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      1 /* @(#)s_cos.c 5.1 93/09/24 */
      2 /*
      3  * ====================================================
      4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
      5  *
      6  * Developed at SunPro, a Sun Microsystems, Inc. business.
      7  * Permission to use, copy, modify, and distribute this
      8  * software is freely granted, provided that this notice
      9  * is preserved.
     10  * ====================================================
     11  */
     12 
     13 #ifndef lint
     14 static char rcsid[] = "$FreeBSD: src/lib/msun/src/s_cos.c,v 1.10 2005/10/24 14:08:36 bde Exp $";
     15 #endif
     16 
     17 /* cos(x)
     18  * Return cosine function of x.
     19  *
     20  * kernel function:
     21  *	__kernel_sin		... sine function on [-pi/4,pi/4]
     22  *	__kernel_cos		... cosine function on [-pi/4,pi/4]
     23  *	__ieee754_rem_pio2	... argument reduction routine
     24  *
     25  * Method.
     26  *      Let S,C and T denote the sin, cos and tan respectively on
     27  *	[-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
     28  *	in [-pi/4 , +pi/4], and let n = k mod 4.
     29  *	We have
     30  *
     31  *          n        sin(x)      cos(x)        tan(x)
     32  *     ----------------------------------------------------------
     33  *	    0	       S	   C		 T
     34  *	    1	       C	  -S		-1/T
     35  *	    2	      -S	  -C		 T
     36  *	    3	      -C	   S		-1/T
     37  *     ----------------------------------------------------------
     38  *
     39  * Special cases:
     40  *      Let trig be any of sin, cos, or tan.
     41  *      trig(+-INF)  is NaN, with signals;
     42  *      trig(NaN)    is that NaN;
     43  *
     44  * Accuracy:
     45  *	TRIG(x) returns trig(x) nearly rounded
     46  */
     47 
     48 #include "math.h"
     49 #include "math_private.h"
     50 
     51 double
     52 cos(double x)
     53 {
     54 	double y[2],z=0.0;
     55 	int32_t n, ix;
     56 
     57     /* High word of x. */
     58 	GET_HIGH_WORD(ix,x);
     59 
     60     /* |x| ~< pi/4 */
     61 	ix &= 0x7fffffff;
     62 	if(ix <= 0x3fe921fb) {
     63 	    if(ix<0x3e400000)			/* if x < 2**-27 */
     64 		if(((int)x)==0) return 1.0;	/* generate inexact */
     65 	    return __kernel_cos(x,z);
     66 	}
     67 
     68     /* cos(Inf or NaN) is NaN */
     69 	else if (ix>=0x7ff00000) return x-x;
     70 
     71     /* argument reduction needed */
     72 	else {
     73 	    n = __ieee754_rem_pio2(x,y);
     74 	    switch(n&3) {
     75 		case 0: return  __kernel_cos(y[0],y[1]);
     76 		case 1: return -__kernel_sin(y[0],y[1],1);
     77 		case 2: return -__kernel_cos(y[0],y[1]);
     78 		default:
     79 		        return  __kernel_sin(y[0],y[1],1);
     80 	    }
     81 	}
     82 }
     83