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Diffstat (limited to 'doc/src/sgml/ref/pgbench.sgml')
| -rw-r--r-- | doc/src/sgml/ref/pgbench.sgml | 67 |
1 files changed, 38 insertions, 29 deletions
diff --git a/doc/src/sgml/ref/pgbench.sgml b/doc/src/sgml/ref/pgbench.sgml index 0ac40f10028..541d17b82a0 100644 --- a/doc/src/sgml/ref/pgbench.sgml +++ b/doc/src/sgml/ref/pgbench.sgml @@ -788,7 +788,7 @@ pgbench <optional> <replaceable>options</> </optional> <replaceable>dbname</> <varlistentry> <term> - <literal>\setrandom <replaceable>varname</> <replaceable>min</> <replaceable>max</> [ uniform | { gaussian | exponential } <replaceable>threshold</> ]</literal> + <literal>\setrandom <replaceable>varname</> <replaceable>min</> <replaceable>max</> [ uniform | { gaussian | exponential } <replaceable>parameter</> ]</literal> </term> <listitem> @@ -804,54 +804,63 @@ pgbench <optional> <replaceable>options</> </optional> <replaceable>dbname</> By default, or when <literal>uniform</> is specified, all values in the range are drawn with equal probability. Specifying <literal>gaussian</> or <literal>exponential</> options modifies this behavior; each - requires a mandatory threshold which determines the precise shape of the + requires a mandatory parameter 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</> + at <literal>-parameter</> on the left and <literal>+parameter</> on the right. + Values in the middle of the interval are more likely to be drawn. 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 + defined as <literal>(max + min) / 2.0</>, with +<literallayout> + f(x) = PHI(2.0 * parameter * (x - mu) / (max - min + 1)) / + (2.0 * PHI(parameter) - 1.0) +</literallayout> + then value <replaceable>i</> between <replaceable>min</> and + <replaceable>max</> inclusive is drawn with probability: + <literal>f(i + 0.5) - f(i - 0.5)</>. + Intuitively, the larger <replaceable>parameter</>, 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. + <replaceable>max</> bounds. About 67% of values are drawn from the + middle <literal>1.0 / parameter</>, that is a relative + <literal>0.5 / parameter</> around the mean, and 95% in the middle + <literal>2.0 / parameter</>, that is a relative + <literal>1.0 / parameter</> around the mean; for instance, if + <replaceable>parameter</> is 4.0, 67% of values are drawn from the + middle quarter (1.0 / 4.0) of the interval (i.e. from + <literal>3.0 / 8.0</> to <literal>5.0 / 8.0</>) and 95% from + the middle half (<literal>2.0 / 4.0</>) of the interval (second and + third quartiles). The minimum <replaceable>parameter</> 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 + For an exponential distribution, <replaceable>parameter</> + controls the distribution by truncating a quickly-decreasing + exponential distribution at <replaceable>parameter</>, and then projecting onto integers between the bounds. - To be precise, value <replaceable>i</> between <replaceable>min</> and + To be precise, with +<literallayout> +f(x) = exp(-parameter * (x - min) / (max - min + 1)) / (1.0 - exp(-parameter)) +</literallayout> + Then 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 + <literal>f(x) - f(x + 1)</>. + Intuitively, the larger <replaceable>parameter</>, 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. + The closer to 0 <replaceable>parameter</>, 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. + <replaceable>parameter</>% of the time. + <replaceable>parameter</> value must be strictly positive. </para> <para> |