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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 add_modulo x y modulus :=
if (modulus <=? x + y) then (x + y) - modulus else (x + y).
(** Logical negation, modulo a number *)
Definition lnot_modulo (v : Z) (modulus : Z) : Z
:= Z.lnot v mod modulus.
(** Boolean negation *)
Definition bneg (v : Z) : Z
:= if dec (v = 0) then 1 else 0.
(* most significant bit *)
Definition cc_m s x := if dec (2 ^ (Z.log2 s) = s) then x >> (Z.log2 s - 1) else x / (s / 2).
(* least significant bit *)
Definition cc_l x := x mod 2.
(* two-register right shift *)
Definition rshi s hi lo n :=
let k := Z.log2 s in
if dec (2 ^ k = s)
then ((lo + (hi << k)) >> n) &' (Z.ones k)
else ((lo + hi * s) >> n) mod s.
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
:= dlet v := add_with_carry c x y in get_carry bitwidth v.
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
:= dlet v := sub_with_borrow c x y in get_borrow bitwidth v.
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
(if Z.geb bitwidth 0
then xy &' Z.ones bitwidth
else xy mod 2^bitwidth,
if Z.geb bitwidth 0
then xy >> bitwidth
else xy / 2^bitwidth).
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).
(** if positive, round up to 2^k-1 (0b11111....); if negative, round down to -2^k (0b...111000000...) *)
Definition round_lor_land_bound (x : Z) : Z
:= if (0 <=? x)%Z
then 2^(Z.log2_up (x+1))-1
else -2^(Z.log2_up (-x)).
End Z.
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