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PODoes Fortran have inherent limitations on numerical accuracy compared to other languages?
 

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  1. PODoes Fortran have inherent limitations on numerical accuracy compared to other languages?
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    <p>While working on a simple programming exercise, I produced a while loop (DO loop in Fortran) that was meant to exit when a real variable had reached a precise value.</p> <p>I noticed that due to the precision being used, the equality was never met and the loop became infinite. This is, of course, not unheard of and one is advised that, rather than comparing two numbers for equality, it is best see if the absolute difference between two numbers is less than a set threshold.</p> <p>What I found disappointing was how low I had to set this threshold, even with variables at double precision, for my loop to exit properly. Furthermore, when I rewrote a "distilled" version of this loop in Perl, I had no problems with numerical accuracy and the loop exited fine.</p> <p>Since the code to produce the problem is so small, in both Perl and Fortran, I'd like to reproduce it here in case I am glossing over an important detail:</p> <p><strong>Fortran Code</strong></p> <pre><code>PROGRAM precision_test IMPLICIT NONE ! Data Dictionary INTEGER :: count = 0 ! Number of times the loop has iterated REAL(KIND=8) :: velocity REAL(KIND=8), PARAMETER :: MACH_2_METERS_PER_SEC = 340.0 velocity = 0.5 * MACH_2_METERS_PER_SEC ! Initial Velocity DO WRITE (*, 300) velocity 300 FORMAT (F20.8) IF (count == 50) EXIT IF (velocity == 5.0 * MACH_2_METERS_PER_SEC) EXIT ! IF (abs(velocity - (5.0 * MACH_2_METERS_PER_SEC)) &lt; 1E-4) EXIT velocity = velocity + 0.1 * MACH_2_METERS_PER_SEC count = count + 1 END DO END PROGRAM precision_test </code></pre> <p><strong>Perl Code</strong></p> <pre><code>#! /usr/bin/perl -w use strict; my $mach_2_meters_per_sec = 340.0; my $velocity = 0.5 * $mach_2_meters_per_sec; while (1) { printf "%20.8f\n", $velocity; exit if ($velocity == 5.0 * $mach_2_meters_per_sec); $velocity = $velocity + 0.1 * $mach_2_meters_per_sec; } </code></pre> <p>The commented-out line in Fortran is what I would need to use for the loop to exit normally. Notice that the threshold is set to 1E-4, which I feel is quite pathetic.</p> <p>The names of the variables come from the self-study-based programming exercise I was performing and don't have any relevance. </p> <p>The intent is that the loop stops when the velocity variable reaches 1700.</p> <p>Here are the truncated outputs:</p> <p><strong>Perl Output</strong></p> <pre><code> 170.00000000 204.00000000 238.00000000 272.00000000 306.00000000 340.00000000 </code></pre> <p>...</p> <pre><code> 1564.00000000 1598.00000000 1632.00000000 1666.00000000 1700.00000000 </code></pre> <p><strong>Fortran Output</strong></p> <pre><code> 170.00000000 204.00000051 238.00000101 272.00000152 306.00000203 340.00000253 </code></pre> <p>...</p> <pre><code> 1564.00002077 1598.00002128 1632.00002179 1666.00002229 1700.00002280 </code></pre> <p>What good is Fortran's speed and ease of parallelization if its accuracy stinks? Reminds me of the three ways to do things:</p> <ol> <li><p>The Right Way</p></li> <li><p>The Wrong Way</p></li> <li><p>The Max Power Way</p></li> </ol> <p>"Isn't that just the wrong way?"</p> <p>"Yeah! But faster!"</p> <p>All kidding aside, I must be doing something wrong.</p> <p>Does Fortran have inherent limitations on numerical accuracy compared to other languages, or am I (quite likely) the one at fault?</p> <p>My compiler is gfortran (gcc version 4.1.2), Perl v5.12.1, on a Dual Core AMD Opteron @ 1 GHZ.</p>
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    1. COShouldn't #3 be "The Max Power way"?
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    2. COWhoops. You're right. Thanks!
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    3. COFortran is using a double here and I suspect Perl to do the same. But checking for an equal with a floating point number is asking for problems (unless you have a "safe" number like `0.0144`). So I would say that it is probably your method of testing that is wrong.
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