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      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 #include  <LibConfig.h>
     13 #include  <sys/EfiCdefs.h>
     14 #if defined(LIBM_SCCS) && !defined(lint)
     15 __RCSID("$NetBSD: k_sin.c,v 1.11 2002/05/26 22:01:53 wiz 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 static const double
     50 half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
     51 S1  = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
     52 S2  =  8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
     53 S3  = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
     54 S4  =  2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
     55 S5  = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
     56 S6  =  1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
     57 
     58 double
     59 __kernel_sin(double x, double y, int iy)
     60 {
     61   double z,r,v;
     62   int32_t ix;
     63   GET_HIGH_WORD(ix,x);
     64   ix &= 0x7fffffff;     /* high word of x */
     65   if(ix<0x3e400000)     /* |x| < 2**-27 */
     66      {if((int)x==0) return x;}    /* generate inexact */
     67   z =  x*x;
     68   v =  z*x;
     69   r =  S2+z*(S3+z*(S4+z*(S5+z*S6)));
     70   if(iy==0) return x+v*(S1+z*r);
     71   else      return x-((z*(half*y-v*r)-y)-v*S1);
     72 }
     73