113618394Sjtc /* @(#)k_sin.c 5.1 93/09/24 */
213618394Sjtc /*
313618394Sjtc * ====================================================
413618394Sjtc * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
513618394Sjtc *
613618394Sjtc * Developed at SunPro, a Sun Microsystems, Inc. business.
713618394Sjtc * Permission to use, copy, modify, and distribute this
813618394Sjtc * software is freely granted, provided that this notice
913618394Sjtc * is preserved.
1013618394Sjtc * ====================================================
1113618394Sjtc */
1213618394Sjtc
13dd7adfbfSlukem #include <sys/cdefs.h>
14d1f06e0bSjtc #if defined(LIBM_SCCS) && !defined(lint)
15*aa30599eSwiz __RCSID("$NetBSD: k_sin.c,v 1.11 2002/05/26 22:01:53 wiz Exp $");
16bc3f7bf6Sjtc #endif
17bc3f7bf6Sjtc
1813618394Sjtc /* __kernel_sin( x, y, iy)
1913618394Sjtc * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
2013618394Sjtc * Input x is assumed to be bounded by ~pi/4 in magnitude.
2113618394Sjtc * Input y is the tail of x.
2213618394Sjtc * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
2313618394Sjtc *
2413618394Sjtc * Algorithm
2513618394Sjtc * 1. Since sin(-x) = -sin(x), we need only to consider positive x.
2613618394Sjtc * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
2713618394Sjtc * 3. sin(x) is approximated by a polynomial of degree 13 on
2813618394Sjtc * [0,pi/4]
2913618394Sjtc * 3 13
3013618394Sjtc * sin(x) ~ x + S1*x + ... + S6*x
3113618394Sjtc * where
3213618394Sjtc *
3313618394Sjtc * |sin(x) 2 4 6 8 10 12 | -58
3413618394Sjtc * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2
3513618394Sjtc * | x |
3613618394Sjtc *
3713618394Sjtc * 4. sin(x+y) = sin(x) + sin'(x')*y
3813618394Sjtc * ~ sin(x) + (1-x*x/2)*y
3913618394Sjtc * For better accuracy, let
4013618394Sjtc * 3 2 2 2 2
4113618394Sjtc * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
4213618394Sjtc * then 3 2
4313618394Sjtc * sin(x) = x + (S1*x + (x *(r-y/2)+y))
4413618394Sjtc */
4513618394Sjtc
468346e333Sjtc #include "math.h"
478346e333Sjtc #include "math_private.h"
4813618394Sjtc
4913618394Sjtc static const double
5013618394Sjtc half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
5113618394Sjtc S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
5213618394Sjtc S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
5313618394Sjtc S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
5413618394Sjtc S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
5513618394Sjtc S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
5613618394Sjtc S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
5713618394Sjtc
58*aa30599eSwiz double
__kernel_sin(double x,double y,int iy)59*aa30599eSwiz __kernel_sin(double x, double y, int iy)
6013618394Sjtc {
6113618394Sjtc double z,r,v;
62b0c9d092Sjtc int32_t ix;
638346e333Sjtc GET_HIGH_WORD(ix,x);
648346e333Sjtc ix &= 0x7fffffff; /* high word of x */
6513618394Sjtc if(ix<0x3e400000) /* |x| < 2**-27 */
6613618394Sjtc {if((int)x==0) return x;} /* generate inexact */
6713618394Sjtc z = x*x;
6813618394Sjtc v = z*x;
6913618394Sjtc r = S2+z*(S3+z*(S4+z*(S5+z*S6)));
7013618394Sjtc if(iy==0) return x+v*(S1+z*r);
7113618394Sjtc else return x-((z*(half*y-v*r)-y)-v*S1);
7213618394Sjtc }
73