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pgbench: Support double constants and functions.
The new functions are pi(), random(), random_exponential(), random_gaussian(), and sqrt(). I was worried that this would be slower than before, but, if anything, it actually turns out to be slightly faster, because we now express the built-in pgbench scripts using fewer lines; each \setrandom can be merged into a subsequent \set. Fabien Coelho
This commit is contained in:
Robert Haas
@ -815,9 +815,10 @@ pgbench <optional> <replaceable>options</> </optional> <replaceable>dbname</>
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<listitem>
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<para>
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Sets variable <replaceable>varname</> to an integer value calculated
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Sets variable <replaceable>varname</> to a value calculated
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from <replaceable>expression</>.
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The expression may contain integer constants such as <literal>5432</>,
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double constants such as <literal>3.14159</>,
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references to variables <literal>:</><replaceable>variablename</>,
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unary operators (<literal>+</>, <literal>-</>) and binary operators
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(<literal>+</>, <literal>-</>, <literal>*</>, <literal>/</>,
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@ -830,7 +831,7 @@ pgbench <optional> <replaceable>options</> </optional> <replaceable>dbname</>
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Examples:
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<programlisting>
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\set ntellers 10 * :scale
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\set aid (1021 * :aid) % (100000 * :scale) + 1
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\set aid (1021 * random(1, 100000 * :scale)) % (100000 * :scale) + 1
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</programlisting></para>
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</listitem>
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</varlistentry>
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@ -850,66 +851,35 @@ pgbench <optional> <replaceable>options</> </optional> <replaceable>dbname</>
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</para>
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<para>
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By default, or when <literal>uniform</> is specified, all values in the
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range are drawn with equal probability. Specifying <literal>gaussian</>
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or <literal>exponential</> options modifies this behavior; each
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requires a mandatory parameter which determines the precise shape of the
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distribution.
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</para>
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<itemizedlist>
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<listitem>
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<para>
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<literal>\setrandom n 1 10</> or <literal>\setrandom n 1 10 uniform</>
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is equivalent to <literal>\set n random(1, 10)</> and uses a uniform
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distribution.
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</para>
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</listitem>
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<para>
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For a Gaussian distribution, the interval is mapped onto a standard
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normal distribution (the classical bell-shaped Gaussian curve) truncated
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at <literal>-parameter</> on the left and <literal>+parameter</>
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on the right.
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Values in the middle of the interval are more likely to be drawn.
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To be precise, if <literal>PHI(x)</> is the cumulative distribution
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function of the standard normal distribution, with mean <literal>mu</>
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defined as <literal>(max + min) / 2.0</>, with
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<literallayout>
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f(x) = PHI(2.0 * parameter * (x - mu) / (max - min + 1)) /
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(2.0 * PHI(parameter) - 1.0)
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</literallayout>
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then value <replaceable>i</> between <replaceable>min</> and
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<replaceable>max</> inclusive is drawn with probability:
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<literal>f(i + 0.5) - f(i - 0.5)</>.
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Intuitively, the larger <replaceable>parameter</>, the more
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frequently values close to the middle of the interval are drawn, and the
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less frequently values close to the <replaceable>min</> and
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<replaceable>max</> bounds. About 67% of values are drawn from the
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middle <literal>1.0 / parameter</>, that is a relative
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<literal>0.5 / parameter</> around the mean, and 95% in the middle
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<literal>2.0 / parameter</>, that is a relative
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<literal>1.0 / parameter</> around the mean; for instance, if
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<replaceable>parameter</> is 4.0, 67% of values are drawn from the
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middle quarter (1.0 / 4.0) of the interval (i.e. from
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<literal>3.0 / 8.0</> to <literal>5.0 / 8.0</>) and 95% from
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the middle half (<literal>2.0 / 4.0</>) of the interval (second and
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third quartiles). The minimum <replaceable>parameter</> is 2.0 for
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performance of the Box-Muller transform.
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</para>
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<listitem>
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<para>
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<literal>\setrandom n 1 10 exponential 3.0</> is equivalent to
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<literal>\set n random_exponential(1, 10, 3.0)</> and uses an
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exponential distribution.
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</para>
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</listitem>
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<para>
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For an exponential distribution, <replaceable>parameter</>
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controls the distribution by truncating a quickly-decreasing
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exponential distribution at <replaceable>parameter</>, and then
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projecting onto integers between the bounds.
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To be precise, with
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<literallayout>
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f(x) = exp(-parameter * (x - min) / (max - min + 1)) / (1.0 - exp(-parameter))
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</literallayout>
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Then value <replaceable>i</> between <replaceable>min</> and
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<replaceable>max</> inclusive is drawn with probability:
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<literal>f(x) - f(x + 1)</>.
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Intuitively, the larger <replaceable>parameter</>, the more
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frequently values close to <replaceable>min</> are accessed, and the
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less frequently values close to <replaceable>max</> are accessed.
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The closer to 0 <replaceable>parameter</>, the flatter (more uniform)
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the access distribution.
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A crude approximation of the distribution is that the most frequent 1%
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values in the range, close to <replaceable>min</>, are drawn
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<replaceable>parameter</>% of the time.
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<replaceable>parameter</> value must be strictly positive.
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<listitem>
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<para>
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<literal>\setrandom n 1 10 gaussian 2.0</> is equivalent to
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<literal>\set n random_gaussian(1, 10, 2.0)</>, and uses a gaussian
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distribution.
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</para>
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</listitem>
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</itemizedlist>
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See the documentation of these functions below for further information
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about the precise shape of these distributions, depending on the value
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of the parameter.
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</para>
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<para>
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@ -990,34 +960,6 @@ f(x) = exp(-parameter * (x - min) / (max - min + 1)) / (1.0 - exp(-parameter))
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</listitem>
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</varlistentry>
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</variablelist>
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<para>
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As an example, the full definition of the built-in TPC-B-like
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transaction is:
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<programlisting>
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\set nbranches :scale
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\set ntellers 10 * :scale
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\set naccounts 100000 * :scale
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\setrandom aid 1 :naccounts
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\setrandom bid 1 :nbranches
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\setrandom tid 1 :ntellers
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\setrandom delta -5000 5000
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BEGIN;
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UPDATE pgbench_accounts SET abalance = abalance + :delta WHERE aid = :aid;
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SELECT abalance FROM pgbench_accounts WHERE aid = :aid;
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UPDATE pgbench_tellers SET tbalance = tbalance + :delta WHERE tid = :tid;
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UPDATE pgbench_branches SET bbalance = bbalance + :delta WHERE bid = :bid;
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INSERT INTO pgbench_history (tid, bid, aid, delta, mtime) VALUES (:tid, :bid, :aid, :delta, CURRENT_TIMESTAMP);
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END;
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</programlisting>
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This script allows each iteration of the transaction to reference
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different, randomly-chosen rows. (This example also shows why it's
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important for each client session to have its own variables —
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otherwise they'd not be independently touching different rows.)
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</para>
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</refsect2>
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<refsect2 id="pgbench-builtin-functions">
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@ -1046,7 +988,7 @@ END;
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<row>
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<entry><literal><function>abs(<replaceable>a</>)</></></>
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<entry>same as <replaceable>a</></>
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<entry>integer value</>
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<entry>integer or double absolute value</>
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<entry><literal>abs(-17)</></>
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<entry><literal>17</></>
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</row>
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@ -1054,8 +996,22 @@ END;
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<entry><literal><function>debug(<replaceable>a</>)</></></>
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<entry>same as <replaceable>a</> </>
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<entry>print to <systemitem>stderr</systemitem> the given argument</>
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<entry><literal>debug(5432)</></>
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<entry><literal>5432</></>
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<entry><literal>debug(5432.1)</></>
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<entry><literal>5432.1</></>
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</row>
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<row>
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<entry><literal><function>double(<replaceable>i</>)</></></>
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<entry>double</>
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<entry>cast to double</>
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<entry><literal>double(5432)</></>
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<entry><literal>5432.0</></>
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</row>
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<row>
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<entry><literal><function>int(<replaceable>x</>)</></></>
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<entry>integer</>
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<entry>cast to int</>
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<entry><literal>int(5.4 + 3.8)</></>
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<entry><literal>9</></>
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</row>
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<row>
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<entry><literal><function>max(<replaceable>i</> [, <replaceable>...</> ] )</></></>
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@ -1071,9 +1027,143 @@ END;
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<entry><literal>min(5, 4, 3, 2)</></>
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<entry><literal>2</></>
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</row>
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<row>
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<entry><literal><function>pi()</></></>
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<entry>double</>
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<entry>value of the PI constant</>
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<entry><literal>pi()</></>
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<entry><literal>3.14159265358979323846</></>
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</row>
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<row>
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<entry><literal><function>random(<replaceable>lb</>, <replaceable>ub</>)</></></>
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<entry>integer</>
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<entry>uniformly-distributed random integer in <literal>[lb, ub]</></>
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<entry><literal>random(1, 10)</></>
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<entry>an integer between <literal>1</> and <literal>10</></>
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</row>
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<row>
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<entry><literal><function>random_exponential(<replaceable>lb</>, <replaceable>ub</>, <replaceable>parameter</>)</></></>
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<entry>integer</>
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<entry>exponentially-distributed random integer in <literal>[lb, ub]</>,
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see below</>
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<entry><literal>random_exponential(1, 10, 3.0)</></>
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<entry>an integer between <literal>1</> and <literal>10</></>
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</row>
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<row>
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<entry><literal><function>random_gaussian(<replaceable>lb</>, <replaceable>ub</>, <replaceable>parameter</>)</></></>
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<entry>integer</>
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<entry>gaussian-distributed random integer in <literal>[lb, ub]</>,
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see below</>
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<entry><literal>random_gaussian(1, 10, 2.5)</></>
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<entry>an integer between <literal>1</> and <literal>10</></>
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</row>
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<row>
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<entry><literal><function>sqrt(<replaceable>x</>)</></></>
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<entry>double</>
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<entry>square root</>
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<entry><literal>sqrt(2.0)</></>
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<entry><literal>1.414213562</></>
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</row>
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</tbody>
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</tgroup>
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</table>
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<para>
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The <literal>random</> function generates values using a uniform
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distribution, that is all the values are drawn within the specified
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range with equal probability. The <literal>random_exponential</> and
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<literal>random_gaussian</> functions require an additional double
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parameter which determines the precise shape of the distribution.
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</para>
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<itemizedlist>
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<listitem>
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<para>
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For an exponential distribution, <replaceable>parameter</>
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controls the distribution by truncating a quickly-decreasing
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exponential distribution at <replaceable>parameter</>, and then
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projecting onto integers between the bounds.
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To be precise, with
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<literallayout>
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f(x) = exp(-parameter * (x - min) / (max - min + 1)) / (1 - exp(-parameter))
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</literallayout>
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Then value <replaceable>i</> between <replaceable>min</> and
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<replaceable>max</> inclusive is drawn with probability:
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<literal>f(x) - f(x + 1)</>.
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</para>
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<para>
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Intuitively, the larger the <replaceable>parameter</>, the more
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frequently values close to <replaceable>min</> are accessed, and the
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less frequently values close to <replaceable>max</> are accessed.
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The closer to 0 <replaceable>parameter</> is, the flatter (more
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uniform) the access distribution.
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A crude approximation of the distribution is that the most frequent 1%
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values in the range, close to <replaceable>min</>, are drawn
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<replaceable>parameter</>% of the time.
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The <replaceable>parameter</> value must be strictly positive.
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</para>
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</listitem>
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<listitem>
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<para>
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For a Gaussian distribution, the interval is mapped onto a standard
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normal distribution (the classical bell-shaped Gaussian curve) truncated
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at <literal>-parameter</> on the left and <literal>+parameter</>
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on the right.
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Values in the middle of the interval are more likely to be drawn.
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To be precise, if <literal>PHI(x)</> is the cumulative distribution
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function of the standard normal distribution, with mean <literal>mu</>
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defined as <literal>(max + min) / 2.0</>, with
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<literallayout>
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f(x) = PHI(2.0 * parameter * (x - mu) / (max - min + 1)) /
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(2.0 * PHI(parameter) - 1)
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</literallayout>
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then value <replaceable>i</> between <replaceable>min</> and
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<replaceable>max</> inclusive is drawn with probability:
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<literal>f(i + 0.5) - f(i - 0.5)</>.
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Intuitively, the larger the <replaceable>parameter</>, the more
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frequently values close to the middle of the interval are drawn, and the
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less frequently values close to the <replaceable>min</> and
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<replaceable>max</> bounds. About 67% of values are drawn from the
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middle <literal>1.0 / parameter</>, that is a relative
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<literal>0.5 / parameter</> around the mean, and 95% in the middle
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<literal>2.0 / parameter</>, that is a relative
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<literal>1.0 / parameter</> around the mean; for instance, if
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<replaceable>parameter</> is 4.0, 67% of values are drawn from the
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middle quarter (1.0 / 4.0) of the interval (i.e. from
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<literal>3.0 / 8.0</> to <literal>5.0 / 8.0</>) and 95% from
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the middle half (<literal>2.0 / 4.0</>) of the interval (second and third
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quartiles). The minimum <replaceable>parameter</> is 2.0 for performance
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of the Box-Muller transform.
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</para>
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</listitem>
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</itemizedlist>
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<para>
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As an example, the full definition of the built-in TPC-B-like
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transaction is:
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<programlisting>
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\set aid random(1, 100000 * :scale)
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\set bid random(1, 1 * :scale)
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\set tid random(1, 10 * :scale)
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\set delta random(-5000, 5000)
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BEGIN;
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UPDATE pgbench_accounts SET abalance = abalance + :delta WHERE aid = :aid;
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SELECT abalance FROM pgbench_accounts WHERE aid = :aid;
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UPDATE pgbench_tellers SET tbalance = tbalance + :delta WHERE tid = :tid;
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UPDATE pgbench_branches SET bbalance = bbalance + :delta WHERE bid = :bid;
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INSERT INTO pgbench_history (tid, bid, aid, delta, mtime) VALUES (:tid, :bid, :aid, :delta, CURRENT_TIMESTAMP);
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END;
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</programlisting>
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This script allows each iteration of the transaction to reference
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different, randomly-chosen rows. (This example also shows why it's
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important for each client session to have its own variables —
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otherwise they'd not be independently touching different rows.)
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</para>
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</refsect2>
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<refsect2>
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@ -1223,13 +1313,10 @@ tps = 618.764555 (including connections establishing)
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tps = 622.977698 (excluding connections establishing)
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script statistics:
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- statement latencies in milliseconds:
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0.004386 \set nbranches 1 * :scale
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0.001343 \set ntellers 10 * :scale
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0.001212 \set naccounts 100000 * :scale
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0.001310 \setrandom aid 1 :naccounts
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0.001073 \setrandom bid 1 :nbranches
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0.001005 \setrandom tid 1 :ntellers
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0.001078 \setrandom delta -5000 5000
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0.002522 \set aid random(1, 100000 * :scale)
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0.005459 \set bid random(1, 1 * :scale)
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0.002348 \set tid random(1, 10 * :scale)
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0.001078 \set delta random(-5000, 5000)
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0.326152 BEGIN;
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0.603376 UPDATE pgbench_accounts SET abalance = abalance + :delta WHERE aid = :aid;
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0.454643 SELECT abalance FROM pgbench_accounts WHERE aid = :aid;
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Reference in New Issue
Block a user