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 __FBSDID("$FreeBSD$");
15
16 /* tan(x)
17 * Return tangent function of x.
18 *
19 * kernel function:
20 * __kernel_tan ... tangent function on [-pi/4,pi/4]
21 * __ieee754_rem_pio2 ... argument reduction routine
22 *
23 * Method.
24 * Let S,C and T denote the sin, cos and tan respectively on
25 * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
26 * in [-pi/4 , +pi/4], and let n = k mod 4.
27 * We have
28 *
29 * n sin(x) cos(x) tan(x)
30 * ----------------------------------------------------------
31 * 0 S C T
32 * 1 C -S -1/T
33 * 2 -S -C T
34 * 3 -C S -1/T
35 * ----------------------------------------------------------
36 *
37 * Special cases:
38 * Let trig be any of sin, cos, or tan.
39 * trig(+-INF) is NaN, with signals;
40 * trig(NaN) is that NaN;
41 *
42 * Accuracy:
43 * TRIG(x) returns trig(x) nearly rounded
44 */
45
46 #include <float.h>
47
48 #include "math.h"
49 #define INLINE_REM_PIO2
50 #include "math_private.h"
51 #include "e_rem_pio2.c"
52
53 double
tan(double x)54 tan(double x)
55 {
56 double y[2],z=0.0;
57 int32_t n, ix;
58
59 /* High word of x. */
60 GET_HIGH_WORD(ix,x);
61
62 /* |x| ~< pi/4 */
63 ix &= 0x7fffffff;
64 if(ix <= 0x3fe921fb) {
65 if(ix<0x3e400000) /* x < 2**-27 */
66 if((int)x==0) return x; /* generate inexact */
67 return __kernel_tan(x,z,1);
68 }
69
70 /* tan(Inf or NaN) is NaN */
71 else if (ix>=0x7ff00000) return x-x; /* NaN */
72
73 /* argument reduction needed */
74 else {
75 n = __ieee754_rem_pio2(x,y);
76 return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even
77 -1 -- n odd */
78 }
79 }
80
81 #if (LDBL_MANT_DIG == 53)
82 __weak_reference(tan, tanl);
83 #endif
84