Pseudo-random numbers/PCG32
- 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.
- https://en.wikipedia.org/wiki/Floor_and_ceiling_functions
- 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.
- https://en.wikipedia.org/wiki/Bitwise_operation#Bit_shifts
- << Logical shift left by given number of bits.
- E.g Binary 00110101 << 2 == Binary 11010100
- << Logical shift left by given number of bits.
- >> Logical shift right by given number of bits.
- E.g Binary 00110101 >> 2 == Binary 00001101
- >> Logical shift right by given number of bits.
- ^ 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)
/* Let u64 denote an unsigned 64 bit integer type. */ /* Let u32 denote an unsigned 32 bit integer type. */ u64 global constant CONST = 6364136223846793005 class Pcg32 u64 instance variable state = HEX 853c49e6748fea9b u64 instance variable inc = HEX da3e39cb94b95bdb /* Always odd */ method seed(u64 seed_state, u64 seed_sequence) state = 0 inc = (seed_sequence << 1) | 1 # shift and | ensures its odd next_int() state = state + seed_state next_int() end method method next_int() u64 old = state state = (old * CONST) + inc u32 xorshifted = ((old >> 18) ^ old) >> 27 u32 rot = old >> 59 u32 answer = (xorshifted >> rot) | (xorshifted << ((-rot) & 31)) return answer end method method next_float(): return float next_int() / (1 << 32) end method end class
- PCG32 Use
random_gen = instance Pcg_32 random_gen.seed(42, 54) print(random_gen.next_int()) /* 2707161783 */ print(random_gen.next_int()) /* 2068313097 */ print(random_gen.next_int()) /* 3122475824 */ print(random_gen.next_int()) /* 2211639955 */ print(random_gen.next_int()) /* 3215226955 */
- Task
- Generate a class/set of functions that generates pseudo-random
numbers as shown above.
- Show that the first five integers genrated with the seed
42, 54
are as shown above
- 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.
Delphi
Velthuis.BigIntegers[1] by Rudy Velthuis.
<lang Delphi> 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. </lang>
- Output:
2707161783 2068313097 3122475824 2211639955 3215226955 The counts for 100,000 repetitions are: 3 : 19809 0 : 20049 4 : 20005 2 : 20115 1 : 20022
Go
<lang go>package main
import (
"fmt" "math"
)
const CONST = 6364136223846793005 const mask32 = (1 << 32) - 1
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) & mask32) rot := uint32((old >> 59) & mask32) 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]) }
}</lang>
- Output:
2707161783 2068313097 3122475824 2211639955 3215226955 The counts for 100,000 repetitions are: 0 : 20049 1 : 20022 2 : 20115 3 : 19809 4 : 20005
Python
<lang python>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)</lang>
- Output:
2707161783 2068313097 3122475824 2211639955 3215226955 {0: 20049, 1: 20022, 2: 20115, 3: 19809, 4: 20005}
Raku
Or... at least, it started out that way.
<lang perl6>class PCG32 {
has $!state; has $!incr; constant mask32 = 2³² - 1; constant mask64 = 2⁶⁴ - 1; constant const = 6364136223846793005;
submethod BUILD ( Int :$seed = 0x853c49e6748fea9b, Int :$incr = 0xda3e39cb94b95bdb ) { $!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
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)
$rng = PCG32.new( :seed(987654321), :incr(1) ); say ( ($rng.next-rat * 5).floor xx 100_000 ).Bag;</lang>
- Output:
2707161783 2068313097 3122475824 2211639955 3215226955 Bag(0(20049) 1(20022) 2(20115) 3(19809) 4(20005))
Wren
As Wren doesn't have a 64-bit integer type, we use BigInt instead. <lang ecmascript>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])")</lang>
- Output:
2707161783 2068313097 3122475824 2211639955 3215226955 The counts for 100,000 repetitions are: 0 : 20049 1 : 20022 2 : 20115 3 : 19809 4 : 20005