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Require Import Coq.ZArith.ZArith.
Require Import Crypto.Util.Decidable.
Require Import Crypto.Util.ZUtil.Notations.
Require Import Crypto.Util.LetIn.
Local Open Scope Z_scope.
Module Z.
Definition pow2_mod n i := (n &' (Z.ones i)).
Definition zselect (cond zero_case nonzero_case : Z) :=
if cond =? 0 then zero_case else nonzero_case.
Definition get_carry (bitwidth : Z) (v : Z) : Z * Z
:= (v mod 2^bitwidth, v / 2^bitwidth).
Definition add_with_carry (c : Z) (x y : Z) : Z
:= c + x + y.
Definition add_with_get_carry (bitwidth : Z) (c : Z) (x y : Z) : Z * Z
:= get_carry bitwidth (add_with_carry c x y).
Definition add_get_carry (bitwidth : Z) (x y : Z) : Z * Z
:= add_with_get_carry bitwidth 0 x y.
Definition get_borrow (bitwidth : Z) (v : Z) : Z * Z
:= let '(v, c) := get_carry bitwidth v in
(v, -c).
Definition sub_with_borrow (c : Z) (x y : Z) : Z
:= add_with_carry (-c) x (-y).
Definition sub_with_get_borrow (bitwidth : Z) (c : Z) (x y : Z) : Z * Z
:= get_borrow bitwidth (sub_with_borrow c x y).
Definition sub_get_borrow (bitwidth : Z) (x y : Z) : Z * Z
:= sub_with_get_borrow bitwidth 0 x y.
(* splits at [bound], not [2^bitwidth]; wrapper to make add_getcarry
work if input is not known to be a power of 2 *)
Definition add_get_carry_full (bound : Z) (x y : Z) : Z * Z
:= if 2 ^ (Z.log2 bound) =? bound
then add_get_carry (Z.log2 bound) x y
else ((x + y) mod bound, (x + y) / bound).
Definition add_with_get_carry_full (bound : Z) (c x y : Z) : Z * Z
:= if 2 ^ (Z.log2 bound) =? bound
then add_with_get_carry (Z.log2 bound) c x y
else ((c + x + y) mod bound, (c + x + y) / bound).
Definition sub_get_borrow_full (bound : Z) (x y : Z) : Z * Z
:= if 2 ^ (Z.log2 bound) =? bound
then sub_get_borrow (Z.log2 bound) x y
else ((x - y) mod bound, -((x - y) / bound)).
Definition sub_with_get_borrow_full (bound : Z) (c x y : Z) : Z * Z
:= if 2 ^ (Z.log2 bound) =? bound
then sub_with_get_borrow (Z.log2 bound) c x y
else ((x - y - c) mod bound, -((x - y - c) / bound)).
Definition mul_split_at_bitwidth (bitwidth : Z) (x y : Z) : Z * Z
:= dlet xy := x * y in
(match bitwidth with
| Z.pos _ | Z0 => xy &' Z.ones bitwidth
| Z.neg _ => xy mod 2^bitwidth
end,
match bitwidth with
| Z.pos _ | Z0 => xy >> bitwidth
| Z.neg _ => xy / 2^bitwidth
end).
Definition mul_split (s x y : Z) : Z * Z
:= if s =? 2^Z.log2 s
then mul_split_at_bitwidth (Z.log2 s) x y
else ((x * y) mod s, (x * y) / s).
End Z.
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