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