1*627f7eb2Smrg /* s_cosl.c -- long double version of s_cos.c.
2*627f7eb2Smrg * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz.
3*627f7eb2Smrg */
4*627f7eb2Smrg
5*627f7eb2Smrg /*
6*627f7eb2Smrg * ====================================================
7*627f7eb2Smrg * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8*627f7eb2Smrg *
9*627f7eb2Smrg * Developed at SunPro, a Sun Microsystems, Inc. business.
10*627f7eb2Smrg * Permission to use, copy, modify, and distribute this
11*627f7eb2Smrg * software is freely granted, provided that this notice
12*627f7eb2Smrg * is preserved.
13*627f7eb2Smrg * ====================================================
14*627f7eb2Smrg */
15*627f7eb2Smrg
16*627f7eb2Smrg /* cosq(x)
17*627f7eb2Smrg * Return cosine function of x.
18*627f7eb2Smrg *
19*627f7eb2Smrg * kernel function:
20*627f7eb2Smrg * __quadmath_kernel_sinq ... sine function on [-pi/4,pi/4]
21*627f7eb2Smrg * __quadmath_kernel_cosq ... cosine 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
cosq(__float128 x)49*627f7eb2Smrg __float128 cosq(__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)
60*627f7eb2Smrg return __quadmath_kernel_cosq(x,z);
61*627f7eb2Smrg
62*627f7eb2Smrg /* cos(Inf or NaN) is NaN */
63*627f7eb2Smrg else if (ix>=0x7fff000000000000LL) {
64*627f7eb2Smrg if (ix == 0x7fff000000000000LL) {
65*627f7eb2Smrg GET_FLT128_LSW64(n,x);
66*627f7eb2Smrg if (n == 0)
67*627f7eb2Smrg errno = EDOM;
68*627f7eb2Smrg }
69*627f7eb2Smrg return x-x;
70*627f7eb2Smrg }
71*627f7eb2Smrg
72*627f7eb2Smrg /* argument reduction needed */
73*627f7eb2Smrg else {
74*627f7eb2Smrg n = __quadmath_rem_pio2q(x,y);
75*627f7eb2Smrg switch(n&3) {
76*627f7eb2Smrg case 0: return __quadmath_kernel_cosq(y[0],y[1]);
77*627f7eb2Smrg case 1: return -__quadmath_kernel_sinq(y[0],y[1],1);
78*627f7eb2Smrg case 2: return -__quadmath_kernel_cosq(y[0],y[1]);
79*627f7eb2Smrg default:
80*627f7eb2Smrg return __quadmath_kernel_sinq(y[0],y[1],1);
81*627f7eb2Smrg }
82*627f7eb2Smrg }
83*627f7eb2Smrg }
84