github.com/afumu/libc@v0.0.6/musl/src/math/atan2.c (about)

     1  /* origin: FreeBSD /usr/src/lib/msun/src/e_atan2.c */
     2  /*
     3   * ====================================================
     4   * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
     5   *
     6   * Developed at SunSoft, a Sun Microsystems, Inc. business.
     7   * Permission to use, copy, modify, and distribute this
     8   * software is freely granted, provided that this notice
     9   * is preserved.
    10   * ====================================================
    11   *
    12   */
    13  /* atan2(y,x)
    14   * Method :
    15   *      1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
    16   *      2. Reduce x to positive by (if x and y are unexceptional):
    17   *              ARG (x+iy) = arctan(y/x)           ... if x > 0,
    18   *              ARG (x+iy) = pi - arctan[y/(-x)]   ... if x < 0,
    19   *
    20   * Special cases:
    21   *
    22   *      ATAN2((anything), NaN ) is NaN;
    23   *      ATAN2(NAN , (anything) ) is NaN;
    24   *      ATAN2(+-0, +(anything but NaN)) is +-0  ;
    25   *      ATAN2(+-0, -(anything but NaN)) is +-pi ;
    26   *      ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
    27   *      ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
    28   *      ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
    29   *      ATAN2(+-INF,+INF ) is +-pi/4 ;
    30   *      ATAN2(+-INF,-INF ) is +-3pi/4;
    31   *      ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
    32   *
    33   * Constants:
    34   * The hexadecimal values are the intended ones for the following
    35   * constants. The decimal values may be used, provided that the
    36   * compiler will convert from decimal to binary accurately enough
    37   * to produce the hexadecimal values shown.
    38   */
    39  
    40  #include "libm.h"
    41  
    42  static const double
    43  pi     = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
    44  pi_lo  = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
    45  
    46  double atan2(double y, double x)
    47  {
    48  	double z;
    49  	uint32_t m,lx,ly,ix,iy;
    50  
    51  	if (isnan(x) || isnan(y))
    52  		return x+y;
    53  	EXTRACT_WORDS(ix, lx, x);
    54  	EXTRACT_WORDS(iy, ly, y);
    55  	if ((ix-0x3ff00000 | lx) == 0)  /* x = 1.0 */
    56  		return atan(y);
    57  	m = ((iy>>31)&1) | ((ix>>30)&2);  /* 2*sign(x)+sign(y) */
    58  	ix = ix & 0x7fffffff;
    59  	iy = iy & 0x7fffffff;
    60  
    61  	/* when y = 0 */
    62  	if ((iy|ly) == 0) {
    63  		switch(m) {
    64  		case 0:
    65  		case 1: return y;   /* atan(+-0,+anything)=+-0 */
    66  		case 2: return  pi; /* atan(+0,-anything) = pi */
    67  		case 3: return -pi; /* atan(-0,-anything) =-pi */
    68  		}
    69  	}
    70  	/* when x = 0 */
    71  	if ((ix|lx) == 0)
    72  		return m&1 ? -pi/2 : pi/2;
    73  	/* when x is INF */
    74  	if (ix == 0x7ff00000) {
    75  		if (iy == 0x7ff00000) {
    76  			switch(m) {
    77  			case 0: return  pi/4;   /* atan(+INF,+INF) */
    78  			case 1: return -pi/4;   /* atan(-INF,+INF) */
    79  			case 2: return  3*pi/4; /* atan(+INF,-INF) */
    80  			case 3: return -3*pi/4; /* atan(-INF,-INF) */
    81  			}
    82  		} else {
    83  			switch(m) {
    84  			case 0: return  0.0; /* atan(+...,+INF) */
    85  			case 1: return -0.0; /* atan(-...,+INF) */
    86  			case 2: return  pi;  /* atan(+...,-INF) */
    87  			case 3: return -pi;  /* atan(-...,-INF) */
    88  			}
    89  		}
    90  	}
    91  	/* |y/x| > 0x1p64 */
    92  	if (ix+(64<<20) < iy || iy == 0x7ff00000)
    93  		return m&1 ? -pi/2 : pi/2;
    94  
    95  	/* z = atan(|y/x|) without spurious underflow */
    96  	if ((m&2) && iy+(64<<20) < ix)  /* |y/x| < 0x1p-64, x<0 */
    97  		z = 0;
    98  	else
    99  		z = atan(fabs(y/x));
   100  	switch (m) {
   101  	case 0: return z;              /* atan(+,+) */
   102  	case 1: return -z;             /* atan(-,+) */
   103  	case 2: return pi - (z-pi_lo); /* atan(+,-) */
   104  	default: /* case 3 */
   105  		return (z-pi_lo) - pi; /* atan(-,-) */
   106  	}
   107  }