Boris Novgorodov

You are right, but also note that condition"if Abs(c) <= eps" really does not refer to "Not meaningful" Only simultaneous zero sums like "if Abs(c) + Abs(s) <= eps" should be considered as extra case

There is List of Delphi language features and version in which they were introduced/deprecated

You show decimal representation while version components correspond to nibbles of hex representation 11264dec = $2C00, so your version number is 2.12.0.0 (2.$C.0.0)

Quick demonstration how space partition methods could help to get significant gain. Code uses simple 64x64 grid with cells 32x32. Each cell contains indexes of points belonging to this cell. At first brute-force method counts (doubled) number of point pairs with distance<= 4. The second code piece checks only cells neighbouring to the cell containing examined point. For 64K points gain is about 200 times. Complexity is O(N^2) vs O(N^3/2) (for proper cell size and uniform point distribution). More advanced structures like kd-tree might provide better performance for complex cases too (worse distribution etc). var Wdt, Hgt, NPts: Integer; i, j, k, r, m: Integer; t: DWord; sqd, maxsqd, cnt, gx, gy: Integer; P: TArray<TPoint>; Grid: array[0..63, 0..63] of TArray<Integer>; begin Wdt := 2048; Hgt := 2048; NPts := 64 * 1024; RandSeed := 42; SetLength(P, NPts); for i := 0 to NPts - 1 do begin P[i] := Point(Random(Wdt), Random(Hgt)); Grid[P[i].Y shr 5, P[i].X shr 5] := Grid[P[i].Y shr 5, P[i].X shr 5] + [i]; end; maxsqd := 16; cnt := 0; t := GetTickCount; for j := 0 to NPts - 1 do for i := 0 to NPts - 1 do begin sqd := Sqr(P[i].X - P[j].X) + Sqr(P[i].Y - P[j].Y); if sqd <= maxsqd then Inc(cnt); end; Memo1.Lines.Add(Format('%d %d', [cnt, GetTickCount - t])); cnt := 0; t := GetTickCount; for i := 0 to NPts - 1 do begin gx := P[i].X shr 5; gy := P[i].Y shr 5; for j := Max(0, gy - 1) to Min(gy + 1, 63) do for k := Max(0, gx - 1) to Min(gx + 1, 63) do for m := 0 to High(Grid[j, k]) do begin r := Grid[j, k, m]; sqd := Sqr(P[i].X - P[r].X) + Sqr(P[i].Y - P[r].Y); if sqd <= maxsqd then Inc(cnt); end; end; Memo1.Lines.Add(Format('%d %d', [cnt, GetTickCount - t])); count time (milliseconds) 115406 11466 115406 62