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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 #include <sys/cdefs.h>
     14 __FBSDID("$FreeBSD$");
     15 
     16 /* cos(x)
     17  * Return cosine function of x.
     18  *
     19  * kernel function:
     20  *	__kernel_sin		... sine function on [-pi/4,pi/4]
     21  *	__kernel_cos		... cosine function on [-pi/4,pi/4]
     22  *	__ieee754_rem_pio2	... 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 <float.h>
     48 
     49 #include "math.h"
     50 #define INLINE_REM_PIO2
     51 #include "math_private.h"
     52 #include "e_rem_pio2.c"
     53 
     54 double
     55 cos(double x)
     56 {
     57 	double y[2],z=0.0;
     58 	int32_t n, ix;
     59 
     60     /* High word of x. */
     61 	GET_HIGH_WORD(ix,x);
     62 
     63     /* |x| ~< pi/4 */
     64 	ix &= 0x7fffffff;
     65 	if(ix <= 0x3fe921fb) {
     66 	    if(ix<0x3e46a09e)			/* if x < 2**-27 * sqrt(2) */
     67 		if(((int)x)==0) return 1.0;	/* generate inexact */
     68 	    return __kernel_cos(x,z);
     69 	}
     70 
     71     /* cos(Inf or NaN) is NaN */
     72 	else if (ix>=0x7ff00000) return x-x;
     73 
     74     /* argument reduction needed */
     75 	else {
     76 	    n = __ieee754_rem_pio2(x,y);
     77 	    switch(n&3) {
     78 		case 0: return  __kernel_cos(y[0],y[1]);
     79 		case 1: return -__kernel_sin(y[0],y[1],1);
     80 		case 2: return -__kernel_cos(y[0],y[1]);
     81 		default:
     82 		        return  __kernel_sin(y[0],y[1],1);
     83 	    }
     84 	}
     85 }
     86 
     87 #if (LDBL_MANT_DIG == 53)
     88 __weak_reference(cos, cosl);
     89 #endif
     90