/src/moddable/xs/tools/fdlibm/e_atan2.c

Source

/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunSoft, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice 
 * is preserved.
 * ====================================================
 *
 */

/* 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_private.h"

static volatile double
tiny  = 1.0e-300;
static const double
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 */
static volatile double
pi_lo   = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */

double
__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|-lx)>>31))>0x7ff00000)||
     ((iy|((ly|-ly)>>31))>0x7ff00000))  /* x or y is NaN */
      return nan_mix(x, y);
  if(hx==0x3ff00000&&lx==0) return s_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) {     /* |y/x| >  2**60 */
      z=pi_o_2+0.5*pi_lo;
      m&=1;
  }
  else if(hx<0&&k<-60) z=0.0;  /* 0 > |y|/x > -2**-60 */
  else z=s_atan(fabs(y/x));   /* safe to do y/x */
  switch (m) {
      case 0: return       z  ; /* atan(+,+) */
      case 1: return      -z  ; /* atan(-,+) */
      case 2: return  pi-(z-pi_lo);/* atan(+,-) */
      default: /* case 3 */
            return  (z-pi_lo)-pi;/* atan(-,-) */
  }
}

Coverage Report

Created: 2025-10-10 06:16

Line	Count	Source
1
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
14		/* atan2(y,x)
15		* Method :
16		* 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
17		* 2. Reduce x to positive by (if x and y are unexceptional):
18		* ARG (x+iy) = arctan(y/x) ... if x > 0,
19		* ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
20		*
21		* Special cases:
22		*
23		* ATAN2((anything), NaN ) is NaN;
24		* ATAN2(NAN , (anything) ) is NaN;
25		* ATAN2(+-0, +(anything but NaN)) is +-0 ;
26		* ATAN2(+-0, -(anything but NaN)) is +-pi ;
27		* ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
28		* ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
29		* ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
30		* ATAN2(+-INF,+INF ) is +-pi/4 ;
31		* ATAN2(+-INF,-INF ) is +-3pi/4;
32		* ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
33		*
34		* Constants:
35		* The hexadecimal values are the intended ones for the following
36		* constants. The decimal values may be used, provided that the
37		* compiler will convert from decimal to binary accurately enough
38		* to produce the hexadecimal values shown.
39		*/
40
41		#include "math_private.h"
42
43		static volatile double
44		tiny = 1.0e-300;
45		static const double
46		zero = 0.0,
47		pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
48		pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
49		pi = 3.1415926535897931160E+00; /* 0x400921FB, 0x54442D18 */
50		static volatile double
51		pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
52
53		double
54		__ieee754_atan2(double y, double x)
55	853k	{
56	853k	double z;
57	853k	int32_t k,m,hx,hy,ix,iy;
58	853k	u_int32_t lx,ly;
59
60	853k	EXTRACT_WORDS(hx,lx,x);
61	853k	ix = hx&0x7fffffff;
62	853k	EXTRACT_WORDS(hy,ly,y);
63	853k	iy = hy&0x7fffffff;
64	853k	if(((ix\|((lx\|-lx)>>31))>0x7ff00000)\|\|
65	664k	((iy\|((ly\|-ly)>>31))>0x7ff00000)) /* x or y is NaN */
66	348k	return nan_mix(x, y);
67	505k	if(hx==0x3ff00000&&lx==0) return s_atan(y); /* x=1.0 */
68	393k	m = ((hy>>31)&1)\|((hx>>30)&2); /* 2sign(x)+sign(y) /
69
70		/* when y = 0 */
71	393k	if((iy\|ly)==0) {
72	18.3k	switch(m) {
73	9.18k	case 0:
74	9.19k	case 1: return y; /* atan(+-0,+anything)=+-0 */
75	1	case 2: return pi+tiny;/* atan(+0,-anything) = pi */
76	9.18k	case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
77	18.3k	}
78	18.3k	}
79		/* when x = 0 */
80	375k	if((ix\|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
81
82		/* when x is INF */
83	330k	if(ix==0x7ff00000) {
84	83.9k	if(iy==0x7ff00000) {
85	18.3k	switch(m) {
86	9.18k	case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
87	1	case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
88	1	case 2: return 3.0pi_o_4+tiny;/atan(+INF,-INF)*/
89	9.18k	case 3: return -3.0pi_o_4-tiny;/atan(-INF,-INF)*/
90	18.3k	}
91	65.5k	} else {
92	65.5k	switch(m) {
93	14	case 0: return zero ; /* atan(+...,+INF) */
94	6	case 1: return -zero ; /* atan(-...,+INF) */
95	65.5k	case 2: return pi+tiny ; /* atan(+...,-INF) */
96	7	case 3: return -pi-tiny ; /* atan(-...,-INF) */
97	65.5k	}
98	65.5k	}
99	83.9k	}
100		/* when y is INF */
101	246k	if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
102
103		/* compute y/x */
104	246k	k = (iy-ix)>>20;
105	246k	if(k > 60) { /* \|y/x\| > 2*60 /
106	2	z=pi_o_2+0.5*pi_lo;
107	2	m&=1;
108	2	}
109	246k	else if(hx<0&&k<-60) z=0.0; /* 0 > \|y\|/x > -2*-60 /
110	246k	else z=s_atan(fabs(y/x)); /* safe to do y/x */
111	246k	switch (m) {
112	74.3k	case 0: return z ; /* atan(+,+) */
113	1	case 1: return -z ; /* atan(-,+) */
114	162k	case 2: return pi-(z-pi_lo);/* atan(+,-) */
115	9.18k	default: /* case 3 */
116	9.18k	return (z-pi_lo)-pi;/* atan(-,-) */
117	246k	}
118	246k	}