mf_epsilon.hlp

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{smcl}
{* 09feb2005}{...}
{cmd:help mata epsilon()}
{hline}
{* index epsilon()}{...}
{* index roundoff error}{...}
{* index machine precision}{...}

{title:Title}

{p 4 8 2}
{bf:[M-5] epsilon() -- unit roundoff error (machine precision)}


{title:Syntax}

{p 8 12 2}
{it:real scalar}
{cmd:epsilon(}{it:real scalar x}{cmd:)}


{title:Description}

{p 4 4 2}
{cmd:epsilon(}{it:x}{cmd:)} returns the unit roundoff error in quantities 
of size {cmd:abs(}{it:x}{cmd:)}.


{title:Remarks}

{p 4 4 2}
On all computers on which Stata and Mata are currently implemented -- 
which are computers following IEEE standards -- 
{cmd:epsilon(1)} is 1.0X-34, or about 2.22045e-16.
This is the smallest amount by which a real number can differ from 1.

{p 4 4 2}
{cmd:epsilon(}{it:x}{cmd:)} is {cmd:abs(}{it:x}{cmd:)}{cmd:*epsilon(1)}.
This is an approximation of 
the smallest amount by which a real number can differ from 
{it:x}.  The approximation is exact at integer powers of 2.


{title:Conformability}

    {cmd:epsilon(}{it:x}{cmd:)}:
		{it:x}:  1 {it:x} 1
	   {it:result}:  1 {it:x} 1


{title:Diagnostics}

{p 4 4 2}
{cmd:epsilon(}{it:x}{cmd:)}
returns missing if {it:x} is missing.


{title:Source code}

{p 4 4 2}
Function is built-in.


{title:Also see}

{p 4 13 2}
Manual:  {hi:[M-5] epsilon()}

{p 4 13 2}
Online:  help for 
{bf:{help mf_mindouble:[M-5] mindouble()}},
{bf:{help mf_edittozero:[M-5] edittozero()}};
{bf:{help m4_utility:[M-4] utility}}
{p_end}