C TEUL 10
C ..................................................................TEUL 20
C TEUL 30
C SUBROUTINE TEUL TEUL 40
C TEUL 50
C PURPOSE TEUL 60
C COMPUTE THE SUM OF FCT(K) FOR K FROM ONE UP TO INFINITY. TEUL 70
C TEUL 80
C USAGE TEUL 90
C CALL TEUL(FCT,SUM,MAX,EPS,IER) TEUL 100
C PARAMETER FCT REQUIRES AN EXTERNAL STATEMENT. TEUL 110
C TEUL 120
C DESCRIPTION OF PARAMETERS TEUL 130
C FCT - NAME OF AN EXTERNAL FUNCTION SUBPROGRAM USED. TEUL 140
C IT COMPUTES THE K-TH TERM OF THE SERIES TO ANY TEUL 150
C GIVEN INDEX K. TEUL 160
C SUM - RESULTANT VALUE CONTAINING ON RETURN THE SUM OF TEUL 170
C THE GIVEN SERIES. TEUL 180
C MAX - INPUT VALUE, WHICH SPECIFIES THE MAXIMAL NUMBER TEUL 190
C OF TERMS OF THE SERIES THAT ARE RESPECTED. TEUL 200
C EPS - INPUT VALUE, WHICH SPECIFIES THE UPPER BOUND OF TEUL 210
C THE RELATIVE ERROR. TEUL 220
C SUMMATION IS STOPPED AS SOON AS FIVE TIMES IN TEUL 230
C SUCCESSION THE ABSOLUTE VALUE OF THE TERMS OF THE TEUL 240
C TRANSFORMED SERIES ARE FOUND TO BE LESS THAN TEUL 250
C EPS*(ABSOLUTE VALUE OF CURRENT SUM). TEUL 260
C IER - RESULTANT ERROR PARAMETER CODED IN THE FOLLOWING TEUL 270
C FORM TEUL 280
C IER=0 - NO ERROR TEUL 290
C IER=1 - REQUIRED ACCURACY NOT REACHED WITH TEUL 300
C MAXIMAL NUMBER OF TERMS TEUL 310
C IER=-1 - THE INTEGER MAX IS LESS THAN ONE. TEUL 320
C TEUL 330
C REMARKS TEUL 340
C NO ACTION BESIDES ERROR MESSAGE IN CASE MAX LESS THAN ONE. TEUL 350
C TEUL 360
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED TEUL 370
C THE EXTERNAL FUNCTION SUBPROGRAM FCT(K) MUST BE FURNISHED TEUL 380
C BY THE USER. TEUL 390
C TEUL 400
C METHOD TEUL 410
C EVALUATION IS DONE BY MEANS OF A SUITABLY REFINED EULER TEUL 420
C TRANSFORMATION. FOR REFERENCE, SEE TEUL 430
C F.B.HILDEBRAND, INTRODUCTION TO NUMERICAL ANALYSIS, TEUL 440
C MCGRAW/HILL, NEW YORK/TORONTO/LONDON, 1956, PP.155-160, AND TEUL 450
C P. NAUR, REPORT ON THE ALGORITHMIC LANGUAGE ALGOL 60, TEUL 460
C CACM, VOL.3, ISS.5 (1960), PP.311. TEUL 470
C TEUL 480
C ..................................................................TEUL 490
C TEUL 500
SUBROUTINE TEUL (FCT,SUM,MAX,EPS,IER) TEUL 510
C TEUL 520
DIMENSION Y(15) TEUL 530
C TEUL 540
C TEST ON WRONG INPUT PARAMETER MAX TEUL 550
C TEUL 560
IF(MAX)1,1,2 TEUL 570
1 IER=-1 TEUL 580
GOTO 12 TEUL 590
C TEUL 600
C INITIALIZE EULER TRANSFORMATION TEUL 610
C TEUL 620
2 IER=1 TEUL 630
I=1 TEUL 640
M=1 TEUL 650
N=1 TEUL 660
Y(1)=FCT(N) TEUL 670
SUM=Y(1)*.5 TEUL 680
C TEUL 690
C START EULER-LOOP TEUL 700
C TEUL 710
3 J=0 TEUL 720
4 I=I+1 TEUL 730
IF(I-MAX)5,5,12 TEUL 740
5 N=I TEUL 750
AMN=FCT(N) TEUL 760
DO 6 K=1,M TEUL 770
AMP=(AMN+Y(K))*.5 TEUL 780
Y(K)=AMN TEUL 790
6 AMN=AMP TEUL 800
C TEUL 810
C CHECK EULER TRANSFORMATION TEUL 820
C TEUL 830
IF(ABS(AMN)-ABS(Y(M)))7,9,9 TEUL 840
7 IF(M-15)8,9,9 TEUL 850
8 M=M+1 TEUL 860
Y(M)=AMN TEUL 870
AMN=.5*AMN TEUL 880
C TEUL 890
C UPDATE SUM TEUL 900
C TEUL 910
9 SUM=SUM+AMN TEUL 920
IF(ABS(AMN)-EPS*ABS(SUM))10,10,3 TEUL 930
C TEUL 940
C TEST END OF PROCEDURE TEUL 950
C TEUL 960
10 J=J+1 TEUL 970
IF(J-5)4,11,11 TEUL 980
11 IER=0 TEUL 990
12 RETURN TEUL1000
END TEUL1010