C-XSC - A C++ Class Library for Extended Scientific Computing 2.5.4
l_rmath.inl
1/*
2** CXSC is a C++ library for eXtended Scientific Computing (V 2.5.4)
3**
4** Copyright (C) 1990-2000 Institut fuer Angewandte Mathematik,
5** Universitaet Karlsruhe, Germany
6** (C) 2000-2014 Wiss. Rechnen/Softwaretechnologie
7** Universitaet Wuppertal, Germany
8**
9** This library is free software; you can redistribute it and/or
10** modify it under the terms of the GNU Library General Public
11** License as published by the Free Software Foundation; either
12** version 2 of the License, or (at your option) any later version.
13**
14** This library is distributed in the hope that it will be useful,
15** but WITHOUT ANY WARRANTY; without even the implied warranty of
16** MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
17** Library General Public License for more details.
18**
19** You should have received a copy of the GNU Library General Public
20** License along with this library; if not, write to the Free
21** Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
22*/
23
24/* CVS $Id: l_rmath.inl,v 1.30 2014/01/30 17:23:46 cxsc Exp $ */
25
26#include "l_interval.hpp"
27#include "l_imath.hpp"
28
29namespace cxsc {
30
31inline l_real sqr(const l_real &x) noexcept
32 { return (x*x); }
33inline l_real sqrt(const l_real & x,int n)
34 { return mid(sqrt(_l_interval(x),n)); }
35inline l_real sqrtp1m1(const l_real & x) noexcept
36 { return mid(sqrtp1m1(_l_interval(x))); }
37inline l_real sqrtx2m1(const l_real & x) noexcept
38 { return mid(sqrtx2m1(_l_interval(x))); } // sqrt(x^2-1);
39inline l_real sqrt1mx2(const l_real& x) noexcept
40 { return mid(sqrt1mx2(_l_interval(x)));}
41inline l_real ln_sqrtx2y2(const l_real& x, const l_real& y) noexcept
42 { return mid(ln_sqrtx2y2(_l_interval(x),_l_interval(y)));}
43inline l_real acoshp1(const l_real& x)
44 { return mid(acoshp1(l_interval(x)));}
45
46inline l_real sin(const l_real & x) noexcept
47 { return mid(sin(_l_interval(x))); }
48inline l_real cos(const l_real & x) noexcept
49 { return mid(cos(_l_interval(x))); }
50inline l_real tan(const l_real & x) noexcept
51 { return mid(tan(_l_interval(x))); }
52inline l_real cot(const l_real & x) noexcept
53 { return mid(cot(_l_interval(x))); }
54
55inline l_real asin(const l_real & x)
56 { return mid(asin(_l_interval(x))); }
57inline l_real acos(const l_real & x)
58 { return mid(acos(_l_interval(x))); }
59inline l_real atan(const l_real & x)
60 { return mid(atan(_l_interval(x))); }
61inline l_real acot(const l_real & x)
62 { return mid(acot(_l_interval(x))); }
63
64inline l_real exp(const l_real & x) noexcept
65 { return mid(exp(_l_interval(x))); }
66inline l_real exp2(const l_real & x) noexcept
67{ return mid(exp2(_l_interval(x))); }
68inline l_real exp10(const l_real & x) noexcept
69{ return mid(exp10(_l_interval(x))); }
70inline l_real expm1(const l_real &x) noexcept
71 { return mid(expm1(l_interval(x))); }
72inline l_real expmx2(const l_real& x) noexcept
73 { return mid(expmx2(l_interval(x)));}
74
75inline l_real ln(const l_real & x)
76 { return mid(ln(_l_interval(x))); }
77inline l_real log2(const l_real & x)
78{ return mid(log2(_l_interval(x))); }
79inline l_real log10(const l_real & x)
80{ return mid(log10(_l_interval(x))); }
81
82inline l_real sinh(const l_real & x) noexcept
83 { return mid(sinh(_l_interval(x))); }
84inline l_real cosh(const l_real & x) noexcept
85 { return mid(cosh(_l_interval(x))); }
86inline l_real tanh(const l_real & x) noexcept
87 { return mid(tanh(_l_interval(x))); }
88inline l_real coth(const l_real & x) noexcept
89 { return mid(coth(_l_interval(x))); }
90
91inline l_real asinh(const l_real & x)
92 { return mid(asinh(_l_interval(x))); }
93inline l_real acosh(const l_real & x)
94 { return mid(acosh(_l_interval(x))); }
95inline l_real atanh(const l_real & x)
96 { return mid(atanh(_l_interval(x))); }
97inline l_real acoth(const l_real & x)
98 { return mid(acoth(_l_interval(x))); }
99
100inline l_real pow(const l_real & x,const l_real & expo)
101 { return mid(pow(_l_interval(x),_l_interval(expo))); }
102
103} // namespace cxsc
104
The Multiple-Precision Data Type l_interval.
The Multiple-Precision Data Type l_real.
Definition l_real.hpp:78
The namespace cxsc, providing all functionality of the class library C-XSC.
Definition cdot.cpp:29
cinterval sqrtp1m1(const cinterval &z) noexcept
Calculates .
Definition cimath.cpp:1054
cinterval exp2(const cinterval &z) noexcept
Calculates .
Definition cimath.cpp:167
cinterval sqrt1mx2(const cinterval &z) noexcept
Calculates .
Definition cimath.cpp:1140
cinterval asinh(const cinterval &z) noexcept
Calculates .
Definition cimath.cpp:2718
cinterval coth(const cinterval &z) noexcept
Calculates .
Definition cimath.cpp:578
cinterval log2(const cinterval &z) noexcept
Calculates .
Definition cimath.cpp:898
cinterval log10(const cinterval &z) noexcept
Calculates .
Definition cimath.cpp:903
cinterval ln(const cinterval &z) noexcept
Calculates .
Definition cimath.cpp:851
cinterval pow(const cinterval &z, const interval &p) noexcept
Calculates .
Definition cimath.cpp:2074
l_interval _l_interval(const real &a) noexcept
interval expmx2(const interval &x)
Calculates .
Definition imath.cpp:192
cinterval sinh(const cinterval &z) noexcept
Calculates .
Definition cimath.cpp:231
cinterval asin(const cinterval &z) noexcept
Calculates .
Definition cimath.cpp:2311
interval acoshp1(const interval &x)
Calculates .
Definition imath.cpp:617
cinterval tan(const cinterval &z) noexcept
Calculates .
Definition cimath.cpp:393
cinterval exp10(const cinterval &z) noexcept
Calculates .
Definition cimath.cpp:172
cinterval acos(const cinterval &z) noexcept
Calculates .
Definition cimath.cpp:2553
cinterval sqrtx2m1(const cinterval &z) noexcept
Calculates .
Definition cimath.cpp:1109
cinterval acosh(const cinterval &z) noexcept
Calculates .
Definition cimath.cpp:2732
cinterval cosh(const cinterval &z) noexcept
Calculates .
Definition cimath.cpp:223
cinterval cos(const cinterval &z) noexcept
Calculates .
Definition cimath.cpp:207
cinterval exp(const cinterval &z) noexcept
Calculates .
Definition cimath.cpp:159
cinterval tanh(const cinterval &z) noexcept
Calculates .
Definition cimath.cpp:565
interval ln_sqrtx2y2(const interval &x, const interval &y) noexcept
Calculates .
Definition imath.cpp:581
cinterval expm1(const cinterval &z) noexcept
Calculates .
Definition cimath.cpp:177
cinterval cot(const cinterval &z) noexcept
Calculates .
Definition cimath.cpp:538
cinterval sqrt(const cinterval &z) noexcept
Calculates .
Definition cimath.cpp:1007
cinterval acot(const cinterval &z) noexcept
Calculates .
Definition cimath.cpp:3130
cinterval sqr(const cinterval &z) noexcept
Calculates .
Definition cimath.cpp:3342
cvector mid(const cimatrix_subv &mv) noexcept
Returns the middle of the matrix.
Definition cimatrix.inl:739
cinterval atan(const cinterval &z) noexcept
Calculates .
Definition cimath.cpp:2938
cinterval atanh(const cinterval &z) noexcept
Calculates .
Definition cimath.cpp:3317
cinterval acoth(const cinterval &z) noexcept
Calculates .
Definition cimath.cpp:3330
cinterval sin(const cinterval &z) noexcept
Calculates .
Definition cimath.cpp:215