<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>
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>
#define LOG_STEP_SECONDS 5 /* seconds between log messages */
#define DEFAULT_NXACTS 10 /* default nxacts */
-#define MIN_GAUSSIAN_THRESHOLD 2.0 /* minimum threshold for gauss */
+#define MIN_GAUSSIAN_PARAM 2.0 /* minimum parameter for gauss */
int nxacts = 0; /* number of transactions per client */
int duration = 0; /* duration in seconds */
/*
* random number generator: exponential distribution from min to max inclusive.
- * the threshold is so that the density of probability for the last cut-off max
- * value is exp(-threshold).
+ * the parameter is so that the density of probability for the last cut-off max
+ * value is exp(-parameter).
*/
static int64
-getExponentialRand(TState *thread, int64 min, int64 max, double threshold)
+getExponentialRand(TState *thread, int64 min, int64 max, double parameter)
{
double cut,
uniform,
rand;
- Assert(threshold > 0.0);
- cut = exp(-threshold);
+ Assert(parameter > 0.0);
+ cut = exp(-parameter);
/* erand in [0, 1), uniform in (0, 1] */
uniform = 1.0 - pg_erand48(thread->random_state);
/*
- * inner expresion in (cut, 1] (if threshold > 0), rand in [0, 1)
+ * inner expresion in (cut, 1] (if parameter > 0), rand in [0, 1)
*/
Assert((1.0 - cut) != 0.0);
- rand = -log(cut + (1.0 - cut) * uniform) / threshold;
+ rand = -log(cut + (1.0 - cut) * uniform) / parameter;
/* return int64 random number within between min and max */
return min + (int64) ((max - min + 1) * rand);
}
/* random number generator: gaussian distribution from min to max inclusive */
static int64
-getGaussianRand(TState *thread, int64 min, int64 max, double threshold)
+getGaussianRand(TState *thread, int64 min, int64 max, double parameter)
{
double stdev;
double rand;
/*
- * Get user specified random number from this loop, with -threshold <
- * stdev <= threshold
+ * Get user specified random number from this loop,
+ * with -parameter < stdev <= parameter
*
* This loop is executed until the number is in the expected range.
*
- * As the minimum threshold is 2.0, the probability of looping is low:
+ * As the minimum parameter is 2.0, the probability of looping is low:
* sqrt(-2 ln(r)) <= 2 => r >= e^{-2} ~ 0.135, then when taking the
* average sinus multiplier as 2/pi, we have a 8.6% looping probability in
- * the worst case. For a 5.0 threshold value, the looping probability is
+ * the worst case. For a parameter value of 5.0, the looping probability is
* about e^{-5} * 2 / pi ~ 0.43%.
*/
do
* over.
*/
}
- while (stdev < -threshold || stdev >= threshold);
+ while (stdev < -parameter || stdev >= parameter);
- /* stdev is in [-threshold, threshold), normalization to [0,1) */
- rand = (stdev + threshold) / (threshold * 2.0);
+ /* stdev is in [-parameter, parameter), normalization to [0,1) */
+ rand = (stdev + parameter) / (parameter * 2.0);
/* return int64 random number within between min and max */
return min + (int64) ((max - min + 1) * rand);
char *var;
int64 min,
max;
- double threshold = 0;
+ double parameter = 0;
char res[64];
if (*argv[2] == ':')
{
if ((var = getVariable(st, argv[5] + 1)) == NULL)
{
- fprintf(stderr, "%s: invalid threshold number: \"%s\"\n",
+ fprintf(stderr, "%s: invalid parameter: \"%s\"\n",
argv[0], argv[5]);
st->ecnt++;
return true;
}
- threshold = strtod(var, NULL);
+ parameter = strtod(var, NULL);
}
else
- threshold = strtod(argv[5], NULL);
+ parameter = strtod(argv[5], NULL);
if (pg_strcasecmp(argv[4], "gaussian") == 0)
{
- if (threshold < MIN_GAUSSIAN_THRESHOLD)
+ if (parameter < MIN_GAUSSIAN_PARAM)
{
- fprintf(stderr, "gaussian threshold must be at least %f (not \"%s\")\n", MIN_GAUSSIAN_THRESHOLD, argv[5]);
+ fprintf(stderr, "gaussian parameter must be at least %f (not \"%s\")\n", MIN_GAUSSIAN_PARAM, argv[5]);
st->ecnt++;
return true;
}
#ifdef DEBUG
- printf("min: " INT64_FORMAT " max: " INT64_FORMAT " random: " INT64_FORMAT "\n", min, max, getGaussianRand(thread, min, max, threshold));
+ printf("min: " INT64_FORMAT " max: " INT64_FORMAT " random: " INT64_FORMAT "\n",
+ min, max,
+ getGaussianRand(thread, min, max, parameter));
#endif
- snprintf(res, sizeof(res), INT64_FORMAT, getGaussianRand(thread, min, max, threshold));
+ snprintf(res, sizeof(res), INT64_FORMAT,
+ getGaussianRand(thread, min, max, parameter));
}
else if (pg_strcasecmp(argv[4], "exponential") == 0)
{
- if (threshold <= 0.0)
+ if (parameter <= 0.0)
{
- fprintf(stderr, "exponential threshold must be greater than zero (not \"%s\")\n", argv[5]);
+ fprintf(stderr,
+ "exponential parameter must be greater than zero (not \"%s\")\n",
+ argv[5]);
st->ecnt++;
return true;
}
#ifdef DEBUG
- printf("min: " INT64_FORMAT " max: " INT64_FORMAT " random: " INT64_FORMAT "\n", min, max, getExponentialRand(thread, min, max, threshold));
+ printf("min: " INT64_FORMAT " max: " INT64_FORMAT " random: " INT64_FORMAT "\n",
+ min, max,
+ getExponentialRand(thread, min, max, parameter));
#endif
- snprintf(res, sizeof(res), INT64_FORMAT, getExponentialRand(thread, min, max, threshold));
+ snprintf(res, sizeof(res), INT64_FORMAT,
+ getExponentialRand(thread, min, max, parameter));
}
}
else /* this means an error somewhere in the parsing phase... */
if (pg_strcasecmp(my_commands->argv[0], "setrandom") == 0)
{
/*
- * parsing: \setrandom variable min max [uniform] \setrandom
- * variable min max (gaussian|exponential) threshold
+ * parsing:
+ * \setrandom variable min max [uniform]
+ * \setrandom variable min max (gaussian|exponential) parameter
*/
if (my_commands->argc < 4)
if (my_commands->argc < 6)
{
syntax_error(source, lineno, my_commands->line, my_commands->argv[0],
- "missing threshold argument", my_commands->argv[4], -1);
+ "missing parameter", my_commands->argv[4], -1);
}
else if (my_commands->argc > 6)
{
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