kc3-lang/SDL/src/libm/k_sin.c

Branch : - branch - v2.28 - tag -

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  Commit

• Author : Gabriel Jacobo
  Date : 2013-11-29 10:06:08
  Hash : f848adff
  Message : Improve Android pause/resume behavior.

• src/libm/k_sin.c

• /* @(#)k_sin.c 5.1 93/09/24 */
  /*
   * ====================================================
   * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   *
   * Developed at SunPro, a Sun Microsystems, Inc. business.
   * Permission to use, copy, modify, and distribute this
   * software is freely granted, provided that this notice
   * is preserved.
   * ====================================================
   */
  
  #if defined(LIBM_SCCS) && !defined(lint)
  static const char rcsid[] =
      "$NetBSD: k_sin.c,v 1.8 1995/05/10 20:46:31 jtc Exp $";
  #endif
  
  /* __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 "math_libm.h"
  #include "math_private.h"
  
  #ifdef __STDC__
  static const double
  #else
  static double
  #endif
    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 */
  
  #ifdef __STDC__
  double attribute_hidden
  __kernel_sin(double x, double y, int iy)
  #else
  double attribute_hidden
  __kernel_sin(x, y, iy)
       double x, y;
       int iy;                    /* iy=0 if y is zero */
  #endif
  {
      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);
  }