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 #include <sys/cdefs.h>
14 #if defined(LIBM_SCCS) && !defined(lint)
15 __RCSID("$NetBSD: s_tan.c,v 1.11 2024/05/08 01:40:27 riastradh Exp $");
16 #endif
17
18 /* tan(x)
19 * Return tangent function of x.
20 *
21 * kernel function:
22 * __kernel_tan ... tangent function on [-pi/4,pi/4]
23 * __ieee754_rem_pio2 ... argument reduction routine
24 *
25 * Method.
26 * Let S,C and T denote the sin, cos and tan respectively on
27 * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
28 * in [-pi/4 , +pi/4], and let n = k mod 4.
29 * We have
30 *
31 * n sin(x) cos(x) tan(x)
32 * ----------------------------------------------------------
33 * 0 S C T
34 * 1 C -S -1/T
35 * 2 -S -C T
36 * 3 -C S -1/T
37 * ----------------------------------------------------------
38 *
39 * Special cases:
40 * Let trig be any of sin, cos, or tan.
41 * trig(+-INF) is NaN, with signals;
42 * trig(NaN) is that NaN;
43 *
44 * Accuracy:
45 * TRIG(x) returns trig(x) nearly rounded
46 */
47
48 #include "namespace.h"
49 #include "math.h"
50 #include "math_private.h"
51
__weak_alias(tan,_tan)52 __weak_alias(tan, _tan)
53
54 double
55 tan(double x)
56 {
57 double y[2],z=0.0;
58 int32_t n, ix;
59
60 /* High word of x. */
61 GET_HIGH_WORD(ix,x);
62
63 /* |x| ~< pi/4 */
64 ix &= 0x7fffffff;
65 if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);
66
67 /* tan(Inf or NaN) is NaN */
68 else if (ix>=0x7ff00000) return x-x; /* NaN */
69
70 /* argument reduction needed */
71 else {
72 n = __ieee754_rem_pio2(x,y);
73 return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even
74 -1 -- n odd */
75 }
76 }
77