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4973 | right-hear | 1 | /* Copyright (C) 1994 DJ Delorie, see COPYING.DJ for details */ |
2 | /* @(#)e_acosh.c 5.1 93/09/24 */ |
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3 | /* |
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4 | * ==================================================== |
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5 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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6 | * |
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7 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
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8 | * Permission to use, copy, modify, and distribute this |
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9 | * software is freely granted, provided that this notice |
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10 | * is preserved. |
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11 | * ==================================================== |
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12 | */ |
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13 | |||
14 | #if defined(LIBM_SCCS) && !defined(lint) |
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15 | static char rcsid[] = "$Id: e_acosh.c,v 1.6 1994/08/18 23:04:54 jtc Exp $"; |
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16 | #endif |
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17 | |||
18 | /* __ieee754_acosh(x) |
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19 | * Method : |
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20 | * Based on |
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21 | * acosh(x) = log [ x + sqrt(x*x-1) ] |
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22 | * we have |
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23 | * acosh(x) := log(x)+ln2, if x is large; else |
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24 | * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else |
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25 | * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. |
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26 | * |
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27 | * Special cases: |
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28 | * acosh(x) is NaN with signal if x<1. |
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29 | * acosh(NaN) is NaN without signal. |
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30 | */ |
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31 | |||
32 | #include "math.h" |
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33 | #include "math_private.h" |
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34 | |||
35 | #ifdef __STDC__ |
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36 | static const double |
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37 | #else |
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38 | static double |
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39 | #endif |
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40 | one = 1.0, |
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41 | ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ |
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42 | |||
43 | #ifdef __STDC__ |
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44 | double __ieee754_acosh(double x) |
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45 | #else |
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46 | double __ieee754_acosh(x) |
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47 | double x; |
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48 | #endif |
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49 | { |
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50 | double t; |
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51 | int32_t hx; |
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52 | u_int32_t lx; |
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53 | EXTRACT_WORDS(hx,lx,x); |
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54 | if(hx<0x3ff00000) { /* x < 1 */ |
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55 | return (x-x)/(x-x); |
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56 | } else if(hx >=0x41b00000) { /* x > 2**28 */ |
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57 | if(hx >=0x7ff00000) { /* x is inf of NaN */ |
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58 | return x+x; |
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59 | } else |
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60 | return __ieee754_log(x)+ln2; /* acosh(huge)=log(2x) */ |
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61 | } else if(((hx-0x3ff00000)|lx)==0) { |
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62 | return 0.0; /* acosh(1) = 0 */ |
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63 | } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ |
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64 | t=x*x; |
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65 | return __ieee754_log(2.0*x-one/(x+sqrt(t-one))); |
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66 | } else { /* 1 |
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67 | t = x-one; |
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68 | return log1p(t+sqrt(2.0*t+t*t)); |
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69 | } |
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70 | }2>>0x3ff00000)>1. |