' Classes/System/Math.ab

#ifndef __SYSTEM_MATH_AB__
#define __SYSTEM_MATH_AB__

Const _System_EPS5 = 0.001

Class Math
Public
	Static Function E() As Double
		return 2.7182818284590452354
	End Function

	Static Function PI() As Double
		return _System_PI
	End Function

	Static Function Abs(value As Double) As Double
		If value<0 then
			return -value
		Else
			return value
		End If
	End Function

	Static Function Abs(value As Single) As Single
		If value<0 then
			return -value
		Else
			return value
		End If
	End Function

	Static Function Abs(value As Char) As Char
		If value<0 then
			return -value
		Else
			return value
		End If
	End Function

	Static Function Abs(value As Integer) As Integer
		If value<0 then
			return -value
		Else
			return value
		End If
	End Function

	Static Function Abs(value As Long) As Long
		If value<0 then
			return -value
		Else
			return value
		End If
	End Function

	Static Function Abs(value As Int64) As Int64
		If value<0 then
			return -value
		Else
			return value
		End If
	End Function

	Static Function Acos(x As Double) As Double
		If x < -1 Or x > 1 Then
			Acos = _System_GetNaN()
		Else
			Acos = _System_HalfPI - ASin(x)
		End If
	End Function

	Static Function Asin(x As Double) As Double
		If x < -1 Or x > 1 Then
			Asin = _System_GetNaN()
		Else
			Asin = ATan(x / Sqrt(1 - x * x))
		End If
	End Function

	Static Function Atan(x As Double) As Double
		If IsNaN(x) Then
			Atan = x
			Exit Function
		ElseIf IsInf(x) Then
			Atan = CopySign(_System_PI, x)
			Exit Function
		End If
		Dim i As Long
		Dim sgn As Long
		Dim dbl = 0 As Double

		If x > 1 Then
			sgn = 1
			x = 1 / x
		ElseIf x < -1 Then
			sgn = -1
			x = 1 / x
		Else
			sgn = 0
		End If

		For i = _System_Atan_N To 1 Step -1
			Dim t As Double
			t = i * x
			dbl = (t * t) / (2 * i + 1 + dbl)
		Next

		If sgn > 0 Then
			Atan = _System_HalfPI - x / (1 + dbl)
		ElseIf sgn < 0 Then
			Atan = -_System_HalfPI - x / (1 + dbl)
		Else
			Atan = x / (1 + dbl)
		End If
	End Function

	Static Function Atan2(y As Double, x As Double) As Double
		If x = 0 Then
			Atan2 = Sgn(y) * _System_HalfPI
		Else
			Atan2 = Atn(y / x)
			If x < 0 Then
				Atan2 += CopySign(_System_PI, y)
			End If
		End If
	End Function

	Static Function BigMul(x As Long, y As Long) As Int64
		Return (x As Int64) * y
	End Function

	Static Function Ceiling(x As Double) As Long
		If Floor(x) = x then
			Return x
		Else
			Return Floor(x) + 1
		End If
	End Function

	Static Function Cos(x As Double) As Double
		If IsNaN(x) Then
			Return x
				ElseIf IsInf(x) Then
			Return _System_GetNaN()
		End If

		Return Math.Sin((_System_HalfPI - Math.Abs(x)) As Double)
	End Function

	Static Function Cosh(value As Double) As Double
		Dim t As Double
		t = Exp(value)
		return (t + 1 / t) * 0.5
	End Function

	Static Function DivRem(x As Long, y As Long, ByRef ret As Long) As Long
		ret = x Mod y
		return x \ y
	End Function

	Static Function DivRem(x As Int64, y As Int64, ByRef ret As Int64) As Int64
		ret = x - (x \ y) * y
		return x \ y
	End Function

	'Equals

	Static Function Exp(x As Double) As Double
		If IsNaN(x) Then
			Return x
		Else If IsInf(x) Then
			If 0 > x Then
				Return 0
			Else
				Return x
			End If
		End If
		Dim i As Long, k As Long
		Dim x2 As Double, w As Double

		If x >= 0 Then
			k = Fix(x / _System_LOG2 + 0.5)
		Else
			k = Fix(x / _System_LOG2 - 0.5)
		End If

		x -= k * _System_LOG2

		x2 = x * x
		w = x2 / 22

		i = 18
		While i >= 6
			w = x2 / (w + i)
			i -= 4
		Wend

		Return ldexp((2 + w + x) / (2 + w - x), k)
	End Function

	Static Function Floor(value As Double) As Long
		return Int(value)
	End Function

	'GetHashCode

	'GetType

	Static Function IEEERemainder(value1 As Double,value2 As Double) As Double
		Dim q As Double
		If value2=0 then return _System_GetNaN()
		q=value1/value2
		If q<>Int(q) then
			If q+0.5<>Int(q+0.5) then
				q=Int(q+0.5)
			ElseIf Int(q+0.5)=Int(q*2+1)/2 then
				q=Int(q+0.5)
			Else
				q=Int(q-0.5)
			End If
		End If
		If x-y*q=0 then
			If x>0 then
				return +0
			Else
				return -0
			End If
		Else
			return x-y*q
		End If
	End Function

	Static Function Log(x As Double) As Double
		If x = 0 Then
			Log = _System_GetInf(TRUE)
		ElseIf x < 0 Or IsNaN(x) Then
			Log = _System_GetNaN()
		ElseIf IsInf(x) Then
			Log = x
		Else
			Dim i As Long, k As Long
			Dim s As Double, t As Double
			frexp(x / _System_SQRT2, k)
			x /= ldexp(1, k)

			x--
			s = 0
			i = _System_Log_N
			While i >= 1
				t = i * x
				s = t / (2 + t / (2 * i + 1 + s))
				i--
			Wend

			Log = _System_LOG2 * k + x / (1 + s)
		End If
	End Function

	Static Function Log10(x As Double) As Double
		Return Log(x) / Log(10)
	End Function

	Static Function Max(value1 As Byte,value2 As Byte) As Byte
		If value1>value2 then
			return value1
		Else
			return value2
		End If
	End Function

	Static Function Max(value1 As Char,value2 As Char) As Char
		If value1>value2 then
			return value1
		Else
			return value2
		End If
	End Function

	Static Function Max(value1 As Word,value2 As Word) As Word
		If value1>value2 then
			return value1
		Else
			return value2
		End If
	End Function

	Static Function Max(value1 As Integer,value2 As Integer) As Integer
		If value1>value2 then
			return value1
		Else
			return value2
		End If
	End Function

	Static Function Max(value1 As DWord,value2 As DWord) As DWord
		If value1>value2 then
			return value1
		Else
			return value2
		End If
	End Function

	Static Function Max(value1 As Long,value2 As Long) As Long
		If value1>value2 then
			return value1
		Else
			return value2
		End If
	End Function

	Static Function Max(value1 As QWord,value2 As QWord) As QWord
		If value1>value2 then
			return value1
		Else
			return value2
		End If
	End Function

	Static Function Max(value1 As Int64,value2 As Int64) As Int64
		If value1>value2 then
			return value1
		Else
			return value2
		End If
	End Function

	Static Function Max(value1 As Single,value2 As Single) As Single
		If value1>value2 then
			return value1
		Else
			return value2
		End If
	End Function

	Static Function Max(value1 As Double,value2 As Double) As Double
		If value1>value2 then
			return value1
		Else
			return value2
		End If
	End Function

	Static Function Min(value1 As Byte,value2 As Byte) As Byte
		If value1<value2 then
			return value1
		Else
			return value2
		End If
	End Function

	Static Function Min(value1 As Char,value2 As Char) As Char
		If value1<value2 then
			return value1
		Else
			return value2
		End If
	End Function

	Static Function Min(value1 As Word,value2 As Word) As Word
		If value1<value2 then
			return value1
		Else
			return value2
		End If
	End Function

	Static Function Min(value1 As Integer,value2 As Integer) As Integer
		If value1<value2 then
			return value1
		Else
			return value2
		End If
	End Function

	Static Function Min(value1 As DWord,value2 As DWord) As DWord
		If value1<value2 then
			return value1
		Else
			return value2
		End If
	End Function

	Static Function Min(value1 As Long,value2 As Long) As Long
		If value1<value2 then
			return value1
		Else
			return value2
		End If
	End Function

	Static Function Min(value1 As QWord,value2 As QWord) As QWord
		If value1<value2 then
			return value1
		Else
			return value2
		End If
	End Function

	Static Function Min(value1 As Int64,value2 As Int64) As Int64
		If value1<value2 then
			return value1
		Else
			return value2
		End If
	End Function

	Static Function Min(value1 As Single,value2 As Single) As Single
		If value1<value2 then
			return value1
		Else
			return value2
		End If
	End Function

	Static Function Min(value1 As Double,value2 As Double) As Double
		If value1<value2 then
			return value1
		Else
			return value2
		End If
	End Function

	Static Function Pow(x As Double, y As Double) As Double
		return pow(x, y)
	End Function

	'ReferenceEquals

	Static Function Round(value As Double) As Double'他のバージョン、誰か頼む。
		If value+0.5<>Int(value+0.5) then
			value=Int(value+0.5)
		ElseIf Int(value+0.5)=Int(value*2+1)/2 then
			value=Int(value+0.5)
		Else
			value=Int(value-0.5)
		End If
	End Function

	Static Function Sign(value As Double) As Long
		If value = 0 then
			return 0
		ElseIf value > 0 then
			return 1
		Else
			return -1
		End If
	End Function

	Static Function Sign(value As Char) As Long
		If value = 0 then
			return 0
		ElseIf value > 0 then
			return 1
		Else
			return -1
		End If
	End Function

	Static Function Sign(value As Integer) As Long
		If value = 0 then
			return 0
		ElseIf value > 0 then
			return 1
		Else
			return -1
		End If
	End Function

	Static Function Sign(value As Long) As Long
		If value = 0 then
			return 0
		ElseIf value > 0 then
			return 1
		Else
			return -1
		End If
	End Function

	Static Function Sign(value As Int64) As Long
		If value = 0 then
			return 0
		ElseIf value > 0 then
			return 1
		Else
			return -1
		End If
	End Function

	Static Function Sign(value As Single) As Long
		If value = 0 then
			return 0
		ElseIf value > 0 then
			return 1
		Else
			return -1
		End If
	End Function

	Static Function Sin(value As Double) As Double
		If IsNaN(value) Then
			Return value
		ElseIf IsInf(value) Then
			Return _System_GetNaN()
			Exit Function
		End If

		Dim k As Long
		Dim t As Double

		t = urTan((value * 0.5) As Double, k)
		t = 2 * t / (1 + t * t)
		If (k And 1) = 0 Then 'k mod 2 = 0 Then
			Return t
		Else
			Return -t
		End If
	End Function

	Static Function Sinh(x As Double) As Double
		If Math.Abs(x) > _System_EPS5 Then
			Dim t As Double
			t = Exp(x)
			Return (t - 1 / t) * 0.5
		Else
			Return x * (1 + x * x * 0.166666666666667) ' x * (1 + x * x / 6)
		End If
	End Function

	Static Function Sqrt(x As Double) As Double
		Dim s As Double, last As Double
		Dim i As *Word, j As Long, jj As Long, k As Long
		If x > 0 Then
			If IsInf(x) Then
				Sqrt = x
			Else
				Sqrt = x
				i = (VarPtr(Sqrt) + 6) As *Word
				jj = GetWord(i)
				j = jj >> 5
				k = jj And &h0000001f
				j = (j+  511) << 4 + k
				SetWord(i, j)
				Do
					last = Sqrt
					Sqrt = (x /Sqrt + Sqrt) * 0.5
				Loop While Sqrt <> last
			End If
		ElseIf x < 0 Then
			Sqrt = _System_GetNaN()
		Else
			'x = 0 Or NaN
			Sqrt = x
		End If
	End Function

	Static Function Tan(x As Double) As Double
		If IsNaN(x) Then
			Tan = x
			Exit Function
		ElseIf IsInf(x) Then
			Tan = _System_GetNaN()
			Exit Function
		End If

		Dim k As Long
		Dim t As Double
		t = urTan(x, k)
		If (k And 1) = 0 Then 'k mod 2 = 0 Then
			Return t
		ElseIf t <> 0 Then
			Return -1 / t
		Else
			Return CopySign(_System_GetInf(FALSE), -t)
		End If
	End Function

	Static Function Tanh(x As Double) As Double
		If x > _System_EPS5 Then
			Return 2 / (1 + Exp(-2 * x)) - 1
		ElseIf x < -_System_EPS5 Then
			Return 1 - 2 / (Exp(2 * x) + 1)
		Else
			Return x * (1 - x * x * 0.333333333333333) 'x * (1 - x * x / 3)
		End If
	End Function

	'ToString

	Static Function Truncate(x As Double) As Double
		return Fix(x)
	End Function

'Private
	Static Function urTan(x As Double, ByRef k As Long) As Double
		Dim i As Long
		Dim t As Double, x2 As Double

		If x >= 0 Then
			k = Fix(x * _System_InverseHalfPI) + 0.5
		Else
			k = Fix(x * _System_InverseHalfPI) - 0.5
		End If
		x = (x - (3217.0 / 2048.0) * k) + _System_D * k
		x2 = x * x
		t = 0
		For i = _System_UrTan_N To 3 Step -2
			t = x2 / (i - t)
		Next i
		urTan =  x / (1 - t)
	End Function
End Class

Const _System_Log_N = 7
Const _System_Atan_N = 20
Const _System_UrTan_N = 17
Const _System_D  = 4.4544551033807686783083602485579e-6
Const _System_HalfPI = (_System_PI * 0.5)
Const _System_InverseHalfPI = (2 / _System_PI) '1 / (PI / 2)

#endif '__SYSTEM_MATH_AB__