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42 :
43 : !> \brief This module contains the mathematical and programming constants.
44 : !> \author Amir Shahmoradi
45 :
46 : module Constants_mod
47 :
48 : use, intrinsic :: iso_fortran_env, only: real32, real64, int32, int64
49 : use, intrinsic :: iso_c_binding, only: CIK => c_int32_t, CRK => c_double
50 : #if defined CFI_ENABLED
51 : use, intrinsic :: iso_c_binding, only: IK => c_int32_t, RK => c_double
52 : #else
53 : use, intrinsic :: iso_fortran_env, only: IK => int32, RK => real64
54 : #endif
55 :
56 : implicit none
57 :
58 : character(*), parameter :: MODULE_NAME = "@Constants_mod"
59 :
60 : ! Constants for computational accuracy
61 :
62 : integer , parameter :: SPR = real32 !< @public single precision real kind
63 : integer , parameter :: DPR = real64 !< @public double precision real kind
64 : integer , parameter :: SPI = int32 !< @public single precision integer kind
65 : integer , parameter :: DPI = int64 !< @public double precision integer kind
66 : integer , parameter :: SPC = kind((1._SPR,1._SPR)) !< @public single-precision complex kind
67 : integer , parameter :: DPC = kind((1._DPR,1._DPR)) !< @public double-precision complex kind
68 : integer , parameter :: CK = kind((1._RK,1._RK)) !< @public complex kind
69 : integer , parameter :: RKP = precision(1._RK) !< @public real kind precision
70 : integer(IK) , parameter :: MAX_REC_LEN = 9999 !< @public maximum string record length
71 :
72 : ! Mathematical constants
73 :
74 : real(RK) , parameter :: PI = 3.141592653589793238462643383279502884197_DPR !< @public = acos(-1._RK) : The irrational number Pi.
75 : real(RK) , parameter :: INVPI = 1._DPR / PI !< @public = inverse Pi.
76 : real(RK) , PARAMETER :: TWOPI = 6.283185307179586476925286766559005768394_DPR !< @public 2*PI
77 : real(RK) , parameter :: LN2 = log(2._RK) !< @public Natural Log of 2 (= 0.693147180559945_RK).
78 : real(RK) , parameter :: INVLN2 = 1._RK / LN2 !< @public Inverse of the natural Log of 2 (= 0.693147180559945_RK).
79 : real(RK) , parameter :: LN10 = log(1.e1_RK) !< @public Natural Log of 10 (= 2.302585092994046_RK).
80 : real(RK) , parameter :: LNPI = log(PI) !< @public ln(2pi) (= 1.144729885849400_RK)
81 : real(RK) , parameter :: LN2PI = log(2._RK*PI) !< @public ln(2pi) (= 1.837877066409345_RK)
82 : real(RK) , parameter :: SQRT2 = sqrt(2._RK) !< @public Square root of 2.
83 : real(RK) , parameter :: NAPIER = exp(1._RK) !< @public Napier number e.
84 : real(RK) , parameter :: SQRTPI = sqrt(PI) !< @public Square root of Pi.
85 : real(RK) , parameter :: SQRT2PI = sqrt(2._RK*acos(-1._RK)) !< @public Square root of 2Pi.
86 : real(RK) , parameter :: INVSQRT2 = 1._RK / SQRT2PI !< @public Square root of 2.
87 : real(RK) , parameter :: HALFLN2PI = 0.5_RK*LN2PI !< @public ln(sqrt(2pi))
88 : real(RK) , parameter :: INVSQRTPI = sqrt(INVPI) !< @public = inverse of the square root of Pi.
89 : real(RK) , parameter :: INVSQRT2PI = 1._RK / SQRT2PI !< @public 1/sqrt(2*Pi) (= 0.398942280401432_RK)
90 : real(RK) , parameter :: LOGINVSQRT2PI = log(INVSQRT2PI) !< @public Log(1/sqrt(2Pi)), used in Gaussian distribution.
91 : real(RK) , parameter :: SQRT_HALF_PI = sqrt(0.5_RK*PI) !< @public Square root of PI/2 (= 1.2533141373155_RK)
92 : real(RK) , parameter :: LOG10NAPIER = log10(NAPIER) !< @public Log10 of Napier constant (= 0.434294481903259_RK).
93 : real(RK) , parameter :: EPS_RK = epsilon(1._RK) !< @public the smallest representable real increment (highest precision) by the machine
94 : real(RK) , parameter :: SQRT_EPS_RK = sqrt(EPS_RK) !< @public the smallest representable real increment (highest precision) by the machine
95 : real(RK) , parameter :: HUGE_RK = huge(1._RK) !< @public largest number of kind RK
96 : real(RK) , parameter :: TINY_RK = tiny(1._RK) !< @public tiniest number of kind RK
97 : real(RK) , parameter :: LOGHUGE_RK = log(HUGE_RK) !< @public log of the largest number of kind RK
98 : real(RK) , parameter :: LOGTINY_RK = log(TINY_RK) !< @public log of the smallest number of kind RK
99 : real(RK) , parameter :: POSINF_RK = HUGE_RK / 1.e1_RK !< @public positive virtual infinite real. The division is done to avoid overflow in output
100 : real(RK) , parameter :: NEGINF_RK = -POSINF_RK !< @public negative virtual infinite real. Defined to avoid underflow/overflow and compatibility with Dynamic languages.
101 : real(RK) , parameter :: LOGINF_RK = log(POSINF_RK) !< @public represents the logarithm of the largest representable number
102 : real(RK) , parameter :: NEGLOGINF_RK = -LOGINF_RK !< @public represents the logarithm of the smallest representable number
103 : integer(IK) , parameter :: HUGE_IK = huge(1_IK) !< @public largest number of kind RK
104 : integer(IK) , parameter :: POSINF_IK = HUGE_IK / 2_IK !< @public positive virtually-infinite integer. the division is done to avoid overflow in output
105 : integer(IK) , parameter :: NEGINF_IK = -POSINF_IK !< @public negative virtually-infinite integer.
106 : real(RK) , parameter :: LOGINF_IK = log(real(POSINF_IK,RK)) !< @public the natural logarithm of the positive virtually-infinite integer.
107 :
108 : real(RK) , parameter :: NULL_RK = -HUGE_RK !< @public the value used to represent unassigned variables.
109 : integer(IK) , parameter :: NULL_IK = -HUGE_IK
110 : character(1), parameter :: NULL_SK = achar(30) ! This must remain a single character as it is assumed to be so in multiple routines: Record separator
111 :
112 : character(1), parameter :: NLC = achar(10) ! the New Line Character
113 : character(1), parameter :: TAB = achar(9) ! the TAB Character
114 : character(*), parameter :: UNDEFINED = "UNDEFINED"
115 :
116 : ! null values
117 :
118 : type, private :: NullType
119 : real(RK) :: RK = NULL_RK
120 : integer(IK) :: IK = NULL_IK
121 : character(1) :: SK = NULL_SK
122 : end type NullType
123 :
124 : type(NullType), protected :: NullVal
125 :
126 : ! Physical constants
127 :
128 : real(RK), parameter :: ERG2KEV = 6.241509125883258e8_RK !< @public 1 (erg) = ERG2KEV (keV)
129 : real(RK), parameter :: KEV2ERG = 1.60217662080000e-9_RK !< @public 1 (keV) = KEV2ERG (erg)
130 : real(RK), parameter :: LOG_ERG2KEV = log(ERG2KEV)
131 : real(RK), parameter :: LOG_KEV2ERG = log(KEV2ERG)
132 :
133 : ! Cosmological constants
134 :
135 : !real(RK), parameter :: LIGHT_SPEED = 3.e5_RK ! LIGHT_SPEED is the speed of light (Km/s).
136 : !real(RK), parameter :: HUBBLE_TIME_GYRS = 13.8_RK ! hubble time (liddle 2003, page 57) in units of gyrs
137 : !real(RK), parameter :: HUBBLE_CONST = 7.1e1_RK ! HUBBLE_CONST is the Hubble constant in units of km/s/MPc.
138 : !real(RK), parameter :: LS2HC = LIGHT_SPEED / HUBBLE_CONST ! the speed of light in units of km/s divided by the Hubble constant.
139 : !real(RK), parameter :: MPC2CM = 3.09e24_RK ! 1 Mega Parsec = MPC2CM centimeters.
140 : !real(RK), parameter :: LOG10MPC2CMSQ4PI = log10(4._RK*PI) + 2*log10(MPC2CM) ! Log10(MPC2CM centimeters.
141 : !real(RK), parameter :: OMEGA_DE = 0.7_RK ! Dark Energy density.
142 : !real(RK), parameter :: OMEGA_DM = 0.3_RK ! Dark Matter density.
143 :
144 : character(len=1), parameter :: CARRIAGE_RETURN = achar(13)
145 : character(len=1), parameter :: ESCAPE = achar(27)
146 : character(len=1), parameter :: ESC = achar(27)
147 : character(len=1), parameter :: CLOCK_TICK(4) = [ "|" , "/" , "-" , "\" ]
148 :
149 : interface getPosInf
150 : module procedure :: getPosInf_RK
151 : end interface getPosInf
152 :
153 : interface getNegInf
154 : module procedure :: getNegInf_RK
155 : end interface getNegInf
156 :
157 : ! file extentions
158 :
159 : type, private :: FileType_type
160 : character(6) :: binary = "binary"
161 : character(6) :: matlab = "MATLAB"
162 : character(6) :: python = "Python"
163 : character(5) :: julia = "Julia"
164 : character(5) :: ascii = "ASCII"
165 : character(1) :: rlang = "R"
166 : end type FileType_type
167 :
168 : type, private :: FileExt_type
169 : character(4) :: binary = ".bin"
170 : character(2) :: matlab = ".m"
171 : character(3) :: python = ".py"
172 : character(3) :: julia = ".jl"
173 : character(4) :: ascii = ".txt"
174 : character(2) :: r = ".R"
175 : end type FileExt_type
176 :
177 : type(FileExt_type) , parameter :: FILE_EXT = FileExt_type()
178 : type(FileType_type) , parameter :: FILE_TYPE = FileType_type()
179 :
180 : !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
181 : ! ParaMonte methods
182 : !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
183 :
184 : type, private :: ParaMonteSamplingMethod_type
185 : integer(IK) :: count = 4_IK
186 : character(8) :: ParaDRAM = "ParaDRAM"
187 : character(8) :: ParaDISE = "ParaDISE"
188 : character(8) :: ParaHDMC = "ParaHDMC"
189 : character(8) :: ParaTemp = "ParaTemp"
190 : character(8) :: ParaNest = "ParaNest"
191 : end type ParaMonteSamplingMethod_type
192 :
193 : type(ParaMonteSamplingMethod_type), parameter :: PMSM = ParaMonteSamplingMethod_type()
194 :
195 : !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
196 :
197 : contains
198 :
199 : !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
200 :
201 2 : pure function getPosInf_RK() result(posInf)
202 : #if INTEL_COMPILER_ENABLED && defined DLL_ENABLED && (OS_IS_WINDOWS || defined OS_IS_DARWIN)
203 : !DEC$ ATTRIBUTES DLLEXPORT :: getPosInf_RK
204 : #endif
205 : !> \brief Return IEEE positive infinity.
206 : !> @param[out] posInf The positive infinity.
207 : use, intrinsic :: ieee_arithmetic, only: ieee_value, ieee_positive_inf
208 : implicit none
209 : real(RK) :: posInf
210 1 : posInf = ieee_value(0._RK, ieee_positive_inf)
211 1 : end function getPosInf_RK
212 :
213 : !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
214 :
215 1 : pure function getNegInf_RK() result(negInf)
216 : #if INTEL_COMPILER_ENABLED && defined DLL_ENABLED && (OS_IS_WINDOWS || defined OS_IS_DARWIN)
217 : !DEC$ ATTRIBUTES DLLEXPORT :: getNegInf_RK
218 : #endif
219 : !> \brief Return IEEE negative infinity.
220 : !> @param[out] posInf The negative infinity.
221 1 : use, intrinsic :: ieee_arithmetic, only: ieee_value, ieee_negative_inf
222 : implicit none
223 : real(RK) :: negInf
224 1 : negInf = ieee_value(0._RK, ieee_negative_inf)
225 1 : end function getNegInf_RK
226 :
227 : !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
228 :
229 : end module Constants_mod ! LCOV_EXCL_LINE
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