1*1e651e1eSRoland Levillain 2*1e651e1eSRoland Levillain /* @(#)k_sin.c 1.3 95/01/18 */ 3*1e651e1eSRoland Levillain /* 4*1e651e1eSRoland Levillain * ==================================================== 5*1e651e1eSRoland Levillain * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6*1e651e1eSRoland Levillain * 7*1e651e1eSRoland Levillain * Developed at SunSoft, a Sun Microsystems, Inc. business. 8*1e651e1eSRoland Levillain * Permission to use, copy, modify, and distribute this 9*1e651e1eSRoland Levillain * software is freely granted, provided that this notice 10*1e651e1eSRoland Levillain * is preserved. 11*1e651e1eSRoland Levillain * ==================================================== 12*1e651e1eSRoland Levillain */ 13*1e651e1eSRoland Levillain 14*1e651e1eSRoland Levillain /* __kernel_sin( x, y, iy) 15*1e651e1eSRoland Levillain * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854 16*1e651e1eSRoland Levillain * Input x is assumed to be bounded by ~pi/4 in magnitude. 17*1e651e1eSRoland Levillain * Input y is the tail of x. 18*1e651e1eSRoland Levillain * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). 19*1e651e1eSRoland Levillain * 20*1e651e1eSRoland Levillain * Algorithm 21*1e651e1eSRoland Levillain * 1. Since ieee_sin(-x) = -ieee_sin(x), we need only to consider positive x. 22*1e651e1eSRoland Levillain * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0. 23*1e651e1eSRoland Levillain * 3. ieee_sin(x) is approximated by a polynomial of degree 13 on 24*1e651e1eSRoland Levillain * [0,pi/4] 25*1e651e1eSRoland Levillain * 3 13 26*1e651e1eSRoland Levillain * sin(x) ~ x + S1*x + ... + S6*x 27*1e651e1eSRoland Levillain * where 28*1e651e1eSRoland Levillain * 29*1e651e1eSRoland Levillain * |ieee_sin(x) 2 4 6 8 10 12 | -58 30*1e651e1eSRoland Levillain * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2 31*1e651e1eSRoland Levillain * | x | 32*1e651e1eSRoland Levillain * 33*1e651e1eSRoland Levillain * 4. ieee_sin(x+y) = ieee_sin(x) + sin'(x')*y 34*1e651e1eSRoland Levillain * ~ ieee_sin(x) + (1-x*x/2)*y 35*1e651e1eSRoland Levillain * For better accuracy, let 36*1e651e1eSRoland Levillain * 3 2 2 2 2 37*1e651e1eSRoland Levillain * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) 38*1e651e1eSRoland Levillain * then 3 2 39*1e651e1eSRoland Levillain * sin(x) = x + (S1*x + (x *(r-y/2)+y)) 40*1e651e1eSRoland Levillain */ 41*1e651e1eSRoland Levillain 42*1e651e1eSRoland Levillain #include "fdlibm.h" 43*1e651e1eSRoland Levillain 44*1e651e1eSRoland Levillain #ifdef __STDC__ 45*1e651e1eSRoland Levillain static const double 46*1e651e1eSRoland Levillain #else 47*1e651e1eSRoland Levillain static double 48*1e651e1eSRoland Levillain #endif 49*1e651e1eSRoland Levillain half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ 50*1e651e1eSRoland Levillain S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ 51*1e651e1eSRoland Levillain S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ 52*1e651e1eSRoland Levillain S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ 53*1e651e1eSRoland Levillain S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ 54*1e651e1eSRoland Levillain S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ 55*1e651e1eSRoland Levillain S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */ 56*1e651e1eSRoland Levillain 57*1e651e1eSRoland Levillain #ifdef __STDC__ __kernel_sin(double x,double y,int iy)58*1e651e1eSRoland Levillain double __kernel_sin(double x, double y, int iy) 59*1e651e1eSRoland Levillain #else 60*1e651e1eSRoland Levillain double __kernel_sin(x, y, iy) 61*1e651e1eSRoland Levillain double x,y; int iy; /* iy=0 if y is zero */ 62*1e651e1eSRoland Levillain #endif 63*1e651e1eSRoland Levillain { 64*1e651e1eSRoland Levillain double z,r,v; 65*1e651e1eSRoland Levillain int ix; 66*1e651e1eSRoland Levillain ix = __HI(x)&0x7fffffff; /* high word of x */ 67*1e651e1eSRoland Levillain if(ix<0x3e400000) /* |x| < 2**-27 */ 68*1e651e1eSRoland Levillain {if((int)x==0) return x;} /* generate inexact */ 69*1e651e1eSRoland Levillain z = x*x; 70*1e651e1eSRoland Levillain v = z*x; 71*1e651e1eSRoland Levillain r = S2+z*(S3+z*(S4+z*(S5+z*S6))); 72*1e651e1eSRoland Levillain if(iy==0) return x+v*(S1+z*r); 73*1e651e1eSRoland Levillain else return x-((z*(half*y-v*r)-y)-v*S1); 74*1e651e1eSRoland Levillain } 75