mathconstants.f90

Go to the documentation of this file.

!-----------------------------------------------------------------------------!
!   CP2K: A general program to perform molecular dynamics simulations         !
!   Copyright (C) 2000 - 2013  CP2K developers group                          !
!-----------------------------------------------------------------------------!

! *****************************************************************************
MODULE mathconstants
  USE f77_blas
  USE kinds,                           ONLY: dp

  IMPLICIT NONE

  PRIVATE

  PUBLIC :: maxfac, pi, pio2, twopi, fourpi, rootpi, oorootpi, zero, one, half, &
            degree, radians, gaussi, fac, ifac, dfac, gamma0, gamma1, euler, &
            sqrthalf, sqrt2, sqrt3, sqrt5, sqrt7, sqrt15, sqrt21, sqrt35, &
            sqrt105

  ! Factorial function fac
  ! Inverse Factorial function ifac
  ! Double factorial function dfac
  ! Gamma functions
  ! gamma(n) = gamma0(n) = (n - 1)!
  ! gamma(n + 1/2) = gamma1(n) = SQRT(pi)/2^n (2n - 1)!!

  INTEGER, PARAMETER :: maxfac = 30
  REAL(KIND=dp), PARAMETER, DIMENSION (0:maxfac) :: fac = (/
 0.10000000000000000000E+01_dp, 0.10000000000000000000E+01_dp, 0.20000000000000000000E+01_dp,
 0.60000000000000000000E+01_dp, 0.24000000000000000000E+02_dp, 0.12000000000000000000E+03_dp,
 0.72000000000000000000E+03_dp, 0.50400000000000000000E+04_dp, 0.40320000000000000000E+05_dp,
 0.36288000000000000000E+06_dp, 0.36288000000000000000E+07_dp, 0.39916800000000000000E+08_dp,
 0.47900160000000000000E+09_dp, 0.62270208000000000000E+10_dp, 0.87178291200000000000E+11_dp,
 0.13076743680000000000E+13_dp, 0.20922789888000000000E+14_dp, 0.35568742809600000000E+15_dp,
 0.64023737057280000000E+16_dp, 0.12164510040883200000E+18_dp, 0.24329020081766400000E+19_dp,
 0.51090942171709440000E+20_dp, 0.11240007277776076800E+22_dp, 0.25852016738884976640E+23_dp,
 0.62044840173323943936E+24_dp, 0.15511210043330985984E+26_dp, 0.40329146112660563558E+27_dp,
 0.10888869450418352161E+29_dp, 0.30488834461171386050E+30_dp, 0.88417619937397019545E+31_dp,
 0.26525285981219105864E+33_dp/)
  REAL(KIND=dp), PARAMETER, DIMENSION (0:maxfac) :: ifac = (/
 0.10000000000000000000E+01_dp, 0.10000000000000000000E+01_dp, 0.50000000000000000000E+00_dp,
 0.16666666666666666667E+00_dp, 0.41666666666666666667E-01_dp, 0.83333333333333333333E-02_dp,
 0.13888888888888888889E-02_dp, 0.19841269841269841270E-03_dp, 0.24801587301587301587E-04_dp,
 0.27557319223985890653E-05_dp, 0.27557319223985890653E-06_dp, 0.25052108385441718775E-07_dp,
 0.20876756987868098979E-08_dp, 0.16059043836821614599E-09_dp, 0.11470745597729724714E-10_dp,
 0.76471637318198164759E-12_dp, 0.47794773323873852974E-13_dp, 0.28114572543455207632E-14_dp,
 0.15619206968586226462E-15_dp, 0.82206352466243297170E-17_dp, 0.41103176233121648585E-18_dp,
 0.19572941063391261231E-19_dp, 0.88967913924505732867E-21_dp, 0.38681701706306840377E-22_dp,
 0.16117375710961183490E-23_dp, 0.64469502843844733962E-25_dp, 0.24795962632247974601E-26_dp,
 0.91836898637955461484E-28_dp, 0.32798892370698379102E-29_dp, 0.11309962886447716932E-30_dp,
 0.37699876288159056439E-32_dp/)
  REAL(KIND=dp), PARAMETER, DIMENSION (-1:2*maxfac+1) :: dfac = (/
 0.10000000000000000000E+01_dp, 0.10000000000000000000E+01_dp, 0.10000000000000000000E+01_dp,
 0.20000000000000000000E+01_dp, 0.30000000000000000000E+01_dp, 0.80000000000000000000E+01_dp,
 0.15000000000000000000E+02_dp, 0.48000000000000000000E+02_dp, 0.10500000000000000000E+03_dp,
 0.38400000000000000000E+03_dp, 0.94500000000000000000E+03_dp, 0.38400000000000000000E+04_dp,
 0.10395000000000000000E+05_dp, 0.46080000000000000000E+05_dp, 0.13513500000000000000E+06_dp,
 0.64512000000000000000E+06_dp, 0.20270250000000000000E+07_dp, 0.10321920000000000000E+08_dp,
 0.34459425000000000000E+08_dp, 0.18579456000000000000E+09_dp, 0.65472907500000000000E+09_dp,
 0.37158912000000000000E+10_dp, 0.13749310575000000000E+11_dp, 0.81749606400000000000E+11_dp,
 0.31623414322500000000E+12_dp, 0.19619905536000000000E+13_dp, 0.79058535806250000000E+13_dp,
 0.51011754393600000000E+14_dp, 0.21345804667687500000E+15_dp, 0.14283291230208000000E+16_dp,
 0.61902833536293750000E+16_dp, 0.42849873690624000000E+17_dp, 0.19189878396251062500E+18_dp,
 0.13711959580999680000E+19_dp, 0.63326598707628506250E+19_dp, 0.46620662575398912000E+20_dp,
 0.22164309547669977187E+21_dp, 0.16783438527143608320E+22_dp, 0.82007945326378915594E+22_dp,
 0.63777066403145711616E+23_dp, 0.31983098677287777082E+24_dp, 0.25510826561258284646E+25_dp,
 0.13113070457687988603E+26_dp, 0.10714547155728479551E+27_dp, 0.56386202968058350995E+27_dp,
 0.47144007485205310027E+28_dp, 0.25373791335626257948E+29_dp, 0.21686243443194442612E+30_dp,
 0.11925681927744341235E+31_dp, 0.10409396852733332454E+32_dp, 0.58435841445947272053E+32_dp,
 0.52046984263666662269E+33_dp, 0.29802279137433108747E+34_dp, 0.27064431817106664380E+35_dp,
 0.15795207942839547636E+36_dp, 0.14614793181237598765E+37_dp, 0.86873643685617511998E+37_dp,
 0.81842841814930553085E+38_dp, 0.49517976900801981839E+39_dp, 0.47468848252659720789E+40_dp,
 0.29215606371473169285E+41_dp, 0.28481308951595832474E+42_dp, 0.17821519886598633264E+43_dp/)
  REAL(KIND=dp), PARAMETER, DIMENSION (0:maxfac) :: gamma0 = (/
 0.00000000000000000000E+00_dp, 0.10000000000000000000E+01_dp, 0.10000000000000000000E+01_dp,
 0.20000000000000000000E+01_dp, 0.60000000000000000000E+01_dp, 0.24000000000000000000E+02_dp,
 0.12000000000000000000E+03_dp, 0.72000000000000000000E+03_dp, 0.50400000000000000000E+04_dp,
 0.40320000000000000000E+05_dp, 0.36288000000000000000E+06_dp, 0.36288000000000000000E+07_dp,
 0.39916800000000000000E+08_dp, 0.47900160000000000000E+09_dp, 0.62270208000000000000E+10_dp,
 0.87178291200000000000E+11_dp, 0.13076743680000000000E+13_dp, 0.20922789888000000000E+14_dp,
 0.35568742809600000000E+15_dp, 0.64023737057280000000E+16_dp, 0.12164510040883200000E+18_dp,
 0.24329020081766400000E+19_dp, 0.51090942171709440000E+20_dp, 0.11240007277776076800E+22_dp,
 0.25852016738884976640E+23_dp, 0.62044840173323943936E+24_dp, 0.15511210043330985984E+26_dp,
 0.40329146112660563558E+27_dp, 0.10888869450418352161E+29_dp, 0.30488834461171386050E+30_dp,
 0.88417619937397019545E+31_dp/)
  REAL(KIND=dp), PARAMETER, DIMENSION (0:maxfac) :: gamma1 = (/
 0.17724538509055160273E+01_dp, 0.88622692545275801365E+00_dp, 0.13293403881791370205E+01_dp,
 0.33233509704478425512E+01_dp, 0.11631728396567448929E+02_dp, 0.52342777784553520181E+02_dp,
 0.28788527781504436100E+03_dp, 0.18712543057977883465E+04_dp, 0.14034407293483412599E+05_dp,
 0.11929246199460900709E+06_dp, 0.11332783889487855673E+07_dp, 0.11899423083962248457E+08_dp,
 0.13684336546556585726E+09_dp, 0.17105420683195732157E+10_dp, 0.23092317922314238412E+11_dp,
 0.33483860987355645697E+12_dp, 0.51899984530401250831E+13_dp, 0.85634974475162063871E+14_dp,
 0.14986120533153361177E+16_dp, 0.27724322986333718178E+17_dp, 0.54062429823350750447E+18_dp,
 0.11082798113786903842E+20_dp, 0.23828015944641843260E+21_dp, 0.53613035875444147334E+22_dp,
 0.12599063430729374624E+24_dp, 0.30867705405286967828E+25_dp, 0.78712648783481767961E+26_dp,
 0.20858851927622668510E+28_dp, 0.57361842800962338401E+29_dp, 0.16348125198274266444E+31_dp,
 0.48226969334909086011E+32_dp/)

  ! Constants related to Pi

  REAL(KIND=dp), PARAMETER :: pi       =  3.14159265358979323846264338_dp ! Pi
  REAL(KIND=dp), PARAMETER :: pio2     =  1.57079632679489661923132169_dp ! Pi/2
  REAL(KIND=dp), PARAMETER :: twopi    =  6.28318530717958647692528677_dp ! 2*Pi
  REAL(KIND=dp), PARAMETER :: fourpi   = 12.56637061435917295385057353_dp ! 4*Pi
  REAL(KIND=dp), PARAMETER :: rootpi   =  1.77245385090551602729816748_dp ! SQRT(Pi)
  REAL(KIND=dp), PARAMETER :: oorootpi =  0.56418958354775628694807945_dp ! 1/SQRT(Pi)

  ! Euler's constant (Euler-Mascheroni constant)

  REAL(KIND=dp), PARAMETER :: euler =  0.57721566490153286060651209_dp

  ! Trivial constants

  REAL(KIND=dp), PARAMETER :: zero = 0.0_dp,
                              half = 0.5_dp,
                              one  = 1.0_dp

  REAL(KIND=dp), PARAMETER :: sqrthalf =  0.70710678118654752440084436_dp, ! SQRT(1/2)
                              sqrt2    =  1.41421356237309504880168872_dp, ! SQRT(2)
                              sqrt3    =  1.73205080756887729352744634_dp, ! SQRT(3)
                              sqrt5    =  2.23606797749978969640917367_dp, ! SQRT(5)
                              sqrt7    =  2.64575131106459059050161575_dp, ! SQRT(7)
                              sqrt15   =  3.87298334620741688517926540_dp, ! SQRT(15)
                              sqrt21   =  4.58257569495584000658804719_dp, ! SQRT(21)
                              sqrt35   =  5.91607978309961604256732829_dp, ! SQRT(35)
                              sqrt105  = 10.24695076595959838322103868_dp   ! SQRT(105)

  ! Conversion factors

  REAL(KIND=dp), PARAMETER :: degree  = 180.0_dp/pi, ! radians -> degree
                              radians = one/degree    ! degree  -> radians

  COMPLEX(KIND=dp), PARAMETER :: gaussi = (0.0_dp,1.0_dp) ! i = SQRT(-1)

END MODULE mathconstants