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'************************************************************************
'Cephes Math Library Release 2.8: June, 2000
'Copyright by Stephen L. Moshier
'
'Contributors:
' * Sergey Bochkanov (ALGLIB project). Translation from C to
' pseudocode.
'
'See subroutines comments for additional copyrights.
'
'Redistribution and use in source and binary forms, with or without
'modification, are permitted provided that the following conditions are
'met:
'
'- Redistributions of source code must retain the above copyright
' notice, this list of conditions and the following disclaimer.
'
'- Redistributions in binary form must reproduce the above copyright
' notice, this list of conditions and the following disclaimer listed
' in this license in the documentation and/or other materials
' provided with the distribution.
'
'- Neither the name of the copyright holders nor the names of its
' contributors may be used to endorse or promote products derived from
' this software without specific prior written permission.
'
'THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
'"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
'LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
'A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
'OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
'SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
'LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
'DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
'THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
'(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
'OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
'************************************************************************
Imports System
Namespace MathEx.GammaFunctions
Public Class igammaf
'************************************************************************
' Incomplete gamma integral
'
' The function is defined by
'
' x
' -
' 1 | | -t a-1
' igam(a,x) = ----- | e t dt.
' - | |
' | (a) -
' 0
'
'
' In this implementation both arguments must be positive.
' The integral is evaluated by either a power series or
' continued fraction expansion, depending on the relative
' values of a and x.
'
' ACCURACY:
'
' Relative error:
' arithmetic domain # trials peak rms
' IEEE 0,30 200000 3.6e-14 2.9e-15
' IEEE 0,100 300000 9.9e-14 1.5e-14
'
' Cephes Math Library Release 2.8: June, 2000
' Copyright 1985, 1987, 2000 by Stephen L. Moshier
' ************************************************************************
Public Shared Function incompletegamma(ByVal a As Double, ByVal x As Double) As Double
Dim result As Double = 0
Dim igammaepsilon As Double = 0
Dim ans As Double = 0
Dim ax As Double = 0
Dim c As Double = 0
Dim r As Double = 0
Dim tmp As Double = 0
igammaepsilon = 0.000000000000001R
If x <= 0 Or a <= 0 Then
result = 0
Return result
End If
If x > 1 And x > a Then
result = 1 - incompletegammac(a, x)
Return result
End If
ax = a * Math.Log(x) - x - gammaf.lngamma(a, tmp)
If ax < -709.782712893384R Then
result = 0
Return result
End If
ax = Math.Exp(ax)
r = a
c = 1
ans = 1
Do
r = r + 1
c = c * x / r
ans = ans + c
Loop While c / ans > igammaepsilon
result = ans * ax / a
Return result
End Function
'************************************************************************
' Complemented incomplete gamma integral
'
' The function is defined by
'
'
' igamc(a,x) = 1 - igam(a,x)
'
' inf.
' -
' 1 | | -t a-1
' = ----- | e t dt.
' - | |
' | (a) -
' x
'
'
' In this implementation both arguments must be positive.
' The integral is evaluated by either a power series or
' continued fraction expansion, depending on the relative
' values of a and x.
'
' ACCURACY:
'
' Tested at random a, x.
' a x Relative error:
' arithmetic domain domain # trials peak rms
' IEEE 0.5,100 0,100 200000 1.9e-14 1.7e-15
' IEEE 0.01,0.5 0,100 200000 1.4e-13 1.6e-15
'
' Cephes Math Library Release 2.8: June, 2000
' Copyright 1985, 1987, 2000 by Stephen L. Moshier
' ************************************************************************
Public Shared Function incompletegammac(ByVal a As Double, ByVal x As Double) As Double
Dim result As Double = 0
Dim igammaepsilon As Double = 0
Dim igammabignumber As Double = 0
Dim igammabignumberinv As Double = 0
Dim ans As Double = 0
Dim ax As Double = 0
Dim c As Double = 0
Dim yc As Double = 0
Dim r As Double = 0
Dim t As Double = 0
Dim y As Double = 0
Dim z As Double = 0
Dim pk As Double = 0
Dim pkm1 As Double = 0
Dim pkm2 As Double = 0
Dim qk As Double = 0
Dim qkm1 As Double = 0
Dim qkm2 As Double = 0
Dim tmp As Double = 0
igammaepsilon = 0.000000000000001R
igammabignumber = 4.5035996273705E+15
igammabignumberinv = 2.22044604925031R * 0.0000000000000001R
If x <= 0 Or a <= 0 Then
result = 1
Return result
End If
If x < 1 Or x < a Then
result = 1 - incompletegamma(a, x)
Return result
End If
ax = a * Math.Log(x) - x - gammaf.lngamma(a, tmp)
If ax < -709.782712893384R Then
result = 0
Return result
End If
ax = Math.Exp(ax)
y = 1 - a
z = x + y + 1
c = 0
pkm2 = 1
qkm2 = x
pkm1 = x + 1
qkm1 = z * x
ans = pkm1 / qkm1
Do
c = c + 1
y = y + 1
z = z + 2
yc = y * c
pk = pkm1 * z - pkm2 * yc
qk = qkm1 * z - qkm2 * yc
If qk <> 0 Then
r = pk / qk
t = Math.Abs((ans - r) / r)
ans = r
Else
t = 1
End If
pkm2 = pkm1
pkm1 = pk
qkm2 = qkm1
qkm1 = qk
If Math.Abs(pk) > igammabignumber Then
pkm2 = pkm2 * igammabignumberinv
pkm1 = pkm1 * igammabignumberinv
qkm2 = qkm2 * igammabignumberinv
qkm1 = qkm1 * igammabignumberinv
End If
Loop While t > igammaepsilon
result = ans * ax
Return result
End Function
'************************************************************************
' Inverse of complemented imcomplete gamma integral
'
' Given p, the function finds x such that
'
' igamc( a, x ) = p.
'
' Starting with the approximate value
'
' 3
' x = a t
'
' where
'
' t = 1 - d - ndtri(p) sqrt(d)
'
' and
'
' d = 1/9a,
'
' the routine performs up to 10 Newton iterations to find the
' root of igamc(a,x) - p = 0.
'
' ACCURACY:
'
' Tested at random a, p in the intervals indicated.
'
' a p Relative error:
' arithmetic domain domain # trials peak rms
' IEEE 0.5,100 0,0.5 100000 1.0e-14 1.7e-15
' IEEE 0.01,0.5 0,0.5 100000 9.0e-14 3.4e-15
' IEEE 0.5,10000 0,0.5 20000 2.3e-13 3.8e-14
'
' Cephes Math Library Release 2.8: June, 2000
' Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
' ************************************************************************
Public Shared Function invincompletegammac(ByVal a As Double, ByVal y0 As Double) As Double
Dim result As Double = 0
Dim igammaepsilon As Double = 0
Dim iinvgammabignumber As Double = 0
Dim x0 As Double = 0
Dim x1 As Double = 0
Dim x As Double = 0
Dim yl As Double = 0
Dim yh As Double = 0
Dim y As Double = 0
Dim d As Double = 0
Dim lgm As Double = 0
Dim dithresh As Double = 0
Dim i As Integer = 0
Dim dir As Integer = 0
Dim tmp As Double = 0
igammaepsilon = 0.000000000000001R
iinvgammabignumber = 4.5035996273705E+15
x0 = iinvgammabignumber
yl = 0
x1 = 0
yh = 1
dithresh = 5 * igammaepsilon
d = 1 / (9 * a)
y = 1 - d - normaldistr.invnormaldistribution(y0) * Math.Sqrt(d)
x = a * y * y * y
lgm = gammaf.lngamma(a, tmp)
i = 0
While i < 10
If x > x0 Or x < x1 Then
d = 0.0625
Exit While
End If
y = incompletegammac(a, x)
If y < yl Or y > yh Then
d = 0.0625
Exit While
End If
If y < y0 Then
x0 = x
yl = y
Else
x1 = x
yh = y
End If
d = (a - 1) * Math.Log(x) - x - lgm
If d < -709.782712893384R Then
d = 0.0625
Exit While
End If
d = -Math.Exp(d)
d = (y - y0) / d
If Math.Abs(d / x) < igammaepsilon Then
result = x
Return result
End If
x = x - d
i = i + 1
End While
If x0 = iinvgammabignumber Then
If x <= 0 Then
x = 1
End If
While x0 = iinvgammabignumber
x = (1 + d) * x
y = incompletegammac(a, x)
If y < y0 Then
x0 = x
yl = y
Exit While
End If
d = d + d
End While
End If
d = 0.5
dir = 0
i = 0
While i < 400
x = x1 + d * (x0 - x1)
y = incompletegammac(a, x)
lgm = (x0 - x1) / (x1 + x0)
If Math.Abs(lgm) < dithresh Then
Exit While
End If
lgm = (y - y0) / y0
If Math.Abs(lgm) < dithresh Then
Exit While
End If
If x <= 0.0R Then
Exit While
End If
If y >= y0 Then
x1 = x
yh = y
If dir < 0 Then
dir = 0
d = 0.5
Else
If dir > 1 Then
d = 0.5 * d + 0.5
Else
d = (y0 - yl) / (yh - yl)
End If
End If
dir = dir + 1
Else
x0 = x
yl = y
If dir > 0 Then
dir = 0
d = 0.5
Else
If dir < -1 Then
d = 0.5 * d
Else
d = (y0 - yl) / (yh - yl)
End If
End If
dir = dir - 1
End If
i = i + 1
End While
result = x
Return result
End Function
End Class
Public Class gammaf
'************************************************************************
' Gamma function
'
' Input parameters:
' X - argument
'
' Domain:
' 0 < X < 171.6
' -170 < X < 0, X is not an integer.
'
' Relative error:
' arithmetic domain # trials peak rms
' IEEE -170,-33 20000 2.3e-15 3.3e-16
' IEEE -33, 33 20000 9.4e-16 2.2e-16
' IEEE 33, 171.6 20000 2.3e-15 3.2e-16
'
' Cephes Math Library Release 2.8: June, 2000
' Original copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
' Translated to AlgoPascal by Bochkanov Sergey (2005, 2006, 2007).
' ************************************************************************
Public Shared Function gamma(ByVal x As Double) As Double
Dim result As Double = 0
Dim p As Double = 0
Dim pp As Double = 0
Dim q As Double = 0
Dim qq As Double = 0
Dim z As Double = 0
Dim i As Integer = 0
Dim sgngam As Double = 0
sgngam = 1
q = Math.Abs(x)
If q > 33.0R Then
If x < 0.0R Then
p = Convert.ToInt32(Math.Floor(q))
i = Convert.ToInt32(Math.Round(p))
If i Mod 2 = 0 Then
sgngam = -1
End If
z = q - p
If z > 0.5 Then
p = p + 1
z = q - p
End If
z = q * Math.Sin(Math.PI * z)
z = Math.Abs(z)
z = Math.PI / (z * gammastirf(q))
Else
z = gammastirf(x)
End If
result = sgngam * z
Return result
End If
z = 1
While x >= 3
x = x - 1
z = z * x
End While
While x < 0
If x > -0.000000001R Then
result = z / ((1 + 0.577215664901533R * x) * x)
Return result
End If
z = z / x
x = x + 1
End While
While x < 2
If x < 0.000000001R Then
result = z / ((1 + 0.577215664901533R * x) * x)
Return result
End If
z = z / x
x = x + 1.0R
End While
If x = 2 Then
result = z
Return result
End If
x = x - 2.0R
pp = 0.000160119522476752R
pp = 0.00119135147006586R + x * pp
pp = 0.0104213797561762R + x * pp
pp = 0.0476367800457137R + x * pp
pp = 0.207448227648436R + x * pp
pp = 0.494214826801497R + x * pp
pp = 1.0R + x * pp
qq = -0.000023158187332412R
qq = 0.000539605580493303R + x * qq
qq = -0.00445641913851797R + x * qq
qq = 0.011813978522206R + x * qq
qq = 0.0358236398605499R + x * qq
qq = -0.234591795718243R + x * qq
qq = 0.0714304917030273R + x * qq
qq = 1.0R + x * qq
result = z * pp / qq
Return result
Return result
End Function
'************************************************************************
' Natural logarithm of gamma function
'
' Input parameters:
' X - argument
'
' Result:
' logarithm of the absolute value of the Gamma(X).
'
' Output parameters:
' SgnGam - sign(Gamma(X))
'
' Domain:
' 0 < X < 2.55e305
' -2.55e305 < X < 0, X is not an integer.
'
' ACCURACY:
' arithmetic domain # trials peak rms
' IEEE 0, 3 28000 5.4e-16 1.1e-16
' IEEE 2.718, 2.556e305 40000 3.5e-16 8.3e-17
' The error criterion was relative when the function magnitude
' was greater than one but absolute when it was less than one.
'
' The following test used the relative error criterion, though
' at certain points the relative error could be much higher than
' indicated.
' IEEE -200, -4 10000 4.8e-16 1.3e-16
'
' Cephes Math Library Release 2.8: June, 2000
' Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
' Translated to AlgoPascal by Bochkanov Sergey (2005, 2006, 2007).
' ************************************************************************
Public Shared Function lngamma(ByVal x As Double, ByRef sgngam As Double) As Double
Dim result As Double = 0
Dim a As Double = 0
Dim b As Double = 0
Dim c As Double = 0
Dim p As Double = 0
Dim q As Double = 0
Dim u As Double = 0
Dim w As Double = 0
Dim z As Double = 0
Dim i As Integer = 0
Dim logpi As Double = 0
Dim ls2pi As Double = 0
Dim tmp As Double = 0
sgngam = 1
logpi = 1.1447298858494R
ls2pi = 0.918938533204673R
If x < -34.0R Then
q = -x
w = lngamma(q, tmp)
p = Convert.ToInt32(Math.Floor(q))
i = Convert.ToInt32(Math.Round(p))
If i Mod 2 = 0 Then
sgngam = -1
Else
sgngam = 1
End If
z = q - p
If z > 0.5 Then
p = p + 1
z = p - q
End If
z = q * Math.Sin(Math.PI * z)
result = logpi - Math.Log(z) - w
Return result
End If
If x < 13 Then
z = 1
p = 0
u = x
While u >= 3
p = p - 1
u = x + p
z = z * u
End While
While u < 2
z = z / u
p = p + 1
u = x + p
End While
If z < 0 Then
sgngam = -1
z = -z
Else
sgngam = 1
End If
If u = 2 Then
result = Math.Log(z)
Return result
End If
p = p - 2
x = x + p
b = -1378.25152569121R
b = -38801.6315134638R + x * b
b = -331612.992738871R + x * b
b = -1162370.97492762R + x * b
b = -1721737.0082084R + x * b
b = -853555.664245765R + x * b
c = 1
c = -351.815701436523R + x * c
c = -17064.2106651881R + x * c
c = -220528.590553854R + x * c
c = -1139334.44367983R + x * c
c = -2532523.07177583R + x * c
c = -2018891.41433533R + x * c
p = x * b / c
result = Math.Log(z) + p
Return result
End If
q = (x - 0.5) * Math.Log(x) - x + ls2pi
If x > 100000000 Then
result = q
Return result
End If
p = 1 / (x * x)
If x >= 1000.0R Then
q = q + ((7.93650793650794R * 0.0001 * p - 2.77777777777778R * 0.001) * p + 0.0833333333333333R) / x
Else
a = 8.11614167470508R * 0.0001
a = -(5.95061904284301R * 0.0001) + p * a
a = 7.93650340457717R * 0.0001 + p * a
a = -(2.777777777301R * 0.001) + p * a
a = 8.33333333333332R * 0.01 + p * a
q = q + a / x
End If
result = q
Return result
End Function
Private Shared Function gammastirf(ByVal x As Double) As Double
Dim result As Double = 0
Dim y As Double = 0
Dim w As Double = 0
Dim v As Double = 0
Dim stir As Double = 0
w = 1 / x
stir = 0.000787311395793094R
stir = -0.000229549961613378R + w * stir
stir = -0.00268132617805781R + w * stir
stir = 0.00347222221605459R + w * stir
stir = 0.0833333333333482R + w * stir
w = 1 + w * stir
y = Math.Exp(x)
If x > 143.01608 Then
v = Math.Pow(x, 0.5 * x - 0.25)
y = v * (v / y)
Else
y = Math.Pow(x, x - 0.5) / y
End If
result = 2.506628274631R * y * w
Return result
End Function
End Class
Class normaldistr
'************************************************************************
' Error function
'
' The integral is
'
' x
' -
' 2 | | 2
' erf(x) = -------- | exp( - t ) dt.
' sqrt(pi) | |
' -
' 0
'
' For 0 <= |x| < 1, erf(x) = x * P4(x**2)/Q5(x**2); otherwise
' erf(x) = 1 - erfc(x).
'
'
' ACCURACY:
'
' Relative error:
' arithmetic domain # trials peak rms
' IEEE 0,1 30000 3.7e-16 1.0e-16
'
' Cephes Math Library Release 2.8: June, 2000
' Copyright 1984, 1987, 1988, 1992, 2000 by Stephen L. Moshier
' ************************************************************************
Public Shared Function erf(ByVal x As Double) As Double
Dim result As Double = 0
Dim xsq As Double = 0
Dim s As Double = 0
Dim p As Double = 0
Dim q As Double = 0
s = Math.Sign(x)
x = Math.Abs(x)
If x < 0.5 Then
xsq = x * x
p = 0.00754772803341863R
p = 0.288805137207594R + xsq * p
p = 14.3383842191748R + xsq * p
p = 38.0140318123903R + xsq * p
p = 3017.82788536508R + xsq * p
p = 7404.07142710151R + xsq * p
p = 80437.363096084R + xsq * p
q = 0.0R
q = 1.0R + xsq * q
q = 38.0190713951939R + xsq * q
q = 658.07015545924R + xsq * q
q = 6379.60017324428R + xsq * q
q = 34216.5257924629R + xsq * q
q = 80437.363096084R + xsq * q
result = s * 1.12837916709551R * x * p / q
Return result
End If
If x >= 10 Then
result = s
Return result
End If
result = s * (1 - erfc(x))
Return result
End Function
'************************************************************************
' Complementary error function
'
' 1 - erf(x) =
'
' inf.
' -
' 2 | | 2
' erfc(x) = -------- | exp( - t ) dt
' sqrt(pi) | |
' -
' x
'
'
' For small x, erfc(x) = 1 - erf(x); otherwise rational
' approximations are computed.
'
'
' ACCURACY:
'
' Relative error:
' arithmetic domain # trials peak rms
' IEEE 0,26.6417 30000 5.7e-14 1.5e-14
'
' Cephes Math Library Release 2.8: June, 2000
' Copyright 1984, 1987, 1988, 1992, 2000 by Stephen L. Moshier
' ************************************************************************
Public Shared Function erfc(ByVal x As Double) As Double
Dim result As Double = 0
Dim p As Double = 0
Dim q As Double = 0
If x < 0 Then
result = 2 - erfc(-x)
Return result
End If
If x < 0.5 Then
result = 1.0R - erf(x)
Return result
End If
If x >= 10 Then
result = 0
Return result
End If
p = 0.0R
p = 0.56418778255074R + x * p
p = 9.67580788298727R + x * p
p = 77.0816173036843R + x * p
p = 368.519615471001R + x * p
p = 1143.26207070389R + x * p
p = 2320.43959025164R + x * p
p = 2898.02932921677R + x * p
p = 1826.33488422951R + x * p
q = 1.0R
q = 17.1498094362761R + x * q
q = 137.125596050062R + x * q
q = 661.736120710765R + x * q
q = 2094.38436778954R + x * q
q = 4429.61280388368R + x * q
q = 6089.54242327244R + x * q
q = 4958.82756472114R + x * q
q = 1826.33488422951R + x * q
result = Math.Exp(-AP.MathEx.Sqr(x)) * p / q
Return result
End Function
'************************************************************************
' Normal distribution function
'
' Returns the area under the Gaussian probability density
' function, integrated from minus infinity to x:
'
' x
' -
' 1 | | 2
' ndtr(x) = --------- | exp( - t /2 ) dt
' sqrt(2pi) | |
' -
' -inf.
'
' = ( 1 + erf(z) ) / 2
' = erfc(z) / 2
'
' where z = x/sqrt(2). Computation is via the functions
' erf and erfc.
'
'
' ACCURACY:
'
' Relative error:
' arithmetic domain # trials peak rms
' IEEE -13,0 30000 3.4e-14 6.7e-15
'
' Cephes Math Library Release 2.8: June, 2000
' Copyright 1984, 1987, 1988, 1992, 2000 by Stephen L. Moshier
' ************************************************************************
Public Shared Function normaldistribution(ByVal x As Double) As Double
Dim result As Double = 0
result = 0.5 * (erf(x / 1.4142135623731R) + 1)
Return result
End Function
'************************************************************************
' Inverse of the error function
'
' Cephes Math Library Release 2.8: June, 2000
' Copyright 1984, 1987, 1988, 1992, 2000 by Stephen L. Moshier
' ************************************************************************
Public Shared Function inverf(ByVal e As Double) As Double
Dim result As Double = 0
result = invnormaldistribution(0.5 * (e + 1)) / Math.Sqrt(2)
Return result
End Function
'************************************************************************
' Inverse of Normal distribution function
'
' Returns the argument, x, for which the area under the
' Gaussian probability density function (integrated from
' minus infinity to x) is equal to y.
'
'
' For small arguments 0 < y < exp(-2), the program computes
' z = sqrt( -2.0 * log(y) ); then the approximation is
' x = z - log(z)/z - (1/z) P(1/z) / Q(1/z).
' There are two rational functions P/Q, one for 0 < y < exp(-32)
' and the other for y up to exp(-2). For larger arguments,
' w = y - 0.5, and x/sqrt(2pi) = w + w**3 R(w**2)/S(w**2)).
'
' ACCURACY:
'
' Relative error:
' arithmetic domain # trials peak rms
' IEEE 0.125, 1 20000 7.2e-16 1.3e-16
' IEEE 3e-308, 0.135 50000 4.6e-16 9.8e-17
'
' Cephes Math Library Release 2.8: June, 2000
' Copyright 1984, 1987, 1988, 1992, 2000 by Stephen L. Moshier
' ************************************************************************
Public Shared Function invnormaldistribution(ByVal y0 As Double) As Double
Dim result As Double = 0
Dim expm2 As Double = 0
Dim s2pi As Double = 0
Dim x As Double = 0
Dim y As Double = 0
Dim z As Double = 0
Dim y2 As Double = 0
Dim x0 As Double = 0
Dim x1 As Double = 0
Dim code As Integer = 0
Dim p0 As Double = 0
Dim q0 As Double = 0
Dim p1 As Double = 0
Dim q1 As Double = 0
Dim p2 As Double = 0
Dim q2 As Double = 0
expm2 = 0.135335283236613R
s2pi = 2.506628274631R
If y0 <= 0 Then
result = -AP.MathEx.MaxRealNumber
Return result
End If
If y0 >= 1 Then
result = AP.MathEx.MaxRealNumber
Return result
End If
code = 1
y = y0
If y > 1.0R - expm2 Then
y = 1.0R - y
code = 0
End If
If y > expm2 Then
y = y - 0.5
y2 = y * y
p0 = -59.9633501014108R
p0 = 98.0010754186R + y2 * p0
p0 = -56.676285746907R + y2 * p0
p0 = 13.931260938728R + y2 * p0
p0 = -1.23916583867381R + y2 * p0
q0 = 1
q0 = 1.95448858338142R + y2 * q0
q0 = 4.67627912898882R + y2 * q0
q0 = 86.3602421390891R + y2 * q0
q0 = -225.462687854119R + y2 * q0
q0 = 200.260212380061R + y2 * q0
q0 = -82.0372256168333R + y2 * q0
q0 = 15.9056225126212R + y2 * q0
q0 = -1.1833162112133R + y2 * q0
x = y + y * y2 * p0 / q0
x = x * s2pi
result = x
Return result
End If
x = Math.Sqrt(-(2.0R * Math.Log(y)))
x0 = x - Math.Log(x) / x
z = 1.0R / x
If x < 8.0R Then
p1 = 4.05544892305962R
p1 = 31.5251094599894R + z * p1
p1 = 57.1628192246421R + z * p1
p1 = 44.0805073893201R + z * p1
p1 = 14.6849561928858R + z * p1
p1 = 2.1866330685079R + z * p1
p1 = -(1.40256079171355R * 0.1) + z * p1
p1 = -(3.50424626827848R * 0.01) + z * p1
p1 = -(8.57456785154685R * 0.0001) + z * p1
q1 = 1
q1 = 15.7799883256467R + z * q1
q1 = 45.3907635128879R + z * q1
q1 = 41.3172038254672R + z * q1
q1 = 15.0425385692908R + z * q1
q1 = 2.50464946208309R + z * q1
q1 = -(1.42182922854788R * 0.1) + z * q1
q1 = -(3.80806407691578R * 0.01) + z * q1
q1 = -(9.33259480895457R * 0.0001) + z * q1
x1 = z * p1 / q1
Else
p2 = 3.23774891776946R
p2 = 6.91522889068984R + z * p2
p2 = 3.93881025292474R + z * p2
p2 = 1.33303460815808R + z * p2
p2 = 2.01485389549179R * 0.1 + z * p2
p2 = 1.2371663481782R * 0.01 + z * p2
p2 = 3.01581553508235R * 0.0001 + z * p2
p2 = 2.65806974686738R * 0.000001R + z * p2
p2 = 6.23974539184983R * 0.000000001R + z * p2
q2 = 1
q2 = 6.02427039364742R + z * q2
q2 = 3.67983563856161R + z * q2
q2 = 1.37702099489081R + z * q2
q2 = 2.16236993594497R * 0.1 + z * q2
q2 = 1.34204006088543R * 0.01 + z * q2
q2 = 3.28014464682128R * 0.0001 + z * q2
q2 = 2.89247864745381R * 0.000001R + z * q2
q2 = 6.79019408009981R * 0.000000001R + z * q2
x1 = z * p2 / q2
End If
x = x0 - x1
If code <> 0 Then
x = -x
End If
result = x
Return result
End Function
End Class
End Namespace