This post is based on the following theory:

<theory>Since Perl's floating point precision is constrained by what can be stored in an NV, the minimal change to a floating point value that Perl should be able to accommodate would be obtained by twiddling the least significant bit in an NV.</theory>

Here's an example (which may be completely bogus) of what I'm getting at. Unfortunately my understanding of Perl's internal representation of a float within an NV is limited, so this approach is at best just intended to explore the possibility.

use strict;
use warnings;

my $fp = 1/2; # m/2^n may be represented perfectly in base 2.
printf "%25.32g\n", $fp;
my $p = pack 'F', $fp;
my $b = unpack 'b*', $p;
print "$b\n";
$b =~ s/(.)/$1 ? 0 : 1/e;
print "$b\n";
my $np = pack 'b*', $b;
my $nfp = unpack 'F', $np;
printf "%25.32g\n", $nfp;

[download]

The output:

                      0.5
0000000000000000000000000000000000000000000000000000011111111100
1000000000000000000000000000000000000000000000000000011111111100
0.50000000000000011102230246251565

[download]

So it would appear that the least significant change that can be represented in an NV that was holding the decimal floating point value of 0.5 would be 0.00000000000000011102230246251565.

In my example, I started with a value that I knew could be represented precisely in native base-2 format, and essentially ended up with another number that can be stored precisely in native base-2. It just happens to be a number that is rather ugly in base 10.

Apologies if this is getting off into the wrong field of weeds, or if my example inadequately implements the theory I put forth, but the topic seemed interesting and I thought I'd post my exploration.


Dave

In reply to Re: Determining the minimum representable increment/decrement possible? by davido
in thread Determining the minimum representable increment/decrement possible? by BrowserUk

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