/* @(#)k_sin.c 1.3 95/01/18 */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunSoft, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ /* __kernel_sin( x, y, iy) * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854 * Input x is assumed to be bounded by ~pi/4 in magnitude. * Input y is the tail of x. * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). * * Algorithm * 1. Since sin(-x) = -sin(x), we need only to consider positive x. * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0. * 3. sin(x) is approximated by a polynomial of degree 13 on * [0,pi/4] * 3 13 * sin(x) ~ x + S1*x + ... + S6*x * where * * |sin(x) 2 4 6 8 10 12 | -58 * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2 * | x | * * 4. sin(x+y) = sin(x) + sin'(x')*y * ~ sin(x) + (1-x*x/2)*y * For better accuracy, let * 3 2 2 2 2 * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) * then 3 2 * sin(x) = x + (S1*x + (x *(r-y/2)+y)) */ #include #include "math_private.h" static const double half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */ double __kernel_sin(double x, double y, int iy) { double z,r,v; int32_t ix; GET_HIGH_WORD(ix,x); ix &= 0x7fffffff; /* high word of x */ if(ix<0x3e400000) /* |x| < 2**-27 */ {if((int)x==0) return x;} /* generate inexact */ z = x*x; v = z*x; r = S2+z*(S3+z*(S4+z*(S5+z*S6))); if(iy==0) return x+v*(S1+z*r); else return x-((z*(half*y-v*r)-y)-v*S1); }