From: Mauricio Fernandez <mfp@...>
Date: 2006-05-18T07:49:34+09:00
Subject: Re: greatest float smaller than 1.0?

On Thu, May 18, 2006 at 06:52:18AM +0900, Joel VanderWerf wrote:
> Joel VanderWerf wrote:
> > polypus wrote:
> >> how do i get the greatest float smaller than 1.0?
> >>
> >> thanks
> >>
> > 
> > Something like this maybe?
> > 
> > irb(main):006:0> [0.9999999999999999].pack "G"
> > => "?\357\377\377\377\377\377\377"
> > 
> > (that was just to find out what floats look like in memory, big-endian).
> > 
> > irb(main):012:0> x = ("?\357" + "\377"*100).unpack "G"
> > => [1.0]
> > irb(main):013:0> "%30f" % x
> > => "0.999999999999999888977697537484"
> > 
> > Dunno if that's safe on all platforms...
> 
> That was completely wrong, please ignore.
> 
> irb(main):059:0> y = 1e-305
> => 1.0e-305
> irb(main):060:0> [y].pack "G"
> => "\000\234\026\305\305%5t"
> irb(main):061:0> [y].pack("G").unpack("G")
> => [1.0e-305]
> 
> It's the exponent that needs to be chosen, not just the mantissa.
> 
> Still, it leaves the question open why Float::EPSILON is nowhere near
> this exponent.

oops

subtraction == funny

x = 1.0 - Float::EPSILON/2      # => 1.0
"%.30f" % x                     # => "0.999999999999999888977697537484"

EPSILON is a bound for the relative error between a real and its floating
point representation, not the smallest (absolute value) representable value.

It's clearer with addition:

x = 1.0 + Float::EPSILON      # => 1.0
"%.30f" % x                   # => "1.000000000000000222044604925031"
x = 1.0 + Float::EPSILON/2     # => 1.0
"%.30f" % x                   # => "1.000000000000000000000000000000"

-- 
Mauricio Fernandez  -   http://eigenclass.org   -  singular Ruby