import "futlib/math"

default(f32)

fun dirvcts(): [2][30]i32 =
    [
            [
                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: i32): i32 = (x >> 1) ^ x

----------------------------------------
--- Sobol Generator
----------------------------------------
fun testBit(n: i32, ind: i32): bool =
    let t = (1 << ind) in (n & t) == t

fun xorInds(n: i32) (dir_vs: [num_bits]i32): i32 =
    let reldv_vals = zipWith (\ 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]i32, n: i32): [m]i32 =
    map (xorInds n) dir_vs

fun sobolIndR(dir_vs:  [m][num_bits]i32) (n: i32 ): [m]f32 =
    let divisor = 2.0 ** f32(num_bits)
    let arri    = sobolIndI( dir_vs, n )
    in map (\ (x: i32): f32  -> f32(x) / divisor) arri

fun main(n: i32): f32 =
    let rand_nums = map (sobolIndR (dirvcts())) (iota n)
    let dists     = map (\xy ->
                           let (x,y) = (xy[0],xy[1]) in f32.sqrt(x*x + y*y))
                        rand_nums

    let bs        = map (\d -> if d <= 1.0f32 then 1 else 0) dists

    let inside    = reduce (+) 0 bs
    in 4.0f32*f32(inside)/f32(n)