<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 mandatorythreshold which determines the precise shape of the

requires a mandatoryparameter 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</>

parametercontrols 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 0the threshold, the flatter (more uniform) the access

distribution.

The closer to 0<replaceable>parameter</>, the flatter (more uniform)

the accessdistribution.

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>

#defineLOG_STEP_SECONDS5/* seconds between log messages */

#defineDEFAULT_NXACTS10/* default nxacts */

#defineMIN_GAUSSIAN_THRESHOLD2.0/* minimumthreshold for gauss */

#defineMIN_GAUSSIAN_PARAM2.0/* minimumparameter for gauss */

intnxacts=0;/* number of transactions per client */

intduration=0;/* duration in seconds */

getExponentialRand(TState*thread,int64min,int64max,doublethreshold)

getExponentialRand(TState*thread,int64min,int64max,doubleparameter)

{

doublecut,

uniform,

rand;

Assert(threshold>0.0);

cut=exp(-threshold);

Assert(parameter>0.0);

cut=exp(-parameter);

uniform=1.0-pg_erand48(thread->random_state);

Assert((1.0-cut)!=0.0);

rand=-log(cut+ (1.0-cut)*uniform) /threshold;

rand=-log(cut+ (1.0-cut)*uniform) /parameter;

returnmin+ (int64) ((max-min+1)*rand);

}

getGaussianRand(TState*thread,int64min,int64max,doublethreshold)

getGaussianRand(TState*thread,int64min,int64max,doubleparameter)

{

doublestdev;

doublerand;

}

while (stdev<-threshold||stdev >=threshold);

while (stdev<-parameter||stdev >=parameter);

rand= (stdev+threshold) / (threshold*2.0);

rand= (stdev+parameter) / (parameter*2.0);

returnmin+ (int64) ((max-min+1)*rand);

char*var;

int64min,

max;

doublethreshold=0;

doubleparameter=0;

charres[64];

if (*argv[2]==':')

{

if ((var=getVariable(st,argv[5]+1))==NULL)

{

fprintf(stderr,"%s: invalidthreshold number: \"%s\"\n",

fprintf(stderr,"%s: invalidparameter: \"%s\"\n",

argv[0],argv[5]);

st->ecnt++;

return true;

}

threshold=strtod(var,NULL);

parameter=strtod(var,NULL);

}

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,"gaussianthreshold must be at least %f (not \"%s\")\n",MIN_GAUSSIAN_THRESHOLD,argv[5]);

fprintf(stderr,"gaussianparameter must be at least %f (not \"%s\")\n",MIN_GAUSSIAN_PARAM,argv[5]);

st->ecnt++;

return true;

}

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));

snprintf(res,sizeof(res),INT64_FORMAT,getGaussianRand(thread,min,max,threshold));

snprintf(res,sizeof(res),INT64_FORMAT,

getGaussianRand(thread,min,max,parameter));

}

elseif (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;

}

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));

snprintf(res,sizeof(res),INT64_FORMAT,getExponentialRand(thread,min,max,threshold));

snprintf(res,sizeof(res),INT64_FORMAT,

getExponentialRand(thread,min,max,parameter));

}

}

if (pg_strcasecmp(my_commands->argv[0],"setrandom")==0)

{

if (my_commands->argc<4)

if (my_commands->argc<6)

{

syntax_error(source,lineno,my_commands->line,my_commands->argv[0],

"missingthreshold argument",my_commands->argv[4],-1);

"missingparameter",my_commands->argv[4],-1);

}

elseif (my_commands->argc>6)

{