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

Branch : - branch - v2.28 - tag -

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  Commit

• Author : Pierre-Loup A. Griffais
  Date : 2014-09-11 19:24:42
  Hash : 24c86b55
  Message : [X11] Reconcile logical keyboard state with physical state on FocusIn since the window system doesn't do it for us like other platforms. This prevents sticky keys and missed keys when going in and out of focus, for example Alt would appear to stick if switching away from an SDL app with Alt-Tab and had to be pressed again. CR: Sam

• 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)