1996-08-30 00:58:28 +00:00
|
|
|
/* s_cosl.c -- long double version of s_cos.c.
|
1999-07-14 00:54:57 +00:00
|
|
|
* Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz.
|
1996-08-30 00:58:28 +00:00
|
|
|
*/
|
|
|
|
|
|
|
|
|
|
/*
|
|
|
|
|
* ====================================================
|
|
|
|
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|
|
|
|
*
|
|
|
|
|
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
|
|
|
|
* Permission to use, copy, modify, and distribute this
|
|
|
|
|
* software is freely granted, provided that this notice
|
|
|
|
|
* is preserved.
|
|
|
|
|
* ====================================================
|
|
|
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* cosl(x)
|
|
|
|
|
* Return cosine function of x.
|
|
|
|
|
*
|
|
|
|
|
* kernel function:
|
|
|
|
|
* __kernel_sinl ... sine function on [-pi/4,pi/4]
|
|
|
|
|
* __kernel_cosl ... cosine function on [-pi/4,pi/4]
|
|
|
|
|
* __ieee754_rem_pio2l ... argument reduction routine
|
|
|
|
|
*
|
|
|
|
|
* Method.
|
|
|
|
|
* Let S,C and T denote the sin, cos and tan respectively on
|
|
|
|
|
* [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
|
|
|
|
|
* in [-pi/4 , +pi/4], and let n = k mod 4.
|
|
|
|
|
* We have
|
|
|
|
|
*
|
|
|
|
|
* n sin(x) cos(x) tan(x)
|
|
|
|
|
* ----------------------------------------------------------
|
|
|
|
|
* 0 S C T
|
|
|
|
|
* 1 C -S -1/T
|
|
|
|
|
* 2 -S -C T
|
|
|
|
|
* 3 -C S -1/T
|
|
|
|
|
* ----------------------------------------------------------
|
|
|
|
|
*
|
|
|
|
|
* Special cases:
|
|
|
|
|
* Let trig be any of sin, cos, or tan.
|
|
|
|
|
* trig(+-INF) is NaN, with signals;
|
|
|
|
|
* trig(NaN) is that NaN;
|
|
|
|
|
*
|
|
|
|
|
* Accuracy:
|
|
|
|
|
* TRIG(x) returns trig(x) nearly rounded
|
|
|
|
|
*/
|
|
|
|
|
|
2009-05-29 19:00:22 +00:00
|
|
|
#include <errno.h>
|
2012-03-09 19:29:16 +00:00
|
|
|
#include <math.h>
|
|
|
|
|
#include <math_private.h>
|
2017-10-06 17:45:05 +00:00
|
|
|
#include <libm-alias-ldouble.h>
|
1996-08-30 00:58:28 +00:00
|
|
|
|
2016-07-20 20:20:51 +00:00
|
|
|
_Float128 __cosl(_Float128 x)
|
1996-08-30 00:58:28 +00:00
|
|
|
{
|
2016-09-02 16:01:07 +00:00
|
|
|
_Float128 y[2],z=0;
|
1999-07-14 00:54:57 +00:00
|
|
|
int64_t n, ix;
|
1996-08-30 00:58:28 +00:00
|
|
|
|
|
|
|
|
/* High word of x. */
|
1999-07-14 00:54:57 +00:00
|
|
|
GET_LDOUBLE_MSW64(ix,x);
|
1996-08-30 00:58:28 +00:00
|
|
|
|
|
|
|
|
/* |x| ~< pi/4 */
|
1999-07-14 00:54:57 +00:00
|
|
|
ix &= 0x7fffffffffffffffLL;
|
|
|
|
|
if(ix <= 0x3ffe921fb54442d1LL)
|
1997-04-15 01:38:39 +00:00
|
|
|
return __kernel_cosl(x,z);
|
1996-08-30 00:58:28 +00:00
|
|
|
|
|
|
|
|
/* cos(Inf or NaN) is NaN */
|
2009-05-29 19:00:22 +00:00
|
|
|
else if (ix>=0x7fff000000000000LL) {
|
|
|
|
|
if (ix == 0x7fff000000000000LL) {
|
|
|
|
|
GET_LDOUBLE_LSW64(n,x);
|
|
|
|
|
if (n == 0)
|
|
|
|
|
__set_errno (EDOM);
|
|
|
|
|
}
|
|
|
|
|
return x-x;
|
|
|
|
|
}
|
1996-08-30 00:58:28 +00:00
|
|
|
|
|
|
|
|
/* argument reduction needed */
|
|
|
|
|
else {
|
|
|
|
|
n = __ieee754_rem_pio2l(x,y);
|
|
|
|
|
switch(n&3) {
|
|
|
|
|
case 0: return __kernel_cosl(y[0],y[1]);
|
|
|
|
|
case 1: return -__kernel_sinl(y[0],y[1],1);
|
|
|
|
|
case 2: return -__kernel_cosl(y[0],y[1]);
|
|
|
|
|
default:
|
|
|
|
|
return __kernel_sinl(y[0],y[1],1);
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
}
|
2017-10-06 17:45:05 +00:00
|
|
|
libm_alias_ldouble (__cos, cos)
|
