1 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 13 #include <sys/cdefs.h> 14 /* __kernel_sin( x, y, iy) 15 * kernel sin function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854 16 * Input x is assumed to be bounded by ~pi/4 in magnitude. 17 * Input y is the tail of x. 18 * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). 19 * 20 * Algorithm 21 * 1. Since sin(-x) = -sin(x), we need only to consider positive x. 22 * 2. Callers must return sin(-0) = -0 without calling here since our 23 * odd polynomial is not evaluated in a way that preserves -0. 24 * Callers may do the optimization sin(x) ~ x for tiny x. 25 * 3. sin(x) is approximated by a polynomial of degree 13 on 26 * [0,pi/4] 27 * 3 13 28 * sin(x) ~ x + S1*x + ... + S6*x 29 * where 30 * 31 * |sin(x) 2 4 6 8 10 12 | -58 32 * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2 33 * | x | 34 * 35 * 4. sin(x+y) = sin(x) + sin'(x')*y 36 * ~ sin(x) + (1-x*x/2)*y 37 * For better accuracy, let 38 * 3 2 2 2 2 39 * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) 40 * then 3 2 41 * sin(x) = x + (S1*x + (x *(r-y/2)+y)) 42 */ 43 44 #include "math.h" 45 #include "math_private.h" 46 47 static const double 48 half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ 49 S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ 50 S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ 51 S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ 52 S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ 53 S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ 54 S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */ 55 56 double 57 __kernel_sin(double x, double y, int iy) 58 { 59 double z,r,v,w; 60 61 z = x*x; 62 w = z*z; 63 r = S2+z*(S3+z*S4) + z*w*(S5+z*S6); 64 v = z*x; 65 if(iy==0) return x+v*(S1+z*r); 66 else return x-((z*(half*y-v*r)-y)-v*S1); 67 } 68