1/* s_tanl.c -- long double version of s_tan.c.
2 * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz.
3 */
4
5/* @(#)s_tan.c 5.1 93/09/24 */
6/*
7 * ====================================================
8 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
9 *
10 * Developed at SunPro, a Sun Microsystems, Inc. business.
11 * Permission to use, copy, modify, and distribute this
12 * software is freely granted, provided that this notice
13 * is preserved.
14 * ====================================================
15 */
16
17/* tanl(x)
18 * Return tangent function of x.
19 *
20 * kernel function:
21 * __kernel_tanl ... tangent function on [-pi/4,pi/4]
22 * __ieee754_rem_pio2l ... argument reduction routine
23 *
24 * Method.
25 * Let S,C and T denote the sin, cos and tan respectively on
26 * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
27 * in [-pi/4 , +pi/4], and let n = k mod 4.
28 * We have
29 *
30 * n sin(x) cos(x) tan(x)
31 * ----------------------------------------------------------
32 * 0 S C T
33 * 1 C -S -1/T
34 * 2 -S -C T
35 * 3 -C S -1/T
36 * ----------------------------------------------------------
37 *
38 * Special cases:
39 * Let trig be any of sin, cos, or tan.
40 * trig(+-INF) is NaN, with signals;
41 * trig(NaN) is that NaN;
42 *
43 * Accuracy:
44 * TRIG(x) returns trig(x) nearly rounded
45 */
46
47#include <errno.h>
48#include <math.h>
49#include <math_private.h>
50
51_Float128 __tanl(_Float128 x)
52{
53 _Float128 y[2],z=0;
54 int64_t n, ix;
55
56 /* High word of x. */
57 GET_LDOUBLE_MSW64(ix,x);
58
59 /* |x| ~< pi/4 */
60 ix &= 0x7fffffffffffffffLL;
61 if(ix <= 0x3ffe921fb54442d1LL) return __kernel_tanl(x,z,1);
62
63 /* tanl(Inf or NaN) is NaN */
64 else if (ix>=0x7fff000000000000LL) {
65 if (ix == 0x7fff000000000000LL) {
66 GET_LDOUBLE_LSW64(n,x);
67 if (n == 0)
68 __set_errno (EDOM);
69 }
70 return x-x; /* NaN */
71 }
72
73 /* argument reduction needed */
74 else {
75 n = __ieee754_rem_pio2l(x,y);
76 return __kernel_tanl(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even
77 -1 -- n odd */
78 }
79}
80weak_alias (__tanl, tanl)
81