From: William James <w_a_x_man@...>
Date: 2007-09-04T11:15:06+09:00
Subject: Re: wierd floating point output

On Sep 3, 9:02 pm, Stefan Rusterholz <apei...@gmx.net> wrote:
> William James wrote:
> > On Sep 3, 5:32 pm, Stefan Rusterholz <apei...@gmx.net> wrote:
> >> >> using delta comparison anyway too.
> >> end
>
> >> (0.01 + 0.05).in_delta?(0.06) # => true
> >> 0.01 + 0.05 =~ 0.06 # => true # can't set the delta, is similarly evil
> >> as ==
>
> > class Numeric
> >   def in_delta?(other, delta=Float::EPSILON*16) # chose the delta
> > wisely
> >     (self-other).abs < delta
> >   end
> >   alias =~ in_delta?
> > end
>
> > p 1.23456789e4.in_delta?( 1.234567892e4 )
> > p 1.23456789e-1.in_delta?( 1.234567892e-1 )
> > p 1.23456789e-6.in_delta?( 1.234567892e-6 )
> > p 1.23456789e-11.in_delta?( 1.234567892e-11 )
>
> > ==== output ====
> > false
> > false
> > true
> > true
>
> That's why, chose your delta wisely.  It is also why the =~ is only
> marginally less surprising than == and still evil.
> Maybe one could improve it a bit using a delta created using the
> magnitude (hello, dear log). Another approach might be to use the
> quotient of the two numbers (its proximity to 1).

Yes, having manually to choose the delta for each
comparison is not good.

Here is a modificaion of a method mentioned
by Michael Ulm earlier.

def eq( x, y )
  x == y  or
  (x-y).abs < (x.abs + y.abs) * Float::EPSILON * 4
end

DATA.each{|s|
  strings = s.chomp.split(";")
  floats = strings.map{|s| eval(s) }
  puts strings.join( " == " ) +
    " : #{ floats[0]==floats[1] }  #{ eq( *floats ) }"
}

__END__
(0.05+0.01);0.06
(0.34+0.01);0.35
0.0;0.0
1.23456789e9;1.234567892e9
1.23456789e4;1.234567892e4
1.23456789e-1;1.234567892e-1
1.23456789e-6;1.234567892e-6
1.23456789e-11;1.234567892e-11
1.23456789012345e9;1.234567890123452e9
1.23456789012345e4;1.234567890123452e4
1.23456789012345e-1;1.234567890123452e-1
1.23456789012345e-6;1.234567890123452e-6
1.23456789012345e-11;1.234567890123452e-11

==== output ====
(0.05+0.01) == 0.06 : false  true
(0.34+0.01) == 0.35 : false  true
0.0 == 0.0 : true  true
1.23456789e9 == 1.234567892e9 : false  false
1.23456789e4 == 1.234567892e4 : false  false
1.23456789e-1 == 1.234567892e-1 : false  false
1.23456789e-6 == 1.234567892e-6 : false  false
1.23456789e-11 == 1.234567892e-11 : false  false
1.23456789012345e9 == 1.234567890123452e9 : false  true
1.23456789012345e4 == 1.234567890123452e4 : false  true
1.23456789012345e-1 == 1.234567890123452e-1 : false  true
1.23456789012345e-6 == 1.234567890123452e-6 : false  true
1.23456789012345e-11 == 1.234567890123452e-11 : false  true


> With both suggestions I have no idea about hazardeous situations, maybe
> somebody with either more recent CS training or daily use of floats can
> shed some light on that. Also it is too late at night to have clear
> thoughts about that.
>
> Regards
> Stefan