Pseudo-random numbers/Xorshift star: Difference between revisions
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=={{header|Julia}}== |
=={{header|Julia}}== |
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{{trans|Python}} |
{{trans|Python}} |
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<lang julia>const |
<lang julia>const mask32 = (0x1 << 32) - 1 |
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const mask32 = (0x1 << 32) - 1 |
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const CONST = 0x2545F4914F6CDD1D |
const CONST = 0x2545F4914F6CDD1D |
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mutable struct XorShiftStar |
mutable struct XorShiftStar |
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state::UInt64 |
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end |
end |
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XorShiftStar(_seed=0x0) = XorShiftStar(UInt(_seed) |
XorShiftStar(_seed=0x0) = XorShiftStar(UInt(_seed)) |
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seed(x::XorShiftStar, num) = begin x.state = num |
seed(x::XorShiftStar, num) = begin x.state = UInt64(num) end |
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"""return random int between 0 and 2**32""" |
"""return random int between 0 and 2**32""" |
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function next_int(x::XorShiftStar) |
function next_int(x::XorShiftStar) |
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x.state = |
x.state = x.state ⊻ (x.state >> 12) |
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x.state = |
x.state = x.state ⊻ (x.state << 25) |
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x.state = |
x.state = x.state ⊻ (x.state >> 27) |
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return |
return ((x.state * CONST) >> 32) & mask32 |
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end |
end |
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Revision as of 03:32, 15 August 2020
- 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
- Xorshift_star Generator (pseudo-code)
/* Let u64 denote an unsigned 64 bit integer type. */ /* Let u32 denote an unsigned 32 bit integer type. */
class Xorshift_star u64 state /* Must be seeded to non-zero initial value */ u64 const = HEX '2545F4914F6CDD1D'
method seed(u64 num): state = num end method method next_int(): u64 x = state x = x ^ (x >> 12) x = x ^ (x << 25) x = x ^ (x >> 27) state = x u32 answer = ((x * const) >> 32) return answer end method method next_float(): return float next_int() / (1 << 32) end method end class
- Xorshift use
random_gen = instance Xorshift_star random_gen.seed(1234567) print(random_gen.next_int()) /* 3540625527 */ print(random_gen.next_int()) /* 2750739987 */ print(random_gen.next_int()) /* 4037983143 */ print(random_gen.next_int()) /* 1993361440 */ print(random_gen.next_int()) /* 3809424708 */
- 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 1234567
are as shown above
- Show that for an initial seed of 987654321, the counts of 100_000 repetitions of
floor(random_gen.next_float() * 5)
- Is as follows:
0: 20103, 1: 19922, 2: 19937, 3: 20031, 4: 20007
- Show your output here, on this page.
F#
The Functions
<lang fsharp> // Xorshift star. Nigel Galloway: August 14th., 2020 let fN=(fun(n:uint64)->n^^^(n>>>12))>>(fun n->n^^^(n<<<25))>>(fun n->n^^^(n>>>27)) let Xstar32=Seq.unfold(fun n->let n=fN n in Some(uint32((n*0x2545F4914F6CDD1DUL)>>>32),n)) let XstarF n=Xstar32 n|>Seq.map(fun n->(float n)/4294967296.0) </lang>
The Tasks
<lang fsharp> Xstar32 1234567UL|>Seq.take 5|>Seq.iter(printfn "%d") </lang>
- Output:
3540625527 2750739987 4037983143 1993361440 3809424708
<lang fsharp> XstarF 987654321UL|>Seq.take 100000|>Seq.countBy(fun n->int(n*5.0))|>Seq.iter(printf "%A");printfn "" </lang>
- Output:
(4, 20007)(2, 19937)(3, 20031)(0, 20103)(1, 19922)
Factor
<lang factor>USING: accessors kernel literals math math.statistics prettyprint sequences ;
CONSTANT: mask64 $[ 1 64 shift 1 - ] CONSTANT: mask32 $[ 1 32 shift 1 - ] CONSTANT: const 0x2545F4914F6CDD1D
! Restrict seed value to positive integers. PREDICATE: positive < integer 0 > ; ERROR: seed-nonpositive seed ;
TUPLE: xorshift* { state positive initial: 1 } ;
- <xorshift*> ( seed -- xorshift* )
dup positive? [ seed-nonpositive ] unless mask64 bitand xorshift* boa ;
- twiddle ( m n -- n ) dupd shift bitxor mask64 bitand ;
- next-int ( obj -- n )
dup state>> -12 twiddle 25 twiddle -27 twiddle tuck swap state<< const * mask64 bitand -32 shift mask32 bitand ;
- next-float ( obj -- x ) next-int 1 32 shift /f ;
! ---=== Task ===--- 1234567 <xorshift*> 5 [ dup next-int . ] times
987654321 >>state 100,000 [ dup next-float 5 * >integer ] replicate nip histogram .</lang>
- Output:
3540625527 2750739987 4037983143 1993361440 3809424708 H{ { 0 20103 } { 1 19922 } { 2 19937 } { 3 20031 } { 4 20007 } }
Go
<lang go>package main
import (
"fmt" "math"
)
const CONST = 0x2545F4914F6CDD1D
type XorshiftStar struct{ state uint64 }
func XorshiftStarNew(state uint64) *XorshiftStar { return &XorshiftStar{state} }
func (xor *XorshiftStar) seed(state uint64) { xor.state = state }
func (xor *XorshiftStar) nextInt() uint32 {
x := xor.state x = x ^ (x >> 12) x = x ^ (x << 25) x = x ^ (x >> 27) xor.state = x return uint32((x * CONST) >> 32)
}
func (xor *XorshiftStar) nextFloat() float64 {
return float64(xor.nextInt()) / (1 << 32)
}
func main() {
randomGen := XorshiftStarNew(1234567) for i := 0; i < 5; i++ { fmt.Println(randomGen.nextInt()) }
var counts [5]int randomGen.seed(987654321) 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:
3540625527 2750739987 4037983143 1993361440 3809424708 The counts for 100,000 repetitions are: 0 : 20103 1 : 19922 2 : 19937 3 : 20031 4 : 20007
Julia
<lang julia>const mask32 = (0x1 << 32) - 1 const CONST = 0x2545F4914F6CDD1D
mutable struct XorShiftStar
state::UInt64
end
XorShiftStar(_seed=0x0) = XorShiftStar(UInt(_seed))
seed(x::XorShiftStar, num) = begin x.state = UInt64(num) end
"""return random int between 0 and 2**32""" function next_int(x::XorShiftStar)
x.state = x.state ⊻ (x.state >> 12) x.state = x.state ⊻ (x.state << 25) x.state = x.state ⊻ (x.state >> 27) return ((x.state * CONST) >> 32) & mask32
end
"""return random float between 0 and 1""" next_float(x::XorShiftStar) = next_int(x) / (1 << 32)
function testXorShiftStar()
random_gen = XorShiftStar() seed(random_gen, 1234567) for i in 1:5 println(next_int(random_gen)) end seed(random_gen, 987654321) hist = fill(0, 5) for _ in 1:100_000 hist[Int(floor(next_float(random_gen) * 5)) + 1] += 1 end foreach(n -> print(n - 1, ": ", hist[n], " "), 1:5)
end
testXorShiftStar()
</lang>
- Output:
3540625527 2750739987 4037983143 1993361440 3809424708 0: 20103 1: 19922 2: 19937 3: 20031 4: 20007
Phix
As per Pseudo-random_numbers/PCG32#Phix, resorting to mpfr/gmp <lang Phix>include mpfr.e mpz const = mpz_init("0x2545F4914F6CDD1D"),
state = mpz_init(), b64 = mpz_init("0x10000000000000000"), -- (truncate to 64 bits) b32 = mpz_init("0x100000000"), -- (truncate to 32 bits) tmp = mpz_init(), x = mpz_init()
procedure seed(integer num)
mpz_set_si(state,num)
end procedure
function next_int()
mpz_set(x,state) -- x := state mpz_tdiv_q_2exp(tmp, x, 12) -- tmp := trunc(x/2^12) mpz_xor(x, x, tmp) -- x := xor_bits(x,tmp) mpz_mul_2exp(tmp, x, 25) -- tmp := x * 2^25. mpz_xor(x, x, tmp) -- x := xor_bits(x,tmp) mpz_fdiv_r(x, x, b64) -- x := remainder(x,b64) mpz_tdiv_q_2exp(tmp, x, 27) -- tmp := trunc(x/2^27) mpz_xor(x, x, tmp) -- x := xor_bits(x,tmp) mpz_fdiv_r(state, x, b64) -- state := remainder(x,b64) mpz_mul(x,x,const) -- x *= const mpz_tdiv_q_2exp(x, x, 32) -- x := trunc(x/2^32) mpz_fdiv_r(x, x, b32) -- x := remainder(x,b32) return mpz_get_atom(x)
end function
function next_float()
return next_int() / (1 << 32)
end function
seed(1234567) for i=1 to 5 do
printf(1,"%d\n",next_int())
end for seed(987654321) sequence r = repeat(0,5) for i=1 to 100000 do
r[floor(next_float()*5)+1] += 1
end for ?r</lang>
- Output:
3540625527 2750739987 4037983143 1993361440 3809424708 {20103,19922,19937,20031,20007}
Python
<lang python>mask64 = (1 << 64) - 1 mask32 = (1 << 32) - 1 const = 0x2545F4914F6CDD1D
class Xorshift_star():
def __init__(self, seed=0): self.state = seed & mask64
def seed(self, num): self.state = num & mask64 def next_int(self): "return random int between 0 and 2**32" x = self.state x = (x ^ (x >> 12)) & mask64 x = (x ^ (x << 25)) & mask64 x = (x ^ (x >> 27)) & mask64 self.state = x answer = (((x * const) & mask64) >> 32) & 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 = Xorshift_star() random_gen.seed(1234567) for i in range(5): print(random_gen.next_int()) random_gen.seed(987654321) 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:
3540625527 2750739987 4037983143 1993361440 3809424708 {0: 20103, 1: 19922, 2: 19937, 3: 20031, 4: 20007}
Raku
Raku does not have unsigned Integers at this time (Integers are arbitrary sized) so use explicit bit masks during bitwise operations. All constants are encapsulated inside the class.
<lang perl6>class Xorshift-star {
has $!state;
submethod BUILD ( Int :$seed where * > 0 = 1 ) { $!state = $seed }
method next-int { $!state +^= $!state +> 12; $!state +^= $!state +< 25 +& (2⁶⁴ - 1); $!state +^= $!state +> 27; ($!state * 0x2545F4914F6CDD1D) +> 32 +& (2³² - 1) }
method next-rat { self.next-int / 2³² }
}
- Test next-int
say 'Seed: 1234567; first five Int values'; my $rng = Xorshift-star.new( :seed(1234567) ); .say for $rng.next-int xx 5;
- Test next-rat (since these are rational numbers by default)
say "\nSeed: 987654321; first 1e5 Rat values histogram"; $rng = Xorshift-star.new( :seed(987654321) ); say ( ($rng.next-rat * 5).floor xx 100_000 ).Bag;
- Test with default seed
say "\nSeed: default; first five Int values"; $rng = Xorshift-star.new; .say for $rng.next-int xx 5;</lang>
- Output:
Seed: 1234567; first five Int values 3540625527 2750739987 4037983143 1993361440 3809424708 Seed: 987654321; first 1e5 Rat values histogram Bag(0(20103), 1(19922), 2(19937), 3(20031), 4(20007)) Seed: default; first five Int values 1206177355 2882512552 3117485455 1303648416 241277360
Wren
As Wren doesn't have a 64-bit integer type, we use BigInt instead. <lang ecmascript>import "/big" for BigInt
var Const = BigInt.fromBaseString("2545F4914F6CDD1D", 16) var Mask64 = (BigInt.one << 64) - BigInt.one var Mask32 = (BigInt.one << 32) - BigInt.one
class XorshiftStar {
construct new(state) { _state = state & Mask64 }
seed(num) { _state = num & Mask64}
nextInt { var x = _state x = (x ^ (x >> 12)) & Mask64 x = (x ^ (x << 25)) & Mask64 x = (x ^ (x >> 27)) & Mask64 _state = x return (((x * Const) & Mask64) >> 32) & Mask32 }
nextFloat { nextInt.toNum / 2.pow(32) }
}
var randomGen = XorshiftStar.new(BigInt.new(1234567)) for (i in 0..4) System.print(randomGen.nextInt)
var counts = List.filled(5, 0) randomGen.seed(BigInt.new(987654321)) 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:
3540625527 2750739987 4037983143 1993361440 3809424708 The counts for 100,000 repetitions are: 0 : 20103 1 : 19922 2 : 19937 3 : 20031 4 : 20007