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 ```/* origin: FreeBSD /usr/src/lib/msun/src/k_sin.c */ ``` ```/* ``` ``` * ==================================================== ``` ``` * 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. ``` ``` * ==================================================== ``` ``` */ ``` ```/* __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 "libm.h" ``` ``` ``` ```static const double ``` ```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 __sin(double x, double y, int iy) ``` ```{ ``` ``` double_t z,r,v,w; ``` ``` ``` ``` z = x*x; ``` ``` w = z*z; ``` ``` r = S2 + z*(S3 + z*S4) + z*w*(S5 + z*S6); ``` ``` v = z*x; ``` ``` if (iy == 0) ``` ``` return x + v*(S1 + z*r); ``` ``` else ``` ``` return x - ((z*(0.5*y - v*r) - y) - v*S1); ``` ```} ``` ``` ```