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      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 /* __kernel_sin( x, y, iy)
     15  * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
     16  * Input x is assumed to be bounded by ~pi/4 in magnitude.
     17  * Input y is the tail of x.
     18  * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
     19  *
     20  * Algorithm
     21  *	1. Since ieee_sin(-x) = -ieee_sin(x), we need only to consider positive x.
     22  *	2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
     23  *	3. ieee_sin(x) is approximated by a polynomial of degree 13 on
     24  *	   [0,pi/4]
     25  *		  	         3            13
     26  *	   	sin(x) ~ x + S1*x + ... + S6*x
     27  *	   where
     28  *
     29  * 	|ieee_sin(x)         2     4     6     8     10     12  |     -58
     30  * 	|----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x  +S6*x   )| <= 2
     31  * 	|  x 					           |
     32  *
     33  *	4. ieee_sin(x+y) = ieee_sin(x) + sin'(x')*y
     34  *		    ~ ieee_sin(x) + (1-x*x/2)*y
     35  *	   For better accuracy, let
     36  *		     3      2      2      2      2
     37  *		r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
     38  *	   then                   3    2
     39  *		sin(x) = x + (S1*x + (x *(r-y/2)+y))
     40  */
     41 
     42 #include "fdlibm.h"
     43 
     44 #ifdef __STDC__
     45 static const double
     46 #else
     47 static double
     48 #endif
     49 half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
     50 S1  = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
     51 S2  =  8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
     52 S3  = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
     53 S4  =  2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
     54 S5  = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
     55 S6  =  1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
     56 
     57 #ifdef __STDC__
     58 	double __kernel_sin(double x, double y, int iy)
     59 #else
     60 	double __kernel_sin(x, y, iy)
     61 	double x,y; int iy;		/* iy=0 if y is zero */
     62 #endif
     63 {
     64 	double z,r,v;
     65 	int ix;
     66 	ix = __HI(x)&0x7fffffff;	/* high word of x */
     67 	if(ix<0x3e400000)			/* |x| < 2**-27 */
     68 	   {if((int)x==0) return x;}		/* generate inexact */
     69 	z	=  x*x;
     70 	v	=  z*x;
     71 	r	=  S2+z*(S3+z*(S4+z*(S5+z*S6)));
     72 	if(iy==0) return x+v*(S1+z*r);
     73 	else      return x-((z*(half*y-v*r)-y)-v*S1);
     74 }
     75