def add_value

bend-collections-laws-crypto@1.0.0.0 · proofs/math/typed/w64add.bend:74

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as C
import bend-collections-laws-crypto@1.0.0.0/spec/math/w64.bend as SW
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/u64.bend as WU
import bend-collections-laws-crypto@1.0.0.0/proofs/math/u64/u64.bend as P64
import bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/width.bend as WW

74def add_value(+a: WU.U64, +b: WU.U64) -> SW.Add.value(a, b):
75  match a b:
76    case WU.U64{+al, +ah} WU.U64{+bl, +bh}:
77      +R = Nat.add(v(U32.add(al, bl)), C.shift(32n, v(U32.add(U32.add(ah, bh), X.b32(U32.is_lt(U32.add(al, bl), al))))))
78      +q = Nat.add(bv(P64.carry32(U32.add(ah, bh), X.b32(U32.is_lt(U32.add(al, bl), al)))), bv(P64.carry32(ah, bh)))
79      +hR = WW.limbs_fit(32n, 32n, v(U32.add(al, bl)), v(U32.add(U32.add(ah, bh), X.b32(U32.is_lt(U32.add(al, bl), al)))), vb(U32.add(al, bl)), vb(U32.add(U32.add(ah, bh), X.b32(U32.is_lt(U32.add(al, bl), al)))))
80      +lq = Equal.trans(Nat, C.low(64n, Nat.add(Nat.add(v(al), C.shift(32n, v(ah))), Nat.add(v(bl), C.shift(32n, v(bh))))), C.low(64n, Nat.add(R, C.shift(64n, q))), R, Equal.cong(Nat, Nat, t => C.low(64n, t), Nat.add(Nat.add(v(al), C.shift(32n, v(ah))), Nat.add(v(bl), C.shift(32n, v(bh)))), Nat.add(R, C.shift(64n, q)), add_eq(al, ah, bl, bh)), WW.low_u(64n, R, q, hR))
81      Equal.sym(Nat, C.low(64n, Nat.add(Nat.add(v(al), C.shift(32n, v(ah))), Nat.add(v(bl), C.shift(32n, v(bh))))), R, lq)