k_sin.c revision 97409
1169691Skan/* @(#)k_sin.c 5.1 93/09/24 */ 2169691Skan/* 3169691Skan * ==================================================== 4169691Skan * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5169691Skan * 6169691Skan * Developed at SunPro, a Sun Microsystems, Inc. business. 7169691Skan * Permission to use, copy, modify, and distribute this 8169691Skan * software is freely granted, provided that this notice 9169691Skan * is preserved. 10169691Skan * ==================================================== 11169691Skan */ 12169691Skan 13169691Skan#ifndef lint 14169691Skanstatic char rcsid[] = "$FreeBSD: head/lib/msun/src/k_sin.c 97409 2002-05-28 17:51:46Z alfred $"; 15169691Skan#endif 16169691Skan 17169691Skan/* __kernel_sin( x, y, iy) 18169691Skan * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854 19169691Skan * Input x is assumed to be bounded by ~pi/4 in magnitude. 20169691Skan * Input y is the tail of x. 21169691Skan * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). 22169691Skan * 23169691Skan * Algorithm 24169691Skan * 1. Since sin(-x) = -sin(x), we need only to consider positive x. 25169691Skan * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0. 26169691Skan * 3. sin(x) is approximated by a polynomial of degree 13 on 27169691Skan * [0,pi/4] 28169691Skan * 3 13 29169691Skan * sin(x) ~ x + S1*x + ... + S6*x 30169691Skan * where 31169691Skan * 32169691Skan * |sin(x) 2 4 6 8 10 12 | -58 33169691Skan * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2 34169691Skan * | x | 35169691Skan * 36169691Skan * 4. sin(x+y) = sin(x) + sin'(x')*y 37169691Skan * ~ sin(x) + (1-x*x/2)*y 38169691Skan * For better accuracy, let 39169691Skan * 3 2 2 2 2 40169691Skan * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) 41169691Skan * then 3 2 42169691Skan * sin(x) = x + (S1*x + (x *(r-y/2)+y)) 43169691Skan */ 44169691Skan 45169691Skan#include "math.h" 46169691Skan#include "math_private.h" 47169691Skan 48169691Skanstatic const double 49169691Skanhalf = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ 50169691SkanS1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ 51169691SkanS2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ 52169691SkanS3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ 53169691SkanS4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ 54169691SkanS5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ 55169691SkanS6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */ 56169691Skan 57169691Skan double __kernel_sin(double x, double y, int iy) 58169691Skan{ 59169691Skan double z,r,v; 60169691Skan int32_t ix; 61169691Skan GET_HIGH_WORD(ix,x); 62169691Skan ix &= 0x7fffffff; /* high word of x */ 63169691Skan if(ix<0x3e400000) /* |x| < 2**-27 */ 64169691Skan {if((int)x==0) return x;} /* generate inexact */ 65169691Skan z = x*x; 66169691Skan v = z*x; 67169691Skan r = S2+z*(S3+z*(S4+z*(S5+z*S6))); 68169691Skan if(iy==0) return x+v*(S1+z*r); 69169691Skan else return x-((z*(half*y-v*r)-y)-v*S1); 70169691Skan} 71169691Skan