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Restrict pgbench's zipfian parameter to ensure good performance.

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Remove the code that supported zipfian distribution parameters less
than 1.0, as it had undocumented performance hazards, and it's not
clear that the case is useful enough to justify either fixing or
documenting those hazards.

Also, since the code path for parameter > 1.0 could perform badly
for values very close to 1.0, establish a minimum allowed value
of 1.001.  This solution seems superior to the previous vague
documentation warning about small values not performing well.

Fabien Coelho, per a gripe from Tomas Vondra

Discussion: https://postgr.es/m/b5e172e9-ad22-48a3-86a3-589afa20e8f7@2ndquadrant.com
This commit is contained in:
Tom Lane
2019-04-01 17:37:26 -04:00
parent 4fd05bb55b
commit 26a76cb640
3 changed files with 32 additions and 193 deletions
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27
doc/src/sgml/ref/pgbench.sgml
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@ -1543,29 +1543,17 @@ f(x) = PHI(2.0 * parameter * (x - mu) / (max - min + 1)) /
middle quarter (1.0 / 4.0) of the interval (i.e. from
<literal>3.0 / 8.0</literal> to <literal>5.0 / 8.0</literal>) and 95% from
the middle half (<literal>2.0 / 4.0</literal>) of the interval (second and third
quartiles). The minimum <replaceable>parameter</replaceable> is 2.0 for performance
of the Box-Muller transform.
quartiles). The minimum allowed <replaceable>parameter</replaceable>
value is 2.0.
</para>
</listitem>
<listitem>
<para>
<literal>random_zipfian</literal> generates an approximated bounded Zipfian
distribution. For <replaceable>parameter</replaceable> in (0, 1), an
approximated algorithm is taken from
"Quickly Generating Billion-Record Synthetic Databases",
Jim Gray et al, SIGMOD 1994. For <replaceable>parameter</replaceable>
in (1, 1000), a rejection method is used, based on
"Non-Uniform Random Variate Generation", Luc Devroye, p. 550-551,
Springer 1986. The distribution is not defined when the parameter's
value is 1.0. The function's performance is poor for parameter values
close and above 1.0 and on a small range.
</para>
<para>
<literal>random_zipfian</literal> generates a bounded Zipfian
distribution.
<replaceable>parameter</replaceable> defines how skewed the distribution
is. The larger the <replaceable>parameter</replaceable>, the more
frequently values closer to the beginning of the interval are drawn.
The closer to 0 <replaceable>parameter</replaceable> is,
the flatter (more uniform) the output distribution.
The distribution is such that, assuming the range starts from 1,
the ratio of the probability of drawing <replaceable>k</replaceable>
versus drawing <replaceable>k+1</replaceable> is
@ -1576,6 +1564,13 @@ f(x) = PHI(2.0 * parameter * (x - mu) / (max - min + 1)) /
itself is produced <literal>(3/2)*2.5 = 2.76</literal> times more
frequently than <literal>3</literal>, and so on.
</para>
<para>
<application>pgbench</application>'s implementation is based on
"Non-Uniform Random Variate Generation", Luc Devroye, p. 550-551,
Springer 1986. Due to limitations of that algorithm,
the <replaceable>parameter</replaceable> value is restricted to
the range [1.001, 1000].
</para>
</listitem>
</itemizedlist>