1 /* 2 * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved. 3 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. 4 * 5 * This code is free software; you can redistribute it and/or modify it 6 * under the terms of the GNU General Public License version 2 only, as 7 * published by the Free Software Foundation. Oracle designates this 8 * particular file as subject to the "Classpath" exception as provided 9 * by Oracle in the LICENSE file that accompanied this code. 10 * 11 * This code is distributed in the hope that it will be useful, but WITHOUT 12 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or 13 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License 14 * version 2 for more details (a copy is included in the LICENSE file that 15 * accompanied this code). 16 * 17 * You should have received a copy of the GNU General Public License version 18 * 2 along with this work; if not, write to the Free Software Foundation, 19 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. 20 * 21 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA 22 * or visit www.oracle.com if you need additional information or have any 23 * questions. 24 */ 25 26 /* __kernel_sin( x, y, iy) 27 * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854 28 * Input x is assumed to be bounded by ~pi/4 in magnitude. 29 * Input y is the tail of x. 30 * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). 31 * 32 * Algorithm 33 * 1. Since sin(-x) = -sin(x), we need only to consider positive x. 34 * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0. 35 * 3. sin(x) is approximated by a polynomial of degree 13 on 36 * [0,pi/4] 37 * 3 13 38 * sin(x) ~ x + S1*x + ... + S6*x 39 * where 40 * 41 * |sin(x) 2 4 6 8 10 12 | -58 42 * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2 43 * | x | 44 * 45 * 4. sin(x+y) = sin(x) + sin'(x')*y 46 * ~ sin(x) + (1-x*x/2)*y 47 * For better accuracy, let 48 * 3 2 2 2 2 49 * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) 50 * then 3 2 51 * sin(x) = x + (S1*x + (x *(r-y/2)+y)) 52 */ 53 54 #include "fdlibm.h" 55 56 #ifdef __STDC__ 57 static const double 58 #else 59 static double 60 #endif 61 half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ 62 S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ 63 S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ 64 S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ 65 S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ 66 S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ 67 S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */ 68 69 #ifdef __STDC__ __kernel_sin(double x,double y,int iy)70 double __kernel_sin(double x, double y, int iy) 71 #else 72 double __kernel_sin(x, y, iy) 73 double x,y; int iy; /* iy=0 if y is zero */ 74 #endif 75 { 76 double z,r,v; 77 int ix; 78 ix = __HI(x)&0x7fffffff; /* high word of x */ 79 if(ix<0x3e400000) /* |x| < 2**-27 */ 80 {if((int)x==0) return x;} /* generate inexact */ 81 z = x*x; 82 v = z*x; 83 r = S2+z*(S3+z*(S4+z*(S5+z*S6))); 84 if(iy==0) return x+v*(S1+z*r); 85 else return x-((z*(half*y-v*r)-y)-v*S1); 86 } 87