[14] | 1 | ' Classes/System/Math.ab
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[1] | 2 |
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| 3 | #ifndef __SYSTEM_MATH_AB__
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| 4 | #define __SYSTEM_MATH_AB__
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| 5 |
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| 6 | Class Math
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| 7 | Public
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| 8 | Static Function E() As Double
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| 9 | return 2.7182818284590452354
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| 10 | End Function
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| 11 |
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| 12 | Static Function PI() As Double
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| 13 | return _System_PI
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| 14 | End Function
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| 15 |
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| 16 | Static Function Abs(value As Double) As Double
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[239] | 17 | SetQWord(VarPtr(Abs), GetQWord(VarPtr(value)) And &h7fffffffffffffff)
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[1] | 18 | End Function
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| 19 |
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| 20 | Static Function Abs(value As Single) As Single
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[239] | 21 | SetDWord(VarPtr(Abs), GetDWord(VarPtr(value)) And &h7fffffff)
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[1] | 22 | End Function
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| 23 |
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[162] | 24 | Static Function Abs(value As SByte) As SByte
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[1] | 25 | If value<0 then
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| 26 | return -value
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| 27 | Else
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| 28 | return value
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| 29 | End If
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| 30 | End Function
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| 31 |
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| 32 | Static Function Abs(value As Integer) As Integer
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| 33 | If value<0 then
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| 34 | return -value
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| 35 | Else
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| 36 | return value
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| 37 | End If
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| 38 | End Function
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| 39 |
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| 40 | Static Function Abs(value As Long) As Long
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| 41 | If value<0 then
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| 42 | return -value
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| 43 | Else
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| 44 | return value
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| 45 | End If
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| 46 | End Function
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| 47 |
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| 48 | Static Function Abs(value As Int64) As Int64
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| 49 | If value<0 then
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| 50 | return -value
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| 51 | Else
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| 52 | return value
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| 53 | End If
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| 54 | End Function
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| 55 |
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| 56 | Static Function Acos(x As Double) As Double
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| 57 | If x < -1 Or x > 1 Then
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| 58 | Acos = _System_GetNaN()
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| 59 | Else
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[232] | 60 | Acos = _System_HalfPI - Asin(x)
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[1] | 61 | End If
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| 62 | End Function
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| 63 |
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| 64 | Static Function Asin(x As Double) As Double
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| 65 | If x < -1 Or x > 1 Then
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| 66 | Asin = _System_GetNaN()
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| 67 | Else
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[233] | 68 | Asin = Math.Atan(x / Sqrt(1 - x * x))
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[1] | 69 | End If
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| 70 | End Function
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| 71 |
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| 72 | Static Function Atan(x As Double) As Double
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| 73 | If IsNaN(x) Then
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| 74 | Atan = x
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| 75 | Exit Function
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| 76 | ElseIf IsInf(x) Then
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| 77 | Atan = CopySign(_System_PI, x)
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| 78 | Exit Function
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| 79 | End If
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| 80 | Dim i As Long
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| 81 | Dim sgn As Long
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| 82 | Dim dbl = 0 As Double
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| 83 |
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| 84 | If x > 1 Then
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| 85 | sgn = 1
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| 86 | x = 1 / x
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| 87 | ElseIf x < -1 Then
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| 88 | sgn = -1
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| 89 | x = 1 / x
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| 90 | Else
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| 91 | sgn = 0
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| 92 | End If
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| 93 |
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| 94 | For i = _System_Atan_N To 1 Step -1
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| 95 | Dim t As Double
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[14] | 96 | t = i * x
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[1] | 97 | dbl = (t * t) / (2 * i + 1 + dbl)
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| 98 | Next
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| 99 |
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| 100 | If sgn > 0 Then
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| 101 | Atan = _System_HalfPI - x / (1 + dbl)
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| 102 | ElseIf sgn < 0 Then
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| 103 | Atan = -_System_HalfPI - x / (1 + dbl)
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| 104 | Else
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| 105 | Atan = x / (1 + dbl)
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| 106 | End If
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| 107 | End Function
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| 108 |
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| 109 | Static Function Atan2(y As Double, x As Double) As Double
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| 110 | If x = 0 Then
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| 111 | Atan2 = Sgn(y) * _System_HalfPI
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| 112 | Else
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| 113 | Atan2 = Atn(y / x)
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| 114 | If x < 0 Then
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[91] | 115 | Atan2 += CopySign(_System_PI, y)
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[1] | 116 | End If
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| 117 | End If
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| 118 | End Function
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| 119 |
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[14] | 120 | Static Function BigMul(x As Long, y As Long) As Int64
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| 121 | Return (x As Int64) * y
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[1] | 122 | End Function
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| 123 |
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| 124 | Static Function Ceiling(x As Double) As Long
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| 125 | If Floor(x) = x then
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[233] | 126 | Return x As Long
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[1] | 127 | Else
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| 128 | Return Floor(x) + 1
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| 129 | End If
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| 130 | End Function
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| 131 |
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[14] | 132 | Static Function Cos(x As Double) As Double
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| 133 | If IsNaN(x) Then
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| 134 | Return x
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[244] | 135 | ElseIf IsInf(x) Then
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[1] | 136 | Return _System_GetNaN()
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| 137 | End If
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| 138 |
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[124] | 139 | Return Math.Sin((_System_HalfPI - Math.Abs(x)) As Double)
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[1] | 140 | End Function
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| 141 |
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| 142 | Static Function Cosh(value As Double) As Double
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| 143 | Dim t As Double
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[233] | 144 | t = Math.Exp(value)
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[1] | 145 | return (t + 1 / t) * 0.5
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| 146 | End Function
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| 147 |
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[14] | 148 | Static Function DivRem(x As Long, y As Long, ByRef ret As Long) As Long
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| 149 | ret = x Mod y
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| 150 | return x \ y
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[1] | 151 | End Function
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| 152 |
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[14] | 153 | Static Function DivRem(x As Int64, y As Int64, ByRef ret As Int64) As Int64
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| 154 | ret = x - (x \ y) * y
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| 155 | return x \ y
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[1] | 156 | End Function
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| 157 |
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| 158 | 'Equals
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| 159 |
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[14] | 160 | Static Function Exp(x As Double) As Double
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[1] | 161 | If IsNaN(x) Then
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| 162 | Return x
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| 163 | Else If IsInf(x) Then
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| 164 | If 0 > x Then
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| 165 | Return 0
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| 166 | Else
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| 167 | Return x
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| 168 | End If
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| 169 | End If
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| 170 | Dim i As Long, k As Long
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| 171 | Dim x2 As Double, w As Double
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| 172 |
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| 173 | If x >= 0 Then
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[14] | 174 | k = Fix(x / _System_LOG2 + 0.5)
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[1] | 175 | Else
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[14] | 176 | k = Fix(x / _System_LOG2 - 0.5)
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[1] | 177 | End If
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| 178 |
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| 179 | x -= k * _System_LOG2
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| 180 |
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| 181 | x2 = x * x
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| 182 | w = x2 / 22
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| 183 |
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| 184 | i = 18
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| 185 | While i >= 6
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| 186 | w = x2 / (w + i)
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| 187 | i -= 4
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| 188 | Wend
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| 189 |
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| 190 | Return ldexp((2 + w + x) / (2 + w - x), k)
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| 191 | End Function
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| 192 |
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| 193 | Static Function Floor(value As Double) As Long
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[237] | 194 | Return Int(value)
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[1] | 195 | End Function
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| 196 |
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| 197 | 'GetHashCode
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| 198 |
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| 199 | 'GetType
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| 200 |
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[237] | 201 | Static Function IEEERemainder(x As Double, y As Double) As Double
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| 202 | If y = 0 Then Return _System_GetNaN()
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| 203 | Dim q = x / y
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| 204 | If q <> Int(q) Then
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| 205 | If q + 0.5 <> Int(q + 0.5) Then
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| 206 | q = Int(q + 0.5)
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| 207 | ElseIf Int(q + 0.5) = Int(q * 2 + 1) / 2 Then
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| 208 | q = Int(q + 0.5)
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[1] | 209 | Else
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[237] | 210 | q = Int(q - 0.5)
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[1] | 211 | End If
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| 212 | End If
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[237] | 213 | If x - y * q = 0 Then
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| 214 | If x > 0 Then
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| 215 | Return +0
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[1] | 216 | Else
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[237] | 217 | Return -0
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[1] | 218 | End If
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| 219 | Else
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[237] | 220 | Return x-y*q
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[1] | 221 | End If
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| 222 | End Function
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| 223 |
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| 224 | Static Function Log(x As Double) As Double
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| 225 | If x = 0 Then
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[244] | 226 | Log = _System_GetInf(True)
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[1] | 227 | ElseIf x < 0 Or IsNaN(x) Then
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| 228 | Log = _System_GetNaN()
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| 229 | ElseIf IsInf(x) Then
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| 230 | Log = x
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| 231 | Else
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[244] | 232 | Dim tmp = x * _System_InverseSqrt2
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| 233 | Dim p = VarPtr(tmp) As *QWord
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| 234 | Dim m = p[0] And &h7FF0000000000000
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| 235 | Dim k = ((m >> 52) As DWord) As Long - 1022
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| 236 | p[0] = m + &h0010000000000000
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| 237 | x /= tmp
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[1] | 238 |
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| 239 | x--
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[244] | 240 | Dim s = 0 As Double
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| 241 | Dim i = _System_Log_N As Long
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[1] | 242 | While i >= 1
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[244] | 243 | Dim t = (i * x) As Double
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[1] | 244 | s = t / (2 + t / (2 * i + 1 + s))
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| 245 | i--
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| 246 | Wend
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| 247 | Log = _System_LOG2 * k + x / (1 + s)
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| 248 | End If
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| 249 | End Function
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| 250 |
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| 251 | Static Function Log10(x As Double) As Double
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[244] | 252 | Return Math.Log(x) * _System_InverseLn10
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[1] | 253 | End Function
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| 254 |
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[244] | 255 | Static Function Max(value1 As Byte, value2 As Byte) As Byte
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[1] | 256 | If value1>value2 then
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| 257 | return value1
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| 258 | Else
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| 259 | return value2
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| 260 | End If
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| 261 | End Function
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| 262 |
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[244] | 263 | Static Function Max(value1 As SByte, value2 As SByte) As SByte
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[1] | 264 | If value1>value2 then
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| 265 | return value1
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| 266 | Else
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| 267 | return value2
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| 268 | End If
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| 269 | End Function
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| 270 |
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[244] | 271 | Static Function Max(value1 As Word, value2 As Word) As Word
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[1] | 272 | If value1>value2 then
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| 273 | return value1
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| 274 | Else
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| 275 | return value2
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| 276 | End If
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| 277 | End Function
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| 278 |
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[244] | 279 | Static Function Max(value1 As Integer, value2 As Integer) As Integer
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[1] | 280 | If value1>value2 then
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| 281 | return value1
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| 282 | Else
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| 283 | return value2
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| 284 | End If
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| 285 | End Function
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| 286 |
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[244] | 287 | Static Function Max(value1 As DWord, value2 As DWord) As DWord
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[1] | 288 | If value1>value2 then
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| 289 | return value1
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| 290 | Else
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| 291 | return value2
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| 292 | End If
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| 293 | End Function
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| 294 |
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[244] | 295 | Static Function Max(value1 As Long, value2 As Long) As Long
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[1] | 296 | If value1>value2 then
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| 297 | return value1
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| 298 | Else
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| 299 | return value2
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| 300 | End If
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| 301 | End Function
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| 302 |
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[244] | 303 | Static Function Max(value1 As QWord, value2 As QWord) As QWord
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[1] | 304 | If value1>value2 then
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| 305 | return value1
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| 306 | Else
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| 307 | return value2
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| 308 | End If
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| 309 | End Function
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| 310 |
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[244] | 311 | Static Function Max(value1 As Int64, value2 As Int64) As Int64
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[1] | 312 | If value1>value2 then
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| 313 | return value1
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| 314 | Else
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| 315 | return value2
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| 316 | End If
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| 317 | End Function
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| 318 |
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[244] | 319 | Static Function Max(value1 As Single, value2 As Single) As Single
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[1] | 320 | If value1>value2 then
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| 321 | return value1
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| 322 | Else
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| 323 | return value2
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| 324 | End If
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| 325 | End Function
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| 326 |
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[244] | 327 | Static Function Max(value1 As Double, value2 As Double) As Double
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[1] | 328 | If value1>value2 then
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| 329 | return value1
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| 330 | Else
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| 331 | return value2
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| 332 | End If
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| 333 | End Function
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| 334 |
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[244] | 335 | Static Function Min(value1 As Byte, value2 As Byte) As Byte
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[1] | 336 | If value1<value2 then
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| 337 | return value1
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| 338 | Else
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| 339 | return value2
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| 340 | End If
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| 341 | End Function
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| 342 |
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[244] | 343 | Static Function Min(value1 As SByte, value2 As SByte) As SByte
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[1] | 344 | If value1<value2 then
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| 345 | return value1
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| 346 | Else
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| 347 | return value2
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| 348 | End If
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| 349 | End Function
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| 350 |
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[244] | 351 | Static Function Min(value1 As Word, value2 As Word) As Word
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[1] | 352 | If value1<value2 then
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| 353 | return value1
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| 354 | Else
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| 355 | return value2
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| 356 | End If
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| 357 | End Function
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| 358 |
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[244] | 359 | Static Function Min(value1 As Integer, value2 As Integer) As Integer
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[1] | 360 | If value1<value2 then
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| 361 | return value1
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| 362 | Else
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| 363 | return value2
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| 364 | End If
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| 365 | End Function
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| 366 |
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[244] | 367 | Static Function Min(value1 As DWord, value2 As DWord) As DWord
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[1] | 368 | If value1<value2 then
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| 369 | return value1
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| 370 | Else
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| 371 | return value2
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| 372 | End If
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| 373 | End Function
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| 374 |
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[244] | 375 | Static Function Min(value1 As Long, value2 As Long) As Long
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[1] | 376 | If value1<value2 then
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| 377 | return value1
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| 378 | Else
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| 379 | return value2
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| 380 | End If
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| 381 | End Function
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| 382 |
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[244] | 383 | Static Function Min(value1 As QWord, value2 As QWord) As QWord
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[1] | 384 | If value1<value2 then
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| 385 | return value1
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| 386 | Else
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| 387 | return value2
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| 388 | End If
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| 389 | End Function
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| 390 |
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[244] | 391 | Static Function Min(value1 As Int64, value2 As Int64) As Int64
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[1] | 392 | If value1<value2 then
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| 393 | return value1
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| 394 | Else
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| 395 | return value2
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| 396 | End If
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| 397 | End Function
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| 398 |
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[244] | 399 | Static Function Min(value1 As Single, value2 As Single) As Single
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[1] | 400 | If value1<value2 then
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| 401 | return value1
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| 402 | Else
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| 403 | return value2
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| 404 | End If
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| 405 | End Function
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| 406 |
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[244] | 407 | Static Function Min(value1 As Double, value2 As Double) As Double
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[1] | 408 | If value1<value2 then
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| 409 | return value1
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| 410 | Else
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| 411 | return value2
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| 412 | End If
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| 413 | End Function
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| 414 |
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[14] | 415 | Static Function Pow(x As Double, y As Double) As Double
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| 416 | return pow(x, y)
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[1] | 417 | End Function
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| 418 |
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| 419 | 'ReferenceEquals
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| 420 |
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| 421 | Static Function Round(value As Double) As Double'他のバージョン、誰か頼む。
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| 422 | If value+0.5<>Int(value+0.5) then
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| 423 | value=Int(value+0.5)
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| 424 | ElseIf Int(value+0.5)=Int(value*2+1)/2 then
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| 425 | value=Int(value+0.5)
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| 426 | Else
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| 427 | value=Int(value-0.5)
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| 428 | End If
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| 429 | End Function
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| 430 |
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| 431 | Static Function Sign(value As Double) As Long
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| 432 | If value = 0 then
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| 433 | return 0
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| 434 | ElseIf value > 0 then
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| 435 | return 1
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| 436 | Else
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| 437 | return -1
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| 438 | End If
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| 439 | End Function
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| 440 |
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[162] | 441 | Static Function Sign(value As SByte) As Long
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[1] | 442 | If value = 0 then
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| 443 | return 0
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| 444 | ElseIf value > 0 then
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| 445 | return 1
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| 446 | Else
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| 447 | return -1
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| 448 | End If
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| 449 | End Function
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| 450 |
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| 451 | Static Function Sign(value As Integer) As Long
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| 452 | If value = 0 then
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| 453 | return 0
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| 454 | ElseIf value > 0 then
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| 455 | return 1
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| 456 | Else
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| 457 | return -1
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| 458 | End If
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| 459 | End Function
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| 460 |
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| 461 | Static Function Sign(value As Long) As Long
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| 462 | If value = 0 then
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| 463 | return 0
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| 464 | ElseIf value > 0 then
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| 465 | return 1
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| 466 | Else
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| 467 | return -1
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| 468 | End If
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| 469 | End Function
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| 470 |
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| 471 | Static Function Sign(value As Int64) As Long
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| 472 | If value = 0 then
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| 473 | return 0
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| 474 | ElseIf value > 0 then
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| 475 | return 1
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| 476 | Else
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| 477 | return -1
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| 478 | End If
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| 479 | End Function
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| 480 |
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| 481 | Static Function Sign(value As Single) As Long
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| 482 | If value = 0 then
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| 483 | return 0
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| 484 | ElseIf value > 0 then
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| 485 | return 1
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| 486 | Else
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| 487 | return -1
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| 488 | End If
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| 489 | End Function
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| 490 |
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| 491 | Static Function Sin(value As Double) As Double
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[53] | 492 | If IsNaN(value) Then
|
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| 493 | Return value
|
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| 494 | ElseIf IsInf(value) Then
|
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[1] | 495 | Return _System_GetNaN()
|
---|
| 496 | Exit Function
|
---|
| 497 | End If
|
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| 498 |
|
---|
[53] | 499 | Dim k As Long
|
---|
[1] | 500 | Dim t As Double
|
---|
| 501 |
|
---|
[92] | 502 | t = urTan((value * 0.5) As Double, k)
|
---|
[1] | 503 | t = 2 * t / (1 + t * t)
|
---|
| 504 | If (k And 1) = 0 Then 'k mod 2 = 0 Then
|
---|
| 505 | Return t
|
---|
| 506 | Else
|
---|
| 507 | Return -t
|
---|
| 508 | End If
|
---|
| 509 | End Function
|
---|
| 510 |
|
---|
| 511 | Static Function Sinh(x As Double) As Double
|
---|
[124] | 512 | If Math.Abs(x) > _System_EPS5 Then
|
---|
[1] | 513 | Dim t As Double
|
---|
[233] | 514 | t = Math.Exp(x)
|
---|
[1] | 515 | Return (t - 1 / t) * 0.5
|
---|
| 516 | Else
|
---|
| 517 | Return x * (1 + x * x * 0.166666666666667) ' x * (1 + x * x / 6)
|
---|
| 518 | End If
|
---|
| 519 | End Function
|
---|
| 520 |
|
---|
| 521 | Static Function Sqrt(x As Double) As Double
|
---|
| 522 | Dim s As Double, last As Double
|
---|
| 523 | Dim i As *Word, j As Long, jj As Long, k As Long
|
---|
[14] | 524 | If x > 0 Then
|
---|
| 525 | If IsInf(x) Then
|
---|
[1] | 526 | Sqrt = x
|
---|
| 527 | Else
|
---|
| 528 | Sqrt = x
|
---|
| 529 | i = (VarPtr(Sqrt) + 6) As *Word
|
---|
| 530 | jj = GetWord(i)
|
---|
| 531 | j = jj >> 5
|
---|
| 532 | k = jj And &h0000001f
|
---|
| 533 | j = (j+ 511) << 4 + k
|
---|
| 534 | SetWord(i, j)
|
---|
| 535 | Do
|
---|
| 536 | last = Sqrt
|
---|
| 537 | Sqrt = (x /Sqrt + Sqrt) * 0.5
|
---|
[23] | 538 | Loop While Sqrt <> last
|
---|
[1] | 539 | End If
|
---|
[14] | 540 | ElseIf x < 0 Then
|
---|
[23] | 541 | Sqrt = _System_GetNaN()
|
---|
[1] | 542 | Else
|
---|
| 543 | 'x = 0 Or NaN
|
---|
| 544 | Sqrt = x
|
---|
| 545 | End If
|
---|
| 546 | End Function
|
---|
| 547 |
|
---|
[14] | 548 | Static Function Tan(x As Double) As Double
|
---|
| 549 | If IsNaN(x) Then
|
---|
| 550 | Tan = x
|
---|
[1] | 551 | Exit Function
|
---|
[14] | 552 | ElseIf IsInf(x) Then
|
---|
[1] | 553 | Tan = _System_GetNaN()
|
---|
| 554 | Exit Function
|
---|
| 555 | End If
|
---|
| 556 |
|
---|
| 557 | Dim k As Long
|
---|
| 558 | Dim t As Double
|
---|
| 559 | t = urTan(x, k)
|
---|
| 560 | If (k And 1) = 0 Then 'k mod 2 = 0 Then
|
---|
| 561 | Return t
|
---|
| 562 | ElseIf t <> 0 Then
|
---|
| 563 | Return -1 / t
|
---|
| 564 | Else
|
---|
| 565 | Return CopySign(_System_GetInf(FALSE), -t)
|
---|
| 566 | End If
|
---|
| 567 | End Function
|
---|
| 568 |
|
---|
| 569 | Static Function Tanh(x As Double) As Double
|
---|
| 570 | If x > _System_EPS5 Then
|
---|
[233] | 571 | Return 2 / (1 + Math.Exp(-2 * x)) - 1
|
---|
[1] | 572 | ElseIf x < -_System_EPS5 Then
|
---|
[233] | 573 | Return 1 - 2 / (Math.Exp(2 * x) + 1)
|
---|
[1] | 574 | Else
|
---|
| 575 | Return x * (1 - x * x * 0.333333333333333) 'x * (1 - x * x / 3)
|
---|
| 576 | End If
|
---|
| 577 | End Function
|
---|
| 578 |
|
---|
[92] | 579 | 'ToString
|
---|
| 580 |
|
---|
[1] | 581 | Static Function Truncate(x As Double) As Double
|
---|
[237] | 582 | Return Fix(x)
|
---|
[1] | 583 | End Function
|
---|
| 584 |
|
---|
[92] | 585 | 'Private
|
---|
[1] | 586 | Static Function urTan(x As Double, ByRef k As Long) As Double
|
---|
| 587 | Dim i As Long
|
---|
| 588 | Dim t As Double, x2 As Double
|
---|
| 589 |
|
---|
| 590 | If x >= 0 Then
|
---|
[233] | 591 | k = ( Fix(x * _System_InverseHalfPI) + 0.5 ) As Long
|
---|
[1] | 592 | Else
|
---|
[233] | 593 | k = ( Fix(x * _System_InverseHalfPI) - 0.5 ) As Long
|
---|
[1] | 594 | End If
|
---|
| 595 | x = (x - (3217.0 / 2048.0) * k) + _System_D * k
|
---|
| 596 | x2 = x * x
|
---|
| 597 | t = 0
|
---|
| 598 | For i = _System_UrTan_N To 3 Step -2
|
---|
| 599 | t = x2 / (i - t)
|
---|
| 600 | Next i
|
---|
| 601 | urTan = x / (1 - t)
|
---|
| 602 | End Function
|
---|
[238] | 603 | Private
|
---|
| 604 | Static Const _System_Log_N = 7 As Long
|
---|
| 605 | Static Const _System_Atan_N = 20 As Long
|
---|
| 606 | Static Const _System_UrTan_N = 17 As Long
|
---|
| 607 | Static Const _System_D = 4.4544551033807686783083602485579e-6 As Double
|
---|
| 608 | Static Const _System_EPS5 = 0.001 As Double
|
---|
[1] | 609 | End Class
|
---|
| 610 |
|
---|
| 611 | Const _System_HalfPI = (_System_PI * 0.5)
|
---|
| 612 | Const _System_InverseHalfPI = (2 / _System_PI) '1 / (PI / 2)
|
---|
[244] | 613 | Const _System_InverseLn10 = 0.43429448190325182765112891891661 '1 / (ln 10)
|
---|
| 614 | Const _System_InverseSqrt2 = 0.70710678118654752440084436210485 '1 / (√2)
|
---|
[1] | 615 |
|
---|
[244] | 616 |
|
---|
[20] | 617 | #endif '__SYSTEM_MATH_AB__
|
---|