C DEL1 10
C ..................................................................DEL1 20
C DEL1 30
C SUBROUTINE DELI1 DEL1 40
C DEL1 50
C PURPOSE DEL1 60
C COMPUTES THE ELLIPTIC INTEGRAL OF FIRST KIND DEL1 70
C DEL1 80
C USAGE DEL1 90
C CALL DELI1(RES,X,CK) DEL1 100
C DEL1 110
C DESCRIPTION OF PARAMETERS DEL1 120
C RES - RESULT VALUE IN DOUBLE PRECISION DEL1 130
C X - UPPER INTEGRATION BOUND (ARGUMENT OF ELLIPTIC DEL1 140
C INTEGRAL OF FIRST KIND) IN DOUBLE PRECISION DEL1 150
C CK - COMPLEMENTARY MODULUS IN DOUBLE PRECISION DEL1 160
C DEL1 170
C REMARKS DEL1 180
C DOUBLE PRECISION MODULUS K = DSQRT(1.D0-CK*CK). DEL1 190
C DEL1 200
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED DEL1 210
C NONE DEL1 220
C DEL1 230
C METHOD DEL1 240
C DEFINITION DEL1 250
C RES=INTEGRAL(1/SQRT((1+T*T)*(1+(CK*T)**2)), SUMMED DEL1 260
C OVER T FROM 0 TO X). DEL1 270
C EQUIVALENT ARE THE DEFINITIONS DEL1 280
C RES=INTEGRAL(1/(COS(T)*SQRT(1+(CK*TAN(T))**2)), SUMMED DEL1 290
C OVER T FROM 0 TO ATAN(X)), DEL1 300
C RES=INTEGRAL(1/SQRT(1-(K*SIN(T))**2), SUMMED OVER DEL1 310
C T FROM 0 TO ATAN(X)). DEL1 320
C EVALUATION DEL1 330
C LANDENS TRANSFORMATION IS USED FOR CALCULATION. DEL1 340
C REFERENCE DEL1 350
C R. BULIRSCH, NUMERICAL CALCULATION OF ELLIPTIC INTEGRALS ANDDEL1 360
C ELLIPTIC FUNCTIONS. DEL1 370
C HANDBOOK SERIES OF SPECIAL FUNCTIONS DEL1 380
C NUMERISCHE MATHEMATIK VOL. 7, 1965, PP. 78-90. DEL1 390
C DEL1 400
C ..................................................................DEL1 410
C DEL1 420
SUBROUTINE DELI1(RES,X,CK) DEL1 430
C DEL1 440
DOUBLE PRECISION RES,X,CK,ANGLE,GEO,ARI,PIM,SQGEO,AARI,TEST DEL1 450
C DEL1 460
IF(X)2,1,2 DEL1 470
1 RES=0.D0 DEL1 480
RETURN DEL1 490
C DEL1 500
2 IF(CK)4,3,4 DEL1 510
3 RES=DLOG(DABS(X)+DSQRT(1.D0+X*X)) DEL1 520
GOTO 13 DEL1 530
C DEL1 540
4 ANGLE=DABS(1.D0/X) DEL1 550
GEO=DABS(CK) DEL1 560
ARI=1.D0 DEL1 570
PIM=0.D0 DEL1 580
5 SQGEO=ARI*GEO DEL1 590
AARI=ARI DEL1 600
ARI=GEO+ARI DEL1 610
ANGLE=-SQGEO/ANGLE+ANGLE DEL1 620
SQGEO=DSQRT(SQGEO) DEL1 630
IF(ANGLE)7,6,7 DEL1 640
C DEL1 650
C REPLACE 0 BY SMALL VALUE DEL1 660
C DEL1 670
6 ANGLE=SQGEO*1.D-17 DEL1 680
7 TEST=AARI*1.D-9 DEL1 690
IF(DABS(AARI-GEO)-TEST)10,10,8 DEL1 700
8 GEO=SQGEO+SQGEO DEL1 710
PIM=PIM+PIM DEL1 720
IF(ANGLE)9,5,5 DEL1 730
9 PIM=PIM+3.1415926535897932 DEL1 740
GOTO 5 DEL1 750
10 IF(ANGLE)11,12,12 DEL1 760
11 PIM=PIM+3.1415926535897932 DEL1 770
12 RES=(DATAN(ARI/ANGLE)+PIM)/ARI DEL1 780
13 IF(X)14,15,15 DEL1 790
14 RES=-RES DEL1 800
15 RETURN DEL1 810
END DEL1 820