[14] | 1 | ' Classes/System/Math.ab
|
---|
[1] | 2 |
|
---|
[268] | 3 | #require <Classes/ActiveBasic/Math/Math.ab>
|
---|
| 4 |
|
---|
[1] | 5 | #ifndef __SYSTEM_MATH_AB__
|
---|
| 6 | #define __SYSTEM_MATH_AB__
|
---|
| 7 |
|
---|
[268] | 8 | Namespace System
|
---|
| 9 |
|
---|
[1] | 10 | Class Math
|
---|
| 11 | Public
|
---|
| 12 | Static Function E() As Double
|
---|
| 13 | return 2.7182818284590452354
|
---|
| 14 | End Function
|
---|
| 15 |
|
---|
| 16 | Static Function PI() As Double
|
---|
| 17 | return _System_PI
|
---|
| 18 | End Function
|
---|
| 19 |
|
---|
| 20 | Static Function Abs(value As Double) As Double
|
---|
[239] | 21 | SetQWord(VarPtr(Abs), GetQWord(VarPtr(value)) And &h7fffffffffffffff)
|
---|
[1] | 22 | End Function
|
---|
| 23 |
|
---|
| 24 | Static Function Abs(value As Single) As Single
|
---|
[239] | 25 | SetDWord(VarPtr(Abs), GetDWord(VarPtr(value)) And &h7fffffff)
|
---|
[1] | 26 | End Function
|
---|
| 27 |
|
---|
[162] | 28 | Static Function Abs(value As SByte) As SByte
|
---|
[1] | 29 | If value<0 then
|
---|
| 30 | return -value
|
---|
| 31 | Else
|
---|
| 32 | return value
|
---|
| 33 | End If
|
---|
| 34 | End Function
|
---|
| 35 |
|
---|
| 36 | Static Function Abs(value As Integer) As Integer
|
---|
| 37 | If value<0 then
|
---|
| 38 | return -value
|
---|
| 39 | Else
|
---|
| 40 | return value
|
---|
| 41 | End If
|
---|
| 42 | End Function
|
---|
| 43 |
|
---|
| 44 | Static Function Abs(value As Long) As Long
|
---|
| 45 | If value<0 then
|
---|
| 46 | return -value
|
---|
| 47 | Else
|
---|
| 48 | return value
|
---|
| 49 | End If
|
---|
| 50 | End Function
|
---|
| 51 |
|
---|
| 52 | Static Function Abs(value As Int64) As Int64
|
---|
| 53 | If value<0 then
|
---|
| 54 | return -value
|
---|
| 55 | Else
|
---|
| 56 | return value
|
---|
| 57 | End If
|
---|
| 58 | End Function
|
---|
| 59 |
|
---|
| 60 | Static Function Acos(x As Double) As Double
|
---|
| 61 | If x < -1 Or x > 1 Then
|
---|
[268] | 62 | Acos = ActiveBasic.Math.Detail.GetNaN()
|
---|
[1] | 63 | Else
|
---|
[232] | 64 | Acos = _System_HalfPI - Asin(x)
|
---|
[1] | 65 | End If
|
---|
| 66 | End Function
|
---|
| 67 |
|
---|
| 68 | Static Function Asin(x As Double) As Double
|
---|
| 69 | If x < -1 Or x > 1 Then
|
---|
[268] | 70 | Asin = ActiveBasic.Math.Detail.GetNaN()
|
---|
[1] | 71 | Else
|
---|
[233] | 72 | Asin = Math.Atan(x / Sqrt(1 - x * x))
|
---|
[1] | 73 | End If
|
---|
| 74 | End Function
|
---|
| 75 |
|
---|
| 76 | Static Function Atan(x As Double) As Double
|
---|
[268] | 77 | If ActiveBasic.Math.IsNaN(x) Then
|
---|
[1] | 78 | Atan = x
|
---|
| 79 | Exit Function
|
---|
[268] | 80 | ElseIf ActiveBasic.Math.IsInf(x) Then
|
---|
| 81 | Atan = ActiveBasic.Math.CopySign(_System_PI, x)
|
---|
[1] | 82 | Exit Function
|
---|
| 83 | End If
|
---|
| 84 | Dim i As Long
|
---|
| 85 | Dim sgn As Long
|
---|
| 86 | Dim dbl = 0 As Double
|
---|
| 87 |
|
---|
| 88 | If x > 1 Then
|
---|
| 89 | sgn = 1
|
---|
| 90 | x = 1 / x
|
---|
| 91 | ElseIf x < -1 Then
|
---|
| 92 | sgn = -1
|
---|
| 93 | x = 1 / x
|
---|
| 94 | Else
|
---|
| 95 | sgn = 0
|
---|
| 96 | End If
|
---|
| 97 |
|
---|
| 98 | For i = _System_Atan_N To 1 Step -1
|
---|
| 99 | Dim t As Double
|
---|
[14] | 100 | t = i * x
|
---|
[1] | 101 | dbl = (t * t) / (2 * i + 1 + dbl)
|
---|
| 102 | Next
|
---|
| 103 |
|
---|
| 104 | If sgn > 0 Then
|
---|
| 105 | Atan = _System_HalfPI - x / (1 + dbl)
|
---|
| 106 | ElseIf sgn < 0 Then
|
---|
| 107 | Atan = -_System_HalfPI - x / (1 + dbl)
|
---|
| 108 | Else
|
---|
| 109 | Atan = x / (1 + dbl)
|
---|
| 110 | End If
|
---|
| 111 | End Function
|
---|
| 112 |
|
---|
| 113 | Static Function Atan2(y As Double, x As Double) As Double
|
---|
| 114 | If x = 0 Then
|
---|
| 115 | Atan2 = Sgn(y) * _System_HalfPI
|
---|
| 116 | Else
|
---|
| 117 | Atan2 = Atn(y / x)
|
---|
| 118 | If x < 0 Then
|
---|
[268] | 119 | Atan2 += ActiveBasic.Math.CopySign(_System_PI, y)
|
---|
[1] | 120 | End If
|
---|
| 121 | End If
|
---|
| 122 | End Function
|
---|
| 123 |
|
---|
[14] | 124 | Static Function BigMul(x As Long, y As Long) As Int64
|
---|
| 125 | Return (x As Int64) * y
|
---|
[1] | 126 | End Function
|
---|
| 127 |
|
---|
| 128 | Static Function Ceiling(x As Double) As Long
|
---|
| 129 | If Floor(x) = x then
|
---|
[233] | 130 | Return x As Long
|
---|
[1] | 131 | Else
|
---|
| 132 | Return Floor(x) + 1
|
---|
| 133 | End If
|
---|
| 134 | End Function
|
---|
| 135 |
|
---|
[14] | 136 | Static Function Cos(x As Double) As Double
|
---|
[268] | 137 | If ActiveBasic.Math.IsNaN(x) Then
|
---|
[14] | 138 | Return x
|
---|
[268] | 139 | ElseIf ActiveBasic.Math.IsInf(x) Then
|
---|
| 140 | Return ActiveBasic.Math.Detail.GetNaN()
|
---|
[1] | 141 | End If
|
---|
| 142 |
|
---|
[124] | 143 | Return Math.Sin((_System_HalfPI - Math.Abs(x)) As Double)
|
---|
[1] | 144 | End Function
|
---|
| 145 |
|
---|
| 146 | Static Function Cosh(value As Double) As Double
|
---|
| 147 | Dim t As Double
|
---|
[233] | 148 | t = Math.Exp(value)
|
---|
[1] | 149 | return (t + 1 / t) * 0.5
|
---|
| 150 | End Function
|
---|
| 151 |
|
---|
[14] | 152 | Static Function DivRem(x As Long, y As Long, ByRef ret As Long) As Long
|
---|
| 153 | ret = x Mod y
|
---|
| 154 | return x \ y
|
---|
[1] | 155 | End Function
|
---|
| 156 |
|
---|
[14] | 157 | Static Function DivRem(x As Int64, y As Int64, ByRef ret As Int64) As Int64
|
---|
| 158 | ret = x - (x \ y) * y
|
---|
| 159 | return x \ y
|
---|
[1] | 160 | End Function
|
---|
| 161 |
|
---|
| 162 | 'Equals
|
---|
| 163 |
|
---|
[14] | 164 | Static Function Exp(x As Double) As Double
|
---|
[268] | 165 | If ActiveBasic.Math.IsNaN(x) Then
|
---|
[1] | 166 | Return x
|
---|
[268] | 167 | Else If ActiveBasic.Math.IsInf(x) Then
|
---|
[1] | 168 | If 0 > x Then
|
---|
| 169 | Return 0
|
---|
| 170 | Else
|
---|
| 171 | Return x
|
---|
| 172 | End If
|
---|
| 173 | End If
|
---|
| 174 | Dim i As Long, k As Long
|
---|
| 175 | Dim x2 As Double, w As Double
|
---|
| 176 |
|
---|
| 177 | If x >= 0 Then
|
---|
[14] | 178 | k = Fix(x / _System_LOG2 + 0.5)
|
---|
[1] | 179 | Else
|
---|
[14] | 180 | k = Fix(x / _System_LOG2 - 0.5)
|
---|
[1] | 181 | End If
|
---|
| 182 |
|
---|
| 183 | x -= k * _System_LOG2
|
---|
| 184 |
|
---|
| 185 | x2 = x * x
|
---|
| 186 | w = x2 / 22
|
---|
| 187 |
|
---|
| 188 | i = 18
|
---|
| 189 | While i >= 6
|
---|
| 190 | w = x2 / (w + i)
|
---|
| 191 | i -= 4
|
---|
| 192 | Wend
|
---|
| 193 |
|
---|
| 194 | Return ldexp((2 + w + x) / (2 + w - x), k)
|
---|
| 195 | End Function
|
---|
| 196 |
|
---|
| 197 | Static Function Floor(value As Double) As Long
|
---|
[237] | 198 | Return Int(value)
|
---|
[1] | 199 | End Function
|
---|
| 200 |
|
---|
| 201 | 'GetHashCode
|
---|
| 202 |
|
---|
| 203 | 'GetType
|
---|
| 204 |
|
---|
[237] | 205 | Static Function IEEERemainder(x As Double, y As Double) As Double
|
---|
[268] | 206 | If y = 0 Then Return ActiveBasic.Math.Detail.GetNaN()
|
---|
[237] | 207 | Dim q = x / y
|
---|
| 208 | If q <> Int(q) Then
|
---|
| 209 | If q + 0.5 <> Int(q + 0.5) Then
|
---|
| 210 | q = Int(q + 0.5)
|
---|
| 211 | ElseIf Int(q + 0.5) = Int(q * 2 + 1) / 2 Then
|
---|
| 212 | q = Int(q + 0.5)
|
---|
[1] | 213 | Else
|
---|
[237] | 214 | q = Int(q - 0.5)
|
---|
[1] | 215 | End If
|
---|
| 216 | End If
|
---|
[237] | 217 | If x - y * q = 0 Then
|
---|
| 218 | If x > 0 Then
|
---|
| 219 | Return +0
|
---|
[1] | 220 | Else
|
---|
[237] | 221 | Return -0
|
---|
[1] | 222 | End If
|
---|
| 223 | Else
|
---|
[237] | 224 | Return x-y*q
|
---|
[1] | 225 | End If
|
---|
| 226 | End Function
|
---|
| 227 |
|
---|
| 228 | Static Function Log(x As Double) As Double
|
---|
| 229 | If x = 0 Then
|
---|
[268] | 230 | Log = ActiveBasic.Math.Detail.GetInf(True)
|
---|
| 231 | ElseIf x < 0 Or ActiveBasic.Math.IsNaN(x) Then
|
---|
| 232 | Log = ActiveBasic.Math.Detail.GetNaN()
|
---|
| 233 | ElseIf ActiveBasic.Math.IsInf(x) Then
|
---|
[1] | 234 | Log = x
|
---|
| 235 | Else
|
---|
[244] | 236 | Dim tmp = x * _System_InverseSqrt2
|
---|
| 237 | Dim p = VarPtr(tmp) As *QWord
|
---|
[257] | 238 | Dim m = GetQWord(p) And &h7FF0000000000000
|
---|
[244] | 239 | Dim k = ((m >> 52) As DWord) As Long - 1022
|
---|
[257] | 240 | SetQWord(p, m + &h0010000000000000)
|
---|
[244] | 241 | x /= tmp
|
---|
[268] | 242 | Log = _System_LOG2 * k + ActiveBasic.Math.Detail.Log1p(x - 1)
|
---|
[1] | 243 | End If
|
---|
| 244 | End Function
|
---|
| 245 |
|
---|
| 246 | Static Function Log10(x As Double) As Double
|
---|
[244] | 247 | Return Math.Log(x) * _System_InverseLn10
|
---|
[1] | 248 | End Function
|
---|
| 249 |
|
---|
[244] | 250 | Static Function Max(value1 As Byte, value2 As Byte) As Byte
|
---|
[1] | 251 | If value1>value2 then
|
---|
| 252 | return value1
|
---|
| 253 | Else
|
---|
| 254 | return value2
|
---|
| 255 | End If
|
---|
| 256 | End Function
|
---|
| 257 |
|
---|
[244] | 258 | Static Function Max(value1 As SByte, value2 As SByte) As SByte
|
---|
[1] | 259 | If value1>value2 then
|
---|
| 260 | return value1
|
---|
| 261 | Else
|
---|
| 262 | return value2
|
---|
| 263 | End If
|
---|
| 264 | End Function
|
---|
| 265 |
|
---|
[244] | 266 | Static Function Max(value1 As Word, value2 As Word) As Word
|
---|
[1] | 267 | If value1>value2 then
|
---|
| 268 | return value1
|
---|
| 269 | Else
|
---|
| 270 | return value2
|
---|
| 271 | End If
|
---|
| 272 | End Function
|
---|
| 273 |
|
---|
[244] | 274 | Static Function Max(value1 As Integer, value2 As Integer) As Integer
|
---|
[1] | 275 | If value1>value2 then
|
---|
| 276 | return value1
|
---|
| 277 | Else
|
---|
| 278 | return value2
|
---|
| 279 | End If
|
---|
| 280 | End Function
|
---|
| 281 |
|
---|
[244] | 282 | Static Function Max(value1 As DWord, value2 As DWord) As DWord
|
---|
[1] | 283 | If value1>value2 then
|
---|
| 284 | return value1
|
---|
| 285 | Else
|
---|
| 286 | return value2
|
---|
| 287 | End If
|
---|
| 288 | End Function
|
---|
| 289 |
|
---|
[244] | 290 | Static Function Max(value1 As Long, value2 As Long) As Long
|
---|
[1] | 291 | If value1>value2 then
|
---|
| 292 | return value1
|
---|
| 293 | Else
|
---|
| 294 | return value2
|
---|
| 295 | End If
|
---|
| 296 | End Function
|
---|
| 297 |
|
---|
[244] | 298 | Static Function Max(value1 As QWord, value2 As QWord) As QWord
|
---|
[1] | 299 | If value1>value2 then
|
---|
| 300 | return value1
|
---|
| 301 | Else
|
---|
| 302 | return value2
|
---|
| 303 | End If
|
---|
| 304 | End Function
|
---|
| 305 |
|
---|
[244] | 306 | Static Function Max(value1 As Int64, value2 As Int64) As Int64
|
---|
[1] | 307 | If value1>value2 then
|
---|
| 308 | return value1
|
---|
| 309 | Else
|
---|
| 310 | return value2
|
---|
| 311 | End If
|
---|
| 312 | End Function
|
---|
| 313 |
|
---|
[244] | 314 | Static Function Max(value1 As Single, value2 As Single) As Single
|
---|
[1] | 315 | If value1>value2 then
|
---|
| 316 | return value1
|
---|
| 317 | Else
|
---|
| 318 | return value2
|
---|
| 319 | End If
|
---|
| 320 | End Function
|
---|
| 321 |
|
---|
[244] | 322 | Static Function Max(value1 As Double, value2 As Double) As Double
|
---|
[1] | 323 | If value1>value2 then
|
---|
| 324 | return value1
|
---|
| 325 | Else
|
---|
| 326 | return value2
|
---|
| 327 | End If
|
---|
| 328 | End Function
|
---|
| 329 |
|
---|
[244] | 330 | Static Function Min(value1 As Byte, value2 As Byte) As Byte
|
---|
[1] | 331 | If value1<value2 then
|
---|
| 332 | return value1
|
---|
| 333 | Else
|
---|
| 334 | return value2
|
---|
| 335 | End If
|
---|
| 336 | End Function
|
---|
| 337 |
|
---|
[244] | 338 | Static Function Min(value1 As SByte, value2 As SByte) As SByte
|
---|
[1] | 339 | If value1<value2 then
|
---|
| 340 | return value1
|
---|
| 341 | Else
|
---|
| 342 | return value2
|
---|
| 343 | End If
|
---|
| 344 | End Function
|
---|
| 345 |
|
---|
[244] | 346 | Static Function Min(value1 As Word, value2 As Word) As Word
|
---|
[1] | 347 | If value1<value2 then
|
---|
| 348 | return value1
|
---|
| 349 | Else
|
---|
| 350 | return value2
|
---|
| 351 | End If
|
---|
| 352 | End Function
|
---|
| 353 |
|
---|
[244] | 354 | Static Function Min(value1 As Integer, value2 As Integer) As Integer
|
---|
[1] | 355 | If value1<value2 then
|
---|
| 356 | return value1
|
---|
| 357 | Else
|
---|
| 358 | return value2
|
---|
| 359 | End If
|
---|
| 360 | End Function
|
---|
| 361 |
|
---|
[244] | 362 | Static Function Min(value1 As DWord, value2 As DWord) As DWord
|
---|
[1] | 363 | If value1<value2 then
|
---|
| 364 | return value1
|
---|
| 365 | Else
|
---|
| 366 | return value2
|
---|
| 367 | End If
|
---|
| 368 | End Function
|
---|
| 369 |
|
---|
[244] | 370 | Static Function Min(value1 As Long, value2 As Long) As Long
|
---|
[1] | 371 | If value1<value2 then
|
---|
| 372 | return value1
|
---|
| 373 | Else
|
---|
| 374 | return value2
|
---|
| 375 | End If
|
---|
| 376 | End Function
|
---|
| 377 |
|
---|
[244] | 378 | Static Function Min(value1 As QWord, value2 As QWord) As QWord
|
---|
[1] | 379 | If value1<value2 then
|
---|
| 380 | return value1
|
---|
| 381 | Else
|
---|
| 382 | return value2
|
---|
| 383 | End If
|
---|
| 384 | End Function
|
---|
| 385 |
|
---|
[244] | 386 | Static Function Min(value1 As Int64, value2 As Int64) As Int64
|
---|
[1] | 387 | If value1<value2 then
|
---|
| 388 | return value1
|
---|
| 389 | Else
|
---|
| 390 | return value2
|
---|
| 391 | End If
|
---|
| 392 | End Function
|
---|
| 393 |
|
---|
[244] | 394 | Static Function Min(value1 As Single, value2 As Single) As Single
|
---|
[1] | 395 | If value1<value2 then
|
---|
| 396 | return value1
|
---|
| 397 | Else
|
---|
| 398 | return value2
|
---|
| 399 | End If
|
---|
| 400 | End Function
|
---|
| 401 |
|
---|
[244] | 402 | Static Function Min(value1 As Double, value2 As Double) As Double
|
---|
[1] | 403 | If value1<value2 then
|
---|
| 404 | return value1
|
---|
| 405 | Else
|
---|
| 406 | return value2
|
---|
| 407 | End If
|
---|
| 408 | End Function
|
---|
| 409 |
|
---|
[14] | 410 | Static Function Pow(x As Double, y As Double) As Double
|
---|
| 411 | return pow(x, y)
|
---|
[1] | 412 | End Function
|
---|
| 413 |
|
---|
| 414 | 'ReferenceEquals
|
---|
| 415 |
|
---|
| 416 | Static Function Round(value As Double) As Double'他のバージョン、誰か頼む。
|
---|
| 417 | If value+0.5<>Int(value+0.5) then
|
---|
| 418 | value=Int(value+0.5)
|
---|
| 419 | ElseIf Int(value+0.5)=Int(value*2+1)/2 then
|
---|
| 420 | value=Int(value+0.5)
|
---|
| 421 | Else
|
---|
| 422 | value=Int(value-0.5)
|
---|
| 423 | End If
|
---|
| 424 | End Function
|
---|
| 425 |
|
---|
| 426 | Static Function Sign(value As Double) As Long
|
---|
| 427 | If value = 0 then
|
---|
| 428 | return 0
|
---|
| 429 | ElseIf value > 0 then
|
---|
| 430 | return 1
|
---|
| 431 | Else
|
---|
| 432 | return -1
|
---|
| 433 | End If
|
---|
| 434 | End Function
|
---|
| 435 |
|
---|
[162] | 436 | Static Function Sign(value As SByte) As Long
|
---|
[1] | 437 | If value = 0 then
|
---|
| 438 | return 0
|
---|
| 439 | ElseIf value > 0 then
|
---|
| 440 | return 1
|
---|
| 441 | Else
|
---|
| 442 | return -1
|
---|
| 443 | End If
|
---|
| 444 | End Function
|
---|
| 445 |
|
---|
| 446 | Static Function Sign(value As Integer) As Long
|
---|
| 447 | If value = 0 then
|
---|
| 448 | return 0
|
---|
| 449 | ElseIf value > 0 then
|
---|
| 450 | return 1
|
---|
| 451 | Else
|
---|
| 452 | return -1
|
---|
| 453 | End If
|
---|
| 454 | End Function
|
---|
| 455 |
|
---|
| 456 | Static Function Sign(value As Long) As Long
|
---|
| 457 | If value = 0 then
|
---|
| 458 | return 0
|
---|
| 459 | ElseIf value > 0 then
|
---|
| 460 | return 1
|
---|
| 461 | Else
|
---|
| 462 | return -1
|
---|
| 463 | End If
|
---|
| 464 | End Function
|
---|
| 465 |
|
---|
| 466 | Static Function Sign(value As Int64) As Long
|
---|
| 467 | If value = 0 then
|
---|
| 468 | return 0
|
---|
| 469 | ElseIf value > 0 then
|
---|
| 470 | return 1
|
---|
| 471 | Else
|
---|
| 472 | return -1
|
---|
| 473 | End If
|
---|
| 474 | End Function
|
---|
| 475 |
|
---|
| 476 | Static Function Sign(value As Single) As Long
|
---|
| 477 | If value = 0 then
|
---|
| 478 | return 0
|
---|
| 479 | ElseIf value > 0 then
|
---|
| 480 | return 1
|
---|
| 481 | Else
|
---|
| 482 | return -1
|
---|
| 483 | End If
|
---|
| 484 | End Function
|
---|
| 485 |
|
---|
| 486 | Static Function Sin(value As Double) As Double
|
---|
[268] | 487 | If ActiveBasic.Math.IsNaN(value) Then
|
---|
[53] | 488 | Return value
|
---|
[268] | 489 | ElseIf ActiveBasic.Math.IsInf(value) Then
|
---|
| 490 | Return ActiveBasic.Math.Detail.GetNaN()
|
---|
[1] | 491 | Exit Function
|
---|
| 492 | End If
|
---|
| 493 |
|
---|
[53] | 494 | Dim k As Long
|
---|
[1] | 495 | Dim t As Double
|
---|
| 496 |
|
---|
[92] | 497 | t = urTan((value * 0.5) As Double, k)
|
---|
[1] | 498 | t = 2 * t / (1 + t * t)
|
---|
| 499 | If (k And 1) = 0 Then 'k mod 2 = 0 Then
|
---|
| 500 | Return t
|
---|
| 501 | Else
|
---|
| 502 | Return -t
|
---|
| 503 | End If
|
---|
| 504 | End Function
|
---|
| 505 |
|
---|
| 506 | Static Function Sinh(x As Double) As Double
|
---|
[124] | 507 | If Math.Abs(x) > _System_EPS5 Then
|
---|
[1] | 508 | Dim t As Double
|
---|
[233] | 509 | t = Math.Exp(x)
|
---|
[1] | 510 | Return (t - 1 / t) * 0.5
|
---|
| 511 | Else
|
---|
| 512 | Return x * (1 + x * x * 0.166666666666667) ' x * (1 + x * x / 6)
|
---|
| 513 | End If
|
---|
| 514 | End Function
|
---|
| 515 |
|
---|
| 516 | Static Function Sqrt(x As Double) As Double
|
---|
| 517 | Dim s As Double, last As Double
|
---|
| 518 | Dim i As *Word, j As Long, jj As Long, k As Long
|
---|
[14] | 519 | If x > 0 Then
|
---|
[268] | 520 | If ActiveBasic.Math.IsInf(x) Then
|
---|
[1] | 521 | Sqrt = x
|
---|
| 522 | Else
|
---|
| 523 | Sqrt = x
|
---|
| 524 | i = (VarPtr(Sqrt) + 6) As *Word
|
---|
| 525 | jj = GetWord(i)
|
---|
| 526 | j = jj >> 5
|
---|
| 527 | k = jj And &h0000001f
|
---|
| 528 | j = (j+ 511) << 4 + k
|
---|
| 529 | SetWord(i, j)
|
---|
| 530 | Do
|
---|
| 531 | last = Sqrt
|
---|
| 532 | Sqrt = (x /Sqrt + Sqrt) * 0.5
|
---|
[23] | 533 | Loop While Sqrt <> last
|
---|
[1] | 534 | End If
|
---|
[14] | 535 | ElseIf x < 0 Then
|
---|
[268] | 536 | Sqrt = ActiveBasic.Math.Detail.GetNaN()
|
---|
[1] | 537 | Else
|
---|
| 538 | 'x = 0 Or NaN
|
---|
| 539 | Sqrt = x
|
---|
| 540 | End If
|
---|
| 541 | End Function
|
---|
| 542 |
|
---|
[14] | 543 | Static Function Tan(x As Double) As Double
|
---|
[268] | 544 | If ActiveBasic.Math.IsNaN(x) Then
|
---|
[14] | 545 | Tan = x
|
---|
[1] | 546 | Exit Function
|
---|
[268] | 547 | ElseIf ActiveBasic.Math.IsInf(x) Then
|
---|
| 548 | Tan = ActiveBasic.Math.Detail.GetNaN()
|
---|
[1] | 549 | Exit Function
|
---|
| 550 | End If
|
---|
| 551 |
|
---|
| 552 | Dim k As Long
|
---|
| 553 | Dim t As Double
|
---|
| 554 | t = urTan(x, k)
|
---|
| 555 | If (k And 1) = 0 Then 'k mod 2 = 0 Then
|
---|
| 556 | Return t
|
---|
| 557 | ElseIf t <> 0 Then
|
---|
| 558 | Return -1 / t
|
---|
| 559 | Else
|
---|
[268] | 560 | Return ActiveBasic.Math.CopySign(ActiveBasic.Math.Detail.GetInf(False), -t)
|
---|
[1] | 561 | End If
|
---|
| 562 | End Function
|
---|
| 563 |
|
---|
| 564 | Static Function Tanh(x As Double) As Double
|
---|
| 565 | If x > _System_EPS5 Then
|
---|
[233] | 566 | Return 2 / (1 + Math.Exp(-2 * x)) - 1
|
---|
[1] | 567 | ElseIf x < -_System_EPS5 Then
|
---|
[233] | 568 | Return 1 - 2 / (Math.Exp(2 * x) + 1)
|
---|
[1] | 569 | Else
|
---|
| 570 | Return x * (1 - x * x * 0.333333333333333) 'x * (1 - x * x / 3)
|
---|
| 571 | End If
|
---|
| 572 | End Function
|
---|
| 573 |
|
---|
[92] | 574 | 'ToString
|
---|
| 575 |
|
---|
[1] | 576 | Static Function Truncate(x As Double) As Double
|
---|
[237] | 577 | Return Fix(x)
|
---|
[1] | 578 | End Function
|
---|
| 579 |
|
---|
[92] | 580 | 'Private
|
---|
[1] | 581 | Static Function urTan(x As Double, ByRef k As Long) As Double
|
---|
| 582 | Dim i As Long
|
---|
| 583 | Dim t As Double, x2 As Double
|
---|
| 584 |
|
---|
| 585 | If x >= 0 Then
|
---|
[233] | 586 | k = ( Fix(x * _System_InverseHalfPI) + 0.5 ) As Long
|
---|
[1] | 587 | Else
|
---|
[233] | 588 | k = ( Fix(x * _System_InverseHalfPI) - 0.5 ) As Long
|
---|
[1] | 589 | End If
|
---|
| 590 | x = (x - (3217.0 / 2048.0) * k) + _System_D * k
|
---|
| 591 | x2 = x * x
|
---|
| 592 | t = 0
|
---|
| 593 | For i = _System_UrTan_N To 3 Step -2
|
---|
| 594 | t = x2 / (i - t)
|
---|
| 595 | Next i
|
---|
| 596 | urTan = x / (1 - t)
|
---|
| 597 | End Function
|
---|
[238] | 598 | Private
|
---|
| 599 | Static Const _System_Atan_N = 20 As Long
|
---|
| 600 | Static Const _System_UrTan_N = 17 As Long
|
---|
| 601 | Static Const _System_D = 4.4544551033807686783083602485579e-6 As Double
|
---|
| 602 | Static Const _System_EPS5 = 0.001 As Double
|
---|
[1] | 603 | End Class
|
---|
| 604 |
|
---|
[268] | 605 | End Namespace
|
---|
| 606 |
|
---|
[1] | 607 | Const _System_HalfPI = (_System_PI * 0.5)
|
---|
| 608 | Const _System_InverseHalfPI = (2 / _System_PI) '1 / (PI / 2)
|
---|
[244] | 609 | Const _System_InverseLn10 = 0.43429448190325182765112891891661 '1 / (ln 10)
|
---|
| 610 | Const _System_InverseSqrt2 = 0.70710678118654752440084436210485 '1 / (√2)
|
---|
[1] | 611 |
|
---|
[20] | 612 | #endif '__SYSTEM_MATH_AB__
|
---|