1 2 /* @(#)k_sin.c 1.3 95/01/18 */ 3 /* 4 * ==================================================== 5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6 * 7 * Developed at SunSoft, a Sun Microsystems, Inc. business. 8 * Permission to use, copy, modify, and distribute this 9 * software is freely granted, provided that this notice 10 * is preserved. 11 * ==================================================== 12 */ 13 14 #include "cdefs-compat.h" 15 //__FBSDID("$FreeBSD: src/lib/msun/src/k_sin.c,v 1.11 2008/02/19 12:54:14 bde Exp $"); 16 17 /* __kernel_sin( x, y, iy) 18 * kernel sin function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854 19 * Input x is assumed to be bounded by ~pi/4 in magnitude. 20 * Input y is the tail of x. 21 * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). 22 * 23 * Algorithm 24 * 1. Since sin(-x) = -sin(x), we need only to consider positive x. 25 * 2. Callers must return sin(-0) = -0 without calling here since our 26 * odd polynomial is not evaluated in a way that preserves -0. 27 * Callers may do the optimization sin(x) ~ x for tiny x. 28 * 3. sin(x) is approximated by a polynomial of degree 13 on 29 * [0,pi/4] 30 * 3 13 31 * sin(x) ~ x + S1*x + ... + S6*x 32 * where 33 * 34 * |sin(x) 2 4 6 8 10 12 | -58 35 * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2 36 * | x | 37 * 38 * 4. sin(x+y) = sin(x) + sin'(x')*y 39 * ~ sin(x) + (1-x*x/2)*y 40 * For better accuracy, let 41 * 3 2 2 2 2 42 * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) 43 * then 3 2 44 * sin(x) = x + (S1*x + (x *(r-y/2)+y)) 45 */ 46 47 #include "openlibm.h" 48 #include "math_private.h" 49 50 static const double 51 half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ 52 S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ 53 S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ 54 S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ 55 S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ 56 S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ 57 S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */ 58 59 double 60 __kernel_sin(double x, double y, int iy) 61 { 62 double z,r,v,w; 63 64 z = x*x; 65 w = z*z; 66 r = S2+z*(S3+z*S4) + z*w*(S5+z*S6); 67 v = z*x; 68 if(iy==0) return x+v*(S1+z*r); 69 else return x-((z*(half*y-v*r)-y)-v*S1); 70 } 71