boost pseudo-random number generator

generator	length of cycle	approx. memory requirements	approx. speed compared to fastest	header file
`minstd_rand0`	2³¹-2	`sizeof(int32_t)`	16%	boost/random/linear_congruential.hpp
`minstd_rand`	2³¹-2	`sizeof(int32_t)`	16%	boost/random/linear_congruential.hpp
`rand48`	2⁴⁸-1	`sizeof(uint64_t)`	64%	boost/random/linear_congruential.hpp
`ecuyer1988`	approx. 2⁶¹	`2*sizeof(int32_t)`	7%	boost/random/additive_combine.hpp
`knuth_b`	?	`257*sizeof(uint32_t)`	12%	boost/random/shuffle_order.hpp
`kreutzer1986`	?	`98*sizeof(uint32_t)`	37%	boost/random/shuffle_order.hpp
`taus88`	~2⁸⁸	`3*sizeof(uint32_t)`	100%	boost/random/taus88.hpp
`hellekalek1995`	2³¹-1	`sizeof(int32_t)`	2%	boost/random/inversive_congruential.hpp
`mt11213b`	2¹¹²¹³-1	`352*sizeof(uint32_t)`	100%	boost/random/mersenne_twister.hpp
`mt19937`	2¹⁹⁹³⁷-1	`625*sizeof(uint32_t)`	93%	boost/random/mersenne_twister.hpp
`mt19937_64`	2¹⁹⁹³⁷-1	`312*sizeof(uint64_t)`	38%	boost/random/mersenne_twister.hpp
`lagged_fibonacci607`	~2³²⁰⁰⁰	`607*sizeof(double)`	59%	boost/random/lagged_fibonacci.hpp
`lagged_fibonacci1279`	~2⁶⁷⁰⁰⁰	`1279*sizeof(double)`	59%	boost/random/lagged_fibonacci.hpp
`lagged_fibonacci2281`	~2¹²⁰⁰⁰⁰	`2281*sizeof(double)`	61%	boost/random/lagged_fibonacci.hpp
`lagged_fibonacci3217`	~2¹⁷⁰⁰⁰⁰	`3217*sizeof(double)`	62%	boost/random/lagged_fibonacci.hpp
`lagged_fibonacci4423`	~2²³⁰⁰⁰⁰	`4423*sizeof(double)`	59%	boost/random/lagged_fibonacci.hpp
`lagged_fibonacci9689`	~2⁵¹⁰⁰⁰⁰	`9689*sizeof(double)`	61%	boost/random/lagged_fibonacci.hpp
`lagged_fibonacci19937`	~2^1050000	`19937*sizeof(double)`	59%	boost/random/lagged_fibonacci.hpp
`lagged_fibonacci23209`	~2^1200000	`23209*sizeof(double)`	61%	boost/random/lagged_fibonacci.hpp
`lagged_fibonacci44497`	~2^2300000	`44497*sizeof(double)`	59%	boost/random/lagged_fibonacci.hpp
`ranlux3`	~10¹⁷¹	`24*sizeof(int)`	5%	boost/random/ranlux.hpp
`ranlux4`	~10¹⁷¹	`24*sizeof(int)`	3%	boost/random/ranlux.hpp
`ranlux64_3`	~10¹⁷¹	`24*sizeof(int64_t)`	5%	boost/random/ranlux.hpp
`ranlux64_4`	~10¹⁷¹	`24*sizeof(int64_t)`	3%	boost/random/ranlux.hpp
`ranlux3_01`	~10¹⁷¹	`24*sizeof(float)`	5%	boost/random/ranlux.hpp
`ranlux4_01`	~10¹⁷¹	`24*sizeof(float)`	3%	boost/random/ranlux.hpp
`ranlux64_3_01`	~10¹⁷¹	`24*sizeof(double)`	5%	boost/random/ranlux.hpp
`ranlux64_4_01`	~10¹⁷¹	`24*sizeof(double)`	3%	boost/random/ranlux.hpp
`ranlux24`	~10¹⁷¹	`24*sizeof(uint32_t)`	5%	boost/random/ranlux.hpp
`ranlux48`	~10¹⁷¹	`12*sizeof(uint64_t)`	3%	boost/random/ranlux.hpp

Table 33.6. Uniform Distributions

distribution	explanation	example	header
`uniform_smallint`	discrete uniform distribution on a small set of integers (much smaller than the range of the underlying generator)	drawing from an urn	boost/random/uniform_smallint.hpp
`uniform_int_distribution`	discrete uniform distribution on a set of integers; the underlying generator may be called several times to gather enough randomness for the output	drawing from an urn	boost/random/uniform_int_distribution.hpp
`uniform_01`	continuous uniform distribution on the range [0,1); important basis for other distributions	-	boost/random/uniform_01.hpp
`uniform_real_distribution`	continuous uniform distribution on some range [min, max) of real numbers	for the range [0, 2pi): randomly dropping a stick and measuring its angle in radians (assuming the angle is uniformly distributed)	boost/random/uniform_real_distribution.hpp

Table 33.7. Bernoulli Distributions

distribution	explanation	example	header
`bernoulli_distribution`	Bernoulli experiment: discrete boolean valued distribution with configurable probability	tossing a coin (p=0.5)	boost/random/bernoulli_distribution.hpp
`binomial_distribution`	counts outcomes of repeated Bernoulli experiments	tossing a coin 20 times and counting how many front sides are shown	boost/random/binomial_distribution.hpp
`geometric_distribution`	measures distance between outcomes of repeated Bernoulli experiments	throwing a die several times and counting the number of tries until a "6" appears for the first time	boost/random/geometric_distribution.hpp
`negative_binomial_distribution`	Counts the number of failures of repeated Bernoulli experiments required to get some constant number of successes.	flipping a coin and counting the number of heads that show up before we get 3 tails	boost/random/negative_binomial_distribution.hpp

Table 33.8. Poisson Distributions

distribution	explanation	example	header
`poisson_distribution`	poisson distribution	counting the number of alpha particles emitted by radioactive matter in a fixed period of time	boost/random/poisson_distribution.hpp
`exponential_distribution`	exponential distribution	measuring the inter-arrival time of alpha particles emitted by radioactive matter
`gamma_distribution`	gamma distribution	-
`hyperexponential_distribution`	hyperexponential distribution	service time of k-parallel servers each with a given service rate and probability to be chosen
`weibull_distribution`	weibull distribution	-
`extreme_value_distribution`	extreme value distribution	-
`beta_distribution`	beta distribution	-
`laplace_distribution`	laplace distribution	-

Table 33.9. Normal Distributions

distribution	explanation	example
`normal_distribution`	counts outcomes of (infinitely) repeated Bernoulli experiments	tossing a coin 10000 times and counting how many front sides are shown
`lognormal_distribution`	lognormal distribution (sometimes used in simulations)	measuring the job completion time of an assembly line worker
`chi_squared_distribution`	chi-squared distribution	-
`non_central_chi_squared_distribution`	non-central chi-squared distribution	-
`cauchy_distribution`	Cauchy distribution	-
`fisher_f_distribution`	Fisher F distribution	-
`student_t_distribution`	Student t distribution	-

Table 33.10. Sampling Distributions

distribution	explanation	example
`discrete_distribution`	discrete distribution with specific probabilities	rolling an unfair die
`piecewise_constant_distribution`	-	-
`piecewise_linear_distribution`	-	-

Table 33.11. Miscellaneous Distributions

distribution	explanation	example
`triangle_distribution`	triangle distribution	-
`uniform_on_sphere`	uniform distribution on a unit sphere of arbitrary dimension	choosing a random point on Earth (assumed to be a sphere) where to spend the next vacations