```   1 ------------------------------------------------------------------------------
2 ------------------------------------------------------------------------------
3 -- This file is part of 'Finite Field Arithmetic', aka 'FFA'.               --
4 --                                                                          --
5 -- (C) 2019 Stanislav Datskovskiy ( www.loper-os.org )                      --
6 -- http://wot.deedbot.org/17215D118B7239507FAFED98B98228A001ABFFC7.html     --
7 --                                                                          --
8 -- You do not have, nor can you ever acquire the right to use, copy or      --
9 -- distribute this software ; Should you use this software for any purpose, --
10 -- or copy and distribute it to anyone or in any manner, you are breaking   --
11 -- the laws of whatever soi-disant jurisdiction, and you promise to         --
12 -- continue doing so for the indefinite future. In any case, please         --
13 -- always : read and understand any software ; verify any PGP signatures    --
14 -- that you use - for any purpose.                                          --
15 --                                                                          --
17 ------------------------------------------------------------------------------
18
19 with Words;    use Words;
20 with FZ_Basic; use FZ_Basic;
21 with FZ_Shift; use FZ_Shift;
22 with FZ_QShft; use FZ_QShft;
23 with FZ_Arith; use FZ_Arith;
24 with FZ_Pred;  use FZ_Pred;
25
26
27 package body FZ_GCD is
28
29    -- Find Greatest Common Divisor (GCD) of X and Y.
30    -- Note that by convention, GCD(0, 0) = 0.
31    procedure FZ_Greatest_Common_Divisor(X      : in  FZ;
32                                         Y      : in  FZ;
33                                         Result : out FZ) is
34
35       -- Widths of X, Y, and Result are equal
36       subtype Width is Word_Index range X'Range;
37
38       -- Working buffers for GCD computation, initially equal to the inputs
39       A      : FZ(Width) := X; -- GCD will appear in A in the end
40       B      : FZ(Width) := Y;
41
42       -- Evenness (negation of lowest bit) of A and B respectively
43       Ae, Be : WBool;
44
45       -- Common power-of-2 factor
46       Twos   : Word := 0;
47
48       -- |A - B|
49       D      : FZ(Width);
50
51       -- This flag is set iff A < B
52       A_lt_B : WBool;
53
54    begin
55
56       -- For convergence, requires number of shots equal to 2 * FZ_Bitness:
57       for i in 1 .. 2 * FZ_Bitness(X) loop
58
59          -- If A is even, A := A >> 1; otherwise A := A
60          Ae := 1 - FZ_OddP(A);
61          FZ_ShiftRight(A, A, WBit_Index(Ae));
62
63          -- If B is even, B := B >> 1; otherwise B := B
64          Be := 1 - FZ_OddP(B);
65          FZ_ShiftRight(B, B, WBit_Index(Be));
66
67          -- If both A and B were even, increment the common power-of-two
68          Twos := Twos + (Ae and Be);
69
70          -- D := |A - B|
71          FZ_Sub_Abs(X => A, Y => B, Difference => D, Underflow => A_lt_B);
72
73          -- B' := min(A, B)
74          FZ_Mux(X => B, Y => A, Result => B, Sel => A_lt_B);
75
76          -- A' := |A - B|
77          A := D;
78
79       end loop;
80
81       -- Reintroduce the common power-of-2 factor stored in 'Twos'
82       FZ_Quiet_ShiftLeft(N => A, ShiftedN => A, Count => Indices(Twos));
83
84       -- Output final result
85       Result := A;
86
87    end FZ_Greatest_Common_Divisor;
88
89 end FZ_GCD;
```