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

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• Hash : b72938c8
  Author :
  Date : 2015-04-20T12:22:44
  

  Windows: Always set the system timer resolution to 1ms by default.
  
  An existing hint lets apps that don't need the timer resolution changed avoid
  this, to save battery, etc, but this fixes several problems in timing, audio
  callbacks not firing fast enough, etc.
  
  Fixes Bugzilla #2944.
  

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• src/libm/s_atan.c

• /*
   * ====================================================
   * 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.
   * ====================================================
   */
  
  /* atan(x)
   * Method
   *   1. Reduce x to positive by atan(x) = -atan(-x).
   *   2. According to the integer k=4t+0.25 chopped, t=x, the argument
   *      is further reduced to one of the following intervals and the
   *      arctangent of t is evaluated by the corresponding formula:
   *
   *      [0,7/16]      atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
   *      [7/16,11/16]  atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
   *      [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
   *      [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
   *      [39/16,INF]   atan(x) = atan(INF) + atan( -1/t )
   *
   * Constants:
   * The hexadecimal values are the intended ones for the following
   * constants. The decimal values may be used, provided that the
   * compiler will convert from decimal to binary accurately enough
   * to produce the hexadecimal values shown.
   */
  
  #include "math_libm.h"
  #include "math_private.h"
  
  static const double atanhi[] = {
    4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
    7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
    9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
    1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
  };
  
  static const double atanlo[] = {
    2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
    3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
    1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
    6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
  };
  
  static const double aT[] = {
    3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
   -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
    1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
   -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
    9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
   -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
    6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
   -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
    4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
   -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
    1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
  };
  
  static const double
  one   = 1.0,
  huge   = 1.0e300;
  
  double atan(double x)
  {
  	double w,s1,s2,z;
  	int32_t ix,hx,id;
  
  	GET_HIGH_WORD(hx,x);
  	ix = hx&0x7fffffff;
  	if(ix>=0x44100000) {	/* if |x| >= 2^66 */
  	    u_int32_t low;
  	    GET_LOW_WORD(low,x);
  	    if(ix>0x7ff00000||
  		(ix==0x7ff00000&&(low!=0)))
  		return x+x;		/* NaN */
  	    if(hx>0) return  atanhi[3]+atanlo[3];
  	    else     return -atanhi[3]-atanlo[3];
  	} if (ix < 0x3fdc0000) {	/* |x| < 0.4375 */
  	    if (ix < 0x3e200000) {	/* |x| < 2^-29 */
  		if(huge+x>one) return x;	/* raise inexact */
  	    }
  	    id = -1;
  	} else {
  	x = fabs(x);
  	if (ix < 0x3ff30000) {		/* |x| < 1.1875 */
  	    if (ix < 0x3fe60000) {	/* 7/16 <=|x|<11/16 */
  		id = 0; x = (2.0*x-one)/(2.0+x);
  	    } else {			/* 11/16<=|x|< 19/16 */
  		id = 1; x  = (x-one)/(x+one);
  	    }
  	} else {
  	    if (ix < 0x40038000) {	/* |x| < 2.4375 */
  		id = 2; x  = (x-1.5)/(one+1.5*x);
  	    } else {			/* 2.4375 <= |x| < 2^66 */
  		id = 3; x  = -1.0/x;
  	    }
  	}}
      /* end of argument reduction */
  	z = x*x;
  	w = z*z;
      /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
  	s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
  	s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
  	if (id<0) return x - x*(s1+s2);
  	else {
  	    z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
  	    return (hx<0)? -z:z;
  	}
  }
  libm_hidden_def(atan)
  
  

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