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      1 /*	$NetBSD: e_asinl.c,v 1.5 2024/06/09 13:35:38 riastradh Exp $	*/
      2 
      3 /* FreeBSD: head/lib/msun/src/e_asin.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 #include <sys/cdefs.h>
     16 __RCSID("$NetBSD: e_asinl.c,v 1.5 2024/06/09 13:35:38 riastradh Exp $");
     17 
     18 /*
     19  * See comments in e_asin.c.
     20  * Converted to long double by David Schultz <das (at) FreeBSD.ORG>.
     21  */
     22 
     23 #include "namespace.h"
     24 
     25 #include <float.h>
     26 #include <machine/ieee.h>
     27 
     28 #include "math.h"
     29 #include "math_private.h"
     30 
     31 #ifdef __HAVE_LONG_DOUBLE
     32 
     33 __weak_alias(asinl, _asinl)
     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 =  1.00000000000000000000e+00,
     49 huge = 1.000e+300;
     50 
     51 long double
     52 asinl(long double x)
     53 {
     54 	union ieee_ext_u u;
     55 	long double t=0.0,w,p,q,c,r,s;
     56 	int16_t expsign, expt;
     57 	u.extu_ld = x;
     58 	expsign = GET_EXPSIGN(&u);
     59 	expt = expsign & 0x7fff;
     60 	if(expt >= BIAS) {		/* |x|>= 1 */
     61 		if(expt==BIAS && ((u.extu_frach&~LDBL_NBIT)|u.extu_fracl)==0)
     62 		    /* asin(1)=+-pi/2 with inexact */
     63 		    return x*pio2_hi+x*pio2_lo;
     64 	    return (x-x)/(x-x);		/* asin(|x|>1) is NaN */
     65 	} else if (expt<BIAS-1) {	/* |x|<0.5 */
     66 	    if(expt<ASIN_LINEAR) {	/* if |x| is small, asinl(x)=x */
     67 		if(huge+x>one) return x;/* return x with inexact if x!=0*/
     68 	    }
     69 	    t = x*x;
     70 	    p = P(t);
     71 	    q = Q(t);
     72 	    w = p/q;
     73 	    return x+x*w;
     74 	}
     75 	/* 1> |x|>= 0.5 */
     76 	w = one-fabsl(x);
     77 	t = w*0.5;
     78 	p = P(t);
     79 	q = Q(t);
     80 	s = sqrtl(t);
     81 	if(u.extu_frach>=THRESH) { 	/* if |x| is close to 1 */
     82 	    w = p/q;
     83 	    t = pio2_hi-(2.0*(s+s*w)-pio2_lo);
     84 	} else {
     85 	    u.extu_ld = s;
     86 	    u.extu_fracl = 0;
     87 	    w = u.extu_ld;
     88 	    c  = (t-w*w)/(s+w);
     89 	    r  = p/q;
     90 	    p  = 2.0*s*r-(pio2_lo-2.0*c);
     91 	    q  = pio4_hi-2.0*w;
     92 	    t  = pio4_hi-(p-q);
     93 	}
     94 	if(expsign>0) return t; else return -t;
     95 }
     96 #endif
     97