XProfan

Window Title upper$("Gauss'sche Fehlerfunktionen Erf(x) and Erfc(x)")
' Q: https://de.wikipedia.org/wiki/Fehlerfunktion#Numerische_Berechnung
' Umsetzung in XPRofan (CL) CopyLeft 2014-10 by P.woodpecker, Wien
' No however geartetet Gewähr!

Proc Erf :parameters x!

    ' Approximation of Erf() for kompletten Wertebereich, maximum Error 1.2E-7
    declare t!,t2!,t3!,t4!,t5!,t6!,t7!,t8!,t9!,dew!
    t!=1/(1+0.5*abs(x!)):t2!=sqr(t!):t3!=t!*t2!:t4!=t2!*t2!
    t5!=t3!*t2!:t6!=t3!*t3!:t7!=t4!*t3!:t8!=t4!*t4!:t9!=t5!*t4!
    dew!=t!*exp(-sqr(x!)-1.26551223+1.00002368*t!+0.37409196*t2!+0.09678418*t3!-0.18628806*t4!+\
    0.27886807*t5!-1.13520398*t6!+1.48851587*t7!-0.82215223*t8!+0.17087277*t9!)
    case x!>=0:return 1-dew!
    return dew!-1

endproc

proc Erfc:parameters x!' Complementäre Fehlerfunktion 1-Erf(x), not zentralsymmetrisch!

    return 1-Erf(x!)

endproc

Window Style 24:Window 0,0-%maxx,%maxy-40
var xh&=width(%hwnd)\2:var yh&=height(%hwnd)\2:var x!=0
var zoomx!=%maxx/1366:var zoomy!=%maxy/768
noamoi:
Cls
'Achsen
usepen 2,1,rgb(0,0,0):line 0,yh&-2*xh&,yh&:line xh&,0-xh&,2*yh&
'Beschriftung
usefont "ARIAL",60*zoomy!,30*zoomx!,0,0,0:textcolor rgb(200,0,200),-1
drawtext 250*zoomx!,30*zoomy!,"Erfc(x)"
textcolor rgb(200,0,0),-1:drawtext 250*zoomx!,430*zoomy!,"Erf(x)":textcolor 0,-1
drawtext 650*zoomx!,1*zoomy!,"2":drawtext 650*zoomx!,120*zoomy!,"1"
drawtext 650*zoomx!,290*zoomy!,"0"
drawtext 650*zoomx!,450*zoomy!,"-1":drawtext 250*zoomx!,320*zoomy!,"-3.5"
drawtext 950*zoomx!,320*zoomy!,"3.5"
'Asymptotenlinien
usepen 0,2,rgb(0,180,0)
line 0,(yh&-yh&*0.5*erf(-5)) - 2*xh&,yh&-yh&*0.5*erf(-5)
line 0,(yh&-yh&*0.5*erf( 5)) - 2*xh&,yh&-yh&*0.5*erf( 5)
'statement of ERF()
usepen 0,4,rgb(200,0,0):Moveto 0,yh&-yh&*0.5*erf(-3.7)

whileloop -xh&,xh&,1 : x!=&Loop*3.7/xh&

    Lineto xh&+x!*xh&/3.7,yh&-yh&*0.5*erf(x!)

endwhile

'Representation of the Komplementärfunktion ErfC(x). she's NOT zentralsymmetrisch!!!
usepen 0,4,rgb(200,0,200):Moveto 0,yh&-yh&*0.5*erfc(-3.7)

whileloop -xh&,xh&,1 : x!=&Loop*3.7/xh&

    Lineto xh&+x!*xh&/3.7 , yh&-yh&*0.5*erfc(x!)

endwhile

'spending the Berechnungswerte to that comparison with nachstender Verifizierungstabelle
waitinput 10000:font 2
locate 1,1:Set("decimals",7)

whileloop 0,3500,50:x!=&Loop/1000

    print x!,erf(x!),erfc(x!)
    case %csrlin>50:waitinput 20000

endwhile

beep
waitinput 20000
GOTO "noamoi"
END
'             scheduler to Verification the Formel:
'-----------------------------------------------------------------
'    x 	erf(x) 	erfc(x) 		      !   x 	erf(x) 	erfc(x)
'---------------------------------!-------------------------------
'    0.00 	0.0000000 	1.0000000   1.30 	0.9340079 	0.0659921
'    0.05 	0.0563720 	0.9436280   1.40 	0.9522851 	0.0477149
'    0.10 	0.1124629 	0.8875371 	1.50 	0.9661051 	0.0338949
'    0.15 	0.1679960 	0.8320040 	1.60 	0.9763484 	0.0236516
'    0.20 	0.2227026 	0.7772974 	1.70 	0.9837905 	0.0162095
'    0.25 	0.2763264 	0.7236736 	1.80 	0.9890905 	0.0109095
'    0.30 	0.3286268 	0.6713732 	1.90 	0.9927904 	0.0072096
'    0.35 	0.3793821 	0.6206179 	2.00 	0.9953223 	0.0046777
'    0.40 	0.4283924 	0.5716076 	2.10 	0.9970205 	0.0029795
'    0.45 	0.4754817 	0.5245183 	2.20 	0.9981372 	0.0018628
'    0.50 	0.5204999 	0.4795001 	2.30 	0.9988568 	0.0011432
'    0.55 	0.5633234 	0.4366766 	2.40 	0.9993115 	0.0006885
'    0.60 	0.6038561 	0.3961439 	2.50 	0.9995930 	0.0004070
'    0.65 	0.6420293 	0.3579707 	2.60 	0.9997640 	0.0002360
'    0.70 	0.6778012 	0.3221988 	2.70 	0.9998657 	0.0001343
'    0.75 	0.7111556 	0.2888444 	2.80 	0.9999250 	0.0000750
'    0.80 	0.7421010 	0.2578990 	2.90 	0.9999589 	0.0000411
'    0.85 	0.7706681 	0.2293319 	3.00 	0.9999779 	0.0000221
'    0.90 	0.7969082 	0.2030918 	3.10 	0.9999884 	0.0000116
'    0.95 	0.8208908 	0.1791092 	3.20 	0.9999940 	0.0000060
'    1.00 	0.8427008 	0.1572992 	3.30 	0.9999969 	0.0000031
'    1.10 	0.8802051 	0.1197949 	3.40 	0.9999985 	0.0000015
'    1.20 	0.9103140 	0.0896860 	3.50 	0.9999993 	0.0000007