```   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_BitOp; use FZ_BitOp;
25 with FZ_Pred;  use FZ_Pred;
26
27
28 package body FZ_GCD is
29
30    -- Find Greatest Common Divisor (GCD) of X and Y.
31    -- Note that by convention, GCD(0, 0) = 0.
32    procedure FZ_Greatest_Common_Divisor(X      : in  FZ;
33                                         Y      : in  FZ;
34                                         Result : out FZ) is
35
36       -- Widths of X, Y, and Result are equal
37       subtype Width is Word_Index range X'Range;
38
39       -- Working buffers for GCD computation, initially equal to the inputs
40       A      : FZ(Width) := X;
41       B      : FZ(Width) := Y;
42
43       -- Evenness (negation of lowest bit) of A and B respectively
44       Ae, Be : WBool;
45
46       -- Common power-of-2 factor: incremented when Ae and Be are both 1
47       Twos   : Word := 0;
48
49       -- This flag is set when A and B are BOTH ODD
50       OO     : WBool;
51
52       -- |A - B|
53       D      : FZ(Width);
54
55       -- This flag is set iff A < B
56       A_lt_B : WBool;
57
58    begin
59
60       -- To converge, requires number of shots equal to (2 * FZ_Bitness) - 1:
61       for i in 1 .. (2 * FZ_Bitness(X)) - 1 loop
62
63          -- Whether A and B are currently BOTH ODD :
64          OO := FZ_OddP(A) and FZ_OddP(B);
65
66          -- D := |A - B|
67          FZ_Sub_Abs(X => A, Y => B, Difference => D, Underflow => A_lt_B);
68
69          -- IFF A,B both ODD, and A < B : B' := A ; otherwise no change :
70          FZ_Mux(X => B, Y => A, Result => B, Sel => OO and A_lt_B);
71
72          -- IFF A,B both ODD: A' := |A - B| ; otherwise no change :
73          FZ_Mux(X => A, Y => D, Result => A, Sel => OO);
74
75          -- If A is now EVEN: A := A >> 1; otherwise no change
76          Ae := 1 - FZ_OddP(A);
77          FZ_ShiftRight(A, A, WBit_Index(Ae));
78
79          -- If B is now EVEN: B := B >> 1; otherwise no change
80          Be := 1 - FZ_OddP(B);
81          FZ_ShiftRight(B, B, WBit_Index(Be));
82
83          -- If both A and B were even, increment the common power-of-two
84          Twos := Twos + (Ae and Be);
85
86       end loop;
87
88       -- Normally, B will contain the GCD, but in the (N,0) N > 0 case -- A.
89       -- The other variable will always equal 0. Hence, take Bitwise-OR(A,B):
90       FZ_Or(X => A, Y => B, Result => A);
91
92       -- Reintroduce the common power-of-2 factor stored in 'Twos'
93       FZ_Quiet_ShiftLeft(N => A, ShiftedN => A, Count => Indices(Twos));
94
95       -- Output final result -- the GCD.
96       Result := A;
97
98    end FZ_Greatest_Common_Divisor;
99
100 end FZ_GCD;
```