Old School
I came across this old NASA document from 1963, where a cross product subroutine is defined in Fortran (based on some of the other routines given, it looks like they were using FORTRAN II):
A cross product function is always a necessary procedure in any orbital mechanics simulation (for example when computing the angular momentum vector \(\mathbf{h} = \mathbf{r} \times \mathbf{v}\)). The interesting thing is that this subroutine will still compile today with any Fortran compiler. Of course, there are a few features used here that are deemed obsolescent in modern Fortran (fixed-form source, implicit typing, and the DIMENSION statement). Also it is using single precision reals (which no one uses anymore in this field). A modernized version would look something like this:
subroutine cross(a,b,c)
implicit none
real(wp),dimension(3),intent(in) :: a,b
real(wp),dimension(3),intent(out) :: c
c(1) = a(2)*b(3)-a(3)*b(2)
c(2) = a(3)*b(1)-a(1)*b(3)
c(3) = a(1)*b(2)-a(2)*b(1)
end subroutine cross
But, basically, except for declaring the real kind, it does exactly the same thing as the one from 1963. The modern routine would presumably be put in a module (in which the WP kind parameter is accessible), for example, a vector utilities module. While a subroutine is perfectly acceptable for this case, my preference would be to use a function like so:
pure function cross(a,b) result(c)
implicit none
real(wp),dimension(3),intent(in) :: a,b
real(wp),dimension(3) :: c
c(1) = a(2)*b(3)-a(3)*b(2)
c(2) = a(3)*b(1)-a(1)*b(3)
c(3) = a(1)*b(2)-a(2)*b(1)
end function cross
This one is a function that return a \(\mathrm{3} \times \mathrm{1}\) vector, and is explicitly declared to be PURE (which can allow for more aggressive code optimizations from the compiler).
This document, which is the programmer's manual for an interplanetary error propagation program, contains a lot of other Fortran gems. It also has some awesome old school flow charts:
See also
- Programmer's Manual for Interplanetary Error Propagation Program, Philco Corp., NASA-CR-69535, Nov 15, 1963