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Merge branch 'bigint' into day24-analytical

This commit is contained in:
Stefan Müller 2024-05-16 17:14:00 +02:00
parent 53827acf9b 62887ad1d7
commit c25317c0fc
4 changed files with 1093 additions and 12 deletions
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178
UBigInt.pas
View File

@ -35,6 +35,8 @@ type
FDigits: TDigits; FDigits: TDigits;
FIsNegative: Boolean; FIsNegative: Boolean;
function GetSign: Integer;
// Copies consecutive digits from this BigInt to create a new one. The result will be positive. Leading zeros are // Copies consecutive digits from this BigInt to create a new one. The result will be positive. Leading zeros are
// removed from the result, but AIndex + ACount must not exceed the number of digits of this BigInt. // removed from the result, but AIndex + ACount must not exceed the number of digits of this BigInt.
// AIndex is the first (least significant) digit to be taken. The digit with this index will become the 0th digit of // AIndex is the first (least significant) digit to be taken. The digit with this index will become the 0th digit of
@ -66,11 +68,19 @@ type
// Sign * (Abs(a) * Abs(b)) // Sign * (Abs(a) * Abs(b))
// where Sign is 1 for ReturnNegative = False and -1 otherwise. // where Sign is 1 for ReturnNegative = False and -1 otherwise.
class function MultiplyAbsoluteValues(constref AA, AB: TBigInt; const AReturnNegative: Boolean): TBigInt; static; class function MultiplyAbsoluteValues(constref AA, AB: TBigInt; const AReturnNegative: Boolean): TBigInt; static;
class function FromHexOrBinString(const AValue: string; const AFromBase: Integer): TBigInt; static;
class function ConvertDigitBlock(const AValue: string; var AStartIndex: Integer; const ACharBlockSize, AFromBase:
Integer): Cardinal;
public public
property IsNegative: Boolean read FIsNegative; property IsNegative: Boolean read FIsNegative;
property Sign: Integer read GetSign;
class property Zero: TBigInt read GetZero; class property Zero: TBigInt read GetZero;
function CompareTo(constref AOther: TBigInt): Integer; function CompareTo(constref AOther: TBigInt): Integer;
function TryToInt64(out AOutput: Int64): Boolean;
class function FromInt64(const AValue: Int64): TBigInt; static; class function FromInt64(const AValue: Int64): TBigInt; static;
class function FromHexadecimalString(const AValue: string): TBigInt; static;
class function FromBinaryString(const AValue: string): TBigInt; static;
end; end;
{ Operators } { Operators }
@ -83,6 +93,10 @@ type
operator shl (const A: TBigInt; const B: Integer): TBigInt; operator shl (const A: TBigInt; const B: Integer): TBigInt;
operator = (const A, B: TBigInt): Boolean; operator = (const A, B: TBigInt): Boolean;
operator <> (const A, B: TBigInt): Boolean; operator <> (const A, B: TBigInt): Boolean;
operator < (const A, B: TBigInt): Boolean;
operator <= (const A, B: TBigInt): Boolean;
operator > (const A, B: TBigInt): Boolean;
operator >= (const A, B: TBigInt): Boolean;
implementation implementation
@ -98,6 +112,16 @@ const
{ TBigInt } { TBigInt }
function TBigInt.GetSign: Integer;
begin
if FIsNegative then
Result := -1
else if (Length(FDigits) > 1) or (FDigits[0] <> 0) then
Result := 1
else
Result := 0;
end;
function TBigInt.GetSegment(const AIndex, ACount: Integer): TBigInt; function TBigInt.GetSegment(const AIndex, ACount: Integer): TBigInt;
var var
trimmedCount: Integer; trimmedCount: Integer;
@ -105,8 +129,7 @@ begin
trimmedCount := ACount; trimmedCount := ACount;
while (trimmedCount > 1) and (FDigits[AIndex + trimmedCount - 1] = 0) do while (trimmedCount > 1) and (FDigits[AIndex + trimmedCount - 1] = 0) do
Dec(trimmedCount); Dec(trimmedCount);
SetLength(Result.FDigits, trimmedCount); Result.FDigits := Copy(FDigits, AIndex, trimmedCount);
Move(FDigits[AIndex], Result.FDigits[0], CDigitSize * trimmedCount);
Result.FIsNegative := False; Result.FIsNegative := False;
end; end;
@ -138,7 +161,7 @@ end;
class function TBigInt.AddAbsoluteValues(constref AA, AB: TBigInt; const AReturnNegative: Boolean): TBigInt; class function TBigInt.AddAbsoluteValues(constref AA, AB: TBigInt; const AReturnNegative: Boolean): TBigInt;
var var
i, lenA, lenB, len, shorter: Integer; i, j, lenA, lenB, len, shorter: Integer;
carry: Cardinal; carry: Cardinal;
begin begin
lenA := Length(AA.FDigits); lenA := Length(AA.FDigits);
@ -185,9 +208,11 @@ begin
// carry-overs. This avoids additional tests for finding the shorter digit array. // carry-overs. This avoids additional tests for finding the shorter digit array.
if (i < lenA) or (i < lenB) then if (i < lenA) or (i < lenB) then
if lenA >= lenB then if lenA >= lenB then
Move(AA.FDigits[i], Result.FDigits[i], CDigitSize * (len - i)) for j := i to len - 1 do
Result.FDigits[j] := AA.FDigits[j]
else else
Move(AB.FDigits[i], Result.FDigits[i], CDigitSize * (len - i)); for j := i to len - 1 do
Result.FDigits[j] := AB.FDigits[j];
// Applies the remaining carry-overs until the end of the prepared result digit array. // Applies the remaining carry-overs until the end of the prepared result digit array.
while (carry > 0) and (i < len) do while (carry > 0) and (i < len) do
@ -212,7 +237,7 @@ class function TBigInt.SubtractAbsoluteValues(constref AA, AB: TBigInt; const AR
var var
a, b: TBigInt; a, b: TBigInt;
carry: Cardinal; carry: Cardinal;
i, lastNonZeroDigitIndex, len: Integer; i, j, lastNonZeroDigitIndex, len: Integer;
begin begin
// Establishes the operand order, such that Abs(a) is not less than Abs(b). // Establishes the operand order, such that Abs(a) is not less than Abs(b).
if (AA.CompareToAbsoluteValues(AB) >= 0) then if (AA.CompareToAbsoluteValues(AB) >= 0) then
@ -277,7 +302,8 @@ begin
// Copies the missing unchanged digits from the longer operand to the result, if any. If there are none, then no trim // Copies the missing unchanged digits from the longer operand to the result, if any. If there are none, then no trim
// needs to occur because the most significant digit is not zero. // needs to occur because the most significant digit is not zero.
if i < len then if i < len then
Move(a.FDigits[i], Result.FDigits[i], CDigitSize * (len - i)) for j := i to len - 1 do
Result.FDigits[j] := a.FDigits[j]
else if (lastNonZeroDigitIndex + 1 < len) then else if (lastNonZeroDigitIndex + 1 < len) then
// Trims leading zeros from the digits array. // Trims leading zeros from the digits array.
Delete(Result.FDigits, lastNonZeroDigitIndex + 1, len - lastNonZeroDigitIndex - 1); Delete(Result.FDigits, lastNonZeroDigitIndex + 1, len - lastNonZeroDigitIndex - 1);
@ -362,6 +388,70 @@ begin
end; end;
end; end;
class function TBigInt.FromHexOrBinString(const AValue: string; const AFromBase: Integer): TBigInt;
var
charBlockSize, offset, i, j, k, remainder: Integer;
d: Cardinal;
begin
// 2 ^ (32 / charBlockSize) = AFromBase
case AFromBase of
2: charBlockSize := 32;
16: charBlockSize := 8;
end;
if AValue[1] = '-' then
begin
offset := 2;
Result.FIsNegative := True;
end
else begin
offset := 1;
Result.FIsNegative := False;
end;
// Calculates the first (most significant) digit d of the result.
DivMod(AValue.Length - offset + 1, charBlockSize, i, remainder);
k := offset;
d := 0;
// Checks the first block of chars that is not a full block.
if remainder > 0 then
d := ConvertDigitBlock(AValue, k, remainder, AFromBase);
// Checks full blocks of chars for first digit.
while (d = 0) and (i > 0) do
begin
Dec(i);
d := ConvertDigitBlock(AValue, k, charBlockSize, AFromBase);
end;
// Checks for zero.
if (d = 0) and (i = 0) then
Result := Zero
else begin
// Initializes the array of digits.
SetLength(Result.FDigits, i + 1);
Result.FDigits[i] := d;
// Calculates the other digits.
for j := i - 1 downto 0 do
Result.FDigits[j] := ConvertDigitBlock(AValue, k, charBlockSize, AFromBase);
end;
end;
class function TBigInt.ConvertDigitBlock(const AValue: string; var AStartIndex: Integer; const ACharBlockSize,
AFromBase: Integer): Cardinal;
var
part: string;
begin
part := Copy(AValue, AStartIndex, ACharBlockSize);
Inc(AStartIndex, ACharBlockSize);
case AFromBase of
2: part := '%' + part;
8: part := '&' + part;
16: part := '$' + part;
end;
Result := StrToDWord(part);
end;
function TBigInt.CompareTo(constref AOther: TBigInt): Integer; function TBigInt.CompareTo(constref AOther: TBigInt): Integer;
begin begin
if FIsNegative = AOther.FIsNegative then if FIsNegative = AOther.FIsNegative then
@ -372,6 +462,35 @@ begin
Result := -Result; Result := -Result;
end; end;
function TBigInt.TryToInt64(out AOutput: Int64): Boolean;
begin
AOutput := 0;
Result := False;
case Length(FDigits) of
0: Result := True;
1: begin
AOutput := FDigits[0];
if FIsNegative then
AOutput := -AOutput;
Result := True;
end;
2: begin
if FDigits[1] <= Integer.MaxValue then
begin
AOutput := FDigits[1] * CBase + FDigits[0];
if FIsNegative then
AOutput := -AOutput;
Result := True;
end
else if (FDigits[1] = Integer.MaxValue + 1) and (FDigits[0] = 0) and FIsNegative then
begin
AOutput := Int64.MinValue;
Result := True;
end;
end;
end;
end;
class function TBigInt.FromInt64(const AValue: Int64): TBigInt; class function TBigInt.FromInt64(const AValue: Int64): TBigInt;
var var
absVal: Int64; absVal: Int64;
@ -391,6 +510,16 @@ begin
end; end;
end; end;
class function TBigInt.FromHexadecimalString(const AValue: string): TBigInt;
begin
Result := FromHexOrBinString(AValue, 16);
end;
class function TBigInt.FromBinaryString(const AValue: string): TBigInt;
begin
Result := FromHexOrBinString(AValue, 2);
end;
{ Operators } { Operators }
operator := (const A: Int64): TBigInt; operator := (const A: Int64): TBigInt;
@ -403,9 +532,13 @@ var
len: Integer; len: Integer;
begin begin
len := Length(A.FDigits); len := Length(A.FDigits);
SetLength(Result.FDigits, len); if (len > 1) or (A.FDigits[0] > 0) then
Move(A.FDigits[0], Result.FDigits[0], len); begin
Result.FIsNegative := not A.FIsNegative; Result.FDigits := Copy(A.FDigits, 0, len);
Result.FIsNegative := not A.FIsNegative;
end
else
Result := TBigInt.Zero;
end; end;
operator + (const A, B: TBigInt): TBigInt; operator + (const A, B: TBigInt): TBigInt;
@ -475,7 +608,10 @@ begin
// Performs full digit shifts by copy if there are no bit shifts. // Performs full digit shifts by copy if there are no bit shifts.
len := Length(A.FDigits); len := Length(A.FDigits);
SetLength(Result.FDigits, len + digitShifts); SetLength(Result.FDigits, len + digitShifts);
Move(A.FDigits[0], Result.FDigits[digitShifts], CDigitSize * len); for i := 0 to digitShifts - 1 do
Result.FDigits[i] := 0;
for i := 0 to len - 1 do
Result.FDigits[i + digitShifts] := A.FDigits[i];
end; end;
Result.FIsNegative := A.IsNegative; Result.FIsNegative := A.IsNegative;
@ -492,5 +628,25 @@ begin
Result := A.CompareTo(B) <> 0; Result := A.CompareTo(B) <> 0;
end; end;
operator < (const A, B: TBigInt): Boolean;
begin
Result := A.CompareTo(B) < 0;
end;
operator <= (const A, B: TBigInt): Boolean;
begin
Result := A.CompareTo(B) <= 0;
end;
operator > (const A, B: TBigInt): Boolean;
begin
Result := A.CompareTo(B) > 0;
end;
operator >= (const A, B: TBigInt): Boolean;
begin
Result := A.CompareTo(B) >= 0;
end;
end. end.

8
tests/AdventOfCodeFPCUnit.lpi
View File

@ -144,10 +144,18 @@
<Filename Value="UPolynomialTestCases.pas"/> <Filename Value="UPolynomialTestCases.pas"/>
<IsPartOfProject Value="True"/> <IsPartOfProject Value="True"/>
</Unit> </Unit>
<Unit>
<Filename Value="..\UPolynomialRoots.pas"/>
<IsPartOfProject Value="True"/>
</Unit>
<Unit> <Unit>
<Filename Value="UPolynomialRootsTestCases.pas"/> <Filename Value="UPolynomialRootsTestCases.pas"/>
<IsPartOfProject Value="True"/> <IsPartOfProject Value="True"/>
</Unit> </Unit>
<Unit>
<Filename Value="UBigIntTestCases.pas"/>
<IsPartOfProject Value="True"/>
</Unit>
</Units> </Units>
</ProjectOptions> </ProjectOptions>
<CompilerOptions> <CompilerOptions>

2
tests/AdventOfCodeFPCUnit.lpr
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@ -9,7 +9,7 @@ uses
UHotSpringsTestCases, UPointOfIncidenceTestCases, UParabolicReflectorDishTestCases, ULensLibraryTestCases, UHotSpringsTestCases, UPointOfIncidenceTestCases, UParabolicReflectorDishTestCases, ULensLibraryTestCases,
UFloorWillBeLavaTestCases, UClumsyCrucibleTestCases, ULavaductLagoonTestCases, UAplentyTestCases, UFloorWillBeLavaTestCases, UClumsyCrucibleTestCases, ULavaductLagoonTestCases, UAplentyTestCases,
UPulsePropagationTestCases, UStepCounterTestCases, USandSlabsTestCases, ULongWalkTestCases, UPulsePropagationTestCases, UStepCounterTestCases, USandSlabsTestCases, ULongWalkTestCases,
UNeverTellMeTheOddsTestCases, UPolynomialTestCases, UPolynomialRootsTestCases; UNeverTellMeTheOddsTestCases, UBigIntTestCases, UPolynomialTestCases, UPolynomialRootsTestCases;
{$R *.res} {$R *.res}

917
tests/UBigIntTestCases.pas Normal file
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@ -0,0 +1,917 @@
{
Solutions to the Advent Of Code.
Copyright (C) 2022-2024 Stefan Müller
This program is free software: you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free Software
Foundation, either version 3 of the License, or (at your option) any later
version.
This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with
this program. If not, see <http://www.gnu.org/licenses/>.
}
unit UBigIntTestCases;
{$mode ObjFPC}{$H+}
interface
uses
Classes, SysUtils, fpcunit, testregistry, UBigInt;
type
// TODO: TBigIntAbsTestCase
// TODO: TBigIntFromDecTestCase
// TestCase('80091110002223289436355210101231765016693209176113648', 10, '80091110002223289436355210101231765016693209176113648');
// TestCase('-3201281944789146858325672846129872035678639439423746384198412894', 10, '-3201281944789146858325672846129872035678639439423746384198412894');
// TestCase('000000000000000000000000000000000000000080091', 10, '80091');
// TestCase('0000000000000000000000000000000000000000000000', 10, '0');
// TestCase('-000000000000000000000000000000004687616873215464763146843215486643215', 10, '-4687616873215464763146843215486643215');
// TestTryFromDec
// TODO: TBigIntFromOctTestCase
// OctValue, 8, DecValue:
// TestCase('3132521', 8, '832849');
// TestCase('772350021110002226514', 8, '9123449598017875276');
// TestCase('-247515726712721', 8, '-11520970560977');
// TestCase('000000000000000000000000000000000000000072', 8, '58');
// TestCase('000000000000000000000000000000000000000000000000000000000', 8, '0');
// OctValue, HexValue:
// TestCase('7440737076307076026772', '3C83BE3E638F82DFA');
// TestCase('1336625076203401614325664', '16F6547C8380E31ABB4');
// TestCase('3254410316166274457257121050201413373225', '6AC84338ECBC97ABCA22840C2DF695');
// TestCase('1441330072562106272767270117307274151276215', '642D81D5C88CBAFBAE09EC75E1A57C8D');
// TestCase('3533665174054677131163436413756431236774257271133', '3ADED4F82CDF964E71E85FBA329EFE2BD725B');
// TestCase('57346415317074055631627141161054073014006076155710653', '5EE686B3C782DCCE5CC271160EC18061F1B791AB');
// TestCase('000000000000000000000000000000245745251354033134', 8, '5838773085550172');
// TestTryFromOct
// TODO: TBigIntUnaryPlusTestCase
// TODO: TBigIntBitwiseLogicalTestCase
// TODO: TBigIntComplementTestCase
// TODO: TBigIntConversionTestCase
// TODO: TBigIntIncrementDecrementTestCase
// TODO: TBigIntQuotientTestCase
// TODO: TBigIntShiftRightTestCase
{ TBigIntSignTestCase }
TBigIntSignTestCase = class(TTestCase)
private
procedure Test(const AHexValue: string; const AExpectedSign: Integer);
published
procedure TestZero;
procedure TestShortPositive;
procedure TestShortNegative;
procedure TestLongPositive;
procedure TestLongNegative;
end;
{ TBigIntFromInt64TestCase }
TBigIntFromInt64TestCase = class(TTestCase)
private
procedure Test(const AValue: Int64);
published
procedure TestShortPositive;
procedure TestShortNegative;
procedure TestLongPositive;
procedure TestLongNegative;
procedure TestZero;
end;
{ TBigIntFromHexTestCase }
TBigIntFromHexTestCase = class(TTestCase)
private
procedure TestShort(const AHexValue: string; const ADecValue: Int64);
published
procedure TestPositive;
procedure TestNegative;
procedure TestZero;
procedure TestLeadingZeros;
// TODO: TestTryFromHex
end;
{ TBigIntFromBinTestCase }
TBigIntFromBinTestCase = class(TTestCase)
private
procedure TestShort(const ABinValue: string; const ADecValue: Int64);
published
procedure TestPositive;
procedure TestNegative;
procedure TestLeadingZeros;
// TODO: TestTryFromBin
end;
{ TBigIntUnaryMinusTestCase }
TBigIntUnaryMinusTestCase = class(TTestCase)
private
procedure Test(const AValue: Int64);
procedure TestTwice(const AValue: Int64);
published
procedure TestZero;
procedure TestPositive;
procedure TestNegative;
procedure TestPositiveTwice;
procedure TestNegativeTwice;
end;
{ TBigIntSumTestCase }
TBigIntSumTestCase = class(TTestCase)
private
procedure Test(const AHexValueLeft, AHexValueRight, AHexValueSum: string);
published
procedure TestShort;
procedure TestPositivePlusPositive;
procedure TestNegativePlusNegative;
procedure TestLargePositivePlusSmallNegative;
procedure TestSmallPositivePlusLargeNegative;
procedure TestLargeNegativePlusSmallPositive;
procedure TestSmallNegativePlusLargePositive;
procedure TestZeroPlusPositive;
procedure TestPositivePlusZero;
procedure TestZero;
procedure TestSumShorterLeft;
procedure TestSumShorterRight;
procedure TestSumEndsInCarry;
procedure TestSumEndsInCarryNewDigit;
procedure TestSumMultiCarry;
end;
{ TBigIntDifferenceTestCase }
TBigIntDifferenceTestCase = class(TTestCase)
private
procedure Test(const AHexValueMinuend, AHexValueSubtrahend, AHexValueDifference: string);
published
procedure TestShort;
procedure TestLargePositiveMinusSmallPositive;
procedure TestSmallPositiveMinusLargePositive;
procedure TestLargeNegativeMinusSmallNegative;
procedure TestSmallNegativeMinusLargeNegative;
procedure TestNegativeMinusPositive;
procedure TestPositiveMinusNegative;
procedure TestLargeOperands;
procedure TestPositiveMinusZero;
procedure TestZeroMinusPositive;
procedure TestZero;
procedure TestDifferenceShorterLeft;
procedure TestDifferenceShorterRight;
procedure TestDifferenceEndsInCarry;
procedure TestDifferenceEndsInCarryLosingDigit;
procedure TestDifferenceMultiCarry;
end;
{ TBigIntProductTestCase }
TBigIntProductTestCase = class(TTestCase)
private
procedure Test(const AHexValueLeft, AHexValueRight, AHexValueProduct: string);
published
procedure TestShort;
procedure TestLongPositiveTimesPositive;
procedure TestLongPositiveTimesNegative;
procedure TestLongNegativeTimesPositive;
procedure TestLongNegativeTimesNegative;
procedure TestZeroTimesPositive;
procedure TestZeroTimesNegative;
procedure TestZero;
end;
{ TBigIntShiftLeftTestCase }
TBigIntShiftLeftTestCase = class(TTestCase)
private
procedure Test(const AHexValueOperand: string; const AShift: Integer; const AHexValueResult: string);
published
procedure TestShort;
procedure TestShortWithCarry;
procedure TestLongWithCarry;
procedure TestLongWithMultiDigitCarry;
procedure TestWithAlignedDigits;
procedure TestZero;
end;
{ TBigIntEqualityTestCase }
TBigIntEqualityTestCase = class(TTestCase)
private
procedure TestEqual(const AValue: Int64);
procedure TestEqualHex(const AHexValue: string);
procedure TestNotEqualHex(const AHexValueLeft, AHexValueRight: string);
published
procedure TestShortEqual;
procedure TestLongEqual;
procedure TestZeroEqual;
procedure TestShortNotEqual;
procedure TestLongNotEqualSign;
procedure TestZeroNotEqual;
end;
{ TBigIntComparisonTestCase }
TBigIntComparisonTestCase = class(TTestCase)
private
procedure TestLessThan(const AHexValueLeft, AHexValueRight: string);
procedure TestGreaterThan(const AHexValueLeft, AHexValueRight: string);
procedure TestEqual(const AHexValue: string);
published
procedure TestLessSameLength;
procedure TestLessShorterLeft;
procedure TestLessNegativeShorterRight;
procedure TestGreaterSameLength;
procedure TestGreaterShorterRight;
procedure TestGreaterNegativeShorterLeft;
procedure TestEqualPositive;
procedure TestEqualNegative;
procedure TestEqualZero;
end;
implementation
{ TBigIntSignTestCase }
procedure TBigIntSignTestCase.Test(const AHexValue: string; const AExpectedSign: Integer);
var
a: TBigInt;
begin
a := TBigInt.FromHexadecimalString(AHexValue);
AssertEquals(AExpectedSign, a.Sign);
end;
procedure TBigIntSignTestCase.TestZero;
begin
Test('0', 0);
end;
procedure TBigIntSignTestCase.TestShortPositive;
begin
Test('36A', 1);
end;
procedure TBigIntSignTestCase.TestShortNegative;
begin
Test('-29B7', -1);
end;
procedure TBigIntSignTestCase.TestLongPositive;
begin
Test('1240168AB09ABDF8283B77124', 1);
end;
procedure TBigIntSignTestCase.TestLongNegative;
begin
Test('-192648F1305DD04757A24C873F29F60B6184B5', -1);
end;
{ TBigIntFromInt64TestCase }
procedure TBigIntFromInt64TestCase.Test(const AValue: Int64);
var
a: TBigInt;
act: Int64;
begin
a := TBigInt.FromInt64(AValue);
AssertTrue('BigInt from ''' + IntToStr(AValue) + ''' could not be converted back to an Int64 value.',
a.TryToInt64(act));
AssertEquals('BigInt from ''' + IntToStr(AValue) + ''' converted back to Int64 was not equal to initial value.',
AValue, act);
end;
procedure TBigIntFromInt64TestCase.TestShortPositive;
begin
Test(17);
Test(4864321);
Test(Cardinal.MaxValue);
end;
procedure TBigIntFromInt64TestCase.TestShortNegative;
begin
Test(-54876);
Test(Integer.MinValue);
end;
procedure TBigIntFromInt64TestCase.TestLongPositive;
begin
Test(5800754643214654);
Test(Int64.MaxValue);
end;
procedure TBigIntFromInt64TestCase.TestLongNegative;
begin
Test(-94136445555883);
Test(Int64.MinValue);
end;
procedure TBigIntFromInt64TestCase.TestZero;
begin
Test(0);
end;
{ TBigIntFromHexTestCase }
procedure TBigIntFromHexTestCase.TestShort(const AHexValue: string; const ADecValue: Int64);
var
a, b: TBigInt;
begin
a := TBigInt.FromHexadecimalString(AHexValue);
b := TBigInt.FromInt64(ADecValue);
AssertTrue('BigInt from hexadecimal string ''' + AHexValue + ''' was not equal to ''' + IntToStr(ADecValue) + '''.',
a = b);
end;
procedure TBigIntFromHexTestCase.TestPositive;
begin
TestShort('91', 145);
TestShort('800E111000222', 2252766466540066);
TestShort('DE0B227802AB233', 999995000000000563);
TestShort('19C0048155000', 453000000000000);
TestShort('3B9ACA00', 1000000000);
end;
procedure TBigIntFromHexTestCase.TestNegative;
begin
TestShort('-47', -71);
TestShort('-800E111000222', -2252766466540066);
TestShort('-4512FF3', -72429555);
end;
procedure TBigIntFromHexTestCase.TestZero;
begin
TestShort('0', 0);
TestShort('-0', 0);
end;
procedure TBigIntFromHexTestCase.TestLeadingZeros;
begin
TestShort('000000000000000000000000000000004B', 75);
TestShort('-00000000000000000000000000000000A2', -162);
TestShort('00000000000000000000000000000000FF452849DB01', 280672493755137);
TestShort('000000000000000000000000000000000000', 0);
TestShort('-000000000000000000000000000000000000', 0);
end;
{ TBigIntFromBinTestCase }
procedure TBigIntFromBinTestCase.TestShort(const ABinValue: string; const ADecValue: Int64);
var
a, b: TBigInt;
begin
a := TBigInt.FromBinaryString(ABinValue);
b := TBigInt.FromInt64(ADecValue);
AssertTrue('BigInt from binary string ''' + ABinValue + ''' was not equal to ''' + IntToStr(ADecValue) + '''.',
a = b);
end;
procedure TBigIntFromBinTestCase.TestPositive;
begin
TestShort('110101010101101101010010110000101010100101001001010100110', 120109162101379750);
end;
procedure TBigIntFromBinTestCase.TestNegative;
begin
TestShort('-11100100111010100111000111100011110000100110110111100101010010', -4123780452057839954);
end;
procedure TBigIntFromBinTestCase.TestLeadingZeros;
begin
TestShort('0000000000000000000000000000000000000000000000000000000000000000000000111', 7);
TestShort('0000000000000000000000000000000000000000000000000000000000000000000000000000000', 0);
end;
{ TBigIntUnaryMinusTestCase }
procedure TBigIntUnaryMinusTestCase.Test(const AValue: Int64);
var
a, b: TBigInt;
begin
a := TBigInt.FromInt64(AValue);
b := TBigInt.FromInt64(-AValue);
AssertTrue('Negative BigInt from ''' + IntToStr(AValue) + ''' was not equal to the BigInt from the negative value.',
b = -a);
end;
procedure TBigIntUnaryMinusTestCase.TestTwice(const AValue: Int64);
var
a: TBigInt;
begin
a := TBigInt.FromInt64(AValue);
AssertTrue('BigInt from ''' + IntToStr(AValue) + '''was not equal to the double negative of itself.',
a = -(-a));
end;
procedure TBigIntUnaryMinusTestCase.TestZero;
begin
Test(0);
end;
procedure TBigIntUnaryMinusTestCase.TestPositive;
begin
Test(234972358233);
end;
procedure TBigIntUnaryMinusTestCase.TestNegative;
begin
Test(-999214927400);
end;
procedure TBigIntUnaryMinusTestCase.TestPositiveTwice;
begin
TestTwice(8647613456601);
end;
procedure TBigIntUnaryMinusTestCase.TestNegativeTwice;
begin
TestTwice(-38600421308534);
end;
{ TBigIntSumTestCase }
procedure TBigIntSumTestCase.Test(const AHexValueLeft, AHexValueRight, AHexValueSum: string);
var
a, b, s: TBigInt;
begin
a := TBigInt.FromHexadecimalString(AHexValueLeft);
b := TBigInt.FromHexadecimalString(AHexValueRight);
s := TBigInt.FromHexadecimalString(AHexValueSum);
AssertTrue('Sum of BigInt from ''' + AHexValueLeft + ''' and from ''' + AHexValueRight
+ ''' was not equal to the BigInt from ''' + AHexValueSum + '''.',
s = a + b);
end;
procedure TBigIntSumTestCase.TestShort;
begin
Test('5', '7', 'C');
end;
procedure TBigIntSumTestCase.TestPositivePlusPositive;
begin
Test('7000822000111', '9000911000333', '10001133000444');
end;
procedure TBigIntSumTestCase.TestNegativePlusNegative;
begin
Test('-129B92A84643D608141', '-4574DBA206951ECFE', '-12E10783E84A6B26E3F');
end;
procedure TBigIntSumTestCase.TestLargePositivePlusSmallNegative;
begin
Test('87BAD26984', '-8DCB20461', '7EDE206523');
end;
procedure TBigIntSumTestCase.TestSmallPositivePlusLargeNegative;
begin
Test('A58301E4006', '-9851DA0FD433', '-8DF9A9F1942D');
end;
procedure TBigIntSumTestCase.TestLargeNegativePlusSmallPositive;
begin
Test('-1FDB60CB5698870', '99CB1E00DE', '-1FDB572EA4B8792');
end;
procedure TBigIntSumTestCase.TestSmallNegativePlusLargePositive;
begin
Test('-1ED598BBFEC2', '59CD4F02ECB56', '57DFF5772CC94');
end;
procedure TBigIntSumTestCase.TestZeroPlusPositive;
begin
Test('0', '9BB000911FF5A000333', '9BB000911FF5A000333');
end;
procedure TBigIntSumTestCase.TestPositivePlusZero;
begin
Test('23009605A16BCBB294A1FD', '0', '23009605A16BCBB294A1FD');
end;
procedure TBigIntSumTestCase.TestZero;
begin
Test('0', '0', '0');
end;
procedure TBigIntSumTestCase.TestSumShorterLeft;
begin
Test('3FFFF', '9000911000222', '9000911040221');
end;
procedure TBigIntSumTestCase.TestSumShorterRight;
begin
Test('9000911000555', '3000EEEE', '900094100F443');
end;
procedure TBigIntSumTestCase.TestSumEndsInCarry;
begin
Test('4000444000220', 'FFFFFFFF', '400054400021F');
end;
procedure TBigIntSumTestCase.TestSumEndsInCarryNewDigit;
begin
Test('99990000', '99990055', '133320055');
end;
procedure TBigIntSumTestCase.TestSumMultiCarry;
begin
Test('FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF', 'FFFFFFFF', '1000000000000000000000000FFFFFFFE');
end;
{ TBigIntDifferenceTestCase }
procedure TBigIntDifferenceTestCase.Test(const AHexValueMinuend, AHexValueSubtrahend, AHexValueDifference: string);
var
a, b, s: TBigInt;
begin
a := TBigInt.FromHexadecimalString(AHexValueMinuend);
b := TBigInt.FromHexadecimalString(AHexValueSubtrahend);
s := TBigInt.FromHexadecimalString(AHexValueDifference);
AssertTrue('Difference of BigInt from ''' + AHexValueMinuend + ''' and from ''' + AHexValueSubtrahend
+ ''' was not equal to the BigInt from ''' + AHexValueDifference + '''.',
s = a - b);
end;
procedure TBigIntDifferenceTestCase.TestShort;
begin
Test('230', '6D', '1C3');
end;
procedure TBigIntDifferenceTestCase.TestLargePositiveMinusSmallPositive;
begin
Test('910AAD86E5002455', '72DE020F932A1', '91037FA6C406F1B4');
end;
procedure TBigIntDifferenceTestCase.TestSmallPositiveMinusLargePositive;
begin
Test('3127541F4C0AA', '3818CD9FBE652B', '-3506585DC9A481');
end;
procedure TBigIntDifferenceTestCase.TestLargeNegativeMinusSmallNegative;
begin
Test('-B12BE1E20098', '-148F3137CED396', '13DE0555ECD2FE');
end;
procedure TBigIntDifferenceTestCase.TestSmallNegativeMinusLargeNegative;
begin
Test('-AF3FF1EC626908C', '-18295', '-AF3FF1EC6250DF7');
end;
procedure TBigIntDifferenceTestCase.TestNegativeMinusPositive;
begin
Test('-E493506B19', '20508ED255', '-104E3DF3D6E');
end;
procedure TBigIntDifferenceTestCase.TestPositiveMinusNegative;
begin
Test('114EEC66851AFD98', '-100AA4308C5249FBBFADEB89CD6A7D9CC', '100AA4308C5249FBC0C2DA5035BC2D764');
end;
procedure TBigIntDifferenceTestCase.TestLargeOperands;
begin
Test('1069FC8EA3D99C39E1C07AA078B77B5CC679CB448563345A878C603D32FB0F8FEFE02AD9574A5EB6',
'1069FC8EA3D99C39E1C07AA078B77B5CC679CB448563345A878C603D32FB0F8FEFE023C522B87F8C',
'7143491DF2A');
end;
procedure TBigIntDifferenceTestCase.TestPositiveMinusZero;
begin
Test('8ABB000911FF5A000333', '0', '8ABB000911FF5A000333');
end;
procedure TBigIntDifferenceTestCase.TestZeroMinusPositive;
begin
Test('0', '243961982DDD64F81B2', '-243961982DDD64F81B2');
end;
procedure TBigIntDifferenceTestCase.TestZero;
begin
Test('0', '0', '0');
end;
procedure TBigIntDifferenceTestCase.TestDifferenceShorterLeft;
begin
Test('3FFFF', '9000911040221', '-9000911000222');
end;
procedure TBigIntDifferenceTestCase.TestDifferenceShorterRight;
begin
Test('900094100F443', '3000EEEE', '9000911000555');
end;
procedure TBigIntDifferenceTestCase.TestDifferenceEndsInCarry;
begin
Test('400054400021F', 'FFFFFFFF', '4000444000220');
end;
procedure TBigIntDifferenceTestCase.TestDifferenceEndsInCarryLosingDigit;
begin
Test('133320055', '99990000', '99990055');
end;
procedure TBigIntDifferenceTestCase.TestDifferenceMultiCarry;
begin
Test('1000000000000000000000000FFFFFFFE', 'FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF', 'FFFFFFFF');
end;
{ TBigIntProductTestCase }
procedure TBigIntProductTestCase.Test(const AHexValueLeft, AHexValueRight, AHexValueProduct: string);
var
a, b, s: TBigInt;
begin
a := TBigInt.FromHexadecimalString(AHexValueLeft);
b := TBigInt.FromHexadecimalString(AHexValueRight);
s := TBigInt.FromHexadecimalString(AHexValueProduct);
AssertTrue('Product of BigInt from ''' + AHexValueLeft + ''' and from ''' + AHexValueRight
+ ''' was not equal to the BigInt from ''' + AHexValueProduct + '''.',
s = a * b);
end;
procedure TBigIntProductTestCase.TestShort;
begin
Test('9', 'B', '63');
Test('29E531A', 'DF5F299', '248E3915103E8A');
end;
procedure TBigIntProductTestCase.TestLongPositiveTimesPositive;
begin
Test('FFFFFFFF', 'FFFFFFFF', 'FFFFFFFE00000001');
Test('4873B23699D07741F1544862221B1966AA84512', '4DE0013', '160A322C656DEB1DD6D721D36E35F2E29B4D2A18192056');
Test('74FD3E6988116762', '22DB271AFC4941', 'FEDC8CD51DEE46BE83C283B5E31E2');
end;
procedure TBigIntProductTestCase.TestLongPositiveTimesNegative;
begin
Test('23401834190D12FF3210F0B0129123AA', '-A4C0530234', '-16AF8B019CA1436BBFD1F1FB08494FFC9EF7E09288');
end;
procedure TBigIntProductTestCase.TestLongNegativeTimesPositive;
begin
Test('-3ACB78882923810', 'F490B8022A4BCBFF34E01', '-382B2B9851BC93CB0308B502C3B036D71810');
end;
procedure TBigIntProductTestCase.TestLongNegativeTimesNegative;
begin
Test('-554923FB201', '-9834FDC032', '32B514C1BA1E774EE8432');
end;
procedure TBigIntProductTestCase.TestZeroTimesPositive;
begin
Test('0', '1AF5D0039B888AC00F299', '0');
end;
procedure TBigIntProductTestCase.TestZeroTimesNegative;
begin
Test('0', '-1AF5D0039B888AC00F299', '0');
end;
procedure TBigIntProductTestCase.TestZero;
begin
Test('0', '0', '0');
end;
{ TBigIntShiftLeftTestCase }
procedure TBigIntShiftLeftTestCase.Test(const AHexValueOperand: string; const AShift: Integer; const AHexValueResult: string);
var
a, s: TBigInt;
begin
a := TBigInt.FromHexadecimalString(AHexValueOperand);
s := TBigInt.FromHexadecimalString(AHexValueResult);
AssertTrue('BigInt from hexadecimal string ''' + AHexValueOperand + ''' shifted left by ''' + IntToStr(AShift)
+ ''' was not equal to BigInt from hexadecimal string ''' + AHexValueResult + '''.',
s = (a << AShift));
end;
procedure TBigIntShiftLeftTestCase.TestShort;
begin
// BIN 101
// BIN 101000
Test('5', 3, '28');
end;
procedure TBigIntShiftLeftTestCase.TestShortWithCarry;
begin
// BIN 1110 1101 0111 0001 1010 1010
// BIN 1 1101 1010 1110 0011 0101 0100 0000 0000 0000
Test('ED71AA', 13, '1DAE354000');
end;
procedure TBigIntShiftLeftTestCase.TestLongWithCarry;
begin
// BIN 1 0011 0000 1011 0010 0011 1110 0100 1100 1111 1001 0101 0100 0100 0101
// BIN 10 0110 0001 0110 0100 0111 1100 1001 1001 1111 0010 1010 1000 1000 1010 0000 0000
Test('130B23E4CF95445', 9, '261647C99F2A88A00');
end;
procedure TBigIntShiftLeftTestCase.TestLongWithMultiDigitCarry;
begin
Test('C99F12A735A3B83901BF92011', 140, 'C99F12A735A3B83901BF9201100000000000000000000000000000000000');
end;
procedure TBigIntShiftLeftTestCase.TestWithAlignedDigits;
begin
// Shifts the left operand by a multiple of the length of full TBigInt digits, so the digits will be shifted, but not
// changed.
Test('10F0F39C5E', 32 * 4, '10F0F39C5E00000000000000000000000000000000');
end;
procedure TBigIntShiftLeftTestCase.TestZero;
begin
Test('0', 119, '0');
end;
{ TBigIntEqualityTestCase }
procedure TBigIntEqualityTestCase.TestEqual(const AValue: Int64);
var
a, b: TBigInt;
begin
a := TBigInt.FromInt64(AValue);
b := TBigInt.FromInt64(AValue);
AssertTrue('Two BigInt from ''' + IntToStr(AValue) + ''' were not equal.', a = b);
AssertFalse('Two BigInt from ''' + IntToStr(AValue) + ''' were un-equal.', a <> b);
end;
procedure TBigIntEqualityTestCase.TestEqualHex(const AHexValue: string);
var
a, b: TBigInt;
begin
a := TBigInt.FromHexadecimalString(AHexValue);
b := TBigInt.FromHexadecimalString(AHexValue);
AssertTrue('Two BigInt from ''' + AHexValue + ''' were not equal.', a = b);
AssertFalse('Two BigInt from ''' + AHexValue + ''' were un-equal.', a <> b);
end;
procedure TBigIntEqualityTestCase.TestNotEqualHex(const AHexValueLeft, AHexValueRight: string);
var
a, b: TBigInt;
begin
a := TBigInt.FromHexadecimalString(AHexValueLeft);
b := TBigInt.FromHexadecimalString(AHexValueRight);
AssertTrue('BigInt from ''' + AHexValueLeft + ''' and from ''' + AHexValueRight + ''' were not un-equal.',
a <> b);
AssertFalse('BigInt from ''' + AHexValueLeft + ''' and from ''' + AHexValueRight + ''' were equal.',
a = b);
end;
procedure TBigIntEqualityTestCase.TestShortEqual;
begin
TestEqual(14);
TestEqualHex('8000111000111');
end;
procedure TBigIntEqualityTestCase.TestLongEqual;
begin
TestEqualHex('5AB60FF292A014BF1DD0A');
end;
procedure TBigIntEqualityTestCase.TestZeroEqual;
begin
TestEqual(0);
end;
procedure TBigIntEqualityTestCase.TestShortNotEqual;
begin
TestNotEqualHex('9FF99920', '100');
TestNotEqualHex('20001110002111', '70001110007111');
end;
procedure TBigIntEqualityTestCase.TestLongNotEqualSign;
begin
TestNotEqualHex('48843AB320FF0041123A', '-48843AB320FF0041123A');
TestNotEqualHex('-B13F79D842A30957DD09523667', 'B13F79D842A30957DD09523667');
end;
procedure TBigIntEqualityTestCase.TestZeroNotEqual;
begin
TestNotEqualHex('0', 'F');
TestNotEqualHex('568F7', '0');
end;
{ TBigIntComparisonTestCase }
procedure TBigIntComparisonTestCase.TestLessThan(const AHexValueLeft, AHexValueRight: string);
var
a, b: TBigInt;
begin
a := TBigInt.FromHexadecimalString(AHexValueLeft);
b := TBigInt.FromHexadecimalString(AHexValueRight);
AssertTrue('BigInt from ''' + AHexValueLeft + ''' was greater than BigInt from ''' + AHexValueRight + '''.',
a < b);
AssertTrue('BigInt from ''' + AHexValueLeft + ''' was greater or equal than BigInt from ''' + AHexValueRight + '''.',
a <= b);
AssertFalse('BigInt from ''' + AHexValueLeft + ''' was greater than BigInt from ''' + AHexValueRight + '''.',
a > b);
AssertFalse('BigInt from ''' + AHexValueLeft + ''' was greater or equal than BigInt from ''' + AHexValueRight + '''.',
a >= b);
end;
procedure TBigIntComparisonTestCase.TestGreaterThan(const AHexValueLeft, AHexValueRight: string);
var
a, b: TBigInt;
begin
a := TBigInt.FromHexadecimalString(AHexValueLeft);
b := TBigInt.FromHexadecimalString(AHexValueRight);
AssertFalse('BigInt from ''' + AHexValueLeft + ''' was less than BigInt from ''' + AHexValueRight + '''.',
a < b);
AssertFalse('BigInt from ''' + AHexValueLeft + ''' was less or equal than BigInt from ''' + AHexValueRight + '''.',
a <= b);
AssertTrue('BigInt from ''' + AHexValueLeft + ''' was less than BigInt from ''' + AHexValueRight + '''.',
a > b);
AssertTrue('BigInt from ''' + AHexValueLeft + ''' was less or equal than BigInt from ''' + AHexValueRight + '''.',
a >= b);
end;
procedure TBigIntComparisonTestCase.TestEqual(const AHexValue: string);
var
a, b: TBigInt;
begin
a := TBigInt.FromHexadecimalString(AHexValue);
b := TBigInt.FromHexadecimalString(AHexValue);
AssertFalse('First BigInt from ''' + AHexValue + ''' was less than the second.',
a < b);
AssertTrue('First BigInt from ''' + AHexValue + ''' was greater than the second.',
a <= b);
AssertFalse('First BigInt from ''' + AHexValue + ''' was greater than the second.',
a > b);
AssertTrue('First BigInt from ''' + AHexValue + ''' was less than the second.',
a >= b);
end;
procedure TBigIntComparisonTestCase.TestLessSameLength;
begin
TestLessThan('104234FF2B29100C012', '234867AB261F1003429103C');
TestLessThan('-9812FB2964AC7632865238BBD3', '294625DF51B2A842582244C18163490');
TestLessThan('-12834653A2856DF8', '-A946C2BF89401B8');
TestLessThan('-2F846', '0');
TestLessThan('0', 'FF67B');
end;
procedure TBigIntComparisonTestCase.TestLessShorterLeft;
begin
TestLessThan('34FF2B29100C012', '234867AB261F1003429103C');
TestLessThan('0', 'BFF008112BA00012');
end;
procedure TBigIntComparisonTestCase.TestLessNegativeShorterRight;
begin
TestLessThan('-9B72844AC', '1F3486B');
TestLessThan('-BB884F022111190', '0');
end;
procedure TBigIntComparisonTestCase.TestGreaterSameLength;
begin
TestGreaterThan('B042104234FF2B29100C012', '23867AB261F1003429103C');
TestGreaterThan('1294B77', '-611F3B93');
TestGreaterThan('-782163498326593562D548AAF715B4DC9143E42C68F39A29BB2', '-FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF');
TestGreaterThan('783BDA0', '0');
TestGreaterThan('0', '-99B6D');
end;
procedure TBigIntComparisonTestCase.TestGreaterShorterRight;
begin
TestGreaterThan('102343234423FF67278B11ADD345F6BB21232C9129100C012', '234867AB261F1003429103C');
TestGreaterThan('249D00F63BBAA8668B23', '0');
end;
procedure TBigIntComparisonTestCase.TestGreaterNegativeShorterLeft;
begin
TestGreaterThan('81F2A7B78B812', '-23490D7F19F247F91A365B1893BB701');
TestGreaterThan('0', '-80F88242B34127');
end;
procedure TBigIntComparisonTestCase.TestEqualPositive;
begin
TestEqual('A44B80191059CA123318921A219BB');
end;
procedure TBigIntComparisonTestCase.TestEqualNegative;
begin
TestEqual('-28912798DD1246DAC9FB4269908012D496896812FF3A8D071B32');
end;
procedure TBigIntComparisonTestCase.TestEqualZero;
begin
TestEqual('0');
end;
initialization
RegisterTest(TBigIntSignTestCase);
RegisterTest(TBigIntFromInt64TestCase);
RegisterTest(TBigIntFromHexTestCase);
RegisterTest(TBigIntFromBinTestCase);
RegisterTest(TBigIntUnaryMinusTestCase);
RegisterTest(TBigIntSumTestCase);
RegisterTest(TBigIntDifferenceTestCase);
RegisterTest(TBigIntProductTestCase);
RegisterTest(TBigIntShiftLeftTestCase);
RegisterTest(TBigIntEqualityTestCase);
RegisterTest(TBigIntComparisonTestCase);
end.