By: Abe Timmerman; Alkmaar, The Netherlands
Send improvements to: A.Timmerman@beta.hsholland.nl

This unit uses an array of bytes to represent a LARGE number. The number is binairy-stored in the array, with the Least Significant Byte (LSB) first and the Most Significant Byte (MSB) last, like all Intel-integer types.

Arithmetic is not 10-based or 2-based, but 256-based, so that each byte represents one (1) digit.

The HugeInttype numbers are Signed Numbers.

When Compiled with the R+ directive, ADD and MUL wil generate an "Arithmetic Overflow Error" (RunError(215)) when needed. Otherwise use the "HugeIntCarry" variable.

Use the "HugeIntDiv0" variable to check on division by zero.

Use {$DEFINE HugeInt_xx } or "Conditional defines" from the "Compiler options" for sizing, where xx is 64, 32 or 16, otherwhise HugeIntSize will be set to 8 bytes.
 

unit HugeInts;
interface

const
{$IFDEF HugeInt_64 }
  HugeIntSize = 64;
{$ELSE}{$IFDEF HugeInt_32 }
  HugeIntSize = 32;
{$ELSE}{$IFDEF HugeInt_16 }
  HugeIntSize = 16;
{$ELSE}
  HugeIntSize = 8;
{$ENDIF}{$ENDIF}{$ENDIF}
  HugeIntMSB  = HugeIntSize-1;

type
  HugeInt = array[0..HugeIntMSB] of Byte;

const
  HugeIntCarry: Boolean = False;
  HugeIntDiv0:  Boolean = False;
 

procedure HugeInt_Min(var a: HugeInt);                 { a := -a }
procedure HugeInt_Inc(var a: HugeInt);                 { a := a + 1 }
procedure HugeInt_Dec(var a: HugeInt);                 { a := a - 1 }
procedure HugeInt_Add(a, b: HugeInt; var R: HugeInt);  { R := a + b }
procedure HugeInt_Sub(a, b: HugeInt; var R: HugeInt);  { R := a - b }
procedure HugeInt_Mul(a, b: HugeInt; var R: HugeInt);  { R := a * b }
procedure HugeInt_Div(a, b: HugeInt; var R: HugeInt);  { R := a div b }
procedure HugeInt_Mod(a, b: HugeInt; var R: HugeInt);  { R := a mod b }

function HugeInt_IsNeg(a: HugeInt): Boolean;
function HugeInt_Zero(a: HugeInt): Boolean;
function HugeInt_Odd(a: HugeInt): Boolean;
function HugeInt_Comp(a, b: HugeInt): Integer;          {-1:a<b; 0; 1:a>b
}
procedure HugeInt_Copy(Src: HugeInt; var Dest: HugeInt);{ Dest := Src }

procedure String2HugeInt(AString: string; var a: HugeInt);
procedure Integer2HugeInt(AInteger: Integer; var a: HugeInt);
procedure HugeInt2String(a: HugeInt; var S: string);

                             implementation

procedure HugeInt_Copy(Src: HugeInt; var Dest: HugeInt);
{ Dest := Src }
begin
  Move(Src, Dest, SizeOf(HugeInt));
end;{ HugeInt_Copy }

function HugeInt_IsNeg(a: HugeInt): Boolean;
begin
  HugeInt_IsNeg := a[HugeIntMSB] and $80 > 0;
end;{ HugeInt_IsNeg }

function HugeInt_Zero(a: HugeInt): Boolean;
var i: Integer;
begin
  HugeInt_Zero := False;
  for i := 0 to HugeIntMSB do
    if a[i] <> 0 then Exit;
  HugeInt_Zero := True;
end;{ HugeInt_Zero }

function HugeInt_Odd(a: HugeInt): Boolean;
begin
  HugeInt_Odd := a[0] and 1 > 0;
end;{ HugeInt_Odd }

function HugeInt_HCD(a: HugeInt): Integer;
var i: Integer;
begin
  i := HugeIntMSB;
  while (i > 0) and (a[i] = 0) do Dec(i);
  HugeInt_HCD := i;
end;{ HugeInt_HCD }

procedure HugeInt_SHL(var a: HugeInt; Digits: Integer);
{ Shift "a" "Digits", digits (bytes) to the left,
  "Digits" bytes will 'fall off' on the MSB side
  Fill the LSB side with 0's }
var t: Integer;
b: HugeInt;
begin
  if Digits > HugeIntMSB then
    FillChar(a, SizeOf(HugeInt), 0)
  else if Digits > 0 then
    begin
      Move(a[0], a[Digits], HugeIntSize-Digits);
      FillChar(a[0], Digits, 0);
    end;{ else if }
end;{ HugeInt_SHL }

procedure HugeInt_SHR(var a: HugeInt; Digits: Integer);
var t: Integer;
begin
  if Digits > HugeIntMSB then
    FillChar(a, SizeOf(HugeInt), 0)
  else if Digits > 0 then
    begin
      Move(a[Digits], a[0], HugeIntSize-Digits);
      FillChar(a[HugeIntSize-Digits], Digits, 0);
    end;{ else if }
end;{ HugeInt_SHR }

procedure HugeInt_Inc(var a: HugeInt);
{ a := a + 1 }
var
  i: Integer;
  h: Word;
begin
  i := 0; h := 1;
  repeat
    h := h + a[i];
    a[i] := Lo(h);
    h := Hi(h);
    Inc(i);
  until (i > HugeIntMSB) or (h = 0);
  HugeIntCarry := h > 0;
  {$IFOPT R+ }
    if HugeIntCarry then RunError(215);
  {$ENDIF}
end;{ HugeInt_Inc }

procedure HugeInt_Dec(var a: HugeInt);
{ a := a - 1 }
var Minus_1: HugeInt;
begin
  { this is the easy way out }
  FillChar(Minus_1, SizeOf(HugeInt), $FF); { -1 }
  HugeInt_Add(a, Minus_1, a);
end;{ HugeInt_Dec }

procedure HugeInt_Min(var a: HugeInt);
{ a := -a }
var i: Integer;
begin
  for i := 0 to HugeIntMSB do
    a[i] := not a[i];
  HugeInt_Inc(a);
end;{ HugeInt_Min }

function HugeInt_Comp(a, b: HugeInt): Integer;
{ a = b: ==0; a > b: ==1; a < b: ==-1 }
var
  A_IsNeg, B_IsNeg: Boolean;
  i:                Integer;
begin
  A_IsNeg := HugeInt_IsNeg(a);
  B_IsNeg := HugeInt_IsNeg(b);
  if A_IsNeg xor B_IsNeg then
    if A_IsNeg then HugeInt_Comp := -1
    else HugeInt_Comp := 1
  else
    begin
      if A_IsNeg then HugeInt_Min(a);
      if B_IsNeg then HugeInt_Min(b);
      i := HugeIntMSB;
      while (i > 0) and (a[i] = b[i]) do Dec(i);
      if A_IsNeg then { both negative! }
        if a[i] > b[i] then HugeInt_Comp := -1
        else if a[i] < b[i] then HugeInt_Comp := 1
        else HugeInt_Comp := 0
      else { both positive }
        if a[i] > b[i] then HugeInt_Comp := 1
        else if a[i] < b[i] then HugeInt_Comp := -1
        else HugeInt_Comp := 0;
    end;{ else }
end;{ HugeInt_Comp }

procedure HugeInt_Add(a, b: HugeInt; var R: HugeInt);
{ R := a + b }
var
  i: Integer;
  h: Word;
begin
  h := 0;
  for i := 0 to HugeIntMSB do
    begin
      h := h + a[i] + b[i];
      R[i] := Lo(h);
      h := Hi(h);
    end;{ for }
  HugeIntCarry := h > 0;
  {$IFOPT R+ }
    if HugeIntCarry then RunError(215);
  {$ENDIF}
end;{ HugeInt_Add }

procedure HugeInt_Sub(a, b: HugeInt; var R: HugeInt);
{ R := a - b }
var
  i: Integer;
  h: Word;
begin
  HugeInt_Min(b);
  HugeInt_Add(a, b, R);
end;{ HugeInt_Sub }

procedure HugeInt_Mul(a, b: HugeInt; var R: HugeInt);
{ R := a * b }
var
  i, j, k:          Integer;
  A_end, B_end:     Integer;
  A_IsNeg, B_IsNeg: Boolean;
  h:                Word;
begin
  A_IsNeg := HugeInt_IsNeg(a);
  B_IsNeg := HugeInt_IsNeg(b);
  if A_IsNeg then HugeInt_Min(a);
  if B_IsNeg then HugeInt_Min(b);
  A_End := HugeInt_HCD(a);
  B_End := HugeInt_HCD(b);
  FillChar(R, SizeOf(R), 0);
  HugeIntCarry := False;
  for i := 0 to A_end do
    begin
      h := 0;
      for j:= 0 to B_end do
        if (i + j) < HugeIntSize then
          begin
            h := h + R[i+j] + a[i] * b[j];
            R[i+j] := Lo(h);
            h := Hi(h);
          end;{ if }
      k := i + B_End + 1;
      while (k < HugeIntSize) and (h > 0) do
        begin
          h := h + R[k];
          R[k] := Lo(h);
          h := Hi(h);
          Inc(k);
        end;{ while }
      HugeIntCarry := h > 0;
     {$IFOPT R+}
        if HugeIntCarry then RunError(215);
     {$ENDIF}
    end;{ for }
  { if all's well... }
  if A_IsNeg xor B_IsNeg then HugeInt_Min(R);
end;{ HugeInt_Mul }

procedure HugeInt_DivMod(var a: HugeInt; b: HugeInt; var R: HugeInt);
{ R := a div b  a := a mod b }
var
  MaxShifts, s, q:  Integer;
  d, e:             HugeInt;
  A_IsNeg, B_IsNeg: Boolean;

begin
  if HugeInt_Zero(b) then
    begin
      HugeIntDiv0 := True;
      Exit;
    end{ if }
  else HugeIntDiv0 := False;
  A_IsNeg := HugeInt_IsNeg(a);
  B_IsNeg := HugeInt_IsNeg(b);
  if A_IsNeg then HugeInt_Min(a);
  if B_IsNeg then HugeInt_Min(b);
  if HugeInt_Comp(a, b) < 0 then
    { a<b; no need to divide }
    FillChar(R, SizeOf(R), 0)
  else
    begin
      FillChar(R, SizeOf(R), 0);
      repeat
        Move(b, d, SizeOf(HugeInt));
        { first work out the number of shifts }
        MaxShifts := HugeInt_HCD(a) - HugeInt_HCD(b);
        s := 0;
        while (s <= MaxShifts) and (HugeInt_Comp(a, d) >= 0) do
          begin
            Inc(s);
            HugeInt_SHL(d, 1);
          end;{ while }
        Dec(s);
        { Make a new copy of b }
        Move(b, d, SizeOf(HugeInt));
        { Shift d as needed }
        HugeInt_ShL(d, S);
        { Use e = -d for addition, faster then  subtracting d }
        Move(d, e, SizeOf(HugeInt));
        HugeInt_Min(e);
        Q := 0;
        { while a >= d do a := a+-d and keep trek of # in Q}
        while HugeInt_Comp(a, d) >= 0 do
          begin
            HugeInt_Add(a, e, a);
            Inc(Q);
          end;{ while }
        { OOps!, one too many subtractions; correct }
        if HugeInt_IsNeg(a) then
          begin
            HugeInt_Add(a, d, a);
            Dec(Q);
          end;{ if }
        HugeInt_SHL(R, 1);
        R[0] := Q;
      until HugeInt_Comp(a, b) < 0;
      if A_IsNeg xor B_IsNeg then HugeInt_Min(R);
    end;{ else }
end;{ HugeInt_Div }

procedure HugeInt_DivMod100(var a: HugeInt; var R: Integer);
{ This works on positive numbers only
  256-Based division: R := a mod 100; a:= a div 100; }
var
  Q: HugeInt;
  S: Integer;
begin
  R := 0; FillChar(Q, SizeOf(Q), 0);
  S := HugeInt_HCD(a);
  repeat
    r := 256*R + a[S];
    HugeInt_SHL(Q, 1);
    Q[0] := R div 100;
    R := R mod 100;
    Dec(S);
  until S < 0;
  Move(Q, a, SizeOf(Q));
end;{  HugeInt_DivMod100 }

procedure HugeInt_Div(a, b: HugeInt; var R: HugeInt);
begin
  HugeInt_DivMod(a, b, R);
end;{ HugeInt_Div }

procedure HugeInt_Mod(a, b: HugeInt; var R: HugeInt);
begin
  HugeInt_DivMod(a, b, R);
  Move(a, R, SizeOf(HugeInt));
end;{ HugeInt_Mod }

procedure HugeInt2String(a: HugeInt; var S: string);
  function Str100(i: Integer): string;
  begin
    Str100 := Chr(i div 10 + Ord('0')) + Chr(i mod 10 + Ord('0'));
  end;{ Str100 }
var
  R:      Integer;
  Is_Neg: Boolean;
begin
  S := '';
  Is_Neg := HugeInt_IsNeg(a);
  if Is_Neg then HugeInt_Min(a);
  repeat
    HugeInt_DivMod100(a, R);
    Insert(Str100(R), S, 1);
  until HugeInt_Zero(a) or (Length(S) = 254);
  while (Length(S) > 1) and (S[1] = '0') do Delete(S, 1, 1);
  if Is_Neg then Insert('-', S, 1);
end;{ HugeInt2String }

procedure String_DivMod256(var S: string; var R: Integer);
{ This works on Positive numbers Only
  10(00)-based division: R := S mod 256; S := S div 256 }
var Q: string;
begin
  FillChar(Q, SizeOf(Q), 0);
  R := 0;
  while S <> '' do
    begin
      R := 10*R + Ord(S[1]) - Ord('0'); Delete(S, 1, 1);
      Q := Q + Chr(R div 256 + Ord('0'));
      R := R  mod 256;
    end;{ while }
  while (Q <> '') and (Q[1] = '0') do Delete(Q, 1, 1);
  S := Q;
end;{ String_DivMod256 }

procedure String2HugeInt(AString: string; var a: HugeInt);
var
  i, h:   Integer;
  Is_Neg: Boolean;
begin
  if AString = '' then AString := '0';
  Is_Neg := AString[1] = '-';
  if Is_Neg then Delete(Astring, 1, 1);
  i := 0;
  while (AString <> '') and (i <= HugeIntMSB) do
    begin
      String_DivMod256(AString, h);
      a[i] := h;
      Inc(i);
    end;{ while }
  if Is_Neg then HugeInt_Min(a);
end;{ String2HugeInt }

procedure Integer2HugeInt(AInteger: Integer; var a: HugeInt);
var Is_Neg: Boolean;
begin
  Is_Neg := AInteger < 0;
  if Is_Neg then AInteger := -AInteger;
  FillChar(a, SizeOf(HugeInt), 0);
  Move(AInteger, a, SizeOf(Integer));
  if Is_Neg then HugeInt_Min(a);
end;{ Integer2HugeInt }

end.