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class rational {
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// Prog : random .h
// define a class for pseudorandom numbers .
namespace ifm {
// class random : definition
class random {
public :
// POST : * this is initialized with the linear congruential
//
random number generator
//
x_i = ( a * x_ {i -1} + c ) mod m
//
with seed x0 .
random ( unsigned int a , unsigned int c ,
unsigned int m , unsigned int x0 );
// POST : return value is the next pseudorandom number
//
in the sequence of the x_i , divided by m
double operator ()();
private :
const unsigned int a_ ; // multiplier
const unsigned int c_ ; // offset
const unsigned int m_ ; // modulus
unsigned int xi_ ;
// current sequence element
};
} // end namespace ifm
Program 34:
2
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// Prog : random .C
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EP namespace ifm {
// class random : implementation
random :: random ( unsigned int a , unsigned int c ,
unsigned int m , unsigned int x0 )
: a_ ( a ) , c_ (c ) , m_ (m ) , xi_ ( x0 )
{}
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{
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xi_ = ( a_ * xi_ + c_ ) % m_ ;
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return double ( xi_ ) / m_ ;
}
} // end namespace ifm
Program 35:
2
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// Prog : loaded_dice.h
// define a class for rolling a loaded dice .
# include < IFM / random .h >
namespace ifm {
// class loaded_dice : definition
class loaded_dice {
public :
// PRE : p1 + p2 + p3 + p4 + p5 <= 1
// POST : * this is initialized to choose the number
//
i in {1 ,... ,6} with probability pi , according
//
to the provided random number generator; here ,
//
p6 = 1 - p1 - p2 - p3 - p4 - p5
loaded_dice ( double p1 , double p2 , double p3 , double p4 ,
double p5 , ifm :: random & generator);
// POST :
//
//
unsigned
return value is the outcome of rolling a loaded
dice , according to the probability distribution
induced by p1 ,... , p6
int operator ()();
private :
// p_upto_i is p1 + ... + pi
const double p_upto_1 ;
const double p_upto_2 ;
const double p_upto_3 ;
const double p_upto_4 ;
const double p_upto_5 ;
// the generator ( we store an alias in order to allow
// several instances to share the same generator)
ifm :: random & g;
EP };
} // end namespace ifm
Program 36:
2
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// Prog : loaded_dice.C
// implement a class for rolling a loaded dice .
# include < IFM / loaded_dice.h >
namespace ifm {
// class loaded_dice : implementation
loaded_dice:: loaded_dice
( double p1 , double p2 , double p3 , double p4 , double p5 ,
ifm :: random & generator)
: p_upto_1 ( p1 ) ,
p_upto_2 ( p_upto_1 + p2 ) ,
p_upto_3 ( p_upto_2 + p3 ) ,
p_upto_4 ( p_upto_3 + p4 ) ,
p_upto_5 ( p_upto_4 + p5 ) ,
g ( generator)
{}
unsigned int loaded_dice :: operator ()()
{
double x = g ();
if ( x <= p_upto_1 ) return 1;
if ( x <= p_upto_2 ) return 2;
if ( x <= p_upto_3 ) return 3;
if ( x <= p_upto_4 ) return 4;
if ( x <= p_upto_5 ) return 5;
return 6;
}
} // end namespace ifm
Program 37:
2
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// Prog : choosing_numbers.C
// let your loaded dice play against your friend ’s dice
// in the game of choosing numbers .
# include < iostream >
# include < IFM / loaded_dice.h >
// POST : return value is the payoff to you ( possibly negative ) ,
//
given the numbers of you and your friend
int your_payoff ( unsigned int you , unsigned int your_friend)
{
if ( you == your_friend) return 0;
// draw
if ( you < your_friend ) {
if ( you + 1 == your_friend ) return 2; // you win 2
return -1;
// you lose 1
} // now we have your_friend < you
if ( your_friend + 1 == you ) return -2; // you lose 2
return 1;
// you win 1
}
int main () {
// the random number generator; let us use the generator
// ANSIC instead of the toy generator knuth8 ; m = 2^31;
EP ifm :: random ansic (1103515245u , 12345 u , 2147483648u , 12345 u );
// your strategy may be to prefer larger numbers and use
// the distribution (1/21 , 2/21 , 3/21 , 4/21 , 5/21 , 6/21)
double p = 1.0/21.0;
ifm :: loaded_dice you (p , 2*p , 3* p , 4* p , 5* p , ansic );
// your friend ’s strategy may be to stay more in the middle
// and use the distribution (1/12 , 2/12 , 3/12 , 3/12 , 2/12 , 1/12)
double q = 1.0/12.0;
ifm :: loaded_dice your_friend (q , 2* q , 3* q , 3* q , 2* q , ansic );
// now simulate 1 million rounds ( the train may be very late ...)
int your_total_payoff = 0;
for ( unsigned int round = 0; round < 1000000; round ++) {
your_total_payoff += your_payoff ( you () , your_friend ());
}
// output the result :
std :: cout < < " Your total payoff is "
< < your_total_payoff < < "\n ";
return 0;
}
Program 38:
2
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