Home | History | Annotate | Download | only in src 
      1 
      2 /* @(#)k_sin.c 1.3 95/01/18 */
      3 /*
      4  * ====================================================
      5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
      6  *
      7  * Developed at SunSoft, a Sun Microsystems, Inc. business.
      8  * Permission to use, copy, modify, and distribute this
      9  * software is freely granted, provided that this notice
     10  * is preserved.
     11  * ====================================================
     12  */
     13 
     14 #ifndef lint
     15 static char rcsid[] = "$FreeBSD: src/lib/msun/src/k_sin.c,v 1.10 2005/11/02 13:06:49 bde Exp $";
     16 #endif
     17 
     18 /* __kernel_sin( x, y, iy)
     19  * kernel sin function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854
     20  * Input x is assumed to be bounded by ~pi/4 in magnitude.
     21  * Input y is the tail of x.
     22  * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
     23  *
     24  * Algorithm
     25  *	1. Since sin(-x) = -sin(x), we need only to consider positive x.
     26  *	2. Callers must return sin(-0) = -0 without calling here since our
     27  *	   odd polynomial is not evaluated in a way that preserves -0.
     28  *	   Callers may do the optimization sin(x) ~ x for tiny x.
     29  *	3. sin(x) is approximated by a polynomial of degree 13 on
     30  *	   [0,pi/4]
     31  *		  	         3            13
     32  *	   	sin(x) ~ x + S1*x + ... + S6*x
     33  *	   where
     34  *
     35  * 	|sin(x)         2     4     6     8     10     12  |     -58
     36  * 	|----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x  +S6*x   )| <= 2
     37  * 	|  x 					           |
     38  *
     39  *	4. sin(x+y) = sin(x) + sin'(x')*y
     40  *		    ~ sin(x) + (1-x*x/2)*y
     41  *	   For better accuracy, let
     42  *		     3      2      2      2      2
     43  *		r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
     44  *	   then                   3    2
     45  *		sin(x) = x + (S1*x + (x *(r-y/2)+y))
     46  */
     47 
     48 #include "math.h"
     49 #include "math_private.h"
     50 
     51 static const double
     52 half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
     53 S1  = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
     54 S2  =  8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
     55 S3  = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
     56 S4  =  2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
     57 S5  = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
     58 S6  =  1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
     59 
     60 double
     61 __kernel_sin(double x, double y, int iy)
     62 {
     63 	double z,r,v;
     64 
     65 	z	=  x*x;
     66 	v	=  z*x;
     67 	r	=  S2+z*(S3+z*(S4+z*(S5+z*S6)));
     68 	if(iy==0) return x+v*(S1+z*r);
     69 	else      return x-((z*(half*y-v*r)-y)-v*S1);
     70 }
     71