Added bisection root finding algorithm with custom upper bound

UPolynomialRoots.pas

@@ -45,6 +45,7 @@ type
     function GetIsolatingInterval(const AC, AK, AH: Cardinal; constref ABound: TBigInt): TIsolatingInterval;
   public
     function Bisect(constref APolynomial: TBigIntPolynomial): TIsolatingIntervals;
+    function Bisect(constref APolynomial: TBigIntPolynomial; constref ABound: TBigInt): TIsolatingIntervals;
   end;
 
 implementation
@@ -85,9 +86,17 @@ begin
   Result.B := (AC + AH) * ABound;
 end;
 
+function TRootIsolation.Bisect(constref APolynomial: TBigIntPolynomial): TIsolatingIntervals;
+var
+  bound: TBigInt;
+begin
+  bound := CalcSimpleRootBound(APolynomial);
+  Result := Bisect(APolynomial, bound);
+end;
+
 // This is adapted from
 // https://en.wikipedia.org/wiki/Real-root_isolation#Bisection_method
-function TRootIsolation.Bisect(constref APolynomial: TBigIntPolynomial): TIsolatingIntervals;
+function TRootIsolation.Bisect(constref APolynomial: TBigIntPolynomial; constref ABound: TBigInt): TIsolatingIntervals;
 type
   TWorkItem = record
     C, K: Cardinal;
@@ -95,7 +104,6 @@ type
   end;
   TWorkStack = specialize TStack<TWorkItem>;
 var
-  bound: TBigInt;
   item: TWorkItem;
   stack: TWorkStack;
   n, v: Integer;
@@ -104,12 +112,10 @@ begin
   Result := TIsolatingIntervals.Create;
   stack := TWorkStack.Create;
 
-  bound := CalcSimpleRootBound(APolynomial);
   n := item.P.Degree;
-
   item.C := 0;
   item.K := 0;
-  item.P := APolynomial.ScaleVariable(bound);
+  item.P := APolynomial.ScaleVariable(ABound);
   stack.Push(item);
 
   while stack.Count > 0 do
@@ -120,7 +126,7 @@ begin
       // Found an integer root at 0.
       item.P := item.P.DivideByVariable;
       Dec(n);
-      Result.Add(GetIsolatingInterval(item.C, item.K, 0, bound));
+      Result.Add(GetIsolatingInterval(item.C, item.K, 0, ABound));
     end;
 
     varq := item.P.RevertOrderOfCoefficients.TranslateVariableByOne;
@@ -128,7 +134,7 @@ begin
     if v = 1 then
     begin
       // Found isolating interval.
-      Result.Add(GetIsolatingInterval(item.C, item.K, 1, bound));
+      Result.Add(GetIsolatingInterval(item.C, item.K, 1, ABound));
     end
     else if v > 1 then
     begin

tests/UPolynomialRootsTestCases.pas

@@ -29,18 +29,43 @@ type
   { TPolynomialRootsTestCase }
 
   TPolynomialRootsTestCase = class(TTestCase)
+  private
+    procedure AssertBisectResult(constref AIsolatingIntervals: TIsolatingIntervals; constref AExpectedRoots:
+      array of Cardinal);
   protected
     FRootIsolation: TRootIsolation;
     procedure SetUp; override;
     procedure TearDown; override;
   published
-    procedure TestBisectionRootIsolation;
+    procedure TestBisectNoBound;
+    procedure TestBisectWithBound;
   end;
 
 implementation
 
 { TPolynomialRootsTestCase }
 
+procedure TPolynomialRootsTestCase.AssertBisectResult(constref AIsolatingIntervals: TIsolatingIntervals; constref
+  AExpectedRoots: array of Cardinal);
+var
+  exp: Cardinal;
+  ri: TIsolatingInterval;
+  found: Boolean;
+begin
+  AssertEquals('Unexpected number of isolating intervals.', Length(AExpectedRoots), AIsolatingIntervals.Count);
+  for exp in AExpectedRoots do
+  begin
+    found := False;
+    for ri in AIsolatingIntervals do
+      if (ri.A <= exp) and (exp <= ri.B) then
+      begin
+        found := True;
+        Break;
+      end;
+    AssertTrue('No isolating interval for expected root ' + IntToStr(exp) + ' found.', found);
+  end;
+end;
+
 procedure TPolynomialRootsTestCase.SetUp;
 begin
   inherited SetUp;
@@ -53,32 +78,34 @@ begin
   inherited TearDown;
 end;
 
-procedure TPolynomialRootsTestCase.TestBisectionRootIsolation;
+procedure TPolynomialRootsTestCase.TestBisectNoBound;
 const
   expRoots: array of Cardinal = (34000, 23017, 5);
 var
-  exp: Cardinal;
   a: TBigIntPolynomial;
   r: TIsolatingIntervals;
-  ri: TIsolatingInterval;
-  found: Boolean;
 begin
   // y = 3 * (x - 34000) * (x - 23017) * (x - 5) * (x^2 - 19) * (x + 112)
   //   = 3 * x^6 - 170730 * x^5 + 2329429920 * x^4 + 251300082690 * x^3 - 1270471872603 * x^2 + 4774763204640 * x - 24979889760000
   a := TBigIntPolynomial.Create([-24979889760000, 4774763204640, -1270471872603, 251300082690, 2329429920, -170730, 3]);
   r := FRootIsolation.Bisect(a);
-  AssertEquals(Length(expRoots), r.Count);
+  AssertBisectResult(r, expRoots);
-  for exp in expRoots do
+  r.Free;
-  begin
-    found := False;
-    for ri in r do
-      if (ri.A <= exp) and (exp <= ri.B) then
-      begin
-        found := True;
-        Break;
-      end;
-    AssertTrue('No isolating interval for expected root ' + IntToStr(exp) + ' found.', found);
 end;
+
+procedure TPolynomialRootsTestCase.TestBisectWithBound;
+const
+  expRoots: array of Cardinal = (23017, 5);
+var
+  a: TBigIntPolynomial;
+  r: TIsolatingIntervals;
+begin
+  // y = 3 * (x - 34000) * (x - 23017) * (x - 5) * (x^2 - 19) * (x + 112)
+  //   = 3 * x^6 - 170730 * x^5 + 2329429920 * x^4 + 251300082690 * x^3 - 1270471872603 * x^2 + 4774763204640 * x - 24979889760000
+  a := TBigIntPolynomial.Create([-24979889760000, 4774763204640, -1270471872603, 251300082690, 2329429920, -170730, 3]);
+  r := FRootIsolation.Bisect(a, TBigInt.One << 15);
+  AssertBisectResult(r, expRoots);
+  r.Free;
 end;
 
 initialization