The function enorm provides the Euclidean norm of a vector. From the MINPACK user guide:

The algorithm used in ENORM is a simplified version of Blue's [1978] algorithm. An advantage of the MINPACK-1 version is that it does not require machine constants; a disadvantage is that nondestructive underflows are allowed.

The function enorm is obsolescent as far as I'm concerned. The Fortran 2008 standard and later provide a norm2 intrinsic function. The standard recommends that processors compute the result without undue overflow or underflow.

Other notable norm implementations include:

• Original MINPACK enorm: https://www.netlib.org/minpack/enorm.f
• SLATEC dnrm2: https://www.netlib.org/slatec/lin/dnrm2.f
• Reference BLAS dnrm2: http://www.netlib.org/lapack/explore-3.1.1-html/dnrm2.f.html
• Fortran intrinsic function norm2: gfortran docs, ifort docs

Here's a quick demonstration program:

program main
  implicit none  
  integer, parameter :: dp = kind(1.0d0)
  real(dp) :: x(20)
  real(dp) :: dnrm2, enorm
  call random_number(x)
  print *, "enorm ", enorm(size(x), x)
  print *, "dnrm2 ", dnrm2(size(x), x, 1)
  print *, "norm2 ", norm2(x)
end program

An example run:

$ gfortran dnrm2.f enorm.f norm_example.f90 
$ ./a.out
 enorm    2.1356777438951129     
 dnrm2    2.1356777438951133     
 norm2    2.1356777438951129     

A potential issue of removing enorm in favor of norm2 are the workarounds needed to support older compilers. One approach could be to use a preprocessor block:

pure real(wp) function enorm(n, x)
  integer, intent(in) :: n
  real(wp), intent(in) :: x(n)
#if MINPACK1_ENORM
  ! ... current MINPACK-1 algorithm ...
#else
  enorm = norm2(x)
#endif
end function

Personally, I'd just replace enorm with norm2 everywhere it occurs. If deemed necessary, the original implementation can be preserved as an external subroutine in a "compatibility" folder for older compilers.

I'd also be interested in learning what type of tests can we come up with to prove the "worthiness" of the intrinsic norm2 over the MINPACK-1 algorithm.

Literature

• A Portable Fortran Program to Find the Euclidean Norm of a Vector (1978) | https://doi.org/10.1145/355769.355771
• Efficient Calculations of Faithfully Rounded l2-Norms of n-Vectors (2015) | https://doi.org/10.1145/2699469
• Remark on Algorithm 539: A Modern Fortran Reference Implementation for Carefully Computing the Euclidean Norm (2017) | https://dl.acm.org/doi/10.1145/3134441
• Algorithm 978: Safe Scaling in the Level 1 BLAS (2017) | https://doi.org/10.1145/3061665
• A Rapid Euclidean Norm Calculation Algorithm that Reduces Overflow and Underflow (2021) | https://doi.org/10.1007/978-3-030-86653-2_7
• Accurate calculation of Euclidean Norms using Double-word arithmetic (2022) | https://hal.archives-ouvertes.fr/hal-03482567/