src/libm/e_atan2.c
author Sam Lantinga <slouken@libsdl.org>
Fri, 26 Aug 2016 12:18:08 -0700
changeset 10226 cb13d22b7f09
parent 7678 286c42d7c5ed
child 11683 48bcba563d9c
permissions -rw-r--r--
Added SDL_PrivateJoystickAdded() and SDL_PrivateJoystickRemoved()
Updated the removal code to iterate over all joystick add messages instead of just the first one.
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/*
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 * ====================================================
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 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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 *
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 * Developed at SunPro, a Sun Microsystems, Inc. business.
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 * Permission to use, copy, modify, and distribute this
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 * software is freely granted, provided that this notice
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 * is preserved.
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 * ====================================================
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 */
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/* __ieee754_atan2(y,x)
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 * Method :
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 *	1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
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 *	2. Reduce x to positive by (if x and y are unexceptional):
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 *		ARG (x+iy) = arctan(y/x)   	   ... if x > 0,
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 *		ARG (x+iy) = pi - arctan[y/(-x)]   ... if x < 0,
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 *
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 * Special cases:
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 *
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 *	ATAN2((anything), NaN ) is NaN;
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 *	ATAN2(NAN , (anything) ) is NaN;
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 *	ATAN2(+-0, +(anything but NaN)) is +-0  ;
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 *	ATAN2(+-0, -(anything but NaN)) is +-pi ;
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 *	ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
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 *	ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
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 *	ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
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 *	ATAN2(+-INF,+INF ) is +-pi/4 ;
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 *	ATAN2(+-INF,-INF ) is +-3pi/4;
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 *	ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
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 *
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 * Constants:
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 * The hexadecimal values are the intended ones for the following
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 * constants. The decimal values may be used, provided that the
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 * compiler will convert from decimal to binary accurately enough
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 * to produce the hexadecimal values shown.
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 */
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#include "math_libm.h"
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#include "math_private.h"
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static const double
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tiny  = 1.0e-300,
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zero  = 0.0,
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pi_o_4  = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
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pi_o_2  = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
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pi      = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
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pi_lo   = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
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double attribute_hidden __ieee754_atan2(double y, double x)
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{
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	double z;
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	int32_t k,m,hx,hy,ix,iy;
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	u_int32_t lx,ly;
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	EXTRACT_WORDS(hx,lx,x);
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	ix = hx&0x7fffffff;
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	EXTRACT_WORDS(hy,ly,y);
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	iy = hy&0x7fffffff;
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	if(((ix|((lx|-(int32_t)lx)>>31))>0x7ff00000)||
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	   ((iy|((ly|-(int32_t)ly)>>31))>0x7ff00000))	/* x or y is NaN */
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	   return x+y;
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	if(((hx-0x3ff00000)|lx)==0) return atan(y);   /* x=1.0 */
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	m = ((hy>>31)&1)|((hx>>30)&2);	/* 2*sign(x)+sign(y) */
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    /* when y = 0 */
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	if((iy|ly)==0) {
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	    switch(m) {
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		case 0:
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		case 1: return y; 	/* atan(+-0,+anything)=+-0 */
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		case 2: return  pi+tiny;/* atan(+0,-anything) = pi */
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		case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
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	    }
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	}
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    /* when x = 0 */
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	if((ix|lx)==0) return (hy<0)?  -pi_o_2-tiny: pi_o_2+tiny;
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    /* when x is INF */
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	if(ix==0x7ff00000) {
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	    if(iy==0x7ff00000) {
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		switch(m) {
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		    case 0: return  pi_o_4+tiny;/* atan(+INF,+INF) */
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		    case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
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		    case 2: return  3.0*pi_o_4+tiny;/* atan(+INF,-INF) */
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		    case 3: return -3.0*pi_o_4-tiny;/* atan(-INF,-INF) */
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		}
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	    } else {
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		switch(m) {
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		    case 0: return  zero  ;	/* atan(+...,+INF) */
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		    case 1: return -zero  ;	/* atan(-...,+INF) */
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		    case 2: return  pi+tiny  ;	/* atan(+...,-INF) */
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		    case 3: return -pi-tiny  ;	/* atan(-...,-INF) */
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		}
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	    }
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	}
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    /* when y is INF */
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	if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
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    /* compute y/x */
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	k = (iy-ix)>>20;
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	if(k > 60) z=pi_o_2+0.5*pi_lo; 	/* |y/x| >  2**60 */
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	else if(hx<0&&k<-60) z=0.0; 	/* |y|/x < -2**60 */
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	else z=atan(fabs(y/x));		/* safe to do y/x */
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	switch (m) {
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	    case 0: return       z  ;	/* atan(+,+) */
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	    case 1: {
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	    	      u_int32_t zh;
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		      GET_HIGH_WORD(zh,z);
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		      SET_HIGH_WORD(z,zh ^ 0x80000000);
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		    }
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		    return       z  ;	/* atan(-,+) */
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	    case 2: return  pi-(z-pi_lo);/* atan(+,-) */
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	    default: /* case 3 */
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	    	    return  (z-pi_lo)-pi;/* atan(-,-) */
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	}
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}