compile time Least Common Multiple, was Re: Ada and Internet stuff

[tmoran@acm.org]

This code may be so bizarre as to be whimsical, but what the heck.

Problem: Given that Stream_Element'size is not necessarily 8 bits,
but can be assumed to be no greater than 128 bits, declare a
Stream_Element_Array subtype that is the shortest possible, but
a multiple of 24 bits.

-- Finding the GCD of 24 and any number from 1 .. 128 takes at most 5
-- iterations.

Larger1 : constant
  := boolean'pos(24 > Stream_Element'size) * 24
     + boolean'pos(24 <= Stream_Element'size) * Stream_Element'size;
Smaller1 : constant
  := boolean'pos(24 > Stream_Element'size) * Stream_Element'size
     + boolean'pos(24 <= Stream_Element'size) * 24;
R1 : constant := Larger1 mod Smaller1;
Is_Zero1 : constant := boolean'pos(R1 = 0);
GCD1 : constant := Is_Zero1 * Smaller1;

-- Once R(n) = 0, then Is_Zero(n) = 1 and Smaller(n+1) = 0
-- so R(n+1) = Larger(n+1) mod 1 = 0.  ie all following R(n+1 ...) = 0
-- and exactly one of Is_Zero(i) is non-zero

Larger2 : constant := Smaller1;
Smaller2 : constant := R1;
R2 : constant := Larger2 mod (Smaller2 + Is_Zero1);
Is_Zero2 : constant := boolean'pos(R2 = 0);
GCD2 : constant := Is_Zero2 * Smaller2;

Larger3 : constant := Smaller2;
Smaller3 : constant := R2;
R3 : constant := Larger3 mod (Smaller3 + Is_Zero2);
Is_Zero3 : constant := boolean'pos(R3 = 0);
GCD3 : constant := Is_Zero3 * Smaller3;

Larger4 : constant := Smaller3;
Smaller4 : constant := R3;
R4 : constant := Larger4 mod (Smaller4 + Is_Zero3);
Is_Zero4 : constant := boolean'pos(R4 = 0);
GCD4 : constant := Is_Zero4 * Smaller4;

Larger5 : constant := Smaller4;
Smaller5 : constant := R4;
R5 : constant := Larger5 mod (Smaller5 + Is_Zero4);
Is_Zero5 : constant := boolean'pos(R5 = 0);
GCD5 : constant := Is_Zero5 * Smaller5;

GCD : constant := GCD1+GCD2+GCD3+GCD4+GCD5;
-- will give the Greatest Common Divisor.

-- LCM is the least common multiple of 24 bits and Stream_Element'size
LCM : constant := 24*Stream_Element'size/GCD;

subtype To_Encode is Stream_Element_Array(1 .. LCM/Stream_Element'size);
-- To_Encode'size = LCM