gonzui

    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: /* __kernel_sin( x, y, iy)
   14:  * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
   15:  * Input x is assumed to be bounded by ~pi/4 in magnitude.
   16:  * Input y is the tail of x.
   17:  * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). 
   18:  *
   19:  * Algorithm
   20:  *      1. Since sin(-x) = -sin(x), we need only to consider positive x. 
   21:  *      2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
   22:  *      3. sin(x) is approximated by a polynomial of degree 13 on
   23:  *         [0,pi/4]
   24:  *                           3            13
   25:  *           sin(x) ~ x + S1*x + ... + S6*x
   26:  *         where
   27:  *      
   28:  *      |sin(x)         2     4     6     8     10     12  |     -58
   29:  *      |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x  +S6*x   )| <= 2
   30:  *      |  x                                                   | 
   31:  * 
   32:  *      4. sin(x+y) = sin(x) + sin'(x')*y
   33:  *                  ~ sin(x) + (1-x*x/2)*y
   34:  *         For better accuracy, let 
   35:  *                   3      2      2      2      2
   36:  *              r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
   37:  *         then                   3    2
   38:  *              sin(x) = x + (S1*x + (x *(r-y/2)+y))
   39:  */
   40: 
   41: #include "math.h"
   42: #include "math_private.h"
   43: 
   44: static const double 
   45: half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
   46: S1  = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
   47: S2  =  8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
   48: S3  = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
   49: S4  =  2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
   50: S5  = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
   51: S6  =  1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
   52: 
   53: double
   54: __kernel_sin(double x, double y, int iy)
   55: {
   56:         double z,r,v;
   57:         int32_t ix;
   58:         GET_HIGH_WORD(ix,x);
   59:         ix &= 0x7fffffff;                      /* high word of x */
   60:         if(ix<0x3e400000)                      /* |x| < 2**-27 */
   61:            {if((int)x==0) return x;}           /* generate inexact */
   62:         z      =  x*x;
   63:         v      =  z*x;
   64:         r      =  S2+z*(S3+z*(S4+z*(S5+z*S6)));
   65:         if(iy==0) return x+v*(S1+z*r);
   66:         else      return x-((z*(half*y-v*r)-y)-v*S1);
   67: }