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Pseudo-random numbers/PCG32

From Rosetta Code
Task
Pseudo-random numbers/PCG32
You are encouraged to solve this task according to the task description, using any language you may know.
Some definitions to help in the explanation
Floor operation
https://en.wikipedia.org/wiki/Floor_and_ceiling_functions
Greatest integer less than or equal to a real number.
Bitwise Logical shift operators (c-inspired)
https://en.wikipedia.org/wiki/Bitwise_operation#Bit_shifts
Binary bits of value shifted left or right, with zero bits shifted in where appropriate.
Examples are shown for 8 bit binary numbers; most significant bit to the left.
<< Logical shift left by given number of bits.
E.g Binary 00110101 << 2 == Binary 11010100
>> Logical shift right by given number of bits.
E.g Binary 00110101 >> 2 == Binary 00001101
^ Bitwise exclusive-or operator
https://en.wikipedia.org/wiki/Exclusive_or
Bitwise comparison for if bits differ
E.g Binary 00110101 ^ Binary 00110011 == Binary 00000110
| Bitwise or operator
https://en.wikipedia.org/wiki/Bitwise_operation#OR
Bitwise comparison gives 1 if any of corresponding bits are 1
E.g Binary 00110101 | Binary 00110011 == Binary 00110111


PCG32 Generator (pseudo-code)

PCG32 has two unsigned 64-bit integers of internal state:

  1. state: All 2**64 values may be attained.
  2. sequence: Determines which of 2**63 sequences that state iterates through. (Once set together with state at time of seeding will stay constant for this generators lifetime).

Values of sequence allow 2**63 different sequences of random numbers from the same state.

The algorithm is given 2 U64 inputs called seed_state, and seed_sequence. The algorithm proceeds in accordance with the following pseudocode:-

const N<-U64 6364136223846793005
const inc<-U64 (seed_sequence << 1) | 1
state<-U64 ((inc+seed_state)*N+inc
do forever
  xs<-U32 (((state>>18)^state)>>27)
  rot<-INT (state>>59)
  OUTPUT U32 (xs>>rot)|(xs<<((-rot)&31))
  state<-state*N+inc
end do

Neoteric languages will support this design pattern with a template called something like unfold.


Task
  • Generate a class/set of functions that generates pseudo-random

numbers using the above.

  • Show that the first five integers generated with the seed 42, 54

are: 2707161783 2068313097 3122475824 2211639955 3215226955


  • Show that for an initial seed of 987654321, 1 the counts of 100_000 repetitions of
   floor(random_gen.next_float() * 5)
Is as follows:
   0: 20049, 1: 20022, 2: 20115, 3: 19809, 4: 20005
  • Show your output here, on this page.


ALGOL 68[edit]

Works with: ALGOL 68G version Any - tested with release 2.8.3.win32
BEGIN # generate some pseudo random numbers using PCG32 #
# note that although LONG INT is 64 bits in Algol 68G, LONG BITS is longer than 64 bits #
LONG BITS state := LONG 16r853c49e6748fea9b;
LONG INT inc := ABS LONG 16rda3e39cb94b95bdb;
LONG BITS mask 64 = LONG 16rffffffffffffffff;
LONG BITS mask 32 = LONG 16rffffffff;
LONG BITS mask 31 = LONG 16r7fffffff;
LONG INT one shl 32 = ABS ( LONG 16r1 SHL 32 );
# XOR and assign convenience operator #
PRIO XORAB = 1;
OP XORAB = ( REF LONG BITS x, LONG BITS v )REF LONG BITS: x := ( x XOR v ) AND mask 64;
# initialises the state to the specified seed #
PROC seed = ( LONG INT seed state, seed sequence )VOID:
BEGIN
state := 16r0;
inc := ABS ( ( ( BIN seed sequence SHL 1 ) OR 16r1 ) AND mask 64 );
next int;
state := SHORTEN ( BIN ( ABS state + seed state ) AND mask 64 );
next int
END # seed # ;
# gets the next pseudo random integer #
PROC next int = LONG INT:
BEGIN
LONG BITS old = state;
LONG INT const = LONG 6364136223846793005;
state := SHORTEN ( mask 64 AND BIN ( ( ABS old * LENG const ) + inc ) );
LONG BITS x := old;
x XORAB ( old SHR 18 );
BITS xor shifted = SHORTEN ( mask 32 AND ( x SHR 27 ) );
INT rot = SHORTEN ABS ( mask 32 AND ( old SHR 59 ) );
INT rot 2 = IF rot = 0 THEN 0 ELSE 32 - rot FI;
BITS xor shr := SHORTEN ( mask 32 AND LENG ( xor shifted SHR rot ) );
BITS xor shl := xor shifted;
TO rot 2 DO
xor shl := SHORTEN ( ( mask 31 AND LENG xor shl ) SHL 1 )
OD;
ABS ( LENG xor shr OR LENG xor shl )
END # next int # ;
# gets the next pseudo random real #
PROC next float = LONG REAL: next int / one shl 32;
BEGIN # task test cases #
seed( 42, 54 );
print( ( whole( next int, 0 ), newline ) ); # 2707161783 #
print( ( whole( next int, 0 ), newline ) ); # 2068313097 #
print( ( whole( next int, 0 ), newline ) ); # 3122475824 #
print( ( whole( next int, 0 ), newline ) ); # 2211639955 #
print( ( whole( next int, 0 ), newline ) ); # 3215226955 #
# count the number of occurances of 0..4 in a sequence of pseudo random reals scaled to be in [0..5) #
seed( 987654321, 1 );
[ 0 : 4 ]INT counts; FOR i FROM LWB counts TO UPB counts DO counts[ i ] := 0 OD;
TO 100 000 DO counts[ SHORTEN ENTIER ( next float * 5 ) ] +:= 1 OD;
FOR i FROM LWB counts TO UPB counts DO
print( ( whole( i, -2 ), ": ", whole( counts[ i ], -6 ) ) )
OD;
print( ( newline ) )
END
END
Output:
2707161783
2068313097
3122475824
2211639955
3215226955
 0:  20049 1:  20022 2:  20115 3:  19809 4:  20005

Delphi[edit]

Velthuis.BigIntegers[1] by Rudy Velthuis.

Translation of: Python
 
program PCG32_test;
 
{$APPTYPE CONSOLE}
uses
System.SysUtils,
Velthuis.BigIntegers,
System.Generics.Collections;
 
type
TPCG32 = class
public
FState: BigInteger;
FInc: BigInteger;
mask64: BigInteger;
mask32: BigInteger;
k: BigInteger;
constructor Create(seedState, seedSequence: BigInteger); overload;
constructor Create(); overload;
destructor Destroy; override;
procedure Seed(seed_state, seed_sequence: BigInteger);
function NextInt(): BigInteger;
function NextIntRange(size: Integer): TArray<BigInteger>;
function NextFloat(): Extended;
end;
 
{ TPCG32 }
 
constructor TPCG32.Create(seedState, seedSequence: BigInteger);
begin
Create();
Seed(seedState, seedSequence);
end;
 
constructor TPCG32.Create;
begin
k := '6364136223846793005';
mask64 := (BigInteger(1) shl 64) - 1;
mask32 := (BigInteger(1) shl 32) - 1;
FState := 0;
FInc := 0;
end;
 
destructor TPCG32.Destroy;
begin
 
inherited;
end;
 
function TPCG32.NextFloat: Extended;
begin
Result := (NextInt.AsExtended / (BigInteger(1) shl 32).AsExtended);
end;
 
function TPCG32.NextInt(): BigInteger;
var
old, xorshifted, rot, answer: BigInteger;
begin
old := FState;
FState := ((old * k) + FInc) and mask64;
xorshifted := (((old shr 18) xor old) shr 27) and mask32;
rot := (old shr 59) and mask32;
answer := (xorshifted shr rot.AsInteger) or (xorshifted shl ((-rot) and
BigInteger(31)).AsInteger);
Result := answer and mask32;
end;
 
function TPCG32.NextIntRange(size: Integer): TArray<BigInteger>;
var
i: Integer;
begin
SetLength(Result, size);
if size = 0 then
exit;
 
for i := 0 to size - 1 do
Result[i] := NextInt;
end;
 
procedure TPCG32.Seed(seed_state, seed_sequence: BigInteger);
begin
FState := 0;
FInc := ((seed_sequence shl 1) or 1) and mask64;
nextint();
Fstate := (Fstate + seed_state);
nextint();
end;
 
var
PCG32: TPCG32;
i, key: Integer;
count: TDictionary<Integer, Integer>;
 
begin
PCG32 := TPCG32.Create(42, 54);
 
for i := 0 to 4 do
Writeln(PCG32.NextInt().ToString);
 
PCG32.seed(987654321, 1);
 
count := TDictionary<Integer, Integer>.Create();
 
for i := 1 to 100000 do
begin
key := Trunc(PCG32.NextFloat * 5);
if count.ContainsKey(key) then
count[key] := count[key] + 1
else
count.Add(key, 1);
end;
 
Writeln(#10'The counts for 100,000 repetitions are:');
 
for key in count.Keys do
Writeln(key, ' : ', count[key]);
 
count.free;
PCG32.free;
Readln;
end.
 
Output:
2707161783
2068313097
3122475824
2211639955
3215226955

The counts for 100,000 repetitions are:
3 : 19809
0 : 20049
4 : 20005
2 : 20115
1 : 20022

F#[edit]

The Functions[edit]

 
// PCG32. Nigel Galloway: August 13th., 2020
let N=6364136223846793005UL
let seed n g=let g=g<<<1|||1UL in (g,(g+n)*N+g)
let pcg32=Seq.unfold(fun(n,g)->let rot,xs=uint32(g>>>59),uint32(((g>>>18)^^^g)>>>27) in Some(uint32((xs>>>(int rot))|||(xs<<<(-(int rot)&&&31))),(n,g*N+n)))
let pcgFloat n=pcg32 n|>Seq.map(fun n-> (float n)/4294967296.0)
 

The Tasks[edit]

 
pcg32(seed 42UL 54UL)|>Seq.take 5|>Seq.iter(printfn "%d")
 
Output:
2707161783
2068313097
3122475824
2211639955
3215226955
 
pcgFloat(seed 987654321UL 1UL)|>Seq.take 100000|>Seq.countBy(fun n->int(n*5.0))|>Seq.iter(printf "%A");printfn ""
 
(2, 20115)(3, 19809)(0, 20049)(4, 20005)(1, 20022)

Factor[edit]

Translation of: Python
USING: accessors kernel locals math math.bitwise math.statistics
prettyprint sequences ;
 
CONSTANT: const 6364136223846793005
 
TUPLE: pcg32 state inc ;
 
: <pcg32> ( -- pcg32 )
0x853c49e6748fea9b 0xda3e39cb94b95bdb pcg32 boa ;
 
:: next-int ( pcg -- n )
pcg state>> :> old
old const * pcg inc>> + 64 bits pcg state<<
old -18 shift old bitxor -27 shift 32 bits :> shifted
old -59 shift 32 bits :> r
shifted r neg shift
shifted r neg 31 bitand shift bitor 32 bits ;
 
: next-float ( pcg -- x ) next-int 1 32 shift /f ;
 
:: seed ( pcg st seq -- )
0x0 pcg state<<
seq 0x1 shift 1 bitor 64 bits pcg inc<<
pcg next-int drop
pcg state>> st + pcg state<<
pcg next-int drop ;
 
! Task
<pcg32> 42 54 [ seed ] keepdd 5 [ dup next-int . ] times
 
987654321 1 [ seed ] keepdd
100,000 [ dup next-float 5 * >integer ] replicate nip
histogram .
Output:
2707161783
2068313097
3122475824
2211639955
3215226955
H{ { 0 20049 } { 1 20022 } { 2 20115 } { 3 19809 } { 4 20005 } }

Go[edit]

Translation of: Python
package main
 
import (
"fmt"
"math"
)
 
const CONST = 6364136223846793005
 
type Pcg32 struct{ state, inc uint64 }
 
func Pcg32New() *Pcg32 { return &Pcg32{0x853c49e6748fea9b, 0xda3e39cb94b95bdb} }
 
func (pcg *Pcg32) seed(seedState, seedSequence uint64) {
pcg.state = 0
pcg.inc = (seedSequence << 1) | 1
pcg.nextInt()
pcg.state = pcg.state + seedState
pcg.nextInt()
}
 
func (pcg *Pcg32) nextInt() uint32 {
old := pcg.state
pcg.state = old*CONST + pcg.inc
pcgshifted := uint32(((old >> 18) ^ old) >> 27)
rot := uint32(old >> 59)
return (pcgshifted >> rot) | (pcgshifted << ((-rot) & 31))
}
 
func (pcg *Pcg32) nextFloat() float64 {
return float64(pcg.nextInt()) / (1 << 32)
}
 
func main() {
randomGen := Pcg32New()
randomGen.seed(42, 54)
for i := 0; i < 5; i++ {
fmt.Println(randomGen.nextInt())
}
 
var counts [5]int
randomGen.seed(987654321, 1)
for i := 0; i < 1e5; i++ {
j := int(math.Floor(randomGen.nextFloat() * 5))
counts[j]++
}
fmt.Println("\nThe counts for 100,000 repetitions are:")
for i := 0; i < 5; i++ {
fmt.Printf("  %d : %d\n", i, counts[i])
}
}
Output:
2707161783
2068313097
3122475824
2211639955
3215226955

The counts for 100,000 repetitions are:
  0 : 20049
  1 : 20022
  2 : 20115
  3 : 19809
  4 : 20005

Julia[edit]

Translation of: Python
const mask32, CONST = 0xffffffff, UInt(6364136223846793005)
 
mutable struct PCG32
state::UInt64
inc::UInt64
PCG32(st=0x853c49e6748fea9b, i=0xda3e39cb94b95bdb) = new(st, i)
end
 
"""return random 32 bit unsigned int"""
function next_int!(x::PCG32)
old = x.state
x.state = (old * CONST) + x.inc
xorshifted = (((old >> 18) ⊻ old) >> 27) & mask32
rot = (old >> 59) & mask32
return ((xorshifted >> rot) | (xorshifted << ((-rot) & 31))) & mask32
end
 
"""return random float between 0 and 1"""
next_float!(x::PCG32) = next_int!(x) / (1 << 32)
 
function seed!(x::PCG32, st, seq)
x.state = 0x0
x.inc = (UInt(seq) << 0x1) | 1
next_int!(x)
x.state = x.state + UInt(st)
next_int!(x)
end
 
function testPCG32()
random_gen = PCG32()
seed!(random_gen, 42, 54)
for _ in 1:5
println(next_int!(random_gen))
end
seed!(random_gen, 987654321, 1)
hist = fill(0, 5)
for _ in 1:100_000
hist[Int(floor(next_float!(random_gen) * 5)) + 1] += 1
end
println(hist)
for n in 1:5
print(n - 1, ": ", hist[n], " ")
end
end
 
testPCG32()
 
Output:
2707161783
2068313097
3122475824
2211639955
3215226955
[20049, 20022, 20115, 19809, 20005]
0: 20049  1: 20022  2: 20115  3: 19809  4: 20005

Phix[edit]

Phix proudly does not support the kind of "maths" whereby 255 plus 1 is 0 (or 127+1 is -128).
Phix atoms are limited to 53/64 bits of precision, however (given the above) this task would need 128 bits.
First, for comparison only, this is the usual recommended native approach for this genre of task (different output)

puts(1,"NB: These are not expected to match the task spec!\n")
set_rand(42)
for i=1 to 5 do
printf(1,"%d\n",rand(-1))
end for
set_rand(987654321)
sequence s = repeat(0,5)
for i=1 to 100000 do
s[floor(rnd()*5)+1] += 1
end for
?s
Output:
NB: These are not expected to match the task spec!
13007222
848581373
2714853861
808614160
2634828316
{20080,19802,19910,20039,20169}

To meet the spec, similar to the Delphi and Wren entries, we resort to using mpfr/gmp, but it is a fair bit longer, and slower, than the above.

include mpfr.e
mpz const = mpz_init("6364136223846793005"),
state = mpz_init("0x853c49e6748fea9b"),
inc = mpz_init("0xda3e39cb94b95bdb"), /* Always odd */
b64 = mpz_init("0x10000000000000000"), -- (truncate to 64 bits)
b32 = mpz_init("0x100000000"), -- (truncate to 32 bits)
old = mpz_init(),
xorsh = mpz_init()
 
procedure seed(integer seed_state, seed_sequence)
mpz_set_si(inc,seed_sequence*2+1)
-- as per the talk page:
-- state := remainder((inc+seed_state)*const+inc,b64)
mpz_add_ui(state,inc,seed_state)
mpz_mul(state,state,const)
mpz_add(state,state,inc)
mpz_fdiv_r(state, state, b64) -- state := remainder(state,b64)
end procedure
 
function next_int()
mpz_set(old,state) -- old := state
mpz_set(state,inc) -- state := inc
mpz_addmul(state,old,const) -- state += old*const
mpz_fdiv_r(state, state, b64) -- state := remainder(state,b64)
mpz_tdiv_q_2exp(xorsh, old, 18) -- xorsh := trunc(old/2^18)
mpz_xor(xorsh, xorsh, old) -- xorsh := xor_bits(xorsh,old)
mpz_tdiv_q_2exp(xorsh, xorsh, 27) -- xorsh := trunc(xorsh/2^17)
mpz_fdiv_r(xorsh, xorsh, b32) -- xorsh := remainder(xorsh,b32)
atom xorshifted = mpz_get_atom(xorsh)
mpz_tdiv_q_2exp(old, old, 59) -- old := trunc(old/2^59)
integer rot = mpz_get_integer(old)
atom answer = xor_bitsu((xorshifted >> rot),(xorshifted << 32-rot))
return answer
end function
 
function next_float()
return next_int() / (1 << 32)
end function
 
seed(42, 54)
for i=1 to 5 do
printf(1,"%d\n",next_int())
end for
seed(987654321,1)
sequence r = repeat(0,5)
for i=1 to 100000 do
r[floor(next_float()*5)+1] += 1
end for
?r
Output:
2707161783
2068313097
3122475824
2211639955
3215226955
{20049,20022,20115,19809,20005}

Python[edit]

mask64 = (1 << 64) - 1
mask32 = (1 << 32) - 1
CONST = 6364136223846793005
 
 
class PCG32():
 
def __init__(self, seed_state=None, seed_sequence=None):
if all(type(x) == int for x in (seed_state, seed_sequence)):
self.seed(seed_state, seed_sequence)
else:
self.state = self.inc = 0
 
def seed(self, seed_state, seed_sequence):
self.state = 0
self.inc = ((seed_sequence << 1) | 1) & mask64
self.next_int()
self.state = (self.state + seed_state)
self.next_int()
 
def next_int(self):
"return random 32 bit unsigned int"
old = self.state
self.state = ((old * CONST) + self.inc) & mask64
xorshifted = (((old >> 18) ^ old) >> 27) & mask32
rot = (old >> 59) & mask32
answer = (xorshifted >> rot) | (xorshifted << ((-rot) & 31))
answer = answer &mask32
 
return answer
 
def next_float(self):
"return random float between 0 and 1"
return self.next_int() / (1 << 32)
 
 
if __name__ == '__main__':
random_gen = PCG32()
random_gen.seed(42, 54)
for i in range(5):
print(random_gen.next_int())
 
random_gen.seed(987654321, 1)
hist = {i:0 for i in range(5)}
for i in range(100_000):
hist[int(random_gen.next_float() *5)] += 1
print(hist)
Output:
2707161783
2068313097
3122475824
2211639955
3215226955
{0: 20049, 1: 20022, 2: 20115, 3: 19809, 4: 20005}

Raku[edit]

Works with: Rakudo version 2020.07
Translation of: Python
Or... at least, it started out that way.

Raku does not have unsigned Integers at this time (Integers are arbitrary sized) so use explicit bit masks during bitwise operations.

class PCG32 {
has $!state;
has $!incr;
constant mask32 = 2³² - 1;
constant mask64 = 2⁶⁴ - 1;
constant const = 6364136223846793005;
 
submethod BUILD (
Int :$seed = 0x853c49e6748fea9b, # default seed
Int :$incr = 0xda3e39cb94b95bdb # default increment
) {
$!incr = $incr +< 1 +| 1 +& mask64;
$!state = (($!incr + $seed) * const + $!incr) +& mask64;
}
 
method next-int {
my $shift = ($!state +> 18 +^ $!state) +> 27 +& mask32;
my $rotate = $!state +> 59 +& 31;
$!state = ($!state * const + $!incr) +& mask64;
($shift +> $rotate) +| ($shift +< (32 - $rotate) +& mask32)
}
 
method next-rat { self.next-int / 2³² }
}
 
 
# Test next-int with custom seed and increment
say 'Seed: 42, Increment: 54; first five Int values:';
my $rng = PCG32.new( :seed(42), :incr(54) );
.say for $rng.next-int xx 5;
 
 
# Test next-rat (since these are rational numbers by default)
say "\nSeed: 987654321, Increment: 1; first 1e5 Rat values histogram:";
$rng = PCG32.new( :seed(987654321), :incr(1) );
say ( ($rng.next-rat * 5).floor xx 100_000 ).Bag;
 
 
# Test next-int with default seed and increment
say "\nSeed: default, Increment: default; first five Int values:";
$rng = PCG32.new;
.say for $rng.next-int xx 5;
Output:
Seed: 42, Increment: 54; first five Int values:
2707161783
2068313097
3122475824
2211639955
3215226955

Seed: 987654321, Increment: 1; first 1e5 Rat values histogram:
Bag(0(20049), 1(20022), 2(20115), 3(19809), 4(20005))

Seed: default, Increment: default; first five Int values:
465482994
3895364073
1746730475
3759121132
2984354868

Wren[edit]

Translation of: Python
Library: Wren-big

As Wren doesn't have a 64-bit integer type, we use BigInt instead.

import "/big" for BigInt
 
var Const = BigInt.new("6364136223846793005")
var Mask64 = (BigInt.one << 64) - BigInt.one
var Mask32 = (BigInt.one << 32) - BigInt.one
 
class Pcg32 {
construct new() {
_state = BigInt.fromBaseString("853c49e6748fea9b", 16)
_inc = BigInt.fromBaseString("da3e39cb94b95bdb", 16)
}
 
seed(seedState, seedSequence) {
_state = BigInt.zero
_inc = ((seedSequence << BigInt.one) | BigInt.one) & Mask64
nextInt
_state = _state + seedState
nextInt
}
 
nextInt {
var old = _state
_state = (old*Const + _inc) & Mask64
var xorshifted = (((old >> 18) ^ old) >> 27) & Mask32
var rot = (old >> 59) & Mask32
return ((xorshifted >> rot) | (xorshifted << ((-rot) & 31))) & Mask32
}
 
nextFloat { nextInt.toNum / 2.pow(32) }
}
 
var randomGen = Pcg32.new()
randomGen.seed(BigInt.new(42), BigInt.new(54))
for (i in 0..4) System.print(randomGen.nextInt)
 
var counts = List.filled(5, 0)
randomGen.seed(BigInt.new(987654321), BigInt.one)
for (i in 1..1e5) {
var i = (randomGen.nextFloat * 5).floor
counts[i] = counts[i] + 1
}
System.print("\nThe counts for 100,000 repetitions are:")
for (i in 0..4) System.print("  %(i) : %(counts[i])")
Output:
2707161783
2068313097
3122475824
2211639955
3215226955

The counts for 100,000 repetitions are:
  0 : 20049
  1 : 20022
  2 : 20115
  3 : 19809
  4 : 20005