1 /* origin: FreeBSD /usr/src/lib/msun/src/k_sin.c */ 2 /* 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 6 * Developed at SunSoft, a Sun Microsystems, Inc. business. 7 * Permission to use, copy, modify, and distribute this 8 * software is freely granted, provided that this notice 9 * is preserved. 10 * ==================================================== 11 */ 12 /* __sin( x, y, iy) 13 * kernel sin function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854 14 * Input x is assumed to be bounded by ~pi/4 in magnitude. 15 * Input y is the tail of x. 16 * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). 17 * 18 * Algorithm 19 * 1. Since sin(-x) = -sin(x), we need only to consider positive x. 20 * 2. Callers must return sin(-0) = -0 without calling here since our 21 * odd polynomial is not evaluated in a way that preserves -0. 22 * Callers may do the optimization sin(x) ~ x for tiny x. 23 * 3. 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 * |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. sin(x+y) = sin(x) + sin'(x')*y 34 * ~ 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 "libm.h" 43 44 static const double 45 S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ 46 S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ 47 S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ 48 S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ 49 S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ 50 S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */ 51 52 double __sin(double x, double y, int iy) 53 { 54 double_t z,r,v,w; 55 56 z = x*x; 57 w = z*z; 58 r = S2 + z*(S3 + z*S4) + z*w*(S5 + z*S6); 59 v = z*x; 60 if (iy == 0) 61 return x + v*(S1 + z*r); 62 else 63 return x - ((z*(0.5*y - v*r) - y) - v*S1); 64 } 65