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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)