C-XSC - A C++ Class Library for Extended Scientific Computing  2.5.4
l_rmath.hpp
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.hpp,v 1.32 2014/01/30 17:23:46 cxsc Exp $ */
25 
26 #ifndef _CXSC_L_RMATH_HPP_INCLUDED
27 #define _CXSC_L_RMATH_HPP_INCLUDED
28 
29 #include "l_real.hpp"
30 
31 namespace cxsc {
32 
34 inline l_real sqr (const l_real&) noexcept; // Sqr(x)
36  l_real sqrt (const l_real&);
37  // Sqrt(x)
39  l_real sqrtx2y2(const l_real&, const l_real&) noexcept;
40  // Sqrt(x^2+y^2)
42  l_real sqrt1px2(const l_real&) noexcept; // Sqrt(1+x^2)
44 inline l_real sqrtp1m1(const l_real &) noexcept;
46 inline l_real sqrtx2m1(const l_real &) noexcept;
48 inline l_real sqrt1mx2(const l_real &) noexcept;
50 inline l_real expm1 (const l_real &x) noexcept;
52 inline l_real expmx2 (const l_real&) noexcept;
54 inline l_real ln_sqrtx2y2(const l_real& x, const l_real& y) noexcept;
56 inline l_real acoshp1 (const l_real& x);
57 
58 // inline l_real sqrt (const l_real &, int); // Sqrt(x, n)
59 // inline l_real sin (const l_real&) noexcept; // Sin(x)
60 // inline l_real cos (const l_real&) noexcept; // Cos(x)
61 // inline l_real tan (const l_real&) noexcept; // Tan(x)
62 // inline l_real cot (const l_real&) noexcept; // Cot(x)
63 // inline l_real asin (const l_real&); // ASin(x)
64 // inline l_real acos (const l_real&); // ACos(x)
65 // inline l_real atan (const l_real&); // ATan(x)
66 // inline l_real acot (const l_real&); // ACot(x)
67 // inline l_real exp (const l_real&) noexcept; // Exp(x)
68 // inline l_real ln (const l_real&); // Ln(x)
69 // inline l_real sinh (const l_real&) noexcept; // Sinh(x)
70 // inline l_real cosh (const l_real&) noexcept; // Cosh(x)
71 // inline l_real tanh (const l_real&) noexcept; // Tanh(x)
72 // inline l_real coth (const l_real&) noexcept; // Coth(x)
73 // inline l_real asinh (const l_real&); // ASinh(x)
74 // inline l_real acosh (const l_real&); // ACosh(x)
75 // inline l_real atanh (const l_real&); // ATanh(x)
76 // inline l_real acoth (const l_real&); // ACoth(x)
77 
79 inline l_real pow (const l_real&, const l_real&); // Pow(x,y)
81 l_real power (const l_real&, const int); // Power(x,n)
82 
83 // real staggered constants (the same as in l_interval.hpp):
84 l_real Ln2_l_real() noexcept; // ln(2)
85 l_real Ln10_l_real() noexcept; // ln(10)
86 l_real Ln10r_l_real() noexcept; // 1/ln(10)
87 l_real Pid4_l_real() noexcept; // Pi/4
88 l_real Sqrt2_l_real() noexcept; // sqrt(2)
89 l_real Sqrt5_l_real() noexcept; // sqrt(5)
90 l_real Sqrt7_l_real() noexcept; // sqrt(7)
91 l_real Ln2r_l_real() noexcept; // 1/ln(2)
92 l_real Pi_l_real() noexcept; // Pi
93 l_real Pid2_l_real() noexcept; // Pi/2
94 l_real Pi2_l_real() noexcept; // 2*Pi
95 l_real Pid3_l_real() noexcept; // Pi/3
96 l_real Pir_l_real() noexcept; // 1/Pi
97 l_real Pi2r_l_real() noexcept; // 1/(2*Pi)
98 l_real SqrtPi_l_real() noexcept; // sqrt(Pi)
99 l_real Sqrt2Pi_l_real() noexcept; // sqrt(2*Pi)
100 l_real SqrtPir_l_real() noexcept; // 1/sqrt(Pi)
101 l_real Sqrt2Pir_l_real() noexcept; // 1/sqrt(2*Pi)
102 l_real Pip2_l_real() noexcept; // Pi^2
103 l_real Sqrt2r_l_real() noexcept; // 1/sqrt(2)
104 l_real Sqrt3_l_real() noexcept; // sqrt(3)
105 l_real Sqrt3d2_l_real() noexcept; // sqrt(3)/2
106 l_real Sqrt3r_l_real() noexcept; // 1/sqrt(3)
107 l_real LnPi_l_real() noexcept; // ln(Pi)
108 l_real Ln2Pi_l_real() noexcept; // ln(2*Pi)
109 l_real E_l_real() noexcept; // e = exp(1)
110 l_real Er_l_real() noexcept; // 1/e
111 l_real Ep2_l_real() noexcept; // e^2
112 l_real Ep2r_l_real() noexcept; // 1/e^2
113 l_real EpPi_l_real() noexcept; // e^Pi
114 l_real Ep2Pi_l_real() noexcept; // e^(2*Pi)
115 l_real EpPid2_l_real() noexcept; // e^(Pi/2)
116 l_real EpPid4_l_real() noexcept; // e^(Pi/4)
117 l_real EulerGa_l_real() noexcept; // EulerGamma
118 l_real Catalan_l_real() noexcept; // Catalan
119 
120 } // namespace cxsc
121 
122 #include "l_rmath.inl"
123 #endif // _CXSC_L_RMATH_HPP_INCLUDED
cxsc::Pip2_l_real
l_real Pip2_l_real() noexcept
Approximation of .
Definition: l_rmath.cpp:244
cxsc::LnPi_l_real
l_real LnPi_l_real() noexcept
Approximation of .
Definition: l_rmath.cpp:254
cxsc::Catalan_l_real
l_real Catalan_l_real() noexcept
Approximation of Catalan Numbers.
Definition: l_rmath.cpp:276
cxsc::EpPid2_l_real
l_real EpPid2_l_real() noexcept
Approximation of .
Definition: l_rmath.cpp:270
cxsc::power
cinterval power(const cinterval &z, int n) noexcept
Calculates .
Definition: cimath.cpp:1941
cxsc::sqrt1px2
cinterval sqrt1px2(const cinterval &z) noexcept
Calculates .
Definition: cimath.cpp:1071
cxsc::Pir_l_real
l_real Pir_l_real() noexcept
Approximation of .
Definition: l_rmath.cpp:232
cxsc::Sqrt2Pir_l_real
l_real Sqrt2Pir_l_real() noexcept
Approximation of .
Definition: l_rmath.cpp:242
cxsc::Ep2_l_real
l_real Ep2_l_real() noexcept
Approximation of .
Definition: l_rmath.cpp:262
cxsc::expmx2
interval expmx2(const interval &x)
Calculates .
Definition: imath.cpp:192
cxsc::Ln2Pi_l_real
l_real Ln2Pi_l_real() noexcept
Approximation of .
Definition: l_rmath.cpp:256
cxsc::sqrt
cinterval sqrt(const cinterval &z) noexcept
Calculates .
Definition: cimath.cpp:1007
cxsc::EpPid4_l_real
l_real EpPid4_l_real() noexcept
Approximation of .
Definition: l_rmath.cpp:272
cxsc::Ln10_l_real
l_real Ln10_l_real() noexcept
Approximation of .
Definition: l_rmath.cpp:210
cxsc::Ln2r_l_real
l_real Ln2r_l_real() noexcept
Approximation of .
Definition: l_rmath.cpp:222
cxsc::Sqrt2Pi_l_real
l_real Sqrt2Pi_l_real() noexcept
Approximation of .
Definition: l_rmath.cpp:238
cxsc::sqrtx2m1
cinterval sqrtx2m1(const cinterval &z) noexcept
Calculates .
Definition: cimath.cpp:1109
cxsc::Ln10r_l_real
l_real Ln10r_l_real() noexcept
Approximation of .
Definition: l_rmath.cpp:212
cxsc::Pid3_l_real
l_real Pid3_l_real() noexcept
Approximation of .
Definition: l_rmath.cpp:230
cxsc::Pi2_l_real
l_real Pi2_l_real() noexcept
Approximation of .
Definition: l_rmath.cpp:228
cxsc::Ep2r_l_real
l_real Ep2r_l_real() noexcept
Approximation of .
Definition: l_rmath.cpp:264
cxsc::acoshp1
interval acoshp1(const interval &x)
Calculates .
Definition: imath.cpp:617
cxsc::Pi2r_l_real
l_real Pi2r_l_real() noexcept
Approximation of .
Definition: l_rmath.cpp:234
cxsc::Sqrt7_l_real
l_real Sqrt7_l_real() noexcept
Approximation of .
Definition: l_rmath.cpp:220
cxsc::E_l_real
l_real E_l_real() noexcept
Approximation of .
Definition: l_rmath.cpp:258
cxsc::Ln2_l_real
l_real Ln2_l_real() noexcept
Approximation of .
Definition: l_rmath.cpp:208
cxsc::Er_l_real
l_real Er_l_real() noexcept
Approximation of .
Definition: l_rmath.cpp:260
cxsc::Sqrt3r_l_real
l_real Sqrt3r_l_real() noexcept
Approximation of .
Definition: l_rmath.cpp:252
cxsc::EulerGa_l_real
l_real EulerGa_l_real() noexcept
Approximation of Euler Gamma.
Definition: l_rmath.cpp:274
cxsc::ln_sqrtx2y2
interval ln_sqrtx2y2(const interval &x, const interval &y) noexcept
Calculates .
Definition: imath.cpp:581
cxsc::Sqrt3_l_real
l_real Sqrt3_l_real() noexcept
Approximation of .
Definition: l_rmath.cpp:248
cxsc::pow
cinterval pow(const cinterval &z, const interval &p) noexcept
Calculates .
Definition: cimath.cpp:2074
cxsc
The namespace cxsc, providing all functionality of the class library C-XSC.
Definition: cdot.cpp:29
cxsc::Sqrt2r_l_real
l_real Sqrt2r_l_real() noexcept
Approximation of .
Definition: l_rmath.cpp:246
cxsc::SqrtPi_l_real
l_real SqrtPi_l_real() noexcept
Approximation of .
Definition: l_rmath.cpp:236
cxsc::sqrtp1m1
cinterval sqrtp1m1(const cinterval &z) noexcept
Calculates .
Definition: cimath.cpp:1054
cxsc::Sqrt3d2_l_real
l_real Sqrt3d2_l_real() noexcept
Approximation of .
Definition: l_rmath.cpp:250
cxsc::Sqrt5_l_real
l_real Sqrt5_l_real() noexcept
Approximation of .
Definition: l_rmath.cpp:218
cxsc::expm1
cinterval expm1(const cinterval &z) noexcept
Calculates .
Definition: cimath.cpp:177
cxsc::SqrtPir_l_real
l_real SqrtPir_l_real() noexcept
Approximation of .
Definition: l_rmath.cpp:240
cxsc::Ep2Pi_l_real
l_real Ep2Pi_l_real() noexcept
Approximation of .
Definition: l_rmath.cpp:268
cxsc::Pid4_l_real
l_real Pid4_l_real() noexcept
Approximation of .
Definition: l_rmath.cpp:214
cxsc::Pi_l_real
l_real Pi_l_real() noexcept
Approximation of .
Definition: l_rmath.cpp:224
cxsc::sqrt1mx2
cinterval sqrt1mx2(const cinterval &z) noexcept
Calculates .
Definition: cimath.cpp:1140
cxsc::sqr
cinterval sqr(const cinterval &z) noexcept
Calculates .
Definition: cimath.cpp:3342
cxsc::Pid2_l_real
l_real Pid2_l_real() noexcept
Approximation of .
Definition: l_rmath.cpp:226
cxsc::EpPi_l_real
l_real EpPi_l_real() noexcept
Approximation of .
Definition: l_rmath.cpp:266
cxsc::sqrtx2y2
interval sqrtx2y2(const interval &x, const interval &y) noexcept
Calculates .
Definition: imath.cpp:80
cxsc::Sqrt2_l_real
l_real Sqrt2_l_real() noexcept
Approximation of .
Definition: l_rmath.cpp:216