☜	$%ARCSIN M[UMPS] by Example					☞

2-Jul–96, 6:54:35
Routine Save for Trigonometry Library function $%ARCSIN^MATH
 ;
 ; Unless otherwise noted, the code below
 ; was approved in document X11/95–12
 ;
 ; If corrections have been applied,
 ; first the original line appears,
 ; with three semicolons at the beginning of the line.
 ;
 ; Then the source of the correction is acknowledged,
 ; then the corrected line appears, followed by a
 ; line containing three semicolons.
 ;
ARCSIN(X) ;
 ; Winfried Gerum (8 June 1995)
 ;  Comment: This version of the function is
 ;           optimized for speed, not for precision.
 ;           The ‘precision’ parameter is not supported,
 ;           and the precision is at best 2 in 10**–8.
 ;
 New A,N,R,SIGN,XX
 If X<–1 Set $Ecode=",M28,"
 If X>1 Set $Ecode=",M28,"
 Set SIGN=1 Set:X<0 X=-X,SIGN=–1
 Set A(0)=1.5707963050,A(1)=–0.2145988016,A(2)=0.0889789874
 Set A(3)=–0.0501743046,A(4)=0.0308918810,A(5)=–0.0170881256
 Set A(6)=0.0066700901,A(7)=–0.0012624911
 Set R=A(0),XX=1 For N=1:1:7 Set XX=XX*X,R=A(N)*XX+R
 ;
 ;;; Set R=$%SQRT^MATH(1-X)*R
 ; Winfried Gerum (8 June 1995)
 Set R=$%SQRT^MATH(1-X,11)*R
 ;;;
 ;
 Set R=$%PI^MATH()/2-R
 Quit R*SIGN
 ;===
 ;
 ;
ARCSIN(X,PREC) ;
 New L,LIM,K,SIGS,VALUE
 Set PREC=$Get(PREC,11)
 ;
 ;;; If $Translate(X,"-")=1 Do  Quit
 ; Winfried Gerum (8 June 1995)
 ; Eli Reidler (28 June 1996)
 If $Translate(X,"-")=1 Do  Quit VALUE
 . ;;;
 . ;
 . Set VALUE=$%PI^MATH()/2*X
 . Quit
 ;
 ;;; If X>0.99999 Do  Quit
 ; Winfried Gerum (8 June 1995)
 ; Eli Reidler (28 June 1996)
 If X>0.99999 Do  Quit VALUE
 . ;;;
 . ;
 . Set SIGS=$Select(X<0:–1,1:1)
 . Set VALUE=1/(1/X/X–1)
 . ;
 . ;;; Set X=$%SQRT^MATH(VALUE)
 . ; Winfried Gerum (8 June 1995)
 . Set X=$%SQRT^MATH(VALUE,PREC)
 . ;;;
 . ;
 . ;;; Set VALUE=$%ARCTAN^MATH(X,10)*SIGS
 . ; Winfried Gerum (8 June 1995)
 . Set VALUE=$%ARCTAN^MATH(X,PREC)*SIGS
 . ;;;
 . ;
 . Quit
 Set (VALUE,L)=X
 Set LIM=$Select((PREC+3)'>11:PREC+3,1:11),@("LIM=1E-"_LIM)
 For K=3:2 Do  Quit:($Translate(L,"-")<LIM)
 . Set L=L*X*X*(K–2)/(K–1)*(K–2)/K,VALUE=VALUE+L
 . Quit
 Quit VALUE
 ;===
 ;
 ;
 ;

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Copyright © Examples: 1995-2024 Ed de Moel;
Copyright © Annotations: 2003-2008 Jacquard Systems Research
Copyright © Annotations: 2008-2024 Ed de Moel.

The information in this page is NOT authoritative and subject to be modified at any moment.
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Some specifications are "approved for inclusion in a future standard". Note that the MUMPS Development Committee cannot guarantee that such future standards will indeed be published.

This page most recently updated on 16-Nov-2023, 14:54:53.

For comments, contact Ed de Moel (demoel@jacquardsystems.com)