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Task/Monte-Carlo-methods/ERRE/monte-carlo-methods.erre

@@ -0,0 +1,24 @@
+PROGRAM RANDOM_PI
+
+!
+! for rosettacode.org
+!
+
+!$DOUBLE
+
+PROCEDURE MONTECARLO(T->RES)
+      LOCAL I,N
+      FOR I=1 TO T DO
+        IF RND(1)^2+RND(1)^2<1 THEN N+=1 END IF
+      END FOR
+      RES=4*N/T
+END PROCEDURE
+
+BEGIN
+      RANDOMIZE(TIMER) ! init rnd number generator
+      MONTECARLO(1000->RES)     PRINT(RES)
+      MONTECARLO(10000->RES)    PRINT(RES)
+      MONTECARLO(100000->RES)   PRINT(RES)
+      MONTECARLO(1000000->RES)  PRINT(RES)
+      MONTECARLO(10000000->RES) PRINT(RES)
+END PROGRAM

Task/Monte-Carlo-methods/FreeBASIC/monte-carlo-methods.freebasic

@@ -0,0 +1,33 @@
+' version 23-10-2016
+' compile with: fbc -s console
+
+Randomize Timer  'seed the random function
+
+Dim As Double x, y, pi, error_
+Dim As UInteger m = 10, n, n_start, n_stop = m, p
+
+Print
+Print " Mumber of throws  Ratio (Pi)     Error"
+Print
+
+Do
+    For n = n_start To n_stop -1
+        x = Rnd
+        y = Rnd
+        If (x * x + y * y) <= 1 Then p = p +1
+    Next
+    Print Using "    ############,  "; m ;
+    pi = p * 4 / m
+    error_ = 3.141592653589793238462643383280 - pi
+    Print RTrim(Str(pi),"0");Tab(35); Using "##.#############"; error_
+    m = m * 10
+    n_start = n_stop
+    n_stop = m
+Loop Until m > 1000000000 ' 1,000,000,000
+
+
+' empty keyboard buffer
+While Inkey <> "" : Wend
+Print : Print "hit any key to end program"
+Sleep
+End

Task/Monte-Carlo-methods/Futhark/monte-carlo-methods.futhark

@@ -0,0 +1,46 @@
+default(f32)
+
+fun dirvcts(): [2][30]int =
+    [
+            [
+                536870912, 268435456, 134217728, 67108864, 33554432, 16777216, 8388608, 4194304, 2097152, 1048576, 524288, 262144, 131072, 65536, 32768, 16384, 8192, 4096, 2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1
+            ],
+            [
+                536870912, 805306368, 671088640, 1006632960, 570425344, 855638016, 713031680, 1069547520, 538968064, 808452096, 673710080, 1010565120, 572653568, 858980352, 715816960, 1073725440, 536879104, 805318656, 671098880, 1006648320, 570434048, 855651072, 713042560, 1069563840, 538976288, 808464432, 673720360, 1010580540, 572662306, 858993459
+            ]
+    ]
+
+
+fun grayCode(x: int): int = (x >> 1) ^ x
+
+----------------------------------------
+--- Sobol Generator
+----------------------------------------
+fun testBit(n: int, ind: int): bool =
+    let t = (1 << ind) in (n & t) == t
+
+fun xorInds(n: int) (dir_vs: [num_bits]int): int =
+    let reldv_vals = zipWith (fn  dv i  =>
+                                if testBit(grayCode n,i)
+                                then dv else 0)
+                             dir_vs (iota num_bits)
+    in reduce (^) 0 reldv_vals
+
+fun sobolIndI (dir_vs: [m][num_bits]int, n: int): [m]int =
+    map (xorInds n) dir_vs
+
+fun sobolIndR(dir_vs:  [m][num_bits]int) (n: int ): [m]f32 =
+    let divisor = 2.0 ** f32(num_bits)
+    let arri    = sobolIndI( dir_vs, n )
+    in map (fn  (x: int): f32  => f32(x) / divisor) arri
+
+fun main(n: int): f32 =
+    let rand_nums = map (sobolIndR (dirvcts())) (iota n)
+    let dists     = map (fn xy =>
+                           let (x,y) = (xy[0],xy[1]) in sqrt32(x*x + y*y))
+                        rand_nums
+
+    let bs        = map (fn d => if d <= 1.0f32 then 1 else 0) dists
+
+    let inside    = reduce (+) 0 bs
+    in 4.0f32*f32(inside)/f32(n)

Task/Monte-Carlo-methods/Nim/monte-carlo-methods.nim

@@ -0,0 +1,12 @@
+import math
+randomize()
+
+proc pi(nthrows): float =
+  var inside = 0
+  for i in 1..int64(nthrows):
+    if hypot(random(1.0), random(1.0)) < 1:
+      inc inside
+  return float(4 * inside) / nthrows
+
+for n in [10e4, 10e6, 10e7, 10e8]:
+  echo pi(n)

Task/Monte-Carlo-methods/Ring/monte-carlo-methods.ring

@@ -0,0 +1,12 @@
+decimals(8)
+see "monteCarlo(1000) = " + monteCarlo(1000) + nl
+see "monteCarlo(10000) = " + monteCarlo(10000) + nl
+see "monteCarlo(100000) = " + monteCarlo(100000) + nl
+
+func monteCarlo t
+     n=0
+     for i = 1 to t
+         if sqrt(pow(random(1),2) + pow(random(1),2)) <= 1 n += 1 ok
+     next
+     t = (4 * n) / t
+     return t

Task/Monte-Carlo-methods/Swift/monte-carlo-methods.swift

@@ -0,0 +1,26 @@
+import Foundation
+
+func mcpi(sampleSize size:Int) -> Double {
+    var x = 0 as Double
+    var y = 0 as Double
+    var m = 0 as Double
+
+    for i in 0..<size {
+        x = Double(arc4random()) / Double(UINT32_MAX)
+        y = Double(arc4random()) / Double(UINT32_MAX)
+
+        if ((x * x) + (y * y) < 1) {
+            m += 1
+        }
+    }
+
+    return (4.0 * m) / Double(size)
+}
+
+println(mcpi(sampleSize: 100))
+println(mcpi(sampleSize: 1000))
+println(mcpi(sampleSize: 10000))
+println(mcpi(sampleSize: 100000))
+println(mcpi(sampleSize: 1000000))
+println(mcpi(sampleSize: 10000000))
+println(mcpi(sampleSize: 100000000))