1141296Sdas
2141296Sdas/* @(#)k_sin.c 1.3 95/01/18 */
32116Sjkh/*
42116Sjkh * ====================================================
52116Sjkh * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
62116Sjkh *
7141296Sdas * Developed at SunSoft, a Sun Microsystems, Inc. business.
82116Sjkh * Permission to use, copy, modify, and distribute this
9141296Sdas * software is freely granted, provided that this notice
102116Sjkh * is preserved.
112116Sjkh * ====================================================
122116Sjkh */
132116Sjkh
14176408Sbde#include <sys/cdefs.h>
15176408Sbde__FBSDID("$FreeBSD$");
162116Sjkh
172116Sjkh/* __kernel_sin( x, y, iy)
18151966Sbde * kernel sin function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854
192116Sjkh * Input x is assumed to be bounded by ~pi/4 in magnitude.
202116Sjkh * Input y is the tail of x.
21141296Sdas * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
222116Sjkh *
232116Sjkh * Algorithm
24141296Sdas *	1. Since sin(-x) = -sin(x), we need only to consider positive x.
25151966Sbde *	2. Callers must return sin(-0) = -0 without calling here since our
26151966Sbde *	   odd polynomial is not evaluated in a way that preserves -0.
27151966Sbde *	   Callers may do the optimization sin(x) ~ x for tiny x.
282116Sjkh *	3. sin(x) is approximated by a polynomial of degree 13 on
292116Sjkh *	   [0,pi/4]
302116Sjkh *		  	         3            13
312116Sjkh *	   	sin(x) ~ x + S1*x + ... + S6*x
322116Sjkh *	   where
33141296Sdas *
342116Sjkh * 	|sin(x)         2     4     6     8     10     12  |     -58
352116Sjkh * 	|----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x  +S6*x   )| <= 2
36141296Sdas * 	|  x 					           |
37141296Sdas *
382116Sjkh *	4. sin(x+y) = sin(x) + sin'(x')*y
392116Sjkh *		    ~ sin(x) + (1-x*x/2)*y
40141296Sdas *	   For better accuracy, let
412116Sjkh *		     3      2      2      2      2
422116Sjkh *		r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
432116Sjkh *	   then                   3    2
442116Sjkh *		sin(x) = x + (S1*x + (x *(r-y/2)+y))
452116Sjkh */
462116Sjkh
472116Sjkh#include "math.h"
482116Sjkh#include "math_private.h"
492116Sjkh
508870Srgrimesstatic const double
512116Sjkhhalf =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
522116SjkhS1  = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
532116SjkhS2  =  8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
542116SjkhS3  = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
552116SjkhS4  =  2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
562116SjkhS5  = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
572116SjkhS6  =  1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
582116Sjkh
5997413Salfreddouble
6097413Salfred__kernel_sin(double x, double y, int iy)
612116Sjkh{
62176408Sbde	double z,r,v,w;
63151620Sbde
642116Sjkh	z	=  x*x;
65176408Sbde	w	=  z*z;
66176408Sbde	r	=  S2+z*(S3+z*S4) + z*w*(S5+z*S6);
672116Sjkh	v	=  z*x;
682116Sjkh	if(iy==0) return x+v*(S1+z*r);
692116Sjkh	else      return x-((z*(half*y-v*r)-y)-v*S1);
702116Sjkh}
71