Hi, Sergey!
You wrote in FAQ:
X-generator is another tool developed exclusively for ALGLIB. It is a generator of wrappers for the C/C# computational cores. This generator is heavily used by Python and VB.NET releases of ALGLIB. It is also used to generate doctests - code snippets, which are used as both examples (doc) and test suite (tests).
Both technologies are kept private, but result we've got with these tools - ALGLIB - is freely available under GPL.
Recently I've manually rewritten function ExponentialIntegralEN from ALGLIB (alglib-2.6.0.vb6.zip) into AutoIt. It works fine. Thanks.
About AutoIt scripting language read here, please:www.autoitscript.com
AutoIt v3 is a freeware BASIC-like scripting language.
Would you like to expand the X-generator for AutoIt (v3) code creation?
Cheers,
Valery
Code:
;===========================================
; E1 <= E_n-Function for n = 1
; http://mathworld.wolfram.com/En-Function.html
; It defined as special case of the exponential integral Ei(x)
; E1(x) = -Ei(-x)
; Rewritten from ExponentialIntegralEN (ALGLIB)
Func E1($x)
Local $Result, $r, $t
Local $yk, $xk, $pk, $pkm1, $pkm2, $qk, $qkm1, $qkm2
Local $psi = 0, $z, $i, $k, $big, $EUL
Local Const $MachineEpsilon = 1.11e-16
$EUL = 0.57721566490153286060
$big = 1.44115188075855872e17
If $x<0 Or $x>170 Or $x=0 then return -1
If $x<=1 then
$psi = -$EUL-Log($x)
$z = -$x
$xk = 0
$yk = 1
$pk = 0
$Result = 0.0
Do
$xk += 1
$yk *= $z/$xk
$pk += 1
If $pk<>0 then $Result += $yk/$pk
If $Result<>0 then
$t = Abs($yk/$Result)
Else
$t = 1
EndIf
Until $t<$MachineEpsilon
$t = 1
$Result = $psi*$t-$Result
return $Result
Else
$k = 1
$pkm2 = 1
$qkm2 = $x
$pkm1 = 1.0
$qkm1 = $x+1
$Result = $pkm1/$qkm1
Do
$k += 1
If Mod($k,2)=1 then
$yk = 1
$xk = 1+($k-1)/2
Else
$yk = $x
$xk = $k/2
Endif
$pk = $pkm1*$yk+$pkm2*$xk
$qk = $qkm1*$yk+$qkm2*$xk
If $qk<>0 then
$r = $pk/$qk
$t = Abs(($Result-$r)/$r)
$Result = $r
Else
$t = 1
EndIf
$pkm2 = $pkm1
$pkm1 = $pk
$qkm2 = $qkm1
$qkm1 = $qk
If Abs($pk) > $big then
$pkm2 /= $big
$pkm1 /= $big
$qkm2 /= $big
$qkm1 /= $big
EndIf
Until $t<$MachineEpsilon
$Result *= exp(-$x)
EndIf
return $Result
EndFunc
; E1 <= E_n-Function for n = 1
; http://mathworld.wolfram.com/En-Function.html
; It defined as special case of the exponential integral Ei(x)
; E1(x) = -Ei(-x)
; Rewritten from ExponentialIntegralEN (ALGLIB)
Func E1($x)
Local $Result, $r, $t
Local $yk, $xk, $pk, $pkm1, $pkm2, $qk, $qkm1, $qkm2
Local $psi = 0, $z, $i, $k, $big, $EUL
Local Const $MachineEpsilon = 1.11e-16
$EUL = 0.57721566490153286060
$big = 1.44115188075855872e17
If $x<0 Or $x>170 Or $x=0 then return -1
If $x<=1 then
$psi = -$EUL-Log($x)
$z = -$x
$xk = 0
$yk = 1
$pk = 0
$Result = 0.0
Do
$xk += 1
$yk *= $z/$xk
$pk += 1
If $pk<>0 then $Result += $yk/$pk
If $Result<>0 then
$t = Abs($yk/$Result)
Else
$t = 1
EndIf
Until $t<$MachineEpsilon
$t = 1
$Result = $psi*$t-$Result
return $Result
Else
$k = 1
$pkm2 = 1
$qkm2 = $x
$pkm1 = 1.0
$qkm1 = $x+1
$Result = $pkm1/$qkm1
Do
$k += 1
If Mod($k,2)=1 then
$yk = 1
$xk = 1+($k-1)/2
Else
$yk = $x
$xk = $k/2
Endif
$pk = $pkm1*$yk+$pkm2*$xk
$qk = $qkm1*$yk+$qkm2*$xk
If $qk<>0 then
$r = $pk/$qk
$t = Abs(($Result-$r)/$r)
$Result = $r
Else
$t = 1
EndIf
$pkm2 = $pkm1
$pkm1 = $pk
$qkm2 = $qkm1
$qkm1 = $qk
If Abs($pk) > $big then
$pkm2 /= $big
$pkm1 /= $big
$qkm2 /= $big
$qkm1 /= $big
EndIf
Until $t<$MachineEpsilon
$Result *= exp(-$x)
EndIf
return $Result
EndFunc