1 /* s_tanl.c -- long double version of s_tan.c.
2 */
3
4 /* @(#)s_tan.c 5.1 93/09/24 */
5 /*
6 * ====================================================
7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8 *
9 * Developed at SunPro, a Sun Microsystems, Inc. business.
10 * Permission to use, copy, modify, and distribute this
11 * software is freely granted, provided that this notice
12 * is preserved.
13 * ====================================================
14 */
15
16 /* tanl(x)
17 * Return tangent function of x.
18 *
19 * kernel function:
20 * __kernel_tanl ... tangent function on [-pi/4,pi/4]
21 * __ieee754_rem_pio2l ... 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 <errno.h>
47 #include <math.h>
48 #include <math_private.h>
49 #include <math_ldbl_opt.h>
50
__tanl(long double x)51 long double __tanl(long double x)
52 {
53 long double y[2],z=0.0L;
54 int64_t n, ix;
55 double xhi;
56
57 /* High word of x. */
58 xhi = ldbl_high (x);
59 EXTRACT_WORDS64 (ix, xhi);
60
61 /* |x| ~< pi/4 */
62 ix &= 0x7fffffffffffffffLL;
63 if(ix <= 0x3fe921fb54442d10LL) return __kernel_tanl(x,z,1);
64
65 /* tanl(Inf or NaN) is NaN */
66 else if (ix>=0x7ff0000000000000LL) {
67 if (ix == 0x7ff0000000000000LL)
68 __set_errno (EDOM);
69 return x-x; /* NaN */
70 }
71 /* argument reduction needed */
72 else {
73 n = __ieee754_rem_pio2l(x,y);
74 return __kernel_tanl(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even
75 -1 -- n odd */
76 }
77 }
78 long_double_symbol (libm, __tanl, tanl);
79