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      1 /*	$NetBSD: e_atan2l.c,v 1.2 2024/01/23 15:45:07 christos Exp $	*/
      2 /* @(#)e_atan2.c 1.3 95/01/18 */
      3 /* FreeBSD: head/lib/msun/src/e_atan2.c 176451 2008-02-22 02:30:36Z das */
      4 /*
      5  * ====================================================
      6  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
      7  *
      8  * Developed at SunSoft, a Sun Microsystems, Inc. business.
      9  * Permission to use, copy, modify, and distribute this
     10  * software is freely granted, provided that this notice
     11  * is preserved.
     12  * ====================================================
     13  *
     14  */
     15 
     16 #include <sys/cdefs.h>
     17 __RCSID("$NetBSD: e_atan2l.c,v 1.2 2024/01/23 15:45:07 christos Exp $");
     18 
     19 /*
     20  * See comments in e_atan2.c.
     21  * Converted to long double by David Schultz <das (at) FreeBSD.ORG>.
     22  */
     23 
     24 #include "namespace.h"
     25 
     26 #ifdef __weak_alias
     27 __weak_alias(atan2l, _atan2l)
     28 #endif
     29 
     30 #include <float.h>
     31 #include <machine/ieee.h>
     32 
     33 #include "math.h"
     34 #include "math_private.h"
     35 
     36 #ifdef __HAVE_LONG_DOUBLE
     37 
     38 #if LDBL_MANT_DIG == 64
     39 #include "../ld80/invtrig.h"
     40 #elif LDBL_MANT_DIG == 113
     41 #include "../ld128/invtrig.h"
     42 #else
     43 #error "Unsupported long double format"
     44 #endif
     45 
     46 #ifdef LDBL_IMPLICIT_NBIT
     47 #define	LDBL_NBIT	0
     48 #endif
     49 
     50 static volatile long double
     51 tiny  = 1.0e-300;
     52 static const long double
     53 zero  = 0.0;
     54 
     55 #ifdef __i386__
     56 /* XXX Work around the fact that gcc truncates long double constants on i386 */
     57 static volatile double
     58 pi1 =  3.14159265358979311600e+00,	/*  0x1.921fb54442d18p+1  */
     59 pi2 =  1.22514845490862001043e-16;	/*  0x1.1a80000000000p-53 */
     60 #define	pi	((long double)pi1 + pi2)
     61 #else
     62 static const long double
     63 pi =  3.14159265358979323846264338327950280e+00L;
     64 #endif
     65 
     66 long double
     67 atan2l(long double y, long double x)
     68 {
     69 	union ieee_ext_u ux, uy;
     70 	long double z;
     71 	int32_t k,m;
     72 	int16_t exptx, expsignx, expty, expsigny;
     73 
     74 	uy.extu_ld = y;
     75 	expsigny = GET_EXPSIGN(&uy);
     76 	expty = expsigny & 0x7fff;
     77 	ux.extu_ld = x;
     78 	expsignx = GET_EXPSIGN(&ux);
     79 	exptx = expsignx & 0x7fff;
     80 
     81 	if ((exptx==BIAS+LDBL_MAX_EXP &&
     82 	     ((ux.extu_frach&~LDBL_NBIT)|ux.extu_fracl)!=0) ||	/* x is NaN */
     83 	    (expty==BIAS+LDBL_MAX_EXP &&
     84 	     ((uy.extu_frach&~LDBL_NBIT)|uy.extu_fracl)!=0))	/* y is NaN */
     85 	    return nan_mix(x, y);
     86 	if (expsignx==BIAS && ((ux.extu_frach&~LDBL_NBIT)|ux.extu_fracl)==0)
     87 	    return atanl(y);					/* x=1.0 */
     88 	m = ((expsigny>>15)&1)|((expsignx>>14)&2);	/* 2*sign(x)+sign(y) */
     89 
     90     /* when y = 0 */
     91 	if(expty==0 && ((uy.extu_frach&~LDBL_NBIT)|uy.extu_fracl)==0) {
     92 	    switch(m) {
     93 		case 0:
     94 		case 1: return y; 	/* atan(+-0,+anything)=+-0 */
     95 		case 2: return  pi+tiny;/* atan(+0,-anything) = pi */
     96 		case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
     97 	    }
     98 	}
     99     /* when x = 0 */
    100 	if(exptx==0 && ((ux.extu_frach&~LDBL_NBIT)|ux.extu_fracl)==0)
    101 	    return (expsigny<0)?  -pio2_hi-tiny: pio2_hi+tiny;
    102 
    103     /* when x is INF */
    104 	if(exptx==BIAS+LDBL_MAX_EXP) {
    105 	    if(expty==BIAS+LDBL_MAX_EXP) {
    106 		switch(m) {
    107 		    case 0: return  pio2_hi*0.5+tiny;/* atan(+INF,+INF) */
    108 		    case 1: return -pio2_hi*0.5-tiny;/* atan(-INF,+INF) */
    109 		    case 2: return  1.5*pio2_hi+tiny;/*atan(+INF,-INF)*/
    110 		    case 3: return -1.5*pio2_hi-tiny;/*atan(-INF,-INF)*/
    111 		}
    112 	    } else {
    113 		switch(m) {
    114 		    case 0: return  zero  ;	/* atan(+...,+INF) */
    115 		    case 1: return -zero  ;	/* atan(-...,+INF) */
    116 		    case 2: return  pi+tiny  ;	/* atan(+...,-INF) */
    117 		    case 3: return -pi-tiny  ;	/* atan(-...,-INF) */
    118 		}
    119 	    }
    120 	}
    121     /* when y is INF */
    122 	if(expty==BIAS+LDBL_MAX_EXP)
    123 	    return (expsigny<0)? -pio2_hi-tiny: pio2_hi+tiny;
    124 
    125     /* compute y/x */
    126 	k = expty-exptx;
    127 	if(k > LDBL_MANT_DIG+2) {			/* |y/x| huge */
    128 	    z=pio2_hi+pio2_lo;
    129 	    m&=1;
    130 	}
    131 	else if(expsignx<0&&k<-LDBL_MANT_DIG-2) z=0.0; 	/* |y/x| tiny, x<0 */
    132 	else z=atanl(fabsl(y/x));		/* safe to do y/x */
    133 	switch (m) {
    134 	    case 0: return       z  ;	/* atan(+,+) */
    135 	    case 1: return      -z  ;	/* atan(-,+) */
    136 	    case 2: return  pi-(z-pi_lo);/* atan(+,-) */
    137 	    default: /* case 3 */
    138 	    	    return  (z-pi_lo)-pi;/* atan(-,-) */
    139 	}
    140 }
    141 
    142 #else
    143 
    144 long double
    145 atan2l(long double y, long double x)
    146 {
    147 	return atan2(y, x);
    148 }
    149 
    150 #endif
    151