1 | |
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2 | /* @(#)s_asinh.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 | |
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14 | /* |
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15 | FUNCTION |
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16 | <<asinh>>, <<asinhf>>---inverse hyperbolic sine |
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17 | |
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18 | INDEX |
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19 | asinh |
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20 | INDEX |
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21 | asinhf |
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22 | |
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23 | SYNOPSIS |
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24 | #include <math.h> |
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25 | double asinh(double <[x]>); |
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26 | float asinhf(float <[x]>); |
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27 | |
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28 | DESCRIPTION |
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29 | <<asinh>> calculates the inverse hyperbolic sine of <[x]>. |
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30 | <<asinh>> is defined as |
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31 | @ifnottex |
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32 | . sgn(<[x]>) * log(abs(<[x]>) + sqrt(1+<[x]>*<[x]>)) |
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33 | @end ifnottex |
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34 | @tex |
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35 | $$sign(x) \times ln\Bigl(|x| + \sqrt{1+x^2}\Bigr)$$ |
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36 | @end tex |
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37 | |
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38 | <<asinhf>> is identical, other than taking and returning floats. |
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39 | |
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40 | RETURNS |
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41 | <<asinh>> and <<asinhf>> return the calculated value. |
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42 | |
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43 | PORTABILITY |
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44 | Neither <<asinh>> nor <<asinhf>> are ANSI C. |
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45 | |
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46 | */ |
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47 | |
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48 | /* asinh(x) |
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49 | * Method : |
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50 | * Based on |
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51 | * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] |
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52 | * we have |
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53 | * asinh(x) := x if 1+x*x=1, |
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54 | * := sign(x)*(log(x)+ln2)) for large |x|, else |
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55 | * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else |
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56 | * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) |
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57 | */ |
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58 | |
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59 | #include "fdlibm.h" |
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60 | |
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61 | #ifndef _DOUBLE_IS_32BITS |
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62 | |
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63 | #ifdef __STDC__ |
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64 | static const double |
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65 | #else |
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66 | static double |
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67 | #endif |
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68 | one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ |
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69 | ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ |
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70 | huge= 1.00000000000000000000e+300; |
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71 | |
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72 | #ifdef __STDC__ |
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73 | double asinh(double x) |
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74 | #else |
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75 | double asinh(x) |
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76 | double x; |
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77 | #endif |
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78 | { |
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79 | double t,w; |
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80 | __int32_t hx,ix; |
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81 | GET_HIGH_WORD(hx,x); |
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82 | ix = hx&0x7fffffff; |
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83 | if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */ |
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84 | if(ix< 0x3e300000) { /* |x|<2**-28 */ |
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85 | if(huge+x>one) return x; /* return x inexact except 0 */ |
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86 | } |
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87 | if(ix>0x41b00000) { /* |x| > 2**28 */ |
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88 | w = __ieee754_log(fabs(x))+ln2; |
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89 | } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ |
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90 | t = fabs(x); |
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91 | w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t)); |
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92 | } else { /* 2.0 > |x| > 2**-28 */ |
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93 | t = x*x; |
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94 | w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t))); |
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95 | } |
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96 | if(hx>0) return w; else return -w; |
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97 | } |
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98 | |
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99 | #endif /* _DOUBLE_IS_32BITS */ |
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