1 |
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2 /* |
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3 * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved. |
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4 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. |
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5 * |
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6 * This code is free software; you can redistribute it and/or modify it |
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7 * under the terms of the GNU General Public License version 2 only, as |
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8 * published by the Free Software Foundation. Oracle designates this |
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9 * particular file as subject to the "Classpath" exception as provided |
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10 * by Oracle in the LICENSE file that accompanied this code. |
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11 * |
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12 * This code is distributed in the hope that it will be useful, but WITHOUT |
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13 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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14 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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15 * version 2 for more details (a copy is included in the LICENSE file that |
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16 * accompanied this code). |
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17 * |
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18 * You should have received a copy of the GNU General Public License version |
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19 * 2 along with this work; if not, write to the Free Software Foundation, |
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20 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. |
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21 * |
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22 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA |
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23 * or visit www.oracle.com if you need additional information or have any |
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24 * questions. |
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25 */ |
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26 |
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27 /* asinh(x) |
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28 * Method : |
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29 * Based on |
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30 * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] |
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31 * we have |
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32 * asinh(x) := x if 1+x*x=1, |
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33 * := sign(x)*(log(x)+ln2)) for large |x|, else |
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34 * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else |
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35 * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) |
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36 */ |
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37 |
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38 #include "fdlibm.h" |
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39 |
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40 #ifdef __STDC__ |
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41 static const double |
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42 #else |
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43 static double |
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44 #endif |
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45 one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ |
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46 ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ |
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47 huge= 1.00000000000000000000e+300; |
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48 |
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49 #ifdef __STDC__ |
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50 double asinh(double x) |
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51 #else |
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52 double asinh(x) |
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53 double x; |
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54 #endif |
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55 { |
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56 double t,w; |
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57 int hx,ix; |
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58 hx = __HI(x); |
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59 ix = hx&0x7fffffff; |
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60 if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */ |
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61 if(ix< 0x3e300000) { /* |x|<2**-28 */ |
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62 if(huge+x>one) return x; /* return x inexact except 0 */ |
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63 } |
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64 if(ix>0x41b00000) { /* |x| > 2**28 */ |
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65 w = __ieee754_log(fabs(x))+ln2; |
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66 } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ |
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67 t = fabs(x); |
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68 w = __ieee754_log(2.0*t+one/(sqrt(x*x+one)+t)); |
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69 } else { /* 2.0 > |x| > 2**-28 */ |
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70 t = x*x; |
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71 w =log1p(fabs(x)+t/(one+sqrt(one+t))); |
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72 } |
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73 if(hx>0) return w; else return -w; |
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74 } |
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