kc3-lang/SDL/src/libm/e_atan2.c

Branch : - branch - v2.28 - tag -

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• Author : Ryan C. Gordon
  Date : 2015-04-20 12:22:44
  Hash : b72938c8
  Message : 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.

• src/libm/e_atan2.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.
   * ====================================================
   */
  
  /* __ieee754_atan2(y,x)
   * Method :
   *	1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
   *	2. Reduce x to positive by (if x and y are unexceptional):
   *		ARG (x+iy) = arctan(y/x)   	   ... if x > 0,
   *		ARG (x+iy) = pi - arctan[y/(-x)]   ... if x < 0,
   *
   * Special cases:
   *
   *	ATAN2((anything), NaN ) is NaN;
   *	ATAN2(NAN , (anything) ) is NaN;
   *	ATAN2(+-0, +(anything but NaN)) is +-0  ;
   *	ATAN2(+-0, -(anything but NaN)) is +-pi ;
   *	ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
   *	ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
   *	ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
   *	ATAN2(+-INF,+INF ) is +-pi/4 ;
   *	ATAN2(+-INF,-INF ) is +-3pi/4;
   *	ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
   *
   * 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
  tiny  = 1.0e-300,
  zero  = 0.0,
  pi_o_4  = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
  pi_o_2  = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
  pi      = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
  pi_lo   = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
  
  double attribute_hidden __ieee754_atan2(double y, double x)
  {
  	double z;
  	int32_t k,m,hx,hy,ix,iy;
  	u_int32_t lx,ly;
  
  	EXTRACT_WORDS(hx,lx,x);
  	ix = hx&0x7fffffff;
  	EXTRACT_WORDS(hy,ly,y);
  	iy = hy&0x7fffffff;
  	if(((ix|((lx|-(int32_t)lx)>>31))>0x7ff00000)||
  	   ((iy|((ly|-(int32_t)ly)>>31))>0x7ff00000))	/* x or y is NaN */
  	   return x+y;
  	if(((hx-0x3ff00000)|lx)==0) return atan(y);   /* x=1.0 */
  	m = ((hy>>31)&1)|((hx>>30)&2);	/* 2*sign(x)+sign(y) */
  
      /* when y = 0 */
  	if((iy|ly)==0) {
  	    switch(m) {
  		case 0:
  		case 1: return y; 	/* atan(+-0,+anything)=+-0 */
  		case 2: return  pi+tiny;/* atan(+0,-anything) = pi */
  		case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
  	    }
  	}
      /* when x = 0 */
  	if((ix|lx)==0) return (hy<0)?  -pi_o_2-tiny: pi_o_2+tiny;
  
      /* when x is INF */
  	if(ix==0x7ff00000) {
  	    if(iy==0x7ff00000) {
  		switch(m) {
  		    case 0: return  pi_o_4+tiny;/* atan(+INF,+INF) */
  		    case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
  		    case 2: return  3.0*pi_o_4+tiny;/* atan(+INF,-INF) */
  		    case 3: return -3.0*pi_o_4-tiny;/* atan(-INF,-INF) */
  		}
  	    } else {
  		switch(m) {
  		    case 0: return  zero  ;	/* atan(+...,+INF) */
  		    case 1: return -zero  ;	/* atan(-...,+INF) */
  		    case 2: return  pi+tiny  ;	/* atan(+...,-INF) */
  		    case 3: return -pi-tiny  ;	/* atan(-...,-INF) */
  		}
  	    }
  	}
      /* when y is INF */
  	if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
  
      /* compute y/x */
  	k = (iy-ix)>>20;
  	if(k > 60) z=pi_o_2+0.5*pi_lo; 	/* |y/x| >  2**60 */
  	else if(hx<0&&k<-60) z=0.0; 	/* |y|/x < -2**60 */
  	else z=atan(fabs(y/x));		/* safe to do y/x */
  	switch (m) {
  	    case 0: return       z  ;	/* atan(+,+) */
  	    case 1: {
  	    	      u_int32_t zh;
  		      GET_HIGH_WORD(zh,z);
  		      SET_HIGH_WORD(z,zh ^ 0x80000000);
  		    }
  		    return       z  ;	/* atan(-,+) */
  	    case 2: return  pi-(z-pi_lo);/* atan(+,-) */
  	    default: /* case 3 */
  	    	    return  (z-pi_lo)-pi;/* atan(-,-) */
  	}
  }