XProfan

English

p.specht

The ArcusSinus, it comes u.a. in Ellipsenformeln to, supply between whom Argumentwerten -1 and 1 The Umkehrung the Sinusfunktion, of course only on the first Wellenzug related. we're it say, how much % of/ one filled revolutions run is, part it us moreover The Bogenlänge on the Einheitskreis in Radiantmetern [wheel] with (lat. arcus is Yes 'Bogen').

an invention the Herrn Taylor allows it, so quite each multiple ableitbare function in a "unendliche" row to develop, The computer relatively rasch to charge can. not always access one thereby The geforderte accuracy, because: somewhere must The row in the reality Yes Cancel. too there different Reihen, The different well suitable are. a Test the standard-Reihenentwicklung around the point 0 around sees one hereinafter, beschleunigbar would the whole too still significantly...

Compile Mark Separation

Window Title "Test of/ one Eigenbau-ArcusSinus(x)-Funktion"
Font 2:randomize:set("decimals",17)
Cls rnd(8^8)
print "  arcsin(x) with x=[-1.0..+1.0]: supply The Bogenlänge [wheel] the 1.Sinus-Wellenzugs"
print "  math.inc-Nachbau:      Eigenbau-TaylorArcSin(x)       Abs.Error:                       "

WhileLoop -1000,1000

    print &Loop,asin(&Loop/1000),
    print tlrasin(&Loop/1000),stature$("%e",tlrasin(&Loop/1000)-asin(&Loop/1000))

    if %csrlin>24:waitInput 10000:cls rnd(8^8):endif

    Wend

    WaitInput
    End

    proc ASIN : parameters x!' = Nachbau the suitable math.inc-function

        var res!=0:var it$=""
        var xx!=x!*x!
        var wur!=1-xx!

        if wur!>=0

            wur!=sqrt(wur!)

            if wur!<>0

                res!=arctan(x!/wur!)

            else

                res!=val("10^-30")
                it$="Div0 in asin()"

            endif

        else

            res!=val("-1*10^-30")
            it$="Nonreal root in asin()"

        endif

        print it$,
        return res!

    endproc

    proc ACOS :parameters x!

        return pi()/2-ASIN(x!)

    endproc

    Proc TlrASin : parameters x!' Eigenbau-arcussinus(x) through Taylorreihe

        ' The true ArcusSinus is definiert for Argumente -1 ,,, +1.
        ' Testergebnisse for Nachbau;
        ' On 5 to put exakt only +/- 0.833 around the Nulldurchgang
        ' On 3 to put exakt only within +/- 0.933
        var tmp!=0:var x2!=x!*x!:var x3!=x2!*x!:var x5!=x3!*x2!:var x7!=x5!*x2!
        var x9!=x7!*x2!:var x11!=x9!*x2!:var x13!=x11!*x2!:var x15!=x13!*x2!
        var x17!=x15!*x2!:var x19!=x17!*x2!:var x21!=x19!*x2!:var x23!=x21!*x2!
        var x25!=x23!*x2!:var x27!=x25!*x2!:var x29!=x27!*x2!:var x31!=x29!*x2!
        var x33!=x31!*x2!:var x35!=x33!*x2!:var x37!=x35!*x2!:var x39!=x37!*x2!
        tmp!=tmp!+x!
        tmp!=tmp!+x3!/3 * 1/2
        tmp!=tmp!+x5!/5 * 1/2*3/4
        tmp!=tmp!+x7!/7 * 1/2*3/4*5/6
        tmp!=tmp!+x9!/9 * 1/2*3/4*5/6*7/8
        tmp!=tmp!+x11!/11 * 1/2*3/4*5/6*7/8*9/10
        tmp!=tmp!+x13!/13 * 1/2*3/4*5/6*7/8*9/10*11/12
        tmp!=tmp!+x15!/15 * 1/2*3/4*5/6*7/8*9/10*11/12*13/14
        tmp!=tmp!+x17!/17 * 1/2*3/4*5/6*7/8*9/10*11/12*13/14*15/16
        tmp!=tmp!+x19!/19 * 1/2*3/4*5/6*7/8*9/10*11/12*13/14*15/16*17/18
        tmp!=tmp!+x21!/21 * 1/2*3/4*5/6*7/8*9/10*11/12*13/14*15/16*17/18*19/20
        tmp!=tmp!+x23!/23 * 1/2*3/4*5/6*7/8*9/10*11/12*13/14*15/16*17/18*19/20*21/22
        tmp!=tmp!+x25!/25 * 1/2*3/4*5/6*7/8*9/10*11/12*13/14*15/16*17/18*19/20*21/22*23/24
        tmp!=tmp!+x27!/27 * 1/2*3/4*5/6*7/8*9/10*11/12*13/14*15/16*17/18*19/20*21/22*23/24*25/26
        tmp!=tmp!+x29!/29 * 1/2*3/4*5/6*7/8*9/10*11/12*13/14*15/16*17/18*19/20*21/22*23/24*25/26*27/28
        tmp!=tmp!+x31!/31 * 1/2*3/4*5/6*7/8*9/10*11/12*13/14*15/16*17/18*19/20*21/22*23/24*25/26*27/28*29/30
        tmp!=tmp!+x33!/33 * 1/2*3/4*5/6*7/8*9/10*11/12*13/14*15/16*17/18*19/20*21/22*23/24*25/26*27/28*29/30*31/32
        tmp!=tmp!+x35!/35 * 1/2*3/4*5/6*7/8*9/10*11/12*13/14*15/16*17/18*19/20*21/22*23/24*25/26*27/28*29/30*31/32*33/34
        tmp!=tmp!+x37!/37 * 1/2*3/4*5/6*7/8*9/10*11/12*13/14*15/16*17/18*19/20*21/22*23/24*25/26*27/28*29/30*31/32*33/34*35/36
        tmp!=tmp!+x39!/39 * 1/2*3/4*5/6*7/8*9/10*11/12*13/14*15/16*17/18*19/20*21/22*23/24*25/26*27/28*29/30*31/32*33/34*35/36*37/38
        return tmp!

    Endproc

XProfan 11
Computer: Gerät, daß es in Mikrosekunden erlaubt, 50.000 Fehler zu machen, zB 'daß' statt 'das'...

05/07/21 ▲

Vollständiges Quote

Absatzweise Quote Zeilenweise Quote

p.specht

It's all right but too differently:

ArcSin iterativ detect
==================
Dass one itself over a Iteration of/ one Quadratwurzel-Formel the Umkehrfunktion the SINUS almost discretionary annähern can, becomes in the subesquent Program demonstrating. there's Yes z.B. situations, where to the one Microprozessor procure would like.

Compile Mark Separation

Window Title "ArcSin by Iteration"
'From Pascal (by J.P.Moreau) to XProfan-11 by P.woodpecker/Vienna
'********************************************************
'*       Program to demonstrate arcsine Iteration       *
'* ---------------------------------------------------- *
'*   Reference: BASIC Scientific Subroutines, Vol. II   *
'*   by F.R. Ruckdeschel, BYTE/McGRAWW-HILL, 1981 [1].  *
'* ---------------------------------------------------- *
'* SAMPLE RUN:                                          *
'*   X       ARCSIN(X)       STEPS        ERROR         *
'*  -----------------------------------------------     *
'*  0.00     0.0000000         0       0.0000000000     *
'*  0.05     0.0500209         7      -0.0000000013     *
'*  0.10     0.1001674         8      -0.0000000025     *
'*  0.15     0.1505683         9      -0.0000000021     *
'*  0.20     0.2013579        10      -0.0000000013     *
'*  0.25     0.2526803        10      -0.0000000025     *
'*  0.30     0.3046927        11      -0.0000000011     *
'*  0.35     0.3575711        11      -0.0000000017     *
'*  0.40     0.4115168        11      -0.0000000025     *
'*  0.45     0.4667653        12      -0.0000000009     *
'*  0.50     0.5235988        12      -0.0000000012     *
'*  0.55     0.5823642        12      -0.0000000016     *
'*  0.60     0.6435011        12      -0.0000000021     *
'*  0.65     0.7075844        13      -0.0000000007     *
'*  0.70     0.7753975        13      -0.0000000008     *
'*  0.75     0.8480621        13      -0.0000000010     *
'*  0.80     0.9272952        13      -0.0000000012     *
'*  0.85     1.0159853        13      -0.0000000014     *
'*  0.90     1.1197695        14      -0.0000000004     *
'*  0.95     1.2532359        14      -0.0000000004     *
'*  1.00     1.5707963         0       0.0000000000     *
'********************************************************
Window Style 24:Cls:font 2:set("decimals",8)
Declare e!,x!,i&,m&,y!,pi!,u0!,u1!,u2!
print "\n X      ArcSinIter(X)       STEPS     ERROR"
print "-------------------------------------------------------------------"
e!=val("1e-15")
x!=0

whileloop 1,21:i&=&Loop

    y!=ArcSinIter(x!)
    print " ";stature$("#0.00",x!),tab(9);stature$("%g",y!),\
    tab(29);m&,tab(34);stature$("%g",sin(y!)-x!)
    x!=x!+0.05

Endwhile

print
beep:Waitinput
End

Proc ArcSinIter :parameters x!

    '************************************************
    '*       Arcsin(x) recursion subroutine         *
    '* Input is x (-1<x<1), output is y=arcsin(x),  *
    '* convergence criteria is e.                   *
    '* -------------------------------------------- *
    '* Reference: Computational Analysis by Henrici *
    '************************************************
    m&=0
    pi!=Pi()
    case e!<0:return y!'Guard against failure
    case x!<>0:y!=Check_range(x!)
    return y!

ENDPROC

Proc Check_range :parameters x!

    case abs(x!)>=1:goto "G1300"
    u0!=x!*sqrt(1-x!*x!)
    u1!=x!

    Repeat

        u2!=u1!*sqrt(2*u1!/(u1!+u0!))
        y!=u2!
        m&=m&+1
        case abs(u2!-u1!)<e!:BREAK
        u0!=u1!:u1!=u2!

    Until 0

    G1300:
    case abs(x!-1)<val("1e-10"):y!=pi!/2
    return y!

Endproc

'End of file ArcsinIter.prf