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pgbench: Allow \setrandom to generate Gaussian/exponential distributions. 

Mitsumasa KONDO and Fabien COELHO, with further wordsmithing by me.
This commit is contained in:
Robert Haas 2014-07-30 13:22:08 -04:00
parent e280c630a8
commit ed802e7dc3
2 changed files with 231 additions and 13 deletions
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183
contrib/pgbench/pgbench.c
View File

@ -98,6 +98,8 @@ 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 */
int nxacts = 0; /* number of transactions per client */
int duration = 0; /* duration in seconds */
@ -471,6 +473,76 @@ getrand(TState *thread, int64 min, int64 max)
return min + (int64) ((max - min + 1) * pg_erand48(thread->random_state));
}
/*
* 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).
*/
static int64
getExponentialRand(TState *thread, int64 min, int64 max, double threshold)
{
double cut, uniform, rand;
Assert(threshold > 0.0);
cut = exp(-threshold);
/* 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)
*/
Assert((1.0 - cut) != 0.0);
rand = - log(cut + (1.0 - cut) * uniform) / threshold;
/* 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)
{
double stdev;
double rand;
/*
* Get user specified random number from this loop, with
* -threshold < stdev <= threshold
*
* 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:
* 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 about e^{-5} * 2 / pi ~ 0.43%.
*/
do
{
/*
* pg_erand48 generates [0,1), but for the basic version of the
* Box-Muller transform the two uniformly distributed random numbers
* are expected in (0, 1] (see http://en.wikipedia.org/wiki/Box_muller)
*/
double rand1 = 1.0 - pg_erand48(thread->random_state);
double rand2 = 1.0 - pg_erand48(thread->random_state);
/* Box-Muller basic form transform */
double var_sqrt = sqrt(-2.0 * log(rand1));
stdev = var_sqrt * sin(2.0 * M_PI * rand2);
/*
* we may try with cos, but there may be a bias induced if the previous
* value fails the test. To be on the safe side, let us try over.
*/
}
while (stdev < -threshold || stdev >= threshold);
/* stdev is in [-threshold, threshold), normalization to [0,1) */
rand = (stdev + threshold) / (threshold * 2.0);
/* return int64 random number within between min and max */
return min + (int64)((max - min + 1) * rand);
}
/* call PQexec() and exit() on failure */
static void
executeStatement(PGconn *con, const char *sql)
@ -1319,6 +1391,7 @@ top:
char *var;
int64 min,
max;
double threshold = 0;
char res[64];
if (*argv[2] == ':')
@ -1364,11 +1437,11 @@ top:
}
/*
* getrand() needs to be able to subtract max from min and add one
* to the result without overflowing. Since we know max > min, we
* can detect overflow just by checking for a negative result. But
* we must check both that the subtraction doesn't overflow, and
* that adding one to the result doesn't overflow either.
* Generate random number functions need to be able to subtract
* max from min and add one to the result without overflowing.
* Since we know max > min, we can detect overflow just by checking
* for a negative result. But we must check both that the subtraction
* doesn't overflow, and that adding one to the result doesn't overflow either.
*/
if (max - min < 0 || (max - min) + 1 < 0)
{
@ -1377,10 +1450,64 @@ top:
return true;
}
if (argc == 4 || /* uniform without or with "uniform" keyword */
(argc == 5 && pg_strcasecmp(argv[4], "uniform") == 0))
{
#ifdef DEBUG
printf("min: " INT64_FORMAT " max: " INT64_FORMAT " random: " INT64_FORMAT "\n", min, max, getrand(thread, min, max));
printf("min: " INT64_FORMAT " max: " INT64_FORMAT " random: " INT64_FORMAT "\n", min, max, getrand(thread, min, max));
#endif
snprintf(res, sizeof(res), INT64_FORMAT, getrand(thread, min, max));
snprintf(res, sizeof(res), INT64_FORMAT, getrand(thread, min, max));
}
else if (argc == 6 &&
((pg_strcasecmp(argv[4], "gaussian") == 0) ||
(pg_strcasecmp(argv[4], "exponential") == 0)))
{
if (*argv[5] == ':')
{
if ((var = getVariable(st, argv[5] + 1)) == NULL)
{
fprintf(stderr, "%s: invalid threshold number %s\n", argv[0], argv[5]);
st->ecnt++;
return true;
}
threshold = strtod(var, NULL);
}
else
threshold = strtod(argv[5], NULL);
if (pg_strcasecmp(argv[4], "gaussian") == 0)
{
if (threshold < MIN_GAUSSIAN_THRESHOLD)
{
fprintf(stderr, "%s: gaussian threshold must be at least %f\n,", argv[5], MIN_GAUSSIAN_THRESHOLD);
st->ecnt++;
return true;
}
#ifdef DEBUG
printf("min: " INT64_FORMAT " max: " INT64_FORMAT " random: " INT64_FORMAT "\n", min, max, getGaussianRand(thread, min, max, threshold));
#endif
snprintf(res, sizeof(res), INT64_FORMAT, getGaussianRand(thread, min, max, threshold));
}
else if (pg_strcasecmp(argv[4], "exponential") == 0)
{
if (threshold <= 0.0)
{
fprintf(stderr, "%s: exponential threshold must be strictly positive\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));
#endif
snprintf(res, sizeof(res), INT64_FORMAT, getExponentialRand(thread, min, max, threshold));
}
}
else /* this means an error somewhere in the parsing phase... */
{
fprintf(stderr, "%s: unexpected arguments\n", argv[0]);
st->ecnt++;
return true;
}
if (!putVariable(st, argv[0], argv[1], res))
{
@ -1914,15 +2041,51 @@ process_commands(char *buf)
if (pg_strcasecmp(my_commands->argv[0], "setrandom") == 0)
{
/* parsing:
* \setrandom variable min max [uniform]
* \setrandom variable min max (gaussian|exponential) threshold
*/
if (my_commands->argc < 4)
{
fprintf(stderr, "%s: missing argument\n", my_commands->argv[0]);
exit(1);
}
/* argc >= 4 */
for (j = 4; j < my_commands->argc; j++)
fprintf(stderr, "%s: extra argument \"%s\" ignored\n",
my_commands->argv[0], my_commands->argv[j]);
if (my_commands->argc == 4 || /* uniform without/with "uniform" keyword */
(my_commands->argc == 5 &&
pg_strcasecmp(my_commands->argv[4], "uniform") == 0))
{
/* nothing to do */
}
else if (/* argc >= 5 */
(pg_strcasecmp(my_commands->argv[4], "gaussian") == 0) ||
(pg_strcasecmp(my_commands->argv[4], "exponential") == 0))
{
if (my_commands->argc < 6)
{
fprintf(stderr, "%s(%s): missing threshold argument\n", my_commands->argv[0], my_commands->argv[4]);
exit(1);
}
else if (my_commands->argc > 6)
{
fprintf(stderr, "%s(%s): too many arguments (extra:",
my_commands->argv[0], my_commands->argv[4]);
for (j = 6; j < my_commands->argc; j++)
fprintf(stderr, " %s", my_commands->argv[j]);
fprintf(stderr, ")\n");
exit(1);
}
}
else /* cannot parse, unexpected arguments */
{
fprintf(stderr, "%s: unexpected arguments (bad:", my_commands->argv[0]);
for (j = 4; j < my_commands->argc; j++)
fprintf(stderr, " %s", my_commands->argv[j]);
fprintf(stderr, ")\n");
exit(1);
}
}
else if (pg_strcasecmp(my_commands->argv[0], "set") == 0)
{

61
doc/src/sgml/pgbench.sgml
View File

@ -748,8 +748,8 @@ pgbench <optional> <replaceable>options</> </optional> <replaceable>dbname</>
<varlistentry>
<term>
<literal>\setrandom <replaceable>varname</> <replaceable>min</> <replaceable>max</></literal>
</term>
<literal>\setrandom <replaceable>varname</> <replaceable>min</> <replaceable>max</> [ uniform | [ { gaussian | exponential } <replaceable>threshold</> ] ]</literal>
</term>
<listitem>
<para>
@ -760,10 +760,65 @@ pgbench <optional> <replaceable>options</> </optional> <replaceable>dbname</>
having an integer value.
</para>
<para>
By default, or when <literal>uniform</> is specified, all values in the
range are drawn with equal probability. Specifiying <literal>gaussian</>
or <literal>exponential</> options modifies this behavior; each
requires a mandatory threshold 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</>
on the right.
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
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.
</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
projecting onto integers between the bounds.
To be precise, 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
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.
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.
</para>
<para>
Example:
<programlisting>
\setrandom aid 1 :naccounts
\setrandom aid 1 :naccounts gaussian 5.0
</programlisting></para>
</listitem>
</varlistentry>