Classes
class	DistributionSampler

class	mt19937_RG

class	RandomGenerator
	Random number generator system. More...

class	ReservoirSampler
	Simple container for keeping K random values. More...

class	uniform_RG
	Uniform random number generator. More...

class	standard_RG
	Generator based on rand() < clib > function. More...

class	WeightedReservoirItem

class	WeightedReservoirSampler

class	WeightedSampler

Typedefs
typedef platform::Size	Size

typedef utility::pointer::shared_ptr< RandomGenerator >	RandomGeneratorOP

typedef utility::pointer::shared_ptr< uniform_RG >	uniform_RG_OP

typedef utility::pointer::shared_ptr< uniform_RG const >	uniform_RG_COP

Functions
static void	lshift128 (w128_t out, const w128_t in, int shift)

static uint32_t	ini_func1 (uint32_t x)

static uint32_t	ini_func2 (uint32_t x)

static int	sformat_idxof (int i)

static void	do_recursion (w128_t r, w128_t a, w128_t b, w128_t c, w128_t *lung)

static THREAD_LOCAL RandomGeneratorOP	random_generator (nullptr)

RandomGenerator &	rg ()
	Return the one-per-thread "singleton" random generator. More...

double	uniform ()
	Generate a random number between 0 and 1. Threadsafe since each thread uses its own random generator. More...

double	gaussian ()
	Generate a random number pulled from a standard normal – i.e. mean of zero and standard deviation of 1. Threadsafe since each thread uses its own random generator. More...

int	random_range (int low, int high)
	Return a number uniformly drawn from the inclusive range between low and high. Threadsafe since each thread uses its own random generator. More...

uniform_RG_OP	createRG (string const &type)
	uniform_RG factory More...

template<typename T >
xyzVector< T >	random_point_on_unit_sphere (RandomGenerator &RG)

template<typename T >
T	random_rotation_angle (T rot_mag, RandomGenerator &RG)
	gamma-distribution-like random angle generation, rot_mag makes exactly the same sense as in gaussian_move More...

template<typename T >
xyzVector< T >	random_translation (T trans_mag, RandomGenerator &RG)
	produce a random translation in xyz space More...

template<typename T >
platform::Size	binary_search_cdf (utility::vector1< T > const &cdf, T urn)
	Return the index in the CDF array such that it is smaller than or equal to the uniform-random-number (urn) and that the next entry in the array is larger than urn. The CDF ought to represent the exclusive cumulative sum of the probabilities of some discrete set so that the width for entry i – the gap between entry i and entry i+1 should be the probability of entry i. More...

template<typename T >
platform::Size	pick_random_index_from_cdf (utility::vector1< T > const &cdf, RandomGenerator &RG)
	Choose an element from an array of positions representing the cumulative distribution function for some target distribution. This uses binary search to quickly find the target index. If any position has the same probability as the preceeding position, then its index won't be returned. More...

template<class T >
void	random_permutation (utility::vector1< T > &vect, RandomGenerator &rg=numeric::random::rg())

template<class T >
void	random_permutation (utility::vector0< T > &vect, RandomGenerator &rg=numeric::random::rg())

template<class T >
void	random_permutation (std::vector< T > &vect, RandomGenerator &rg=numeric::random::rg())

template<typename RandomAccessIterator >
void	random_permutation (RandomAccessIterator first, RandomAccessIterator last, RandomGenerator &rg=numeric::random::rg())
	randomly shuffle elements of a sequence More...

xyzVector< Real >	uniform_vector_sphere (numeric::Real radius=1)
	A random vector chosen uniformly from the ball (volume enclosed within a sphere) of the given radius around the origin. More...

xyzVector< Real >	random_vector_spherical ()
	A random vector chosen with spherical symmetry around the origin. More...

xyzVector< Real >	random_vector_unit_cube ()
	A random vector chosen uniformly from within the volume of a unit cube with opposite verticies at (0,0,0) and (1,1,1) More...

xyzVector< Real >	random_vector ()
	A random vector chosen with spherical symmetry around the origin. More...

xyzVector< Real >	random_normal ()
	A random vector chosens uniformly from the surface of a unit sphere centered on the origin. More...

Quaternion< Real >	random_unit_quaternion ()

xyzMatrix< Real >	random_rotation ()

xyzTransform< Real >	random_xform ()

xyzTransform< Real >	gaussian_random_xform (Real const &angsd, Real const &movsd)

numeric::Real	reservoir_sample_accept_prob (numeric::Size n_wanted, numeric::Size n_seen)
	Returns the probability that the Nth value in a sequence should be accepted using the reservoir sampling criterion. More...

template<typename T >
utility::vector1< T >	reservoir_sample (utility::vector1< T > const &vec, numeric::Size n_wanted, RandomGenerator &rg=numeric::random::rg())

std::ostream &	operator<< (std::ostream &out, WeightedSampler const &sampler)

Typedef Documentation

◆ RandomGeneratorOP

typedef utility::pointer::shared_ptr< RandomGenerator > numeric::random::RandomGeneratorOP

◆ Size

typedef platform::Size numeric::random::Size

◆ uniform_RG_COP

typedef utility::pointer::shared_ptr< uniform_RG const > numeric::random::uniform_RG_COP

◆ uniform_RG_OP

typedef utility::pointer::shared_ptr< uniform_RG > numeric::random::uniform_RG_OP

Function Documentation

◆ binary_search_cdf()

template<typename T >

platform::Size numeric::random::binary_search_cdf	(	utility::vector1< T > const &	cdf,
		T	urn
	)

Return the index in the CDF array such that it is smaller than or equal to the uniform-random-number (urn) and that the next entry in the array is larger than urn. The CDF ought to represent the exclusive cumulative sum of the probabilities of some discrete set so that the width for entry i – the gap between entry i and entry i+1 should be the probability of entry i.

References test_terpenes::lower, and test_terpenes::upper.

Referenced by pick_random_index_from_cdf().

◆ createRG()

uniform_RG_OP numeric::random::createRG ( string const & type )

uniform_RG factory

References utility_exit_with_message.

Referenced by numeric::random::RandomGenerator::set_seed().

◆ do_recursion()

static void numeric::random::do_recursion	(	w128_t *	r,
		w128_t *	a,
		w128_t *	b,
		w128_t *	c,
		w128_t *	lung
	)

inlinestatic

This function represents the recursion formula.

Parameters

r	output
a	a 128-bit part of the internal state array
b	a 128-bit part of the internal state array
c	a 128-bit part of the internal state array
lung	a 128-bit part of the internal state array

References a, compute_difference::b, kmeans_adaptive_kernel_density_bb_dependent_rotlib::c, DSFMT_HIGH_CONST, DSFMT_LOW_MASK, DSFMT_MSK1, DSFMT_MSK2, DSFMT_SL1, DSFMT_SL2, DSFMT_SR1, DSFMT_SR2, lshift128(), create_a3b_hbs::r, W128_T::u, and x.

Referenced by numeric::random::mt19937_RG::gen_rand_all().

◆ gaussian()

double numeric::random::gaussian ( )

Generate a random number pulled from a standard normal – i.e. mean of zero and standard deviation of 1. Threadsafe since each thread uses its own random generator.

References numeric::random::RandomGenerator::gaussian(), and rg().

Referenced by CycBBMover::apply(), LigChiMover::apply(), DuboisChiMover::apply(), BBMover::apply(), SymRBMover::apply(), SimpleBBMover::apply(), MyTransMover::apply(), MyRotMover::apply(), MembraneMinMover::apply(), capri_t033_trim_dock_test(), HubDenovo::cen_fold(), doit(), protocols::abinitio::JumpSpecificAbrelax::fold(), gaussian_random_xform(), main(), make_bonded_rna_move(), random_vector_spherical(), CCParam::randomize(), and test_deriv().

◆ gaussian_random_xform()

numeric::xyzTransform< numeric::Real > numeric::random::gaussian_random_xform	(	Real const &	angsd,
		Real const &	movsd
	)

References gaussian(), and numeric::rotation_matrix_degrees().

◆ ini_func1()

static uint32_t numeric::random::ini_func1 ( uint32_t x )

inlinestatic

This function represents a function used in the initialization by init_by_array

Parameters

x	32-bit integer

Returns: 32-bit integer

References x.

Referenced by numeric::random::mt19937_RG::init_by_array().

◆ ini_func2()

static uint32_t numeric::random::ini_func2 ( uint32_t x )

inlinestatic

This function represents a function used in the initialization by init_by_array

Parameters

x	32-bit integer

Returns: 32-bit integer

References x.

Referenced by numeric::random::mt19937_RG::init_by_array().

◆ lshift128()

static void numeric::random::lshift128	(	w128_t *	out,
		const w128_t *	in,
		int	shift
	)

inlinestatic

This function simulates SIMD 128-bit left shift by the standard C. The 128-bit integer given in in is shifted by (shift * 8) bits. This function simulates the LITTLE ENDIAN SIMD.

Parameters

out	the output of this function
in	the 128-bit data to be shifted
shift	the shift value

References shift.

Referenced by do_recursion().

◆ operator<<()

std::ostream & numeric::random::operator<<	(	std::ostream &	out,
		WeightedSampler const &	sampler
	)

References create_a3b_hbs::ii, erraser_single_res_analysis::out, numeric::random::WeightedSampler::size(), and numeric::random::WeightedSampler::weights().

◆ pick_random_index_from_cdf()

template<typename T >

platform::Size numeric::random::pick_random_index_from_cdf	(	utility::vector1< T > const &	cdf,
		RandomGenerator &	RG
	)

Choose an element from an array of positions representing the cumulative distribution function for some target distribution. This uses binary search to quickly find the target index. If any position has the same probability as the preceeding position, then its index won't be returned.

References binary_search_cdf(), RG, and numeric::random::RandomGenerator::uniform().

◆ random_generator()

static THREAD_LOCAL RandomGeneratorOP numeric::random::random_generator ( nullptr )

static

◆ random_normal()

numeric::xyzVector< numeric::Real > numeric::random::random_normal ( )

A random vector chosens uniformly from the surface of a unit sphere centered on the origin.

References numeric::xyzVector< T >::is_zero(), numeric::xyzVector< T >::normalized_or_zero(), and random_vector_spherical().

◆ random_permutation() [1/4]

template<typename RandomAccessIterator >

void numeric::random::random_permutation	(	RandomAccessIterator	first,
		RandomAccessIterator	last,
		RandomGenerator &	rg = `numeric::random::rg()`
	)

randomly shuffle elements of a sequence

References create_a3b_hbs::first, create_a3b_hbs::i, rg(), and numeric::random::RandomGenerator::uniform().

◆ random_permutation() [2/4]

template<class T >

void numeric::random::random_permutation	(	std::vector< T > &	vect,
		RandomGenerator &	rg = `numeric::random::rg()`
	)

References create_a3b_hbs::ii, rg(), erraser_analysis::temp, and numeric::random::RandomGenerator::uniform().

◆ random_permutation() [3/4]

template<class T >

void numeric::random::random_permutation	(	utility::vector0< T > &	vect,
		RandomGenerator &	rg = `numeric::random::rg()`
	)

References create_a3b_hbs::ii, rg(), erraser_analysis::temp, and numeric::random::RandomGenerator::uniform().

◆ random_permutation() [4/4]

template<class T >

void numeric::random::random_permutation	(	utility::vector1< T > &	vect,
		RandomGenerator &	rg = `numeric::random::rg()`
	)

References create_a3b_hbs::ii, rg(), erraser_analysis::temp, and numeric::random::RandomGenerator::uniform().

Referenced by LoopHashRelax_Sampler::apply(), design_test(), determine_residues_to_rebuild(), distribute_jobs(), dna_stats(), PerturbStruct::do_mutate(), CrystDesign::do_reversion(), CrystDesign::greedy_revert_unsats(), ligand_dock_main_jd1(), main(), run_pep_prep(), RunPepSpec(), and trim_dock_rebuild_relax_test().

◆ random_point_on_unit_sphere()

template<typename T >

xyzVector< T > numeric::random::random_point_on_unit_sphere ( RandomGenerator & RG )

inline

@detail generate uniformly distributed vector on the unit sphere

Author: Zhe Zhang; Justin R. Porter @detail generate uniformly distributed unit vector @detail a random normal distribution of coordinates gives a uniform distribution of directions. @detail same functionality as the commented random_point_on_unit_sphere(), but simpler algorithm @detail rename as random_uniform_distributed_direction()?; Zhe Zhang

References numeric::random::RandomGenerator::gaussian(), RG, and vec().

◆ random_range()

int numeric::random::random_range	(	int	low,
		int	high
	)

Return a number uniformly drawn from the inclusive range between low and high. Threadsafe since each thread uses its own random generator.

References numeric::random::RandomGenerator::random_range(), and rg().

Referenced by numeric::random::ReservoirSampler< T >::add_value(), HemeBindingMover::apply(), MPFindInterfaceTestMover::apply(), MembraneMinMover::apply(), StepwiseTorsionMover::apply(), choose_centroids(), create_and_score_fragments(), generate_sequence_binary_alphabet(), get_change_in_distance(), FragMonteCarlo::initialize_frag_assignment(), main(), ClosureMover::naive_apply(), BreadthMover::omega_apply(), BreadthMover::rama_apply(), random_alignment_move(), FragmentAssemblyMover::run(), run(), FragMonteCarlo::run(), run_parallel_docking(), and BreadthMover::uniform_apply().

◆ random_rotation()

numeric::xyzMatrix< numeric::Real > numeric::random::random_rotation ( )

References numeric::xyzMatrix< T >::cols(), enumerate_junctions::q, and random_unit_quaternion().

Referenced by random_xform(), and rb_entropy_test().

◆ random_rotation_angle()

template<typename T >

T numeric::random::random_rotation_angle	(	T	rot_mag,
		RandomGenerator &	RG
	)

inline

gamma-distribution-like random angle generation, rot_mag makes exactly the same sense as in gaussian_move

@detail generate axis and angle for axis-angle rotation for random rotation move in R/RT degrees of freedom. rotation axis: uniformly distributed on unit sphere, rotation angle: chosen to mimic the distribution of rotation angles obtained from gaussian distrbuted Euler angles (core/kinematics/Jump.cc), which is a gamma-distribution-like distribution

Note: gaussian distributed Euler angles do not give unbiased sampling in rotational space by applying this angle to a uniformly chosen rotation axis unbiased rotational sampling is achieved

Author: Zhe Zhang @auhtor Justin R. Porter

References numeric::random::RandomGenerator::gaussian(), mat, RG, numeric::rotation_axis(), numeric::x_rotation_matrix_degrees(), numeric::y_rotation_matrix_degrees(), and numeric::z_rotation_matrix_degrees().

◆ random_translation()

template<typename T >

xyzVector< T > numeric::random::random_translation	(	T	trans_mag,
		RandomGenerator &	RG
	)

inline

produce a random translation in xyz space

Author: Zhe Zhang; Justin R. Porter

References numeric::random::RandomGenerator::gaussian(), and RG.

Referenced by rb_entropy_test().

◆ random_unit_quaternion()

numeric::Quaternion< numeric::Real > numeric::random::random_unit_quaternion ( )

References numeric::constants::d::pi_2, and uniform().

Referenced by random_rotation().

◆ random_vector()

numeric::xyzVector< numeric::Real > numeric::random::random_vector ( )

A random vector chosen with spherical symmetry around the origin.

Actual distribution is a 3D gaussian with unit variance centered at the origin.

References random_vector_spherical().

◆ random_vector_spherical()

numeric::xyzVector< numeric::Real > numeric::random::random_vector_spherical ( )

A random vector chosen with spherical symmetry around the origin.

Actual distribution is a 3D gaussian with unit variance centered at the origin.

References gaussian().

Referenced by random_normal(), random_vector(), and random_xform().

◆ random_vector_unit_cube()

numeric::xyzVector< numeric::Real > numeric::random::random_vector_unit_cube ( )

A random vector chosen uniformly from within the volume of a unit cube with opposite verticies at (0,0,0) and (1,1,1)

References uniform().

◆ random_xform()

numeric::xyzTransform< numeric::Real > numeric::random::random_xform ( )

References random_rotation(), and random_vector_spherical().

◆ reservoir_sample()

template<typename T >

utility::vector1< T > numeric::random::reservoir_sample	(	utility::vector1< T > const &	vec,
		numeric::Size	n_wanted,
		RandomGenerator &	rg = `numeric::random::rg()`
	)

References end, kmeans_adaptive_kernel_density_bb_dependent_rotlib::idx, numeric::random::RandomGenerator::random_range(), reservoir_sample_accept_prob(), rg(), numeric::random::RandomGenerator::uniform(), test.T040_Types::values, and vec().

◆ reservoir_sample_accept_prob()

numeric::Real numeric::random::reservoir_sample_accept_prob	(	numeric::Size	n_wanted,
		numeric::Size	n_seen
	)

inline

Returns the probability that the Nth value in a sequence should be accepted using the reservoir sampling criterion.

If we've seen N values and we want to keep K of them, the probability of the Nth value being accepted is min(K/N,1.0).

References min().

Referenced by numeric::random::ReservoirSampler< T >::add_value(), and reservoir_sample().

◆ rg()

RandomGenerator & numeric::random::rg ( )

Return the one-per-thread "singleton" random generator.

Referenced by align_backbone_by_chunk(), ChiMover::apply(), TorsionVectorMover::apply(), LoopHashRelax_Sampler::apply(), DockGlycansProtocol::apply(), CenRotSidechainMover::apply(), CenRotCanonicalMover::apply(), backrub_protocol(), create_random_angle_from_range(), create_random_angle_from_range_list(), create_random_nucleoside_torsion(), create_random_suite_torsion(), create_random_torsions(), design_test(), determine_residues_to_rebuild(), devel_main(), distribute_jobs(), dna_stats(), PerturbStruct::do_mutate(), CrystDesign::do_reversion(), doit(), double_helix_test(), erraser_monte_carlo(), PerformanceBenchmark::execute(), fit_helix_in_map(), gaussian(), gaussian_angle_move(), gen_pep_bb_frag(), gen_pep_bb_frag_old(), gen_pep_bb_rama(), gen_pep_bb_sequential(), generate_sequence_binary_alphabet(), CenRotSidechainMover::get_random_rotamer(), CrystDesign::greedy_revert_unsats(), helix_ST(), basic::random::init_random_generators(), initialize_free_and_fixed(), initialize_peptide(), protocols::abinitio::JumpSpecificAbrelax::insert_template_frags(), apps::pilot::KicSandbox::KicSandbox(), lariat_modeling(), ligand_dock_main_jd1(), main(), make_1mer_frags(), make_random_perturbation(), MC_run(), mutate_random_residue(), my_main(), nucleoside_sampling(), one_chain_MC_sampling(), one_chain_ST_MC(), perturb_and_rescore(), UniformPerturber::perturb_chain(), myspace::Scheduler::pick_hashing_res(), pick_random_solution(), ChallengeMover::pick_random_template(), populate_database_with_dummy_data(), protocols_main(), random_angle(), random_delta(), random_element(), random_permutation(), random_range(), numeric::random::WeightedSampler::random_sample(), randomly_open_pose_loop(), rb_entropy_test(), ChallengeMover::realign(), repack_cluster(), reservoir_sample(), myMC::roll(), core::pack::annealer::FixbbSimAnnealer::run(), myspace::Scheduler::run_combine(), myspace::Scheduler::run_NM(), run_parallel_docking(), run_pep_prep(), RunPepSpec(), basic::database::safely_read_from_database(), sample_near_current_torsion(), sample_near_nucleoside_torsion(), sample_near_suite_torsion(), set_pep_csts(), ConstraintToolMover::show_cstset(), simple_loop_modeling_test(), simple_opte_test(), SomeThing::SomeThing(), test(), myspace::test_bbgauss(), trim_dock_rebuild_relax_test(), uniform(), update_torsion_set(), OutputManager::write_header(), write_new_respair_to_database(), and write_scores_and_hbond_geoms_to_database().

◆ sformat_idxof()

static int numeric::random::sformat_idxof ( int i )

inlinestatic

This function simulate a 32-bit array index overlapped to 64-bit array of LITTLE ENDIAN in BIG ENDIAN machine.

References create_a3b_hbs::i.

Referenced by numeric::random::mt19937_RG::init_by_array(), and numeric::random::mt19937_RG::setSeed().

◆ uniform()

double numeric::random::uniform ( )

Generate a random number between 0 and 1. Threadsafe since each thread uses its own random generator.

References rg(), and numeric::random::RandomGenerator::uniform().

Referenced by numeric::random::ReservoirSampler< T >::add_value(), HemeBindingMover::apply(), CycBBMover::apply(), MoveThenFixHMin::apply(), MoveThenFixH::apply(), LigChiMover::apply(), BBMover::apply(), SymRBMover::apply(), SimpleBBMover::apply(), ChiMover::apply(), MyTransMover::apply(), MyRotMover::apply(), FloatScRotMover::apply(), TorsionVectorMover::apply(), DockGlycansProtocol::apply(), FloatScRandomChi::apply(), StepwiseTorsionMover::apply(), ConcertedTorsionMover::apply(), ConstraintConfig::apply_bb_csts(), backrub_protocol(), capri_t033_trim_dock_test(), HubDenovo::cen_fold(), numeric::random::WeightedReservoirSampler< T >::consider_sample(), create_random_pose(), MatchSet::cross(), diversify_sam_loop_test(), dock(), doit(), doit_refine(), dostuff(), fa_refine_and_design(), gaussian-sampling::final_accept(), gen_pep_bb_frag(), gen_pep_bb_frag_old(), gen_pep_bb_rama(), gen_pep_bb_sequential(), helix_ST(), idealize_tf_pose(), gaussian-sampling::initial_accept(), initialize_peptide(), protocols::abinitio::JumpSpecificAbrelax::insert_template_frags(), main(), make_1mer_frags(), make_bonded_rna_move(), make_helix(), make_rand_ss(), make_rand_ss_h(), make_rand_ss_hs(), MC_run(), Mutate1Randomizer::mutate(), mutate_random_residue(), my_main(), nucleoside_sampling(), BreadthMover::omega_apply(), one_chain_ST_MC(), UniformPerturber::perturb_chain(), ConstraintConfig::pick_sequence(), process_ss_str(), rand_rot(), Bola::random_close_phipsi_from_rama(), Bola::random_move(), numeric::random::RandomGenerator::random_range(), numeric::random::WeightedSampler::random_sample(), random_torsions(), random_unit_quaternion(), random_unit_vector(), random_vector_unit_cube(), CCParam::randomize(), randomly_open_pose_loop(), randomly_shift_and_tilt_pose(), randomly_shift_and_tilt_poses(), randvec(), rb_entropy_test(), report(), myMC::roll(), FragmentAssemblyMover::run(), core::pack::annealer::FixbbSimAnnealer::run(), FragMonteCarlo::run(), HubDenovo::run(), myspace::Scheduler::run_combine(), run_parallel_docking(), run_pep_prep(), RunPepSpec(), basic::database::safely_read_from_database(), numeric::random::DistributionSampler< T >::sample(), sample_near_current_torsion(), sample_near_nucleoside_torsion(), sample_near_suite_torsion(), select_string(), set_pep_csts(), MPDomainAssembly::set_random_torsion(), setup_loops_from_mapping(), simple_loop_modeling_test(), simulate_ERMS(), test(), test_MAT_VEC(), test_Random(), BreadthMover::uniform_apply(), uniform_vector_sphere(), SamplingManager::update(), update_torsion_set(), and wriggle_test().

◆ uniform_vector_sphere()

numeric::xyzVector< numeric::Real > numeric::random::uniform_vector_sphere ( numeric::Real radius )

A random vector chosen uniformly from the ball (volume enclosed within a sphere) of the given radius around the origin.

References numeric::distance(), oop_conformations::phi, numeric::constants::ld::pi, basic::options::OptionKeys::cluster::radius, docking::U, uniform(), numeric::xyzVector< T >::x(), numeric::xyzVector< T >::y(), and numeric::xyzVector< T >::z().

Classes

Typedefs

Functions

Typedef Documentation

◆ RandomGeneratorOP

◆ Size

◆ uniform_RG_COP

◆ uniform_RG_OP

Function Documentation

◆ binary_search_cdf()

◆ createRG()

◆ do_recursion()

◆ gaussian()

◆ gaussian_random_xform()

◆ ini_func1()

◆ ini_func2()

◆ lshift128()

◆ operator<<()

◆ pick_random_index_from_cdf()

◆ random_generator()

◆ random_normal()

◆ random_permutation() [1/4]

◆ random_permutation() [2/4]

◆ random_permutation() [3/4]

◆ random_permutation() [4/4]

◆ random_point_on_unit_sphere()

◆ random_range()

◆ random_rotation()

◆ random_rotation_angle()

◆ random_translation()

◆ random_unit_quaternion()

◆ random_vector()

◆ random_vector_spherical()

◆ random_vector_unit_cube()

◆ random_xform()

◆ reservoir_sample()

◆ reservoir_sample_accept_prob()

◆ rg()

◆ sformat_idxof()

◆ uniform()

◆ uniform_vector_sphere()