{ -----------------------------------
汎用共通処理関数ユニット
2004/08/18
・作成
・RoundOFF関数などを実装
・CeilEx/FloorExも実装
2004/10/02
・RandomRangeExを実装

//----------------------------------- }
unit MathUnit;

interface

uses
  Math,
  XPtest;

function RoundOff(X: Extended): Int64;
function RoundOffEx(const X: Extended; DigitNumber: Integer): Extended;
function IsSame(A, B: Extended; e: Extended=0): Boolean;
procedure testRoundOff;
function CeilEx(const X: Extended; DigitNumber: Integer): Extended;
procedure testCeil;
function FloorEx(const X: Extended; DigitNumber: Integer): Extended; overload;
procedure testFloor;

function RandomRangeEx(const AFrom, ATo: Extended; Digit: Byte): Extended;

implementation

{-------------------------------
//  HELPにのっているRoundOff
備考:
履歴:       2004/08/18
              LongintからInt64に変更した
//------------------------------}
function RoundOff(X: Extended): Int64;
begin
  if x >= 0 then Result := Trunc(x + 0.5)
  else Result := Trunc(x - 0.5);
end;
//------------------------------

{-------------------------------
//  RoundOffEx
機能:       任意の桁で四捨五入します。
引数説明:   X: 四捨五入対象
            DigitNumber: 桁数
              3:100の桁
              2:10の桁
              1:一桁目
              0:処理しない
              -1:少数点第一位(通常のRoundOffと同じ処理)
              -2:少数点第二位
              -3:少数点第三位
戻り値:     四捨五入後のX
            処理できない場合Xの値そのままが入るはず
備考:
履歴:       2001/09/04
//------------------------------}
function RoundOffEx(const X: Extended; DigitNumber: Integer): Extended;
var
  CalcDigit: Extended;
begin
  Result := X;
  if X = 0 then Exit;

  case DigitNumber of
    0: Exit;
    1..High(DigitNumber):
    begin
      CalcDigit := IntPower(10, DigitNumber);
      Result := Roundoff(X / CalcDigit) * CalcDigit;
    end;
    Low(DigitNumber)..-1:
    begin
      CalcDigit := IntPower(10, Abs(DigitNumber)-1);
      Result := Roundoff(X * CalcDigit) / CalcDigit;
    end;
  end;
end;
//------------------------------

{-------------------------------
//  IsSame
機能:       適当に小さい誤差の範囲内で
            浮動小数点値が等しいかどうかを調べる関数
引数説明:   A, B: 比較対照
            e: ±の誤差
戻り値:     true:等しい false:等しくない
備考:
履歴:       2001/09/05
//------------------------------}
function IsSame(A, B: Extended; e: Extended=0): Boolean;
begin
  Result := Abs(A-B) <= e;
end;
//------------------------------

procedure testRoundOff;
begin
  Check(True, IsSame(150, RoundOffEx(145, 1),0.000001));
  Check(True, IsSame(150, RoundOffEx(154, 1),0.000001));
  Check(True, IsSame(140, RoundOffEx(144, 1),0.000001));
  Check(True, IsSame(160, RoundOffEx(155, 1),0.000001));
  Check(True, IsSame(150, RoundOffEx(150, 1),0.000001));
  Check(True, IsSame( 10, RoundOffEx( 14, 1),0.000001));
  Check(True, IsSame( 10, RoundOffEx(  5, 1),0.000001));
  Check(True, IsSame(  0, RoundOffEx(  4, 1),0.000001));
  Check(True, IsSame( 20, RoundOffEx( 15, 1),0.000001));
  Check(True, IsSame( 10, RoundOffEx( 10, 1),0.000001));

  Check(True, IsSame(200, RoundOffEx(150, 2),0.000001));
  Check(True, IsSame(100, RoundOffEx(140, 2),0.000001));
  Check(True, IsSame(100, RoundOffEx(149, 2),0.000001));
  Check(True, IsSame(200, RoundOffEx(249, 2),0.000001));
  Check(True, IsSame(100, RoundOffEx( 50, 2),0.000001));

  Check(True, IsSame(1000, RoundOffEx(1400, 3),0.000001));
  Check(True, IsSame(2000, RoundOffEx(1500, 3),0.000001));
  Check(True, IsSame(2000, RoundOffEx(1600, 3),0.000001));
  Check(True, IsSame(1000, RoundOffEx(1499, 3),0.000001));
  Check(True, IsSame(2000, RoundOffEx(2480, 3),0.000001));

  Check(True, IsSame(-150, RoundOffEx(-145, 1),0.000001));
  Check(True, IsSame(-150, RoundOffEx(-154, 1),0.000001));
  Check(True, IsSame(-140, RoundOffEx(-144, 1),0.000001));
  Check(True, IsSame(-160, RoundOffEx(-155, 1),0.000001));
  Check(True, IsSame(-150, RoundOffEx(-150, 1),0.000001));
  Check(True, IsSame(- 10, RoundOffEx( -14, 1),0.000001));
  Check(True, IsSame(- 10, RoundOffEx(  -5, 1),0.000001));
  Check(True, IsSame(-  0, RoundOffEx(  -4, 1),0.000001));
  Check(True, IsSame(- 20, RoundOffEx( -15, 1),0.000001));
  Check(True, IsSame(- 10, RoundOffEx( -10, 1),0.000001));

  Check(True, IsSame(-200, RoundOffEx(-150, 2),0.000001));
  Check(True, IsSame(-100, RoundOffEx(-140, 2),0.000001));
  Check(True, IsSame(-100, RoundOffEx(-149, 2),0.000001));
  Check(True, IsSame(-200, RoundOffEx(-249, 2),0.000001));
  Check(True, IsSame(-100, RoundOffEx( -50, 2),0.000001));

  Check(True, IsSame(-1000, RoundOffEx(-1400, 3),0.000001));
  Check(True, IsSame(-2000, RoundOffEx(-1500, 3),0.000001));
  Check(True, IsSame(-2000, RoundOffEx(-1600, 3),0.000001));
  Check(True, IsSame(-1000, RoundOffEx(-1499, 3),0.000001));
  Check(True, IsSame(-2000, RoundOffEx(-2480, 3),0.000001));

  Check(True, IsSame(0, RoundOffEx(0.49, -1),0.000001));
  Check(True, IsSame(1, RoundOffEx(0.50, -1),0.000001));
  Check(True, IsSame(1, RoundOffEx(1.49, -1),0.000001));
  Check(True, IsSame(2, RoundOffEx(1.50, -1),0.000001));
  Check(True, IsSame(1.0, RoundOffEx(1.04, -2),0.000001));
  Check(TRue, IsSame(1.1, RoundOffEx(1.05, -2),0.000001));

  Check(True, IsSame(1.0001, RoundOffEx(1.00005000, -5),0.00000001));
  Check(True, IsSame(1.0000, RoundOffEx(1.00004999, -5),0.000001));
  Check(True, IsSame(1.000050, RoundOffEx(1.00005000, -6),0.000001));
  Check(True, IsSame(1.000050, RoundOffEx(1.00004999, -6),0.000001));
  Check(True, IsSame(1.000040, RoundOffEx(1.00004499, -6),0.000001));

  Check(True, IsSame(-0, RoundOffEx(-0.49, -1),0.000001));
  Check(True, IsSame(-1, RoundOffEx(-0.50, -1),0.000001));
  Check(True, IsSame(-1, RoundOffEx(-1.49, -1),0.000001));
  Check(True, IsSame(-2, RoundOffEx(-1.50, -1),0.000001));
  Check(True, IsSame(-1.0, RoundOffEx(-1.04, -2),0.000001));
  Check(TRue, IsSame(-1.1, RoundOffEx(-1.05, -2),0.000001));

  Check(True, IsSame(-1.0001, RoundOffEx(-1.00005000, -5),0.00000001));
  Check(True, IsSame(-1.0000, RoundOffEx(-1.00004999, -5),0.000001));
  Check(True, IsSame(-1.000050, RoundOffEx(-1.00005000, -6),0.000001));
  Check(True, IsSame(-1.000050, RoundOffEx(-1.00004999, -6),0.000001));
  Check(True, IsSame(-1.000040, RoundOffEx(-1.00004499, -6),0.000001));
end;

{-------------------------------
//  CeilEx/FloorEx
機能:       任意の桁で切り上げ/切り下げします
            切り上げは正の絶対値方向、切り下げは負の無限大方向に
            行われるので、負の値の場合動作に気をつけること。
引数説明:   X: 計算対象
            DigitNumber: 桁数
              3:100の桁
              2:10の桁
              1:一桁目
              0:処理しない
              -1:少数点第一位(通常のRoundOffと同じ処理)
              -2:少数点第二位
              -3:少数点第三位
戻り値:     計算後のX
            処理できない場合Xの値そのままが入る
備考:
履歴:       2004/08/18
//------------------------------}
function CeilEx(const X: Extended; DigitNumber: Integer): Extended;
var
  CalcDigit: Extended;
begin
  Result := X;
  if X = 0 then Exit;

  case DigitNumber of
    0: Exit;
    1..High(DigitNumber):
    begin
      CalcDigit := IntPower(10, DigitNumber);
      Result := Math.Ceil(X / CalcDigit) * CalcDigit;
    end;
    Low(DigitNumber)..-1:
    begin
      CalcDigit := IntPower(10, Abs(DigitNumber)-1);
      Result := Math.Ceil(X * CalcDigit) / CalcDigit;
    end;
  end;
end;

procedure testCeil;
begin
  Check(True, IsSame(150, CeilEx(145, 1),0.000001));
  Check(True, IsSame(160, CeilEx(154, 1),0.000001));
  Check(True, IsSame(150, CeilEx(144, 1),0.000001));
  Check(True, IsSame(160, CeilEx(155, 1),0.000001));
  Check(True, IsSame(150, CeilEx(150, 1),0.000001));
  Check(True, IsSame( 20, CeilEx( 14, 1),0.000001));
  Check(True, IsSame( 10, CeilEx(  5, 1),0.000001));
  Check(True, IsSame( 10, CeilEx(  4, 1),0.000001));
  Check(True, IsSame( 20, CeilEx( 15, 1),0.000001));
  Check(True, IsSame( 10, CeilEx( 10, 1),0.000001));

  Check(True, IsSame(200, CeilEx(150, 2),0.000001));
  Check(True, IsSame(200, CeilEx(140, 2),0.000001));
  Check(True, IsSame(200, CeilEx(149, 2),0.000001));
  Check(True, IsSame(300, CeilEx(249, 2),0.000001));
  Check(True, IsSame(100, CeilEx( 50, 2),0.000001));

  Check(True, IsSame(2000, CeilEx(1400, 3),0.000001));
  Check(True, IsSame(2000, CeilEx(1500, 3),0.000001));
  Check(True, IsSame(2000, CeilEx(1600, 3),0.000001));
  Check(True, IsSame(2000, CeilEx(1499, 3),0.000001));
  Check(True, IsSame(3000, CeilEx(2480, 3),0.000001));

  Check(True, IsSame(-140, CeilEx(-145, 1),0.000001));
  Check(True, IsSame(-150, CeilEx(-154, 1),0.000001));
  Check(True, IsSame(-140, CeilEx(-144, 1),0.000001));
  Check(True, IsSame(-150, CeilEx(-155, 1),0.000001));
  Check(True, IsSame(-150, CeilEx(-150, 1),0.000001));
  Check(True, IsSame(- 10, CeilEx( -14, 1),0.000001));
  Check(True, IsSame(   0, CeilEx(  -5, 1),0.000001));
  Check(True, IsSame(   0, CeilEx(  -4, 1),0.000001));
  Check(True, IsSame(- 10, CeilEx( -15, 1),0.000001));
  Check(True, IsSame(- 10, CeilEx( -10, 1),0.000001));

  Check(True, IsSame(-100, CeilEx(-150, 2),0.000001));
  Check(True, IsSame(-100, CeilEx(-140, 2),0.000001));
  Check(True, IsSame(-100, CeilEx(-149, 2),0.000001));
  Check(True, IsSame(-200, CeilEx(-249, 2),0.000001));
  Check(True, IsSame(   0, CeilEx( -50, 2),0.000001));

  Check(True, IsSame(-1000, CeilEx(-1400, 3),0.000001));
  Check(True, IsSame(-1000, CeilEx(-1500, 3),0.000001));
  Check(True, IsSame(-1000, CeilEx(-1600, 3),0.000001));
  Check(True, IsSame(-1000, CeilEx(-1499, 3),0.000001));
  Check(True, IsSame(-2000, CeilEx(-2480, 3),0.000001));

  Check(True, IsSame(1, CeilEx(0.49, -1),0.000001));
  Check(True, IsSame(1, CeilEx(0.50, -1),0.000001));
  Check(True, IsSame(2, CeilEx(1.49, -1),0.000001));
  Check(True, IsSame(2, CeilEx(1.50, -1),0.000001));
  Check(True, IsSame(1.1, CeilEx(1.04, -2),0.000001));
  Check(TRue, IsSame(1.1, CeilEx(1.05, -2),0.000001));

  Check(True, IsSame(1.0001,   CeilEx(1.00005000, -5),0.00000001));
  Check(True, IsSame(1.0001,   CeilEx(1.00004999, -5),0.000001));
  Check(True, IsSame(1.000050, CeilEx(1.00005000, -6),0.000001));
  Check(True, IsSame(1.000050, CeilEx(1.00004999, -6),0.000001));
  Check(True, IsSame(1.000050, CeilEx(1.00004499, -6),0.000001));

  Check(True, IsSame(-0, CeilEx(-0.49, -1),0.000001));
  Check(True, IsSame(-0, CeilEx(-0.50, -1),0.000001));
  Check(True, IsSame(-1, CeilEx(-1.49, -1),0.000001));
  Check(True, IsSame(-1, CeilEx(-1.50, -1),0.000001));
  Check(True, IsSame(-1.0, CeilEx(-1.04, -2),0.000001));
  Check(TRue, IsSame(-1.0, CeilEx(-1.05, -2),0.000001));

  Check(True, IsSame(-1.0000,   CeilEx(-1.00005000, -5),0.00000001));
  Check(True, IsSame(-1.0000,   CeilEx(-1.00004999, -5),0.000001));
  Check(True, IsSame(-1.000050, CeilEx(-1.00005000, -6),0.000001));
  Check(True, IsSame(-1.000040, CeilEx(-1.00004999, -6),0.000001));
  Check(True, IsSame(-1.000040, CeilEx(-1.00004499, -6),0.000001));
end;


function FloorEx(const X: Extended; DigitNumber: Integer): Extended; overload;
var
  CalcDigit: Extended;
begin
  Result := X;
  if X = 0 then Exit;

  case DigitNumber of
    0: Exit;
    1..High(DigitNumber):
    begin
      CalcDigit := IntPower(10, DigitNumber);
      Result := Math.Floor(X / CalcDigit) * CalcDigit;
    end;
    Low(DigitNumber)..-1:
    begin
      CalcDigit := IntPower(10, Abs(DigitNumber)-1);
      Result := Math.Floor(X * CalcDigit) / CalcDigit;
    end;
  end;
end;

procedure testFloor;
begin
  Check(True, IsSame(140, FloorEx(145, 1),0.000001));
  Check(True, IsSame(150, FloorEx(154, 1),0.000001));
  Check(True, IsSame(140, FloorEx(144, 1),0.000001));
  Check(True, IsSame(150, FloorEx(155, 1),0.000001));
  Check(True, IsSame(150, FloorEx(150, 1),0.000001));
  Check(True, IsSame( 10, FloorEx( 14, 1),0.000001));
  Check(True, IsSame(  0, FloorEx(  5, 1),0.000001));
  Check(True, IsSame(  0, FloorEx(  4, 1),0.000001));
  Check(True, IsSame( 10, FloorEx( 15, 1),0.000001));
  Check(True, IsSame( 10, FloorEx( 10, 1),0.000001));

  Check(True, IsSame(100, FloorEx(150, 2),0.000001));
  Check(True, IsSame(100, FloorEx(140, 2),0.000001));
  Check(True, IsSame(100, FloorEx(149, 2),0.000001));
  Check(True, IsSame(200, FloorEx(249, 2),0.000001));
  Check(True, IsSame(  0, FloorEx( 50, 2),0.000001));

  Check(True, IsSame(1000, FloorEx(1400, 3),0.000001));
  Check(True, IsSame(1000, FloorEx(1500, 3),0.000001));
  Check(True, IsSame(1000, FloorEx(1600, 3),0.000001));
  Check(True, IsSame(1000, FloorEx(1499, 3),0.000001));
  Check(True, IsSame(2000, FloorEx(2480, 3),0.000001));

  Check(True, IsSame(-150, FloorEx(-145, 1),0.000001));
  Check(True, IsSame(-160, FloorEx(-154, 1),0.000001));
  Check(True, IsSame(-150, FloorEx(-144, 1),0.000001));
  Check(True, IsSame(-160, FloorEx(-155, 1),0.000001));
  Check(True, IsSame(-150, FloorEx(-150, 1),0.000001));
  Check(True, IsSame(- 20, FloorEx( -14, 1),0.000001));
  Check(True, IsSame(- 10, FloorEx(  -5, 1),0.000001));
  Check(True, IsSame(- 10, FloorEx(  -4, 1),0.000001));
  Check(True, IsSame(- 20, FloorEx( -15, 1),0.000001));
  Check(True, IsSame(- 10, FloorEx( -10, 1),0.000001));

  Check(True, IsSame(-200, FloorEx(-150, 2),0.000001));
  Check(True, IsSame(-200, FloorEx(-140, 2),0.000001));
  Check(True, IsSame(-200, FloorEx(-149, 2),0.000001));
  Check(True, IsSame(-300, FloorEx(-249, 2),0.000001));
  Check(True, IsSame(-100, FloorEx( -50, 2),0.000001));

  Check(True, IsSame(-2000, FloorEx(-1400, 3),0.000001));
  Check(True, IsSame(-2000, FloorEx(-1500, 3),0.000001));
  Check(True, IsSame(-2000, FloorEx(-1600, 3),0.000001));
  Check(True, IsSame(-2000, FloorEx(-1499, 3),0.000001));
  Check(True, IsSame(-3000, FloorEx(-2480, 3),0.000001));

  Check(True, IsSame(0, FloorEx(0.49, -1),0.000001));
  Check(True, IsSame(0, FloorEx(0.50, -1),0.000001));
  Check(True, IsSame(1, FloorEx(1.49, -1),0.000001));
  Check(True, IsSame(1, FloorEx(1.50, -1),0.000001));
  Check(True, IsSame(1.0, FloorEx(1.04, -2),0.000001));
  Check(TRue, IsSame(1.0, FloorEx(1.05, -2),0.000001));

  Check(True, IsSame(1.0000,   FloorEx(1.00005000, -5),0.00000001));
  Check(True, IsSame(1.0000,   FloorEx(1.00004999, -5),0.000001));
  Check(True, IsSame(1.000050, FloorEx(1.00005000, -6),0.000001));
  Check(True, IsSame(1.000040, FloorEx(1.00004999, -6),0.000001));
  Check(True, IsSame(1.000040, FloorEx(1.00004499, -6),0.000001));

  Check(True, IsSame(-1, FloorEx(-0.49, -1),0.000001));
  Check(True, IsSame(-1, FloorEx(-0.50, -1),0.000001));
  Check(True, IsSame(-2, FloorEx(-1.49, -1),0.000001));
  Check(True, IsSame(-2, FloorEx(-1.50, -1),0.000001));
  Check(True, IsSame(-1.1, FloorEx(-1.04, -2),0.000001));
  Check(TRue, IsSame(-1.1, FloorEx(-1.05, -2),0.000001));

  Check(True, IsSame(-1.0001,   FloorEx(-1.00005000, -5),0.00000001));
  Check(True, IsSame(-1.0001,   FloorEx(-1.00004999, -5),0.000001));
  Check(True, IsSame(-1.000050, FloorEx(-1.00005000, -6),0.000001));
  Check(True, IsSame(-1.000050, FloorEx(-1.00004999, -6),0.000001));
  Check(True, IsSame(-1.000050, FloorEx(-1.00004499, -6),0.000001));
end;

{-------------------------------
//  RandomRangeEx
機能:       任意桁の範囲でRandomRangeする関数
引数説明:   AFrom/ATo: 範囲
            Digit: 桁数
              1:小数点1桁
              2:小数点2桁
              3:小数点3桁
              0:処理しない
戻り値:     AFrom/AToで示される範囲の乱数
備考:
履歴:       2004/10/02
//------------------------------}
function RandomRangeEx(const AFrom, ATo: Extended; Digit: Byte): Extended;
var
  CalcDigit: Extended;
begin
  CalcDigit := IntPower(10, Digit); //
  Result := RandomRange(RoundOff(AFrom*CalcDigit), RoundOff(ATo*CalcDigit)) / CalcDigit;
end;
//------------------------------

end.