def first_case

bend-collections-laws-crypto@1.0.0.0 · proofs/math/random/uint64n.bend:239

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/math/w64.bend as SW
import bend-collections-laws-crypto@1.0.0.0/spec/math/random/rand.bend as SR
import bend-collections-laws-crypto@1.0.0.0/src/math/u64.bend as WU
import bend-collections-laws-crypto@1.0.0.0/src/math/w64.bend as X
import bend-collections-laws-crypto@1.0.0.0/src/math/random/rand.bend as R
import bend-collections-laws-crypto@1.0.0.0/spec/math/random.bend as SRM

239# the first draw: accepted at once when lo >= n, else the loop
240def first_case(~S: Data, ~next: S -> WU.U64 & S, +one: Nat, +h1: {one == 1n : Nat}, +n: WU.U64, +m: Nat, +x: WU.U64, +s1: S, +hv: {SW.value(n) == 1n+m : Nat}, +hz: {X.is_zero(n) == False{} : Bool}, +hp: {Nat.is_eq(SR.and_bits(64n, 1n+m, m), 0n) == False{} : Bool}, +htn: {Nat.is_lt(SR.pow2mod(64n, 1n+m), 1n+m) == True{} : Bool}, +c: Bool, +hc: {X.lt(X.pfst(X.mul128(x, n)), n) == c : Bool}) -> {SRM.val_pair(S, R.lemire_small(~S, ~next, n, X.psnd(X.mul128(x, n)), X.pfst(X.mul128(x, n)), s1, c)) == cont(~S, ~next, 127n, 1n+m, SW.value(x), s1) : Nat & S}:
241  match c:
242    case True{}:
243      loop(~S, ~next, 127n, n, m, R.thresh(n), (x, s1), hv, hp, htn, thresh_m(one, h1, n, m, hv, hz))
244    case False{}:
245      first_false(~S, ~next, n, m, x, s1, hv, hp, htn, hc)