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Re: Math cube root

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On Wed, 11 May 2011 21:45:42 +0200, Sergey Avseyev  
<sergey.avseyev@gmail.com> wrote:

> How can you explain this:
>
>     $ irb
>     1.9.2p180 (main):001:0> 1000 ** (1.0/3)
>     9.999999999999998
>     1.9.2p180 (main):002:0> Math.sqrt(100)
>     10.0

Floating-point numbers have a finite precision. As a result, the outcome  
of a numerical (computer) calculation usually differs from the outcome of  
the mathematical calculation. Assume you only can operate with integers  
and want to compute the square root of 133. You may then end up with  
either 11 (11² = 121) or 12 (12² = 144) while the actual result is  
approximately 11.5 (11.5² = 121 + 11 + 0.25 = 132.25; more precisely  
11.5325625947).

You may like to use formatted output of numbers that suppresses digits  
beyond the actual precision:

jupp@pen2:~ $ irb
irb(main):001:0> "%.15f" % 1000 ** (1.0/3)
=> "9.999999999999998"
irb(main):002:0> "%.14f" % 1000 ** (1.0/3)
=> "10.00000000000000"

The above example turns the numerical value into a string displaying a  
fractional part with 15 and 14 digits, respectively. Assuming that IEEE  
754 double precision floating point numbers (i.e. those used by Ruby) have  
a precision of a little less than 16 (decimal) digits it is safe to assume  
that the complexity of operation you perform results in a value that is  
precise to a little less than 15 digits - which means that you can assume  
14 digits to be correct. By chance it MAY be precise to more digits as it  
is the case for Math.sqrt(100) - but that is nothing you can rely on  
unless you learn some gory details of numerical mathematics.

HTH

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Re: Math cube root Sergey Avseyev <sergey.avseyev@gmail.com> - 2011-05-11 14:45 -0500
  Re: Math cube root Jeremy Bopp <jeremy@bopp.net> - 2011-05-11 15:06 -0500
  Re: Math cube root Josef 'Jupp' Schugt <jupp@gmx.de> - 2011-05-12 07:25 -0500
    Re: Math cube root serialhex <serialhex@gmail.com> - 2011-05-12 08:54 -0500
      Re: Math cube root Colin Bartlett <colinb2r@googlemail.com> - 2011-05-12 10:26 -0500
        Re: Math cube root Josh Cheek <josh.cheek@gmail.com> - 2011-05-12 13:30 -0500
          Re: Math cube root serialhex <serialhex@gmail.com> - 2011-05-12 13:46 -0500
          Re: Math cube root Rob Biedenharn <Rob@AgileConsultingLLC.com> - 2011-05-12 13:53 -0500
            Re: Math cube root jzakiya <jzakiya@gmail.com> - 2011-05-12 13:20 -0700
              Re: Math cube root serialhex <serialhex@gmail.com> - 2011-05-12 15:36 -0500
          Re: Math cube root Martin DeMello <martindemello@gmail.com> - 2011-05-14 13:12 -0500

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