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 #ifndef lint 15 static char rcsid[] = "$FreeBSD$"; 16 #endif 17 18 /* __kernel_sin( x, y, iy) 19 * kernel sin function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854 20 * Input x is assumed to be bounded by ~pi/4 in magnitude. 21 * Input y is the tail of x. 22 * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). 23 * 24 * Algorithm 25 * 1. Since sin(-x) = -sin(x), we need only to consider positive x. 26 * 2. Callers must return sin(-0) = -0 without calling here since our 27 * odd polynomial is not evaluated in a way that preserves -0. 28 * Callers may do the optimization sin(x) ~ x for tiny x. 29 * 3. sin(x) is approximated by a polynomial of degree 13 on 30 * [0,pi/4] 31 * 3 13 32 * sin(x) ~ x + S1*x + ... + S6*x 33 * where 34 * 35 * |sin(x) 2 4 6 8 10 12 | -58 36 * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2 37 * | x | 38 * 39 * 4. sin(x+y) = sin(x) + sin'(x')*y 40 * ~ sin(x) + (1-x*x/2)*y 41 * For better accuracy, let 42 * 3 2 2 2 2 43 * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) 44 * then 3 2 45 * sin(x) = x + (S1*x + (x *(r-y/2)+y)) 46 */ 47 48 #include "math.h" 49 #include "math_private.h" 50 51 static const double 52 half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ 53 S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ 54 S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ 55 S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ 56 S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ 57 S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ 58 S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */ 59 60 double 61 __kernel_sin(double x, double y, int iy) 62 { 63 double z,r,v; 64 65 z = x*x; 66 v = z*x; 67 r = S2+z*(S3+z*(S4+z*(S5+z*S6))); 68 if(iy==0) return x+v*(S1+z*r); 69 else return x-((z*(half*y-v*r)-y)-v*S1); 70 } 71