EDK2 doxygen online documents - Firmware Encoding Index 1
EDK2 doxygen online documents - Firmware Encoding Index

StdLib/LibC/Math/k_sin.c

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00001 /* @(#)k_sin.c 5.1 93/09/24 */
00002 /*
00003  * ====================================================
00004  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
00005  *
00006  * Developed at SunPro, a Sun Microsystems, Inc. business.
00007  * Permission to use, copy, modify, and distribute this
00008  * software is freely granted, provided that this notice
00009  * is preserved.
00010  * ====================================================
00011  */
00012 #include  <LibConfig.h>
00013 #include  <sys/EfiCdefs.h>
00014 #if defined(LIBM_SCCS) && !defined(lint)
00015 __RCSID("$NetBSD: k_sin.c,v 1.11 2002/05/26 22:01:53 wiz Exp $");
00016 #endif
00017 
00018 /* __kernel_sin( x, y, iy)
00019  * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
00020  * Input x is assumed to be bounded by ~pi/4 in magnitude.
00021  * Input y is the tail of x.
00022  * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
00023  *
00024  * Algorithm
00025  *  1. Since sin(-x) = -sin(x), we need only to consider positive x.
00026  *  2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
00027  *  3. sin(x) is approximated by a polynomial of degree 13 on
00028  *     [0,pi/4]
00029  *                 3            13
00030  *      sin(x) ~ x + S1*x + ... + S6*x
00031  *     where
00032  *
00033  *  |sin(x)         2     4     6     8     10     12  |     -58
00034  *  |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x  +S6*x   )| <= 2
00035  *  |  x                     |
00036  *
00037  *  4. sin(x+y) = sin(x) + sin'(x')*y
00038  *        ~ sin(x) + (1-x*x/2)*y
00039  *     For better accuracy, let
00040  *         3      2      2      2      2
00041  *    r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
00042  *     then                   3    2
00043  *    sin(x) = x + (S1*x + (x *(r-y/2)+y))
00044  */
00045 
00046 #include "math.h"
00047 #include "math_private.h"
00048 
00049 static const double
00050 half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
00051 S1  = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
00052 S2  =  8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
00053 S3  = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
00054 S4  =  2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
00055 S5  = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
00056 S6  =  1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
00057 
00058 double
00059 __kernel_sin(double x, double y, int iy)
00060 {
00061   double z,r,v;
00062   int32_t ix;
00063   GET_HIGH_WORD(ix,x);
00064   ix &= 0x7fffffff;     /* high word of x */
00065   if(ix<0x3e400000)     /* |x| < 2**-27 */
00066      {if((int)x==0) return x;}    /* generate inexact */
00067   z =  x*x;
00068   v =  z*x;
00069   r =  S2+z*(S3+z*(S4+z*(S5+z*S6)));
00070   if(iy==0) return x+v*(S1+z*r);
00071   else      return x-((z*(half*y-v*r)-y)-v*S1);
00072 }
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