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 /* tanq(x)
18 * Return tangent function of x.
19 *
20 * kernel function:
21 * __quadmath_kernel_tanq ... tangent function on [-pi/4,pi/4]
22 * __quadmath_rem_pio2q ... 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 "quadmath-imp.h"
48
tanq(__float128 x)49 __float128 tanq(__float128 x)
50 {
51 __float128 y[2],z=0;
52 int64_t n, ix;
53
54 /* High word of x. */
55 GET_FLT128_MSW64(ix,x);
56
57 /* |x| ~< pi/4 */
58 ix &= 0x7fffffffffffffffLL;
59 if(ix <= 0x3ffe921fb54442d1LL) return __quadmath_kernel_tanq(x,z,1);
60
61 /* tanq(Inf or NaN) is NaN */
62 else if (ix>=0x7fff000000000000LL) {
63 if (ix == 0x7fff000000000000LL) {
64 GET_FLT128_LSW64(n,x);
65 if (n == 0)
66 errno = EDOM;
67 }
68 return x-x; /* NaN */
69 }
70
71 /* argument reduction needed */
72 else {
73 n = __quadmath_rem_pio2q(x,y);
74 return __quadmath_kernel_tanq(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even
75 -1 -- n odd */
76 }
77 }
78