src/libm/e_atan2.c
author Philipp Wiesemann <philipp.wiesemann@arcor.de>
Sun, 28 Dec 2014 22:00:24 +0100
changeset 9301 7377a9a3aed6
parent 7678 286c42d7c5ed
child 11683 48bcba563d9c
permissions -rw-r--r--
Renamed README-emscripten.txt to README-emscripten.md.
     1 /*
     2  * ====================================================
     3  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
     4  *
     5  * Developed at SunPro, a Sun Microsystems, Inc. business.
     6  * Permission to use, copy, modify, and distribute this
     7  * software is freely granted, provided that this notice
     8  * is preserved.
     9  * ====================================================
    10  */
    11 
    12 /* __ieee754_atan2(y,x)
    13  * Method :
    14  *	1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
    15  *	2. Reduce x to positive by (if x and y are unexceptional):
    16  *		ARG (x+iy) = arctan(y/x)   	   ... if x > 0,
    17  *		ARG (x+iy) = pi - arctan[y/(-x)]   ... if x < 0,
    18  *
    19  * Special cases:
    20  *
    21  *	ATAN2((anything), NaN ) is NaN;
    22  *	ATAN2(NAN , (anything) ) is NaN;
    23  *	ATAN2(+-0, +(anything but NaN)) is +-0  ;
    24  *	ATAN2(+-0, -(anything but NaN)) is +-pi ;
    25  *	ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
    26  *	ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
    27  *	ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
    28  *	ATAN2(+-INF,+INF ) is +-pi/4 ;
    29  *	ATAN2(+-INF,-INF ) is +-3pi/4;
    30  *	ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
    31  *
    32  * Constants:
    33  * The hexadecimal values are the intended ones for the following
    34  * constants. The decimal values may be used, provided that the
    35  * compiler will convert from decimal to binary accurately enough
    36  * to produce the hexadecimal values shown.
    37  */
    38 
    39 #include "math_libm.h"
    40 #include "math_private.h"
    41 
    42 static const double
    43 tiny  = 1.0e-300,
    44 zero  = 0.0,
    45 pi_o_4  = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
    46 pi_o_2  = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
    47 pi      = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
    48 pi_lo   = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
    49 
    50 double attribute_hidden __ieee754_atan2(double y, double x)
    51 {
    52 	double z;
    53 	int32_t k,m,hx,hy,ix,iy;
    54 	u_int32_t lx,ly;
    55 
    56 	EXTRACT_WORDS(hx,lx,x);
    57 	ix = hx&0x7fffffff;
    58 	EXTRACT_WORDS(hy,ly,y);
    59 	iy = hy&0x7fffffff;
    60 	if(((ix|((lx|-(int32_t)lx)>>31))>0x7ff00000)||
    61 	   ((iy|((ly|-(int32_t)ly)>>31))>0x7ff00000))	/* x or y is NaN */
    62 	   return x+y;
    63 	if(((hx-0x3ff00000)|lx)==0) return atan(y);   /* x=1.0 */
    64 	m = ((hy>>31)&1)|((hx>>30)&2);	/* 2*sign(x)+sign(y) */
    65 
    66     /* when y = 0 */
    67 	if((iy|ly)==0) {
    68 	    switch(m) {
    69 		case 0:
    70 		case 1: return y; 	/* atan(+-0,+anything)=+-0 */
    71 		case 2: return  pi+tiny;/* atan(+0,-anything) = pi */
    72 		case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
    73 	    }
    74 	}
    75     /* when x = 0 */
    76 	if((ix|lx)==0) return (hy<0)?  -pi_o_2-tiny: pi_o_2+tiny;
    77 
    78     /* when x is INF */
    79 	if(ix==0x7ff00000) {
    80 	    if(iy==0x7ff00000) {
    81 		switch(m) {
    82 		    case 0: return  pi_o_4+tiny;/* atan(+INF,+INF) */
    83 		    case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
    84 		    case 2: return  3.0*pi_o_4+tiny;/* atan(+INF,-INF) */
    85 		    case 3: return -3.0*pi_o_4-tiny;/* atan(-INF,-INF) */
    86 		}
    87 	    } else {
    88 		switch(m) {
    89 		    case 0: return  zero  ;	/* atan(+...,+INF) */
    90 		    case 1: return -zero  ;	/* atan(-...,+INF) */
    91 		    case 2: return  pi+tiny  ;	/* atan(+...,-INF) */
    92 		    case 3: return -pi-tiny  ;	/* atan(-...,-INF) */
    93 		}
    94 	    }
    95 	}
    96     /* when y is INF */
    97 	if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
    98 
    99     /* compute y/x */
   100 	k = (iy-ix)>>20;
   101 	if(k > 60) z=pi_o_2+0.5*pi_lo; 	/* |y/x| >  2**60 */
   102 	else if(hx<0&&k<-60) z=0.0; 	/* |y|/x < -2**60 */
   103 	else z=atan(fabs(y/x));		/* safe to do y/x */
   104 	switch (m) {
   105 	    case 0: return       z  ;	/* atan(+,+) */
   106 	    case 1: {
   107 	    	      u_int32_t zh;
   108 		      GET_HIGH_WORD(zh,z);
   109 		      SET_HIGH_WORD(z,zh ^ 0x80000000);
   110 		    }
   111 		    return       z  ;	/* atan(-,+) */
   112 	    case 2: return  pi-(z-pi_lo);/* atan(+,-) */
   113 	    default: /* case 3 */
   114 	    	    return  (z-pi_lo)-pi;/* atan(-,-) */
   115 	}
   116 }