def mont_lt

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/u64mont.bend:201

import Base
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as C
import bend-collections-laws-math@1.0.0.0/spec/math/w64.bend as SW
import bend-collections-laws-math@1.0.0.0/src/math/w64.bend as X
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as WU

201# Montgomery multiplication: mont(a, b) < m and mont(a, b) 2^64 == a b (mod m)
202def mont_lt(+one: Nat, +h1: {one == 1n : Nat}, +bp: Nat, +m: WU.U64, +mp: WU.U64, +hM: {SW.value(m) == 1n+bp : Nat}, +hinv: {1n+C.low(64n, Nat.mul(1n+bp, SW.value(mp))) == C.shift(64n, one) : Nat}, +h63: {Nat.is_lt(1n+bp, C.shift(63n, one)) == True{} : Bool}, +a: WU.U64, +b: WU.U64, +ha: {Nat.is_lt(SW.value(a), 1n+bp) == True{} : Bool}, +hb: {Nat.is_lt(SW.value(b), 1n+bp) == True{} : Bool}) -> {Nat.is_lt(SW.value(X.mont(m, mp, a, b)), 1n+bp) == True{} : Bool}:
203  rd_lt(one, h1, bp, m, mp, hM, hinv, h63, X.mul128(a, b), Nat.mul(SW.value(a), SW.value(b)), m128v(a, b), ab_lt(bp, SW.value(a), SW.value(b), ha, hb))