pic_random_dist

Distributions whose output is an integer or a logical, and which are therefore bit-identical on every supported compiler.

Why a separate module from the real-valued one

A textbook exponential deviate is -mean * log(u). That calls libm, and libm is not the same function on every platform: GNU, Intel and NVIDIA do not agree to the last bit, and they are not obliged to. Any value derived that way is unusable in state that has to be compared across runs or across compilers.

Everything in this module is computed with integer arithmetic only – no real type appears in any expression that reaches a result – so a given generator and seed produce the same sequence everywhere. The tests pin the first outputs of every routine for a fixed seed, and those pins are the contract.

The real-valued distributions live in pic_random_dist_real. Keeping them in a different module means a translation unit that only uses this one cannot reach a non-reproducible deviate by accident.

Quick start

use pic_rng, only: splitmix64_t
use pic_random_dist, only: next_range, next_bernoulli_ppm, &
                           next_exponential_int

type(splitmix64_t) :: gen
call gen%seed(20250914_int64)

die = next_range(gen, 1, 6)                  ! inclusive
stolen = next_bernoulli_ppm(gen, 2500)       ! 0.25% chance
gap_ms = next_exponential_int(gen, 4000_int64)   ! mean 4 seconds

Uses

Help

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Variables

Type	Visibility	Attributes		Name		Initial
integer(kind=int64),	public,	parameter	::	EXPONENTIAL_MAX_MEAN	=	2147483647_int64	Largest `mean` `next_exponential_int` accepts, `huge(int32)` as an `int64`. The bound is what makes the final fixed-point multiply provably free of signed overflow; see `scale_by_mean`.
integer(kind=default_int),	public,	parameter	::	POISSON_MAX_MEAN_MILLI	=	1000000_default_int	Largest `mean_milli` `next_poisson_int` accepts, that is a mean of 1000 events. The sampler is O(mean), so this is a guard against silently getting slow rather than an arithmetic limit.
integer(kind=default_int),	public,	parameter	::	PPM_ONE	=	1000000_default_int	Parts per million corresponding to certainty, for `next_bernoulli_ppm`.
integer(kind=default_int),	private,	parameter	::	EXP_CELLS	=	4096_default_int	Number of cells in `EXP_TABLE`, and so 2**EXP_CELL_BITS.
integer(kind=default_int),	private,	parameter	::	EXP_CELL_BITS	=	12_default_int	Number of random bits that select a table cell; 2**12 == 4096.
integer(kind=int64),	private,	parameter	::	EXP_LN_CELLS	=	EXP_TABLE(EXP_TOP_CELL)	ln(4096) in Q32.32. Taken from the table rather than written out again, because `-ln(1 - 4095/4096)` is exactly `ln(4096)` and a second copy of it could drift. Added once per turn around the tail loop.
integer(kind=default_int),	private,	parameter	::	EXP_MAX_TAIL	=	8_default_int	Most times the tail loop may go round. Each turn needs the 12-bit draw to hit exactly one value, so reaching the cap has probability 4096*-8, about 3e-29, and bounds the result at 9ln(4096) means.
integer(kind=int64),	private,	parameter	::	EXP_TABLE(0:EXP_TOP_CELL)	=	[0_int64, 1048704_int64, 2097664_int64, 3146881_int64, 4196353_int64, 5246083_int64, 6296069_int64, 7346311_int64, 8396811_int64, 9447567_int64, 10498581_int64, 11549852_int64, 12601380_int64, 13653166_int64, 14705209_int64, 15757511_int64, 16810070_int64, 17862887_int64, 18915962_int64, 19969295_int64, 21022887_int64, 22076738_int64, 23130847_int64, 24185215_int64, 25239841_int64, 26294727_int64, 27349872_int64, 28405276_int64, 29460940_int64, 30516863_int64, 31573046_int64, 32629488_int64, 33686191_int64, 34743153_int64, 35800376_int64, 36857859_int64, 37915602_int64, 38973606_int64, 40031871_int64, 41090397_int64, 42149183_int64, 43208231_int64, 44267539_int64, 45327110_int64, 46386941_int64, 47447034_int64, 48507389_int64, 49568006_int64, 50628884_int64, 51690025_int64, 52751428_int64, 53813094_int64, 54875022_int64, 55937212_int64, 56999665_int64, 58062381_int64, 59125361_int64, 60188603_int64, 61252108_int64, 62315877_int64, 63379910_int64, 64444206_int64, 65508766_int64, 66573590_int64, 67638678_int64, 68704030_int64, 69769647_int64, 70835528_int64, 71901673_int64, 72968084_int64, 74034759_int64, 75101699_int64, 76168904_int64, 77236374_int64, 78304110_int64, 79372112_int64, 80440379_int64, 81508911_int64, 82577710_int64, 83646775_int64, 84716105_int64, 85785703_int64, 86855566_int64, 87925696_int64, 88996093_int64, 90066757_int64, 91137687_int64, 92208885_int64, 93280350_int64, 94352082_int64, 95424082_int64, 96496350_int64, 97568885_int64, 98641688_int64, 99714759_int64, 100788099_int64, 101861706_int64, 102935582_int64, 104009727_int64, 105084140_int64, 106158822_int64, 107233774_int64, 108308994_int64, 109384483_int64, 110460242_int64, 111536271_int64, 112612569_int64, 113689136_int64, 114765974_int64, 115843082_int64, 116920460_int64, 117998108_int64, 119076027_int64, 120154216_int64, 121232676_int64, 122311407_int64, 123390409_int64, 124469683_int64, 125549227_int64, 126629043_int64, 127709130_int64, 128789489_int64, 129870120_int64, 130951023_int64, 132032198_int64, 133113645_int64, 134195364_int64, 135277356_int64, 136359621_int64, 137442158_int64, 138524969_int64, 139608052_int64, 140691409_int64, 141775039_int64, 142858942_int64, 143943119_int64, 145027570_int64, 146112295_int64, 147197293_int64, 148282566_int64, 149368113_int64, 150453935_int64, 151540031_int64, 152626402_int64, 153713048_int64, 154799969_int64, 155887164_int64, 156974636_int64, 158062382_int64, 159150404_int64, 160238702_int64, 161327276_int64, 162416125_int64, 163505251_int64, 164594653_int64, 165684331_int64, 166774286_int64, 167864518_int64, 168955026_int64, 170045812_int64, 171136874_int64, 172228214_int64, 173319831_int64, 174411725_int64, 175503898_int64, 176596348_int64, 177689076_int64, 178782082_int64, 179875366_int64, 180968929_int64, 182062770_int64, 183156890_int64, 184251288_int64, 185345966_int64, 186440922_int64, 187536158_int64, 188631673_int64, 189727468_int64, 190823542_int64, 191919897_int64, 193016531_int64, 194113445_int64, 195210639_int64, 196308114_int64, 197405869_int64, 198503905_int64, 199602222_int64, 200700819_int64, 201799698_int64, 202898858_int64, 203998299_int64, 205098022_int64, 206198026_int64, 207298313_int64, 208398881_int64, 209499731_int64, 210600863_int64, 211702278_int64, 212803976_int64, 213905956_int64, 215008219_int64, 216110765_int64, 217213594_int64, 218316706_int64, 219420101_int64, 220523780_int64, 221627743_int64, 222731990_int64, 223836520_int64, 224941335_int64, 226046434_int64, 227151818_int64, 228257486_int64, 229363438_int64, 230469676_int64, 231576198_int64, 232683006_int64, 233790099_int64, 234897478_int64, 236005142_int64, 237113091_int64, 238221327_int64, 239329849_int64, 240438657_int64, 241547751_int64, 242657132_int64, 243766799_int64, 244876753_int64, 245986994_int64, 247097522_int64, 248208337_int64, 249319440_int64, 250430830_int64, 251542508_int64, 252654474_int64, 253766727_int64, 254879269_int64, 255992099_int64, 257105217_int64, 258218624_int64, 259332320_int64, 260446305_int64, 261560578_int64, 262675141_int64, 263789993_int64, 264905134_int64, 266020565_int64, 267136286_int64, 268252297_int64, 269368598_int64, 270485189_int64, 271602070_int64, 272719242_int64, 273836704_int64, 274954458_int64, 276072502_int64, 277190838_int64, 278309464_int64, 279428382_int64, 280547592_int64, 281667094_int64, 282786887_int64, 283906972_int64, 285027350_int64, 286148020_int64, 287268982_int64, 288390237_int64, 289511785_int64, 290633626_int64, 291755760_int64, 292878187_int64, 294000907_int64, 295123921_int64, 296247229_int64, 297370831_int64, 298494726_int64, 299618916_int64, 300743400_int64, 301868179_int64, 302993252_int64, 304118620_int64, 305244284_int64, 306370242_int64, 307496495_int64, 308623044_int64, 309749888_int64, 310877028_int64, 312004464_int64, 313132196_int64, 314260224_int64, 315388549_int64, 316517170_int64, 317646088_int64, 318775302_int64, 319904814_int64, 321034622_int64, 322164728_int64, 323295131_int64, 324425832_int64, 325556831_int64, 326688127_int64, 327819722_int64, 328951615_int64, 330083806_int64, 331216296_int64, 332349084_int64, 333482172_int64, 334615558_int64, 335749243_int64, 336883228_int64, 338017512_int64, 339152096_int64, 340286980_int64, 341422164_int64, 342557647_int64, 343693431_int64, 344829516_int64, 345965901_int64, 347102587_int64, 348239573_int64, 349376861_int64, 350514450_int64, 351652341_int64, 352790532_int64, 353929026_int64, 355067822_int64, 356206919_int64, 357346319_int64, 358486021_int64, 359626026_int64, 360766333_int64, 361906943_int64, 363047856_int64, 364189072_int64, 365330592_int64, 366472415_int64, 367614542_int64, 368756972_int64, 369899706_int64, 371042745_int64, 372186088_int64, 373329735_int64, 374473687_int64, 375617944_int64, 376762505_int64, 377907372_int64, 379052544_int64, 380198021_int64, 381343804_int64, 382489893_int64, 383636287_int64, 384782988_int64, 385929995_int64, 387077308_int64, 388224928_int64, 389372855_int64, 390521088_int64, 391669629_int64, 392818476_int64, 393967632_int64, 395117094_int64, 396266865_int64, 397416943_int64, 398567329_int64, 399718024_int64, 400869027_int64, 402020338_int64, 403171958_int64, 404323887_int64, 405476125_int64, 406628673_int64, 407781529_int64, 408934695_int64, 410088171_int64, 411241957_int64, 412396053_int64, 413550459_int64, 414705175_int64, 415860202_int64, 417015539_int64, 418171188_int64, 419327147_int64, 420483418_int64, 421640000_int64, 422796893_int64, 423954099_int64, 425111616_int64, 426269445_int64, 427427586_int64, 428586040_int64, 429744806_int64, 430903885_int64, 432063277_int64, 433222982_int64, 434383000_int64, 435543332_int64, 436703977_int64, 437864936_int64, 439026209_int64, 440187796_int64, 441349697_int64, 442511912_int64, 443674442_int64, 444837287_int64, 446000447_int64, 447163922_int64, 448327712_int64, 449491817_int64, 450656238_int64, 451820975_int64, 452986028_int64, 454151397_int64, 455317082_int64, 456483084_int64, 457649402_int64, 458816038_int64, 459982990_int64, 461150259_int64, 462317846_int64, 463485750_int64, 464653971_int64, 465822511_int64, 466991369_int64, 468160544_int64, 469330039_int64, 470499851_int64, 471669983_int64, 472840433_int64, 474011202_int64, 475182291_int64, 476353699_int64, 477525426_int64, 478697474_int64, 479869841_int64, 481042528_int64, 482215536_int64, 483388864_int64, 484562513_int64, 485736482_int64, 486910773_int64, 488085384_int64, 489260317_int64, 490435571_int64, 491611148_int64, 492787046_int64, 493963266_int64, 495139808_int64, 496316672_int64, 497493860_int64, 498671369_int64, 499849202_int64, 501027358_int64, 502205837_int64, 503384640_int64, 504563766_int64, 505743216_int64, 506922990_int64, 508103088_int64, 509283511_int64, 510464258_int64, 511645330_int64, 512826726_int64, 514008448_int64, 515190495_int64, 516372867_int64, 517555565_int64, 518738589_int64, 519921938_int64, 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35724533662_int64]
integer(kind=default_int),	private,	parameter	::	EXP_TOP_CELL	=	EXP_CELLS-1_default_int	Index of the cell that runs off to infinity; handled by recursion.
integer(kind=default_int),	private,	parameter	::	FRAC_BITS	=	31_default_int	Bits used to interpolate within a cell. Thirty-one and not thirty-two so that `gap * frac` fits a signed `int64` in a single multiply: the widest gap is below 232 (asserted by the table generator), and (232 - 1) * (2**31 - 1) is below huge(int64).
integer(kind=int64),	private,	parameter	::	POISSON_WINDOW	=	2097152_int64	2*21 ticks. The count is the number of exponential inter-arrivals that fit in this window. Chosen as the largest power of two with `POISSON_WINDOW 1000` still inside `EXPONENTIAL_MAX_MEAN`, so that a mean of one thousandth of an event is still expressible.
integer(kind=int64),	private,	parameter	::	Q32_HALF	=	2147483648_int64	2**31, the Q32.32 representation of 0.5, added before the final shift so that the fraction rounds to nearest instead of truncating.
integer(kind=int64),	private,	parameter	::	Q32_MASK	=	4294967295_int64	2**32 - 1, to take the fractional part of a Q32.32 value.

Interfaces

public interface next_bernoulli_ppm

Return true with probability ppm in a million.

ppm is clamped to [0, PPM_ONE], so 0 never fires and 1000000 always does, and no value in between can be mistyped into an error. Parts per million rather than a real probability because this reaches simulation state: an incident either happened or it did not, and two runs must agree on which.

private function splitmix64_next_bernoulli_ppm(gen, ppm) result(r)

True with probability ppm in a million, from a splitmix64_t generator.

Arguments

Type	Intent	Optional	Attributes		Name
type(splitmix64_t),	intent(inout)			::	gen	Generator, advanced by the draw unless `ppm` is 0 or `PPM_ONE`.
integer(kind=default_int),	intent(in)			::	ppm	Probability in parts per million, clamped to `[0, PPM_ONE]`.

Return Value logical

private function pcg32_next_bernoulli_ppm(gen, ppm) result(r)

True with probability ppm in a million, from a pcg32_t generator.

Arguments

Type	Intent	Optional	Attributes		Name
type(pcg32_t),	intent(inout)			::	gen	Generator, advanced by the draw unless `ppm` is 0 or `PPM_ONE`.
integer(kind=default_int),	intent(in)			::	ppm	Probability in parts per million, clamped to `[0, PPM_ONE]`.

Return Value logical

public interface next_exponential_int

Draw an exponentially distributed integer with the given mean, in whatever unit mean is expressed in.

Sampling is a table lookup and two integer multiplies. EXP_TABLE holds the inverse CDF -ln(1 - k/4096) in Q32.32 fixed point, generated once by tools/autogen/gen_exp_table.py with 60-digit decimal arithmetic. Twelve random bits choose a cell, thirty-one more interpolate linearly inside it, and the result is scaled by mean.

The tail

The top cell runs to infinity and cannot be interpolated into. It is handled with the memorylessness of the exponential instead: if U is uniform on the top cell then -ln(1 - U) is distributed as ln(4096) plus a fresh exponential, so the sampler adds ln(4096) and draws again. That is exact, and it costs an extra draw with probability 1/4096.

Capping the top entry at a finite value and interpolating into it – the obvious alternative – biases the mean by 0.147%. This scheme leaves 0.002%, and all of that residue is linear interpolation inside the body cells, not the tail.

mean must be in [0, EXPONENTIAL_MAX_MEAN]. A mean of zero always returns zero without consuming a draw. Out of range returns zero and, if err is present, sets ERROR_VALIDATION.

private function splitmix64_next_exponential_int(gen, mean, err) result(r)

Exponential integer with the given mean, from a splitmix64_t generator.

Arguments

Type	Intent	Optional		Name
type(splitmix64_t),	intent(inout)		::	gen	Generator, advanced by one draw, or more in the tail.
integer(kind=int64),	intent(in)		::	mean	Mean of the distribution, in `[0, EXPONENTIAL_MAX_MEAN]`.
type(error_t),	intent(inout),	optional	::	err	Set to `ERROR_VALIDATION` when `mean` is out of range.

Return Value integer(kind=int64)

private function pcg32_next_exponential_int(gen, mean, err) result(r)

Exponential integer with the given mean, from a pcg32_t generator.

Arguments

Type	Intent	Optional		Name
type(pcg32_t),	intent(inout)		::	gen	Generator, advanced by one draw, or more in the tail.
integer(kind=int64),	intent(in)		::	mean	Mean of the distribution, in `[0, EXPONENTIAL_MAX_MEAN]`.
type(error_t),	intent(inout),	optional	::	err	Set to `ERROR_VALIDATION` when `mean` is out of range.

Return Value integer(kind=int64)

public interface next_poisson_int

Draw a Poisson-distributed count with mean mean_milli/1000.

The mean is given a thousand times over so that fractional means are expressible without a real type: mean_milli = 2500 means 2.5 events.

Counts the exponential inter-arrivals that fit inside a fixed window, which is the defining construction of a Poisson process rather than an approximation of one. Cost is O(mean).

mean_milli must be in [0, POISSON_MAX_MEAN_MILLI]. Zero returns zero without consuming a draw. Out of range returns zero and, if err is present, sets ERROR_VALIDATION.

private function splitmix64_next_poisson_int(gen, mean_milli, err) result(r)

Poisson count with mean mean_milli/1000, from a splitmix64_t generator.

Arguments

Type	Intent	Optional		Name
type(splitmix64_t),	intent(inout)		::	gen	Generator, advanced once per inter-arrival drawn.
integer(kind=default_int),	intent(in)		::	mean_milli	A thousand times the mean, in `[0, POISSON_MAX_MEAN_MILLI]`.
type(error_t),	intent(inout),	optional	::	err	Set to `ERROR_VALIDATION` when `mean_milli` is out of range.

Return Value integer(kind=int32)

private function pcg32_next_poisson_int(gen, mean_milli, err) result(r)

Poisson count with mean mean_milli/1000, from a pcg32_t generator.

Arguments

Type	Intent	Optional		Name
type(pcg32_t),	intent(inout)		::	gen	Generator, advanced once per inter-arrival drawn.
integer(kind=default_int),	intent(in)		::	mean_milli	A thousand times the mean, in `[0, POISSON_MAX_MEAN_MILLI]`.
type(error_t),	intent(inout),	optional	::	err	Set to `ERROR_VALIDATION` when `mean_milli` is out of range.

Return Value integer(kind=int32)

public interface next_range

Draw a uniform integer in the inclusive range [lo, hi].

The span is computed in unsigned 64-bit arithmetic, so the full range of default_int works: next_range(gen, -huge(1)-1, huge(1)) spans every int32 value and is still exactly uniform. Rejection sampling gives every value in range exactly one preimage per draw, so there is no modulo bias.

hi < lo is a usage error: it returns lo and, if err is present, sets ERROR_VALIDATION. lo == hi returns lo without consuming a draw.

private function splitmix64_next_range(gen, lo, hi, err) result(r)

Uniform integer in [lo, hi] from a splitmix64_t generator.

Arguments

Type	Intent	Optional		Name
type(splitmix64_t),	intent(inout)		::	gen	Generator, advanced by the draw.
integer(kind=default_int),	intent(in)		::	lo	Inclusive lower bound.
integer(kind=default_int),	intent(in)		::	hi	Inclusive upper bound; must not be below `lo`.
type(error_t),	intent(inout),	optional	::	err	Set to `ERROR_VALIDATION` when `hi < lo`.

Return Value integer(kind=default_int)

private function pcg32_next_range(gen, lo, hi, err) result(r)

Uniform integer in [lo, hi] from a pcg32_t generator.

Arguments

Type	Intent	Optional		Name
type(pcg32_t),	intent(inout)		::	gen	Generator, advanced by the draw.
integer(kind=default_int),	intent(in)		::	lo	Inclusive lower bound.
integer(kind=default_int),	intent(in)		::	hi	Inclusive upper bound; must not be below `lo`.
type(error_t),	intent(inout),	optional	::	err	Set to `ERROR_VALIDATION` when `hi < lo`.

Return Value integer(kind=default_int)

Functions

private function pcg32_next_bernoulli_ppm(gen, ppm) result(r)

True with probability ppm in a million, from a pcg32_t generator.

Arguments

Type	Intent	Optional	Attributes		Name
type(pcg32_t),	intent(inout)			::	gen	Generator, advanced by the draw unless `ppm` is 0 or `PPM_ONE`.
integer(kind=default_int),	intent(in)			::	ppm	Probability in parts per million, clamped to `[0, PPM_ONE]`.

Return Value logical

private function pcg32_next_exponential_int(gen, mean, err) result(r)

Exponential integer with the given mean, from a pcg32_t generator.

Arguments

Type	Intent	Optional		Name
type(pcg32_t),	intent(inout)		::	gen	Generator, advanced by one draw, or more in the tail.
integer(kind=int64),	intent(in)		::	mean	Mean of the distribution, in `[0, EXPONENTIAL_MAX_MEAN]`.
type(error_t),	intent(inout),	optional	::	err	Set to `ERROR_VALIDATION` when `mean` is out of range.

Return Value integer(kind=int64)

private function pcg32_next_poisson_int(gen, mean_milli, err) result(r)

Poisson count with mean mean_milli/1000, from a pcg32_t generator.

Arguments

Type	Intent	Optional		Name
type(pcg32_t),	intent(inout)		::	gen	Generator, advanced once per inter-arrival drawn.
integer(kind=default_int),	intent(in)		::	mean_milli	A thousand times the mean, in `[0, POISSON_MAX_MEAN_MILLI]`.
type(error_t),	intent(inout),	optional	::	err	Set to `ERROR_VALIDATION` when `mean_milli` is out of range.

Return Value integer(kind=int32)

private function pcg32_next_range(gen, lo, hi, err) result(r)

Uniform integer in [lo, hi] from a pcg32_t generator.

Arguments

Type	Intent	Optional		Name
type(pcg32_t),	intent(inout)		::	gen	Generator, advanced by the draw.
integer(kind=default_int),	intent(in)		::	lo	Inclusive lower bound.
integer(kind=default_int),	intent(in)		::	hi	Inclusive upper bound; must not be below `lo`.
type(error_t),	intent(inout),	optional	::	err	Set to `ERROR_VALIDATION` when `hi < lo`.

Return Value integer(kind=default_int)

private function pcg32_uniform_below(gen, span_minus_1) result(r)

Uniform unsigned integer in [0, span_minus_1], by rejection.

Arguments

Type	Intent	Optional	Attributes		Name
type(pcg32_t),	intent(inout)			::	gen
integer(kind=int64),	intent(in)			::	span_minus_1	Inclusive upper bound, read as unsigned.

Return Value integer(kind=int64)

private pure function rejection_mask(span_minus_1) result(mask)

Smallest 2**k - 1 that covers span_minus_1 read as unsigned.

Arguments

Type	Intent	Optional	Attributes		Name
integer(kind=int64),	intent(in)			::	span_minus_1	One less than the number of distinct values wanted, unsigned.

Return Value integer(kind=int64)

private pure function scale_by_mean(x_q32, mean) result(r)

Multiply a Q32.32 value by an integer mean and drop the fraction.

Arguments

Type	Intent	Optional	Attributes		Name
integer(kind=int64),	intent(in)			::	x_q32	Deviate in Q32.32 fixed point.
integer(kind=int64),	intent(in)			::	mean	Mean, in `[0, EXPONENTIAL_MAX_MEAN]`.

Return Value integer(kind=int64)

private function splitmix64_next_bernoulli_ppm(gen, ppm) result(r)

True with probability ppm in a million, from a splitmix64_t generator.

Arguments

Type	Intent	Optional	Attributes		Name
type(splitmix64_t),	intent(inout)			::	gen	Generator, advanced by the draw unless `ppm` is 0 or `PPM_ONE`.
integer(kind=default_int),	intent(in)			::	ppm	Probability in parts per million, clamped to `[0, PPM_ONE]`.

Return Value logical

private function splitmix64_next_exponential_int(gen, mean, err) result(r)

Exponential integer with the given mean, from a splitmix64_t generator.

Arguments

Type	Intent	Optional		Name
type(splitmix64_t),	intent(inout)		::	gen	Generator, advanced by one draw, or more in the tail.
integer(kind=int64),	intent(in)		::	mean	Mean of the distribution, in `[0, EXPONENTIAL_MAX_MEAN]`.
type(error_t),	intent(inout),	optional	::	err	Set to `ERROR_VALIDATION` when `mean` is out of range.

Return Value integer(kind=int64)

private function splitmix64_next_poisson_int(gen, mean_milli, err) result(r)

Poisson count with mean mean_milli/1000, from a splitmix64_t generator.

Arguments

Type	Intent	Optional		Name
type(splitmix64_t),	intent(inout)		::	gen	Generator, advanced once per inter-arrival drawn.
integer(kind=default_int),	intent(in)		::	mean_milli	A thousand times the mean, in `[0, POISSON_MAX_MEAN_MILLI]`.
type(error_t),	intent(inout),	optional	::	err	Set to `ERROR_VALIDATION` when `mean_milli` is out of range.

Return Value integer(kind=int32)

private function splitmix64_next_range(gen, lo, hi, err) result(r)

Uniform integer in [lo, hi] from a splitmix64_t generator.

Arguments

Type	Intent	Optional		Name
type(splitmix64_t),	intent(inout)		::	gen	Generator, advanced by the draw.
integer(kind=default_int),	intent(in)		::	lo	Inclusive lower bound.
integer(kind=default_int),	intent(in)		::	hi	Inclusive upper bound; must not be below `lo`.
type(error_t),	intent(inout),	optional	::	err	Set to `ERROR_VALIDATION` when `hi < lo`.

Return Value integer(kind=default_int)

private function splitmix64_uniform_below(gen, span_minus_1) result(r)

Uniform unsigned integer in [0, span_minus_1], by rejection.

Arguments

Type	Intent	Optional	Attributes		Name
type(splitmix64_t),	intent(inout)			::	gen
integer(kind=int64),	intent(in)			::	span_minus_1	Inclusive upper bound, read as unsigned.

pic_random_dist Module

Contents

Variables

Interfaces

Functions

Why a separate module from the real-valued one

Quick start

Uses

Variables

Interfaces

public interface next_bernoulli_ppm

private function splitmix64_next_bernoulli_ppm(gen, ppm) result(r)

Arguments

Return Value logical

private function pcg32_next_bernoulli_ppm(gen, ppm) result(r)

Arguments

Return Value logical

public interface next_exponential_int

The tail

private function splitmix64_next_exponential_int(gen, mean, err) result(r)

Arguments

Return Value integer(kind=int64)

private function pcg32_next_exponential_int(gen, mean, err) result(r)

Arguments

Return Value integer(kind=int64)

public interface next_poisson_int

private function splitmix64_next_poisson_int(gen, mean_milli, err) result(r)

Arguments

Return Value integer(kind=int32)

private function pcg32_next_poisson_int(gen, mean_milli, err) result(r)

Arguments

Return Value integer(kind=int32)

public interface next_range

private function splitmix64_next_range(gen, lo, hi, err) result(r)

Arguments

Return Value integer(kind=default_int)

private function pcg32_next_range(gen, lo, hi, err) result(r)

Arguments

Return Value integer(kind=default_int)

Functions

private function pcg32_next_bernoulli_ppm(gen, ppm) result(r)

Arguments

Return Value logical

private function pcg32_next_exponential_int(gen, mean, err) result(r)

Arguments

Return Value integer(kind=int64)

private function pcg32_next_poisson_int(gen, mean_milli, err) result(r)

Arguments

Return Value integer(kind=int32)

private function pcg32_next_range(gen, lo, hi, err) result(r)

Arguments

Return Value integer(kind=default_int)

private function pcg32_uniform_below(gen, span_minus_1) result(r)

Arguments

Return Value integer(kind=int64)

private pure function rejection_mask(span_minus_1) result(mask)

Arguments

Return Value integer(kind=int64)

private pure function scale_by_mean(x_q32, mean) result(r)

Arguments

Return Value integer(kind=int64)

private function splitmix64_next_bernoulli_ppm(gen, ppm) result(r)

Arguments

Return Value logical

private function splitmix64_next_exponential_int(gen, mean, err) result(r)

Arguments

Return Value integer(kind=int64)

private function splitmix64_next_poisson_int(gen, mean_milli, err) result(r)

Arguments

Return Value integer(kind=int32)

private function splitmix64_next_range(gen, lo, hi, err) result(r)

Arguments

Return Value integer(kind=default_int)

private function splitmix64_uniform_below(gen, span_minus_1) result(r)

Arguments

Return Value integer(kind=int64)