Nimber arithmetic: Difference between revisions

=={{header|Delphi}}==

{{libheader| System.SysUtils}}

{{libheader| System.Math}}

{{Trans|Go}}

<lang Delphi>

program Nimber_arithmetic;

uses

System.SysUtils, System.Math;

Type

TFnop = record

fn: TFunc<Cardinal, Cardinal, Cardinal>;

op: string;

end;

// Highest power of two that divides a given number.

function hpo2(n: Cardinal): Cardinal;

begin

Result := n and (-n)

end;

// Base 2 logarithm of the highest power of 2 dividing a given number.

function lhpo2(n: Cardinal): Cardinal;

var

m: Cardinal;

begin

Result := 0;

m := hpo2(n);

while m mod 2 = 0 do

begin

m := m shr 1;

inc(Result);

end;

end;

// nim-sum of two numbers.

function nimsum(x, y: Cardinal): Cardinal;

begin

Result := x xor y;

end;

function nimprod(x, y: Cardinal): Cardinal;

var

h, xp, yp, comp: Cardinal;

begin

if (x < 2) or (y < 2) then

exit(x * y);

h := hpo2(x);

if x > h then

exit((nimprod(h, y) xor nimprod((x xor h), y)));

if hpo2(y) < y then

exit(nimprod(y, x)); // break y into powers of 2 by flipping operands

xp := lhpo2(x);

yp := lhpo2(y);

comp := xp and yp;

if comp = 0 then

exit(x * y); // no Fermat power in common

h := hpo2(comp);

// a Fermat number square is its sequimultiple

Result := nimprod(nimprod(x shr h, y shr h), 3 shl (h - 1));

end;

var

fnop: array [0 .. 1] of TFnop;

f: TFnop;

i, j, a, b: Cardinal;

begin

with fnop[0] do

begin

fn := nimsum;

op := '+';

end;

with fnop[1] do

begin

fn := nimprod;

op := '*';

end;

for f in fnop do

begin

write(' ', f.op, ' |');

for i := 0 to 15 do

Write(i:3);

Writeln;

Writeln('--- ', string.Create('-', 48));

for i := 0 to 15 do

begin

write(i:2, ' |');

for j := 0 to 15 do

write(f.fn(i, j):3);

Writeln;

end;

Writeln;

end;

a := 21508;

b := 42689;

Writeln(Format('%d + %d = %d', [a, b, nimsum(a, b)]));

Writeln(Format('%d * %d = %d', [a, b, nimprod(a, b)]));

readln;

end.</lang>