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$%ARCCOS

M[UMPS] by Example

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2-Jul–96, 6:54:35
Routine Save for Trigonometry Library function $%ARCCOS^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.
 ;
ARCCOS(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
 ;;;
 ;
 Quit R*SIGN
 ;===
 ;
 ;
ARCCOS(X,PREC) ;
 ;
 ;;; New L,LIM,K,SIG,SIGS
 ; Winfried Gerum (8 June 1995)
 New L,LIM,K,SIG,SIGS,VALUE
 ;;;
 ;
 If X<–1 Set $Ecode=",M28,"
 If X>1 Set $Ecode=",M28,"
 Set PREC=$Get(PREC,11)
 ;
 ;;; If $Translate(X,"-")=1 Set VALUE=0 Quit
 ; Winfried Gerum (8 June 1995)
 ; Eli Reidler (28 June 1996)
 If $Translate(X,"-")=1 Quit 0
 ;;;
 ;
 Set SIG=$Select(X<0:–1,1:1),VALUE=1-(X*X)
 ;
 ;;; Set X=$%SQRT^MATH(VALUE)
 ; Winfried Gerum (8 June 1995)
 Set X=$%SQRT^MATH(VALUE,PREC)
 ;;;
 ;
 ;;; 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>0.9 Do  Quit
 ; Winfried Gerum (8 June 1995)
 ; Eli Reidler (28 June 1996)
 If X>0.9 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 $Select(SIG<0:$%PI^MATH()-VALUE,1:VALUE)
 ;===
 ;
 ;
 ;
Button for 1977 Button for 1984 Button for 1990 Button for 1995 Button for MDC Button for notes Button for examples

Copyright © Standard Documents; 1977-2018 MUMPS Development Committee;
Copyright © Examples: 1995-2018 Ed de Moel;
Copyright © Annotations: 2003-2008 Jacquard Systems Research
Copyright © Annotations: 2008-2018 Ed de Moel.

The information in this page is NOT authoritative and subject to be modified at any moment.
Please consult the appropriate (draft) language standard for an authoritative definition.

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 30-Nov-2011, 19:46:55 .

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