Merge branch 'bigint' into day24-analytical

UBigInt.pas

@@ -76,6 +76,10 @@ type
     property IsNegative: Boolean read FIsNegative;
     property Sign: Integer read GetSign;
     class property Zero: TBigInt read GetZero;
+
+    // Returns the index of the most significant bit, i.e. returns integer k, where 2^k is the largest power of 2 that
+    // is less than or equal to the absolute value of the number itself. Returns -1 if the given number is 0.
+    function GetMostSignificantBitIndex: Int64;
     function CompareTo(constref AOther: TBigInt): Integer;
     function TryToInt64(out AOutput: Int64): Boolean;
     // TODO: ToString is currently for debug output only.
@@ -461,6 +465,21 @@ begin
   Result := StrToDWord(part);
 end;
 
+function TBigInt.GetMostSignificantBitIndex: Int64;
+var
+  high, i: Integer;
+begin
+  high := Length(FDigits) - 1;
+  if (high = 0) and (FDigits[0] = 0) then
+    Result := -1
+  else begin
+    i := CBitsPerDigit - 1;
+    while ((1 << i) and FDigits[high]) = 0 do
+      Dec(i);
+    Result := high * CBitsPerDigit + i;
+  end;
+end;
+
 function TBigInt.CompareTo(constref AOther: TBigInt): Integer;
 begin
   if FIsNegative = AOther.FIsNegative then
@@ -549,6 +568,7 @@ end;
 operator := (const A: Int64): TBigInt;
 begin
   Result := TBigInt.FromInt64(A);
+  //WriteLn(':=a op: ', Result.ToString);
 end;
 
 operator - (const A: TBigInt): TBigInt;
@@ -563,6 +583,8 @@ begin
   end
   else
     Result := TBigInt.Zero;
+  //WriteLn('            a: ', A.ToString);
+  //WriteLn('-a  op: ', Result.ToString);
 end;
 
 operator + (const A, B: TBigInt): TBigInt;
@@ -571,6 +593,9 @@ begin
     Result := TBigInt.AddAbsoluteValues(A, B, A.IsNegative)
   else
     Result := TBigInt.SubtractAbsoluteValues(A, B, A.IsNegative);
+  //WriteLn('            a: ', A.ToString);
+  //WriteLn('            b: ', B.ToString);
+  //WriteLn('a+b op: ', Result.ToString);
 end;
 
 operator - (const A, B: TBigInt): TBigInt;
@@ -579,6 +604,9 @@ begin
     Result := TBigInt.SubtractAbsoluteValues(A, B, A.IsNegative)
   else
     Result := TBigInt.AddAbsoluteValues(A, B, A.IsNegative);
+  //WriteLn('            a: ', A.ToString);
+  //WriteLn('            b: ', B.ToString);
+  //WriteLn('a-b op: ', Result.ToString);
 end;
 
 operator * (const A, B: TBigInt): TBigInt;
@@ -587,6 +615,9 @@ begin
     Result := TBigInt.Zero
   else
     Result := TBigInt.MultiplyAbsoluteValues(A, B, A.IsNegative <> B.IsNegative);
+  //WriteLn('            a: ', A.ToString);
+  //WriteLn('            b: ', B.ToString);
+  //WriteLn('a*b op: ', Result.ToString);
 end;
 
 operator shl(const A: TBigInt; const B: Integer): TBigInt;
@@ -639,6 +670,8 @@ begin
 
     Result.FIsNegative := A.IsNegative;
   end;
+  //WriteLn('            a: ', A.ToString);
+  //WriteLn('a<< op: ', Result.ToString);
 end;
 
 operator = (const A, B: TBigInt): Boolean;

tests/UBigIntTestCases.pas

@@ -70,6 +70,17 @@ type
     procedure TestLongNegative;
   end;
 
+  { TBigIntMostSignificantBitIndexTestCase }
+
+  TBigIntMostSignificantBitIndexTestCase = class(TTestCase)
+  private
+    procedure Test(const ABinValue: string; const AExpectedIndex: Int64);
+  published
+    procedure TestZero;
+    procedure TestShort;
+    procedure TestLong;
+  end;
+
   { TBigIntFromInt64TestCase }
 
   TBigIntFromInt64TestCase = class(TTestCase)
@@ -271,6 +282,37 @@ begin
   Test('-192648F1305DD04757A24C873F29F60B6184B5', -1);
 end;
 
+{ TBigIntMostSignificantBitIndexTestCase }
+
+procedure TBigIntMostSignificantBitIndexTestCase.Test(const ABinValue: string; const AExpectedIndex: Int64);
+var
+  a: TBigInt;
+begin
+  a := TBigInt.FromBinaryString(ABinValue);
+  AssertEquals('BigInt from binary string ''' + ABinValue + ''' did not have its most significant bit at index '''
+    + IntToStr(AExpectedIndex) + '''.',
+    AExpectedIndex, a.GetMostSignificantBitIndex);
+end;
+
+procedure TBigIntMostSignificantBitIndexTestCase.TestZero;
+begin
+  Test('0', -1);
+end;
+
+procedure TBigIntMostSignificantBitIndexTestCase.TestShort;
+begin
+  Test('1', 0);
+  Test('11111101111001', 13);
+  Test('10010111101100001110110101111000', 31);
+end;
+
+procedure TBigIntMostSignificantBitIndexTestCase.TestLong;
+begin
+  Test('111100010101010100011101010100011', 32);
+  Test('11101001101010111101000101010001010101010101111111001010101010010100101000101011111001000111001001100011', 103);
+  Test('111101100011110110111011010111100000000001010111101110101101101100101010110111101011010101001100', 95);
+end;
+
 { TBigIntFromInt64TestCase }
 
 procedure TBigIntFromInt64TestCase.Test(const AValue: Int64);
@@ -903,6 +945,7 @@ end;
 initialization
 
   RegisterTest(TBigIntSignTestCase);
+  RegisterTest(TBigIntMostSignificantBitIndexTestCase);
   RegisterTest(TBigIntFromInt64TestCase);
   RegisterTest(TBigIntFromHexTestCase);
   RegisterTest(TBigIntFromBinTestCase);