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pgbench: Change terminology from "threshold" to "parameter".

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Per a recommendation from Tomas Vondra, it's more helpful to refer to
the value that determines how skewed a Gaussian or exponential
distribution is as a parameter rather than a threshold.

Since it's not quite too late to get this right in 9.5, where it was
introduced, back-patch this.  Most of the patch changes only comments
and documentation, but a few pgbench messages are altered to match.

Fabien Coelho, reviewed by Michael Paquier and by me.
This commit is contained in:
Robert Haas 2015-12-18 13:24:51 -05:00
parent 6e7b335930
commit 3c7042a7d7
2 changed files with 78 additions and 60 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

67
doc/src/sgml/ref/pgbench.sgml
View File

@ -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>

71
src/bin/pgbench/pgbench.c
View File

@ -90,7 +90,7 @@ static int pthread_join(pthread_t th, void **thread_return);
#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 */
@ -488,47 +488,47 @@ getrand(TState *thread, int64 min, int64 max)
/*
* 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
@ -553,10 +553,10 @@ getGaussianRand(TState *thread, int64 min, int64 max, double threshold)
* 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);
@ -1483,7 +1483,7 @@ top:
char *var;
int64 min,
max;
double threshold = 0;
double parameter = 0;
char res[64];
if (*argv[2] == ':')
@ -1554,41 +1554,49 @@ top:
{
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... */
@ -2282,8 +2290,9 @@ process_commands(char *buf, const char *source, const int lineno)
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)
@ -2308,7 +2317,7 @@ process_commands(char *buf, const char *source, const int lineno)
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)
{