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Gustafson's Law (Parallel Scaling)

Core Numerical Engine in Fortran 90 โ€ข 31 total downloads

gustafson.f90 
! =========================================================================
! Source File: gustafson.f90
! =========================================================================

!==============================================================================
! ThermoFluidCalc โ€” Calculator #31 : Gustafson's Law
!==============================================================================
! S(N) = 1 + f*(N-1)   (scaled speedup / weak scaling)
! Alternatively: S = s + f*N  where s = 1-f
! Comparison with Amdahl: S_amdahl = 1/((1-f)+f/N)
! Reference : Gupta, ยง5.8, Eq. 5.95
! Build: gfortran -O2 -o gustafson gustafson.f90
!==============================================================================
program gustafson
  implicit none
  integer, parameter :: dp = selected_real_kind(15,307)
  integer, parameter :: MX = 10000
  integer :: mode, N, Nmin, Nmax, npts, i
  real(dp) :: f, Sg, Sa, Eg, Ea, df, fv, dN

  read(*,*) mode

  select case(mode)

  ! MODE 1 : Single point โ€” both laws
  case(1)
    backspace(5); read(*,*) mode, f, N
    if(f<0) f=0; if(f>1) f=1; if(N<1) N=1
    Sg = 1.0_dp + f*real(N-1,dp)
    Eg = Sg / real(N,dp)
    Sa = 1.0_dp / ((1.0_dp-f) + f/real(N,dp))
    Ea = Sa / real(N,dp)

    write(*,'(A,I1)')    'MODE=', mode
    write(*,'(A)')       'MODE_NAME=Single Point'
    write(*,'(A,F10.6)') 'F=', f
    write(*,'(A,I8)')    'N=', N
    write(*,'(A,F12.4)') 'S_GUSTAFSON=', Sg
    write(*,'(A,F10.4)') 'E_GUSTAFSON=', Eg
    write(*,'(A,F12.4)') 'S_AMDAHL=', Sa
    write(*,'(A,F10.4)') 'E_AMDAHL=', Ea

  ! MODE 2 : N sweep โ€” both laws
  case(2)
    backspace(5); read(*,*) mode, f, Nmin, Nmax, npts
    if(f<0) f=0; if(f>1) f=1
    if(Nmin<1) Nmin=1; if(Nmax<Nmin) Nmax=Nmin
    if(npts<2) npts=2; if(npts>MX) npts=MX

    write(*,'(A,I1)')    'MODE=', mode
    write(*,'(A)')       'MODE_NAME=N Sweep'
    write(*,'(A,F10.6)') 'F=', f

    dN = real(Nmax-Nmin,dp)/real(npts-1,dp)
    write(*,'(A)') 'DATA_START'
    do i = 0, npts-1
      N = Nmin + nint(real(i,dp)*dN)
      if(N<1) N=1
      Sg = 1.0_dp + f*real(N-1,dp)
      Sa = 1.0_dp / ((1.0_dp-f) + f/real(N,dp))
      Eg = Sg / real(N,dp)
      write(*,'(I8,A,F12.4,A,F12.4,A,F10.6)') N, ',', Sg, ',', Sa, ',', Eg
    end do
    write(*,'(A)') 'DATA_END'

  ! MODE 3 : f sweep โ€” both laws for fixed N
  case(3)
    backspace(5); read(*,*) mode, N, npts
    if(N<1) N=1; if(npts<2) npts=2; if(npts>MX) npts=MX

    write(*,'(A,I1)')  'MODE=', mode
    write(*,'(A)')     'MODE_NAME=f Sweep'
    write(*,'(A,I8)')  'N=', N

    df = 1.0_dp/real(npts-1,dp)
    write(*,'(A)') 'DATA_START'
    do i = 0, npts-1
      fv = real(i,dp)*df
      Sg = 1.0_dp + fv*real(N-1,dp)
      Sa = 1.0_dp / ((1.0_dp-fv) + fv/real(N,dp))
      write(*,'(F10.6,A,F12.4,A,F12.4)') fv, ',', Sg, ',', Sa
    end do
    write(*,'(A)') 'DATA_END'

  case default
    write(*,'(A)') 'ERROR=Invalid mode (1-3).'; stop
  end select
end program gustafson

Solver Description

Calculate scaled speedup for parallel applications where workload size grows with processing power.

Key Numerical Methods & Architecture

  • Input Redirection: Reads parameters sequentially from standard input (`stdin`) using Fortran sequential read (`read(*,*)`), ensuring modular integration.
  • Modular Design: Formulated using pure mathematical routines, separation of equations from output formatting, and precise numerical solvers (e.g. bisection, Newton-Raphson).
  • Standard Compliant: Written in clean, standards-compliant Fortran 90 to ensure cross-compiler compatibility.

๐Ÿ› ๏ธ Local Compilation

To test this code on your machine, compile the source code file(s) using a standard Fortran compiler (e.g., `gfortran`).

Compilation Command:

gfortran -O3 gustafson.f90 -o gustafson

Execution Command:

Execute the program by feeding the sample input file into the program using stdin redirection:

gustafson < input.txt

๐Ÿ“ฅ Downloads & Local Files

Preview of the required input file (input.txt):

! f_in\nN (processors)
0.9
! Parameter 2
8
๐Ÿ“ฆ Download Offline Bundle (ZIP) 7 dl ๐Ÿ“„ Download input.txt 9 dl ๐Ÿ“ฅ Download gustafson.f90 15 dl