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      1 /*	$NetBSD: s_atanl.c,v 1.8 2024/07/17 12:00:48 riastradh Exp $	*/
      2 
      3 /* FreeBSD: head/lib/msun/src/s_atan.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 SunPro, 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 #include <sys/cdefs.h>
     16 __RCSID("$NetBSD: s_atanl.c,v 1.8 2024/07/17 12:00:48 riastradh Exp $");
     17 
     18 #include "namespace.h"
     19 
     20 #include <float.h>
     21 #include <machine/ieee.h>
     22 
     23 #include "math.h"
     24 #include "math_private.h"
     25 
     26 #ifdef __HAVE_LONG_DOUBLE
     27 
     28 /*
     29  * See comments in s_atan.c.
     30  * Converted to long double by David Schultz <das (at) FreeBSD.ORG>.
     31  */
     32 
     33 __weak_alias(atanl, _atanl)
     34 
     35 #if LDBL_MANT_DIG == 64
     36 #include "../ld80/invtrig.h"
     37 #elif LDBL_MANT_DIG == 113
     38 #include "../ld128/invtrig.h"
     39 #else
     40 #error "Unsupported long double format"
     41 #endif
     42 
     43 #ifdef LDBL_IMPLICIT_NBIT
     44 #define	LDBL_NBIT	0
     45 #endif
     46 
     47 static const long double
     48 one   = 1.0,
     49 huge   = 1.0e300;
     50 
     51 long double
     52 atanl(long double x)
     53 {
     54 	union ieee_ext_u u;
     55 	long double w,s1,s2,z;
     56 	int id;
     57 	int16_t expsign, expt;
     58 	int32_t expman;
     59 
     60 	u.extu_ld = x;
     61 	expsign = GET_EXPSIGN(&u);
     62 	expt = expsign & 0x7fff;
     63 	if(expt >= ATAN_CONST) {	/* if |x| is large, atan(x)~=pi/2 */
     64 	    if(expt == BIAS + LDBL_MAX_EXP &&
     65 	       ((u.extu_frach&~LDBL_NBIT)|u.extu_fracl)!=0)
     66 		return x+x;		/* NaN */
     67 	    if(expsign>0) return  atanhi[3]+atanlo[3];
     68 	    else     return -atanhi[3]-atanlo[3];
     69 	}
     70 	/* Extract the exponent and the first few bits of the significand. */
     71 	/* XXX There should be a more convenient way to do this. */
     72 	expman = (expt << 8) | ((u.extu_frach >> (MANH_SIZE - 9)) & 0xff);
     73 	if (expman < ((BIAS - 2) << 8) + 0xc0) {	/* |x| < 0.4375 */
     74 	    if (expt < ATAN_LINEAR) {	/* if |x| is small, atanl(x)~=x */
     75 		if(huge+x>one) return x;	/* raise inexact */
     76 	    }
     77 	    id = -1;
     78 	} else {
     79 	x = fabsl(x);
     80 	if (expman < (BIAS << 8) + 0x30) {		/* |x| < 1.1875 */
     81 	    if (expman < ((BIAS - 1) << 8) + 0x60) {	/* 7/16 <=|x|<11/16 */
     82 		id = 0; x = (2.0*x-one)/(2.0+x);
     83 	    } else {			/* 11/16<=|x|< 19/16 */
     84 		id = 1; x  = (x-one)/(x+one);
     85 	    }
     86 	} else {
     87 	    if (expman < ((BIAS + 1) << 8) + 0x38) {	/* |x| < 2.4375 */
     88 		id = 2; x  = (x-1.5)/(one+1.5*x);
     89 	    } else {			/* 2.4375 <= |x| < 2^ATAN_CONST */
     90 		id = 3; x  = -1.0/x;
     91 	    }
     92 	}}
     93     /* end of argument reduction */
     94 	z = x*x;
     95 	w = z*z;
     96     /* break sum aT[i]z**(i+1) into odd and even poly */
     97 	s1 = z*T_even(w);
     98 	s2 = w*T_odd(w);
     99 	if (id<0) return x - x*(s1+s2);
    100 	else {
    101 	    z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
    102 	    return (expsign<0)? -z:z;
    103 	}
    104 }
    105 #endif
    106