Utilities to peek Float internals on IEEE 754 platform.
require "ieee754hack" implies class Float ; include Ieee754hack ; end
IEEE 754 defines such a bit layout for double precision floating point numbers.
0 1 12 64
+-+-----------+----------------------------------------------------+
|s| e (11bits)| m (52bits) |
+-+-----------+----------------------------------------------------+
s: sign (1 for -1, 0 for +1); e: exponent; m: mantissa
Depending on the magnitude of the number, five different interpretations are defined.
type e m value
---------------------------------------------------------
normal 1..2046 any sign * 1.m * 2**(e-1023)
zero 0 zero sign * 0.0
infinity 2047 zero sign * Infinity
nan 2047 non-zero Not a Number
denormal 0 non-zero sign * 0.m * 2**-1022
where "1.m" stands for a binary string concatenation "1." and 52 bit binary string m.
This library adds several methods to Float class to inspect those representations. For example
1.0.human_readable
#=> "+1 * 0b1.0000000000000000000000000000000000000000000000000000 * 2**(1023-1023)"
You can see what 0.1*3 != 0.3 is.
[0.1*3, 0.3].map{|e| e.human_readable}
#=>
# ["+1 * 0b1.0011001100110011001100110011001100110011001100110100 * 2**(1021-1023)",
# "+1 * 0b1.0011001100110011001100110011001100110011001100110011 * 2**(1021-1023)"]
For more information about IEEE 754, please see https://en.wikipedia.org/wiki/IEEE_754.
Add this line to your application's Gemfile:
gem 'ieee754hack'And then execute:
$ bundle install
Or install it yourself as:
$ gem install ieee754hack
ri Ieee754hack
The gem is available as open source under the terms of the MIT License.