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 #include <LibConfig.h>
13 #include <sys/EfiCdefs.h>
14 #if defined(LIBM_SCCS) && !defined(lint)
15 __RCSID("$NetBSD: s_tan.c,v 1.10 2002/05/26 22:01:58 wiz 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 "math.h"
49 #include "math_private.h"
50
51 double
tan(double x)52 tan(double x)
53 {
54 double y[2],z=0.0;
55 int32_t n, ix;
56
57 /* High word of x. */
58 GET_HIGH_WORD(ix,x);
59
60 /* |x| ~< pi/4 */
61 ix &= 0x7fffffff;
62 if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);
63
64 /* tan(Inf or NaN) is NaN */
65 else if (ix>=0x7ff00000) return x-x; /* NaN */
66
67 /* argument reduction needed */
68 else {
69 n = __ieee754_rem_pio2(x,y);
70 return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even
71 -1 -- n odd */
72 }
73 }
74