| |
| /* @(#)k_sin.c 1.3 95/01/18 */ |
| /* |
| * ==================================================== |
| * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| * |
| * Developed at SunSoft, a Sun Microsystems, Inc. business. |
| * Permission to use, copy, modify, and distribute this |
| * software is freely granted, provided that this notice |
| * is preserved. |
| * ==================================================== |
| */ |
| |
| #ifndef lint |
| static char rcsid[] = "$FreeBSD: src/lib/msun/src/k_sin.c,v 1.10 2005/11/02 13:06:49 bde Exp $"; |
| #endif |
| |
| /* __kernel_sin( x, y, iy) |
| * kernel sin function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854 |
| * Input x is assumed to be bounded by ~pi/4 in magnitude. |
| * Input y is the tail of x. |
| * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). |
| * |
| * Algorithm |
| * 1. Since sin(-x) = -sin(x), we need only to consider positive x. |
| * 2. Callers must return sin(-0) = -0 without calling here since our |
| * odd polynomial is not evaluated in a way that preserves -0. |
| * Callers may do the optimization sin(x) ~ x for tiny x. |
| * 3. sin(x) is approximated by a polynomial of degree 13 on |
| * [0,pi/4] |
| * 3 13 |
| * sin(x) ~ x + S1*x + ... + S6*x |
| * where |
| * |
| * |sin(x) 2 4 6 8 10 12 | -58 |
| * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2 |
| * | x | |
| * |
| * 4. sin(x+y) = sin(x) + sin'(x')*y |
| * ~ sin(x) + (1-x*x/2)*y |
| * For better accuracy, let |
| * 3 2 2 2 2 |
| * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) |
| * then 3 2 |
| * sin(x) = x + (S1*x + (x *(r-y/2)+y)) |
| */ |
| |
| #include "math.h" |
| #include "math_private.h" |
| |
| static const double |
| half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ |
| S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ |
| S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ |
| S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ |
| S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ |
| S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ |
| S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */ |
| |
| double |
| __kernel_sin(double x, double y, int iy) |
| { |
| double z,r,v; |
| |
| z = x*x; |
| v = z*x; |
| r = S2+z*(S3+z*(S4+z*(S5+z*S6))); |
| if(iy==0) return x+v*(S1+z*r); |
| else return x-((z*(half*y-v*r)-y)-v*S1); |
| } |