By: Abe Timmerman; Alkmaar, The Netherlands
Send improvements to: A.Timmerman@beta.hsholland.nlThis 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< 0; 1:a>
}
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.
{ This code came from Lloyd's help file! }
From: "Bobby W. Jones II"<ctech@earthlink.net>
Another alternative is to create a function like the one native in Clipper, called PadL(string,width,character), like the following:
function TfrmFunc.PadL(cVal: string; nWide: integer; cChr: char): string;
var
i1,nStart: integer;
begin
if length(cVal) < nWide then
begin
nStart:=length(cVal);
for i1:=nStart to nWide-1 do cVal:=cChar+cVal;
end;
PadL:=cVal;
end;
This then can be called with any string that you want to make a specific length. As with your example, PadL(A,length(B),'0'); It also gives you the flexibility to pad with any character and to be able to set a fixed length (like making sure your text counters remain the same width -- PadL(A,6,'0');
From: "Earl F. Glynn" <EarlGlynn@postoffice.worldnet.att.net>
the Delphi 1.0 UNIT follows (slight changes must be made for Delphi 2.0):
UNIT CRC32;
{CRC32 calculates a cyclic redundancy code (CRC), known as CRC-32, using
a byte-wise algorithm.
(C) Copyright 1989, 1995-1996 Earl F. Glynn, Overland Park, KS.
All Rights Reserved.
This UNIT was derived from the CRCT FORTRAN 77 program given in
"Byte-wise CRC Calculations" by Aram Perez in IEEE Micro, June 1983,
pp. 40-50. The constants here are for the CRC-32 generator polynomial,
as defined in the Microsoft Systems Journal, March 1995, pp. 107-108
This CRC algorithm emphasizes speed at the expense of the 512 element
lookup table.}
INTERFACE
PROCEDURE CalcCRC32 (p: pointer; nbyte: WORD; VAR CRCvalue: LongInt);
PROCEDURE CalcFileCRC32 (FromName: STRING; VAR CRCvalue: LongInt;
VAR IOBuffer: pointer; BufferSize: WORD; VAR TotalBytes: LongInt;
VAR error: WORD);
IMPLEMENTATION
CONST
table: ARRAY[0..255] OF LongInt =
($00000000, $77073096, $EE0E612C, $990951BA,
$076DC419, $706AF48F, $E963A535, $9E6495A3,
$0EDB8832, $79DCB8A4, $E0D5E91E, $97D2D988,
$09B64C2B, $7EB17CBD, $E7B82D07, $90BF1D91,
$1DB71064, $6AB020F2, $F3B97148, $84BE41DE,
$1ADAD47D, $6DDDE4EB, $F4D4B551, $83D385C7,
$136C9856, $646BA8C0, $FD62F97A, $8A65C9EC,
$14015C4F, $63066CD9, $FA0F3D63, $8D080DF5,
$3B6E20C8, $4C69105E, $D56041E4, $A2677172,
$3C03E4D1, $4B04D447, $D20D85FD, $A50AB56B,
$35B5A8FA, $42B2986C, $DBBBC9D6, $ACBCF940,
$32D86CE3, $45DF5C75, $DCD60DCF, $ABD13D59,
$26D930AC, $51DE003A, $C8D75180, $BFD06116,
$21B4F4B5, $56B3C423, $CFBA9599, $B8BDA50F,
$2802B89E, $5F058808, $C60CD9B2, $B10BE924,
$2F6F7C87, $58684C11, $C1611DAB, $B6662D3D,
$76DC4190, $01DB7106, $98D220BC, $EFD5102A,
$71B18589, $06B6B51F, $9FBFE4A5, $E8B8D433,
$7807C9A2, $0F00F934, $9609A88E, $E10E9818,
$7F6A0DBB, $086D3D2D, $91646C97, $E6635C01,
$6B6B51F4, $1C6C6162, $856530D8, $F262004E,
$6C0695ED, $1B01A57B, $8208F4C1, $F50FC457,
$65B0D9C6, $12B7E950, $8BBEB8EA, $FCB9887C,
$62DD1DDF, $15DA2D49, $8CD37CF3, $FBD44C65,
$4DB26158, $3AB551CE, $A3BC0074, $D4BB30E2,
$4ADFA541, $3DD895D7, $A4D1C46D, $D3D6F4FB,
$4369E96A, $346ED9FC, $AD678846, $DA60B8D0,
$44042D73, $33031DE5, $AA0A4C5F, $DD0D7CC9,
$5005713C, $270241AA, $BE0B1010, $C90C2086,
$5768B525, $206F85B3, $B966D409, $CE61E49F,
$5EDEF90E, $29D9C998, $B0D09822, $C7D7A8B4,
$59B33D17, $2EB40D81, $B7BD5C3B, $C0BA6CAD,
$EDB88320, $9ABFB3B6, $03B6E20C, $74B1D29A,
$EAD54739, $9DD277AF, $04DB2615, $73DC1683,
$E3630B12, $94643B84, $0D6D6A3E, $7A6A5AA8,
$E40ECF0B, $9309FF9D, $0A00AE27, $7D079EB1,
$F00F9344, $8708A3D2, $1E01F268, $6906C2FE,
$F762575D, $806567CB, $196C3671, $6E6B06E7,
$FED41B76, $89D32BE0, $10DA7A5A, $67DD4ACC,
$F9B9DF6F, $8EBEEFF9, $17B7BE43, $60B08ED5,
$D6D6A3E8, $A1D1937E, $38D8C2C4, $4FDFF252,
$D1BB67F1, $A6BC5767, $3FB506DD, $48B2364B,
$D80D2BDA, $AF0A1B4C, $36034AF6, $41047A60,
$DF60EFC3, $A867DF55, $316E8EEF, $4669BE79,
$CB61B38C, $BC66831A, $256FD2A0, $5268E236,
$CC0C7795, $BB0B4703, $220216B9, $5505262F,
$C5BA3BBE, $B2BD0B28, $2BB45A92, $5CB36A04,
$C2D7FFA7, $B5D0CF31, $2CD99E8B, $5BDEAE1D,
$9B64C2B0, $EC63F226, $756AA39C, $026D930A,
$9C0906A9, $EB0E363F, $72076785, $05005713,
$95BF4A82, $E2B87A14, $7BB12BAE, $0CB61B38,
$92D28E9B, $E5D5BE0D, $7CDCEFB7, $0BDBDF21,
$86D3D2D4, $F1D4E242, $68DDB3F8, $1FDA836E,
$81BE16CD, $F6B9265B, $6FB077E1, $18B74777,
$88085AE6, $FF0F6A70, $66063BCA, $11010B5C,
$8F659EFF, $F862AE69, $616BFFD3, $166CCF45,
$A00AE278, $D70DD2EE, $4E048354, $3903B3C2,
$A7672661, $D06016F7, $4969474D, $3E6E77DB,
$AED16A4A, $D9D65ADC, $40DF0B66, $37D83BF0,
$A9BCAE53, $DEBB9EC5, $47B2CF7F, $30B5FFE9,
$BDBDF21C, $CABAC28A, $53B39330, $24B4A3A6,
$BAD03605, $CDD70693, $54DE5729, $23D967BF,
$B3667A2E, $C4614AB8, $5D681B02, $2A6F2B94,
$B40BBE37, $C30C8EA1, $5A05DF1B, $2D02EF8D);
TYPE
buffer = ARRAY[1..65521] OF BYTE; {largest buffer that can be}
{allocated on heap }
VAR
i: WORD;
q: ^buffer;
PROCEDURE CalcCRC32 (p: pointer; nbyte: WORD; VAR CRCvalue: LongInt);
{The following is a little cryptic (but executes very quickly).
The algorithm is as follows:
1. exclusive-or the input byte with the low-order portion of
the CRC register to get an INDEX
2. shift the CRC register eight bits to the right
3. exclusive-or the CRC register with the contents of
Table[INDEX]
4. repeat steps 1 through 3 for all bytes}
BEGIN
q := p;
FOR i := 1 TO nBYTE DO
CRCvalue := (CRCvalue SHR 8) XOR
Table[ q^[i] XOR (CRCvalue AND $000000FF) ]
END {CalcCRC32};
PROCEDURE CalcFileCRC32 (FromName: STRING; VAR CRCvalue: LongInt;
VAR IOBuffer: pointer; BufferSize: WORD; VAR TotalBytes: LongInt;
VAR error: WORD);
VAR
BytesRead: WORD;
FromFile : FILE;
i : WORD;
BEGIN
FileMode := 0; {Turbo default is 2 for R/W; 0 is for R/O}
CRCValue := $FFFFFFFF;
ASSIGN (FromFile,FromName);
{$I-} RESET (FromFile,1); {$I+}
error := IOResult;
IF error = 0
THEN BEGIN
TotalBytes := 0;
REPEAT
BlockRead (FromFile,IOBuffer^,BufferSize,BytesRead);
CalcCRC32 (IOBuffer,BytesRead,CRCvalue);
INC (TotalBytes, BytesRead)
UNTIL BytesRead = 0;
CLOSE (FromFile)
END;
CRCvalue := NOT CRCvalue
END {CalcFileCRC32};
END {CRC}.
Paul Cunningham (pjcunningham@cix.compulink.co.uk)
Question[
This may sound trivial, but how do you raise a value to a power?
eg). 2^12 = 4095
]
The question is not that trivial. The trouble is that the power function
is not that simple. Several distinct situations need to be considered for
the function Power(X, N) i.e X^N.
interface
type
EPowerException = class(Exception)
end;
implementation
function Power(X, N : real) : extended;
var
t : longint;
r : real;
isInteger : boolean;
begin
if N = 0 then begin
result := 1.0;
exit;
end;
if X = 1.0 then begin
result := 1.0;
exit;
end;
if X = 0.0 then begin
if N > 0.0 then
begin
result := 0.0;
exit;
end
else
raise EPowerException.Create('Infinite Result');
end;
if (X > 0) then
try
result := exp(N * ln(X));
exit;
except
raise EPowerException.Create('Overflow/Underflow Result');
end;
{ X is negative but we still may compute the result if n is an integer}
{ try and get integer portion of n into a longint, it will be quicker to
} { compute odd n}
try
t := trunc(n);
if (n - t) = 0 then
isInteger := true
else
isInteger := False;
except
{Bit superfluous as result will probably underflow/overflow anyway}
r := int(n);
if (n - r) = 0 then
begin
isInteger := true;
if frac(r/2) = 0.5 then
t := 1
else
t := 2;
end
else
isInteger := False;
end;
if isInteger then
begin
{n is an integer}
if odd(t) then
{n is odd}
try
result := -exp(N * ln(-X));
exit;
except
raise EPowerException.Create('Overflow/Underflow Result');
end
else
{n is even}
try
result := exp(N * ln(-X));
exit;
except
raise EPowerException.Create('Overflow/Underflow Result');
end;
end
else
raise EPowerException.Create('Complex Result');
end;
unit uNum2Str;
// Possible enhancements
// Move strings out to resource files
// Put in a general num2str utility
interface
function Num2Dollars( dNum: double ) : String;
implementation
uses SysUtils;
function LessThan99( dNum: double ) : String; forward;
// floating point modulus
function FloatMod( i,j: double ): double;
begin
result := i - (Int(i/j) * j);
end;
function Hundreds( dNum: double ) : String;
var
workVar: double;
begin
if ( dNum < 100 ) or ( dNum > 999 ) then
raise Exception.Create( 'hundreds range exceeded' );
result := '';
workVar := Int( dNum / 100 );
if workVar > 0 then
result := LessThan99(workVar) + ' Hundred';
end;
function OneToNine( dNum: Double ) : String;
begin
if ( dNum < 1 ) or (dNum > 9 ) then
raise exception.create( 'onetonine: value out of range' );
result := 'woops';
if dNum = 1 then result := 'One'
else if dNum = 2 then result := 'Two'
else if dNum = 3 then result := 'Three'
else if dNum = 4 then result := 'Four'
else if dNum = 5.0 then result := 'Five'
else if dNum = 6 then result := 'Six'
else if dNum = 7 then result := 'Seven'
else if dNum = 8 then result := 'Eight'
else if dNum = 9 then result := 'Nine';
end;
function ZeroTo19( dNum: double ) : String;
begin
if (dNum < 0) or (dNum > 19) then
raise Exception.Create( 'Bad value in dNum' );
result := '';
if dNum = 0 then result := 'Zero'
else if (dNum >= 1) and (dNum <= 9) then result := OneToNine( dNum )
else if dNum = 10 then result := 'Ten'
else if dNum = 11 then result := 'Eleven'
else if dNum = 12 then result := 'Twelve'
else if dNum = 13 then result := 'Thirteen'
else if dNum = 14 then result := 'Fourteen'
else if dNum = 15 then result := 'Fifteen'
else if dNum = 16 then result := 'Sixteen'
else if dNum = 17 then result := 'Seventeen'
else if dNum = 18 then result := 'Eighteen'
else if dNum = 19 then result := 'Nineteen'
else result := 'woops!';
end;
function TwentyTo99( dNum: double ) : String;
var
BigNum: String;
begin
if ( dNum < 20 ) or ( dNum > 99 ) then
raise exception.Create( 'TwentyTo99: dNum out of range!' );
BigNum := 'woops';
if dNum >= 90 then BigNum := 'Ninety'
else if dNum >= 80 then BigNum := 'Eighty'
else if dNum >= 70 then BigNum := 'Seventy'
else if dNum >= 60 then BigNum := 'Sixty'
else if dNum >= 50 then BigNum := 'Fifty'
else if dNum >= 40 then BigNum := 'Forty'
else if dNum >= 30 then BigNum := 'Thirty'
else if dNum >= 20 then BigNum := 'Twenty';
// lose the big num
dNum := FloatMod( dNum, 10 );
if dNum > 0.00 then
result := BigNum + ' ' + OneToNine( dNum )
else
result := BigNum;
end;
function LessThan99( dNum: double ) : String;
begin
if dNum <= 19 then
result := ZeroTo19(dNum)
else
result := TwentyTo99(dNum);
end;
function Num2Dollars( dNum: double ) : String;
var
centsString: String;
cents: double;
workVar: double;
begin
result := '';
if dNum < 0 then
raise Exception.Create( 'Negative numbers not supported' );
if dNum > 999999999.99 then
raise Exception.Create( 'Num2Dollars only supports up to the millions at this point!' );
cents := (dNum - Int( dNum )) * 100.0;
if cents = 0.0 then
centsString := 'and 00/100 Dollars'
else if cents < 10 then
centsString := Format( 'and 0%1.0f/100 Dollars', [cents] )
else
centsString := Format( 'and %2.0f/100 Dollars', [cents] );
dNum := Int( dNum - (cents / 100.0) ); // lose the cents
// deal with million's
if (dNum >= 1000000 ) and ( dNum <= 999999999 ) then
begin
workVar := dNum / 1000000;
workVar := Int( workVar );
if (workVar <= 9) then
result := ZeroTo19(workVar)
else if ( workVar <= 99 ) then
result := LessThan99( workVar )
else if ( workVar <= 999 ) then
result := Hundreds( workVar )
else
result := 'mill fubar';
result := result + ' Million';
dNum := dNum - ( workVar * 1000000 );
end;
// deal with 1000's
if (dNum >= 1000 ) and ( dNum <= 999999.99 ) then
begin
// doing the two below statements in one line of code yields some really
// freaky floating point errors
workVar := dNum/1000;
workVar := Int( workVar );
if (workVar <= 9) then
result := ZeroTo19(workVar)
else if ( workVar <= 99 ) then
result := LessThan99( workVar )
else if ( workVar <= 999 ) then
result := Hundreds( workVar )
else
result := 'thou fubar';
result := result + ' Thousand';
dNum := dNum - ( workVar * 1000 );
end;
// deal with 100's
if (dNum >= 100.00 ) and (dNum <= 999.99) then
begin
result := result + ' ' + Hundreds( dNum );
dNum := FloatMod( dNum, 100 );
end;
// format in anything less than 100
if ( dNum > 0) or ((dNum = 0) and (Length( result ) = 0)) then
begin
result := result + ' ' + LessThan99( dNum );
end;
result := result + ' ' + centsString;
end;
end.
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