XProfan

English

p.specht

(... and who whom Sinus has, has so too Cosinus and Tangens!)
remarkable: in the area 0-90° remaining the thing under 0,047 % Error. prerequisite is though a detailed Computerarithmetik - and who The has, the has usually already a Sinusfunktion installed. still mathematically interestingly. Note: in the FPU the PC go trigonometrische Funktonen ditto through Approximation determined, alledings through CORDIC Algorithmus. The is hold yet accurate, setting but "gehobene" rechentechnische Kenntnisse ahead...

Compile Mark Separation

Window Title "Sinus-substitute through Padé-Approximation"
' fountain: https://www.dattalo.com/technical/theory/theory.html
' In XProfan 11.2 umgesetzt of P. woodpecker 2012-05; Jedwede Gewähr impossible!
' Möglicherweise rights Third, therefore go ahead Demonstrationszwecken!
Font 2:randomize:cls rnd(8^8)
set("decimals",10)
'{ Konstanten for Own sinus()-function
var pi!=3.14159265358979323846264338327950288419716939937510
var pi2!=2*pi!
var pih!=pi!/2
var r2g!=pi!/180
var n1!=-325523/2283996
var n2!=34911/7613320
var n3!=479249/(1.1511339840*10^10)
var d1!=18381/761332
var d2!=1261/4567992
var d3!=2623/(1.644477120*10^9)
'}
'{ Hauptschleife
declare w!,af!,rf!
var txt$="Grad    Sin()    Sinus-Approx  Absol.Err   Relativfehler\n"
print txt$

WhileLoop 0,360,1

    w!=r2g!*&Loop
    af!=sinus(w!)-sin(w!)
    rf!=100*af!/(sin(w!)+10^-36)
    case &Loop<100:print " ";
    case &Loop<10 :print " ";
    print &Loop,sin(w!),sinus(w!),af!,rf!;" [%]"

    if %csrlin>26

        waitinput
        cls rnd(8^8)
        print txt$

    endif

EndWhile

print "OK."
Waitinput
'}
End

proc sinus : parameters x!

    declare num!,whom!,x2!,x4!,x6!,sinus!,vz!
    ' 0-90° Rel.Err < 0,047%
    ' Zyklischen Wertebereich produce
    x!=x!-pi2!*int(x!/pi2!)
    vz!=1:if x!>=pi!:x!=x!-pi!-1.24*10^-16:vz!= -1:endif
    case x!>=pih!:x!=pi!-x!
    ' Padé-Approximation
    x2!=x!*x!:x4!=x2!*x2!:x6!=x4!*x2!
    num! = 1 + n1!*x2! + n2!*x4! + n3!*x6!
    whom! = 1 + d1!*x2! + d2!*x6! + d3!*x6!
    sinus! = vz! * x! * num! / whom!
    return sinus!

endproc

proc cosinus :parameters x!

    return sinus(x!)+pih!

endproc

proc tangens : parameters x!

    return sinus(x!)/sinus!(x!-pih!)

endproc