# Alternative Binary Number Notations

Faster but less safe parsers and printers of positive, N, Z.
By default, literals in types positive, N, Z are parsed and printed via the Number Notation command, by conversion from/to the Decimal.int representation. When working with numbers with thousands of digits and more, conversion from/to Decimal.int can become significantly slow. If that becomes a problem for your development, this file provides some alternative Number Notation commands that use Z as bridge type. To enable these commands, just be sure to Require this file after other files defining numeral notations.
Note: up to Coq 8.8, literals in types positive, N, Z were parsed and printed using a native ML library of arbitrary precision integers named bigint.ml. From 8.9, the default is to parse and print using a Coq library converting sequences of digits, hence reducing the amount of ML code to trust. But this method is slower. This file then gives access to the legacy method, trading efficiency against a larger ML trust base relying on bigint.ml.

Require Import BinNums.

positive

Definition pos_of_z z :=
match z with
| Zpos p => Some p
| _ => None
end.

Definition pos_to_z p := Zpos p.

Number Notation positive pos_of_z pos_to_z : positive_scope.

N

Definition n_of_z z :=
match z with
| Z0 => Some N0
| Zpos p => Some (Npos p)
| Zneg _ => None
end.

Definition n_to_z n :=
match n with
| N0 => Z0
| Npos p => Zpos p
end.

Number Notation N n_of_z n_to_z : N_scope.

Z

Definition z_of_z (z:Z) := z.

Number Notation Z z_of_z z_of_z : Z_scope.