☜	$%COS M[UMPS] by Example					☞

2-Jul–96, 6:54:35
Routine Save for Trigonometry Library function $%COS^MATH
 ;
 ; Unless otherwise noted, the code below
 ; was approved in document X11/95–12
 ;
 ; If corrections have been applied,
 ; first the original line appears,
 ; with three semicolons at the beginning of the line.
 ;
 ; Then the source of the correction is acknowledged,
 ; then the corrected line appears, followed by a
 ; line containing three semicolons.
 ;
COS(X,PREC) ;
 New L,LIM,K,SIGN,VALUE
 ;
 ;;; Set:X[":" X=$%DMSDEC^MATH(X,12)
 ; Winfried Gerum (8 June 1995)
 ;    Comment: The official description does not mention than
 ;             the function may also be called with the first
 ;             parameter in degrees, minutes and seconds.
 Set:X[":" X=$%DMSDEC^MATH(X)
 ;;;
 ;
 Set PREC=$Get(PREC,11)
 Set X=X#(2*$%PI^MATH())
 Set (VALUE,L)=1,SIGN=–1
 Set LIM=$Select((PREC+3)'>11:PREC+3,1:11),@("LIM=1E-"_LIM)
 For K=2:2 Do  Quit:($Translate(L,"-")<LIM)  Set SIGN=SIGN*–1
 . Set L=L*X*X/(K–1*K),VALUE=VALUE+(SIGN*L)
 . Quit
 Quit VALUE
 ;===
 ;
 ;
COS(X) ;
 ; Winfried Gerum (8 June 1995)
 ;  Comment: This version of the function is
 ;           optimized for speed, not for precision.
 ;           The ‘precision’ parameter is not supported,
 ;           and the precision is at best 1 in 10**–9.
 ;           Note that this function does not accept its
 ;           parameter in degrees, minutes and seconds.
 ;
 New A,N,PI,R,SIGN,XX
 ;
 ; This approximation only works for 0 <= x <= pi/2
 ; so reduce angle to correct quadrant.
 ;
 Set PI=$%PI^MATH(),X=X#(PI*2),SIGN=1
 Set:X>PI X=2*PI-X
 Set:X*2>PI X=PI-X,SIGN=–1
 ;
 Set XX=X*X,A(1)=–0.4999999963,A(2)=0.0416666418
 Set A(3)=–0.0013888397,A(4)=0.0000247609,A(5)=–0.0000002605
 Set (X,R)=1 For N=1:1:5 Set X=X*XX,R=A(N)*X+R
 Quit R*SIGN
 ;===
 ;
 ;
 ;

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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.
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 16-Nov-2023, 16:49:04.

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