Attribute VB_Name = "Math2"
'Shift Bits to Left (0001 = 0010)
Public Function LSHIFT(ByVal number As Long, ShiftBits As Integer) As Long
    If ShiftBits > 31 Or ShiftBits <= 0 Then
        If ShiftBits = 0 Then
            LSHIFT = number
            Return
        Else
            LSHIFT = 0
            Return
        End If
    End If

    LSHIFT = number * 2 ^ ShiftBits
End Function

'Shift Bits to Right (0010 = 0001)
Public Function RSHIFT(ByVal number As Long, ShiftBits As Integer) As Long
    If ShiftBits > 31 Or ShiftBits <= 0 Then
        If ShiftBits = 0 Then
            RSHIFT = number
            Return
        Else
            RSHIFT = 0
            Return
        End If
    End If
    RSHIFT = number \ 2 ^ ShiftBits
End Function

Public Function POW(ByVal number As Double, ByVal p As Integer) As Double
    Dim i As Integer
    If p <= 0 Then
        POW = 0
    Else
        POW = number
        If p > 1 Then
            For i = 2 To p
                POW = POW * number
            Next
        End If
    End If
End Function

Public Function Min(a As Variant, b As Variant) As Variant
    If a < b Then Min = a Else Min = b
End Function

Public Function Max(a As Variant, b As Variant) As Variant
    If a > b Then Max = a Else Max = b
End Function

'Simplifies a fraction where you give the numerator and denominator.
'Make sure there are no decimals in the numberator/denominator!
'Example: mystring$ = Math_Simplify(30, 10) - will return 3/1 as the answer in mystring$
'Example 2: mystring2$ = Math_Simplify(3.2, 4.6) - will not return an answer. Rather, make it Math_Simplify(32, 46) and an answer will be given
Public Function Math_Simplify(numerator As Double, denominator As Double) As String
    If Math_IsInteger(numerator) Then
        If Math_IsInteger(denominator) Then
            n = numerator
            d = denominator
            x = Math_GCF(Val(n), Val(d))
            n = n / Val(x)
            d = d / Val(x)
            Math_Simplify = Trim(str(n)) + "/" + Trim(str(d))
        End If
    End If
End Function

'This gets the rooth root of a number. The rooth root is always positive in this case. Although -3 * -3 = 3 * 3, which are both 9, it will only give 3 as the answer.
'If the number is 9, and you put in a root of 2, it will get the positive square root of 9 = 3.
'Example: Math_Root 2, 2 - gets the square root of 2.
'Note: Do not make 0 the root - it will be number ^ infinity!
Public Function Math_Root(number As Double, root As Double) As Double
    If root > 0 Then
        Math_Root = number ^ (1 / root)
    End If
End Function


'Determines if a number is odd or not
'Note: This determines if a negative number (< 0) is odd. If the absolute value is odd, then the negative number is also classified as odd...
Public Function Math_IsOdd(number As Double) As Boolean
    Math_IsOdd = (Int(Abs(number)) And 1)
End Function

'Solves the equation a ^ x + b = c for x when the value for a and b are given
'Example: Math_GetExponent(3, 0, 5) - returns the value 1.464.... The equation is 3^x + 0 = 5.
'Example: Math_GetExponent(2, 1, 2) - solves the equation 2^x + 1 = 2. The answer is 0.
Public Function Math_GetExponent(a As Double, b As Double, c As Double) As Double
    c = c - b
    Math_GetExponent = Log(c) / Log(a)
End Function

'Solves the equation the x root of a + b = c for x, or x | a + b = c where | = the root sign.
'Example: Math_GetRoot(9, 0, 3) - returns a value of 2, since the square root of 9 is 3. Solves x | 9 + 0 = 3.
'Example: Math_GetRoot(4, 1, 5) - solves x | 4 + 1 = 5. In this case the answer is 1.
Public Function Math_GetRoot(a As Double, b As Double, c As Double) As Double
    c = c - b
    Math_GetRoot = Log(a) / Log(c)
End Function

Public Function Math_IsInteger(obj As Variant) As Boolean
    Math_IsInteger = (CDbl(Val(obj)) = CInt(Val(obj)))
End Function

'Gets the greatest common factor between two numbers: n1 and n2. Can take a few seconds of time.
'Make sure n1 and n2 are positive nonzero numbers; it will not work otherwise!
'Example: theGCF = Math_GCF(4, 200) - will return 4 as the GCF
'Example: theGCF = Math_GCF(8, 12) - will return 4 as the GCF
Public Function Math_GCF(number1 As Double, number2 As Double) As Double
    Dim i As Long
    For i = 1 To CLng(IIf(number1 <= number2, number1, number2))
        DoEvents
        If Math_IsInteger(Math_LCM(number1, number2) / i) Then
            If Math_IsInteger(number1 / i) Then
                If Math_IsInteger(number2 / i) Then
                    Math_GCF = i
                End If
            End If
        End If
    Next
End Function

'Gets the least common multiple between two numbers.
'Example: Call Math_LCM(3, 5) - will return 15.
'Example: Math_LCM(6, 4) - will return 12.
Public Function Math_LCM(n1 As Double, n2 As Double) As Double
    Math_LCM = n1 * n2
    Dim x As Long
    For x = 2 To Math_LCM
        If Math_IsInteger(x / n1) Then
            If Math_IsInteger(x / n2) Then
                Math_LCM = n1 / x
            End If
        End If
    Next
End Function

' Secant
Function Sec(x As Double) As Double
   Sec = 1 / Cos(x)
End Function

' Cosecant
Function CoSec(x As Double) As Double
   CoSec = 1 / Sin(x)
End Function

' Cotangent
Function CoTan(x As Double) As Double
   CoTan = 1 / Tan(x)
End Function

' Inverse Sine
Function ArcSin(x As Double) As Double
   ArcSin = Atn(x / Sqr(-x * x + 1))
End Function

' Inverse Cosine
Function ArcCos(x As Double) As Double
   ArcCos = Atn(-x / Sqr(-x * x + 1)) + 2 * Atn(1)
End Function

' Inverse Secant
Function ArcSec(x As Double) As Double
   ArcSec = Atn(x / Sqr(x * x - 1)) + Sgn(x - 1) * (2 * Atn(1))
End Function

' Inverse Cosecant
Function ArcCoSec(x As Double) As Double
   ArcCoSec = Atn(x / Sqr(x * x - 1)) + (Sgn(x) - 1) * (2 * Atn(1))
End Function

' Inverse Cotangent
Function ArcCoTan(x As Double) As Double
   ArcCoTan = Atn(x) + 2 * Atn(1)
End Function

' Hyperbolic Sine
Function HSin(x As Double) As Double
   HSin = (Exp(x) - Exp(-x)) / 2
End Function

' Hyperbolic Cosine
Function HCos(x As Double) As Double
   HCos = (Exp(x) + Exp(-x)) / 2
End Function

' Hyperbolic Tangent
Function HTan(x As Double) As Double
   HTan = (Exp(x) - Exp(-x)) / (Exp(x) + Exp(-x))
End Function

' Hyperbolic Secant
Function HSec(x As Double) As Double
   HSec = 2 / (Exp(x) + Exp(-x))
End Function

' Hyperbolic Cosecant
Function HCoSec(x As Double) As Double
   HCoSec = 2 / (Exp(x) - Exp(-x))
End Function

' Hyperbolic Cotangent
Function HCotan(x As Double) As Double
   HCotan = (Exp(x) + Exp(-x)) / (Exp(x) - Exp(-x))
End Function

' Inverse Hyperbolic Sine
Function HArcSin(x As Double) As Double
   HArcSin = Log(x + Sqr(x * x + 1))
End Function

' Inverse Hyperbolic Cosine
Function HArcCos(x As Double) As Double
   HArcCos = Log(x + Sqr(x * x - 1))
End Function

' Inverse Hyperbolic Tangent
Function HArcTan(x As Double) As Double
   HArcTan = Log((1 + x) / (1 - x)) / 2
End Function

' Inverse Hyperbolic Secant
Function HArcSec(x As Double) As Double
   HArcSec = Log((Sqr(-x * x + 1) + 1) / x)
End Function

' Inverse Hyperbolic Cosecant
Function HArcCoSec(x As Double) As Double
   HArcCoSec = Log((Sgn(x) * Sqr(x * x + 1) + 1) / x)
End Function

' Inverse Hyperbolic Cotangent
Function HArcCoTan(x As Double) As Double
   HArcCoTan = Log((x + 1) / (x - 1)) / 2
End Function

' Logarithm to base N
Function LogN(x As Double, n As Double) As Double
   LogN = Log(x) / Log(n)
End Function