# noise.ludic — Noise.* determinism and structural invariants. Fixed-point noise
# can't be checked against a float reference bit-for-bit (that difference is the
# whole point), so we assert the properties that must hold: Perlin is exactly 0
# at integer lattice points, every sampler stays within [-1,1] (±65536 fixed),
# the same (x,y,seed) always reproduces, the seed changes the field, and cellular
# distance is non-negative. Running it prints: 1 2 3 4 5 6 7 8 9 10 11
program Noise {
  entry {
    let seed = 1337

    # gradient noise is exactly 0 at integer lattice points (zero offset vectors)
    if Noise.perlin2(fixed(0), fixed(0), seed) == 0 { print(1) }
    if Noise.perlin2(fixed(3), fixed(5), seed) == 0 { print(2) }

    # determinism: identical inputs -> identical output
    let a = Noise.simplex2(20000, 100, seed)
    let b = Noise.simplex2(20000, 100, seed)
    if a == b { print(3) }

    # range: every sampler stays within [-1, 1] (comparisons are in the fixed domain)
    let lo = fixed(0) - fixed(1)
    let hi = fixed(1)
    let p = Noise.perlin2(12345, 54321, seed)
    if p >= lo and p <= hi { print(4) }
    let s = Noise.simplex2(12345, 54321, seed)
    if s >= lo and s <= hi { print(5) }
    let v = Noise.value2(12345, 54321, seed)
    if v >= lo and v <= hi { print(6) }
    let f = Noise.fbm2(12345, 54321, seed, 5)
    if f >= lo and f <= hi { print(7) }

    # unit() remaps [-1,1] -> [0,1]: endpoints and midpoint (all in the fixed domain)
    let half = fixed(1) / fixed(2)
    if Noise.unit(fixed(1)) == fixed(1) and Noise.unit(fixed(0) - fixed(1)) == fixed(0) and Noise.unit(fixed(0)) == half { print(8) }

    # the seed selects the world: different seeds -> different fields
    if Noise.value2(12345, 54321, 1) != Noise.value2(12345, 54321, 2) { print(9) }

    # cellular F1 distance is non-negative; the cell id is deterministic
    if Noise.cellular2(12345, 54321, seed) >= 0 { print(10) }
    if Noise.cellular2_id(12345, 54321, seed) == Noise.cellular2_id(12345, 54321, seed) { print(11) }
  }
}