Multiplication in Fortran giving different results with ifort and gfortran

Question

I have a program that is compiled either on Linux with gfortran-9, either on Windows with ifort. The windows compilation is kind of a black box on which I don't have much access.

Anyway, at some point both code have to do the same multiplication but the result is different at the 13th decimal.

Here the test code I wrote to test this multiplication on my Linux machine:

      implicit none
      double precision:: a,b,c,d
 200  format(F35.20)
      b=20.17865682672815452747d0
      c=3.75000000000000000000d0
      d=32.17399999999999948841d0
      a=b*c*d
      write(*,200)a
      end program

On Linux with gfortran I have 2434.60539278681835639873 value. On Windows with ifort the same multiplication is done and gives 2434.60539278681881114608. Both are compiled with -O2 option.

I can't think of a reason why it differs. Is it because the double precision can't be more precise and that I should move to the real(16) ?

Thanks for your insights.

Answer 1

There are 3 different ways that the multiplication can be ordered. Gfortran and ifort happen to choose different orders. Using brackets you can see what is going on:

ian@eris:~/work/stack$ cat mult.f90
implicit none
      double precision:: a,b,c,d
 200  format(F35.20)
      b=20.17865682672815452747d0
      c=3.75000000000000000000d0
      d=32.17399999999999948841d0
      a=(b*c)*d
      write(*,200)a
      b=20.17865682672815452747d0
      c=3.75000000000000000000d0
      d=32.17399999999999948841d0
      a=b*(c*d)
      write(*,200)a
      b=20.17865682672815452747d0
      c=3.75000000000000000000d0
      d=32.17399999999999948841d0
      a=c*(b*d)
      write(*,200)a
      end program
ian@eris:~/work/stack$ gfortran --version
GNU Fortran (Ubuntu 7.4.0-1ubuntu1~18.04.1) 7.4.0
Copyright (C) 2017 Free Software Foundation, Inc.
This is free software; see the source for copying conditions.  There is NO
warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

ian@eris:~/work/stack$ gfortran -O2 mult.f90
ian@eris:~/work/stack$ ./a.out
          2434.60539278681835639873
          2434.60539278681881114608
          2434.60539278681881114608

Both answers are perfectly correct - you are just seeing one of the effects of floating point maths.