1*627f7eb2Smrg /* s_tanl.c -- long double version of s_tan.c.
2*627f7eb2Smrg * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz.
3*627f7eb2Smrg */
4*627f7eb2Smrg
5*627f7eb2Smrg /* @(#)s_tan.c 5.1 93/09/24 */
6*627f7eb2Smrg /*
7*627f7eb2Smrg * ====================================================
8*627f7eb2Smrg * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
9*627f7eb2Smrg *
10*627f7eb2Smrg * Developed at SunPro, a Sun Microsystems, Inc. business.
11*627f7eb2Smrg * Permission to use, copy, modify, and distribute this
12*627f7eb2Smrg * software is freely granted, provided that this notice
13*627f7eb2Smrg * is preserved.
14*627f7eb2Smrg * ====================================================
15*627f7eb2Smrg */
16*627f7eb2Smrg
17*627f7eb2Smrg /* tanq(x)
18*627f7eb2Smrg * Return tangent function of x.
19*627f7eb2Smrg *
20*627f7eb2Smrg * kernel function:
21*627f7eb2Smrg * __quadmath_kernel_tanq ... tangent function on [-pi/4,pi/4]
22*627f7eb2Smrg * __quadmath_rem_pio2q ... argument reduction routine
23*627f7eb2Smrg *
24*627f7eb2Smrg * Method.
25*627f7eb2Smrg * Let S,C and T denote the sin, cos and tan respectively on
26*627f7eb2Smrg * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
27*627f7eb2Smrg * in [-pi/4 , +pi/4], and let n = k mod 4.
28*627f7eb2Smrg * We have
29*627f7eb2Smrg *
30*627f7eb2Smrg * n sin(x) cos(x) tan(x)
31*627f7eb2Smrg * ----------------------------------------------------------
32*627f7eb2Smrg * 0 S C T
33*627f7eb2Smrg * 1 C -S -1/T
34*627f7eb2Smrg * 2 -S -C T
35*627f7eb2Smrg * 3 -C S -1/T
36*627f7eb2Smrg * ----------------------------------------------------------
37*627f7eb2Smrg *
38*627f7eb2Smrg * Special cases:
39*627f7eb2Smrg * Let trig be any of sin, cos, or tan.
40*627f7eb2Smrg * trig(+-INF) is NaN, with signals;
41*627f7eb2Smrg * trig(NaN) is that NaN;
42*627f7eb2Smrg *
43*627f7eb2Smrg * Accuracy:
44*627f7eb2Smrg * TRIG(x) returns trig(x) nearly rounded
45*627f7eb2Smrg */
46*627f7eb2Smrg
47*627f7eb2Smrg #include "quadmath-imp.h"
48*627f7eb2Smrg
tanq(__float128 x)49*627f7eb2Smrg __float128 tanq(__float128 x)
50*627f7eb2Smrg {
51*627f7eb2Smrg __float128 y[2],z=0;
52*627f7eb2Smrg int64_t n, ix;
53*627f7eb2Smrg
54*627f7eb2Smrg /* High word of x. */
55*627f7eb2Smrg GET_FLT128_MSW64(ix,x);
56*627f7eb2Smrg
57*627f7eb2Smrg /* |x| ~< pi/4 */
58*627f7eb2Smrg ix &= 0x7fffffffffffffffLL;
59*627f7eb2Smrg if(ix <= 0x3ffe921fb54442d1LL) return __quadmath_kernel_tanq(x,z,1);
60*627f7eb2Smrg
61*627f7eb2Smrg /* tanq(Inf or NaN) is NaN */
62*627f7eb2Smrg else if (ix>=0x7fff000000000000LL) {
63*627f7eb2Smrg if (ix == 0x7fff000000000000LL) {
64*627f7eb2Smrg GET_FLT128_LSW64(n,x);
65*627f7eb2Smrg if (n == 0)
66*627f7eb2Smrg errno = EDOM;
67*627f7eb2Smrg }
68*627f7eb2Smrg return x-x; /* NaN */
69*627f7eb2Smrg }
70*627f7eb2Smrg
71*627f7eb2Smrg /* argument reduction needed */
72*627f7eb2Smrg else {
73*627f7eb2Smrg n = __quadmath_rem_pio2q(x,y);
74*627f7eb2Smrg return __quadmath_kernel_tanq(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even
75*627f7eb2Smrg -1 -- n odd */
76*627f7eb2Smrg }
77*627f7eb2Smrg }
78