File : fz_gcd.adb
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 -- --
16 -- See also http://trilema.com/2015/a-new-software-licensing-paradigm . --
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;