NUMAL Section 2.3

BEGIN SECTION : 2.3 (May, 1974)

AUTHOR   : H.FIOLET

INSTITUTE: MATHEMATICAL CENTRE.

RECEIVED: 731105.

BRIEF DESCRIPTION:

    JFRAC CALCULATES A TERMINATING CONTINUED FRACTION.

KEYWORDS:

    CONTINUED FRACTION,
    TERMINATING CONTINUED FRACTION.

CALLING SEQUENCE:
    THE HEADING OF THE PROCEDURE READS:
    "REAL" "PROCEDURE" JFRAC(N,A,B);
    "VALUE" N;"INTEGER" N;"ARRAY" A,B;
    "CODE" 35083;

    JFRAC DELIVERS THE VALUE OF THE TERMINATING CONTINUED FRACTION:
    B[0]+A[1]/(B[1]+A[2]/(B[2]+A[3]/(B[3]+ . . . + A[N]/B[N])))...))

    THE MEANING OF THE FORMAL PARAMETERS IS:
    N:         <ARITHMETIC EXPRESSION>;
               THE UPPER INDEX OF THE ARRAYS A AND B;
    A,B:       <ARRAY IDENTIFIER>;
               "ARRAY" A[1:N];
               "ARRAY" B[0:N];
               THE ELEMENTS OF THE CONTINUED FRACTION:
               B[0]+A[1]/(B[1]+A[2]/(B[2]+A[3]/(B[3]+ . . . +
               + A[N]/B[N])))...)).

PROCEDURES USED: NONE.

RUNNING TIME: PROPORTIONAL TO N.

EXAMPLE OF USE:

    "BEGIN"
    "REAL" "ARRAY" P[1:10],Q[0:10];
    "INTEGER" I;
    "FOR" I:=1 "STEP" 1 "UNTIL" 10 "DO"
    "BEGIN" P[I]:=1;Q[I]:=2 "END";
    Q[0]:=1;
    "FOR" I:=7 "STEP" 1 "UNTIL" 10 "DO"
    OUTPUT(61,"("N/")",JFRAC(I,P,Q))
    "END"

    DELIVERS:

    +1.4142156862745"+000
    +1.4142131979695"+000
    +1.4142136248949"+000
    +1.4142135516461"+000     .

SOURCE TEXT:

"CODE" 35083;