quickrnd_oct_m Module Reference

Data Types
interface	hash_combine_ids
interface	quickrnd
interface	splitmix64_mixer
interface	to_double_open01

Functions/Subroutines
integer(int64) function	xorshift64 (x)
	xorshift64 pseudorandom number generator More...
real(real64) function	to_double (x)
	Generating uniform doubles in the unit interval. More...
subroutine	dquickrnd_single (iseed, rnd)
subroutine	dquickrnd_array (iseed, nn, rnd)
subroutine	zquickrnd_array (iseed, nn, rnd)
subroutine, public	shiftseed (iseed, n)
integer(int64) function	random_integer_in_range (x_min, x_max, seed)
	Generate a random int64 in the range \( [x_{min}, x_{max}] \). More...
subroutine, public	fisher_yates_shuffle (m, n, seed, values)
	Return m random numbers from a range of \([1, n]\) with no replacement. More...
real(real64) function, public	u01_from_ids (ids)
	Mix an integer array of ids to give a random number in the range U(0,1), which is deterministic w.r.t. input ids. More...

Variables
integer(int64), parameter, public	splitmix64_123 = int(Z'B4DC9BD462DE412B', int64)
integer(int64), parameter, public	splitmix64_321 = int(Z'E95F1C4EFCF85DEE', int64)

Function/Subroutine Documentation

xorshift64()

integer(int64) function quickrnd_oct_m::xorshift64 ( integer(int64), intent(inout)  x )

private

xorshift64 pseudorandom number generator

Marsaglia, G. (2003). Xorshift RNGs. Journal of Statistical Software, 8(14). https:

Parameters

[in,out]

x

PRNG state

Returns

next random number in the sequence

Definition at line 174 of file quickrnd.F90.

to_double()

real(real64) function quickrnd_oct_m::to_double ( integer(int64), intent(in)  x )

private

Generating uniform doubles in the unit interval.

We consider x to be an unsigned 64-bit integer which can represent the range \([0,2^{64})\). First we shift x right by 11 places which puts it in the range \([0,2^{53})\). Then we convert it to a double and multiply by \(2^{-53}\) which puts the result in the range \([0,1)\).

https:

Parameters

[in]

x

64-bit integer

Returns

double precision floating point number in the interval [0,1)

Definition at line 195 of file quickrnd.F90.

dquickrnd_single()

subroutine quickrnd_oct_m::dquickrnd_single ( integer(int64), intent(inout)  iseed, real(real64), intent(out)  rnd  )

private

Definition at line 205 of file quickrnd.F90.

dquickrnd_array()

subroutine quickrnd_oct_m::dquickrnd_array ( integer(int64), intent(inout)  iseed, integer, intent(in)  nn, real(real64), dimension(:), intent(inout)  rnd  )

private

Definition at line 217 of file quickrnd.F90.

zquickrnd_array()

subroutine quickrnd_oct_m::zquickrnd_array ( integer(int64), intent(inout)  iseed, integer, intent(in)  nn, complex(real64), dimension(:), intent(inout)  rnd  )

private

Definition at line 236 of file quickrnd.F90.

shiftseed()

subroutine, public quickrnd_oct_m::shiftseed	(	integer(int64), intent(inout)	iseed,
		integer(int64), intent(in)	n
	)

Definition at line 259 of file quickrnd.F90.

random_integer_in_range()

integer(int64) function quickrnd_oct_m::random_integer_in_range ( integer(int64), intent(in)  x_min, integer(int64), intent(in)  x_max, integer(int64), intent(inout)  seed  )

private

Generate a random int64 in the range \( [x_{min}, x_{max}] \).

The function includes bias, where the per-value probability can differ from perfect uniform by ~ range / 2^63, where range = x_max - x_min + 1. This is the standard modulo-mapping bound when taking MOD(seed, range) with a positive range and a 64-bit seed.

Examples (relative worst-case bias):

• For range = 10^6, bias ~ 10^6 / 2^63 = 1.1e−13
• For range = 10^9, bias ~ 10^9 / 2^63 = 1.1e−10

  Parameters

  [in]	x_max	range [x_min, x_max]
  [in,out]	seed	integer seed

  Returns

  integer in the interval [x_min, x_max]

Definition at line 287 of file quickrnd.F90.

fisher_yates_shuffle()

subroutine, public quickrnd_oct_m::fisher_yates_shuffle	(	integer(int32), intent(in)	m,
		integer(int64), intent(in)	n,
		integer(int64), intent(inout)	seed,
		integer(int64), dimension(:), intent(out)	values
	)

Return m random numbers from a range of \([1, n]\) with no replacement.

The simple implementation is O(n) in memory. More details can be found on the [wikipedia page](https:

Parameters

[in]	m	Subset of random numbers to sample
[in]	n	Max random integer
[in,out]	seed	Initial seed

Definition at line 308 of file quickrnd.F90.

u01_from_ids()

real(real64) function, public quickrnd_oct_m::u01_from_ids

(

integer(int64), dimension(:), intent(in)

ids

)

Mix an integer array of ids to give a random number in the range U(0,1), which is deterministic w.r.t. input ids.

The algorithm is defined by these steps:

1. Hash-combine the integer ids to give an initial deterministic number.
2. Apply a splitmix finaliser to generate a non-linear 64-bit hash, giving a RN from a reasonable, near-uniform distribution.
3. Map the RN integer to a real64, in the range (0,1)

   Parameters

   [in]

   ids

   RNG invariant to the order of the ids

Definition at line 349 of file quickrnd.F90.

Variable Documentation

splitmix64_123

integer(int64), parameter, public quickrnd_oct_m::splitmix64_123 = int(Z'B4DC9BD462DE412B', int64)

Definition at line 138 of file quickrnd.F90.

splitmix64_321

integer(int64), parameter, public quickrnd_oct_m::splitmix64_321 = int(Z'E95F1C4EFCF85DEE', int64)

Definition at line 138 of file quickrnd.F90.