| 1/* from: FreeBSD: head/lib/msun/src/e_atanh.c 176451 2008-02-22 02:30:36Z das */
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1 2/* @(#)e_atanh.c 1.3 95/01/18 */ 3/* 4 * ==================================================== 5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6 * 7 * Developed at SunSoft, a Sun Microsystems, Inc. business. 8 * Permission to use, copy, modify, and distribute this 9 * software is freely granted, provided that this notice 10 * is preserved. 11 * ==================================================== 12 * 13 */ 14 15#include <sys/cdefs.h>
| 2 3/* @(#)e_atanh.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>
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16__FBSDID("$FreeBSD: head/lib/msun/src/e_atanh.c 176451 2008-02-22 02:30:36Z das $");
| 17__FBSDID("$FreeBSD: head/lib/msun/src/e_atanhl.c 251599 2013-06-10 06:04:58Z das $");
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17
| 18
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18/* __ieee754_atanh(x) 19 * Method : 20 * 1.Reduced x to positive by atanh(-x) = -atanh(x) 21 * 2.For x>=0.5 22 * 1 2x x 23 * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) 24 * 2 1 - x 1 - x 25 * 26 * For x<0.5 27 * atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
| 19/* 20 * See e_atanh.c for complete comments.
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28 *
| 21 *
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29 * Special cases: 30 * atanh(x) is NaN if |x| > 1 with signal; 31 * atanh(NaN) is that NaN with no signal; 32 * atanh(+-1) is +-INF with signal. 33 *
| 22 * Converted to long double by David Schultz <das@FreeBSD.ORG> and 23 * Bruce D. Evans.
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34 */ 35
| 24 */ 25
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| 26#include <float.h> 27#ifdef __i386__ 28#include <ieeefp.h> 29#endif 30 31#include "fpmath.h"
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36#include "math.h" 37#include "math_private.h" 38
| 32#include "math.h" 33#include "math_private.h" 34
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| 35/* EXP_TINY is the threshold below which we use atanh(x) ~= x. */ 36#if LDBL_MANT_DIG == 64 37#define EXP_TINY -34 38#elif LDBL_MANT_DIG == 113 39#define EXP_TINY -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
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39static const double one = 1.0, huge = 1e300; 40static const double zero = 0.0; 41
| 51static const double one = 1.0, huge = 1e300; 52static const double zero = 0.0; 53
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42double 43__ieee754_atanh(double x)
| 54long double 55atanhl(long double x)
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44{
| 56{
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45 double t; 46 int32_t hx,ix; 47 u_int32_t lx; 48 EXTRACT_WORDS(hx,lx,x); 49 ix = hx&0x7fffffff; 50 if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */ 51 return (x-x)/(x-x); 52 if(ix==0x3ff00000) 53 return x/zero; 54 if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */ 55 SET_HIGH_WORD(x,ix); 56 if(ix<0x3fe00000) { /* x < 0.5 */
| 57 long double t; 58 uint16_t hx, ix; 59 60 ENTERI(); 61 GET_LDBL_EXPSIGN(hx, x); 62 ix = hx & 0x7fff; 63 if (ix >= 0x3fff) /* |x| >= 1, or NaN or misnormal */ 64 RETURNI(fabsl(x) == 1 ? x / zero : (x - x) / (x - x)); 65 if (ix < BIAS + EXP_TINY && (huge + x) > zero) 66 RETURNI(x); /* x is tiny */ 67 SET_LDBL_EXPSIGN(x, ix); 68 if (ix < 0x3ffe) { /* |x| < 0.5, or misnormal */
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57 t = x+x;
| 69 t = x+x;
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58 t = 0.5*log1p(t+t*x/(one-x));
| 70 t = 0.5*log1pl(t+t*x/(one-x));
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59 } else
| 71 } else
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60 t = 0.5*log1p((x+x)/(one-x)); 61 if(hx>=0) return t; else return -t;
| 72 t = 0.5*log1pl((x+x)/(one-x)); 73 RETURNI((hx & 0x8000) == 0 ? t : -t);
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62}
| 74}
|