ParaMonte Fortran 2.0.0
Parallel Monte Carlo and Machine Learning Library
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pm_mathConst.F90
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33
34!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
35
36module pm_mathConst
37
38 use pm_kind, only: SK, RKB
39
40 implicit none
41
42 character(*,SK), parameter :: MODULE_NAME = "@pm_mathConst"
43
44 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
45 ! \pi-related constants.
46 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
47
48 real(RKB) , parameter :: PI = acos(-1._RKB)
49 real(RKB) , parameter :: TWO_PI = 2 * PI
50 real(RKB) , parameter :: HALF_PI = .5_RKB * PI
51 real(RKB) , parameter :: INVERSE_PI = 1._RKB / PI
52 real(RKB) , parameter :: QUARTER_PI = .25_RKB * PI
53 real(RKB) , parameter :: LOG_PI = log(PI)
54 real(RKB) , parameter :: SQRT_PI = sqrt(PI)
55 real(RKB) , parameter :: LOG_TWO_PI = log(TWO_PI)
56 real(RKB) , parameter :: SQRT_TWO_PI = sqrt(TWO_PI)
57 real(RKB) , parameter :: SQRT_HALF_PI = sqrt(HALF_PI)
58 real(RKB) , parameter :: INVERSE_SQRT_PI = sqrt(INVERSE_PI)
59 real(RKB) , parameter :: INVERSE_SQRT_TWO_PI = 1._RKB / SQRT_TWO_PI
60 real(RKB) , parameter :: LOG_INVERSE_SQRT_TWO_PI = log(INVERSE_SQRT_TWO_PI)
61
62 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
63 ! Common numeric constants.
64 !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
65
66 real(RKB) , parameter :: NAPIER = exp(1._RKB)
67 real(RKB) , parameter :: LOG_TWO = log(2._RKB)
68 real(RKB) , parameter :: LOG_TEN = log(1.e1_RKB)
69 real(RKB) , parameter :: LOG_HALF = log(0.5_RKB)
70 real(RKB) , parameter :: SQRT_TWO = sqrt(2._RKB)
71 real(RKB) , parameter :: LOG10_NAPIER = log10(NAPIER)
72 real(RKB) , parameter :: INVERSE_LOG_TWO = 1._RKB / LOG_TWO
73 real(RKB) , parameter :: INVERSE_SQRT_TWO = 1._RKB / SQRT_TWO
74
75!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
76
102 type :: origin_type; end type
103
104!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
105
131 type(origin_type), parameter :: ORIGIN = origin_type()
132
133!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
134
189 real(RKB) , parameter :: EULER_CONST = 0.577215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749_RKB
190
191!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
192
222 real(RKB) , parameter :: APERY_CONST = 1.20205690315959428539973816151144999076498629234049888179227155534183820578631309018645587360933525814619915_RKB
223
224!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
225
246 real(RKB) , parameter :: PRIME_CONST = .414682509851111660248109622154307708365774238137916977868245414488640960619357334196290048428475777939616_RKB
247
248!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
249
283 real(RKB) , parameter :: GOLDEN_RATIO = .5_RKB * (1._RKB + sqrt(5._RKB))
284
285!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
286
329 real(RKB) , parameter :: SILVER_RATIO = 1._RKB + sqrt(2._RKB)
330
331!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
332
379 real(RKB) , parameter :: SUPER_GOLDEN_RATIO = (2._RKB * cosh(acosh(29._RKB / 2._RKB) / 3._RKB) + 1._RKB) / 3._RKB
380
381!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
382
406 type :: ninf_type
407 end type
408
423 type(ninf_type) , parameter :: ninf = ninf_type()
424#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
425 !DIR$ ATTRIBUTES DLLEXPORT :: ninf
426#endif
427
428!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
429
453 type :: pinf_type
454 end type
455
470 type(pinf_type) , parameter :: pinf = pinf_type()
471#if __INTEL_COMPILER && DLL_ENABLED && (_WIN32 || _WIN64)
472 !DIR$ ATTRIBUTES DLLEXPORT :: pinf
473#endif
474
475!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
476
477end module pm_mathConst ! LCOV_EXCL_LINE
pm_kind
This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte librar...
Definition: pm_kind.F90:268
pm_kind::RKB
integer, parameter RKB
The scalar integer constant of intrinsic default kind, representing the Best-precision real kind supp...
Definition: pm_kind.F90:1371
pm_kind::SK
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in C-Fortran Intero...
Definition: pm_kind.F90:539
pm_mathConst
This module contains relevant mathematical constants.
Definition: pm_mathConst.F90:36
pm_mathConst::INVERSE_PI
real(RKB), parameter INVERSE_PI
The scalar real constant of kind with highest available precision RKB representing the inverse of the...
Definition: pm_mathConst.F90:51
pm_mathConst::INVERSE_SQRT_TWO_PI
real(RKB), parameter INVERSE_SQRT_TWO_PI
The scalar real constant of kind with highest available precision RKB representing .
Definition: pm_mathConst.F90:59
pm_mathConst::SUPER_GOLDEN_RATIO
real(RKB), parameter SUPER_GOLDEN_RATIO
The scalar real constant of kind with highest available precision RKB representing the Supergolden Ra...
Definition: pm_mathConst.F90:379
pm_mathConst::SQRT_PI
real(RKB), parameter SQRT_PI
The scalar real constant of kind with highest available precision RKB representing .
Definition: pm_mathConst.F90:54
pm_mathConst::LOG_TEN
real(RKB), parameter LOG_TEN
The scalar real constant of kind with highest available precision RKB representing .
Definition: pm_mathConst.F90:68
pm_mathConst::SQRT_TWO
real(RKB), parameter SQRT_TWO
The scalar real constant of kind with highest available precision RKB representing .
Definition: pm_mathConst.F90:70
pm_mathConst::MODULE_NAME
character(*, SK), parameter MODULE_NAME
Definition: pm_mathConst.F90:42
pm_mathConst::SQRT_HALF_PI
real(RKB), parameter SQRT_HALF_PI
The scalar real constant of kind with highest available precision RKB representing .
Definition: pm_mathConst.F90:57
pm_mathConst::QUARTER_PI
real(RKB), parameter QUARTER_PI
The scalar real constant of kind with highest available precision RKB representing a quarter of the i...
Definition: pm_mathConst.F90:52
pm_mathConst::LOG_TWO_PI
real(RKB), parameter LOG_TWO_PI
The scalar real constant of kind with highest available precision RKB representing .
Definition: pm_mathConst.F90:55
pm_mathConst::TWO_PI
real(RKB), parameter TWO_PI
The scalar real constant of kind with highest available precision RKB representing twice the irration...
Definition: pm_mathConst.F90:49
pm_mathConst::LOG_PI
real(RKB), parameter LOG_PI
The scalar real constant of kind with highest available precision RKB representing .
Definition: pm_mathConst.F90:53
pm_mathConst::ORIGIN
type(origin_type), parameter ORIGIN
The scalar constant object of type origin_type representing the geometric origin of the coordinates.
Definition: pm_mathConst.F90:131
pm_mathConst::INVERSE_SQRT_PI
real(RKB), parameter INVERSE_SQRT_PI
The scalar real constant of kind with highest available precision RKB representing .
Definition: pm_mathConst.F90:58
pm_mathConst::HALF_PI
real(RKB), parameter HALF_PI
The scalar real constant of kind with highest available precision RKB representing half the irrationa...
Definition: pm_mathConst.F90:50
pm_mathConst::PRIME_CONST
real(RKB), parameter PRIME_CONST
The scalar real constant of kind with highest available precision RKB representing the irrational Pri...
Definition: pm_mathConst.F90:246
pm_mathConst::SQRT_TWO_PI
real(RKB), parameter SQRT_TWO_PI
The scalar real constant of kind with highest available precision RKB representing .
Definition: pm_mathConst.F90:56
pm_mathConst::SILVER_RATIO
real(RKB), parameter SILVER_RATIO
The scalar real constant of kind with highest available precision RKB representing the Silver Ratio c...
Definition: pm_mathConst.F90:329
pm_mathConst::LOG_HALF
real(RKB), parameter LOG_HALF
The scalar real constant of kind with highest available precision RKB representing .
Definition: pm_mathConst.F90:69
pm_mathConst::LOG_INVERSE_SQRT_TWO_PI
real(RKB), parameter LOG_INVERSE_SQRT_TWO_PI
The scalar real constant of kind with highest available precision RKB representing ,...
Definition: pm_mathConst.F90:60
pm_mathConst::PI
real(RKB), parameter PI
The scalar real constant of kind with highest available precision RKB representing the irrational num...
Definition: pm_mathConst.F90:48
pm_mathConst::GOLDEN_RATIO
real(RKB), parameter GOLDEN_RATIO
The scalar real constant of kind with highest available precision RKB representing the Golden Ratio c...
Definition: pm_mathConst.F90:283
pm_mathConst::ninf
type(ninf_type), parameter ninf
The scalar constant object of type ninf_type that indicates the use of the negative infinity as an i...
Definition: pm_mathConst.F90:423
pm_mathConst::INVERSE_SQRT_TWO
real(RKB), parameter INVERSE_SQRT_TWO
The scalar real constant of kind with highest available precision RKB representing .
Definition: pm_mathConst.F90:73
pm_mathConst::APERY_CONST
real(RKB), parameter APERY_CONST
The scalar real constant of kind with highest available precision RKB representing the Apery constant...
Definition: pm_mathConst.F90:222
pm_mathConst::NAPIER
real(RKB), parameter NAPIER
The scalar real constant of kind with highest available precision RKB representing the Napier constan...
Definition: pm_mathConst.F90:66
pm_mathConst::LOG_TWO
real(RKB), parameter LOG_TWO
The scalar real constant of kind with highest available precision RKB representing .
Definition: pm_mathConst.F90:67
pm_mathConst::LOG10_NAPIER
real(RKB), parameter LOG10_NAPIER
The scalar real constant of kind with highest available precision RKB representing .
Definition: pm_mathConst.F90:71
pm_mathConst::pinf
type(pinf_type), parameter pinf
The scalar constant object of type pinf_type that indicates the use of the positive infinity as an i...
Definition: pm_mathConst.F90:470
pm_mathConst::INVERSE_LOG_TWO
real(RKB), parameter INVERSE_LOG_TWO
The scalar real constant of kind with highest available precision RKB representing .
Definition: pm_mathConst.F90:72
pm_mathConst::EULER_CONST
real(RKB), parameter EULER_CONST
The scalar real constant of kind with highest available precision RKB representing the Euler-Maschero...
Definition: pm_mathConst.F90:189
pm_mathConst::ninf_type
This is the indicator type for generating instances of objects that indicate the use of the negative ...
Definition: pm_mathConst.F90:406
pm_mathConst::origin_type
This is the derived type origin_type representing the geometric origin of the coordinates.
Definition: pm_mathConst.F90:102
pm_mathConst::pinf_type
This is the indicator type for generating instances of objects that indicate the use of the positive ...
Definition: pm_mathConst.F90:453