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-- This file is part of 'Finite Field Arithmetic', aka 'FFA'.               --
--                                                                          --
-- (C) 2019 Stanislav Datskovskiy ( www.loper-os.org )                      --
-- http://wot.deedbot.org/17215D118B7239507FAFED98B98228A001ABFFC7.html     --
--                                                                          --
-- You do not have, nor can you ever acquire the right to use, copy or      --
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-- continue doing so for the indefinite future. In any case, please         --
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-- See also http://trilema.com/2015/a-new-software-licensing-paradigm .     --
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with Words;   use Words;
with FZ_Type; use FZ_Type;


package FZ_Prime is
   
   pragma Pure;
   
   -- Constant-Time Miller-Rabin Test on N using the given Witness.
   -- Witness will be used as-is if it conforms to the valid bounds,
   -- i.e. 2 <= Witness <= N - 2; otherwise will be transformed into a
   -- valid Witness via modular arithmetic.
   -- Outputs ONE if N WAS FOUND composite; ZERO if NOT FOUND.
   -- Handles degenerate cases of N that M-R per se cannot eat:
   -- N=0, N=1: ALWAYS 'FOUND COMPOSITE'; 2, 3 - ALWAYS 'NOT FOUND'.
   -- If N is Even and not equal to 2, N is ALWAYS 'FOUND COMPOSITE.'
   -- For ALL other N, the output is equal to that of the M-R test.
   function FZ_MR_Composite_On_Witness(N       : in  FZ;
                                       Witness : in  FZ) return WBool
     with Pre => N'Length = Witness'Length;
   
end FZ_Prime;