def fT

bend-collections-laws-math@1.0.0.0 · proofs/math/random/pcg/impl.bend:33

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/u64.bend as WU
import bend-collections-laws-math@1.0.0.0/src/math/w64.bend as X
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64add.bend as WA
import bend-collections-laws-math@1.0.0.0/proofs/math/random/pcg/step.bend as ST

33# the cross products mod 2^64
34def fT(+hi: WU.U64, +lo: WU.U64, +ml: WU.U64, +mh: WU.U64) -> {C.low(64n, SW.value(X.add(X.mul(hi, ml), X.mul(lo, mh)))) == C.low(64n, Nat.add(Nat.mul(SW.value(hi), SW.value(ml)), Nat.mul(SW.value(lo), SW.value(mh)))) : Nat}:
35  +m1 = X.mul(hi, ml)
36  +m2 = X.mul(lo, mh)
37  Equal.trans(Nat, C.low(64n, SW.value(X.add(m1, m2))), C.low(64n, Nat.add(SW.value(m1), SW.value(m2))), C.low(64n, Nat.add(Nat.mul(SW.value(hi), SW.value(ml)), Nat.mul(SW.value(lo), SW.value(mh)))),
38    eqm_of(SW.value(X.add(m1, m2)), Nat.add(SW.value(m1), SW.value(m2)), WA.add_value(m1, m2)),
39    ST.low_add(64n, SW.value(m1), Nat.mul(SW.value(hi), SW.value(ml)), SW.value(m2), Nat.mul(SW.value(lo), SW.value(mh)), eqm_of(SW.value(m1), Nat.mul(SW.value(hi), SW.value(ml)), WA.mul_value(hi, ml)), eqm_of(SW.value(m2), Nat.mul(SW.value(lo), SW.value(mh)), WA.mul_value(lo, mh))))