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      1 /* from: FreeBSD: head/lib/msun/src/e_acosh.c 176451 2008-02-22 02:30:36Z das */
      2 
      3 /* @(#)e_acosh.c 1.3 95/01/18 */
      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 __FBSDID("$FreeBSD$");
     18 
     19 /*
     20  * See e_acosh.c for complete comments.
     21  *
     22  * Converted to long double by David Schultz <das (at) FreeBSD.ORG> and
     23  * Bruce D. Evans.
     24  */
     25 
     26 #include <float.h>
     27 #ifdef __i386__
     28 #include <ieeefp.h>
     29 #endif
     30 
     31 #include "fpmath.h"
     32 #include "math.h"
     33 #include "math_private.h"
     34 
     35 /* EXP_LARGE is the threshold above which we use acosh(x) ~= log(2x). */
     36 #if LDBL_MANT_DIG == 64
     37 #define	EXP_LARGE	34
     38 #elif LDBL_MANT_DIG == 113
     39 #define	EXP_LARGE	58
     40 #else
     41 #error "Unsupported long double format"
     42 #endif
     43 
     44 #if LDBL_MAX_EXP != 0x4000
     45 /* We also require the usual expsign encoding. */
     46 #error "Unsupported long double format"
     47 #endif
     48 
     49 #define	BIAS	(LDBL_MAX_EXP - 1)
     50 
     51 static const double
     52 one	= 1.0;
     53 
     54 #if LDBL_MANT_DIG == 64
     55 static const union IEEEl2bits
     56 u_ln2 =  LD80C(0xb17217f7d1cf79ac, -1, 6.93147180559945309417e-1L);
     57 #define	ln2	u_ln2.e
     58 #elif LDBL_MANT_DIG == 113
     59 static const long double
     60 ln2 =  6.93147180559945309417232121458176568e-1L;	/* 0x162e42fefa39ef35793c7673007e6.0p-113 */
     61 #else
     62 #error "Unsupported long double format"
     63 #endif
     64 
     65 long double
     66 acoshl(long double x)
     67 {
     68 	long double t;
     69 	int16_t hx;
     70 
     71 	ENTERI();
     72 	GET_LDBL_EXPSIGN(hx, x);
     73 	if (hx < 0x3fff) {		/* x < 1, or misnormal */
     74 	    RETURNI((x-x)/(x-x));
     75 	} else if (hx >= BIAS + EXP_LARGE) { /* x >= LARGE */
     76 	    if (hx >= 0x7fff) {		/* x is inf, NaN or misnormal */
     77 	        RETURNI(x+x);
     78 	    } else
     79 		RETURNI(logl(x)+ln2);	/* acosh(huge)=log(2x), or misnormal */
     80 	} else if (hx == 0x3fff && x == 1) {
     81 	    RETURNI(0.0);		/* acosh(1) = 0 */
     82 	} else if (hx >= 0x4000) {	/* LARGE > x >= 2, or misnormal */
     83 	    t=x*x;
     84 	    RETURNI(logl(2.0*x-one/(x+sqrtl(t-one))));
     85 	} else {			/* 1<x<2 */
     86 	    t = x-one;
     87 	    RETURNI(log1pl(t+sqrtl(2.0*t+t*t)));
     88 	}
     89 }
     90