例如要精确到小数点后面多少位或者100位的数字相加减
下面是一个单元：
huge numbers
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.