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pgbench: Allow \setrandom to generate Gaussian/exponential distributions.

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Mitsumasa KONDO and Fabien COELHO, with further wordsmithing by me.
This commit is contained in:
Robert Haas
2014-07-30 13:22:08 -04:00
parent e280c630a8
commit ed802e7dc3
2 changed files with 231 additions and 13 deletions
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61
doc/src/sgml/pgbench.sgml
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@ -748,8 +748,8 @@ pgbench <optional> <replaceable>options</> </optional> <replaceable>dbname</>
<varlistentry>
<term>
<literal>\setrandom <replaceable>varname</> <replaceable>min</> <replaceable>max</></literal>
</term>
<literal>\setrandom <replaceable>varname</> <replaceable>min</> <replaceable>max</> [ uniform | [ { gaussian | exponential } <replaceable>threshold</> ] ]</literal>
</term>
<listitem>
<para>
@ -760,10 +760,65 @@ pgbench <optional> <replaceable>options</> </optional> <replaceable>dbname</>
having an integer value.
</para>
<para>
By default, or when <literal>uniform</> is specified, all values in the
range are drawn with equal probability. Specifiying <literal>gaussian</>
or <literal>exponential</> options modifies this behavior; each
requires a mandatory threshold which determines the precise shape of the
distribution.
</para>
<para>
For a Gaussian distribution, the interval is mapped onto a standard
normal distribution (the classical bell-shaped Gaussian curve) truncated
at <literal>-threshold</> on the left and <literal>+threshold</>
on the right.
To be precise, if <literal>PHI(x)</> is the cumulative distribution
function of the standard normal distribution, with mean <literal>mu</>
defined as <literal>(max + min) / 2.0</>, then value <replaceable>i</>
between <replaceable>min</> and <replaceable>max</> inclusive is drawn
with probability:
<literal>
(PHI(2.0 * threshold * (i - min - mu + 0.5) / (max - min + 1)) -
PHI(2.0 * threshold * (i - min - mu - 0.5) / (max - min + 1))) /
(2.0 * PHI(threshold) - 1.0)
</>
Intuitively, the larger the <replaceable>threshold</>, the more
frequently values close to the middle of the interval are drawn, and the
less frequently values close to the <replaceable>min</> and
<replaceable>max</> bounds.
About 67% of values are drawn from the middle <literal>1.0 / threshold</>
and 95% in the middle <literal>2.0 / threshold</>; for instance, if
<replaceable>threshold</> is 4.0, 67% of values are drawn from the middle
quarter and 95% from the middle half of the interval.
The minimum <replaceable>threshold</> is 2.0 for performance of
the Box-Muller transform.
</para>
<para>
For an exponential distribution, the <replaceable>threshold</>
parameter controls the distribution by truncating a quickly-decreasing
exponential distribution at <replaceable>threshold</>, and then
projecting onto integers between the bounds.
To be precise, value <replaceable>i</> between <replaceable>min</> and
<replaceable>max</> inclusive is drawn with probability:
<literal>(exp(-threshold*(i-min)/(max+1-min)) -
exp(-threshold*(i+1-min)/(max+1-min))) / (1.0 - exp(-threshold))</>.
Intuitively, the larger the <replaceable>threshold</>, the more
frequently values close to <replaceable>min</> are accessed, and the
less frequently values close to <replaceable>max</> are accessed.
The closer to 0 the threshold, the flatter (more uniform) the access
distribution.
A crude approximation of the distribution is that the most frequent 1%
values in the range, close to <replaceable>min</>, are drawn
<replaceable>threshold</>% of the time.
The <replaceable>threshold</> value must be strictly positive.
</para>
<para>
Example:
<programlisting>
\setrandom aid 1 :naccounts
\setrandom aid 1 :naccounts gaussian 5.0
</programlisting></para>
</listitem>
</varlistentry>