| 1 | 'Classes/ActiveBasic/Math/Math.ab
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| 2 |
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| 3 | Namespace ActiveBasic
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| 4 | Namespace Math
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| 5 |
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| 6 | Const PI = _System_PI
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| 7 |
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| 8 | '----
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| 9 | '浮動小数点数補助
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| 10 | Function ldexp(x As Double, n As Long) As Double
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| 11 | If x = 0 Then
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| 12 | ldexp = 0
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| 13 | Exit Function
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| 14 | End If
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| 15 | Dim pSrc = VarPtr(x) As *QWord
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| 16 | Dim pDest = VarPtr(ldexp) As *QWord
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| 17 | n += (pSrc[0] >> 52) As DWord And &h7FF
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| 18 | pDest[0] = n << 52 Or (pSrc[0] And &h800FFFFFFFFFFFFF)
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| 19 | End Function
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| 20 |
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| 21 | Function frexp(x As Double, ByRef n As Long) As Double
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| 22 | If x = 0 Then
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| 23 | n = 0
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| 24 | frexp = 0
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| 25 | Exit Function
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| 26 | End If
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| 27 |
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| 28 | Dim pSrc = VarPtr(x) As *QWord
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| 29 | Dim pDest = VarPtr(frexp) As *QWord
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| 30 | n = ((pSrc[0] >> 52) As DWord And &h7FF) - 1022
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| 31 | pDest[0] = (pSrc[0] And &h800FFFFFFFFFFFFF) Or &h3FE0000000000000
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| 32 | End Function
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| 33 |
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| 34 | Function frexp(x As Single, ByRef n As Long) As Single
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| 35 | If x = 0 Then
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| 36 | n = 0
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| 37 | frexp = 0
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| 38 | Exit Function
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| 39 | End If
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| 40 |
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| 41 | Dim pSrc As *DWord, pDest As *DWord
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| 42 | pSrc = VarPtr(x) As *DWord
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| 43 | pDest = VarPtr(frexp) As *DWord
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| 44 | n = ((pSrc[0] >> 23) And &hFF) - 126
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| 45 | pDest[0] = (pSrc[0] And &h807FFFFF) Or &h7E000000
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| 46 | End Function
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| 47 |
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| 48 | '----
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| 49 | '冪乗
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| 50 | Function pow(x As Double, n As Long) As Double
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| 51 | Dim abs_n As Long
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| 52 | Dim r = 1 As Double
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| 53 |
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| 54 | abs_n=Abs(n) As Long
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| 55 | While abs_n<>0
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| 56 | If abs_n and 1 Then r *= x
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| 57 | x = x * x
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| 58 | abs_n >>= 1 ' abs_n \= 2
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| 59 | Wend
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| 60 |
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| 61 | If n>=0 Then
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| 62 | pow=r
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| 63 | Else
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| 64 | pow=1/r
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| 65 | End If
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| 66 | End Function
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| 67 |
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| 68 | Function pow(x As Double, y As Double) As Double
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| 69 | Dim yi = y As Long
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| 70 | If y = yi Then
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| 71 | pow = pow(x, yi)
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| 72 | ElseIf x>0 Then
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| 73 | pow = Exp(y * Log(x))
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| 74 | Exit Function
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| 75 | ElseIf x<>0 or y<=0 Then
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| 76 | pow = Detail.GetNaN()
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| 77 | Else
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| 78 | pow = 0
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| 79 | End If
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| 80 | End Function
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| 81 |
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| 82 | Function Sqrt(x As Double) As Double
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| 83 | If x > 0 Then
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| 84 | If IsInf(x) Then
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| 85 | Sqrt = x
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| 86 | Else
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| 87 | Sqrt = x
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| 88 | Dim i = (VarPtr(Sqrt) + 6) As *Word
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| 89 | Dim jj = GetWord(i) As Long
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| 90 | Dim j = jj >> 5 As Long
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| 91 | Dim k = (jj And &h0000001f) As Long
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| 92 | j = ((j + 511) << 4) + k
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| 93 | SetWord(i, j)
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| 94 | Dim last As Double
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| 95 | Do
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| 96 | last = Sqrt
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| 97 | Sqrt = (x / Sqrt + Sqrt) * 0.5
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| 98 | Loop While Sqrt <> last
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| 99 | End If
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| 100 | ElseIf x < 0 Then
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| 101 | Sqrt = Detail.GetNaN()
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| 102 | Else
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| 103 | 'x = 0 Or NaN
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| 104 | Sqrt = x
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| 105 | End If
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| 106 | End Function
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| 107 |
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| 108 | 'xの符号だけをyのものにした値を返す。
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| 109 | '引数 x 元となる絶対値
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| 110 | '引数 y 元となる符号
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| 111 | Function CopySign(x As Double, y As Double) As Double
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| 112 | SetQWord(VarPtr(CopySign), (GetQWord(VarPtr(x)) And &h7fffffffffffffff) Or (GetQWord(VarPtr(y)) And &h8000000000000000))
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| 113 | End Function
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| 114 |
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| 115 | Function CopySign(x As Single, y As Single) As Single
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| 116 | SetDWord(VarPtr(CopySign), (GetDWord(VarPtr(x)) And &h7fffffff) Or (GetDWord(VarPtr(y)) And &h80000000))
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| 117 | End Function
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| 118 |
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| 119 | '----
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| 120 | '絶対値
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| 121 | Function Abs(n As Double) As Double
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| 122 | If n < 0 Then
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| 123 | Abs = -n
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| 124 | Else
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| 125 | Abs = n
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| 126 | End If
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| 127 | End Function
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| 128 |
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| 129 | Function Abs(n As Single) As Single
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| 130 | If n < 0 Then
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| 131 | Abs = -n
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| 132 | Else
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| 133 | Abs = n
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| 134 | End If
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| 135 | End Function
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| 136 |
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| 137 | Function Abs(n As Int64) As Int64
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| 138 | If n < 0 Then
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| 139 | Abs = -n
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| 140 | Else
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| 141 | Abs = n
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| 142 | End If
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| 143 | End Function
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| 144 |
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| 145 | Function Abs(n As Long) As Long
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| 146 | If n < 0 Then
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| 147 | Abs = -n
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| 148 | Else
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| 149 | Abs = n
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| 150 | End If
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| 151 | End Function
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| 152 |
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| 153 | Function Abs(n As Integer) As Integer
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| 154 | If n < 0 Then
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| 155 | Abs = -n
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| 156 | Else
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| 157 | Abs = n
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| 158 | End If
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| 159 | End Function
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| 160 |
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| 161 | Function Abs(n As SByte) As SByte
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| 162 | If n < 0 Then
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| 163 | Abs = -n
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| 164 | Else
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| 165 | Abs = n
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| 166 | End If
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| 167 | End Function
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| 168 |
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| 169 | '----
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| 170 | '指数・対数
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| 171 |
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| 172 | Function Exp(x As Double) As Double
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| 173 | If IsNaN(x) Then
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| 174 | Return x
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| 175 | Else If IsInf(x) Then
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| 176 | If 0 > x Then
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| 177 | Return 0
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| 178 | Else
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| 179 | Return x
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| 180 | End If
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| 181 | End If
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| 182 | Dim k As Long
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| 183 | If x >= 0 Then
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| 184 | k = Fix(x / Detail._System_LOG2 + 0.5)
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| 185 | Else
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| 186 | k = Fix(x / Detail._System_LOG2 - 0.5)
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| 187 | End If
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| 188 |
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| 189 | x -= k * Detail._System_LOG2
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| 190 |
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| 191 | Dim x2 = x * x
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| 192 | Dim w = x2 / 22
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| 193 |
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| 194 | Dim i = 18
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| 195 | While i >= 6
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| 196 | w = x2 / (w + i)
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| 197 | i -= 4
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| 198 | Wend
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| 199 |
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| 200 | Return ldexp((2 + w + x) / (2 + w - x), k)
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| 201 | End Function
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| 202 |
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| 203 | Function Log1p(x As Double) As Double
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| 204 | If x < -1 Or IsNaN(x) Then
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| 205 | Log1p = Detail.GetNaN()
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| 206 | ElseIf x = 0 Then
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| 207 | x = 0
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| 208 | ElseIf IsInf(x) Then
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| 209 | Log1p = x
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| 210 | Else
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| 211 | Log1p = Detail.Log1p(x)
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| 212 | End If
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| 213 | End Function
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| 214 |
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| 215 | Function Log(x As Double) As Double
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| 216 | If x = 0 Then
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| 217 | Log = Detail.GetInf(True)
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| 218 | ElseIf x < 0 Or IsNaN(x) Then
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| 219 | Log = Detail.GetNaN()
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| 220 | ElseIf IsInf(x) Then
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| 221 | Log = x
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| 222 | Else
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| 223 | Dim tmp = x * Detail._System_InverseSqrt2
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| 224 | Dim p = VarPtr(tmp) As *QWord
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| 225 | Dim m = GetQWord(p) And &h7FF0000000000000
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| 226 | Dim k = ((m >> 52) As DWord) As Long - 1022
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| 227 | SetQWord(p, m + &h0010000000000000)
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| 228 | x /= tmp
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| 229 | Log = Detail._System_LOG2 * k + Detail.Log1p(x - 1)
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| 230 | End If
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| 231 | End Function
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| 232 |
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| 233 | Function Log10(x As Double) As Double
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| 234 | Return Log(x) * Detail._System_InverseLn10
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| 235 | End Function
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| 236 |
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| 237 | '----
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| 238 | '三角関数
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| 239 | Function Sin(x As Double) As Double
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| 240 | If IsNaN(x) Then
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| 241 | Return x
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| 242 | ElseIf IsInf(x) Then
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| 243 | Return Detail.GetNaN()
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| 244 | Exit Function
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| 245 | End If
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| 246 |
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| 247 | Dim k As Long
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| 248 | Dim t As Double
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| 249 |
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| 250 | t = Detail._Support_tan((x * 0.5) As Double, k)
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| 251 | t = 2 * t / (1 + t * t)
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| 252 | If (k And 1) = 0 Then 'k mod 2 = 0 Then
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| 253 | Return t
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| 254 | Else
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| 255 | Return -t
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| 256 | End If
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| 257 | End Function
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| 258 |
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| 259 | Function Cos(x As Double) As Double
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| 260 | If IsNaN(x) Then
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| 261 | Return x
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| 262 | ElseIf IsInf(x) Then
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| 263 | Return Detail.GetNaN()
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| 264 | End If
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| 265 |
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| 266 | Return Sin((Detail._System_HalfPI - Abs(x)) As Double)
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| 267 | End Function
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| 268 |
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| 269 | Function Tan(x As Double) As Double
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| 270 | If IsNaN(x) Then
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| 271 | Tan = x
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| 272 | Exit Function
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| 273 | ElseIf IsInf(x) Then
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| 274 | Tan = Detail.GetNaN()
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| 275 | Exit Function
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| 276 | End If
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| 277 |
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| 278 | Dim k As Long
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| 279 | Dim t As Double
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| 280 | t = Detail._Support_tan(x, k)
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| 281 | If (k And 1) = 0 Then 'k mod 2 = 0 Then
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| 282 | Return t
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| 283 | ElseIf t <> 0 Then
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| 284 | Return -1 / t
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| 285 | Else
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| 286 | Return CopySign(Detail.GetInf(False), -t)
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| 287 | End If
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| 288 | End Function
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| 289 |
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| 290 | '--
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| 291 | '三角関数の逆関数
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| 292 | Function Asin(x As Double) As Double
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| 293 | If x < -1 Or x > 1 Then
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| 294 | Asin = Detail.GetNaN()
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| 295 | Else
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| 296 | Asin = Atan(x / Sqrt(1 - x * x))
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| 297 | End If
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| 298 | End Function
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| 299 |
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| 300 | Function Acos(x As Double) As Double
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| 301 | If x < -1 Or x > 1 Then
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| 302 | Acos = Detail.GetNaN()
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| 303 | Else
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| 304 | Acos = Detail._System_HalfPI - Asin(x)
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| 305 | End If
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| 306 | End Function
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| 307 |
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| 308 | Function Atan(x As Double) As Double
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| 309 | If IsNaN(x) Then
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| 310 | Atan = x
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| 311 | Exit Function
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| 312 | ElseIf IsInf(x) Then
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| 313 | Atan = CopySign(_System_PI, x)
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| 314 | Exit Function
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| 315 | End If
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| 316 | Dim i As Long
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| 317 | Dim sgn As Long
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| 318 | Dim dbl = 0 As Double
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| 319 |
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| 320 | If x > 1 Then
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| 321 | sgn = 1
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| 322 | x = 1 / x
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| 323 | ElseIf x < -1 Then
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| 324 | sgn = -1
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| 325 | x = 1 / x
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| 326 | Else
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| 327 | sgn = 0
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| 328 | End If
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| 329 |
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| 330 | For i = Detail._System_Atan_N To 1 Step -1
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| 331 | Dim t As Double
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| 332 | t = i * x
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| 333 | dbl = (t * t) / (2 * i + 1 + dbl)
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| 334 | Next
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| 335 |
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| 336 | If sgn > 0 Then
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| 337 | Atan = Detail._System_HalfPI - x / (1 + dbl)
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| 338 | ElseIf sgn < 0 Then
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| 339 | Atan = -Detail._System_HalfPI - x / (1 + dbl)
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| 340 | Else
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| 341 | Atan = x / (1 + dbl)
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| 342 | End If
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| 343 | End Function
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| 344 |
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| 345 | Function Atan2(y As Double, x As Double) As Double
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| 346 | If x = 0 Then
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| 347 | Atan2 = Sgn(y) * Detail._System_HalfPI
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| 348 | Else
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| 349 | Atan2 = Atn(y / x)
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| 350 | If x < 0 Then
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| 351 | Atan2 += CopySign(_System_PI, y)
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| 352 | End If
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| 353 | End If
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| 354 | End Function
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| 355 |
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| 356 | '----
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| 357 | '双曲線関数
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| 358 | Function Sinh(x As Double) As Double
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| 359 | If Abs(x) > Detail._System_EPS5 Then
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| 360 | Dim t As Double
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| 361 | t = Exp(x)
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| 362 | Return (t - 1 / t) * 0.5
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| 363 | Else
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| 364 | Return x * (1 + x * x * 0.166666666666667) ' x * (1 + x * x / 6)
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| 365 | End If
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| 366 | End Function
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| 367 |
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| 368 | Function Tanh(x As Double) As Double
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| 369 | If x > Detail._System_EPS5 Then
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| 370 | Return 2 / (1 + Exp(-2 * x)) - 1
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| 371 | ElseIf x < -Detail._System_EPS5 Then
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| 372 | Return 1 - 2 / (Exp(2 * x) + 1)
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| 373 | Else
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| 374 | Return x * (1 - x * x * 0.333333333333333) 'x * (1 - x * x / 3)
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| 375 | End If
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| 376 | End Function
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| 377 |
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| 378 |
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| 379 | '----
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| 380 | '浮動小数点数判定
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| 381 | Function IsNaN(ByVal x As Double) As Boolean
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| 382 | Dim p = VarPtr(x) As *DWord
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| 383 | IsNaN = False
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| 384 | If (p[1] And &H7FF00000) = &H7FF00000 Then
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| 385 | If (p[0] <> 0) Or ((p[1] And &HFFFFF) <> 0) Then
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| 386 | IsNaN = True
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| 387 | End If
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| 388 | End If
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| 389 | End Function
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| 390 |
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| 391 | Function IsInf(x As Double) As Boolean
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| 392 | Dim p = VarPtr(x) As *DWord
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| 393 | p[1] And= &h7fffffff
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| 394 | Dim inf = Detail.GetInf(False)
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| 395 | IsInf = (memcmp(p As *Byte, VarPtr(inf), SizeOf (Double)) = 0)
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| 396 | End Function
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| 397 |
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| 398 | Function IsFinite(x As Double) As Boolean
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| 399 | Dim p = VarPtr(x) As *DWord
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| 400 | p[1] And= &H7FF00000
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| 401 | IsFinite = ( p[1] And &H7FF00000 ) = &H7FF00000
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| 402 | End Function
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| 403 |
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| 404 | '----
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| 405 | 'その他
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| 406 | Function Hypot(x As Double, y As Double) As Double
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| 407 | If x = 0 Then
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| 408 | Hypot = Abs(y)
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| 409 | Else If y = 0 Then
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| 410 | Hypot = Abs(x)
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| 411 | Else
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| 412 | Dim ax = Abs(x)
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| 413 | Dim ay = Abs(y)
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| 414 | If ay > ax Then
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| 415 | Dim t = x / y
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| 416 | Hypot = ay * Sqr(1 + t * t)
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| 417 | Else
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| 418 | Dim t = y / x
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| 419 | Hypot = ax * Sqr(1 + t * t)
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| 420 | End If
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| 421 | End If
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| 422 | End Function
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| 423 |
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| 424 | Namespace Detail
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| 425 |
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| 426 | Function SetSign(x As Double, isNegative As Long) As Double
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| 427 | #ifdef _WIN64
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| 428 | SetQWord(AddressOf(CopySign), (GetQWord(VarPtr(x)) And &h7fffffffffffffff) Or (isNegative << 63))
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| 429 | #else
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| 430 | SetDWord(AddressOf(CopySign), GetDWord(VarPtr(x)))
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| 431 | SetDWord(AddressOf(CopySign) + SizeOf (DWord), GetQWord(VarPtr(x) + SizeOf (DWord)) And &h7fffffff Or (isNegative << 31))
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| 432 | #endif
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| 433 | End Function
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| 434 |
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| 435 | #ifdef _WIN64
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| 436 |
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| 437 | Function GetNaN() As Double
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| 438 | SetQWord(VarPtr(GetNaN) As *QWord, &H7FF8000000000000)
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| 439 | End Function
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| 440 |
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| 441 | Function GetInf(sign As Boolean) As Double
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| 442 | Dim s = 0 As QWord
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| 443 | If sign Then s = 1 << 63
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| 444 | SetQWord(VarPtr(GetInf) As *QWord, &h7FF0000000000000 Or s)
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| 445 | End Function
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| 446 |
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| 447 | #else
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| 448 |
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| 449 | Function GetNaN() As Double
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| 450 | Dim p = VarPtr(GetNaN) As *DWord
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| 451 | p[0] = 0
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| 452 | p[1] = &H7FF80000
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| 453 | End Function
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| 454 |
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| 455 | Function GetInf(sign As Boolean) As Double
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| 456 | Dim s = 0 As DWord
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| 457 | If sign Then s = (1 As DWord) << 31
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| 458 | Dim p = VarPtr(GetInf) As *DWord
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| 459 | p[0] = 0
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| 460 | p[1] = &h7FF00000 Or s
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| 461 | End Function
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| 462 |
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| 463 | #endif
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| 464 |
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| 465 | Function Log1p(x As Double) As Double
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| 466 | Dim s = 0 As Double
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| 467 | Dim i = _System_Log_N As Long
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| 468 | While i >= 1
|
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| 469 | Dim t = (i * x) As Double
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| 470 | s = t * (2 * i + 1 + s) / (2 + t)
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| 471 | i--
|
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| 472 | Wend
|
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| 473 | Return x / (1 + s)
|
|---|
| 474 | End Function
|
|---|
| 475 |
|
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| 476 | Function _Support_tan(x As Double, ByRef k As Long) As Double
|
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| 477 | If x >= 0 Then
|
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| 478 | k = ( Fix(x * _System_InverseHalfPI) + 0.5 ) As Long
|
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| 479 | Else
|
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| 480 | k = ( Fix(x * _System_InverseHalfPI) - 0.5 ) As Long
|
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| 481 | End If
|
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| 482 |
|
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| 483 | x = (x - (3217.0 / 2048.0) * k) + _System_D * k
|
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| 484 |
|
|---|
| 485 | Dim x2 = x * x
|
|---|
| 486 | Dim t = 0 As Double
|
|---|
| 487 |
|
|---|
| 488 | Dim i As Long
|
|---|
| 489 | For i = _System_UrTan_N To 3 Step -2
|
|---|
| 490 | t = x2 / (i - t)
|
|---|
| 491 | Next
|
|---|
| 492 |
|
|---|
| 493 | _Support_tan = x / (1 - t)
|
|---|
| 494 | End Function
|
|---|
| 495 |
|
|---|
| 496 | Const _System_D = 4.4544551033807686783083602485579e-6 As Double
|
|---|
| 497 | Const _System_UrTan_N = 19 As Long
|
|---|
| 498 | Const _System_EPS5 = 0.001 As Double
|
|---|
| 499 | Const _System_Atan_N = 20 As Long
|
|---|
| 500 | Const _System_HalfPI = (_System_PI * 0.5)
|
|---|
| 501 | Const _System_InverseHalfPI = (2 / _System_PI) '1 / (PI / 2)
|
|---|
| 502 | Const _System_InverseLn10 = 0.43429448190325182765112891891661 '1 / (ln 10)
|
|---|
| 503 | Const _System_InverseSqrt2 = 0.70710678118654752440084436210485 '1 / (√2)
|
|---|
| 504 | Const _System_LOG2 = 0.6931471805599453094172321214581765680755
|
|---|
| 505 | Const _System_Log_N = 7 As Long
|
|---|
| 506 |
|
|---|
| 507 | End Namespace 'Detail
|
|---|
| 508 | End Namespace 'Math
|
|---|
| 509 | End Namespace 'ActiveBasic
|
|---|
