1 /* @(#)k_sin.c 5.1 93/09/24 */ 2 /* 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 6 * Developed at SunPro, 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 #if defined(LIBM_SCCS) && !defined(lint) 15 __RCSID("$NetBSD: k_sin.c,v 1.9 1997/10/09 11:30:24 lukem Exp $"); 16 #endif 17 18 /* __kernel_sin( x, y, iy) 19 * kernel sin function on [-pi/4, pi/4], 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. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0. 27 * 3. sin(x) is approximated by a polynomial of degree 13 on 28 * [0,pi/4] 29 * 3 13 30 * sin(x) ~ x + S1*x + ... + S6*x 31 * where 32 * 33 * |sin(x) 2 4 6 8 10 12 | -58 34 * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2 35 * | x | 36 * 37 * 4. sin(x+y) = sin(x) + sin'(x')*y 38 * ~ sin(x) + (1-x*x/2)*y 39 * For better accuracy, let 40 * 3 2 2 2 2 41 * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) 42 * then 3 2 43 * sin(x) = x + (S1*x + (x *(r-y/2)+y)) 44 */ 45 46 #include "math.h" 47 #include "math_private.h" 48 49 #ifdef __STDC__ 50 static const double 51 #else 52 static double 53 #endif 54 half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ 55 S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ 56 S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ 57 S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ 58 S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ 59 S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ 60 S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */ 61 62 #ifdef __STDC__ 63 double __kernel_sin(double x, double y, int iy) 64 #else 65 double __kernel_sin(x, y, iy) 66 double x,y; int iy; /* iy=0 if y is zero */ 67 #endif 68 { 69 double z,r,v; 70 int32_t ix; 71 GET_HIGH_WORD(ix,x); 72 ix &= 0x7fffffff; /* high word of x */ 73 if(ix<0x3e400000) /* |x| < 2**-27 */ 74 {if((int)x==0) return x;} /* generate inexact */ 75 z = x*x; 76 v = z*x; 77 r = S2+z*(S3+z*(S4+z*(S5+z*S6))); 78 if(iy==0) return x+v*(S1+z*r); 79 else return x-((z*(half*y-v*r)-y)-v*S1); 80 } 81