From:

jkherciueh@gmx.net

Newsgroups:

comp.std.c++

Date:

Wed, 14 Nov 2007 11:17:09 CST

Message-ID:

<fhe8i6$827$1@aioe.org>

On 2007-11-12 11:10 AM, jkherciueh@gmx.net wrote:

[snip]

a) Support for unpredictable seeds

==================================

The default constructor for all engines creates an object with fully

predictable state. In order to create a random number generator whose

initial state is different, one needs to provide a seed. If I want to

create a random sequence that varies between runs of the program, I will

need a somewhat unpredictable seed. May I suggest to add a convenience

function in the utilities section 26.4.7:

<implementation defined arithmetic type> unpredictable_seed ();

This should return (through implementation-defined means) what the name

suggests: a seed-value that is hard to guess (at least harder than the

current time).

==================================

The default constructor for all engines creates an object with fully

predictable state. In order to create a random number generator whose

initial state is different, one needs to provide a seed. If I want to

create a random sequence that varies between runs of the program, I will

need a somewhat unpredictable seed. May I suggest to add a convenience

function in the utilities section 26.4.7:

<implementation defined arithmetic type> unpredictable_seed ();

This should return (through implementation-defined means) what the name

suggests: a seed-value that is hard to guess (at least harder than the

current time).

This is the sort of use for which the seed_seq utility was intended. By

constructing a seed_seq object from, say, the current time and the

process id, one obtains an entity that makes a good seed for any engine.

Even if many seeds are needed (e.g., for tasks executing

concurrently), even small differences in the time and/or the process id

will lead to large differences in the outputs obtained from seed_seq's

constructed from them, and hence also to large differences in the

initial states of the engines.

Thanks for the explanation.

b) Basic support for combinatorial distributions

================================================

I understand the rationale from N1588 (section 5) that it would not be

feasible to include distributions that return collections of values

instead of values. However, I think it would be possible and useful to

make it easier for users to build such distributions on top of the

sampling distributions provided by the library. In particular, I think it

would be useful to add a discrete distribution with modifiable weights to

26.4.8.5, something like this:

template < typename WeightType = unsigned long, typename IntType = int

> class dynamic_discrete_distribution {

public:

typedef WeightType weight_type;

typedef IntType result_type;

class param_type {

public:

typedef dynamic_discrete_distribution distribution_type;

typedef WeightType weight_type;

typedef IntType result_type;

param_type ();

template < typename InputIterator >

param_type ( InputIterator firstW, InputIterator lastW );

vector< double > probabilities ( void ) const;

result_type min ( void ) const;

result_type max ( void ) const;

weight_type weight ( result_type index ) const;

void weight ( result_type index, weight_type new_weight );

weight_type total ( void ) const;

}; // param_type

dynamic_discrete_distribution ();

template < typename InputIterator >

dynamic_discrete_distribution

( InputIterator firstW, InputIterator lastW );

explicit

dynamic_discrete_distribution ( param_type const & parm );

vector< double > probabilities ( void ) const;

param_type param ( void ) const;

void param ( param_type const & parm );

result_type min ( void ) const;

result_type max ( void ) const;

weight_type weight ( result_type index ) const;

void weight ( result_type index, weight_type new_weight );

weight_type total ( void ) const;

void reset ( void );

template < typename UniformRNG >

result_type operator() ( UniformRNG & urng, param_type const & parm

);

template < typename UniformRNG >

result_type operator() ( UniformRNG & urng );

}; // dynamic_discrete_distribution

Note: the sum of weights can be 0, however in that state,

sampling has undefined behavior.

Of course, sampling from a distribution with changing weights can be

realized on top of discrete_distribution<>. However, there is (a) a

performance penalty in the case of many weights and many modifications;

and one suffers (b) from a loss in code-coherence: Consider the following

piece (which is the core part of generating a random combination without

repetitions):

std::tr1::mt19937 urng;

dynamic_discrete_distribution< unsigned int > box

( count.begin(), count.end() );

while ( box.total() > 0 ) {

unsigned int index = box( urng );

box.weight( index, box.weight( index ) - 1 );

std::cout << index << '\n';

}

versus:

std::tr1::mt19937 urng;

unsigned int total = std::accumulate ( count.begin(), count.end(), 0u

); discrete_distribution<> dist;

while ( total > 0 ) {

kubux::discrete_distribution<>::param_type parm

( count.begin(), count.end() );

unsigned int index = dist( urng, parm );

-- count[index];

-- total;

std::cout << index << '\n';

}

In the second snippet, the programmer faces the alternative of either

recomputing the total from scratch each iteration (not shown) or updating

the total manually (shown). In the first snippet, the data is centralized

and all invariants are handled by the box-object.

================================================

I understand the rationale from N1588 (section 5) that it would not be

feasible to include distributions that return collections of values

instead of values. However, I think it would be possible and useful to

make it easier for users to build such distributions on top of the

sampling distributions provided by the library. In particular, I think it

would be useful to add a discrete distribution with modifiable weights to

26.4.8.5, something like this:

template < typename WeightType = unsigned long, typename IntType = int

> class dynamic_discrete_distribution {

public:

typedef WeightType weight_type;

typedef IntType result_type;

class param_type {

public:

typedef dynamic_discrete_distribution distribution_type;

typedef WeightType weight_type;

typedef IntType result_type;

param_type ();

template < typename InputIterator >

param_type ( InputIterator firstW, InputIterator lastW );

vector< double > probabilities ( void ) const;

result_type min ( void ) const;

result_type max ( void ) const;

weight_type weight ( result_type index ) const;

void weight ( result_type index, weight_type new_weight );

weight_type total ( void ) const;

}; // param_type

dynamic_discrete_distribution ();

template < typename InputIterator >

dynamic_discrete_distribution

( InputIterator firstW, InputIterator lastW );

explicit

dynamic_discrete_distribution ( param_type const & parm );

vector< double > probabilities ( void ) const;

param_type param ( void ) const;

void param ( param_type const & parm );

result_type min ( void ) const;

result_type max ( void ) const;

weight_type weight ( result_type index ) const;

void weight ( result_type index, weight_type new_weight );

weight_type total ( void ) const;

void reset ( void );

template < typename UniformRNG >

result_type operator() ( UniformRNG & urng, param_type const & parm

);

template < typename UniformRNG >

result_type operator() ( UniformRNG & urng );

}; // dynamic_discrete_distribution

Note: the sum of weights can be 0, however in that state,

sampling has undefined behavior.

Of course, sampling from a distribution with changing weights can be

realized on top of discrete_distribution<>. However, there is (a) a

performance penalty in the case of many weights and many modifications;

and one suffers (b) from a loss in code-coherence: Consider the following

piece (which is the core part of generating a random combination without

repetitions):

std::tr1::mt19937 urng;

dynamic_discrete_distribution< unsigned int > box

( count.begin(), count.end() );

while ( box.total() > 0 ) {

unsigned int index = box( urng );

box.weight( index, box.weight( index ) - 1 );

std::cout << index << '\n';

}

versus:

std::tr1::mt19937 urng;

unsigned int total = std::accumulate ( count.begin(), count.end(), 0u

); discrete_distribution<> dist;

while ( total > 0 ) {

kubux::discrete_distribution<>::param_type parm

( count.begin(), count.end() );

unsigned int index = dist( urng, parm );

-- count[index];

-- total;

std::cout << index << '\n';

}

In the second snippet, the programmer faces the alternative of either

recomputing the total from scratch each iteration (not shown) or updating

the total manually (shown). In the first snippet, the data is centralized

and all invariants are handled by the box-object.

We agree that this is an interesting distribution. However, it is not

clear that it is sufficiently general to warrant inclusion in the C++0X

standard.

We view your use case as simulating the drawing, without replacement, of

numbered objects from a box. An alternative solution, only making use

of existing library components, would entail creating an std:vector<> to

contain instances of the numbered objects, then applying

std::random_shuffle() to that vector, then "drawing" sequentially from

the resulting shuffled vector.

I understand that something has to be expected to be useful before it can be

considered for inclusion into the standard. So, allow me to strengthen my

case by presenting a few other possible use cases, which I think are harder

to deal with using only means that are currently proposed.

Consider the following simulation of diffusion:

int main ( void ) {

std::tr1::mt19937 urng;

/*

Setup: we are given two boxes A and B and n kinds of items.

Box A contains a_1, a2_, ..., a_n items of each kind and

box B contains b_1, b_2, ..., b_n items of each kind. At each

step an item is picked at random and moved to the other box.

*/

// We model the case n = 4;

// The following vector is the vector a_1,...,a_n,b1,...,b_n

// We start with all items in box A.

std::vector< unsigned long > counts;

counts.push_back( 200000 );

counts.push_back( 150000 );

counts.push_back( 4000000 );

counts.push_back( 50000 );

counts.push_back( 0 );

counts.push_back( 0 );

counts.push_back( 0 );

counts.push_back( 0 );

dynamic_discrete_distribution< unsigned long > two_row_grid

( counts.begin(), counts.end() );

while ( true ) {

for ( int i = 0; i < 1000; ++i ) {

unsigned long index = two_row_grid( urng );

unsigned long where_to_put = ( index + 4 ) % 8;

two_row_grid.weight( index,

two_row_grid.weight( index ) -1 );

two_row_grid.weight( where_to_put,

two_row_grid.weight( where_to_put ) + 1 );

}

for ( int i = 0; i < 4; ++i ) {

std::cout << std::setw(8) << two_row_grid.weight( i ) << " ";

}

std::cout << std::endl;

for ( int i = 4; i < 8; ++i ) {

std::cout << std::setw(8) << two_row_grid.weight( i ) << " ";

}

std::cout << std::endl;

std::cout << std::endl;

}

}

If you did this using 4,000,000+200,000 + 150,000 + 50,000 = 4,400,000

objects in a vector, each keeping track in which box it currently is, the

program would use much more resources and spend most of the time computing

totals for reporting.

I think that a discrete distribution with modifiable weights would be a very

useful building block in simulations where items move around, die or

procreate, and the number of items is large enough to warant not modeling

them individually but using counts. Think of colored dots moving within a

graph where the probabilities of a dot being chosen for some action

(possibly involving moving to a neighbor) depend on how many dots of each

color are present at the given vertex. For more complicated graphs, it

becomes less and less obvious how to model that using standard containers

and random draws and shuffles. Here is a simple random walk simulation to

illustrate the point:

int main ( void ) {

std::tr1::mt19937 urng;

/*

Simple random walk with destruction at either right end.

We have n sites arranged in a line. At each step an object

is chosen at random. It then moves to the left or right

with equal probability. If it leaves the range, it drops

out.

*/

// Setup:

unsigned int const num_sites = 10;

std::vector< unsigned long > counts;

for ( unsigned int i = 0; i < num_sites; ++i ) {

counts.push_back( 1000 );

}

bernouli_distribution coin;

dynamic_discrete_distribution< unsigned int > walk

( counts.begin(), counts.end() );

// Simulation:

while ( walk.total() > 0 ) {

unsigned int site = walk( urng );

walk.weight( site, walk.weight( site ) - 1 );

bool left = coin( urng );

if ( left ) {

if ( site > 0 ) {

--site;

walk.weight( site, walk.weight( site ) + 1 );

}

} else {

if ( site < walk.max() ) {

++site;

walk.weight( site, walk.weight( site ) + 1 );

}

}

for ( unsigned int i = 0; i < num_sites; ++i ) {

std::cout << walk.weight( i ) << " ";

}

std::cout << std::endl;

}

}

Note: when such a stochastic model arises from discretization of a

continuous phenomenon (like heat), the number of sites can easily grow

large, and the number of items moving around can be huge.

More complex use cases also exist where the weights are not just item

counts, e.g., a battle simulation where rifles and machine guns are

involved. Simulating each bullet, the firing frequencies will determine the

probability of the bullet coming from a machine gun or a riffle. Thus, the

weight change for a party depends on whether a riffle or a machine gun

carrier got hit.

Also, even in the simple drawing from a box example one can already see a

certain space overhead in the vector+shuffle solution. If the number of

objects is huge, that can be a drawback.

(BTW: the use cases so far suggest that changing the weight is more useful

than setting the weight. So, the interface is up for debate, I guess.)

c) Convenient generation of uniform samples in half-open ranges

===============================================================

This would probably be what occasional users of the random-facilities

will be looking for most often. To make their life easier (predicting

that they will resort to rand() if not handed something that is _very_

convenient to use), I would suggest to add a convenience class to 26.4.7

along the following lines:

template < typename Engine = implementation_defined >

class urandom {

// default construct with unpredictable inital state

urandom ();

// construct from seed

template < typename SeedType >

urandom ( SeedType const & seed )

// return a uniform deviate in [0,bound)

template < typename ArithmeticType >

ArithmeticType operator() ( ArithmeticType bound );

}; // urandom

It can be used to create a (static) rng-object, which can replace rand()

and takes care of the most basic sampling problem.

===============================================================

This would probably be what occasional users of the random-facilities

will be looking for most often. To make their life easier (predicting

that they will resort to rand() if not handed something that is _very_

convenient to use), I would suggest to add a convenience class to 26.4.7

along the following lines:

template < typename Engine = implementation_defined >

class urandom {

// default construct with unpredictable inital state

urandom ();

// construct from seed

template < typename SeedType >

urandom ( SeedType const & seed )

// return a uniform deviate in [0,bound)

template < typename ArithmeticType >

ArithmeticType operator() ( ArithmeticType bound );

}; // urandom

It can be used to create a (static) rng-object, which can replace rand()

and takes care of the most basic sampling problem.

We are sympathetic to this idea, but believe there is insufficient time

to craft a formal proposal before C++0X is finalized. In part, this is

because the above urandom template meets neither the requirements of an

engine nor those of a distribution, and so we would need to spell out

very carefully (especially in light of the forthcoming Concepts work)

what its exact requirements would be.

I see. Which papers should I read to get up to speed in this Concepts issue?

As for the requirements, I had in mind that the SeedType would be either any

arithmetic type or seed_seq. This way, the constructors would be largely

parallel to the constructors of engines.

With regard to the ArithmeticType, I had in mind that integer and floating

point types should be allowed. Maybe, in view of the general requirements

clause 26.4.1.1 one could specify that by splitting the case into the

following signatures:

template < typename IntType >

IntType operator() ( IntType bound );

requires: bound > 0;

returns: a random integer evenly distributed in [0,bound)

template < typename RealType >

RealType operator() ( RealType bound );

requires: bound > 0;

returns: a random real evenly distributed in [0,bound)

However, there is a second Technical Report already being drafted. We

would be willing to work with you to craft a formal proposal targeting

that future TR.

would be willing to work with you to craft a formal proposal targeting

that future TR.

Sounds good.

Thanks

Kai-Uwe Bux

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