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ffa_ch15_gcd.kv         1 ------------------------------------------------------------------------------
ffa_ch15_gcd.kv         2 ------------------------------------------------------------------------------
ffa_ch15_gcd.kv         3 -- This file is part of 'Finite Field Arithmetic', aka 'FFA'.               --
ffa_ch15_gcd.kv         4 --                                                                          --
ffa_ch15_gcd.kv         5 -- (C) 2019 Stanislav Datskovskiy ( www.loper-os.org )                      --
ffa_ch15_gcd.kv         6 -- http://wot.deedbot.org/17215D118B7239507FAFED98B98228A001ABFFC7.html     --
ffa_ch15_gcd.kv         7 --                                                                          --
ffa_ch15_gcd.kv         8 -- You do not have, nor can you ever acquire the right to use, copy or      --
ffa_ch15_gcd.kv         9 -- distribute this software ; Should you use this software for any purpose, --
ffa_ch15_gcd.kv        10 -- or copy and distribute it to anyone or in any manner, you are breaking   --
ffa_ch15_gcd.kv        11 -- the laws of whatever soi-disant jurisdiction, and you promise to         --
ffa_ch15_gcd.kv        12 -- continue doing so for the indefinite future. In any case, please         --
ffa_ch15_gcd.kv        13 -- always : read and understand any software ; verify any PGP signatures    --
ffa_ch15_gcd.kv        14 -- that you use - for any purpose.                                          --
ffa_ch15_gcd.kv        15 --                                                                          --
ffa_ch15_gcd.kv        16 -- See also http://trilema.com/2015/a-new-software-licensing-paradigm .     --
ffa_ch15_gcd.kv        17 ------------------------------------------------------------------------------
ffa_ch15_gcd.kv        18 
ffa_ch15_gcd.kv        19 with Words;    use Words;
ffa_ch15_gcd.kv        20 with FZ_Basic; use FZ_Basic;
ffa_ch15_gcd.kv        21 with FZ_Shift; use FZ_Shift;
ffa_ch15_gcd.kv        22 with FZ_QShft; use FZ_QShft;
ffa_ch15_gcd.kv        23 with FZ_Arith; use FZ_Arith;
ffa_ch15_gcd.kv        24 with FZ_Pred;  use FZ_Pred;
ffa_ch15_gcd.kv        25 
ffa_ch15_gcd.kv        26 
ffa_ch15_gcd.kv        27 package body FZ_GCD is
ffa_ch15_gcd.kv        28    
ffa_ch15_gcd.kv        29    -- Find Greatest Common Divisor (GCD) of X and Y.
ffa_ch15_gcd.kv        30    -- Note that by convention, GCD(0, 0) = 0.
ffa_ch15_gcd.kv        31    procedure FZ_Greatest_Common_Divisor(X      : in  FZ;
ffa_ch15_gcd.kv        32                                         Y      : in  FZ;
ffa_ch15_gcd.kv        33                                         Result : out FZ) is
ffa_ch15_gcd.kv        34       
ffa_ch15_gcd.kv        35       -- Widths of X, Y, and Result are equal
ffa_ch15_gcd.kv        36       subtype Width is Word_Index range X'Range;
ffa_ch15_gcd.kv        37       
ffa_ch15_gcd.kv        38       -- Working buffers for GCD computation, initially equal to the inputs
ffa_ch15_gcd.kv        39       A      : FZ(Width) := X; -- GCD will appear in A in the end
ffa_ch15_gcd.kv        40       B      : FZ(Width) := Y;
ffa_ch15_gcd.kv        41       
ffa_ch15_gcd.kv        42       -- Evenness (negation of lowest bit) of A and B respectively
ffa_ch15_gcd.kv        43       Ae, Be : WBool;
ffa_ch15_gcd.kv        44       
ffa_ch15_gcd.kv        45       -- Common power-of-2 factor
ffa_ch15_gcd.kv        46       Twos   : Word := 0;
ffa_ch15_gcd.kv        47       
ffa_ch15_gcd.kv        48       -- |A - B|
ffa_ch15_gcd.kv        49       D      : FZ(Width);
ffa_ch15_gcd.kv        50       
ffa_ch15_gcd.kv        51       -- This flag is set iff A < B
ffa_ch15_gcd.kv        52       A_lt_B : WBool;
ffa_ch15_gcd.kv        53       
ffa_ch15_gcd.kv        54    begin
ffa_ch15_gcd.kv        55       
ffa_ch15_gcd.kv        56       -- For convergence, requires number of shots equal to 2 * FZ_Bitness:
ffa_ch15_gcd.kv        57       for i in 1 .. 2 * FZ_Bitness(X) loop
ffa_ch15_gcd.kv        58          
ffa_ch15_gcd.kv        59          -- If A is even, A := A >> 1; otherwise A := A
ffa_ch15_gcd.kv        60          Ae := 1 - FZ_OddP(A);
ffa_ch15_gcd.kv        61          FZ_ShiftRight(A, A, WBit_Index(Ae));
ffa_ch15_gcd.kv        62          
ffa_ch15_gcd.kv        63          -- If B is even, B := B >> 1; otherwise B := B
ffa_ch15_gcd.kv        64          Be := 1 - FZ_OddP(B);
ffa_ch15_gcd.kv        65          FZ_ShiftRight(B, B, WBit_Index(Be));
ffa_ch15_gcd.kv        66          
ffa_ch15_gcd.kv        67          -- If both A and B were even, increment the common power-of-two
ffa_ch15_gcd.kv        68          Twos := Twos + (Ae and Be);
ffa_ch15_gcd.kv        69          
ffa_ch15_gcd.kv        70          -- D := |A - B|
ffa_ch15_gcd.kv        71          FZ_Sub_Abs(X => A, Y => B, Difference => D, Underflow => A_lt_B);
ffa_ch15_gcd.kv        72          
ffa_ch15_gcd.kv        73          -- B' := min(A, B)
ffa_ch15_gcd.kv        74          FZ_Mux(X => B, Y => A, Result => B, Sel => A_lt_B);
ffa_ch15_gcd.kv        75          
ffa_ch15_gcd.kv        76          -- A' := |A - B|
ffa_ch15_gcd.kv        77          A := D;
ffa_ch15_gcd.kv        78          
ffa_ch15_gcd.kv        79       end loop;
ffa_ch15_gcd.kv        80       
ffa_ch15_gcd.kv        81       -- Reintroduce the common power-of-2 factor stored in 'Twos'
ffa_ch15_gcd.kv        82       FZ_Quiet_ShiftLeft(N => A, ShiftedN => A, Count => Indices(Twos));
ffa_ch15_gcd.kv        83       
ffa_ch15_gcd.kv        84       -- Output final result
ffa_ch15_gcd.kv        85       Result := A;
ffa_ch15_gcd.kv        86       
ffa_ch15_gcd.kv        87    end FZ_Greatest_Common_Divisor;
ffa_ch15_gcd.kv        88    
ffa_ch15_gcd.kv        89 end FZ_GCD;