From: Robert Klemme <shortcutter@...>
Date: 2007-08-20T03:04:58+09:00
Subject: Re: Float addition problem / Processor bug?

On 19.08.2007 19:49, Christian Luginbuehl wrote:
> Hi,
> 
> Check out this weird IRB output:
> 
> === START ===
> irb(main):001:0> a = 2.95 + 2.95 + 2.95
> => 8.85
> irb(main):002:0> puts 8.85 - a
> -1.77635683940025e-15
> => nil
> === END ===
> 
> I'm running "ruby 1.8.6 (2007-06-07 patchlevel 36) [i486-linux]" on 
> Xubuntu beta with this processor:
> 
> === START cat /proc/cpuinfo ===
> processor       : 0
> vendor_id       : GenuineIntel
> cpu family      : 15
> model           : 2
> model name      : Intel(R) Pentium(R) 4 CPU 2.26GHz
> stepping        : 4
> cpu MHz         : 2271.951
> cache size      : 512 KB
> fdiv_bug        : no
> hlt_bug         : no
> f00f_bug        : no
> coma_bug        : no
> fpu             : yes
> fpu_exception   : yes
> cpuid level     : 2
> wp              : yes
> flags           : fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge 
> mca cmov pat pse36 clflush dts acpi mmx fxsr sse sse2 ss ht tm up
> bogomips        : 4547.85
> clflush size    : 64
> === END cat /proc/cpuinfo ===
> 
> Is it a processor bug, a simple rounding problem or a ruby error?

The second one.  This is a standard rounding issue.  The short 
explanation is that you see the numbers in decimal system while the 
computer uses binary representation for floats.

> How do I proceed?

Live with it or use other data types like BigDecimal or Rational.

irb(main):001:0> require 'bigdecimal'
=> true
irb(main):002:0> x = BigDecimal.new "2.95"
=> #<BigDecimal:7ff8def8,'0.295E1',8(8)>
irb(main):003:0> a = x + x + x
=> #<BigDecimal:7ff82d78,'0.885E1',8(16)>
irb(main):004:0> 8.85 - a
=> 0.0
irb(main):005:0> (8.85 - a).class
=> Float
irb(main):007:0> BigDecimal.new("8.85") - a
=> #<BigDecimal:7ff70128,'0.0',4(16)>
irb(main):008:0>

Kind regards

	robert