59 if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);
60
61 /* tan(Inf or NaN) is NaN */
62 else if (ix>=0x7ff00000) return x-x; /* NaN */
63
64 /* argument reduction needed */
65 else {
66 n = __ieee754_rem_pio2(x,y);
67 return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even
68 -1 -- n odd */
69 }
70 }
71 DEF_STD(tan);
72 LDBL_MAYBE_UNUSED_CLONE(tan);
73