Re: Floating point multiplication in python

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From	Terry Reedy <tjreedy@udel.edu>
Subject	Re: Floating point multiplication in python
Date	Wed, 07 Sep 2011 05:37:32 -0400
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On 9/7/2011 12:51 AM, Steven D'Aprano wrote:

> So given a float x, when you square it you get this:
>
> Exact values: a*a = a**2
>
> Float values: x*x = (a+e)(a+e)
>                    = a**2 + 2*a*e + e**2
>
> So the error term has increased from e to (2*a*e+e**2). It is usual to
> assume that e**2 is small enough that it underflows to zero, so we have the
> error term e increasing to 2*a*e as a fairly simple estimate of the new
> error.

And the relative error, which is what is often important, increases from 
e/a to 2e/a.

-- 
Terry Jan Reedy

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Thread

Floating point multiplication in python xyz <xyzhtml@163.com> - 2011-09-06 13:57 +0800
  Re: Floating point multiplication in python Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2011-09-06 17:11 +1000
  Re: Floating point multiplication in python Thomas Rachel <nutznetz-0c1b6768-bfa9-48d5-a470-7603bd3aa915@spamschutz.glglgl.de> - 2011-09-06 12:14 +0200
    Re: Floating point multiplication in python Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2011-09-06 18:07 +0200
      Re: Floating point multiplication in python Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2011-09-07 14:51 +1000
        Re: Floating point multiplication in python Dennis Lee Bieber <wlfraed@ix.netcom.com> - 2011-09-06 23:35 -0700
        Re: Floating point multiplication in python Gelonida N <gelonida@gmail.com> - 2011-09-07 10:57 +0200
        Re: Floating point multiplication in python Terry Reedy <tjreedy@udel.edu> - 2011-09-07 05:37 -0400

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