[14] | 1 | ' Classes/System/Math.ab
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[1] | 2 |
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[268] | 3 | #require <Classes/ActiveBasic/Math/Math.ab>
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| 4 |
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[1] | 5 | #ifndef __SYSTEM_MATH_AB__
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| 6 | #define __SYSTEM_MATH_AB__
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| 7 |
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[268] | 8 | Namespace System
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| 9 |
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[1] | 10 | Class Math
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| 11 | Public
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| 12 | Static Function E() As Double
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| 13 | return 2.7182818284590452354
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| 14 | End Function
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[299] | 15 | /*
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[1] | 16 | Static Function PI() As Double
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| 17 | return _System_PI
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| 18 | End Function
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[299] | 19 | */
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[1] | 20 | Static Function Abs(value As Double) As Double
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[239] | 21 | SetQWord(VarPtr(Abs), GetQWord(VarPtr(value)) And &h7fffffffffffffff)
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[1] | 22 | End Function
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| 23 |
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| 24 | Static Function Abs(value As Single) As Single
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[239] | 25 | SetDWord(VarPtr(Abs), GetDWord(VarPtr(value)) And &h7fffffff)
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[1] | 26 | End Function
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| 27 |
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[162] | 28 | Static Function Abs(value As SByte) As SByte
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[1] | 29 | If value<0 then
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| 30 | return -value
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| 31 | Else
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| 32 | return value
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| 33 | End If
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| 34 | End Function
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| 35 |
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| 36 | Static Function Abs(value As Integer) As Integer
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| 37 | If value<0 then
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| 38 | return -value
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| 39 | Else
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| 40 | return value
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| 41 | End If
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| 42 | End Function
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| 43 |
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| 44 | Static Function Abs(value As Long) As Long
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| 45 | If value<0 then
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| 46 | return -value
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| 47 | Else
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| 48 | return value
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| 49 | End If
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| 50 | End Function
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| 51 |
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| 52 | Static Function Abs(value As Int64) As Int64
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| 53 | If value<0 then
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| 54 | return -value
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| 55 | Else
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| 56 | return value
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| 57 | End If
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| 58 | End Function
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| 59 |
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| 60 | Static Function Acos(x As Double) As Double
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| 61 | If x < -1 Or x > 1 Then
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[268] | 62 | Acos = ActiveBasic.Math.Detail.GetNaN()
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[1] | 63 | Else
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[232] | 64 | Acos = _System_HalfPI - Asin(x)
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[1] | 65 | End If
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| 66 | End Function
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| 67 |
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| 68 | Static Function Asin(x As Double) As Double
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| 69 | If x < -1 Or x > 1 Then
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[268] | 70 | Asin = ActiveBasic.Math.Detail.GetNaN()
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[1] | 71 | Else
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[233] | 72 | Asin = Math.Atan(x / Sqrt(1 - x * x))
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[1] | 73 | End If
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| 74 | End Function
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| 75 |
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| 76 | Static Function Atan(x As Double) As Double
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[268] | 77 | If ActiveBasic.Math.IsNaN(x) Then
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[1] | 78 | Atan = x
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| 79 | Exit Function
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[268] | 80 | ElseIf ActiveBasic.Math.IsInf(x) Then
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| 81 | Atan = ActiveBasic.Math.CopySign(_System_PI, x)
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[1] | 82 | Exit Function
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| 83 | End If
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| 84 | Dim i As Long
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| 85 | Dim sgn As Long
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| 86 | Dim dbl = 0 As Double
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| 87 |
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| 88 | If x > 1 Then
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| 89 | sgn = 1
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| 90 | x = 1 / x
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| 91 | ElseIf x < -1 Then
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| 92 | sgn = -1
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| 93 | x = 1 / x
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| 94 | Else
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| 95 | sgn = 0
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| 96 | End If
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| 97 |
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| 98 | For i = _System_Atan_N To 1 Step -1
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| 99 | Dim t As Double
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[14] | 100 | t = i * x
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[1] | 101 | dbl = (t * t) / (2 * i + 1 + dbl)
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| 102 | Next
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| 103 |
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| 104 | If sgn > 0 Then
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| 105 | Atan = _System_HalfPI - x / (1 + dbl)
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| 106 | ElseIf sgn < 0 Then
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| 107 | Atan = -_System_HalfPI - x / (1 + dbl)
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| 108 | Else
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| 109 | Atan = x / (1 + dbl)
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| 110 | End If
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| 111 | End Function
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| 112 |
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| 113 | Static Function Atan2(y As Double, x As Double) As Double
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| 114 | If x = 0 Then
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| 115 | Atan2 = Sgn(y) * _System_HalfPI
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| 116 | Else
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| 117 | Atan2 = Atn(y / x)
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| 118 | If x < 0 Then
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[268] | 119 | Atan2 += ActiveBasic.Math.CopySign(_System_PI, y)
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[1] | 120 | End If
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| 121 | End If
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| 122 | End Function
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| 123 |
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[14] | 124 | Static Function BigMul(x As Long, y As Long) As Int64
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| 125 | Return (x As Int64) * y
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[1] | 126 | End Function
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| 127 |
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| 128 | Static Function Ceiling(x As Double) As Long
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[457] | 129 | Ceiling = Floor(x)
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| 130 | If Ceiling <> x Then
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| 131 | Ceiling++
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[1] | 132 | End If
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| 133 | End Function
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| 134 |
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[14] | 135 | Static Function Cos(x As Double) As Double
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[268] | 136 | If ActiveBasic.Math.IsNaN(x) Then
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[14] | 137 | Return x
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[268] | 138 | ElseIf ActiveBasic.Math.IsInf(x) Then
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| 139 | Return ActiveBasic.Math.Detail.GetNaN()
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[1] | 140 | End If
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| 141 |
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[124] | 142 | Return Math.Sin((_System_HalfPI - Math.Abs(x)) As Double)
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[1] | 143 | End Function
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| 144 |
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| 145 | Static Function Cosh(value As Double) As Double
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[457] | 146 | Dim t = Math.Exp(value)
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[1] | 147 | return (t + 1 / t) * 0.5
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| 148 | End Function
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| 149 |
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[14] | 150 | Static Function DivRem(x As Long, y As Long, ByRef ret As Long) As Long
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| 151 | ret = x Mod y
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| 152 | return x \ y
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[1] | 153 | End Function
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| 154 |
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[14] | 155 | Static Function DivRem(x As Int64, y As Int64, ByRef ret As Int64) As Int64
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[457] | 156 | DivRem = x \ y
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| 157 | ret = x - (DivRem) * y
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[1] | 158 | End Function
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| 159 |
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| 160 | 'Equals
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| 161 |
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[14] | 162 | Static Function Exp(x As Double) As Double
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[268] | 163 | If ActiveBasic.Math.IsNaN(x) Then
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[1] | 164 | Return x
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[268] | 165 | Else If ActiveBasic.Math.IsInf(x) Then
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[1] | 166 | If 0 > x Then
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| 167 | Return 0
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| 168 | Else
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| 169 | Return x
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| 170 | End If
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| 171 | End If
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[285] | 172 | Dim k As Long
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[1] | 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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[285] | 181 | Dim x2 = x * x
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| 182 | Dim w = x2 / 22
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[1] | 183 |
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[285] | 184 | Dim i = 18
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[1] | 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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[237] | 197 | Static Function IEEERemainder(x As Double, y As Double) As Double
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[268] | 198 | If y = 0 Then Return ActiveBasic.Math.Detail.GetNaN()
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[237] | 199 | Dim q = x / y
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| 200 | If q <> Int(q) Then
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| 201 | If q + 0.5 <> Int(q + 0.5) Then
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| 202 | q = Int(q + 0.5)
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| 203 | ElseIf Int(q + 0.5) = Int(q * 2 + 1) / 2 Then
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| 204 | q = Int(q + 0.5)
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[1] | 205 | Else
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[237] | 206 | q = Int(q - 0.5)
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[1] | 207 | End If
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| 208 | End If
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[237] | 209 | If x - y * q = 0 Then
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| 210 | If x > 0 Then
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| 211 | Return +0
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[1] | 212 | Else
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[237] | 213 | Return -0
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[1] | 214 | End If
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| 215 | Else
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[237] | 216 | Return x-y*q
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[1] | 217 | End If
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| 218 | End Function
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| 219 |
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| 220 | Static Function Log(x As Double) As Double
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| 221 | If x = 0 Then
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[268] | 222 | Log = ActiveBasic.Math.Detail.GetInf(True)
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| 223 | ElseIf x < 0 Or ActiveBasic.Math.IsNaN(x) Then
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| 224 | Log = ActiveBasic.Math.Detail.GetNaN()
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| 225 | ElseIf ActiveBasic.Math.IsInf(x) Then
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[1] | 226 | Log = x
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| 227 | Else
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[244] | 228 | Dim tmp = x * _System_InverseSqrt2
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| 229 | Dim p = VarPtr(tmp) As *QWord
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[257] | 230 | Dim m = GetQWord(p) And &h7FF0000000000000
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[244] | 231 | Dim k = ((m >> 52) As DWord) As Long - 1022
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[257] | 232 | SetQWord(p, m + &h0010000000000000)
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[244] | 233 | x /= tmp
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[268] | 234 | Log = _System_LOG2 * k + ActiveBasic.Math.Detail.Log1p(x - 1)
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[1] | 235 | End If
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| 236 | End Function
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| 237 |
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| 238 | Static Function Log10(x As Double) As Double
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[244] | 239 | Return Math.Log(x) * _System_InverseLn10
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[1] | 240 | End Function
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| 241 |
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[244] | 242 | Static Function Max(value1 As Byte, value2 As Byte) As Byte
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[1] | 243 | If value1>value2 then
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| 244 | return value1
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| 245 | Else
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| 246 | return value2
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| 247 | End If
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| 248 | End Function
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| 249 |
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[244] | 250 | Static Function Max(value1 As SByte, value2 As SByte) As SByte
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[1] | 251 | If value1>value2 then
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| 252 | return value1
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| 253 | Else
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| 254 | return value2
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| 255 | End If
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| 256 | End Function
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| 257 |
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[244] | 258 | Static Function Max(value1 As Word, value2 As Word) As Word
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[1] | 259 | If value1>value2 then
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| 260 | return value1
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| 261 | Else
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| 262 | return value2
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| 263 | End If
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| 264 | End Function
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| 265 |
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[244] | 266 | Static Function Max(value1 As Integer, value2 As Integer) As Integer
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[1] | 267 | If value1>value2 then
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| 268 | return value1
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| 269 | Else
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| 270 | return value2
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| 271 | End If
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| 272 | End Function
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| 273 |
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[244] | 274 | Static Function Max(value1 As DWord, value2 As DWord) As DWord
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[1] | 275 | If value1>value2 then
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| 276 | return value1
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| 277 | Else
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| 278 | return value2
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| 279 | End If
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| 280 | End Function
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| 281 |
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[244] | 282 | Static Function Max(value1 As Long, value2 As Long) As Long
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[1] | 283 | If value1>value2 then
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| 284 | return value1
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| 285 | Else
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| 286 | return value2
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| 287 | End If
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| 288 | End Function
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| 289 |
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[244] | 290 | Static Function Max(value1 As QWord, value2 As QWord) As QWord
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[1] | 291 | If value1>value2 then
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| 292 | return value1
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| 293 | Else
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| 294 | return value2
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| 295 | End If
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| 296 | End Function
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| 297 |
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[244] | 298 | Static Function Max(value1 As Int64, value2 As Int64) As Int64
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[1] | 299 | If value1>value2 then
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| 300 | return value1
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| 301 | Else
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| 302 | return value2
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| 303 | End If
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| 304 | End Function
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| 305 |
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[244] | 306 | Static Function Max(value1 As Single, value2 As Single) As Single
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[1] | 307 | If value1>value2 then
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| 308 | return value1
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| 309 | Else
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| 310 | return value2
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| 311 | End If
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| 312 | End Function
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| 313 |
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[244] | 314 | Static Function Max(value1 As Double, value2 As Double) As Double
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[1] | 315 | If value1>value2 then
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| 316 | return value1
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| 317 | Else
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| 318 | return value2
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| 319 | End If
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| 320 | End Function
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| 321 |
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[244] | 322 | Static Function Min(value1 As Byte, value2 As Byte) As Byte
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[1] | 323 | If value1<value2 then
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| 324 | return value1
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| 325 | Else
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| 326 | return value2
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| 327 | End If
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| 328 | End Function
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| 329 |
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[244] | 330 | Static Function Min(value1 As SByte, value2 As SByte) As SByte
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[1] | 331 | If value1<value2 then
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| 332 | return value1
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| 333 | Else
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| 334 | return value2
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| 335 | End If
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| 336 | End Function
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| 337 |
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[244] | 338 | Static Function Min(value1 As Word, value2 As Word) As Word
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[1] | 339 | If value1<value2 then
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| 340 | return value1
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| 341 | Else
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| 342 | return value2
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| 343 | End If
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| 344 | End Function
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| 345 |
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[244] | 346 | Static Function Min(value1 As Integer, value2 As Integer) As Integer
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[1] | 347 | If value1<value2 then
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| 348 | return value1
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| 349 | Else
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| 350 | return value2
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| 351 | End If
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| 352 | End Function
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| 353 |
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[244] | 354 | Static Function Min(value1 As DWord, value2 As DWord) As DWord
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[1] | 355 | If value1<value2 then
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| 356 | return value1
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| 357 | Else
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| 358 | return value2
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| 359 | End If
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| 360 | End Function
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| 361 |
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[244] | 362 | Static Function Min(value1 As Long, value2 As Long) As Long
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[1] | 363 | If value1<value2 then
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| 364 | return value1
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| 365 | Else
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| 366 | return value2
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| 367 | End If
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| 368 | End Function
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| 369 |
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[244] | 370 | Static Function Min(value1 As QWord, value2 As QWord) As QWord
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[1] | 371 | If value1<value2 then
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| 372 | return value1
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| 373 | Else
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| 374 | return value2
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| 375 | End If
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| 376 | End Function
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| 377 |
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[244] | 378 | Static Function Min(value1 As Int64, value2 As Int64) As Int64
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[1] | 379 | If value1<value2 then
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| 380 | return value1
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| 381 | Else
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| 382 | return value2
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| 383 | End If
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| 384 | End Function
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| 385 |
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[244] | 386 | Static Function Min(value1 As Single, value2 As Single) As Single
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[1] | 387 | If value1<value2 then
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| 388 | return value1
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| 389 | Else
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| 390 | return value2
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| 391 | End If
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| 392 | End Function
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| 393 |
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[244] | 394 | Static Function Min(value1 As Double, value2 As Double) As Double
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[1] | 395 | If value1<value2 then
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| 396 | return value1
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| 397 | Else
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| 398 | return value2
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| 399 | End If
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| 400 | End Function
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| 401 |
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[14] | 402 | Static Function Pow(x As Double, y As Double) As Double
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| 403 | return pow(x, y)
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[1] | 404 | End Function
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| 405 |
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| 406 | 'ReferenceEquals
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| 407 |
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| 408 | Static Function Round(value As Double) As Double'他のバージョン、誰か頼む。
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| 409 | If value+0.5<>Int(value+0.5) then
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| 410 | value=Int(value+0.5)
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| 411 | ElseIf Int(value+0.5)=Int(value*2+1)/2 then
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| 412 | value=Int(value+0.5)
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| 413 | Else
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| 414 | value=Int(value-0.5)
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| 415 | End If
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| 416 | End Function
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| 417 |
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| 418 | Static Function Sign(value As Double) As Long
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| 419 | If value = 0 then
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| 420 | return 0
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| 421 | ElseIf value > 0 then
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| 422 | return 1
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| 423 | Else
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| 424 | return -1
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| 425 | End If
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| 426 | End Function
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| 427 |
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[162] | 428 | Static Function Sign(value As SByte) As Long
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[1] | 429 | If value = 0 then
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| 430 | return 0
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| 431 | ElseIf value > 0 then
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| 432 | return 1
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| 433 | Else
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| 434 | return -1
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| 435 | End If
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| 436 | End Function
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| 437 |
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| 438 | Static Function Sign(value As Integer) As Long
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| 439 | If value = 0 then
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| 440 | return 0
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| 441 | ElseIf value > 0 then
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| 442 | return 1
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| 443 | Else
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| 444 | return -1
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| 445 | End If
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| 446 | End Function
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| 447 |
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| 448 | Static Function Sign(value As Long) As Long
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| 449 | If value = 0 then
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| 450 | return 0
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| 451 | ElseIf value > 0 then
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| 452 | return 1
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| 453 | Else
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| 454 | return -1
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| 455 | End If
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| 456 | End Function
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| 457 |
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| 458 | Static Function Sign(value As Int64) As Long
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| 459 | If value = 0 then
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| 460 | return 0
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| 461 | ElseIf value > 0 then
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| 462 | return 1
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| 463 | Else
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| 464 | return -1
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| 465 | End If
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| 466 | End Function
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| 467 |
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| 468 | Static Function Sign(value As Single) As Long
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| 469 | If value = 0 then
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| 470 | return 0
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| 471 | ElseIf value > 0 then
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| 472 | return 1
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| 473 | Else
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| 474 | return -1
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| 475 | End If
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| 476 | End Function
|
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| 477 |
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| 478 | Static Function Sin(value As Double) As Double
|
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[268] | 479 | If ActiveBasic.Math.IsNaN(value) Then
|
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[53] | 480 | Return value
|
---|
[268] | 481 | ElseIf ActiveBasic.Math.IsInf(value) Then
|
---|
| 482 | Return ActiveBasic.Math.Detail.GetNaN()
|
---|
[1] | 483 | Exit Function
|
---|
| 484 | End If
|
---|
| 485 |
|
---|
[53] | 486 | Dim k As Long
|
---|
[1] | 487 | Dim t As Double
|
---|
| 488 |
|
---|
[92] | 489 | t = urTan((value * 0.5) As Double, k)
|
---|
[1] | 490 | t = 2 * t / (1 + t * t)
|
---|
| 491 | If (k And 1) = 0 Then 'k mod 2 = 0 Then
|
---|
| 492 | Return t
|
---|
| 493 | Else
|
---|
| 494 | Return -t
|
---|
| 495 | End If
|
---|
| 496 | End Function
|
---|
| 497 |
|
---|
| 498 | Static Function Sinh(x As Double) As Double
|
---|
[124] | 499 | If Math.Abs(x) > _System_EPS5 Then
|
---|
[1] | 500 | Dim t As Double
|
---|
[233] | 501 | t = Math.Exp(x)
|
---|
[1] | 502 | Return (t - 1 / t) * 0.5
|
---|
| 503 | Else
|
---|
| 504 | Return x * (1 + x * x * 0.166666666666667) ' x * (1 + x * x / 6)
|
---|
| 505 | End If
|
---|
| 506 | End Function
|
---|
| 507 |
|
---|
| 508 | Static Function Sqrt(x As Double) As Double
|
---|
[14] | 509 | If x > 0 Then
|
---|
[268] | 510 | If ActiveBasic.Math.IsInf(x) Then
|
---|
[1] | 511 | Sqrt = x
|
---|
| 512 | Else
|
---|
| 513 | Sqrt = x
|
---|
[457] | 514 | Dim i = (VarPtr(Sqrt) + 6) As *Word
|
---|
| 515 | Dim jj = GetWord(i) As Long
|
---|
| 516 | Dim j = jj >> 5 As Long
|
---|
| 517 | Dim k = (jj And &h0000001f) As Long
|
---|
| 518 | j = (j + 511) << 4 + k
|
---|
[1] | 519 | SetWord(i, j)
|
---|
[457] | 520 | Dim last As Double
|
---|
[1] | 521 | Do
|
---|
| 522 | last = Sqrt
|
---|
[457] | 523 | Sqrt = (x / Sqrt + Sqrt) * 0.5
|
---|
[23] | 524 | Loop While Sqrt <> last
|
---|
[1] | 525 | End If
|
---|
[14] | 526 | ElseIf x < 0 Then
|
---|
[268] | 527 | Sqrt = ActiveBasic.Math.Detail.GetNaN()
|
---|
[1] | 528 | Else
|
---|
| 529 | 'x = 0 Or NaN
|
---|
| 530 | Sqrt = x
|
---|
| 531 | End If
|
---|
| 532 | End Function
|
---|
| 533 |
|
---|
[14] | 534 | Static Function Tan(x As Double) As Double
|
---|
[268] | 535 | If ActiveBasic.Math.IsNaN(x) Then
|
---|
[14] | 536 | Tan = x
|
---|
[1] | 537 | Exit Function
|
---|
[268] | 538 | ElseIf ActiveBasic.Math.IsInf(x) Then
|
---|
| 539 | Tan = ActiveBasic.Math.Detail.GetNaN()
|
---|
[1] | 540 | Exit Function
|
---|
| 541 | End If
|
---|
| 542 |
|
---|
| 543 | Dim k As Long
|
---|
| 544 | Dim t As Double
|
---|
| 545 | t = urTan(x, k)
|
---|
| 546 | If (k And 1) = 0 Then 'k mod 2 = 0 Then
|
---|
| 547 | Return t
|
---|
| 548 | ElseIf t <> 0 Then
|
---|
| 549 | Return -1 / t
|
---|
| 550 | Else
|
---|
[268] | 551 | Return ActiveBasic.Math.CopySign(ActiveBasic.Math.Detail.GetInf(False), -t)
|
---|
[1] | 552 | End If
|
---|
| 553 | End Function
|
---|
| 554 |
|
---|
| 555 | Static Function Tanh(x As Double) As Double
|
---|
| 556 | If x > _System_EPS5 Then
|
---|
[233] | 557 | Return 2 / (1 + Math.Exp(-2 * x)) - 1
|
---|
[1] | 558 | ElseIf x < -_System_EPS5 Then
|
---|
[233] | 559 | Return 1 - 2 / (Math.Exp(2 * x) + 1)
|
---|
[1] | 560 | Else
|
---|
| 561 | Return x * (1 - x * x * 0.333333333333333) 'x * (1 - x * x / 3)
|
---|
| 562 | End If
|
---|
| 563 | End Function
|
---|
| 564 |
|
---|
[92] | 565 | 'ToString
|
---|
| 566 |
|
---|
[1] | 567 | Static Function Truncate(x As Double) As Double
|
---|
[237] | 568 | Return Fix(x)
|
---|
[1] | 569 | End Function
|
---|
| 570 |
|
---|
[92] | 571 | 'Private
|
---|
[1] | 572 | Static Function urTan(x As Double, ByRef k As Long) As Double
|
---|
| 573 | Dim i As Long
|
---|
| 574 | Dim t As Double, x2 As Double
|
---|
| 575 |
|
---|
| 576 | If x >= 0 Then
|
---|
[233] | 577 | k = ( Fix(x * _System_InverseHalfPI) + 0.5 ) As Long
|
---|
[1] | 578 | Else
|
---|
[233] | 579 | k = ( Fix(x * _System_InverseHalfPI) - 0.5 ) As Long
|
---|
[1] | 580 | End If
|
---|
| 581 | x = (x - (3217.0 / 2048.0) * k) + _System_D * k
|
---|
| 582 | x2 = x * x
|
---|
| 583 | t = 0
|
---|
| 584 | For i = _System_UrTan_N To 3 Step -2
|
---|
| 585 | t = x2 / (i - t)
|
---|
| 586 | Next i
|
---|
| 587 | urTan = x / (1 - t)
|
---|
| 588 | End Function
|
---|
[238] | 589 | Private
|
---|
| 590 | Static Const _System_Atan_N = 20 As Long
|
---|
| 591 | Static Const _System_UrTan_N = 17 As Long
|
---|
| 592 | Static Const _System_D = 4.4544551033807686783083602485579e-6 As Double
|
---|
| 593 | Static Const _System_EPS5 = 0.001 As Double
|
---|
[1] | 594 | End Class
|
---|
| 595 |
|
---|
[268] | 596 | End Namespace
|
---|
| 597 |
|
---|
[1] | 598 | Const _System_HalfPI = (_System_PI * 0.5)
|
---|
| 599 | Const _System_InverseHalfPI = (2 / _System_PI) '1 / (PI / 2)
|
---|
[244] | 600 | Const _System_InverseLn10 = 0.43429448190325182765112891891661 '1 / (ln 10)
|
---|
| 601 | Const _System_InverseSqrt2 = 0.70710678118654752440084436210485 '1 / (√2)
|
---|
[1] | 602 |
|
---|
[20] | 603 | #endif '__SYSTEM_MATH_AB__
|
---|