1 /* cosq.c -- __float128 version of s_cos.c.
2 * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz.
3 */
4
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 /* cosq(x)
17 * Return cosine function of x.
18 *
19 * kernel function:
20 * __quadmath_kernel_sinq ... sine function on [-pi/4,pi/4]
21 * __quadmath_kernel_cosq ... cosine 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
49 __float128
cosq(__float128 x)50 cosq (__float128 x)
51 {
52 __float128 y[2],z=0.0Q;
53 int64_t n, ix;
54
55 /* High word of x. */
56 GET_FLT128_MSW64(ix,x);
57
58 /* |x| ~< pi/4 */
59 ix &= 0x7fffffffffffffffLL;
60 if(ix <= 0x3ffe921fb54442d1LL)
61 return __quadmath_kernel_cosq(x,z);
62
63 /* cos(Inf or NaN) is NaN */
64 else if (ix>=0x7fff000000000000LL) {
65 if (ix == 0x7fff000000000000LL) {
66 GET_FLT128_LSW64(n,x);
67 }
68 return x-x;
69 }
70
71 /* argument reduction needed */
72 else {
73 n = __quadmath_rem_pio2q(x,y);
74 switch(n&3) {
75 case 0: return __quadmath_kernel_cosq(y[0],y[1]);
76 case 1: return -__quadmath_kernel_sinq(y[0],y[1],1);
77 case 2: return -__quadmath_kernel_cosq(y[0],y[1]);
78 default:
79 return __quadmath_kernel_sinq(y[0],y[1],1);
80 }
81 }
82 }
83