The original source code for the book
Computer Methods for Mathematical Computations
by Forsythe, Malcolm and Moler was developed prior to the
release of the Fortran 77 standard.
The following notes summarize the changes made to the original
pre-Fortran 77 library to make it into modern Fortran.
- The routines all compile under Essential Lahey Fortran (ELF).
This requires that there is no implicit typing, the intent of
all procedure arguments is declared, no obsolete control
statements are used, no COMMON or EQUIVALENCE statements are
used and numerous ELF requirements on syntax are honored.
They also compile with no warnings with the strict-Fortran-95
flag with both gfortran and g95.
- No dimensions are passed as arguments.
The intrinsic function SIZE is used by all procedures to
determine the size of the vectors and matrices.
- All DO-loops are converted to DO-END DO without statement numbers.
CYCLE and EXIT are used for loop navigation.
Loops that count down now use the third argument of -1 for decrementing.
- There are no input or output statements anywhere in the library.
All procedures that had warning messages now have error code variables
that signal error conditions.
- There are single and double precision versions of all procedures.
There are MODULE INTERFACE statements that allow the same subroutine
name to be used, regardless of the precision chosen.
- I have not performed what might be called an "aggressive" recoding of
the older Fortran code.
In particular, there are still GO TO statements and a number of loops
could still be converted to array notation or inner-product constructions.
- If you have studied the codes in
Numerical Recipes in Fortran 90,
you will see numerous occurrences of outerprod, spread, swap, imaxloc and
other constructions that may shorten the code and possibly make it more
efficient, but at the expense of requiring the use of a package of
I have chosen to avoid this.
- I have avoided all temptations of "improving" the numerical algorithms
You should get the same numerical values as the original coding.
- The routines Zeroin and Fmin have been recoded with additional
arguments for added control.
The original Zeroin and Fmin functions are still included as wrappers
for the new BrentZero and BrentMin subroutines.
- The original library included a portable random number generator.
Since there is now a standard intrinsic in Fortran, I have omitted
- The original library was written entirely in upper case and the authors
were rather fond of the upper-case letter L as a subscript.
The variables are now lower case, and
I personally abhor the lower case letter l as a subscript due to its
resemblance to the number one and uppercase I.
I have removed almost all such occurrences.
One great value of the original code was that the original authors put no
restrictions on the distribution of the code and it may be downloaded
I declare that all of my added value to the library is contributed to the
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