Monte Carlo methods: Difference between revisions

=={{header|Futhark}}==

Since Futhark is a pure language, random numbers are implemented using Sobol sequences.

<lang Futhark>

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)

</lang>