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torben |
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// Upgraded to Delphi 2009: Sebastian Zierer
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(* ***** BEGIN LICENSE BLOCK *****
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* Version: MPL 1.1
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*
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* The contents of this file are subject to the Mozilla Public License Version
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* 1.1 (the "License"); you may not use this file except in compliance with
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* the License. You may obtain a copy of the License at
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* http://www.mozilla.org/MPL/
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*
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* Software distributed under the License is distributed on an "AS IS" basis,
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* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
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* for the specific language governing rights and limitations under the
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* License.
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*
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* The Original Code is TurboPower SysTools
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*
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* The Initial Developer of the Original Code is
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* TurboPower Software
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*
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* Portions created by the Initial Developer are Copyright (C) 1996-2002
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* the Initial Developer. All Rights Reserved.
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*
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* Contributor(s):
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*
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* ***** END LICENSE BLOCK ***** *)
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{*********************************************************}
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{* SysTools: StDecMth.pas 4.04 *}
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{*********************************************************}
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{* SysTools: Class for doing decimal arithmetic *}
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{*********************************************************}
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{$I StDefine.inc}
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unit StDecMth;
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interface
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{Note: StDecMth declares and implements TStDecimal. This is a fixed-
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point value with a total of 38 significant digits of which
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16 are to the right of the decimal point.}
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uses
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SysUtils;
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type
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TStRoundMethod = ( {different rounding methods...}
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rmNormal, {..normal (round away from zero if half way)}
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rmTrunc, {..truncate (always round to zero)}
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rmBankers, {..bankers (round to even digit if half way)}
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rmUp); {..force round up (always round from zero)}
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TStInt128 = array [0..3] of longint; // must be longint, not DWORD
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TStDecimal = class
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private
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FInt : TStInt128;
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protected
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function dcGetAsStr : AnsiString;
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procedure dcSetFromStr(const aValue : AnsiString); {!!.02}
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public
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constructor Create;
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destructor Destroy; override;
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function Compare(X : TStDecimal) : integer;
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{-returns <0 if Self < X, 0 is equal, >0 otherwise}
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function IsNegative : boolean;
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{-returns Self < 0.0}
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function IsOne : boolean;
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{-returns Self = 1.0}
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function IsPositive : boolean;
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{-returns Self > 0.0}
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function IsZero : boolean;
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{-returns Self = 0.0}
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procedure SetToOne;
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{-sets Self equal to 1.0}
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procedure SetToZero;
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{-sets Self equal to 0.0}
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procedure Assign(X : TStDecimal);
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{-sets Self equal to X}
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procedure AssignFromFloat(aValue : double);
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{-sets Self equal to aValue}
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procedure AssignFromInt(aValue : integer);
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{-sets Self equal to aValue}
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function AsFloat : double;
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{-returns Self as an floating point value}
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function AsInt(aRound : TStRoundMethod) : integer;
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{-returns Self as an integer, rounded}
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procedure Abs;
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{-calculates Self := Abs(Self)}
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procedure Add(X : TStDecimal);
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{-calculates Self := Self + X}
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procedure AddOne;
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{-calculates Self := Self + 1.0}
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procedure ChangeSign;
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{-calculates Self := ChgSign(Self)}
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procedure Divide(X : TStDecimal);
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{-calculates Self := Self div X}
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procedure Multiply(X : TStDecimal);
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{-calculates Self := Self * X}
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procedure RaiseToPower(N : integer);
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{-calculates Self := Self ^ N}
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procedure Round(aRound : TStRoundMethod; aDecPl : integer);
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{-calculates Self := Round(Self)}
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procedure Subtract(X : TStDecimal);
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{-calculates Self := Self - X}
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procedure SubtractOne;
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{-calculates Self := Self - 1}
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property AsString : AnsiString read dcGetAsStr write dcSetFromStr;
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{-returns Self as a string, sets Self from a string}
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end;
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implementation
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uses
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StConst,
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StBase;
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type
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TStInt256 = array [0..7] of integer;
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TStInt192 = array [0..5] of integer;
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const
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MaxDecPl = 16;
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Int128One_0 = longint($6FC10000);
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Int128One_1 = longint($002386F2);
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PowerOf10 : array [0..MaxDecPl div 2] of integer =
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(1, 10, 100, 1000, 10000, 100000, 1000000, 10000000,
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100000000);
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{===Helper routines==================================================}
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procedure Int256Div10E8(var X : TStInt256; var aRem : integer);
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{Note: this routine assumes X is positive}
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asm
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push ebx // save ebx
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push edx // save address of remainder variable
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mov ecx, 100000000 // we're dividing by 10^8
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mov ebx, eax // ebx points to X
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xor edx, edx // start off with high dividend digit zero
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mov eax, [ebx+28] // get last 32-bit digit
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div ecx // divide by 10: eax is quotient, edx remainder
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mov [ebx+28], eax // save highest quotient digit
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mov eax, [ebx+24] // get next 32-bit digit
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div ecx // divide by 10: eax is quotient, edx remainder
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mov [ebx+24], eax // save next quotient digit
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mov eax, [ebx+20] // get next 32-bit digit
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div ecx // divide by 10: eax is quotient, edx remainder
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mov [ebx+20], eax // save next quotient digit
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mov eax, [ebx+16] // get next 32-bit digit
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div ecx // divide by 10: eax is quotient, edx remainder
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mov [ebx+16], eax // save next quotient digit
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mov eax, [ebx+12] // get next 32-bit digit
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div ecx // divide by 10: eax is quotient, edx remainder
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mov [ebx+12], eax // save next quotient digit
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mov eax, [ebx+8] // get next 32-bit digit
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div ecx // divide by 10: eax is quotient, edx remainder
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mov [ebx+8], eax // save next quotient digit
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mov eax, [ebx+4] // get next 32-bit digit
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div ecx // divide by 10: eax is quotient, edx remainder
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mov [ebx+4], eax // save next quotient digit
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mov eax, [ebx] // get first 32-bit digit
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div ecx // divide by 10: eax is quotient, edx remainder
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mov [ebx], eax // save first quotient digit
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pop eax // pop off the address of remainder variable
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mov [eax], edx // store remainder
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pop ebx // restore ebx
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end;
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{--------}
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procedure Int192Times10E8(var X : TStInt192);
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{Note: this routine assumes X is positive}
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asm
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push ebx // save ebx
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push ebp // save ebp
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mov ecx, 100000000 // we're multiplying by 10^8
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mov ebx, eax // ebx points to X
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mov eax, [ebx] // get the first 32-bit digit
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mul ecx // multiply it by 10^8 to give answer in edx:eax
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mov [ebx], eax // save first digit of result
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mov ebp, edx // save overflow
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mov eax, [ebx+4] // get the second 32-bit digit
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mul ecx // multiply it by 10^8 to give answer in edx:eax
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add eax, ebp // add the overflow from the first digit
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adc edx, 0
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mov [ebx+4], eax // save second digit of result
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mov ebp, edx // save overflow
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mov eax, [ebx+8] // get the third 32-bit digit
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mul ecx // multiply it by 10^8 to give answer in edx:eax
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add eax, ebp // add the overflow from the second digit
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adc edx, 0
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mov [ebx+8], eax // save third digit of result
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mov ebp, edx // save overflow
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mov eax, [ebx+12] // get the fourth 32-bit digit
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mul ecx // multiply it by 10^8 to give answer in edx:eax
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add eax, ebp // add the overflow from the third digit
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adc edx, 0
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mov [ebx+12], eax // save fourth digit of result
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mov ebp, edx // save overflow
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mov eax, [ebx+16] // get the fifth 32-bit digit
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mul ecx // multiply it by 10^8 to give answer in edx:eax
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add eax, ebp // add the overflow from the fourth digit
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adc edx, 0
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mov [ebx+16], eax // save fifth digit of result
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mov ebp, edx // save overflow
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mov eax, [ebx+20] // get the sixth 32-bit digit
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mul ecx // multiply it by 10^8 to give answer in edx:eax
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add eax, ebp // add the overflow from the fifth digit
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mov [ebx+20], eax // save sixth digit of result
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pop ebp // restore ebp
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pop ebx // restore ebx
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end;
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{--------}
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function Int32MultPrim(X, Y : longint;
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var P : longint; Carry : longint) : longint;
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asm
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{Note: calculates X * Y + P + Carry
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returns answer in P, with overflow as result value}
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mul edx
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add eax, [ecx]
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adc edx, 0
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add eax, Carry
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adc edx, 0
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mov [ecx], eax
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mov eax, edx
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end;
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{--------}
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procedure Int128Add(var X : TStInt128; const Y : TStInt128);
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asm
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push ebx
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mov ecx, [edx]
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mov ebx, [edx+4]
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add [eax], ecx
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adc [eax+4], ebx
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mov ecx, [edx+8]
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mov ebx, [edx+12]
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adc [eax+8], ecx
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adc [eax+12], ebx
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pop ebx
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end;
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{--------}
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procedure Int128AddInt(var X : TStInt128; aDigit : integer);
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asm
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add [eax], edx
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adc dword ptr [eax+4], 0
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adc dword ptr [eax+8], 0
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adc dword ptr [eax+12], 0
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end;
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{--------}
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procedure Int128ChgSign(var X : TStInt128);
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asm
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mov ecx, [eax]
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mov edx, [eax+4]
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not ecx
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not edx
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add ecx, 1
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adc edx, 0
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mov [eax], ecx
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mov [eax+4], edx
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mov ecx, [eax+8]
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mov edx, [eax+12]
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not ecx
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not edx
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adc ecx, 0
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adc edx, 0
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mov [eax+8], ecx
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mov [eax+12], edx
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end;
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{--------}
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function Int128Compare(const X, Y : TStInt128) : integer;
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asm
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// Can be called from pascal
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// All registers are preserved, except eax, which returns the
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// result of the comparison
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push ebx
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push ecx
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mov ecx, [eax+12]
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mov ebx, [edx+12]
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xor ecx, $80000000
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xor ebx, $80000000
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cmp ecx, ebx
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jb @@LessThan
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ja @@GreaterThan
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mov ecx, [eax+8]
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mov ebx, [edx+8]
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cmp ecx, ebx
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jb @@LessThan
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ja @@GreaterThan
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mov ecx, [eax+4]
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mov ebx, [edx+4]
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cmp ecx, ebx
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jb @@LessThan
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ja @@GreaterThan
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mov ecx, [eax]
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mov ebx, [edx]
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cmp ecx, ebx
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jb @@LessThan
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ja @@GreaterThan
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xor eax, eax
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jmp @@Exit
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@@LessThan:
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mov eax, -1
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jmp @@Exit
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@@GreaterThan:
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mov eax, 1
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@@Exit:
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pop ecx
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pop ebx
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end;
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{--------}
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procedure Int192SHL(var X : TStInt192);
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asm
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// DO NOT CALL FROM PASCAL
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// IN: eax -> 192-bit integer to shift left
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// OUT: eax -> 192-bit integer shifted left
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// CF = most significant bit shifted out
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// All registers are preserved
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push ebx
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push ecx
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mov ebx, [eax]
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mov ecx, [eax+4]
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shl ebx, 1
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rcl ecx, 1
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mov [eax], ebx
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mov [eax+4], ecx
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mov ebx, [eax+8]
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mov ecx, [eax+12]
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rcl ebx, 1
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rcl ecx, 1
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mov [eax+8], ebx
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mov [eax+12], ecx
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mov ebx, [eax+16]
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mov ecx, [eax+20]
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rcl ebx, 1
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rcl ecx, 1
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mov [eax+16], ebx
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|
|
mov [eax+20], ecx
|
363 |
|
|
pop ecx
|
364 |
|
|
pop ebx
|
365 |
|
|
end;
|
366 |
|
|
{--------}
|
367 |
|
|
procedure Int128RCL(var X : TStInt128);
|
368 |
|
|
asm
|
369 |
|
|
// DO NOT CALL FROM PASCAL
|
370 |
|
|
// IN: eax -> 128-bit integer to shift left
|
371 |
|
|
// CF = least significant bit to shift in
|
372 |
|
|
// OUT: eax -> 128-bit integer shifted left
|
373 |
|
|
// CF -> topmost bit shifted out
|
374 |
|
|
// All registers are preserved
|
375 |
|
|
push ebx
|
376 |
|
|
push ecx
|
377 |
|
|
mov ebx, [eax]
|
378 |
|
|
mov ecx, [eax+4]
|
379 |
|
|
rcl ebx, 1
|
380 |
|
|
rcl ecx, 1
|
381 |
|
|
mov [eax], ebx
|
382 |
|
|
mov [eax+4], ecx
|
383 |
|
|
mov ebx, [eax+8]
|
384 |
|
|
mov ecx, [eax+12]
|
385 |
|
|
rcl ebx, 1
|
386 |
|
|
rcl ecx, 1
|
387 |
|
|
mov [eax+8], ebx
|
388 |
|
|
mov [eax+12], ecx
|
389 |
|
|
pop ecx
|
390 |
|
|
pop ebx
|
391 |
|
|
end;
|
392 |
|
|
{--------}
|
393 |
|
|
procedure Int128FastDivide(var X : TStInt192;
|
394 |
|
|
var Y, aRem : TStInt128);
|
395 |
|
|
asm
|
396 |
|
|
push ebp
|
397 |
|
|
push ebx
|
398 |
|
|
push edi
|
399 |
|
|
push esi
|
400 |
|
|
|
401 |
|
|
mov esi, eax // esi -> dividend
|
402 |
|
|
mov edi, edx // edi -> divisor
|
403 |
|
|
mov ebp, ecx // ebp -> remainder
|
404 |
|
|
|
405 |
|
|
mov ecx, 192 // we'll do the loop for all 192 bits in the
|
406 |
|
|
// dividend
|
407 |
|
|
|
408 |
|
|
xor eax, eax // zero the remainder
|
409 |
|
|
mov [ebp], eax
|
410 |
|
|
mov [ebp+4], eax
|
411 |
|
|
mov [ebp+8], eax
|
412 |
|
|
mov [ebp+12], eax
|
413 |
|
|
|
414 |
|
|
@@GetNextBit:
|
415 |
|
|
mov eax, esi // shift the dividend left, and...
|
416 |
|
|
call Int192SHL
|
417 |
|
|
mov eax, ebp // ...shift the topmost bit into the remainder
|
418 |
|
|
call Int128RCL
|
419 |
|
|
|
420 |
|
|
mov eax, ebp // compare the remainder with the divisor
|
421 |
|
|
mov edx, edi
|
422 |
|
|
call Int128Compare
|
423 |
|
|
|
424 |
|
|
cmp eax, 0 // if the remainder is smaller, we can't
|
425 |
|
|
jl @@TooSmall // subtract the divisor
|
426 |
|
|
|
427 |
|
|
// essentially we've shown that the divisor
|
428 |
|
|
// divides the remainder exactly once, so
|
429 |
|
|
|
430 |
|
|
add dword ptr [esi], 1 // add one to the quotient
|
431 |
|
|
|
432 |
|
|
mov eax, [ebp] // subtract the divisor from the remainder
|
433 |
|
|
mov ebx, [ebp+4]
|
434 |
|
|
sub eax, [edi]
|
435 |
|
|
sbb ebx, [edi+4]
|
436 |
|
|
mov [ebp], eax
|
437 |
|
|
mov [ebp+4], ebx
|
438 |
|
|
mov eax, [ebp+8]
|
439 |
|
|
mov ebx, [ebp+12]
|
440 |
|
|
sbb eax, [edi+8]
|
441 |
|
|
sbb ebx, [edi+12]
|
442 |
|
|
mov [ebp+8], eax
|
443 |
|
|
mov [ebp+12], ebx
|
444 |
|
|
|
445 |
|
|
@@TooSmall:
|
446 |
|
|
dec ecx // go get the next bit to work on
|
447 |
|
|
jnz @@GetNextBit
|
448 |
|
|
|
449 |
|
|
pop esi
|
450 |
|
|
pop edi
|
451 |
|
|
pop ebx
|
452 |
|
|
pop ebp
|
453 |
|
|
end;
|
454 |
|
|
{--------}
|
455 |
|
|
function Int128DivInt(var X : TStInt128; aDivisor : integer) : integer;
|
456 |
|
|
{Note: this routine assumes X is positive}
|
457 |
|
|
asm
|
458 |
|
|
push ebx // save ebx
|
459 |
|
|
|
460 |
|
|
mov ecx, edx // ecx is now the divisor
|
461 |
|
|
mov ebx, eax // ebx points to X
|
462 |
|
|
|
463 |
|
|
xor edx, edx // start off with high dividend digit zero
|
464 |
|
|
mov eax, [ebx+12] // get last 32-bit digit
|
465 |
|
|
div ecx // divide by ecx: eax is quotient, edx remainder
|
466 |
|
|
mov [ebx+12], eax // save highest quotient digit
|
467 |
|
|
|
468 |
|
|
mov eax, [ebx+8] // get next 32-bit digit
|
469 |
|
|
div ecx // divide by ecx: eax is quotient, edx remainder
|
470 |
|
|
mov [ebx+8], eax // save next quotient digit
|
471 |
|
|
|
472 |
|
|
mov eax, [ebx+4] // get next 32-bit digit
|
473 |
|
|
div ecx // divide by ecx: eax is quotient, edx remainder
|
474 |
|
|
mov [ebx+4], eax // save next quotient digit
|
475 |
|
|
|
476 |
|
|
mov eax, [ebx] // get first 32-bit digit
|
477 |
|
|
div ecx // divide by ecx: eax is quotient, edx remainder
|
478 |
|
|
mov [ebx], eax // save first quotient digit
|
479 |
|
|
|
480 |
|
|
mov eax, edx // return remainder
|
481 |
|
|
|
482 |
|
|
pop ebx // restore ebx
|
483 |
|
|
end;
|
484 |
|
|
{--------}
|
485 |
|
|
procedure Int128Divide(var X, Y : TStInt128);
|
486 |
|
|
var
|
487 |
|
|
XTemp : TStInt192;
|
488 |
|
|
Rem : TStInt128;
|
489 |
|
|
begin
|
490 |
|
|
{note: the easy cases have been dealt with
|
491 |
|
|
X and Y are both positive
|
492 |
|
|
X will be set to the quotient X/Y and Y will be trashed}
|
493 |
|
|
|
494 |
|
|
{we need to increase the number of decimal places to 32, so convert
|
495 |
|
|
the 128 bit dividend to a 192 bit one and multiply by 10^16}
|
496 |
|
|
XTemp[0] := X[0];
|
497 |
|
|
XTemp[1] := X[1];
|
498 |
|
|
XTemp[2] := X[2];
|
499 |
|
|
XTemp[3] := X[3];
|
500 |
|
|
XTemp[4] := 0;
|
501 |
|
|
XTemp[5] := 0;
|
502 |
|
|
Int192Times10E8(XTemp);
|
503 |
|
|
Int192Times10E8(XTemp);
|
504 |
|
|
|
505 |
|
|
{Note: this algorithm follows that described by Knuth in volume 2 of
|
506 |
|
|
The Art of Computer Programming. Algorithm D of section 4.3
|
507 |
|
|
as applied to binary numbers (radix=2)}
|
508 |
|
|
|
509 |
|
|
{divide the 192-bit dividend by the 128-bit divisor}
|
510 |
|
|
Int128FastDivide(XTemp, Y, Rem);
|
511 |
|
|
|
512 |
|
|
{have we overflowed? ie, have we divided a very big number by one
|
513 |
|
|
much less than zero}
|
514 |
|
|
if (XTemp[3] < 0) or (XTemp[4] <> 0) or (XTemp[5] <> 0) then
|
515 |
|
|
raise EStDecMathError.Create(stscDecMathDivOverflowS);
|
516 |
|
|
|
517 |
|
|
{return the result of the computation}
|
518 |
|
|
X[0] := XTemp[0];
|
519 |
|
|
X[1] := XTemp[1];
|
520 |
|
|
X[2] := XTemp[2];
|
521 |
|
|
X[3] := XTemp[3];
|
522 |
|
|
end;
|
523 |
|
|
{--------}
|
524 |
|
|
procedure Int128Multiply(var X, Y : TStInt128);
|
525 |
|
|
var
|
526 |
|
|
P : TStInt256;
|
527 |
|
|
XIsNeg : boolean;
|
528 |
|
|
YIsNeg : boolean;
|
529 |
|
|
YInx : integer;
|
530 |
|
|
YDigit : integer;
|
531 |
|
|
Carry : integer;
|
532 |
|
|
YTemp : TStInt128;
|
533 |
|
|
begin
|
534 |
|
|
{Note: calculates X * Y and puts the answer in X}
|
535 |
|
|
|
536 |
|
|
{get rid of the easy cases where one of the operands is zero}
|
537 |
|
|
if (X[0] = 0) and (X[1] = 0) and (X[2] = 0) and (X[3] = 0) then
|
538 |
|
|
Exit;
|
539 |
|
|
if (Y[0] = 0) and (Y[1] = 0) and (Y[2] = 0) and (Y[3] = 0) then begin
|
540 |
|
|
X[0] := 0;
|
541 |
|
|
X[1] := 0;
|
542 |
|
|
X[2] := 0;
|
543 |
|
|
X[3] := 0;
|
544 |
|
|
Exit;
|
545 |
|
|
end;
|
546 |
|
|
|
547 |
|
|
{we might need to trash Y, so we use a local variable}
|
548 |
|
|
YTemp[0] := Y[0];
|
549 |
|
|
YTemp[1] := Y[1];
|
550 |
|
|
YTemp[2] := Y[2];
|
551 |
|
|
YTemp[3] := Y[3];
|
552 |
|
|
|
553 |
|
|
{convert both operands to positive values: we'll fix the sign later}
|
554 |
|
|
XIsNeg := X[3] < 0;
|
555 |
|
|
if XIsNeg then
|
556 |
|
|
Int128ChgSign(X);
|
557 |
|
|
YIsNeg := YTemp[3] < 0;
|
558 |
|
|
if YIsNeg then
|
559 |
|
|
Int128ChgSign(YTemp);
|
560 |
|
|
|
561 |
|
|
{initialize the temporary product}
|
562 |
|
|
P[0] := 0;
|
563 |
|
|
P[1] := 0;
|
564 |
|
|
P[2] := 0;
|
565 |
|
|
P[3] := 0;
|
566 |
|
|
P[4] := 0;
|
567 |
|
|
P[5] := 0;
|
568 |
|
|
P[6] := 0;
|
569 |
|
|
P[7] := 0;
|
570 |
|
|
|
571 |
|
|
{for every digit in Y we shall multiply by all the X digits and sum}
|
572 |
|
|
for YInx := 0 to 3 do begin
|
573 |
|
|
|
574 |
|
|
{get the Y digit}
|
575 |
|
|
YDigit := YTemp[YInx];
|
576 |
|
|
|
577 |
|
|
{there's only something to do if the Y digit is non-zero}
|
578 |
|
|
if (YDigit <> 0) then begin
|
579 |
|
|
|
580 |
|
|
{multiply this digit with all the X digits, storing the result
|
581 |
|
|
in the temporary product}
|
582 |
|
|
Carry := Int32MultPrim(X[0], YDigit, P[YInx], 0);
|
583 |
|
|
Carry := Int32MultPrim(X[1], YDigit, P[YInx + 1], Carry);
|
584 |
|
|
Carry := Int32MultPrim(X[2], YDigit, P[YInx + 2], Carry);
|
585 |
|
|
P[YInx + 4] := Int32MultPrim(X[3], YDigit, P[YInx + 3], Carry);
|
586 |
|
|
end;
|
587 |
|
|
end;
|
588 |
|
|
|
589 |
|
|
{the product has 32 decimal places, so divide by 10^8 twice to get
|
590 |
|
|
the answer to the 16 decimal places we need}
|
591 |
|
|
Int256Div10E8(P, Carry);
|
592 |
|
|
Int256Div10E8(P, Carry);
|
593 |
|
|
|
594 |
|
|
{note: if Carry <> 0 then we're losing precision}
|
595 |
|
|
|
596 |
|
|
{check for multiplication overflow}
|
597 |
|
|
if (P[3] < 0) or
|
598 |
|
|
(P[4] <> 0) or (P[5] <> 0) or (P[6] <> 0) or (P[7] <> 0) then
|
599 |
|
|
raise EStDecMathError.Create(stscDecMathMultOverflowS);
|
600 |
|
|
|
601 |
|
|
{return the value in X, remembering to set the sign}
|
602 |
|
|
X[0] := P[0];
|
603 |
|
|
X[1] := P[1];
|
604 |
|
|
X[2] := P[2];
|
605 |
|
|
X[3] := P[3];
|
606 |
|
|
|
607 |
|
|
(*
|
608 |
|
|
{round if necessary}
|
609 |
|
|
if (Carry >= 500000000) then
|
610 |
|
|
Int128AddInt(X, 1);
|
611 |
|
|
*)
|
612 |
|
|
|
613 |
|
|
{set the sign}
|
614 |
|
|
if (XIsNeg xor YIsNeg) then
|
615 |
|
|
Int128ChgSign(X);
|
616 |
|
|
end;
|
617 |
|
|
{--------}
|
618 |
|
|
procedure Int128TimesInt(var X : TStInt128; aValue : integer);
|
619 |
|
|
{Note: this routine assumes X is positive}
|
620 |
|
|
asm
|
621 |
|
|
push ebx // save ebx
|
622 |
|
|
push ebp // save ebp
|
623 |
|
|
|
624 |
|
|
mov ecx, edx // we're multiplying by aValue
|
625 |
|
|
mov ebx, eax // ebx points to X
|
626 |
|
|
|
627 |
|
|
mov eax, [ebx] // get the first 32-bit digit
|
628 |
|
|
mul ecx // multiply it by 10 to give answer in edx:eax
|
629 |
|
|
mov [ebx], eax // save first digit of result
|
630 |
|
|
mov ebp, edx // save overflow
|
631 |
|
|
|
632 |
|
|
mov eax, [ebx+4] // get the second 32-bit digit
|
633 |
|
|
mul ecx // multiply it by 10 to give answer in edx:eax
|
634 |
|
|
add eax, ebp // add the overflow from the first digit
|
635 |
|
|
adc edx, 0
|
636 |
|
|
mov [ebx+4], eax // save second digit of result
|
637 |
|
|
mov ebp, edx // save overflow
|
638 |
|
|
|
639 |
|
|
mov eax, [ebx+8] // get the third 32-bit digit
|
640 |
|
|
mul ecx // multiply it by 10 to give answer in edx:eax
|
641 |
|
|
add eax, ebp // add the overflow from the second digit
|
642 |
|
|
adc edx, 0
|
643 |
|
|
mov [ebx+8], eax // save second digit of result
|
644 |
|
|
mov ebp, edx // save overflow
|
645 |
|
|
|
646 |
|
|
mov eax, [ebx+12] // get the third 32-bit digit
|
647 |
|
|
mul ecx // multiply it by 10 to give answer in edx:eax
|
648 |
|
|
add eax, ebp // add the overflow from the second digit
|
649 |
|
|
mov [ebx+12], eax // save third digit of result
|
650 |
|
|
|
651 |
|
|
pop ebp // restore ebp
|
652 |
|
|
pop ebx // restore ebx
|
653 |
|
|
end;
|
654 |
|
|
{--------}
|
655 |
|
|
procedure Int128Round(var X : TStInt128;
|
656 |
|
|
aRound : TStRoundMethod;
|
657 |
|
|
aDecPl : integer);
|
658 |
|
|
var
|
659 |
|
|
Rem : integer;
|
660 |
|
|
HadRem : boolean;
|
661 |
|
|
AddOne : boolean;
|
662 |
|
|
Expnt : integer;
|
663 |
|
|
NeedInt : boolean;
|
664 |
|
|
begin
|
665 |
|
|
{Assumptions: X is positive, 0 <= aDecPl <= MaxDecPl
|
666 |
|
|
--the caller *must* ensure these}
|
667 |
|
|
|
668 |
|
|
{if the number of decimal places is -1, it's a special signal to
|
669 |
|
|
perform the rounding to an integer, but not to multiply the result
|
670 |
|
|
by 10^16 at the end; the caller is AsInt, in other words}
|
671 |
|
|
if (aDecPl >= 0) then
|
672 |
|
|
NeedInt := false
|
673 |
|
|
else begin
|
674 |
|
|
NeedInt := true;
|
675 |
|
|
aDecPl := 0;
|
676 |
|
|
end;
|
677 |
|
|
|
678 |
|
|
{if we're asked to round to the precision of the type, there's
|
679 |
|
|
nothing to do}
|
680 |
|
|
if (aDecPl = MaxDecPl) then
|
681 |
|
|
Exit;
|
682 |
|
|
|
683 |
|
|
{perform the required rounding}
|
684 |
|
|
AddOne := false; // keep the compiler happy
|
685 |
|
|
case aRound of
|
686 |
|
|
rmNormal :
|
687 |
|
|
begin
|
688 |
|
|
{to do normal rounding: divide by the required power of ten,
|
689 |
|
|
if the most significant digit of the remainder was 5 or more,
|
690 |
|
|
we'll add one to the result}
|
691 |
|
|
Expnt := MaxDecPl - aDecPl - 1;
|
692 |
|
|
if (Expnt > 0) then begin
|
693 |
|
|
if (Expnt > 8) then begin
|
694 |
|
|
Int128DivInt(X, PowerOf10[8]);
|
695 |
|
|
dec(Expnt, 8);
|
696 |
|
|
end;
|
697 |
|
|
Int128DivInt(X, PowerOf10[Expnt]);
|
698 |
|
|
end;
|
699 |
|
|
AddOne := Int128DivInt(X, 10) >= 5;
|
700 |
|
|
end;
|
701 |
|
|
rmTrunc :
|
702 |
|
|
begin
|
703 |
|
|
{to truncate: just divide by the required power of ten}
|
704 |
|
|
Expnt := MaxDecPl - aDecPl;
|
705 |
|
|
if (Expnt > 8) then begin
|
706 |
|
|
Int128DivInt(X, PowerOf10[8]);
|
707 |
|
|
dec(Expnt, 8);
|
708 |
|
|
end;
|
709 |
|
|
Int128DivInt(X, PowerOf10[Expnt]);
|
710 |
|
|
AddOne := false;
|
711 |
|
|
end;
|
712 |
|
|
rmBankers :
|
713 |
|
|
begin
|
714 |
|
|
{to do bankers rounding:
|
715 |
|
|
- divide by the required power of ten, checking to see if
|
716 |
|
|
there's a non-zero remainder
|
717 |
|
|
- if the most significant digit of the remainder was greater
|
718 |
|
|
than 5, we'll add one to the result
|
719 |
|
|
- if the most significant digit of the remainder was 5 and
|
720 |
|
|
there was at least one other digit in the remainder, we'll
|
721 |
|
|
add one to the result
|
722 |
|
|
- if the most significant digit of the remainder was 5 and
|
723 |
|
|
there were no other digits in the remainder, determine if
|
724 |
|
|
the result is odd; if it is, we'll add one to the result}
|
725 |
|
|
HadRem := false;
|
726 |
|
|
if ((MaxDecPl - aDecPl) > 1) then begin
|
727 |
|
|
Expnt := MaxDecPl - aDecPl - 1;
|
728 |
|
|
if (Expnt > 8) then begin
|
729 |
|
|
if (Int128DivInt(X, PowerOf10[8]) <> 0) then
|
730 |
|
|
HadRem := true;
|
731 |
|
|
dec(Expnt, 8);
|
732 |
|
|
end;
|
733 |
|
|
if (Int128DivInt(X, PowerOf10[Expnt]) <> 0) then
|
734 |
|
|
HadRem := true;
|
735 |
|
|
end;
|
736 |
|
|
Rem := Int128DivInt(X, 10);
|
737 |
|
|
AddOne := (Rem > 5) or
|
738 |
|
|
((Rem = 5) and HadRem) or
|
739 |
|
|
((Rem = 5) and Odd(X[0]));
|
740 |
|
|
end;
|
741 |
|
|
rmUp :
|
742 |
|
|
begin
|
743 |
|
|
{to always round up: divide by the required power of ten,
|
744 |
|
|
if there was a remainder, we'll add one to the result}
|
745 |
|
|
AddOne := false;
|
746 |
|
|
Expnt := MaxDecPl - aDecPl;
|
747 |
|
|
if (Expnt > 8) then begin
|
748 |
|
|
if (Int128DivInt(X, PowerOf10[8]) <> 0) then
|
749 |
|
|
AddOne := true;
|
750 |
|
|
dec(Expnt, 8);
|
751 |
|
|
end;
|
752 |
|
|
if (Int128DivInt(X, PowerOf10[Expnt]) <> 0) then
|
753 |
|
|
AddOne := true;
|
754 |
|
|
end;
|
755 |
|
|
end;{case}
|
756 |
|
|
|
757 |
|
|
{add one to the result, if required}
|
758 |
|
|
if AddOne then
|
759 |
|
|
Int128AddInt(X, 1);
|
760 |
|
|
|
761 |
|
|
{finally, multiply by the required power of ten}
|
762 |
|
|
if not NeedInt then begin
|
763 |
|
|
Expnt := MaxDecPl - aDecPl;
|
764 |
|
|
if (Expnt > 8) then begin
|
765 |
|
|
Int128TimesInt(X, PowerOf10[8]);
|
766 |
|
|
dec(Expnt, 8);
|
767 |
|
|
end;
|
768 |
|
|
Int128TimesInt(X, PowerOf10[Expnt]);
|
769 |
|
|
end;
|
770 |
|
|
end;
|
771 |
|
|
{====================================================================}
|
772 |
|
|
|
773 |
|
|
|
774 |
|
|
{====================================================================}
|
775 |
|
|
constructor TStDecimal.Create;
|
776 |
|
|
begin
|
777 |
|
|
{create the ancestor}
|
778 |
|
|
inherited Create;
|
779 |
|
|
{note: the internal number will be automatically zero}
|
780 |
|
|
end;
|
781 |
|
|
{--------}
|
782 |
|
|
destructor TStDecimal.Destroy;
|
783 |
|
|
begin
|
784 |
|
|
{free the ancestor}
|
785 |
|
|
inherited Destroy;
|
786 |
|
|
end;
|
787 |
|
|
{--------}
|
788 |
|
|
procedure TStDecimal.Abs;
|
789 |
|
|
begin
|
790 |
|
|
if (FInt[3] < 0) then
|
791 |
|
|
Int128ChgSign(FInt);
|
792 |
|
|
end;
|
793 |
|
|
{--------}
|
794 |
|
|
procedure TStDecimal.Add(X : TStDecimal);
|
795 |
|
|
begin
|
796 |
|
|
if (X <> nil) then
|
797 |
|
|
Int128Add(FInt, X.FInt);
|
798 |
|
|
end;
|
799 |
|
|
{--------}
|
800 |
|
|
procedure TStDecimal.AddOne;
|
801 |
|
|
var
|
802 |
|
|
One : TStInt128;
|
803 |
|
|
begin
|
804 |
|
|
One[0] := Int128One_0;
|
805 |
|
|
One[1] := Int128One_1;
|
806 |
|
|
One[2] := 0;
|
807 |
|
|
One[3] := 0;
|
808 |
|
|
Int128Add(FInt, One);
|
809 |
|
|
end;
|
810 |
|
|
{--------}
|
811 |
|
|
function TStDecimal.AsFloat : double;
|
812 |
|
|
begin
|
813 |
|
|
Result := StrToFloat(AsString);
|
814 |
|
|
end;
|
815 |
|
|
{--------}
|
816 |
|
|
function TStDecimal.AsInt(aRound : TStRoundMethod) : integer;
|
817 |
|
|
var
|
818 |
|
|
X : TStInt128;
|
819 |
|
|
IsNeg : boolean;
|
820 |
|
|
begin
|
821 |
|
|
{get the current value locally}
|
822 |
|
|
X[0] := FInt[0];
|
823 |
|
|
X[1] := FInt[1];
|
824 |
|
|
X[2] := FInt[2];
|
825 |
|
|
X[3] := FInt[3];
|
826 |
|
|
|
827 |
|
|
{force it to be positive}
|
828 |
|
|
IsNeg := X[3] < 0;
|
829 |
|
|
if IsNeg then
|
830 |
|
|
Int128ChgSign(X);
|
831 |
|
|
|
832 |
|
|
{round it to an integer}
|
833 |
|
|
Int128Round(X, aRound, -1);
|
834 |
|
|
|
835 |
|
|
{check for errors (the least significant digit cannot be negative,
|
836 |
|
|
and all the others must be zero)}
|
837 |
|
|
if (X[0] < 0) or (X[1] <> 0) or (X[2] <> 0) or (X[3] <> 0) then
|
838 |
|
|
raise EStDecMathError.Create(stscDecMathAsIntOverflowS);
|
839 |
|
|
|
840 |
|
|
{return the result}
|
841 |
|
|
if IsNeg then
|
842 |
|
|
Result := -X[0]
|
843 |
|
|
else
|
844 |
|
|
Result := X[0];
|
845 |
|
|
end;
|
846 |
|
|
{--------}
|
847 |
|
|
procedure TStDecimal.Assign(X : TStDecimal);
|
848 |
|
|
begin
|
849 |
|
|
if (X = nil) then
|
850 |
|
|
SetToZero
|
851 |
|
|
else begin
|
852 |
|
|
FInt[0] := X.FInt[0];
|
853 |
|
|
FInt[1] := X.FInt[1];
|
854 |
|
|
FInt[2] := X.FInt[2];
|
855 |
|
|
FInt[3] := X.FInt[3];
|
856 |
|
|
end;
|
857 |
|
|
end;
|
858 |
|
|
{--------}
|
859 |
|
|
procedure TStDecimal.AssignFromFloat(aValue : double);
|
860 |
|
|
begin
|
861 |
|
|
AsString := Format('%38.16f', [aValue]);
|
862 |
|
|
end;
|
863 |
|
|
{--------}
|
864 |
|
|
procedure TStDecimal.AssignFromInt(aValue : integer);
|
865 |
|
|
begin
|
866 |
|
|
FInt[0] := System.Abs(aValue);
|
867 |
|
|
FInt[1] := 0;
|
868 |
|
|
FInt[2] := 0;
|
869 |
|
|
FInt[3] := 0;
|
870 |
|
|
Int128TimesInt(FInt, PowerOf10[8]);
|
871 |
|
|
Int128TimesInt(FInt, PowerOf10[8]);
|
872 |
|
|
if (aValue < 0) then
|
873 |
|
|
Int128ChgSign(FInt);
|
874 |
|
|
end;
|
875 |
|
|
{--------}
|
876 |
|
|
procedure TStDecimal.ChangeSign;
|
877 |
|
|
begin
|
878 |
|
|
Int128ChgSign(FInt);
|
879 |
|
|
end;
|
880 |
|
|
{--------}
|
881 |
|
|
function TStDecimal.Compare(X : TStDecimal) : integer;
|
882 |
|
|
begin
|
883 |
|
|
Compare := Int128Compare(FInt, X.FInt);
|
884 |
|
|
end;
|
885 |
|
|
{--------}
|
886 |
|
|
function TStDecimal.dcGetAsStr : AnsiString;
|
887 |
|
|
var
|
888 |
|
|
X : TStInt128;
|
889 |
|
|
i : integer;
|
890 |
|
|
Rem : integer;
|
891 |
|
|
IsNeg : boolean;
|
892 |
|
|
ChStack: array [0..47] of AnsiChar;
|
893 |
|
|
// this is ample for 38 digits + punctuation
|
894 |
|
|
ChSP : integer;
|
895 |
|
|
begin
|
896 |
|
|
{initialize the stack}
|
897 |
|
|
ChSP := 0;
|
898 |
|
|
|
899 |
|
|
{since we're going to trash the value, store it locally}
|
900 |
|
|
X[0] := FInt[0];
|
901 |
|
|
X[1] := FInt[1];
|
902 |
|
|
X[2] := FInt[2];
|
903 |
|
|
X[3] := FInt[3];
|
904 |
|
|
|
905 |
|
|
{make sure it's positive}
|
906 |
|
|
IsNeg := X[3] < 0;
|
907 |
|
|
if IsNeg then
|
908 |
|
|
Int128ChgSign(X);
|
909 |
|
|
|
910 |
|
|
{push the least significant digits (those that will appear after the
|
911 |
|
|
radix point)}
|
912 |
|
|
for i := 1 to MaxDecPl do begin
|
913 |
|
|
Rem := Int128DivInt(X, 10);
|
914 |
|
|
ChStack[ChSP] := AnsiChar(Rem + ord('0'));
|
915 |
|
|
inc(ChSP);
|
916 |
|
|
end;
|
917 |
|
|
|
918 |
|
|
{push the radix point}
|
919 |
|
|
ChStack[ChSP] := AnsiChar({$IFDEF DELPHIXE2}FormatSettings.{$ENDIF}DecimalSeparator);
|
920 |
|
|
inc(ChSP);
|
921 |
|
|
|
922 |
|
|
{repeat until the local value is zero}
|
923 |
|
|
repeat
|
924 |
|
|
Rem := Int128DivInt(X, 10);
|
925 |
|
|
ChStack[ChSP] := AnsiChar(Rem + ord('0'));
|
926 |
|
|
inc(ChSP);
|
927 |
|
|
until (X[0] = 0) and (X[1] = 0) and (X[2] = 0) and (X[3] = 0);
|
928 |
|
|
|
929 |
|
|
{if the value was negative, push a minus sign}
|
930 |
|
|
if IsNeg then begin
|
931 |
|
|
ChStack[ChSP] := '-';
|
932 |
|
|
inc(ChSP);
|
933 |
|
|
end;
|
934 |
|
|
|
935 |
|
|
{construct the result value by popping off characters}
|
936 |
|
|
SetLength(Result, ChSP);
|
937 |
|
|
i := 1;
|
938 |
|
|
while (ChSP <> 0) do begin
|
939 |
|
|
dec(ChSP);
|
940 |
|
|
Result[i] := ChStack[ChSP];
|
941 |
|
|
inc(i);
|
942 |
|
|
end;
|
943 |
|
|
end;
|
944 |
|
|
{--------}
|
945 |
|
|
procedure TStDecimal.dcSetFromStr(const aValue : AnsiString); {!!.02}
|
946 |
|
|
var
|
947 |
|
|
State : (ScanStart, ScanSign, ScanRadix, ScanBefore,
|
948 |
|
|
ScanAfter, ScanEnd, GotError);
|
949 |
|
|
i : integer;
|
950 |
|
|
Ch : AnsiChar;
|
951 |
|
|
IsNeg : boolean;
|
952 |
|
|
DecPlCount : integer;
|
953 |
|
|
begin
|
954 |
|
|
{Note: this implements the following DFA:
|
955 |
|
|
|
956 |
|
|
ScanStart --space--> ScanStart
|
957 |
|
|
ScanStart --plus---> ScanSign
|
958 |
|
|
ScanStart --minus--> ScanSign
|
959 |
|
|
ScanStart --digit--> ScanBefore
|
960 |
|
|
ScanStart --radix--> ScanRadix
|
961 |
|
|
|
962 |
|
|
ScanSign --radix--> ScanRadix
|
963 |
|
|
ScanSign --digit--> ScanBefore
|
964 |
|
|
|
965 |
|
|
ScanRadix --digit--> ScanAfter
|
966 |
|
|
|
967 |
|
|
ScanBefore --radix--> ScanAfter
|
968 |
|
|
ScanBefore --digit--> ScanBefore
|
969 |
|
|
ScanBefore --space--> ScanEnd
|
970 |
|
|
|
971 |
|
|
ScanAfter --digit--> ScanAfter
|
972 |
|
|
ScanAfter --space--> ScanEnd
|
973 |
|
|
|
974 |
|
|
ScanEnd --space--> ScanEnd
|
975 |
|
|
|
976 |
|
|
The terminating states are ScanBefore, ScanAfter and ScanEnd; in
|
977 |
|
|
other words, a valid numeric string cannot end in a radix point.
|
978 |
|
|
}
|
979 |
|
|
|
980 |
|
|
{initialize}
|
981 |
|
|
SetToZero;
|
982 |
|
|
DecPlCount := 0;
|
983 |
|
|
IsNeg := false;
|
984 |
|
|
State := ScanStart;
|
985 |
|
|
|
986 |
|
|
{read through the input string}
|
987 |
|
|
for i := 1 to length(aValue) do begin
|
988 |
|
|
|
989 |
|
|
{get the current character}
|
990 |
|
|
Ch := aValue[i];
|
991 |
|
|
|
992 |
|
|
case State of
|
993 |
|
|
ScanStart :
|
994 |
|
|
begin
|
995 |
|
|
if ('0' <= Ch) and (Ch <= '9') then begin
|
996 |
|
|
FInt[0] := ord(Ch) - ord('0');
|
997 |
|
|
State := ScanBefore;
|
998 |
|
|
end
|
999 |
|
|
else if (Ch = '+') then begin
|
1000 |
|
|
State := ScanSign;
|
1001 |
|
|
end
|
1002 |
|
|
else if (Ch = '-') then begin
|
1003 |
|
|
IsNeg := true;
|
1004 |
|
|
State := ScanSign;
|
1005 |
|
|
end
|
1006 |
|
|
else if (Ch = AnsiChar({$IFDEF DELPHIXE2}FormatSettings.{$ENDIF}DecimalSeparator)) then begin
|
1007 |
|
|
State := ScanRadix;
|
1008 |
|
|
end
|
1009 |
|
|
else if (Ch <> ' ') then
|
1010 |
|
|
State := GotError;
|
1011 |
|
|
end;
|
1012 |
|
|
ScanSign :
|
1013 |
|
|
begin
|
1014 |
|
|
if ('0' <= Ch) and (Ch <= '9') then begin
|
1015 |
|
|
FInt[0] := ord(Ch) - ord('0');
|
1016 |
|
|
State := ScanBefore;
|
1017 |
|
|
end
|
1018 |
|
|
else if (Ch = AnsiChar({$IFDEF DELPHIXE2}FormatSettings.{$ENDIF}DecimalSeparator)) then begin
|
1019 |
|
|
State := ScanRadix;
|
1020 |
|
|
end
|
1021 |
|
|
else
|
1022 |
|
|
State := GotError;
|
1023 |
|
|
end;
|
1024 |
|
|
ScanRadix :
|
1025 |
|
|
begin
|
1026 |
|
|
if ('0' <= Ch) and (Ch <= '9') then begin
|
1027 |
|
|
inc(DecPlCount);
|
1028 |
|
|
Int128TimesInt(FInt, 10);
|
1029 |
|
|
Int128AddInt(FInt, ord(Ch) - ord('0'));
|
1030 |
|
|
State := ScanAfter;
|
1031 |
|
|
end
|
1032 |
|
|
else
|
1033 |
|
|
State := GotError;
|
1034 |
|
|
end;
|
1035 |
|
|
ScanBefore :
|
1036 |
|
|
begin
|
1037 |
|
|
if ('0' <= Ch) and (Ch <= '9') then begin
|
1038 |
|
|
Int128TimesInt(FInt, 10);
|
1039 |
|
|
Int128AddInt(FInt, ord(Ch) - ord('0'));
|
1040 |
|
|
end
|
1041 |
|
|
else if (Ch = AnsiChar({$IFDEF DELPHIXE2}FormatSettings.{$ENDIF}DecimalSeparator)) then begin
|
1042 |
|
|
State := ScanAfter;
|
1043 |
|
|
end
|
1044 |
|
|
else if (Ch = ' ') then
|
1045 |
|
|
State := ScanEnd
|
1046 |
|
|
else
|
1047 |
|
|
State := GotError;
|
1048 |
|
|
end;
|
1049 |
|
|
ScanAfter :
|
1050 |
|
|
begin
|
1051 |
|
|
if ('0' <= Ch) and (Ch <= '9') then begin
|
1052 |
|
|
inc(DecPlCount);
|
1053 |
|
|
if (DecPlCount <= MaxDecPl) then begin
|
1054 |
|
|
Int128TimesInt(FInt, 10);
|
1055 |
|
|
Int128AddInt(FInt, ord(Ch) - ord('0'));
|
1056 |
|
|
end;
|
1057 |
|
|
end
|
1058 |
|
|
else if (Ch = ' ') then
|
1059 |
|
|
State := ScanEnd
|
1060 |
|
|
else
|
1061 |
|
|
State := GotError;
|
1062 |
|
|
end;
|
1063 |
|
|
ScanEnd :
|
1064 |
|
|
begin
|
1065 |
|
|
if (Ch <> ' ') then
|
1066 |
|
|
State := GotError;
|
1067 |
|
|
end;
|
1068 |
|
|
GotError :
|
1069 |
|
|
begin
|
1070 |
|
|
Break;
|
1071 |
|
|
end;
|
1072 |
|
|
end;
|
1073 |
|
|
end;
|
1074 |
|
|
|
1075 |
|
|
if (State <> ScanBefore) and
|
1076 |
|
|
(State <> ScanAfter) and
|
1077 |
|
|
(State <> ScanEnd) then
|
1078 |
|
|
raise EStDecMathError.Create(stscDecMathConversionS);
|
1079 |
|
|
|
1080 |
|
|
{make sure we have the correct number of decimal places}
|
1081 |
|
|
if (MaxDecPl > DecPlCount) then begin
|
1082 |
|
|
DecPlCount := MaxDecPl - DecPlCount;
|
1083 |
|
|
if (DecPlCount > 8) then begin
|
1084 |
|
|
Int128TimesInt(FInt, Powerof10[8]);
|
1085 |
|
|
dec(DecPlCount, 8);
|
1086 |
|
|
end;
|
1087 |
|
|
Int128TimesInt(FInt, Powerof10[DecPlCount]);
|
1088 |
|
|
end;
|
1089 |
|
|
|
1090 |
|
|
{force negative, if required}
|
1091 |
|
|
if IsNeg then
|
1092 |
|
|
Int128ChgSign(FInt);
|
1093 |
|
|
end;
|
1094 |
|
|
{--------}
|
1095 |
|
|
procedure TStDecimal.Divide(X : TStDecimal);
|
1096 |
|
|
var
|
1097 |
|
|
TempX : TStInt128;
|
1098 |
|
|
IsNeg : boolean;
|
1099 |
|
|
XIsNeg : boolean;
|
1100 |
|
|
begin
|
1101 |
|
|
{easy case: X is nil or zero}
|
1102 |
|
|
if (X = nil) or X.IsZero then
|
1103 |
|
|
raise EStDecMathError.Create(stscDecMathDivByZeroS);
|
1104 |
|
|
|
1105 |
|
|
{easy case: Self is zero}
|
1106 |
|
|
if IsZero then
|
1107 |
|
|
Exit;
|
1108 |
|
|
|
1109 |
|
|
{we might have to change X, so make it local}
|
1110 |
|
|
TempX[0] := X.FInt[0];
|
1111 |
|
|
TempX[1] := X.FInt[1];
|
1112 |
|
|
TempX[2] := X.FInt[2];
|
1113 |
|
|
TempX[3] := X.FInt[3];
|
1114 |
|
|
|
1115 |
|
|
{force the divisor and dividend positive}
|
1116 |
|
|
IsNeg := FInt[3] < 0;
|
1117 |
|
|
if IsNeg then
|
1118 |
|
|
Int128ChgSign(FInt);
|
1119 |
|
|
XIsNeg := TempX[3] < 0;
|
1120 |
|
|
if XIsNeg then
|
1121 |
|
|
Int128ChgSign(TempX);
|
1122 |
|
|
|
1123 |
|
|
{easy case: X is 1.0: set the correct sign}
|
1124 |
|
|
if (TempX[0] = Int128One_0) and (TempX[1] = Int128One_1) and
|
1125 |
|
|
(TempX[2] = 0) and (TempX[3] = 0) then begin
|
1126 |
|
|
if (IsNeg xor XIsNeg) then
|
1127 |
|
|
Int128ChgSign(FInt);
|
1128 |
|
|
Exit;
|
1129 |
|
|
end;
|
1130 |
|
|
|
1131 |
|
|
{easy case: compare the dividend and divisor: if they're equal,
|
1132 |
|
|
set ourselves to 1.0 with the correct sign}
|
1133 |
|
|
if (Int128Compare(FInt, TempX) = 0) then begin
|
1134 |
|
|
FInt[0] := Int128One_0;
|
1135 |
|
|
FInt[1] := Int128One_1;
|
1136 |
|
|
FInt[2] := 0;
|
1137 |
|
|
FInt[3] := 0;
|
1138 |
|
|
if (IsNeg xor XIsNeg) then
|
1139 |
|
|
Int128ChgSign(FInt);
|
1140 |
|
|
Exit;
|
1141 |
|
|
end;
|
1142 |
|
|
|
1143 |
|
|
{no more easy cases: just do the division}
|
1144 |
|
|
Int128Divide(FInt, TempX);
|
1145 |
|
|
|
1146 |
|
|
{set the sign}
|
1147 |
|
|
if (IsNeg xor XIsNeg) then
|
1148 |
|
|
Int128ChgSign(FInt);
|
1149 |
|
|
end;
|
1150 |
|
|
{--------}
|
1151 |
|
|
function TStDecimal.IsNegative : boolean;
|
1152 |
|
|
begin
|
1153 |
|
|
{if the most significant longint is negative, so is the value}
|
1154 |
|
|
Result := FInt[3] < 0;
|
1155 |
|
|
end;
|
1156 |
|
|
{--------}
|
1157 |
|
|
function TStDecimal.IsOne : boolean;
|
1158 |
|
|
begin
|
1159 |
|
|
Result := (FInt[0] = Int128One_0) and (FInt[1] = Int128One_1) and
|
1160 |
|
|
(FInt[2] = 0) and (FInt[3] = 0);
|
1161 |
|
|
end;
|
1162 |
|
|
{--------}
|
1163 |
|
|
function TStDecimal.IsPositive : boolean;
|
1164 |
|
|
begin
|
1165 |
|
|
{if the most significant longint is positive, so is the value; if it
|
1166 |
|
|
is zero, one of the other longints must be non-zero for the value
|
1167 |
|
|
to be positive}
|
1168 |
|
|
Result := (FInt[3] > 0) or
|
1169 |
|
|
((FInt[3] = 0) and
|
1170 |
|
|
((FInt[2] <> 0) or (FInt[1] <> 0) or (FInt[0] <> 0)));
|
1171 |
|
|
end;
|
1172 |
|
|
{--------}
|
1173 |
|
|
function TStDecimal.IsZero : boolean;
|
1174 |
|
|
begin
|
1175 |
|
|
Result := (FInt[0] = 0) and (FInt[1] = 0) and
|
1176 |
|
|
(FInt[2] = 0) and (FInt[3] = 0);
|
1177 |
|
|
end;
|
1178 |
|
|
{--------}
|
1179 |
|
|
procedure TStDecimal.Multiply(X : TStDecimal);
|
1180 |
|
|
begin
|
1181 |
|
|
if (X = nil) then
|
1182 |
|
|
SetToZero
|
1183 |
|
|
else
|
1184 |
|
|
Int128Multiply(FInt, X.FInt);
|
1185 |
|
|
end;
|
1186 |
|
|
{--------}
|
1187 |
|
|
procedure TStDecimal.RaiseToPower(N : integer);
|
1188 |
|
|
var
|
1189 |
|
|
Accum : TStInt128;
|
1190 |
|
|
Mask : longint;
|
1191 |
|
|
IsNeg : boolean;
|
1192 |
|
|
begin
|
1193 |
|
|
{take care of some easy cases}
|
1194 |
|
|
if (N < 0) then
|
1195 |
|
|
raise EStDecMathError.Create(stscDecMathNegExpS);
|
1196 |
|
|
if (N = 0) then begin
|
1197 |
|
|
SetToOne;
|
1198 |
|
|
Exit;
|
1199 |
|
|
end;
|
1200 |
|
|
if (N = 1) then
|
1201 |
|
|
Exit;
|
1202 |
|
|
|
1203 |
|
|
{force the value positive}
|
1204 |
|
|
IsNeg := FInt[3] < 0;
|
1205 |
|
|
if IsNeg then
|
1206 |
|
|
Int128ChgSign(FInt);
|
1207 |
|
|
|
1208 |
|
|
{initialize the accumulator to 1.0}
|
1209 |
|
|
Accum[0] := Int128One_0;
|
1210 |
|
|
Accum[1] := Int128One_1;
|
1211 |
|
|
Accum[2] := 0;
|
1212 |
|
|
Accum[3] := 0;
|
1213 |
|
|
|
1214 |
|
|
{set the bit mask}
|
1215 |
|
|
Mask := longint($80000000);
|
1216 |
|
|
|
1217 |
|
|
{find the first set bit in the exponent}
|
1218 |
|
|
while ((N and Mask) = 0) do
|
1219 |
|
|
Mask := Mask shr 1;
|
1220 |
|
|
|
1221 |
|
|
{calculate the power}
|
1222 |
|
|
while (Mask <> 0) do begin
|
1223 |
|
|
Int128Multiply(Accum, Accum);
|
1224 |
|
|
if ((N and Mask) <> 0) then
|
1225 |
|
|
Int128Multiply(Accum, FInt);
|
1226 |
|
|
Mask := Mask shr 1;
|
1227 |
|
|
end;
|
1228 |
|
|
|
1229 |
|
|
{save the calculated value}
|
1230 |
|
|
FInt[0] := Accum[0];
|
1231 |
|
|
FInt[1] := Accum[1];
|
1232 |
|
|
FInt[2] := Accum[2];
|
1233 |
|
|
FInt[3] := Accum[3];
|
1234 |
|
|
|
1235 |
|
|
{force the value negative if required}
|
1236 |
|
|
if IsNeg and Odd(N) then
|
1237 |
|
|
Int128ChgSign(FInt);
|
1238 |
|
|
end;
|
1239 |
|
|
{--------}
|
1240 |
|
|
procedure TStDecimal.Round(aRound : TStRoundMethod; aDecPl : integer);
|
1241 |
|
|
var
|
1242 |
|
|
IsNeg : boolean;
|
1243 |
|
|
begin
|
1244 |
|
|
{check decimal places parameter to be in range}
|
1245 |
|
|
if not ((0 <= aDecPl) and (aDecPl <= MaxDecPl)) then
|
1246 |
|
|
raise EStDecMathError.Create(stscDecMathRoundPlacesS);
|
1247 |
|
|
|
1248 |
|
|
{force the value positive}
|
1249 |
|
|
IsNeg := FInt[3] < 0;
|
1250 |
|
|
if IsNeg then
|
1251 |
|
|
Int128ChgSign(FInt);
|
1252 |
|
|
|
1253 |
|
|
{perform the rounding}
|
1254 |
|
|
Int128Round(FInt, aRound, aDecPl);
|
1255 |
|
|
|
1256 |
|
|
{force the value negative if it was negative}
|
1257 |
|
|
if IsNeg then
|
1258 |
|
|
Int128ChgSign(FInt);
|
1259 |
|
|
end;
|
1260 |
|
|
{--------}
|
1261 |
|
|
procedure TStDecimal.SetToOne;
|
1262 |
|
|
begin
|
1263 |
|
|
FInt[0] := Int128One_0;
|
1264 |
|
|
FInt[1] := Int128One_1;
|
1265 |
|
|
FInt[2] := 0;
|
1266 |
|
|
FInt[3] := 0;
|
1267 |
|
|
end;
|
1268 |
|
|
{--------}
|
1269 |
|
|
procedure TStDecimal.SetToZero;
|
1270 |
|
|
begin
|
1271 |
|
|
FInt[0] := 0;
|
1272 |
|
|
FInt[1] := 0;
|
1273 |
|
|
FInt[2] := 0;
|
1274 |
|
|
FInt[3] := 0;
|
1275 |
|
|
end;
|
1276 |
|
|
{--------}
|
1277 |
|
|
procedure TStDecimal.Subtract(X : TStDecimal);
|
1278 |
|
|
var
|
1279 |
|
|
MinusX : TStInt128;
|
1280 |
|
|
begin
|
1281 |
|
|
if (X <> nil) then begin
|
1282 |
|
|
MinusX[0] := X.FInt[0];
|
1283 |
|
|
MinusX[1] := X.FInt[1];
|
1284 |
|
|
MinusX[2] := X.FInt[2];
|
1285 |
|
|
MinusX[3] := X.FInt[3];
|
1286 |
|
|
Int128ChgSign(MinusX);
|
1287 |
|
|
Int128Add(Fint, MinusX);
|
1288 |
|
|
end;
|
1289 |
|
|
end;
|
1290 |
|
|
{--------}
|
1291 |
|
|
procedure TStDecimal.SubtractOne;
|
1292 |
|
|
var
|
1293 |
|
|
MinusOne : TStInt128;
|
1294 |
|
|
begin
|
1295 |
|
|
MinusOne[0] := Int128One_0;
|
1296 |
|
|
MinusOne[1] := Int128One_1;
|
1297 |
|
|
MinusOne[2] := 0;
|
1298 |
|
|
MinusOne[3] := 0;
|
1299 |
|
|
Int128ChgSign(MinusOne);
|
1300 |
|
|
Int128Add(FInt, MinusOne);
|
1301 |
|
|
end;
|
1302 |
|
|
{====================================================================}
|
1303 |
|
|
|
1304 |
|
|
end.
|