Computational Physics - Department of Physics

2.4 Programming Examples on Loss of Precision and Round-offErrors 29

IMPLICITNONE

REAL(DP) :: x, term, final_sum

INTEGER:: n, loop_over_x

! loop over x-values

DOloop_over_x=0, 100, 10

x=loop_over_x

! initialize the EXP sum

final_sum= 0.0_dp; term = 1.0_dp; n = 0

DOWHILE( ABS(term) > truncation)

term = ((-1.0_dp)**n)*(x**n)/ factorial(n)

final_sum=final_sum+term

n=n+1

ENDDO

! write the argument x, the exact value, the computed value and n

WRITE(*,*) x ,EXP(-x), final_sum, n

ENDDO

END PROGRAMexp_prog

TheMODULEdeclaration in Fortran allows one to place functions like the one which calculates
the factorials. Note also the usage of the moduleconstantswhere we define double and
complex variables. If one wishes to switch to another precision, one just needs to change
the declaration in one part of the program only. This hinderspossible errors which arise if
one has to change variable declarations in every function and subroutine. In addition we
have defined a global variabletruncationwhich is accessible to all functions which have the
USE constantsdeclaration. These declarations have to come before any variable declara-
tions andIMPLICIT NONEstatement.
http://folk.uio.no/mhjensen/compphys/programs/chapter02/Fortran/program5.f90
! In this module you can define for example global constants
MODULEconstants
! definition of variables for double precisions and complexvariables
INTEGER,PARAMETER:: dp =KIND(1.0D0)
INTEGER,PARAMETER:: dpc =KIND((1.0D0,1.0D0))
! Global Truncation parameter
REAL(DP),PARAMETER,PUBLIC:: truncation=1.0E-10
END MODULEconstants

PROGRAMimproved_exp
USEconstants
IMPLICITNONE
REAL(dp) :: x, term, final_sum
INTEGER:: n, loop_over_x
! loop over x-values, no floats as loop variables
DOloop_over_x=0, 100, 10
x=loop_over_x
! initialize the EXP sum
final_sum=1.0 ; term=1.0 ; n = 1
DOWHILE( ABS(term) > truncation)
term = -termx/FLOAT(n)
final_sum=final_sum+term
n=n+1
ENDDO
! write the argument x, the exact value, the computed value and n
WRITE(,*) x ,EXP(-x), final_sum, n
ENDDO

END PROGRAMimproved_exp