☜	$%ARCTAN Draft MDC Standard					☞

2 MATH Library
2.10 ARCTAN

ARCTAN(X,PREC) ;
	New FOLD,HI,L,LIM,LO,K,SIGN,SIGS,SIGT,VALUE
	Set PREC=$Get(PREC,11)
	Set LO=0.0000000001,HI=9999999999
	Set SIGT=$Select(X<0:–1,1:1),X=$Translate(X,"-")
	Set X=$Select(X<LO:LO,X>HI:HI,1:X)
	Set FOLD=$Select(X'<1:0,1:1)
	Set X=$Select(FOLD:1/X,1:X)
	Set L=X,VALUE=$%PI^MATH()/2-(1/X),SIGN=1
	If X<1.3 Do  Quit VALUE
	. Set X=$Select(FOLD:1/X,1:X),VALUE=1/((1/X/X)+1)
	. Set X=$%SQRT^MATH(VALUE,PREC)
	. If $Translate(X,"-")=1 Do  Quit
	. . Set VALUE=$%PI^MATH()/2*X
	. . Quit
	. If X>0.9 Do  Quit
	. . Set SIGS=$Select(X<0:–1,1:1)
	. . Set VALUE=1/(1/X/X–1)
	. . Set X=$%SQRT^MATH(VALUE)
	. . Set VALUE=$$ARCTAN(X,10)
	. . Set VALUE=VALUE*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
	. Set VALUE=$Select(SIGT<1:-VALUE,1:VALUE)
	. Quit
	Set LIM=$Select((PREC+3)'>11:PREC+3,1:11),@("LIM=1E-"_LIM)
	For K=3:2 Do  Quit:($Translate(1/L,"-")<LIM)
	. Set L=L*X*X,VALUE=VALUE+(1/(K*L)*SIGN)
	. Set SIGN=SIGN*–1
	. Quit
	Set VALUE=$Select(FOLD:$%PI^MATH()/2-VALUE,1:VALUE)
	Set VALUE=$Select(SIGT<1:-VALUE,1:VALUE)
	Quit VALUE

Copyright © Standard Documents; 1977-2024 MUMPS Development Committee;
Copyright © Examples: 1995-2024 Ed de Moel;
Copyright © Annotations: 2003-2008 Jacquard Systems Research
Copyright © Annotations: 2008-2024 Ed de Moel.

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, 16:48:37.

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