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      1 /* @(#)s_sin.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 #if defined(LIBM_SCCS) && !defined(lint)
     15 __RCSID("$NetBSD: s_sin.c,v 1.12 2024/05/08 01:40:27 riastradh Exp $");
     16 #endif
     17 
     18 /* sin(x)
     19  * Return sine function of x.
     20  *
     21  * kernel function:
     22  *	__kernel_sin		... sine function on [-pi/4,pi/4]
     23  *	__kernel_cos		... cose function on [-pi/4,pi/4]
     24  *	__ieee754_rem_pio2	... argument reduction routine
     25  *
     26  * Method.
     27  *      Let S,C and T denote the sin, cos and tan respectively on
     28  *	[-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
     29  *	in [-pi/4 , +pi/4], and let n = k mod 4.
     30  *	We have
     31  *
     32  *          n        sin(x)      cos(x)        tan(x)
     33  *     ----------------------------------------------------------
     34  *	    0	       S	   C		 T
     35  *	    1	       C	  -S		-1/T
     36  *	    2	      -S	  -C		 T
     37  *	    3	      -C	   S		-1/T
     38  *     ----------------------------------------------------------
     39  *
     40  * Special cases:
     41  *      Let trig be any of sin, cos, or tan.
     42  *      trig(+-INF)  is NaN, with signals;
     43  *      trig(NaN)    is that NaN;
     44  *
     45  * Accuracy:
     46  *	TRIG(x) returns trig(x) nearly rounded
     47  */
     48 
     49 #include "namespace.h"
     50 #include "math.h"
     51 #include "math_private.h"
     52 
     53 __weak_alias(sin, _sin)
     54 
     55 double
     56 sin(double x)
     57 {
     58 	double y[2],z=0.0;
     59 	int32_t n, ix;
     60 
     61     /* High word of x. */
     62 	GET_HIGH_WORD(ix,x);
     63 
     64     /* |x| ~< pi/4 */
     65 	ix &= 0x7fffffff;
     66 	if(ix <= 0x3fe921fb) return __kernel_sin(x,z,0);
     67 
     68     /* sin(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_sin(y[0],y[1],1);
     76 		case 1: return  __kernel_cos(y[0],y[1]);
     77 		case 2: return -__kernel_sin(y[0],y[1],1);
     78 		default:
     79 			return -__kernel_cos(y[0],y[1]);
     80 	    }
     81 	}
     82 }
     83