Re^2: Help me make a test case for Math::BigFloat

[fizbin]

I don't care what I'm initializing something with, there shouldn't be any way to create $ev such that both $ev and 1-$ev print as "1".

And as for initializing everything as strings, look at this code:

#!perl
use Math::BigFloat;
print ((new Math::BigFloat("1")) -
       exp(new Math::BigFloat("-7") /
             (new Math::BigFloat("10")**(new Math::BigFloat("17")))));
# Properly prints "0"
# (well, something like 7e-17 would be closer, but I'll accept 0)

Compare it to this code, which is the same but with a use bignum:

#!perl
use bignum;
use Math::BigFloat;
print ((new Math::BigFloat("1")) -
       exp(new Math::BigFloat("-7") /
             (new Math::BigFloat("10")**(new Math::BigFloat("17")))));
# Incorrectly prints "1"

It would appear then that we have a bug not so much in Math::BigFloat directly, but somewhere in the intersection of Math::BigFloat, bignum, and the magic bignum sprinkles on exp.

[BrowserUk]

Hmm. There seem to be two interacting problems here.

1. exp doesn't appear to be overloaded by either bignum or Math::BigFloat?

   #!perl -slw
   use strict;
   use overload;
   #use bignum;
   use Math::BigFloat;
   
   printf "exp(-7e-17): %.17f\n", my $exp = exp( Math::BigFloat->new( '-7
   +e-17' ) );
   
   eval{ print overload::Overloaded( $exp ) } or warn $@;
   print overload::StrVal( $exp );
   
   printf "1-exp(-7-e17): %.17f\n", Math::BigFloat->new("1") - $exp;
   __END__
   C:\test>junk7
   exp(-7e-17): 0.99999999999999989
   Can't call method "can" without a package or object reference at c:/Pe
   +rl/lib/overload.pm line 54.
   1
   1-exp(-7-e17): 0.00000000000000000
   

2. And with bignum enabled, Math::BigFloat seems to forget how to do math? At least if the math involves one BigMath object and one normal perl number.

   #!perl -slw
   use strict;
   use overload;
   use bignum;
   use Math::BigFloat;
   
   printf "exp(-7e-17): %.17f\n", my $exp = exp( Math::BigFloat->new( '-7
   +e-17' ) );
   
   eval{ print overload::Overloaded( $exp ) } or warn $@;
   print overload::StrVal( $exp );
   
   printf "1-exp(-7-e17): %.17f\n", Math::BigFloat->new("1") - $exp;
   
   __END__
   C:\test>junk7
   exp(-7e-17): 0.99999999999999989
   Can't call method "can" without a package or object reference at c:/Pe
   +rl/lib/overload.pm line 54.
   1
   1-exp(-7-e17): 1.00000000000000000
   

All of which makes me glad that I rarely need the accuracy beyond 53-bits and when I do, 64-bit ints suffice.

[spiritway]

All of which makes me glad that I rarely need the accuracy beyond 53-bits and when I do, 64-bit ints suffice.

This is why I prefer to keep things as rationals (or bigrats), rather than floats - it's possible to represent them accurately without encountering the inevitable rounding or truncating errors. True, all the irrational numbers will still truncate, but the rationals won't. I only use the decimal representation for display purposes, sometimes.

[fizbin]

Note that all the brokenness here can be gotten also by saying use bigrat; instead of use bignum; - there's something about those modules that causes weirdness with exp of certain close-to-zero quantities. (but not all - change the -7e-17 to a -7e-18 and all is right with the universe again.)