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Require Import Coq.ZArith.Zpower Coq.ZArith.ZArith.
Require Import Crypto.Util.ListUtil.
Require Import Coq.Lists.List.
Local Open Scope Z_scope.
Section Pow2Base.
Context (limb_widths : list Z).
Local Notation "w[ i ]" := (nth_default 0 limb_widths i).
Fixpoint base_from_limb_widths limb_widths :=
match limb_widths with
| nil => nil
| w :: lw => 1 :: map (Z.mul (two_p w)) (base_from_limb_widths lw)
end.
Local Notation base := (base_from_limb_widths limb_widths).
Definition bounded us := forall i, 0 <= nth_default 0 us i < 2 ^ w[i].
Definition upper_bound := 2 ^ (sum_firstn limb_widths (length limb_widths)).
End Pow2Base.
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