1b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 2b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project/* @(#)k_sin.c 1.3 95/01/18 */ 3b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project/* 4b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * ==================================================== 5b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 7b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Developed at SunSoft, a Sun Microsystems, Inc. business. 8b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Permission to use, copy, modify, and distribute this 9b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * software is freely granted, provided that this notice 10b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * is preserved. 11b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * ==================================================== 12b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project */ 13b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 14b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project/* __kernel_sin( x, y, iy) 15b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854 16b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Input x is assumed to be bounded by ~pi/4 in magnitude. 17b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Input y is the tail of x. 18b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). 19b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 20b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Algorithm 21b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 1. Since ieee_sin(-x) = -ieee_sin(x), we need only to consider positive x. 22b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0. 23b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 3. ieee_sin(x) is approximated by a polynomial of degree 13 on 24b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * [0,pi/4] 25b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 3 13 26b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * sin(x) ~ x + S1*x + ... + S6*x 27b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * where 28b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 29b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * |ieee_sin(x) 2 4 6 8 10 12 | -58 30b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2 31b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * | x | 32b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 33b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 4. ieee_sin(x+y) = ieee_sin(x) + sin'(x')*y 34b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * ~ ieee_sin(x) + (1-x*x/2)*y 35b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * For better accuracy, let 36b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 3 2 2 2 2 37b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) 38b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * then 3 2 39b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * sin(x) = x + (S1*x + (x *(r-y/2)+y)) 40b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project */ 41b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 42b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#include "fdlibm.h" 43b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 44b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 45b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic const double 46b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 47b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic double 48b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 49b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projecthalf = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ 50b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source ProjectS1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ 51b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source ProjectS2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ 52b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source ProjectS3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ 53b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source ProjectS4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ 54b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source ProjectS5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ 55b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source ProjectS6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */ 56b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 57b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 58b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double __kernel_sin(double x, double y, int iy) 59b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 60b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double __kernel_sin(x, y, iy) 61b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double x,y; int iy; /* iy=0 if y is zero */ 62b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 63b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project{ 64b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double z,r,v; 65b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project int ix; 66b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project ix = __HI(x)&0x7fffffff; /* high word of x */ 67b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(ix<0x3e400000) /* |x| < 2**-27 */ 68b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project {if((int)x==0) return x;} /* generate inexact */ 69b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project z = x*x; 70b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project v = z*x; 71b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project r = S2+z*(S3+z*(S4+z*(S5+z*S6))); 72b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(iy==0) return x+v*(S1+z*r); 73b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project else return x-((z*(half*y-v*r)-y)-v*S1); 74b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project} 75