Multiple Precision Interval Arithmetic

Dr. David M. Smith
Professor of Mathematics (Emeritus)
Loyola Marymount University
Los Angeles, CA


Overview of the FM interval arithmetic package

The package performs multiple-precision real interval arithmetic.
It provides the intrinsic Fortran numerical functions, as well as many special
functions that are not included in the Fortran standard.

One of the primary uses of the package is to study the accuracy and stability of numerical
algorithms by using interval arithmetic, giving results that are intervals guaranteed to
contain the exact solution.

The precision and base for the arithmetic can be set by the user.

The program SampleFMinterval.f95 below gives examples of using FM for interval calculations.


Files for the FM interval arithmetic package:


The actual files shown on this page are in this archive that contains all the FM files from this
website: FM_files.zip

The individual file pointers here display as pdf files for browsing. The longer files are cut
off after 20 pages.


fm_interval.f95
Subroutine library for multiple-precision interval operations. 22,346 lines of code

TestFMinterval.f95
Checks several operations for each of the fm_interval routines. 19,886 lines of code

SampleFMinterval.f95
Small sample program using fm_interval. 661 lines of code

SampleFMinterval.chk
Expected output file from SampleFMinterval.f95. 192 lines

IntervalExamplesFM.f95
Interval examples from "A Multiple-Precision Interval Arithmetic Package". 1,099 lines of code

IntervalExamplesFM.chk
Expected output file from IntervalExamplesFM.f95. 360 lines

FM_Interval_User_Manual.txt
User's guide for the package, along with a list of the files, and an example set of
compiler/linker commands for building the programs. 182 lines


Paper (in pdf format)

This paper describes the package and discusses several examples showing cases where interval
arithmetic works well and also cases where it doesn't.

A Multiple-Precision Interval Arithmetic Package
http://myweb.lmu.edu/dmsmith/FMLIB.html (2014) 1 -- 13


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