def next_fit

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/poly1305/value.bend:344

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/src/crypto/poly1305/limbs.bend as Li
import bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/w64sh.bend as SH
import bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/shrn.bend as SHN
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/arith.bend as A

344# the next carry high(8, s) fits 8 + j bits again
345def next_fit(+ds: List<&2, U32>, +u: U32, +j: Nat, +hj: {Nat.is_le(Nat.add(9n, j), 32n) == True{} : Bool}, +hd: {fit_all(ds, Nat.add(8n, j)) == True{} : Bool}, +hu: {C.fits(Nat.add(8n, j), v(u)) == True{} : Bool}) -> {C.fits(Nat.add(8n, j), v(U32.shrn(U32.add(u, Li.hd0(ds)), 8n))) == True{} : Bool}:
346  +s = U32.add(u, Li.hd0(ds))
347  +h1 = A.fits_subst(Nat.add(9n, j), Nat.add(v(u), v(Li.hd0(ds))), v(s), A.sy(v(s), Nat.add(v(u), v(Li.hd0(ds))), step_ev(ds, u, j, hj, hd, hu)), step_fit(ds, u, j, hd, hu))
348  +h2 = SH.fits_high(8n, 1n+j, v(s), h1)
349  +h3 = SH.fits_mono(1n+j, Nat.add(8n, j), C.high(8n, v(s)), A.le_add_l(7n, j), h2)
350  A.fits_subst(Nat.add(8n, j), C.high(8n, v(s)), v(U32.shrn(s, 8n)), A.sy(v(U32.shrn(s, 8n)), C.high(8n, v(s)), SHN.shrn_high(s, 8n)), h3)