ddeabm.f File Reference

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Functions/Subroutines
subroutine	ddeabm (DF, NEQ, T, Y, TOUT, INFO, RTOL, ATOL, IDID, RWORK, LRW, IWORK, LIW, RPAR, IPAR)
subroutine	ddes (DF, NEQ, T, Y, TOUT, INFO, RTOL, ATOL, IDID, YPOUT, YP, YY, WT, P, PHI, ALPHA, BETA, PSI, V, W, SIG, G, GI, H, EPS, X, XOLD, HOLD, TOLD, DELSGN, TSTOP, TWOU, FOURU, START, PHASE1, NORND, STIFF, INTOUT, NS, KORD, KOLD, INIT, KSTEPS, KLE4, IQUIT, KPREV, IVC, IV, KGI, RPAR, IPAR)
subroutine	dintp (X, Y, XOUT, YOUT, YPOUT, NEQN, KOLD, PHI, IVC, IV, KGI, GI, ALPHA, OG, OW, OX, OY)
subroutine	xermsg (LIBRAR, SUBROU, MESSG, NERR, LEVEL)
subroutine	xerprn (PREFIX, NPREF, MESSG, NWRAP)
subroutine	xersve (LIBRAR, SUBROU, MESSG, KFLAG, NERR, LEVEL, ICOUNT)
double precision function	d1mach (I)
subroutine	xgetua (IUNITA, N)
subroutine	dsteps (DF, NEQN, Y, X, H, EPS, WT, START, HOLD, K, KOLD, CRASH, PHI, P, YP, PSI, ALPHA, BETA, SIG, V, W, G, PHASE1, NS, NORND, KSTEPS, TWOU, FOURU, XOLD, KPREV, IVC, IV, KGI, GI, RPAR, IPAR)
subroutine	fdump
integer function	i1mach (I)
subroutine	dhstrt (DF, NEQ, A, B, Y, YPRIME, ETOL, MORDER, SMALL, BIG, SPY, PV, YP, SF, RPAR, IPAR, H)
double precision function	dhvnrm (V, NCOMP)
function	j4save (IWHICH, IVALUE, ISET)
subroutine	xercnt (LIBRAR, SUBROU, MESSG, NERR, LEVEL, KONTRL)
subroutine	xerhlt (MESSG)

Function/Subroutine Documentation

d1mach()

double precision function d1mach

(

I

)

C***BEGIN PROLOGUE  D1MACH
C***PURPOSE  Return floating point machine dependent constants.
C***LIBRARY   SLATEC
C***CATEGORY  R1
C***TYPE      DOUBLE PRECISION (R1MACH-S, D1MACH-D)
C***KEYWORDS  MACHINE CONSTANTS
C***AUTHOR  Fox, P. A., (Bell Labs)
C           Hall, A. D., (Bell Labs)
C           Schryer, N. L., (Bell Labs)
C***DESCRIPTION
C
C   D1MACH can be used to obtain machine-dependent parameters for the
C   local machine environment.  It is a function subprogram with one
C   (input) argument, and can be referenced as follows:
C
C        D = D1MACH(I)
C
C   where I=1,...,5.  The (output) value of D above is determined by
C   the (input) value of I.  The results for various values of I are
C   discussed below.
C
C   D1MACH( 1) = B**(EMIN-1), the smallest positive magnitude.
C   D1MACH( 2) = B**EMAX*(1 - B**(-T)), the largest magnitude.
C   D1MACH( 3) = B**(-T), the smallest relative spacing.
C   D1MACH( 4) = B**(1-T), the largest relative spacing.
C   D1MACH( 5) = LOG10(B)
C
C   Assume double precision numbers are represented in the T-digit,
C   base-B form
C
C              sign (B**E)*( (X(1)/B) + ... + (X(T)/B**T) )
C
C   where 0 .LE. X(I) .LT. B for I=1,...,T, 0 .LT. X(1), and
C   EMIN .LE. E .LE. EMAX.
C
C   The values of B, T, EMIN and EMAX are provided in I1MACH as
C   follows:
C   I1MACH(10) = B, the base.
C   I1MACH(14) = T, the number of base-B digits.
C   I1MACH(15) = EMIN, the smallest exponent E.
C   I1MACH(16) = EMAX, the largest exponent E.
C
C   To alter this function for a particular environment, the desired
C   set of DATA statements should be activated by removing the C from
C   column 1.  Also, the values of D1MACH(1) - D1MACH(4) should be
C   checked for consistency with the local operating system.
C
C***REFERENCES  P. A. Fox, A. D. Hall and N. L. Schryer, Framework for
C                 a portable library, ACM Transactions on Mathematical
C                 Software 4, 2 (June 1978), pp. 177-188.
C***ROUTINES CALLED  XERMSG
C***REVISION HISTORY  (YYMMDD)
C   750101  DATE WRITTEN
C   890213  REVISION DATE from Version 3.2
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C   900315  CALLs to XERROR changed to CALLs to XERMSG.  (THJ)
C   900618  Added DEC RISC constants.  (WRB)
C   900723  Added IBM RS 6000 constants.  (WRB)
C   900911  Added SUN 386i constants.  (WRB)
C   910710  Added HP 730 constants.  (SMR)
C   911114  Added Convex IEEE constants.  (WRB)
C   920121  Added SUN -r8 compiler option constants.  (WRB)
C   920229  Added Touchstone Delta i860 constants.  (WRB)
C   920501  Reformatted the REFERENCES section.  (WRB)
C   920625  Added CONVEX -p8 and -pd8 compiler option constants.
C           (BKS, WRB)
C   930201  Added DEC Alpha and SGI constants.  (RWC and WRB)
C   010817  Elevated IEEE to highest importance; see next set of
C           comments below.  (DWL)
C***END PROLOGUE  D1MACH
C
      INTEGER small(4)
      INTEGER large(4)
      INTEGER right(4)
      INTEGER diver(4)
      INTEGER log10(4)
C
C Initial data here correspond to the IEEE standard.  The values for
C DMACH(1), DMACH(3) and DMACH(4) are slight upper bounds.  The value
C for DMACH(2) is a slight lower bound.  The value for DMACH(5) is
C a 20-digit approximation.  If one of the sets of initial data below
C is preferred, do the necessary commenting and uncommenting. (DWL)
      DOUBLE PRECISION dmach(5)
      DATA dmach / 2.23d-308, 1.79d+308, 1.111d-16, 2.222d-16,
     1             0.30102999566398119521d0 /
      SAVE dmach
C
cc      EQUIVALENCE (DMACH(1),SMALL(1))
cc      EQUIVALENCE (DMACH(2),LARGE(1))
cc      EQUIVALENCE (DMACH(3),RIGHT(1))
cc      EQUIVALENCE (DMACH(4),DIVER(1))
cc      EQUIVALENCE (DMACH(5),LOG10(1))
C
C     MACHINE CONSTANTS FOR THE AMIGA
C     ABSOFT FORTRAN COMPILER USING THE 68020/68881 COMPILER OPTION
C
C     DATA SMALL(1), SMALL(2) / Z'00100000', Z'00000000' /
C     DATA LARGE(1), LARGE(2) / Z'7FEFFFFF', Z'FFFFFFFF' /
C     DATA RIGHT(1), RIGHT(2) / Z'3CA00000', Z'00000000' /
C     DATA DIVER(1), DIVER(2) / Z'3CB00000', Z'00000000' /
C     DATA LOG10(1), LOG10(2) / Z'3FD34413', Z'509F79FF' /
C
C     MACHINE CONSTANTS FOR THE AMIGA
C     ABSOFT FORTRAN COMPILER USING SOFTWARE FLOATING POINT
C
C     DATA SMALL(1), SMALL(2) / Z'00100000', Z'00000000' /
C     DATA LARGE(1), LARGE(2) / Z'7FDFFFFF', Z'FFFFFFFF' /
C     DATA RIGHT(1), RIGHT(2) / Z'3CA00000', Z'00000000' /
C     DATA DIVER(1), DIVER(2) / Z'3CB00000', Z'00000000' /
C     DATA LOG10(1), LOG10(2) / Z'3FD34413', Z'509F79FF' /
C
C     MACHINE CONSTANTS FOR THE APOLLO
C
C     DATA SMALL(1), SMALL(2) / 16#00100000, 16#00000000 /
C     DATA LARGE(1), LARGE(2) / 16#7FFFFFFF, 16#FFFFFFFF /
C     DATA RIGHT(1), RIGHT(2) / 16#3CA00000, 16#00000000 /
C     DATA DIVER(1), DIVER(2) / 16#3CB00000, 16#00000000 /
C     DATA LOG10(1), LOG10(2) / 16#3FD34413, 16#509F79FF /
C
C     MACHINE CONSTANTS FOR THE BURROUGHS 1700 SYSTEM
C
C     DATA SMALL(1) / ZC00800000 /
C     DATA SMALL(2) / Z000000000 /
C     DATA LARGE(1) / ZDFFFFFFFF /
C     DATA LARGE(2) / ZFFFFFFFFF /
C     DATA RIGHT(1) / ZCC5800000 /
C     DATA RIGHT(2) / Z000000000 /
C     DATA DIVER(1) / ZCC6800000 /
C     DATA DIVER(2) / Z000000000 /
C     DATA LOG10(1) / ZD00E730E7 /
C     DATA LOG10(2) / ZC77800DC0 /
C
C     MACHINE CONSTANTS FOR THE BURROUGHS 5700 SYSTEM
C
C     DATA SMALL(1) / O1771000000000000 /
C     DATA SMALL(2) / O0000000000000000 /
C     DATA LARGE(1) / O0777777777777777 /
C     DATA LARGE(2) / O0007777777777777 /
C     DATA RIGHT(1) / O1461000000000000 /
C     DATA RIGHT(2) / O0000000000000000 /
C     DATA DIVER(1) / O1451000000000000 /
C     DATA DIVER(2) / O0000000000000000 /
C     DATA LOG10(1) / O1157163034761674 /
C     DATA LOG10(2) / O0006677466732724 /
C
C     MACHINE CONSTANTS FOR THE BURROUGHS 6700/7700 SYSTEMS
C
C     DATA SMALL(1) / O1771000000000000 /
C     DATA SMALL(2) / O7770000000000000 /
C     DATA LARGE(1) / O0777777777777777 /
C     DATA LARGE(2) / O7777777777777777 /
C     DATA RIGHT(1) / O1461000000000000 /
C     DATA RIGHT(2) / O0000000000000000 /
C     DATA DIVER(1) / O1451000000000000 /
C     DATA DIVER(2) / O0000000000000000 /
C     DATA LOG10(1) / O1157163034761674 /
C     DATA LOG10(2) / O0006677466732724 /
C
C     MACHINE CONSTANTS FOR THE CDC 170/180 SERIES USING NOS/VE
C
C     DATA SMALL(1) / Z"3001800000000000" /
C     DATA SMALL(2) / Z"3001000000000000" /
C     DATA LARGE(1) / Z"4FFEFFFFFFFFFFFE" /
C     DATA LARGE(2) / Z"4FFE000000000000" /
C     DATA RIGHT(1) / Z"3FD2800000000000" /
C     DATA RIGHT(2) / Z"3FD2000000000000" /
C     DATA DIVER(1) / Z"3FD3800000000000" /
C     DATA DIVER(2) / Z"3FD3000000000000" /
C     DATA LOG10(1) / Z"3FFF9A209A84FBCF" /
C     DATA LOG10(2) / Z"3FFFF7988F8959AC" /
C
C     MACHINE CONSTANTS FOR THE CDC 6000/7000 SERIES
C
C     DATA SMALL(1) / 00564000000000000000B /
C     DATA SMALL(2) / 00000000000000000000B /
C     DATA LARGE(1) / 37757777777777777777B /
C     DATA LARGE(2) / 37157777777777777777B /
C     DATA RIGHT(1) / 15624000000000000000B /
C     DATA RIGHT(2) / 00000000000000000000B /
C     DATA DIVER(1) / 15634000000000000000B /
C     DATA DIVER(2) / 00000000000000000000B /
C     DATA LOG10(1) / 17164642023241175717B /
C     DATA LOG10(2) / 16367571421742254654B /
C
C     MACHINE CONSTANTS FOR THE CELERITY C1260
C
C     DATA SMALL(1), SMALL(2) / Z'00100000', Z'00000000' /
C     DATA LARGE(1), LARGE(2) / Z'7FEFFFFF', Z'FFFFFFFF' /
C     DATA RIGHT(1), RIGHT(2) / Z'3CA00000', Z'00000000' /
C     DATA DIVER(1), DIVER(2) / Z'3CB00000', Z'00000000' /
C     DATA LOG10(1), LOG10(2) / Z'3FD34413', Z'509F79FF' /
C
C     MACHINE CONSTANTS FOR THE CONVEX
C     USING THE -fn OR -pd8 COMPILER OPTION
C
C     DATA DMACH(1) / Z'0010000000000000' /
C     DATA DMACH(2) / Z'7FFFFFFFFFFFFFFF' /
C     DATA DMACH(3) / Z'3CC0000000000000' /
C     DATA DMACH(4) / Z'3CD0000000000000' /
C     DATA DMACH(5) / Z'3FF34413509F79FF' /
C
C     MACHINE CONSTANTS FOR THE CONVEX
C     USING THE -fi COMPILER OPTION
C
C     DATA DMACH(1) / Z'0010000000000000' /
C     DATA DMACH(2) / Z'7FEFFFFFFFFFFFFF' /
C     DATA DMACH(3) / Z'3CA0000000000000' /
C     DATA DMACH(4) / Z'3CB0000000000000' /
C     DATA DMACH(5) / Z'3FD34413509F79FF' /
C
C     MACHINE CONSTANTS FOR THE CONVEX
C     USING THE -p8 COMPILER OPTION
C
C     DATA DMACH(1) / Z'00010000000000000000000000000000' /
C     DATA DMACH(2) / Z'7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF' /
C     DATA DMACH(3) / Z'3F900000000000000000000000000000' /
C     DATA DMACH(4) / Z'3F910000000000000000000000000000' /
C     DATA DMACH(5) / Z'3FFF34413509F79FEF311F12B35816F9' /
C
C     MACHINE CONSTANTS FOR THE CRAY
C
C     DATA SMALL(1) / 201354000000000000000B /
C     DATA SMALL(2) / 000000000000000000000B /
C     DATA LARGE(1) / 577767777777777777777B /
C     DATA LARGE(2) / 000007777777777777774B /
C     DATA RIGHT(1) / 376434000000000000000B /
C     DATA RIGHT(2) / 000000000000000000000B /
C     DATA DIVER(1) / 376444000000000000000B /
C     DATA DIVER(2) / 000000000000000000000B /
C     DATA LOG10(1) / 377774642023241175717B /
C     DATA LOG10(2) / 000007571421742254654B /
C
C     MACHINE CONSTANTS FOR THE DATA GENERAL ECLIPSE S/200
C     NOTE - IT MAY BE APPROPRIATE TO INCLUDE THE FOLLOWING CARD -
C     STATIC DMACH(5)
C
C     DATA SMALL /    20K, 3*0 /
C     DATA LARGE / 77777K, 3*177777K /
C     DATA RIGHT / 31420K, 3*0 /
C     DATA DIVER / 32020K, 3*0 /
C     DATA LOG10 / 40423K, 42023K, 50237K, 74776K /
C
C     MACHINE CONSTANTS FOR THE DEC ALPHA
C     USING G_FLOAT
C
C     DATA DMACH(1) / '0000000000000010'X /
C     DATA DMACH(2) / 'FFFFFFFFFFFF7FFF'X /
C     DATA DMACH(3) / '0000000000003CC0'X /
C     DATA DMACH(4) / '0000000000003CD0'X /
C     DATA DMACH(5) / '79FF509F44133FF3'X /
C
C     MACHINE CONSTANTS FOR THE DEC ALPHA
C     USING IEEE_FORMAT
C
C     DATA DMACH(1) / '0010000000000000'X /
C     DATA DMACH(2) / '7FEFFFFFFFFFFFFF'X /
C     DATA DMACH(3) / '3CA0000000000000'X /
C     DATA DMACH(4) / '3CB0000000000000'X /
C     DATA DMACH(5) / '3FD34413509F79FF'X /
C
C     MACHINE CONSTANTS FOR THE DEC RISC
C
C     DATA SMALL(1), SMALL(2) / Z'00000000', Z'00100000'/
C     DATA LARGE(1), LARGE(2) / Z'FFFFFFFF', Z'7FEFFFFF'/
C     DATA RIGHT(1), RIGHT(2) / Z'00000000', Z'3CA00000'/
C     DATA DIVER(1), DIVER(2) / Z'00000000', Z'3CB00000'/
C     DATA LOG10(1), LOG10(2) / Z'509F79FF', Z'3FD34413'/
C
C     MACHINE CONSTANTS FOR THE DEC VAX
C     USING D_FLOATING
C     (EXPRESSED IN INTEGER AND HEXADECIMAL)
C     THE HEX FORMAT BELOW MAY NOT BE SUITABLE FOR UNIX SYSTEMS
C     THE INTEGER FORMAT SHOULD BE OK FOR UNIX SYSTEMS
C
C     DATA SMALL(1), SMALL(2) /        128,           0 /
C     DATA LARGE(1), LARGE(2) /     -32769,          -1 /
C     DATA RIGHT(1), RIGHT(2) /       9344,           0 /
C     DATA DIVER(1), DIVER(2) /       9472,           0 /
C     DATA LOG10(1), LOG10(2) /  546979738,  -805796613 /
C
C     DATA SMALL(1), SMALL(2) / Z00000080, Z00000000 /
C     DATA LARGE(1), LARGE(2) / ZFFFF7FFF, ZFFFFFFFF /
C     DATA RIGHT(1), RIGHT(2) / Z00002480, Z00000000 /
C     DATA DIVER(1), DIVER(2) / Z00002500, Z00000000 /
C     DATA LOG10(1), LOG10(2) / Z209A3F9A, ZCFF884FB /
C
C     MACHINE CONSTANTS FOR THE DEC VAX
C     USING G_FLOATING
C     (EXPRESSED IN INTEGER AND HEXADECIMAL)
C     THE HEX FORMAT BELOW MAY NOT BE SUITABLE FOR UNIX SYSTEMS
C     THE INTEGER FORMAT SHOULD BE OK FOR UNIX SYSTEMS
C
C     DATA SMALL(1), SMALL(2) /         16,           0 /
C     DATA LARGE(1), LARGE(2) /     -32769,          -1 /
C     DATA RIGHT(1), RIGHT(2) /      15552,           0 /
C     DATA DIVER(1), DIVER(2) /      15568,           0 /
C     DATA LOG10(1), LOG10(2) /  1142112243, 2046775455 /
C
C     DATA SMALL(1), SMALL(2) / Z00000010, Z00000000 /
C     DATA LARGE(1), LARGE(2) / ZFFFF7FFF, ZFFFFFFFF /
C     DATA RIGHT(1), RIGHT(2) / Z00003CC0, Z00000000 /
C     DATA DIVER(1), DIVER(2) / Z00003CD0, Z00000000 /
C     DATA LOG10(1), LOG10(2) / Z44133FF3, Z79FF509F /
C
C     MACHINE CONSTANTS FOR THE ELXSI 6400
C     (ASSUMING REAL*8 IS THE DEFAULT DOUBLE PRECISION)
C
C     DATA SMALL(1), SMALL(2) / '00100000'X,'00000000'X /
C     DATA LARGE(1), LARGE(2) / '7FEFFFFF'X,'FFFFFFFF'X /
C     DATA RIGHT(1), RIGHT(2) / '3CB00000'X,'00000000'X /
C     DATA DIVER(1), DIVER(2) / '3CC00000'X,'00000000'X /
C     DATA LOG10(1), LOG10(2) / '3FD34413'X,'509F79FF'X /
C
C     MACHINE CONSTANTS FOR THE HARRIS 220
C
C     DATA SMALL(1), SMALL(2) / '20000000, '00000201 /
C     DATA LARGE(1), LARGE(2) / '37777777, '37777577 /
C     DATA RIGHT(1), RIGHT(2) / '20000000, '00000333 /
C     DATA DIVER(1), DIVER(2) / '20000000, '00000334 /
C     DATA LOG10(1), LOG10(2) / '23210115, '10237777 /
C
C     MACHINE CONSTANTS FOR THE HONEYWELL 600/6000 SERIES
C
C     DATA SMALL(1), SMALL(2) / O402400000000, O000000000000 /
C     DATA LARGE(1), LARGE(2) / O376777777777, O777777777777 /
C     DATA RIGHT(1), RIGHT(2) / O604400000000, O000000000000 /
C     DATA DIVER(1), DIVER(2) / O606400000000, O000000000000 /
C     DATA LOG10(1), LOG10(2) / O776464202324, O117571775714 /
C
C     MACHINE CONSTANTS FOR THE HP 730
C
C     DATA DMACH(1) / Z'0010000000000000' /
C     DATA DMACH(2) / Z'7FEFFFFFFFFFFFFF' /
C     DATA DMACH(3) / Z'3CA0000000000000' /
C     DATA DMACH(4) / Z'3CB0000000000000' /
C     DATA DMACH(5) / Z'3FD34413509F79FF' /
C
C     MACHINE CONSTANTS FOR THE HP 2100
C     THREE WORD DOUBLE PRECISION OPTION WITH FTN4
C
C     DATA SMALL(1), SMALL(2), SMALL(3) / 40000B,       0,       1 /
C     DATA LARGE(1), LARGE(2), LARGE(3) / 77777B, 177777B, 177776B /
C     DATA RIGHT(1), RIGHT(2), RIGHT(3) / 40000B,       0,    265B /
C     DATA DIVER(1), DIVER(2), DIVER(3) / 40000B,       0,    276B /
C     DATA LOG10(1), LOG10(2), LOG10(3) / 46420B,  46502B,  77777B /
C
C     MACHINE CONSTANTS FOR THE HP 2100
C     FOUR WORD DOUBLE PRECISION OPTION WITH FTN4
C
C     DATA SMALL(1), SMALL(2) /  40000B,       0 /
C     DATA SMALL(3), SMALL(4) /       0,       1 /
C     DATA LARGE(1), LARGE(2) /  77777B, 177777B /
C     DATA LARGE(3), LARGE(4) / 177777B, 177776B /
C     DATA RIGHT(1), RIGHT(2) /  40000B,       0 /
C     DATA RIGHT(3), RIGHT(4) /       0,    225B /
C     DATA DIVER(1), DIVER(2) /  40000B,       0 /
C     DATA DIVER(3), DIVER(4) /       0,    227B /
C     DATA LOG10(1), LOG10(2) /  46420B,  46502B /
C     DATA LOG10(3), LOG10(4) /  76747B, 176377B /
C
C     MACHINE CONSTANTS FOR THE HP 9000
C
C     DATA SMALL(1), SMALL(2) / 00040000000B, 00000000000B /
C     DATA LARGE(1), LARGE(2) / 17737777777B, 37777777777B /
C     DATA RIGHT(1), RIGHT(2) / 07454000000B, 00000000000B /
C     DATA DIVER(1), DIVER(2) / 07460000000B, 00000000000B /
C     DATA LOG10(1), LOG10(2) / 07764642023B, 12047674777B /
C
C     MACHINE CONSTANTS FOR THE IBM 360/370 SERIES,
C     THE XEROX SIGMA 5/7/9, THE SEL SYSTEMS 85/86, AND
C     THE PERKIN ELMER (INTERDATA) 7/32.
C
C     DATA SMALL(1), SMALL(2) / Z00100000, Z00000000 /
C     DATA LARGE(1), LARGE(2) / Z7FFFFFFF, ZFFFFFFFF /
C     DATA RIGHT(1), RIGHT(2) / Z33100000, Z00000000 /
C     DATA DIVER(1), DIVER(2) / Z34100000, Z00000000 /
C     DATA LOG10(1), LOG10(2) / Z41134413, Z509F79FF /
C
C     MACHINE CONSTANTS FOR THE IBM PC
C     ASSUMES THAT ALL ARITHMETIC IS DONE IN DOUBLE PRECISION
C     ON 8088, I.E., NOT IN 80 BIT FORM FOR THE 8087.
C
C     DATA SMALL(1) / 2.23D-308  /
C     DATA LARGE(1) / 1.79D+308  /
C     DATA RIGHT(1) / 1.11D-16   /
C     DATA DIVER(1) / 2.22D-16   /
C     DATA LOG10(1) / 0.301029995663981195D0 /
C
C     MACHINE CONSTANTS FOR THE IBM RS 6000
C
C     DATA DMACH(1) / Z'0010000000000000' /
C     DATA DMACH(2) / Z'7FEFFFFFFFFFFFFF' /
C     DATA DMACH(3) / Z'3CA0000000000000' /
C     DATA DMACH(4) / Z'3CB0000000000000' /
C     DATA DMACH(5) / Z'3FD34413509F79FF' /
C
C     MACHINE CONSTANTS FOR THE INTEL i860
C
C     DATA DMACH(1) / Z'0010000000000000' /
C     DATA DMACH(2) / Z'7FEFFFFFFFFFFFFF' /
C     DATA DMACH(3) / Z'3CA0000000000000' /
C     DATA DMACH(4) / Z'3CB0000000000000' /
C     DATA DMACH(5) / Z'3FD34413509F79FF' /
C
C     MACHINE CONSTANTS FOR THE PDP-10 (KA PROCESSOR)
C
C     DATA SMALL(1), SMALL(2) / "033400000000, "000000000000 /
C     DATA LARGE(1), LARGE(2) / "377777777777, "344777777777 /
C     DATA RIGHT(1), RIGHT(2) / "113400000000, "000000000000 /
C     DATA DIVER(1), DIVER(2) / "114400000000, "000000000000 /
C     DATA LOG10(1), LOG10(2) / "177464202324, "144117571776 /
C
C     MACHINE CONSTANTS FOR THE PDP-10 (KI PROCESSOR)
C
C     DATA SMALL(1), SMALL(2) / "000400000000, "000000000000 /
C     DATA LARGE(1), LARGE(2) / "377777777777, "377777777777 /
C     DATA RIGHT(1), RIGHT(2) / "103400000000, "000000000000 /
C     DATA DIVER(1), DIVER(2) / "104400000000, "000000000000 /
C     DATA LOG10(1), LOG10(2) / "177464202324, "476747767461 /
C
C     MACHINE CONSTANTS FOR PDP-11 FORTRAN SUPPORTING
C     32-BIT INTEGERS (EXPRESSED IN INTEGER AND OCTAL).
C
C     DATA SMALL(1), SMALL(2) /    8388608,           0 /
C     DATA LARGE(1), LARGE(2) / 2147483647,          -1 /
C     DATA RIGHT(1), RIGHT(2) /  612368384,           0 /
C     DATA DIVER(1), DIVER(2) /  620756992,           0 /
C     DATA LOG10(1), LOG10(2) / 1067065498, -2063872008 /
C
C     DATA SMALL(1), SMALL(2) / O00040000000, O00000000000 /
C     DATA LARGE(1), LARGE(2) / O17777777777, O37777777777 /
C     DATA RIGHT(1), RIGHT(2) / O04440000000, O00000000000 /
C     DATA DIVER(1), DIVER(2) / O04500000000, O00000000000 /
C     DATA LOG10(1), LOG10(2) / O07746420232, O20476747770 /
C
C     MACHINE CONSTANTS FOR PDP-11 FORTRAN SUPPORTING
C     16-BIT INTEGERS (EXPRESSED IN INTEGER AND OCTAL).
C
C     DATA SMALL(1), SMALL(2) /    128,      0 /
C     DATA SMALL(3), SMALL(4) /      0,      0 /
C     DATA LARGE(1), LARGE(2) /  32767,     -1 /
C     DATA LARGE(3), LARGE(4) /     -1,     -1 /
C     DATA RIGHT(1), RIGHT(2) /   9344,      0 /
C     DATA RIGHT(3), RIGHT(4) /      0,      0 /
C     DATA DIVER(1), DIVER(2) /   9472,      0 /
C     DATA DIVER(3), DIVER(4) /      0,      0 /
C     DATA LOG10(1), LOG10(2) /  16282,   8346 /
C     DATA LOG10(3), LOG10(4) / -31493, -12296 /
C
C     DATA SMALL(1), SMALL(2) / O000200, O000000 /
C     DATA SMALL(3), SMALL(4) / O000000, O000000 /
C     DATA LARGE(1), LARGE(2) / O077777, O177777 /
C     DATA LARGE(3), LARGE(4) / O177777, O177777 /
C     DATA RIGHT(1), RIGHT(2) / O022200, O000000 /
C     DATA RIGHT(3), RIGHT(4) / O000000, O000000 /
C     DATA DIVER(1), DIVER(2) / O022400, O000000 /
C     DATA DIVER(3), DIVER(4) / O000000, O000000 /
C     DATA LOG10(1), LOG10(2) / O037632, O020232 /
C     DATA LOG10(3), LOG10(4) / O102373, O147770 /
C
C     MACHINE CONSTANTS FOR THE SILICON GRAPHICS
C
C     DATA SMALL(1), SMALL(2) / Z'00100000', Z'00000000' /
C     DATA LARGE(1), LARGE(2) / Z'7FEFFFFF', Z'FFFFFFFF' /
C     DATA RIGHT(1), RIGHT(2) / Z'3CA00000', Z'00000000' /
C     DATA DIVER(1), DIVER(2) / Z'3CB00000', Z'00000000' /
C     DATA LOG10(1), LOG10(2) / Z'3FD34413', Z'509F79FF' /
C
C     MACHINE CONSTANTS FOR THE SUN
C
C     DATA DMACH(1) / Z'0010000000000000' /
C     DATA DMACH(2) / Z'7FEFFFFFFFFFFFFF' /
C     DATA DMACH(3) / Z'3CA0000000000000' /
C     DATA DMACH(4) / Z'3CB0000000000000' /
C     DATA DMACH(5) / Z'3FD34413509F79FF' /
C
C     MACHINE CONSTANTS FOR THE SUN
C     USING THE -r8 COMPILER OPTION
C
C     DATA DMACH(1) / Z'00010000000000000000000000000000' /
C     DATA DMACH(2) / Z'7FFEFFFFFFFFFFFFFFFFFFFFFFFFFFFF' /
C     DATA DMACH(3) / Z'3F8E0000000000000000000000000000' /
C     DATA DMACH(4) / Z'3F8F0000000000000000000000000000' /
C     DATA DMACH(5) / Z'3FFD34413509F79FEF311F12B35816F9' /
C
C     MACHINE CONSTANTS FOR THE SUN 386i
C
C     DATA SMALL(1), SMALL(2) / Z'FFFFFFFD', Z'000FFFFF' /
C     DATA LARGE(1), LARGE(2) / Z'FFFFFFB0', Z'7FEFFFFF' /
C     DATA RIGHT(1), RIGHT(2) / Z'000000B0', Z'3CA00000' /
C     DATA DIVER(1), DIVER(2) / Z'FFFFFFCB', Z'3CAFFFFF'
C     DATA LOG10(1), LOG10(2) / Z'509F79E9', Z'3FD34413' /
C
C     MACHINE CONSTANTS FOR THE UNIVAC 1100 SERIES FTN COMPILER
C
C     DATA SMALL(1), SMALL(2) / O000040000000, O000000000000 /
C     DATA LARGE(1), LARGE(2) / O377777777777, O777777777777 /
C     DATA RIGHT(1), RIGHT(2) / O170540000000, O000000000000 /
C     DATA DIVER(1), DIVER(2) / O170640000000, O000000000000 /
C     DATA LOG10(1), LOG10(2) / O177746420232, O411757177572 /
C
C***FIRST EXECUTABLE STATEMENT  D1MACH
      IF (i .LT. 1 .OR. i .GT. 5) CALL xermsg ('SLATEC', 'D1MACH',
     +   'I OUT OF BOUNDS', 1, 2)
C
      d1mach = dmach(i)
      RETURN
C

ddeabm()

subroutine ddeabm	(	external	DF,
		integer	NEQ,
		double precision	T,
		double precision, dimension(*)	Y,
		double precision	TOUT,
		integer, dimension(15)	INFO,
		double precision, dimension(*)	RTOL,
		double precision, dimension(*)	ATOL,
		integer	IDID,
		double precision, dimension(*)	RWORK,
		integer	LRW,
		integer, dimension(*)	IWORK,
		integer	LIW,
		double precision, dimension(*)	RPAR,
		integer, dimension(*)	IPAR
	)

C***BEGIN PROLOGUE  DDEABM
C***PURPOSE  Solve an initial value problem in ordinary differential
C            equations using an Adams-Bashforth method.
C***LIBRARY   SLATEC (DEPAC)
C***CATEGORY  I1A1B
C***TYPE      DOUBLE PRECISION (DEABM-S, DDEABM-D)
C***KEYWORDS  ADAMS-BASHFORTH METHOD, DEPAC, INITIAL VALUE PROBLEMS,
C             ODE, ORDINARY DIFFERENTIAL EQUATIONS, PREDICTOR-CORRECTOR
C***AUTHOR  Shampine, L. F., (SNLA)
C           Watts, H. A., (SNLA)
C***DESCRIPTION
C
C   This is the Adams code in the package of differential equation
C   solvers DEPAC, consisting of the codes DDERKF, DDEABM, and DDEBDF.
C   Design of the package was by L. F. Shampine and H. A. Watts.
C   It is documented in
C        SAND79-2374 , DEPAC - Design of a User Oriented Package of ODE
C                              Solvers.
C   DDEABM is a driver for a modification of the code ODE written by
C             L. F. Shampine and M. K. Gordon
C             Sandia Laboratories
C             Albuquerque, New Mexico 87185
C
C **********************************************************************
C * ABSTRACT *
C ************
C
C   Subroutine DDEABM uses the Adams-Bashforth-Moulton
C   Predictor-Corrector formulas of orders one through twelve to
C   integrate a system of NEQ first order ordinary differential
C   equations of the form
C                         DU/DX = DF(X,U)
C   when the vector Y(*) of initial values for U(*) at X=T is given.
C   The subroutine integrates from T to TOUT. It is easy to continue the
C   integration to get results at additional TOUT.  This is the interval
C   mode of operation.  It is also easy for the routine to return with
C   the solution at each intermediate step on the way to TOUT.  This is
C   the intermediate-output mode of operation.
C
C   DDEABM uses subprograms DDES, DSTEPS, DINTP, DHSTRT, DHVNRM,
C   D1MACH, and the error handling routine XERMSG.  The only machine
C   dependent parameters to be assigned appear in D1MACH.
C
C **********************************************************************
C * Description of The Arguments To DDEABM (An Overview) *
C **********************************************************************
C
C   The Parameters are
C
C      DF -- This is the name of a subroutine which you provide to
C             define the differential equations.
C
C      NEQ -- This is the number of (first order) differential
C             equations to be integrated.
C
C      T -- This is a DOUBLE PRECISION value of the independent
C           variable.
C
C      Y(*) -- This DOUBLE PRECISION array contains the solution
C              components at T.
C
C      TOUT -- This is a DOUBLE PRECISION point at which a solution is
C              desired.
C
C      INFO(*) -- The basic task of the code is to integrate the
C             differential equations from T to TOUT and return an
C             answer at TOUT.  INFO(*) is an INTEGER array which is used
C             to communicate exactly how you want this task to be
C             carried out.
C
C      RTOL, ATOL -- These DOUBLE PRECISION quantities represent
C                    relative and absolute error tolerances which you
C                    provide to indicate how accurately you wish the
C                    solution to be computed.  You may choose them to be
C                    both scalars or else both vectors.
C
C      IDID -- This scalar quantity is an indicator reporting what
C             the code did.  You must monitor this INTEGER variable to
C             decide what action to take next.
C
C      RWORK(*), LRW -- RWORK(*) is a DOUBLE PRECISION work array of
C             length LRW which provides the code with needed storage
C             space.
C
C      IWORK(*), LIW -- IWORK(*) is an INTEGER work array of length LIW
C             which provides the code with needed storage space and an
C             across call flag.
C
C      RPAR, IPAR -- These are DOUBLE PRECISION and INTEGER parameter
C             arrays which you can use for communication between your
C             calling program and the DF subroutine.
C
C  Quantities which are used as input items are
C             NEQ, T, Y(*), TOUT, INFO(*),
C             RTOL, ATOL, RWORK(1), LRW and LIW.
C
C  Quantities which may be altered by the code are
C             T, Y(*), INFO(1), RTOL, ATOL,
C             IDID, RWORK(*) and IWORK(*).
C
C **********************************************************************
C * INPUT -- What To Do On The First Call To DDEABM *
C **********************************************************************
C
C   The first call of the code is defined to be the start of each new
C   problem.  Read through the descriptions of all the following items,
C   provide sufficient storage space for designated arrays, set
C   appropriate variables for the initialization of the problem, and
C   give information about how you want the problem to be solved.
C
C
C      DF -- Provide a subroutine of the form
C                               DF(X,U,UPRIME,RPAR,IPAR)
C             to define the system of first order differential equations
C             which is to be solved.  For the given values of X and the
C             vector  U(*)=(U(1),U(2),...,U(NEQ)) , the subroutine must
C             evaluate the NEQ components of the system of differential
C             equations  DU/DX=DF(X,U)  and store the derivatives in the
C             array UPRIME(*), that is,  UPRIME(I) = * DU(I)/DX *  for
C             equations I=1,...,NEQ.
C
C             Subroutine DF must NOT alter X or U(*).  You must declare
C             the name df in an external statement in your program that
C             calls DDEABM.  You must dimension U and UPRIME in DF.
C
C             RPAR and IPAR are DOUBLE PRECISION and INTEGER parameter
C             arrays which you can use for communication between your
C             calling program and subroutine DF. They are not used or
C             altered by DDEABM.  If you do not need RPAR or IPAR,
C             ignore these parameters by treating them as dummy
C             arguments. If you do choose to use them, dimension them in
C             your calling program and in DF as arrays of appropriate
C             length.
C
C      NEQ -- Set it to the number of differential equations.
C             (NEQ .GE. 1)
C
C      T -- Set it to the initial point of the integration.
C             You must use a program variable for T because the code
C             changes its value.
C
C      Y(*) -- Set this vector to the initial values of the NEQ solution
C             components at the initial point.  You must dimension Y at
C             least NEQ in your calling program.
C
C      TOUT -- Set it to the first point at which a solution
C             is desired.  You can take TOUT = T, in which case the code
C             will evaluate the derivative of the solution at T and
C             return. Integration either forward in T  (TOUT .GT. T)  or
C             backward in T  (TOUT .LT. T)  is permitted.
C
C             The code advances the solution from T to TOUT using
C             step sizes which are automatically selected so as to
C             achieve the desired accuracy.  If you wish, the code will
C             return with the solution and its derivative following
C             each intermediate step (intermediate-output mode) so that
C             you can monitor them, but you still must provide TOUT in
C             accord with the basic aim of the code.
C
C             The first step taken by the code is a critical one
C             because it must reflect how fast the solution changes near
C             the initial point.  The code automatically selects an
C             initial step size which is practically always suitable for
C             the problem. By using the fact that the code will not step
C             past TOUT in the first step, you could, if necessary,
C             restrict the length of the initial step size.
C
C             For some problems it may not be permissible to integrate
C             past a point TSTOP because a discontinuity occurs there
C             or the solution or its derivative is not defined beyond
C             TSTOP.  When you have declared a TSTOP point (see INFO(4)
C             and RWORK(1)), you have told the code not to integrate
C             past TSTOP.  In this case any TOUT beyond TSTOP is invalid
C             input.
C
C      INFO(*) -- Use the INFO array to give the code more details about
C             how you want your problem solved.  This array should be
C             dimensioned of length 15 to accommodate other members of
C             DEPAC or possible future extensions, though DDEABM uses
C             only the first four entries.  You must respond to all of
C             the following items which are arranged as questions.  The
C             simplest use of the code corresponds to answering all
C             questions as YES ,i.e. setting ALL entries of INFO to 0.
C
C        INFO(1) -- This parameter enables the code to initialize
C               itself.  You must set it to indicate the start of every
C               new problem.
C
C            **** Is this the first call for this problem ...
C                  YES -- set INFO(1) = 0
C                   NO -- not applicable here.
C                         See below for continuation calls.  ****
C
C        INFO(2) -- How much accuracy you want of your solution
C               is specified by the error tolerances RTOL and ATOL.
C               The simplest use is to take them both to be scalars.
C               To obtain more flexibility, they can both be vectors.
C               The code must be told your choice.
C
C            **** Are both error tolerances RTOL, ATOL scalars ...
C                  YES -- set INFO(2) = 0
C                         and input scalars for both RTOL and ATOL
C                   NO -- set INFO(2) = 1
C                         and input arrays for both RTOL and ATOL ****
C
C        INFO(3) -- The code integrates from T in the direction
C               of TOUT by steps.  If you wish, it will return the
C               computed solution and derivative at the next
C               intermediate step (the intermediate-output mode) or
C               TOUT, whichever comes first.  This is a good way to
C               proceed if you want to see the behavior of the solution.
C               If you must have solutions at a great many specific
C               TOUT points, this code will compute them efficiently.
C
C            **** Do you want the solution only at
C                 TOUT (and not at the next intermediate step) ...
C                  YES -- set INFO(3) = 0
C                   NO -- set INFO(3) = 1 ****
C
C        INFO(4) -- To handle solutions at a great many specific
C               values TOUT efficiently, this code may integrate past
C               TOUT and interpolate to obtain the result at TOUT.
C               Sometimes it is not possible to integrate beyond some
C               point TSTOP because the equation changes there or it is
C               not defined past TSTOP.  Then you must tell the code
C               not to go past.
C
C            **** Can the integration be carried out without any
C                 Restrictions on the independent variable T ...
C                  YES -- set INFO(4)=0
C                   NO -- set INFO(4)=1
C                         and define the stopping point TSTOP by
C                         setting RWORK(1)=TSTOP ****
C
C      RTOL, ATOL -- You must assign relative (RTOL) and absolute (ATOL)
C             error tolerances to tell the code how accurately you want
C             the solution to be computed.  They must be defined as
C             program variables because the code may change them.  You
C             have two choices --
C                  Both RTOL and ATOL are scalars. (INFO(2)=0)
C                  Both RTOL and ATOL are vectors. (INFO(2)=1)
C             In either case all components must be non-negative.
C
C             The tolerances are used by the code in a local error test
C             at each step which requires roughly that
C                     ABS(LOCAL ERROR) .LE. RTOL*ABS(Y)+ATOL
C             for each vector component.
C             (More specifically, a Euclidean norm is used to measure
C             the size of vectors, and the error test uses the magnitude
C             of the solution at the beginning of the step.)
C
C             The true (global) error is the difference between the true
C             solution of the initial value problem and the computed
C             approximation.  Practically all present day codes,
C             including this one, control the local error at each step
C             and do not even attempt to control the global error
C             directly.  Roughly speaking, they produce a solution Y(T)
C             which satisfies the differential equations with a
C             residual R(T),    DY(T)/DT = DF(T,Y(T)) + R(T)   ,
C             and, almost always, R(T) is bounded by the error
C             tolerances.  Usually, but not always, the true accuracy of
C             the computed Y is comparable to the error tolerances. This
C             code will usually, but not always, deliver a more accurate
C             solution if you reduce the tolerances and integrate again.
C             By comparing two such solutions you can get a fairly
C             reliable idea of the true error in the solution at the
C             bigger tolerances.
C
C             Setting ATOL=0.D0 results in a pure relative error test on
C             that component. Setting RTOL=0. results in a pure absolute
C             error test on that component.  A mixed test with non-zero
C             RTOL and ATOL corresponds roughly to a relative error
C             test when the solution component is much bigger than ATOL
C             and to an absolute error test when the solution component
C             is smaller than the threshold ATOL.
C
C             Proper selection of the absolute error control parameters
C             ATOL  requires you to have some idea of the scale of the
C             solution components.  To acquire this information may mean
C             that you will have to solve the problem more than once. In
C             the absence of scale information, you should ask for some
C             relative accuracy in all the components (by setting  RTOL
C             values non-zero) and perhaps impose extremely small
C             absolute error tolerances to protect against the danger of
C             a solution component becoming zero.
C
C             The code will not attempt to compute a solution at an
C             accuracy unreasonable for the machine being used.  It will
C             advise you if you ask for too much accuracy and inform
C             you as to the maximum accuracy it believes possible.
C
C      RWORK(*) -- Dimension this DOUBLE PRECISION work array of length
C             LRW in your calling program.
C
C      RWORK(1) -- If you have set INFO(4)=0, you can ignore this
C             optional input parameter.  Otherwise you must define a
C             stopping point TSTOP by setting   RWORK(1) = TSTOP.
C             (for some problems it may not be permissible to integrate
C             past a point TSTOP because a discontinuity occurs there
C             or the solution or its derivative is not defined beyond
C             TSTOP.)
C
C      LRW -- Set it to the declared length of the RWORK array.
C             You must have  LRW .GE. 130+21*NEQ
C
C      IWORK(*) -- Dimension this INTEGER work array of length LIW in
C             your calling program.
C
C      LIW -- Set it to the declared length of the IWORK array.
C             You must have  LIW .GE. 51
C
C      RPAR, IPAR -- These are parameter arrays, of DOUBLE PRECISION and
C             INTEGER type, respectively.  You can use them for
C             communication between your program that calls DDEABM and
C             the  DF subroutine.  They are not used or altered by
C             DDEABM.  If you do not need RPAR or IPAR, ignore these
C             parameters by treating them as dummy arguments.  If you do
C             choose to use them, dimension them in your calling program
C             and in DF as arrays of appropriate length.
C
C **********************************************************************
C * OUTPUT -- After Any Return From DDEABM *
C **********************************************************************
C
C   The principal aim of the code is to return a computed solution at
C   TOUT, although it is also possible to obtain intermediate results
C   along the way.  To find out whether the code achieved its goal
C   or if the integration process was interrupted before the task was
C   completed, you must check the IDID parameter.
C
C
C      T -- The solution was successfully advanced to the
C             output value of T.
C
C      Y(*) -- Contains the computed solution approximation at T.
C             You may also be interested in the approximate derivative
C             of the solution at T.  It is contained in
C             RWORK(21),...,RWORK(20+NEQ).
C
C      IDID -- Reports what the code did
C
C                         *** Task Completed ***
C                   Reported by positive values of IDID
C
C             IDID = 1 -- A step was successfully taken in the
C                       intermediate-output mode.  The code has not
C                       yet reached TOUT.
C
C             IDID = 2 -- The integration to TOUT was successfully
C                       completed (T=TOUT) by stepping exactly to TOUT.
C
C             IDID = 3 -- The integration to TOUT was successfully
C                       completed (T=TOUT) by stepping past TOUT.
C                       Y(*) is obtained by interpolation.
C
C                         *** Task Interrupted ***
C                   Reported by negative values of IDID
C
C             IDID = -1 -- A large amount of work has been expended.
C                       (500 steps attempted)
C
C             IDID = -2 -- The error tolerances are too stringent.
C
C             IDID = -3 -- The local error test cannot be satisfied
C                       because you specified a zero component in ATOL
C                       and the corresponding computed solution
C                       component is zero.  Thus, a pure relative error
C                       test is impossible for this component.
C
C             IDID = -4 -- The problem appears to be stiff.
C
C             IDID = -5,-6,-7,..,-32  -- Not applicable for this code
C                       but used by other members of DEPAC or possible
C                       future extensions.
C
C                         *** Task Terminated ***
C                   Reported by the value of IDID=-33
C
C             IDID = -33 -- The code has encountered trouble from which
C                       it cannot recover.  A message is printed
C                       explaining the trouble and control is returned
C                       to the calling program. For example, this occurs
C                       when invalid input is detected.
C
C      RTOL, ATOL -- These quantities remain unchanged except when
C             IDID = -2.  In this case, the error tolerances have been
C             increased by the code to values which are estimated to be
C             appropriate for continuing the integration.  However, the
C             reported solution at T was obtained using the input values
C             of RTOL and ATOL.
C
C      RWORK, IWORK -- Contain information which is usually of no
C             interest to the user but necessary for subsequent calls.
C             However, you may find use for
C
C             RWORK(11)--which contains the step size H to be
C                        attempted on the next step.
C
C             RWORK(12)--if the tolerances have been increased by the
C                        code (IDID = -2) , they were multiplied by the
C                        value in RWORK(12).
C
C             RWORK(13)--Which contains the current value of the
C                        independent variable, i.e. the farthest point
C                        integration has reached. This will be different
C                        from T only when interpolation has been
C                        performed (IDID=3).
C
C             RWORK(20+I)--Which contains the approximate derivative
C                        of the solution component Y(I).  In DDEABM, it
C                        is obtained by calling subroutine DF to
C                        evaluate the differential equation using T and
C                        Y(*) when IDID=1 or 2, and by interpolation
C                        when IDID=3.
C
C **********************************************************************
C * INPUT -- What To Do To Continue The Integration *
C *             (calls after the first)             *
C **********************************************************************
C
C        This code is organized so that subsequent calls to continue the
C        integration involve little (if any) additional effort on your
C        part. You must monitor the IDID parameter in order to determine
C        what to do next.
C
C        Recalling that the principal task of the code is to integrate
C        from T to TOUT (the interval mode), usually all you will need
C        to do is specify a new TOUT upon reaching the current TOUT.
C
C        Do not alter any quantity not specifically permitted below,
C        in particular do not alter NEQ, T, Y(*), RWORK(*), IWORK(*) or
C        the differential equation in subroutine DF. Any such alteration
C        constitutes a new problem and must be treated as such, i.e.
C        you must start afresh.
C
C        You cannot change from vector to scalar error control or vice
C        versa (INFO(2)) but you can change the size of the entries of
C        RTOL, ATOL.  Increasing a tolerance makes the equation easier
C        to integrate.  Decreasing a tolerance will make the equation
C        harder to integrate and should generally be avoided.
C
C        You can switch from the intermediate-output mode to the
C        interval mode (INFO(3)) or vice versa at any time.
C
C        If it has been necessary to prevent the integration from going
C        past a point TSTOP (INFO(4), RWORK(1)), keep in mind that the
C        code will not integrate to any TOUT beyond the currently
C        specified TSTOP.  Once TSTOP has been reached you must change
C        the value of TSTOP or set INFO(4)=0.  You may change INFO(4)
C        or TSTOP at any time but you must supply the value of TSTOP in
C        RWORK(1) whenever you set INFO(4)=1.
C
C        The parameter INFO(1) is used by the code to indicate the
C        beginning of a new problem and to indicate whether integration
C        is to be continued.  You must input the value  INFO(1) = 0
C        when starting a new problem.  You must input the value
C        INFO(1) = 1  if you wish to continue after an interrupted task.
C        Do not set  INFO(1) = 0  on a continuation call unless you
C        want the code to restart at the current T.
C
C                         *** Following A Completed Task ***
C         If
C             IDID = 1, call the code again to continue the integration
C                     another step in the direction of TOUT.
C
C             IDID = 2 or 3, define a new TOUT and call the code again.
C                     TOUT must be different from T. You cannot change
C                     the direction of integration without restarting.
C
C                         *** Following An Interrupted Task ***
C                     To show the code that you realize the task was
C                     interrupted and that you want to continue, you
C                     must take appropriate action and reset INFO(1) = 1
C         If
C             IDID = -1, the code has attempted 500 steps.
C                     If you want to continue, set INFO(1) = 1 and
C                     call the code again. An additional 500 steps
C                     will be allowed.
C
C             IDID = -2, the error tolerances RTOL, ATOL have been
C                     increased to values the code estimates appropriate
C                     for continuing.  You may want to change them
C                     yourself.  If you are sure you want to continue
C                     with relaxed error tolerances, set INFO(1)=1 and
C                     call the code again.
C
C             IDID = -3, a solution component is zero and you set the
C                     corresponding component of ATOL to zero.  If you
C                     are sure you want to continue, you must first
C                     alter the error criterion to use positive values
C                     for those components of ATOL corresponding to zero
C                     solution components, then set INFO(1)=1 and call
C                     the code again.
C
C             IDID = -4, the problem appears to be stiff.  It is very
C                     inefficient to solve such problems with DDEABM.
C                     The code DDEBDF in DEPAC handles this task
C                     efficiently.  If you are absolutely sure you want
C                     to continue with DDEABM, set INFO(1)=1 and call
C                     the code again.
C
C             IDID = -5,-6,-7,..,-32  --- cannot occur with this code
C                     but used by other members of DEPAC or possible
C                     future extensions.
C
C                         *** Following A Terminated Task ***
C         If
C             IDID = -33, you cannot continue the solution of this
C                     problem.  An attempt to do so will result in your
C                     run being terminated.
C
C **********************************************************************
C *Long Description:
C
C **********************************************************************
C *             DEPAC Package Overview           *
C **********************************************************************
C
C ....   You have a choice of three differential equation solvers from
C ....   DEPAC. The following brief descriptions are meant to aid you in
C ....   choosing the most appropriate code for your problem.
C
C ....   DDERKF is a fifth order Runge-Kutta code. It is the simplest of
C ....   the three choices, both algorithmically and in the use of the
C ....   code. DDERKF is primarily designed to solve non-stiff and
C ....   mildly stiff differential equations when derivative evaluations
C ....   are not expensive. It should generally not be used to get high
C ....   accuracy results nor answers at a great many specific points.
C ....   Because DDERKF has very low overhead costs, it will usually
C ....   result in the least expensive integration when solving
C ....   problems requiring a modest amount of accuracy and having
C ....   equations that are not costly to evaluate. DDERKF attempts to
C ....   discover when it is not suitable for the task posed.
C
C ....   DDEABM is a variable order (one through twelve) Adams code.
C ....   Its complexity lies somewhere between that of DDERKF and
C ....   DDEBDF.  DDEABM is primarily designed to solve non-stiff and
C ....   mildly stiff differential equations when derivative evaluations
C ....   are expensive, high accuracy results are needed or answers at
C ....   many specific points are required. DDEABM attempts to discover
C ....   when it is not suitable for the task posed.
C
C ....   DDEBDF is a variable order (one through five) backward
C ....   differentiation formula code. it is the most complicated of
C ....   the three choices. DDEBDF is primarily designed to solve stiff
C ....   differential equations at crude to moderate tolerances.
C ....   If the problem is very stiff at all, DDERKF and DDEABM will be
C ....   quite inefficient compared to DDEBDF. However, DDEBDF will be
C ....   inefficient compared to DDERKF and DDEABM on non-stiff problems
C ....   because it uses much more storage, has a much larger overhead,
C ....   and the low order formulas will not give high accuracies
C ....   efficiently.
C
C ....   The concept of stiffness cannot be described in a few words.
C ....   If you do not know the problem to be stiff, try either DDERKF
C ....   or DDEABM. Both of these codes will inform you of stiffness
C ....   when the cost of solving such problems becomes important.
C
C *********************************************************************
C
C***REFERENCES  L. F. Shampine and H. A. Watts, DEPAC - design of a user
C                 oriented package of ODE solvers, Report SAND79-2374,
C                 Sandia Laboratories, 1979.
C***ROUTINES CALLED  DDES, XERMSG
C***REVISION HISTORY  (YYMMDD)
C   820301  DATE WRITTEN
C   890531  Changed all specific intrinsics to generic.  (WRB)
C   890831  Modified array declarations.  (WRB)
C   891006  Cosmetic changes to prologue.  (WRB)
C   891024  Changed references from DVNORM to DHVNRM.  (WRB)
C   891024  REVISION DATE from Version 3.2
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C   900510  Convert XERRWV calls to XERMSG calls.  (RWC)
C   920501  Reformatted the REFERENCES section.  (WRB)
C***END PROLOGUE  DDEABM
C
      INTEGER ialpha, ibeta, idelsn, idid, ifouru, ig, ihold,
     1      info, ip, ipar, iphi, ipsi, isig, itold, itstar, itwou,
     2      iv, iw, iwork, iwt, iyp, iypout, iyy, liw, lrw, neq
      DOUBLE PRECISION atol, rpar, rtol, rwork, t, tout, y
      LOGICAL start,phase1,nornd,stiff,intout
C
      dimension y(*),info(15),rtol(*),atol(*),rwork(*),iwork(*),
     1          rpar(*),ipar(*)
C
      CHARACTER*8 xern1
      CHARACTER*16 xern3
C
      EXTERNAL df
C
C     CHECK FOR AN APPARENT INFINITE LOOP
C
C***FIRST EXECUTABLE STATEMENT  DDEABM
      IF ( info(1) .EQ. 0 ) iwork(liw) = 0
      IF (iwork(liw) .GE. 5) THEN
         IF (t .EQ. rwork(21 + neq)) THEN
            WRITE (xern3, '(1PE15.6)') t
            CALL xermsg ('SLATEC', 'DDEABM',
     *         'AN APPARENT INFINITE LOOP HAS BEEN DETECTED.$$' //
     *         'YOU HAVE MADE REPEATED CALLS AT T = ' // xern3 //
     *         ' AND THE INTEGRATION HAS NOT ADVANCED.  CHECK THE ' //
     *         'WAY YOU HAVE SET PARAMETERS FOR THE CALL TO THE ' //
     *         'CODE, PARTICULARLY INFO(1).', 13, 2)
            RETURN
         ENDIF
      ENDIF
C
C     CHECK LRW AND LIW FOR SUFFICIENT STORAGE ALLOCATION
C
      idid=0
      IF (lrw .LT. 130+21*neq) THEN
         WRITE (xern1, '(I8)') lrw
         CALL xermsg ('SLATEC', 'DDEABM', 'THE LENGTH OF THE RWORK ' //
     *      'ARRAY MUST BE AT LEAST 130 + 21*NEQ.$$' //
     *      'YOU HAVE CALLED THE CODE WITH LRW = ' // xern1, 1, 1)
         idid=-33
      ENDIF
C
      IF (liw .LT. 51) THEN
         WRITE (xern1, '(I8)') liw
         CALL xermsg ('SLATEC', 'DDEABM', 'THE LENGTH OF THE IWORK ' //
     *      'ARRAY MUST BE AT LEAST 51.$$YOU HAVE CALLED THE CODE ' //
     *      'WITH LIW = ' // xern1, 2, 1)
         idid=-33
      ENDIF
C
C     COMPUTE THE INDICES FOR THE ARRAYS TO BE STORED IN THE WORK ARRAY
C
      iypout = 21
      itstar = neq + 21
      iyp = 1 + itstar
      iyy = neq + iyp
      iwt = neq + iyy
      ip = neq + iwt
      iphi = neq + ip
      ialpha = (neq*16) + iphi
      ibeta = 12 + ialpha
      ipsi = 12 + ibeta
      iv = 12 + ipsi
      iw = 12 + iv
      isig = 12 + iw
      ig = 13 + isig
      igi = 13 + ig
      ixold = 11 + igi
      ihold = 1 + ixold
      itold = 1 + ihold
      idelsn = 1 + itold
      itwou = 1 + idelsn
      ifouru = 1 + itwou
C
      rwork(itstar) = t
      IF (info(1) .EQ. 0) GO TO 50
      start = iwork(21) .NE. (-1)
      phase1 = iwork(22) .NE. (-1)
      nornd = iwork(23) .NE. (-1)
      stiff = iwork(24) .NE. (-1)
      intout = iwork(25) .NE. (-1)
C
 50   CALL ddes(df,neq,t,y,tout,info,rtol,atol,idid,rwork(iypout),
     1         rwork(iyp),rwork(iyy),rwork(iwt),rwork(ip),rwork(iphi),
     2         rwork(ialpha),rwork(ibeta),rwork(ipsi),rwork(iv),
     3         rwork(iw),rwork(isig),rwork(ig),rwork(igi),rwork(11),
     4         rwork(12),rwork(13),rwork(ixold),rwork(ihold),
     5         rwork(itold),rwork(idelsn),rwork(1),rwork(itwou),
     5         rwork(ifouru),start,phase1,nornd,stiff,intout,iwork(26),
     6         iwork(27),iwork(28),iwork(29),iwork(30),iwork(31),
     7         iwork(32),iwork(33),iwork(34),iwork(35),iwork(45),
     8         rpar,ipar)
C
      iwork(21) = -1
      IF (start) iwork(21) = 1
      iwork(22) = -1
      IF (phase1) iwork(22) = 1
      iwork(23) = -1
      IF (nornd) iwork(23) = 1
      iwork(24) = -1
      IF (stiff) iwork(24) = 1
      iwork(25) = -1
      IF (intout) iwork(25) = 1
C
      IF (idid .NE. (-2)) iwork(liw) = iwork(liw) + 1
      IF (t .NE. rwork(itstar)) iwork(liw) = 0
C
      RETURN

ddes()

subroutine ddes	(	external	DF,
		integer	NEQ,
		double precision	T,
		double precision, dimension(*)	Y,
		double precision	TOUT,
		integer, dimension(15)	INFO,
		double precision, dimension(*)	RTOL,
		double precision, dimension(*)	ATOL,
		integer	IDID,
		double precision, dimension(*)	YPOUT,
		double precision, dimension(*)	YP,
		double precision, dimension(*)	YY,
		double precision, dimension(*)	WT,
		double precision, dimension(*)	P,
		double precision, dimension(neq,16)	PHI,
		double precision, dimension(12)	ALPHA,
		double precision, dimension(12)	BETA,
		double precision, dimension(12)	PSI,
		double precision, dimension(12)	V,
		double precision, dimension(12)	W,
		double precision, dimension(13)	SIG,
		double precision, dimension(13)	G,
		double precision, dimension(11)	GI,
		double precision	H,
		double precision	EPS,
		double precision	X,
		double precision	XOLD,
		double precision	HOLD,
		double precision	TOLD,
		double precision	DELSGN,
		double precision	TSTOP,
		double precision	TWOU,
		double precision	FOURU,
		logical	START,
		logical	PHASE1,
		logical	NORND,
		logical	STIFF,
		logical	INTOUT,
		integer	NS,
		integer	KORD,
		integer	KOLD,
		integer	INIT,
		integer	KSTEPS,
		integer	KLE4,
		integer	IQUIT,
		integer	KPREV,
		integer	IVC,
		integer, dimension(10)	IV,
		integer	KGI,
		double precision, dimension(*)	RPAR,
		integer, dimension(*)	IPAR
	)

C***BEGIN PROLOGUE  DDES
C***SUBSIDIARY
C***PURPOSE  Subsidiary to DDEABM
C***LIBRARY   SLATEC
C***TYPE      DOUBLE PRECISION (DES-S, DDES-D)
C***AUTHOR  Watts, H. A., (SNLA)
C***DESCRIPTION
C
C   DDEABM merely allocates storage for DDES to relieve the user of the
C   inconvenience of a long call list.  Consequently  DDES  is used as
C   described in the comments for  DDEABM .
C
C***SEE ALSO  DDEABM
C***ROUTINES CALLED  D1MACH, DINTP, DSTEPS, XERMSG
C***REVISION HISTORY  (YYMMDD)
C   820301  DATE WRITTEN
C   890531  Changed all specific intrinsics to generic.  (WRB)
C   890831  Modified array declarations.  (WRB)
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C   900328  Added TYPE section.  (WRB)
C   900510  Convert XERRWV calls to XERMSG calls, cvt GOTOs to
C           IF-THEN-ELSE.  (RWC)
C   910722  Updated AUTHOR section.  (ALS)
C***END PROLOGUE  DDES
C
      INTEGER idid, info, init, ipar, iquit, iv, ivc, k, kgi, kle4,
     1      kold, kord, kprev, ksteps, l, ltol, maxnum, natolp, neq,
     2      nrtolp, ns
      DOUBLE PRECISION a, absdel, alpha, atol, beta, d1mach,
     1      del, delsgn, dt, eps, fouru, g, gi, h,
     2      ha, hold, p, phi, psi, rpar, rtol, sig, t, told, tout,
     3      tstop, twou, u, v, w, wt, x, xold, y, yp, ypout, yy
      LOGICAL stiff,crash,start,phase1,nornd,intout
C
      dimension y(*),yy(*),wt(*),phi(neq,16),p(*),yp(*),
     1  ypout(*),psi(12),alpha(12),beta(12),sig(13),v(12),w(12),g(13),
     2  gi(11),iv(10),info(15),rtol(*),atol(*),rpar(*),ipar(*)
      CHARACTER*8 xern1
      CHARACTER*16 xern3, xern4
C
      EXTERNAL df
C
C.......................................................................
C
C  THE EXPENSE OF SOLVING THE PROBLEM IS MONITORED BY COUNTING THE
C  NUMBER OF  STEPS ATTEMPTED. WHEN THIS EXCEEDS  MAXNUM, THE COUNTER
C  IS RESET TO ZERO AND THE USER IS INFORMED ABOUT POSSIBLE EXCESSIVE
C  WORK.
C
      SAVE maxnum
      DATA maxnum/500/
C
C.......................................................................
C
C***FIRST EXECUTABLE STATEMENT  DDES
      IF (info(1) .EQ. 0) THEN
C
C ON THE FIRST CALL , PERFORM INITIALIZATION --
C        DEFINE THE MACHINE UNIT ROUNDOFF QUANTITY  U  BY CALLING THE
C        FUNCTION ROUTINE  D1MACH. THE USER MUST MAKE SURE THAT THE
C        VALUES SET IN D1MACH ARE RELEVANT TO THE COMPUTER BEING USED.
C
         u=d1mach(4)
C                       -- SET ASSOCIATED MACHINE DEPENDENT PARAMETERS
         twou=2.d0*u
         fouru=4.d0*u
C                       -- SET TERMINATION FLAG
         iquit=0
C                       -- SET INITIALIZATION INDICATOR
         init=0
C                       -- SET COUNTER FOR ATTEMPTED STEPS
         ksteps=0
C                       -- SET INDICATOR FOR INTERMEDIATE-OUTPUT
         intout= .false.
C                       -- SET INDICATOR FOR STIFFNESS DETECTION
         stiff= .false.
C                       -- SET STEP COUNTER FOR STIFFNESS DETECTION
         kle4=0
C                       -- SET INDICATORS FOR STEPS CODE
         start= .true.
         phase1= .true.
         nornd= .true.
C                       -- RESET INFO(1) FOR SUBSEQUENT CALLS
         info(1)=1
      ENDIF
C
C.......................................................................
C
C      CHECK VALIDITY OF INPUT PARAMETERS ON EACH ENTRY
C
      IF (info(1) .NE. 0  .AND.  info(1) .NE. 1) THEN
         WRITE (xern1, '(I8)') info(1)
         CALL xermsg ('SLATEC', 'DDES', 'IN DDEABM, INFO(1) MUST BE ' //
     *      'SET TO 0 FOR THE START OF A NEW PROBLEM, AND MUST BE ' //
     *      'SET TO 1 FOLLOWING AN INTERRUPTED TASK.  YOU ARE ' //
     *      'ATTEMPTING TO CONTINUE THE INTEGRATION ILLEGALLY BY ' //
     *      'CALLING THE CODE WITH INFO(1) = ' // xern1, 3, 1)
         idid=-33
      ENDIF
C
      IF (info(2) .NE. 0  .AND.  info(2) .NE. 1) THEN
         WRITE (xern1, '(I8)') info(2)
         CALL xermsg ('SLATEC', 'DDES', 'IN DDEABM, INFO(2) MUST BE ' //
     *      '0 OR 1 INDICATING SCALAR AND VECTOR ERROR TOLERANCES, ' //
     *      'RESPECTIVELY.  YOU HAVE CALLED THE CODE WITH INFO(2) = ' //
     *      xern1, 4, 1)
         idid=-33
      ENDIF
C
      IF (info(3) .NE. 0  .AND.  info(3) .NE. 1) THEN
         WRITE (xern1, '(I8)') info(3)
         CALL xermsg ('SLATEC', 'DDES', 'IN DDEABM, INFO(3) MUST BE ' //
     *      '0 OR 1 INDICATING THE INTERVAL OR INTERMEDIATE-OUTPUT ' //
     *      'MODE OF INTEGRATION, RESPECTIVELY.  YOU HAVE CALLED ' //
     *      'THE CODE WITH  INFO(3) = ' // xern1, 5, 1)
         idid=-33
      ENDIF
C
      IF (info(4) .NE. 0  .AND.  info(4) .NE. 1) THEN
         WRITE (xern1, '(I8)') info(4)
         CALL xermsg ('SLATEC', 'DDES', 'IN DDEABM, INFO(4) MUST BE ' //
     *      '0 OR 1 INDICATING WHETHER OR NOT THE INTEGRATION ' //
     *      'INTERVAL IS TO BE RESTRICTED BY A POINT TSTOP.  YOU ' //
     *      'HAVE CALLED THE CODE WITH INFO(4) = ' // xern1, 14, 1)
         idid=-33
      ENDIF
C
      IF (neq .LT. 1) THEN
         WRITE (xern1, '(I8)') neq
         CALL xermsg ('SLATEC', 'DDES', 'IN DDEABM,  THE NUMBER OF ' //
     *      'EQUATIONS NEQ MUST BE A POSITIVE INTEGER.  YOU HAVE ' //
     *      'CALLED THE CODE WITH  NEQ = ' // xern1, 6, 1)
         idid=-33
      ENDIF
C
      nrtolp = 0
      natolp = 0
      DO 90 k=1,neq
         IF (nrtolp .EQ. 0 .AND. rtol(k) .LT. 0.d0) THEN
            WRITE (xern1, '(I8)') k
            WRITE (xern3, '(1PE15.6)') rtol(k)
            CALL xermsg ('SLATEC', 'DDES', 'IN DDEABM, THE RELATIVE ' //
     *         'ERROR TOLERANCES RTOL MUST BE NON-NEGATIVE.  YOU ' //
     *         'HAVE CALLED THE CODE WITH  RTOL(' // xern1 // ') = ' //
     *         xern3 // '.  IN THE CASE OF VECTOR ERROR TOLERANCES, ' //
     *         'NO FURTHER CHECKING OF RTOL COMPONENTS IS DONE.', 7, 1)
            idid = -33
            nrtolp = 1
         ENDIF
C
         IF (natolp .EQ. 0 .AND. atol(k) .LT. 0.d0) THEN
            WRITE (xern1, '(I8)') k
            WRITE (xern3, '(1PE15.6)') atol(k)
            CALL xermsg ('SLATEC', 'DDES', 'IN DDEABM, THE ABSOLUTE ' //
     *         'ERROR TOLERANCES ATOL MUST BE NON-NEGATIVE.  YOU ' //
     *         'HAVE CALLED THE CODE WITH  ATOL(' // xern1 // ') = ' //
     *         xern3 // '.  IN THE CASE OF VECTOR ERROR TOLERANCES, ' //
     *         'NO FURTHER CHECKING OF ATOL COMPONENTS IS DONE.', 8, 1)
            idid = -33
            natolp = 1
         ENDIF
C
         IF (info(2) .EQ. 0) GO TO 100
         IF (natolp.GT.0 .AND. nrtolp.GT.0) GO TO 100
   90 CONTINUE
C
  100 IF (info(4) .EQ. 1) THEN
         IF (sign(1.d0,tout-t) .NE. sign(1.d0,tstop-t)
     1      .OR. abs(tout-t) .GT. abs(tstop-t)) THEN
            WRITE (xern3, '(1PE15.6)') tout
            WRITE (xern4, '(1PE15.6)') tstop
            CALL xermsg ('SLATEC', 'DDES', 'IN DDEABM, YOU HAVE ' //
     *         'CALLED THE CODE WITH  TOUT = ' // xern3 // ' BUT ' //
     *         'YOU HAVE ALSO TOLD THE CODE (INFO(4) = 1) NOT TO ' //
     *         'INTEGRATE PAST THE POINT TSTOP = ' // xern4 //
     *         ' THESE INSTRUCTIONS CONFLICT.', 14, 1)
            idid=-33
         ENDIF
      ENDIF
C
C     CHECK SOME CONTINUATION POSSIBILITIES
C
      IF (init .NE. 0) THEN
         IF (t .EQ. tout) THEN
            WRITE (xern3, '(1PE15.6)') t
            CALL xermsg ('SLATEC', 'DDES', 'IN DDEABM, YOU HAVE ' //
     *         'CALLED THE CODE WITH  T = TOUT = ' // xern3 //
     *         '$$THIS IS NOT ALLOWED ON CONTINUATION CALLS.', 9, 1)
            idid=-33
         ENDIF
C
         IF (t .NE. told) THEN
            WRITE (xern3, '(1PE15.6)') told
            WRITE (xern4, '(1PE15.6)') t
            CALL xermsg ('SLATEC', 'DDES', 'IN DDEABM, YOU HAVE ' //
     *         'CHANGED THE VALUE OF T FROM ' // xern3 // ' TO ' //
     *         xern4 //'  THIS IS NOT ALLOWED ON CONTINUATION CALLS.',
     *         10, 1)
            idid=-33
         ENDIF
C
         IF (init .NE. 1) THEN
            IF (delsgn*(tout-t) .LT. 0.d0) THEN
               WRITE (xern3, '(1PE15.6)') tout
               CALL xermsg ('SLATEC', 'DDES', 'IN DDEABM, BY ' //
     *            'CALLING THE CODE WITH TOUT = ' // xern3 //
     *            ' YOU ARE ATTEMPTING TO CHANGE THE DIRECTION OF ' //
     *            'INTEGRATION.$$THIS IS NOT ALLOWED WITHOUT ' //
     *            'RESTARTING.', 11, 1)
               idid=-33
            ENDIF
         ENDIF
      ENDIF
C
C     INVALID INPUT DETECTED
C
      IF (idid .EQ. (-33)) THEN
         IF (iquit .NE. (-33)) THEN
            iquit = -33
            info(1) = -1
         ELSE
            CALL xermsg ('SLATEC', 'DDES', 'IN DDEABM, INVALID ' //
     *         'INPUT WAS DETECTED ON SUCCESSIVE ENTRIES.  IT IS ' //
     *         'IMPOSSIBLE TO PROCEED BECAUSE YOU HAVE NOT ' //
     *         'CORRECTED THE PROBLEM, SO EXECUTION IS BEING ' //
     *         'TERMINATED.', 12, 2)
         ENDIF
         RETURN
      ENDIF
C
C.......................................................................
C
C     RTOL = ATOL = 0. IS ALLOWED AS VALID INPUT AND INTERPRETED AS
C     ASKING FOR THE MOST ACCURATE SOLUTION POSSIBLE. IN THIS CASE,
C     THE RELATIVE ERROR TOLERANCE RTOL IS RESET TO THE SMALLEST VALUE
C     FOURU WHICH IS LIKELY TO BE REASONABLE FOR THIS METHOD AND MACHINE
C
      DO 180 k=1,neq
        IF (rtol(k)+atol(k) .GT. 0.d0) GO TO 170
        rtol(k)=fouru
        idid=-2
  170   IF (info(2) .EQ. 0) GO TO 190
  180   CONTINUE
C
  190 IF (idid .NE. (-2)) GO TO 200
C                       RTOL=ATOL=0 ON INPUT, SO RTOL IS CHANGED TO A
C                                                SMALL POSITIVE VALUE
      info(1)=-1
      RETURN
C
C     BRANCH ON STATUS OF INITIALIZATION INDICATOR
C            INIT=0 MEANS INITIAL DERIVATIVES AND NOMINAL STEP SIZE
C                   AND DIRECTION NOT YET SET
C            INIT=1 MEANS NOMINAL STEP SIZE AND DIRECTION NOT YET SET
C            INIT=2 MEANS NO FURTHER INITIALIZATION REQUIRED
C
  200 IF (init .EQ. 0) GO TO 210
      IF (init .EQ. 1) GO TO 220
      GO TO 240
C
C.......................................................................
C
C     MORE INITIALIZATION --
C                         -- EVALUATE INITIAL DERIVATIVES
C
  210 init=1
      a=t
      CALL df(a,y,yp,rpar,ipar)
      IF (t .NE. tout) GO TO 220
      idid=2
      DO 215 l = 1,neq
  215    ypout(l) = yp(l)
      told=t
      RETURN
C
C                         -- SET INDEPENDENT AND DEPENDENT VARIABLES
C                                              X AND YY(*) FOR STEPS
C                         -- SET SIGN OF INTEGRATION DIRECTION
C                         -- INITIALIZE THE STEP SIZE
C
  220 init = 2
      x = t
      DO 230 l = 1,neq
  230   yy(l) = y(l)
      delsgn = sign(1.0d0,tout-t)
      h = sign(max(fouru*abs(x),abs(tout-x)),tout-x)
C
C.......................................................................
C
C   ON EACH CALL SET INFORMATION WHICH DETERMINES THE ALLOWED INTERVAL
C   OF INTEGRATION BEFORE RETURNING WITH AN ANSWER AT TOUT
C
  240 del = tout - t
      absdel = abs(del)
C
C.......................................................................
C
C   IF ALREADY PAST OUTPUT POINT, INTERPOLATE AND RETURN
C
  250 IF(abs(x-t) .LT. absdel) GO TO 260
      CALL dintp(x,yy,tout,y,ypout,neq,kold,phi,ivc,iv,kgi,gi,
     1                                        alpha,g,w,xold,p)
      idid = 3
      IF (x .NE. tout) GO TO 255
      idid = 2
      intout = .false.
  255 t = tout
      told = t
      RETURN
C
C   IF CANNOT GO PAST TSTOP AND SUFFICIENTLY CLOSE,
C   EXTRAPOLATE AND RETURN
C
  260 IF (info(4) .NE. 1) GO TO 280
      IF (abs(tstop-x) .GE. fouru*abs(x)) GO TO 280
      dt = tout - x
      DO 270 l = 1,neq
  270   y(l) = yy(l) + dt*yp(l)
      CALL df(tout,y,ypout,rpar,ipar)
      idid = 3
      t = tout
      told = t
      RETURN
C
  280 IF (info(3) .EQ. 0  .OR.  .NOT.intout) GO TO 300
C
C   INTERMEDIATE-OUTPUT MODE
C
      idid = 1
      DO 290 l = 1,neq
        y(l)=yy(l)
  290   ypout(l) = yp(l)
      t = x
      told = t
      intout = .false.
      RETURN
C
C.......................................................................
C
C     MONITOR NUMBER OF STEPS ATTEMPTED
C
  300 IF (ksteps .LE. maxnum) GO TO 330
C
C                       A SIGNIFICANT AMOUNT OF WORK HAS BEEN EXPENDED
      idid=-1
      ksteps=0
      IF (.NOT. stiff) GO TO 310
C
C                       PROBLEM APPEARS TO BE STIFF
      idid=-4
      stiff= .false.
      kle4=0
C
  310 DO 320 l = 1,neq
        y(l) = yy(l)
  320   ypout(l) = yp(l)
      t = x
      told = t
      info(1) = -1
      intout = .false.
      RETURN
C
C.......................................................................
C
C   LIMIT STEP SIZE, SET WEIGHT VECTOR AND TAKE A STEP
C
  330 ha = abs(h)
      IF (info(4) .NE. 1) GO TO 340
      ha = min(ha,abs(tstop-x))
  340 h = sign(ha,h)
      eps = 1.0d0
      ltol = 1
      DO 350 l = 1,neq
        IF (info(2) .EQ. 1) ltol = l
        wt(l) = rtol(ltol)*abs(yy(l)) + atol(ltol)
        IF (wt(l) .LE. 0.0d0) GO TO 360
  350   CONTINUE
      GO TO 380
C
C                       RELATIVE ERROR CRITERION INAPPROPRIATE
  360 idid = -3
      DO 370 l = 1,neq
        y(l) = yy(l)
  370   ypout(l) = yp(l)
      t = x
      told = t
      info(1) = -1
      intout = .false.
      RETURN
C
  380 CALL dsteps(df,neq,yy,x,h,eps,wt,start,hold,kord,kold,crash,phi,p,
     1           yp,psi,alpha,beta,sig,v,w,g,phase1,ns,nornd,ksteps,
     2           twou,fouru,xold,kprev,ivc,iv,kgi,gi,rpar,ipar)
C
C.......................................................................
C
      IF(.NOT.crash) GO TO 420
C
C                       TOLERANCES TOO SMALL
      idid = -2
      rtol(1) = eps*rtol(1)
      atol(1) = eps*atol(1)
      IF (info(2) .EQ. 0) GO TO 400
      DO 390 l = 2,neq
        rtol(l) = eps*rtol(l)
  390   atol(l) = eps*atol(l)
  400 DO 410 l = 1,neq
        y(l) = yy(l)
  410   ypout(l) = yp(l)
      t = x
      told = t
      info(1) = -1
      intout = .false.
      RETURN
C
C   (STIFFNESS TEST) COUNT NUMBER OF CONSECUTIVE STEPS TAKEN WITH THE
C   ORDER OF THE METHOD BEING LESS OR EQUAL TO FOUR
C
  420 kle4 = kle4 + 1
      IF(kold .GT. 4) kle4 = 0
      IF(kle4 .GE. 50) stiff = .true.
      intout = .true.
      GO TO 250

dhstrt()

subroutine dhstrt	(	external	DF,
		integer	NEQ,
		double precision	A,
		double precision	B,
		double precision, dimension(*)	Y,
		double precision, dimension(*)	YPRIME,
		double precision, dimension(*)	ETOL,
		integer	MORDER,
		double precision	SMALL,
		double precision	BIG,
		double precision, dimension(*)	SPY,
		double precision, dimension(*)	PV,
		double precision, dimension(*)	YP,
		double precision, dimension(*)	SF,
		double precision, dimension(*)	RPAR,
		integer, dimension(*)	IPAR,
		double precision	H
	)

C***BEGIN PROLOGUE  DHSTRT
C***SUBSIDIARY
C***PURPOSE  Subsidiary to DDEABM, DDEBDF and DDERKF
C***LIBRARY   SLATEC
C***TYPE      DOUBLE PRECISION (HSTART-S, DHSTRT-D)
C***AUTHOR  Watts, H. A., (SNLA)
C***DESCRIPTION
C
C   DHSTRT computes a starting step size to be used in solving initial
C   value problems in ordinary differential equations.
C
C **********************************************************************
C  ABSTRACT
C
C     Subroutine DHSTRT computes a starting step size to be used by an
C     initial value method in solving ordinary differential equations.
C     It is based on an estimate of the local Lipschitz constant for the
C     differential equation   (lower bound on a norm of the Jacobian) ,
C     a bound on the differential equation  (first derivative) , and
C     a bound on the partial derivative of the equation with respect to
C     the independent variable.
C     (all approximated near the initial point A)
C
C     Subroutine DHSTRT uses a function subprogram DHVNRM for computing
C     a vector norm. The maximum norm is presently utilized though it
C     can easily be replaced by any other vector norm. It is presumed
C     that any replacement norm routine would be carefully coded to
C     prevent unnecessary underflows or overflows from occurring, and
C     also, would not alter the vector or number of components.
C
C **********************************************************************
C  On input you must provide the following
C
C      DF -- This is a subroutine of the form
C                               DF(X,U,UPRIME,RPAR,IPAR)
C             which defines the system of first order differential
C             equations to be solved. For the given values of X and the
C             vector  U(*)=(U(1),U(2),...,U(NEQ)) , the subroutine must
C             evaluate the NEQ components of the system of differential
C             equations  DU/DX=DF(X,U)  and store the derivatives in the
C             array UPRIME(*), that is,  UPRIME(I) = * DU(I)/DX *  for
C             equations I=1,...,NEQ.
C
C             Subroutine DF must not alter X or U(*). You must declare
C             the name DF in an external statement in your program that
C             calls DHSTRT. You must dimension U and UPRIME in DF.
C
C             RPAR and IPAR are DOUBLE PRECISION and INTEGER parameter
C             arrays which you can use for communication between your
C             program and subroutine DF. They are not used or altered by
C             DHSTRT. If you do not need RPAR or IPAR, ignore these
C             parameters by treating them as dummy arguments. If you do
C             choose to use them, dimension them in your program and in
C             DF as arrays of appropriate length.
C
C      NEQ -- This is the number of (first order) differential equations
C             to be integrated.
C
C      A -- This is the initial point of integration.
C
C      B -- This is a value of the independent variable used to define
C             the direction of integration. A reasonable choice is to
C             set  B  to the first point at which a solution is desired.
C             You can also use  B, if necessary, to restrict the length
C             of the first integration step because the algorithm will
C             not compute a starting step length which is bigger than
C             ABS(B-A), unless  B  has been chosen too close to  A.
C             (it is presumed that DHSTRT has been called with  B
C             different from  A  on the machine being used. Also see the
C             discussion about the parameter  SMALL.)
C
C      Y(*) -- This is the vector of initial values of the NEQ solution
C             components at the initial point  A.
C
C      YPRIME(*) -- This is the vector of derivatives of the NEQ
C             solution components at the initial point  A.
C             (defined by the differential equations in subroutine DF)
C
C      ETOL -- This is the vector of error tolerances corresponding to
C             the NEQ solution components. It is assumed that all
C             elements are positive. Following the first integration
C             step, the tolerances are expected to be used by the
C             integrator in an error test which roughly requires that
C                        ABS(LOCAL ERROR)  .LE.  ETOL
C             for each vector component.
C
C      MORDER -- This is the order of the formula which will be used by
C             the initial value method for taking the first integration
C             step.
C
C      SMALL -- This is a small positive machine dependent constant
C             which is used for protecting against computations with
C             numbers which are too small relative to the precision of
C             floating point arithmetic.  SMALL  should be set to
C             (approximately) the smallest positive DOUBLE PRECISION
C             number such that  (1.+SMALL) .GT. 1.  on the machine being
C             used. The quantity  SMALL**(3/8)  is used in computing
C             increments of variables for approximating derivatives by
C             differences.  Also the algorithm will not compute a
C             starting step length which is smaller than
C             100*SMALL*ABS(A).
C
C      BIG -- This is a large positive machine dependent constant which
C             is used for preventing machine overflows. A reasonable
C             choice is to set big to (approximately) the square root of
C             the largest DOUBLE PRECISION number which can be held in
C             the machine.
C
C      SPY(*),PV(*),YP(*),SF(*) -- These are DOUBLE PRECISION work
C             arrays of length NEQ which provide the routine with needed
C             storage space.
C
C      RPAR,IPAR -- These are parameter arrays, of DOUBLE PRECISION and
C             INTEGER type, respectively, which can be used for
C             communication between your program and the DF subroutine.
C             They are not used or altered by DHSTRT.
C
C **********************************************************************
C  On Output  (after the return from DHSTRT),
C
C      H -- is an appropriate starting step size to be attempted by the
C             differential equation method.
C
C           All parameters in the call list remain unchanged except for
C           the working arrays SPY(*),PV(*),YP(*), and SF(*).
C
C **********************************************************************
C
C***SEE ALSO  DDEABM, DDEBDF, DDERKF
C***ROUTINES CALLED  DHVNRM
C***REVISION HISTORY  (YYMMDD)
C   820301  DATE WRITTEN
C   890531  Changed all specific intrinsics to generic.  (WRB)
C   890831  Modified array declarations.  (WRB)
C   890911  Removed unnecessary intrinsics.  (WRB)
C   891024  Changed references from DVNORM to DHVNRM.  (WRB)
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C   900328  Added TYPE section.  (WRB)
C   910722  Updated AUTHOR section.  (ALS)
C***END PROLOGUE  DHSTRT
C
      INTEGER ipar, j, k, lk, morder, neq
      DOUBLE PRECISION a, absdx, b, big, da, delf, dely,
     1      dfdub, dfdxb, dhvnrm,
     2      dx, dy, etol, fbnd, h, pv, relper, rpar, sf, small, spy,
     3      srydpb, tolexp, tolmin, tolp, tolsum, y, ydpb, yp, yprime
      dimension y(*),yprime(*),etol(*),spy(*),pv(*),yp(*),
     1          sf(*),rpar(*),ipar(*)
      EXTERNAL df
C
C     ..................................................................
C
C     BEGIN BLOCK PERMITTING ...EXITS TO 160
C***FIRST EXECUTABLE STATEMENT  DHSTRT
         dx = b - a
         absdx = abs(dx)
         relper = small**0.375d0
C
C        ...............................................................
C
C             COMPUTE AN APPROXIMATE BOUND (DFDXB) ON THE PARTIAL
C             DERIVATIVE OF THE EQUATION WITH RESPECT TO THE
C             INDEPENDENT VARIABLE. PROTECT AGAINST AN OVERFLOW.
C             ALSO COMPUTE A BOUND (FBND) ON THE FIRST DERIVATIVE
C             LOCALLY.
C
         da = sign(max(min(relper*abs(a),absdx),
     1                    100.0d0*small*abs(a)),dx)
         IF (da .EQ. 0.0d0) da = relper*dx
         CALL df(a+da,y,sf,rpar,ipar)
         DO 10 j = 1, neq
            yp(j) = sf(j) - yprime(j)
   10    CONTINUE
         delf = dhvnrm(yp,neq)
         dfdxb = big
         IF (delf .LT. big*abs(da)) dfdxb = delf/abs(da)
         fbnd = dhvnrm(sf,neq)
C
C        ...............................................................
C
C             COMPUTE AN ESTIMATE (DFDUB) OF THE LOCAL LIPSCHITZ
C             CONSTANT FOR THE SYSTEM OF DIFFERENTIAL EQUATIONS. THIS
C             ALSO REPRESENTS AN ESTIMATE OF THE NORM OF THE JACOBIAN
C             LOCALLY.  THREE ITERATIONS (TWO WHEN NEQ=1) ARE USED TO
C             ESTIMATE THE LIPSCHITZ CONSTANT BY NUMERICAL DIFFERENCES.
C             THE FIRST PERTURBATION VECTOR IS BASED ON THE INITIAL
C             DERIVATIVES AND DIRECTION OF INTEGRATION. THE SECOND
C             PERTURBATION VECTOR IS FORMED USING ANOTHER EVALUATION OF
C             THE DIFFERENTIAL EQUATION.  THE THIRD PERTURBATION VECTOR
C             IS FORMED USING PERTURBATIONS BASED ONLY ON THE INITIAL
C             VALUES. COMPONENTS THAT ARE ZERO ARE ALWAYS CHANGED TO
C             NON-ZERO VALUES (EXCEPT ON THE FIRST ITERATION). WHEN
C             INFORMATION IS AVAILABLE, CARE IS TAKEN TO ENSURE THAT
C             COMPONENTS OF THE PERTURBATION VECTOR HAVE SIGNS WHICH ARE
C             CONSISTENT WITH THE SLOPES OF LOCAL SOLUTION CURVES.
C             ALSO CHOOSE THE LARGEST BOUND (FBND) FOR THE FIRST
C             DERIVATIVE.
C
C                               PERTURBATION VECTOR SIZE IS HELD
C                               CONSTANT FOR ALL ITERATIONS. COMPUTE
C                               THIS CHANGE FROM THE
C                                       SIZE OF THE VECTOR OF INITIAL
C                                       VALUES.
         dely = relper*dhvnrm(y,neq)
         IF (dely .EQ. 0.0d0) dely = relper
         dely = sign(dely,dx)
         delf = dhvnrm(yprime,neq)
         fbnd = max(fbnd,delf)
         IF (delf .EQ. 0.0d0) GO TO 30
C           USE INITIAL DERIVATIVES FOR FIRST PERTURBATION
            DO 20 j = 1, neq
               spy(j) = yprime(j)
               yp(j) = yprime(j)
   20       CONTINUE
         GO TO 50
   30    CONTINUE
C           CANNOT HAVE A NULL PERTURBATION VECTOR
            DO 40 j = 1, neq
               spy(j) = 0.0d0
               yp(j) = 1.0d0
   40       CONTINUE
            delf = dhvnrm(yp,neq)
   50    CONTINUE
C
         dfdub = 0.0d0
         lk = min(neq+1,3)
         DO 140 k = 1, lk
C           DEFINE PERTURBED VECTOR OF INITIAL VALUES
            DO 60 j = 1, neq
               pv(j) = y(j) + dely*(yp(j)/delf)
   60       CONTINUE
            IF (k .EQ. 2) GO TO 80
C              EVALUATE DERIVATIVES ASSOCIATED WITH PERTURBED
C              VECTOR  AND  COMPUTE CORRESPONDING DIFFERENCES
               CALL df(a,pv,yp,rpar,ipar)
               DO 70 j = 1, neq
                  pv(j) = yp(j) - yprime(j)
   70          CONTINUE
            GO TO 100
   80       CONTINUE
C              USE A SHIFTED VALUE OF THE INDEPENDENT VARIABLE
C                                    IN COMPUTING ONE ESTIMATE
               CALL df(a+da,pv,yp,rpar,ipar)
               DO 90 j = 1, neq
                  pv(j) = yp(j) - sf(j)
   90          CONTINUE
  100       CONTINUE
C           CHOOSE LARGEST BOUNDS ON THE FIRST DERIVATIVE
C                          AND A LOCAL LIPSCHITZ CONSTANT
            fbnd = max(fbnd,dhvnrm(yp,neq))
            delf = dhvnrm(pv,neq)
C        ...EXIT
            IF (delf .GE. big*abs(dely)) GO TO 150
            dfdub = max(dfdub,delf/abs(dely))
C     ......EXIT
            IF (k .EQ. lk) GO TO 160
C           CHOOSE NEXT PERTURBATION VECTOR
            IF (delf .EQ. 0.0d0) delf = 1.0d0
            DO 130 j = 1, neq
               IF (k .EQ. 2) GO TO 110
                  dy = abs(pv(j))
                  IF (dy .EQ. 0.0d0) dy = delf
               GO TO 120
  110          CONTINUE
                  dy = y(j)
                  IF (dy .EQ. 0.0d0) dy = dely/relper
  120          CONTINUE
               IF (spy(j) .EQ. 0.0d0) spy(j) = yp(j)
               IF (spy(j) .NE. 0.0d0) dy = sign(dy,spy(j))
               yp(j) = dy
  130       CONTINUE
            delf = dhvnrm(yp,neq)
  140    CONTINUE
  150    CONTINUE
C
C        PROTECT AGAINST AN OVERFLOW
         dfdub = big
  160 CONTINUE
C
C     ..................................................................
C
C          COMPUTE A BOUND (YDPB) ON THE NORM OF THE SECOND DERIVATIVE
C
      ydpb = dfdxb + dfdub*fbnd
C
C     ..................................................................
C
C          DEFINE THE TOLERANCE PARAMETER UPON WHICH THE STARTING STEP
C          SIZE IS TO BE BASED.  A VALUE IN THE MIDDLE OF THE ERROR
C          TOLERANCE RANGE IS SELECTED.
C
      tolmin = big
      tolsum = 0.0d0
      DO 170 k = 1, neq
         tolexp = log10(etol(k))
         tolmin = min(tolmin,tolexp)
         tolsum = tolsum + tolexp
  170 CONTINUE
      tolp = 10.0d0**(0.5d0*(tolsum/neq + tolmin)/(morder+1))
C
C     ..................................................................
C
C          COMPUTE A STARTING STEP SIZE BASED ON THE ABOVE FIRST AND
C          SECOND DERIVATIVE INFORMATION
C
C                            RESTRICT THE STEP LENGTH TO BE NOT BIGGER
C                            THAN ABS(B-A).   (UNLESS  B  IS TOO CLOSE
C                            TO  A)
      h = absdx
C
      IF (ydpb .NE. 0.0d0 .OR. fbnd .NE. 0.0d0) GO TO 180
C
C        BOTH FIRST DERIVATIVE TERM (FBND) AND SECOND
C                     DERIVATIVE TERM (YDPB) ARE ZERO
         IF (tolp .LT. 1.0d0) h = absdx*tolp
      GO TO 200
  180 CONTINUE
C
      IF (ydpb .NE. 0.0d0) GO TO 190
C
C        ONLY SECOND DERIVATIVE TERM (YDPB) IS ZERO
         IF (tolp .LT. fbnd*absdx) h = tolp/fbnd
      GO TO 200
  190 CONTINUE
C
C        SECOND DERIVATIVE TERM (YDPB) IS NON-ZERO
         srydpb = sqrt(0.5d0*ydpb)
         IF (tolp .LT. srydpb*absdx) h = tolp/srydpb
  200 CONTINUE
C
C     FURTHER RESTRICT THE STEP LENGTH TO BE NOT
C                               BIGGER THAN  1/DFDUB
      IF (h*dfdub .GT. 1.0d0) h = 1.0d0/dfdub
C
C     FINALLY, RESTRICT THE STEP LENGTH TO BE NOT
C     SMALLER THAN  100*SMALL*ABS(A).  HOWEVER, IF
C     A=0. AND THE COMPUTED H UNDERFLOWED TO ZERO,
C     THE ALGORITHM RETURNS  SMALL*ABS(B)  FOR THE
C                                     STEP LENGTH.
      h = max(h,100.0d0*small*abs(a))
      IF (h .EQ. 0.0d0) h = small*abs(b)
C
C     NOW SET DIRECTION OF INTEGRATION
      h = sign(h,dx)
C
      RETURN

dhvnrm()

double precision function dhvnrm	(	double precision, dimension(*)	V,
		integer	NCOMP
	)

C***BEGIN PROLOGUE  DHVNRM
C***SUBSIDIARY
C***PURPOSE  Subsidiary to DDEABM, DDEBDF and DDERKF
C***LIBRARY   SLATEC
C***TYPE      DOUBLE PRECISION (HVNRM-S, DHVNRM-D)
C***AUTHOR  Watts, H. A., (SNLA)
C***DESCRIPTION
C
C     Compute the maximum norm of the vector V(*) of length NCOMP and
C     return the result as DHVNRM
C
C***SEE ALSO  DDEABM, DDEBDF, DDERKF
C***ROUTINES CALLED  (NONE)
C***REVISION HISTORY  (YYMMDD)
C   820301  DATE WRITTEN
C   890531  Changed all specific intrinsics to generic.  (WRB)
C   890831  Modified array declarations.  (WRB)
C   891024  Changed references from DVNORM to DHVNRM.  (WRB)
C   891024  Changed routine name from DVNORM to DHVNRM.  (WRB)
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C   900328  Added TYPE section.  (WRB)
C   910722  Updated AUTHOR section.  (ALS)
C***END PROLOGUE  DHVNRM
C
      INTEGER k, ncomp
      DOUBLE PRECISION v
      dimension v(*)
C***FIRST EXECUTABLE STATEMENT  DHVNRM
      dhvnrm = 0.0d0
      DO 10 k = 1, ncomp
         dhvnrm = max(dhvnrm,abs(v(k)))
   10 CONTINUE
      RETURN

dintp()

subroutine dintp	(	double precision	X,
		double precision, dimension(*)	Y,
		double precision	XOUT,
		double precision, dimension(*)	YOUT,
		double precision, dimension(*)	YPOUT,
		integer	NEQN,
		integer	KOLD,
		double precision, dimension(neqn,16)	PHI,
		integer	IVC,
		integer, dimension(10)	IV,
		integer	KGI,
		double precision, dimension(11)	GI,
		double precision, dimension(12)	ALPHA,
		double precision, dimension(13)	OG,
		double precision, dimension(12)	OW,
		double precision	OX,
		double precision, dimension(*)	OY
	)

C***BEGIN PROLOGUE  DINTP
C***PURPOSE  Approximate the solution at XOUT by evaluating the
C            polynomial computed in DSTEPS at XOUT.  Must be used in
C            conjunction with DSTEPS.
C***LIBRARY   SLATEC (DEPAC)
C***CATEGORY  I1A1B
C***TYPE      DOUBLE PRECISION (SINTRP-S, DINTP-D)
C***KEYWORDS  ADAMS METHOD, DEPAC, INITIAL VALUE PROBLEMS, ODE,
C             ORDINARY DIFFERENTIAL EQUATIONS, PREDICTOR-CORRECTOR,
C             SMOOTH INTERPOLANT
C***AUTHOR  Watts, H. A., (SNLA)
C***DESCRIPTION
C
C   The methods in subroutine  DSTEPS  approximate the solution near  X
C   by a polynomial.  Subroutine  DINTP  approximates the solution at
C   XOUT  by evaluating the polynomial there.  Information defining this
C   polynomial is passed from  DSTEPS  so  DINTP  cannot be used alone.
C
C   Subroutine DSTEPS is completely explained and documented in the text
C   "Computer Solution of Ordinary Differential Equations, the Initial
C   Value Problem"  by L. F. Shampine and M. K. Gordon.
C
C   Input to DINTP --
C
C   The user provides storage in the calling program for the arrays in
C   the call list
C      DIMENSION Y(NEQN),YOUT(NEQN),YPOUT(NEQN),PHI(NEQN,16),OY(NEQN)
C                AND ALPHA(12),OG(13),OW(12),GI(11),IV(10)
C   and defines
C      XOUT -- point at which solution is desired.
C   The remaining parameters are defined in  DSTEPS  and passed to
C   DINTP  from that subroutine
C
C   Output from  DINTP --
C
C      YOUT(*) -- solution at  XOUT
C      YPOUT(*) -- derivative of solution at  XOUT
C   The remaining parameters are returned unaltered from their input
C   values.  Integration with  DSTEPS  may be continued.
C
C***REFERENCES  H. A. Watts, A smoother interpolant for DE/STEP, INTRP
C                 II, Report SAND84-0293, Sandia Laboratories, 1984.
C***ROUTINES CALLED  (NONE)
C***REVISION HISTORY  (YYMMDD)
C   840201  DATE WRITTEN
C   890831  Modified array declarations.  (WRB)
C   890831  REVISION DATE from Version 3.2
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C   920501  Reformatted the REFERENCES section.  (WRB)
C***END PROLOGUE  DINTP
C
      INTEGER i, iq, iv, ivc, iw, j, jq, kgi, kold, kp1, kp2,
     1        l, m, neqn
      DOUBLE PRECISION alp, alpha, c, g, gdi, gdif, gi, gamma, h, hi,
     1       hmu, og, ow, ox, oy, phi, rmu, sigma, temp1, temp2, temp3,
     2       w, x, xi, xim1, xiq, xout, y, yout, ypout
C
      dimension y(*),yout(*),ypout(*),phi(neqn,16),oy(*)
      dimension g(13),c(13),w(13),og(13),ow(12),alpha(12),gi(11),iv(10)
C
C***FIRST EXECUTABLE STATEMENT  DINTP
      kp1 = kold + 1
      kp2 = kold + 2
C
      hi = xout - ox
      h = x - ox
      xi = hi/h
      xim1 = xi - 1.d0
C
C   INITIALIZE W(*) FOR COMPUTING G(*)
C
      xiq = xi
      DO 10 iq = 1,kp1
        xiq = xi*xiq
        temp1 = iq*(iq+1)
 10     w(iq) = xiq/temp1
C
C   COMPUTE THE DOUBLE INTEGRAL TERM GDI
C
      IF (kold .LE. kgi) GO TO 50
      IF (ivc .GT. 0) GO TO 20
      gdi = 1.0d0/temp1
      m = 2
      GO TO 30
 20   iw = iv(ivc)
      gdi = ow(iw)
      m = kold - iw + 3
 30   IF (m .GT. kold) GO TO 60
      DO 40 i = m,kold
 40     gdi = ow(kp2-i) - alpha(i)*gdi
      GO TO 60
 50   gdi = gi(kold)
C
C   COMPUTE G(*) AND C(*)
C
 60   g(1) = xi
      g(2) = 0.5d0*xi*xi
      c(1) = 1.0d0
      c(2) = xi
      IF (kold .LT. 2) GO TO 90
      DO 80 i = 2,kold
        alp = alpha(i)
        gamma = 1.0d0 + xim1*alp
        l = kp2 - i
        DO 70 jq = 1,l
 70       w(jq) = gamma*w(jq) - alp*w(jq+1)
        g(i+1) = w(1)
 80     c(i+1) = gamma*c(i)
C
C   DEFINE INTERPOLATION PARAMETERS
C
 90   sigma = (w(2) - xim1*w(1))/gdi
      rmu = xim1*c(kp1)/gdi
      hmu = rmu/h
C
C   INTERPOLATE FOR THE SOLUTION -- YOUT
C   AND FOR THE DERIVATIVE OF THE SOLUTION -- YPOUT
C
      DO 100 l = 1,neqn
        yout(l) = 0.0d0
 100    ypout(l) = 0.0d0
      DO 120 j = 1,kold
        i = kp2 - j
        gdif = og(i) - og(i-1)
        temp2 = (g(i) - g(i-1)) - sigma*gdif
        temp3 = (c(i) - c(i-1)) + rmu*gdif
        DO 110 l = 1,neqn
          yout(l) = yout(l) + temp2*phi(l,i)
 110      ypout(l) = ypout(l) + temp3*phi(l,i)
 120    CONTINUE
      DO 130 l = 1,neqn
        yout(l) = ((1.0d0 - sigma)*oy(l) + sigma*y(l)) +
     1             h*(yout(l) + (g(1) - sigma*og(1))*phi(l,1))
 130    ypout(l) = hmu*(oy(l) - y(l)) +
     1                (ypout(l) + (c(1) + rmu*og(1))*phi(l,1))
C
      RETURN

dsteps()

subroutine dsteps	(	external	DF,
		integer	NEQN,
		double precision, dimension(*)	Y,
		double precision	X,
		double precision	H,
		double precision	EPS,
		double precision, dimension(*)	WT,
		logical	START,
		double precision	HOLD,
		integer	K,
		integer	KOLD,
		logical	CRASH,
		double precision, dimension(neqn,16)	PHI,
		double precision, dimension(*)	P,
		double precision, dimension(*)	YP,
		double precision, dimension(12)	PSI,
		double precision, dimension(12)	ALPHA,
		double precision, dimension(12)	BETA,
		double precision, dimension(13)	SIG,
		double precision, dimension(12)	V,
		double precision, dimension(12)	W,
		double precision, dimension(13)	G,
		logical	PHASE1,
		integer	NS,
		logical	NORND,
		integer	KSTEPS,
		double precision	TWOU,
		double precision	FOURU,
		double precision	XOLD,
			KPREV,
			IVC,
		dimension(10)	IV,
			KGI,
		double precision, dimension(11)	GI,
		double precision, dimension(*)	RPAR,
		integer, dimension(*)	IPAR
	)

C***BEGIN PROLOGUE  DSTEPS
C***PURPOSE  Integrate a system of first order ordinary differential
C            equations one step.
C***LIBRARY   SLATEC (DEPAC)
C***CATEGORY  I1A1B
C***TYPE      DOUBLE PRECISION (STEPS-S, DSTEPS-D)
C***KEYWORDS  ADAMS METHOD, DEPAC, INITIAL VALUE PROBLEMS, ODE,
C             ORDINARY DIFFERENTIAL EQUATIONS, PREDICTOR-CORRECTOR
C***AUTHOR  Shampine, L. F., (SNLA)
C           Gordon, M. K., (SNLA)
C             MODIFIED BY H.A. WATTS
C***DESCRIPTION
C
C   Written by L. F. Shampine and M. K. Gordon
C
C   Abstract
C
C   Subroutine  DSTEPS  is normally used indirectly through subroutine
C   DDEABM .  Because  DDEABM  suffices for most problems and is much
C   easier to use, using it should be considered before using  DSTEPS
C   alone.
C
C   Subroutine DSTEPS integrates a system of  NEQN  first order ordinary
C   differential equations one step, normally from X to X+H, using a
C   modified divided difference form of the Adams Pece formulas.  Local
C   extrapolation is used to improve absolute stability and accuracy.
C   The code adjusts its order and step size to control the local error
C   per unit step in a generalized sense.  Special devices are included
C   to control roundoff error and to detect when the user is requesting
C   too much accuracy.
C
C   This code is completely explained and documented in the text,
C   Computer Solution of Ordinary Differential Equations, The Initial
C   Value Problem  by L. F. Shampine and M. K. Gordon.
C   Further details on use of this code are available in "Solving
C   Ordinary Differential Equations with ODE, STEP, and INTRP",
C   by L. F. Shampine and M. K. Gordon, SLA-73-1060.
C
C
C   The parameters represent --
C      DF -- subroutine to evaluate derivatives
C      NEQN -- number of equations to be integrated
C      Y(*) -- solution vector at X
C      X -- independent variable
C      H -- appropriate step size for next step.  Normally determined by
C           code
C      EPS -- local error tolerance
C      WT(*) -- vector of weights for error criterion
C      START -- logical variable set .TRUE. for first step,  .FALSE.
C           otherwise
C      HOLD -- step size used for last successful step
C      K -- appropriate order for next step (determined by code)
C      KOLD -- order used for last successful step
C      CRASH -- logical variable set .TRUE. when no step can be taken,
C           .FALSE. otherwise.
C      YP(*) -- derivative of solution vector at  X  after successful
C           step
C      KSTEPS -- counter on attempted steps
C      TWOU -- 2.*U where U is machine unit roundoff quantity
C      FOURU -- 4.*U where U is machine unit roundoff quantity
C      RPAR,IPAR -- parameter arrays which you may choose to use
C            for communication between your program and subroutine F.
C            They are not altered or used by DSTEPS.
C   The variables X,XOLD,KOLD,KGI and IVC and the arrays Y,PHI,ALPHA,G,
C   W,P,IV and GI are required for the interpolation subroutine SINTRP.
C   The remaining variables and arrays are included in the call list
C   only to eliminate local retention of variables between calls.
C
C   Input to DSTEPS
C
C      First call --
C
C   The user must provide storage in his calling program for all arrays
C   in the call list, namely
C
C     DIMENSION Y(NEQN),WT(NEQN),PHI(NEQN,16),P(NEQN),YP(NEQN),PSI(12),
C    1  ALPHA(12),BETA(12),SIG(13),V(12),W(12),G(13),GI(11),IV(10),
C    2  RPAR(*),IPAR(*)
C
C    **Note**
C
C   The user must also declare  START ,  CRASH ,  PHASE1  and  NORND
C   logical variables and  DF  an EXTERNAL subroutine, supply the
C   subroutine  DF(X,Y,YP)  to evaluate
C      DY(I)/DX = YP(I) = DF(X,Y(1),Y(2),...,Y(NEQN))
C   and initialize only the following parameters.
C      NEQN -- number of equations to be integrated
C      Y(*) -- vector of initial values of dependent variables
C      X -- initial value of the independent variable
C      H -- nominal step size indicating direction of integration
C           and maximum size of step.  Must be variable
C      EPS -- local error tolerance per step.  Must be variable
C      WT(*) -- vector of non-zero weights for error criterion
C      START -- .TRUE.
C      YP(*) -- vector of initial derivative values
C      KSTEPS -- set KSTEPS to zero
C      TWOU -- 2.*U where U is machine unit roundoff quantity
C      FOURU -- 4.*U where U is machine unit roundoff quantity
C   Define U to be the machine unit roundoff quantity by calling
C   the function routine  D1MACH,  U = D1MACH(4), or by
C   computing U so that U is the smallest positive number such
C   that 1.0+U .GT. 1.0.
C
C   DSTEPS  requires that the L2 norm of the vector with components
C   LOCAL ERROR(L)/WT(L)  be less than  EPS  for a successful step.  The
C   array  WT  allows the user to specify an error test appropriate
C   for his problem.  For example,
C      WT(L) = 1.0  specifies absolute error,
C            = ABS(Y(L))  error relative to the most recent value of the
C                 L-th component of the solution,
C            = ABS(YP(L))  error relative to the most recent value of
C                 the L-th component of the derivative,
C            = MAX(WT(L),ABS(Y(L)))  error relative to the largest
C                 magnitude of L-th component obtained so far,
C            = ABS(Y(L))*RELERR/EPS + ABSERR/EPS  specifies a mixed
C                 relative-absolute test where  RELERR  is relative
C                 error,  ABSERR  is absolute error and  EPS =
C                 MAX(RELERR,ABSERR) .
C
C      Subsequent calls --
C
C   Subroutine  DSTEPS  is designed so that all information needed to
C   continue the integration, including the step size  H  and the order
C   K , is returned with each step.  With the exception of the step
C   size, the error tolerance, and the weights, none of the parameters
C   should be altered.  The array  WT  must be updated after each step
C   to maintain relative error tests like those above.  Normally the
C   integration is continued just beyond the desired endpoint and the
C   solution interpolated there with subroutine  SINTRP .  If it is
C   impossible to integrate beyond the endpoint, the step size may be
C   reduced to hit the endpoint since the code will not take a step
C   larger than the  H  input.  Changing the direction of integration,
C   i.e., the sign of  H , requires the user set  START = .TRUE. before
C   calling  DSTEPS  again.  This is the only situation in which  START
C   should be altered.
C
C   Output from DSTEPS
C
C      Successful Step --
C
C   The subroutine returns after each successful step with  START  and
C   CRASH  set .FALSE. .  X  represents the independent variable
C   advanced one step of length  HOLD  from its value on input and  Y
C   the solution vector at the new value of  X .  All other parameters
C   represent information corresponding to the new  X  needed to
C   continue the integration.
C
C      Unsuccessful Step --
C
C   When the error tolerance is too small for the machine precision,
C   the subroutine returns without taking a step and  CRASH = .TRUE. .
C   An appropriate step size and error tolerance for continuing are
C   estimated and all other information is restored as upon input
C   before returning.  To continue with the larger tolerance, the user
C   just calls the code again.  A restart is neither required nor
C   desirable.
C
C***REFERENCES  L. F. Shampine and M. K. Gordon, Solving ordinary
C                 differential equations with ODE, STEP, and INTRP,
C                 Report SLA-73-1060, Sandia Laboratories, 1973.
C***ROUTINES CALLED  D1MACH, DHSTRT
C***REVISION HISTORY  (YYMMDD)
C   740101  DATE WRITTEN
C   890531  Changed all specific intrinsics to generic.  (WRB)
C   890831  Modified array declarations.  (WRB)
C   890831  REVISION DATE from Version 3.2
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C   920501  Reformatted the REFERENCES section.  (WRB)
C***END PROLOGUE  DSTEPS
C
      INTEGER i, ifail, im1, ip1, ipar, iq, j, k, km1, km2, knew,
     1      kold, kp1, kp2, ksteps, l, limit1, limit2, neqn, ns, nsm2,
     2      nsp1, nsp2
      DOUBLE PRECISION absh, alpha, beta, big, d1mach,
     1      eps, erk, erkm1, erkm2, erkp1, err,
     2      fouru, g, gi, gstr, h, hnew, hold, p, p5eps, phi, psi, r,
     3      reali, realns, rho, round, rpar, sig, tau, temp1,
     4      temp2, temp3, temp4, temp5, temp6, two, twou, u, v, w, wt,
     5      x, xold, y, yp
      LOGICAL start,crash,phase1,nornd
      dimension y(*),wt(*),phi(neqn,16),p(*),yp(*),psi(12),
     1  alpha(12),beta(12),sig(13),v(12),w(12),g(13),gi(11),iv(10),
     2  rpar(*),ipar(*)
      dimension two(13),gstr(13)
      EXTERNAL df
      SAVE two, gstr
C
      DATA two(1),two(2),two(3),two(4),two(5),two(6),two(7),two(8),
     1     two(9),two(10),two(11),two(12),two(13)
     2     /2.0d0,4.0d0,8.0d0,16.0d0,32.0d0,64.0d0,128.0d0,256.0d0,
     3      512.0d0,1024.0d0,2048.0d0,4096.0d0,8192.0d0/
      DATA gstr(1),gstr(2),gstr(3),gstr(4),gstr(5),gstr(6),gstr(7),
     1     gstr(8),gstr(9),gstr(10),gstr(11),gstr(12),gstr(13)
     2     /0.5d0,0.0833d0,0.0417d0,0.0264d0,0.0188d0,0.0143d0,0.0114d0,
     3      0.00936d0,0.00789d0,0.00679d0,0.00592d0,0.00524d0,0.00468d0/
C
C       ***     BEGIN BLOCK 0     ***
C   CHECK IF STEP SIZE OR ERROR TOLERANCE IS TOO SMALL FOR MACHINE
C   PRECISION.  IF FIRST STEP, INITIALIZE PHI ARRAY AND ESTIMATE A
C   STARTING STEP SIZE.
C                   ***
C
C   IF STEP SIZE IS TOO SMALL, DETERMINE AN ACCEPTABLE ONE
C
C***FIRST EXECUTABLE STATEMENT  DSTEPS
      crash = .true.
      IF(abs(h) .GE. fouru*abs(x)) GO TO 5
      h = sign(fouru*abs(x),h)
      RETURN
 5    p5eps = 0.5d0*eps
C
C   IF ERROR TOLERANCE IS TOO SMALL, INCREASE IT TO AN ACCEPTABLE VALUE
C
      round = 0.0d0
      DO 10 l = 1,neqn
 10     round = round + (y(l)/wt(l))**2
      round = twou*sqrt(round)
      IF(p5eps .GE. round) GO TO 15
      eps = 2.0d0*round*(1.0d0 + fouru)
      RETURN
 15   crash = .false.
      g(1) = 1.0d0
      g(2) = 0.5d0
      sig(1) = 1.0d0
      IF(.NOT.start) GO TO 99
C
C   INITIALIZE.  COMPUTE APPROPRIATE STEP SIZE FOR FIRST STEP
C
C     CALL DF(X,Y,YP,RPAR,IPAR)
C     SUM = 0.0
      DO 20 l = 1,neqn
        phi(l,1) = yp(l)
   20   phi(l,2) = 0.0d0
C20     SUM = SUM + (YP(L)/WT(L))**2
C     SUM = SQRT(SUM)
C     ABSH = ABS(H)
C     IF(EPS .LT. 16.0*SUM*H*H) ABSH = 0.25*SQRT(EPS/SUM)
C     H = SIGN(MAX(ABSH,FOURU*ABS(X)),H)
C
      u = d1mach(4)
      big = sqrt(d1mach(2))
      CALL dhstrt(df,neqn,x,x+h,y,yp,wt,1,u,big,
     1             phi(1,3),phi(1,4),phi(1,5),phi(1,6),rpar,ipar,h)
C
      hold = 0.0d0
      k = 1
      kold = 0
      kprev = 0
      start = .false.
      phase1 = .true.
      nornd = .true.
      IF(p5eps .GT. 100.0d0*round) GO TO 99
      nornd = .false.
      DO 25 l = 1,neqn
 25     phi(l,15) = 0.0d0
 99   ifail = 0
C       ***     END BLOCK 0     ***
C
C       ***     BEGIN BLOCK 1     ***
C   COMPUTE COEFFICIENTS OF FORMULAS FOR THIS STEP.  AVOID COMPUTING
C   THOSE QUANTITIES NOT CHANGED WHEN STEP SIZE IS NOT CHANGED.
C                   ***
C
 100  kp1 = k+1
      kp2 = k+2
      km1 = k-1
      km2 = k-2
C
C   NS IS THE NUMBER OF DSTEPS TAKEN WITH SIZE H, INCLUDING THE CURRENT
C   ONE.  WHEN K.LT.NS, NO COEFFICIENTS CHANGE
C
      IF(h .NE. hold) ns = 0
      IF (ns.LE.kold) ns = ns+1
      nsp1 = ns+1
      IF (k .LT. ns) GO TO 199
C
C   COMPUTE THOSE COMPONENTS OF ALPHA(*),BETA(*),PSI(*),SIG(*) WHICH
C   ARE CHANGED
C
      beta(ns) = 1.0d0
      realns = ns
      alpha(ns) = 1.0d0/realns
      temp1 = h*realns
      sig(nsp1) = 1.0d0
      IF(k .LT. nsp1) GO TO 110
      DO 105 i = nsp1,k
        im1 = i-1
        temp2 = psi(im1)
        psi(im1) = temp1
        beta(i) = beta(im1)*psi(im1)/temp2
        temp1 = temp2 + h
        alpha(i) = h/temp1
        reali = i
 105    sig(i+1) = reali*alpha(i)*sig(i)
 110  psi(k) = temp1
C
C   COMPUTE COEFFICIENTS G(*)
C
C   INITIALIZE V(*) AND SET W(*).
C
      IF(ns .GT. 1) GO TO 120
      DO 115 iq = 1,k
        temp3 = iq*(iq+1)
        v(iq) = 1.0d0/temp3
 115    w(iq) = v(iq)
      ivc = 0
      kgi = 0
      IF (k .EQ. 1) GO TO 140
      kgi = 1
      gi(1) = w(2)
      GO TO 140
C
C   IF ORDER WAS RAISED, UPDATE DIAGONAL PART OF V(*)
C
 120  IF(k .LE. kprev) GO TO 130
      IF (ivc .EQ. 0) GO TO 122
      jv = kp1 - iv(ivc)
      ivc = ivc - 1
      GO TO 123
 122  jv = 1
      temp4 = k*kp1
      v(k) = 1.0d0/temp4
      w(k) = v(k)
      IF (k .NE. 2) GO TO 123
      kgi = 1
      gi(1) = w(2)
 123  nsm2 = ns-2
      IF(nsm2 .LT. jv) GO TO 130
      DO 125 j = jv,nsm2
        i = k-j
        v(i) = v(i) - alpha(j+1)*v(i+1)
 125    w(i) = v(i)
      IF (i .NE. 2) GO TO 130
      kgi = ns - 1
      gi(kgi) = w(2)
C
C   UPDATE V(*) AND SET W(*)
C
 130  limit1 = kp1 - ns
      temp5 = alpha(ns)
      DO 135 iq = 1,limit1
        v(iq) = v(iq) - temp5*v(iq+1)
 135    w(iq) = v(iq)
      g(nsp1) = w(1)
      IF (limit1 .EQ. 1) GO TO 137
      kgi = ns
      gi(kgi) = w(2)
 137  w(limit1+1) = v(limit1+1)
      IF (k .GE. kold) GO TO 140
      ivc = ivc + 1
      iv(ivc) = limit1 + 2
C
C   COMPUTE THE G(*) IN THE WORK VECTOR W(*)
C
 140  nsp2 = ns + 2
      kprev = k
      IF(kp1 .LT. nsp2) GO TO 199
      DO 150 i = nsp2,kp1
        limit2 = kp2 - i
        temp6 = alpha(i-1)
        DO 145 iq = 1,limit2
 145      w(iq) = w(iq) - temp6*w(iq+1)
 150    g(i) = w(1)
 199    CONTINUE
C       ***     END BLOCK 1     ***
C
C       ***     BEGIN BLOCK 2     ***
C   PREDICT A SOLUTION P(*), EVALUATE DERIVATIVES USING PREDICTED
C   SOLUTION, ESTIMATE LOCAL ERROR AT ORDER K AND ERRORS AT ORDERS K,
C   K-1, K-2 AS IF CONSTANT STEP SIZE WERE USED.
C                   ***
C
C   INCREMENT COUNTER ON ATTEMPTED DSTEPS
C
      ksteps = ksteps + 1
C
C   CHANGE PHI TO PHI STAR
C
      IF(k .LT. nsp1) GO TO 215
      DO 210 i = nsp1,k
        temp1 = beta(i)
        DO 205 l = 1,neqn
 205      phi(l,i) = temp1*phi(l,i)
 210    CONTINUE
C
C   PREDICT SOLUTION AND DIFFERENCES
C
 215  DO 220 l = 1,neqn
        phi(l,kp2) = phi(l,kp1)
        phi(l,kp1) = 0.0d0
 220    p(l) = 0.0d0
      DO 230 j = 1,k
        i = kp1 - j
        ip1 = i+1
        temp2 = g(i)
        DO 225 l = 1,neqn
          p(l) = p(l) + temp2*phi(l,i)
 225      phi(l,i) = phi(l,i) + phi(l,ip1)
 230    CONTINUE
      IF(nornd) GO TO 240
      DO 235 l = 1,neqn
        tau = h*p(l) - phi(l,15)
        p(l) = y(l) + tau
 235    phi(l,16) = (p(l) - y(l)) - tau
      GO TO 250
 240  DO 245 l = 1,neqn
 245    p(l) = y(l) + h*p(l)
 250  xold = x
      x = x + h
      absh = abs(h)
      CALL df(x,p,yp,rpar,ipar)
C
C   ESTIMATE ERRORS AT ORDERS K,K-1,K-2
C
      erkm2 = 0.0d0
      erkm1 = 0.0d0
      erk = 0.0d0
      DO 265 l = 1,neqn
        temp3 = 1.0d0/wt(l)
        temp4 = yp(l) - phi(l,1)
        IF(km2)265,260,255
 255    erkm2 = erkm2 + ((phi(l,km1)+temp4)*temp3)**2
 260    erkm1 = erkm1 + ((phi(l,k)+temp4)*temp3)**2
 265    erk = erk + (temp4*temp3)**2
      IF(km2)280,275,270
 270  erkm2 = absh*sig(km1)*gstr(km2)*sqrt(erkm2)
 275  erkm1 = absh*sig(k)*gstr(km1)*sqrt(erkm1)
 280  temp5 = absh*sqrt(erk)
      err = temp5*(g(k)-g(kp1))
      erk = temp5*sig(kp1)*gstr(k)
      knew = k
C
C   TEST IF ORDER SHOULD BE LOWERED
C
      IF(km2)299,290,285
 285  IF(max(erkm1,erkm2) .LE. erk) knew = km1
      GO TO 299
 290  IF(erkm1 .LE. 0.5d0*erk) knew = km1
C
C   TEST IF STEP SUCCESSFUL
C
 299  IF(err .LE. eps) GO TO 400
C       ***     END BLOCK 2     ***
C
C       ***     BEGIN BLOCK 3     ***
C   THE STEP IS UNSUCCESSFUL.  RESTORE  X, PHI(*,*), PSI(*) .
C   IF THIRD CONSECUTIVE FAILURE, SET ORDER TO ONE.  IF STEP FAILS MORE
C   THAN THREE TIMES, CONSIDER AN OPTIMAL STEP SIZE.  DOUBLE ERROR
C   TOLERANCE AND RETURN IF ESTIMATED STEP SIZE IS TOO SMALL FOR MACHINE
C   PRECISION.
C                   ***
C
C   RESTORE X, PHI(*,*) AND PSI(*)
C
      phase1 = .false.
      x = xold
      DO 310 i = 1,k
        temp1 = 1.0d0/beta(i)
        ip1 = i+1
        DO 305 l = 1,neqn
 305      phi(l,i) = temp1*(phi(l,i) - phi(l,ip1))
 310    CONTINUE
      IF(k .LT. 2) GO TO 320
      DO 315 i = 2,k
 315    psi(i-1) = psi(i) - h
C
C   ON THIRD FAILURE, SET ORDER TO ONE.  THEREAFTER, USE OPTIMAL STEP
C   SIZE
C
 320  ifail = ifail + 1
      temp2 = 0.5d0
      IF(ifail - 3) 335,330,325
 325  IF(p5eps .LT. 0.25d0*erk) temp2 = sqrt(p5eps/erk)
 330  knew = 1
 335  h = temp2*h
      k = knew
      ns = 0
      IF(abs(h) .GE. fouru*abs(x)) GO TO 340
      crash = .true.
      h = sign(fouru*abs(x),h)
      eps = eps + eps
      RETURN
 340  GO TO 100
C       ***     END BLOCK 3     ***
C
C       ***     BEGIN BLOCK 4     ***
C   THE STEP IS SUCCESSFUL.  CORRECT THE PREDICTED SOLUTION, EVALUATE
C   THE DERIVATIVES USING THE CORRECTED SOLUTION AND UPDATE THE
C   DIFFERENCES.  DETERMINE BEST ORDER AND STEP SIZE FOR NEXT STEP.
C                   ***
 400  kold = k
      hold = h
C
C   CORRECT AND EVALUATE
C
      temp1 = h*g(kp1)
      IF(nornd) GO TO 410
      DO 405 l = 1,neqn
        temp3 = y(l)
        rho = temp1*(yp(l) - phi(l,1)) - phi(l,16)
        y(l) = p(l) + rho
        phi(l,15) = (y(l) - p(l)) - rho
 405    p(l) = temp3
      GO TO 420
 410  DO 415 l = 1,neqn
        temp3 = y(l)
        y(l) = p(l) + temp1*(yp(l) - phi(l,1))
 415    p(l) = temp3
 420  CALL df(x,y,yp,rpar,ipar)
C
C   UPDATE DIFFERENCES FOR NEXT STEP
C
      DO 425 l = 1,neqn
        phi(l,kp1) = yp(l) - phi(l,1)
 425    phi(l,kp2) = phi(l,kp1) - phi(l,kp2)
      DO 435 i = 1,k
        DO 430 l = 1,neqn
 430      phi(l,i) = phi(l,i) + phi(l,kp1)
 435    CONTINUE
C
C   ESTIMATE ERROR AT ORDER K+1 UNLESS:
C     IN FIRST PHASE WHEN ALWAYS RAISE ORDER,
C     ALREADY DECIDED TO LOWER ORDER,
C     STEP SIZE NOT CONSTANT SO ESTIMATE UNRELIABLE
C
      erkp1 = 0.0d0
      IF(knew .EQ. km1  .OR.  k .EQ. 12) phase1 = .false.
      IF(phase1) GO TO 450
      IF(knew .EQ. km1) GO TO 455
      IF(kp1 .GT. ns) GO TO 460
      DO 440 l = 1,neqn
 440    erkp1 = erkp1 + (phi(l,kp2)/wt(l))**2
      erkp1 = absh*gstr(kp1)*sqrt(erkp1)
C
C   USING ESTIMATED ERROR AT ORDER K+1, DETERMINE APPROPRIATE ORDER
C   FOR NEXT STEP
C
      IF(k .GT. 1) GO TO 445
      IF(erkp1 .GE. 0.5d0*erk) GO TO 460
      GO TO 450
 445  IF(erkm1 .LE. min(erk,erkp1)) GO TO 455
      IF(erkp1 .GE. erk  .OR.  k .EQ. 12) GO TO 460
C
C   HERE ERKP1 .LT. ERK .LT. MAX(ERKM1,ERKM2) ELSE ORDER WOULD HAVE
C   BEEN LOWERED IN BLOCK 2.  THUS ORDER IS TO BE RAISED
C
C   RAISE ORDER
C
 450  k = kp1
      erk = erkp1
      GO TO 460
C
C   LOWER ORDER
C
 455  k = km1
      erk = erkm1
C
C   WITH NEW ORDER DETERMINE APPROPRIATE STEP SIZE FOR NEXT STEP
C
 460  hnew = h + h
      IF(phase1) GO TO 465
      IF(p5eps .GE. erk*two(k+1)) GO TO 465
      hnew = h
      IF(p5eps .GE. erk) GO TO 465
      temp2 = k+1
      r = (p5eps/erk)**(1.0d0/temp2)
      hnew = absh*max(0.5d0,min(0.9d0,r))
      hnew = sign(max(hnew,fouru*abs(x)),h)
 465  h = hnew
      RETURN
C       ***     END BLOCK 4     ***

fdump()

subroutine fdump

(

)

C***BEGIN PROLOGUE  FDUMP
C***PURPOSE  Symbolic dump (should be locally written).
C***LIBRARY   SLATEC (XERROR)
C***CATEGORY  R3
C***TYPE      ALL (FDUMP-A)
C***KEYWORDS  ERROR, XERMSG
C***AUTHOR  Jones, R. E., (SNLA)
C***DESCRIPTION
C
C        ***Note*** Machine Dependent Routine
C        FDUMP is intended to be replaced by a locally written
C        version which produces a symbolic dump.  Failing this,
C        it should be replaced by a version which prints the
C        subprogram nesting list.  Note that this dump must be
C        printed on each of up to five files, as indicated by the
C        XGETUA routine.  See XSETUA and XGETUA for details.
C
C     Written by Ron Jones, with SLATEC Common Math Library Subcommittee
C
C***REFERENCES  (NONE)
C***ROUTINES CALLED  (NONE)
C***REVISION HISTORY  (YYMMDD)
C   790801  DATE WRITTEN
C   861211  REVISION DATE from Version 3.2
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C***END PROLOGUE  FDUMP
C***FIRST EXECUTABLE STATEMENT  FDUMP
      RETURN

i1mach()

integer function i1mach

(

I

)

C***BEGIN PROLOGUE  I1MACH
C***PURPOSE  Return integer machine dependent constants.
C***LIBRARY   SLATEC
C***CATEGORY  R1
C***TYPE      INTEGER (I1MACH-I)
C***KEYWORDS  MACHINE CONSTANTS
C***AUTHOR  Fox, P. A., (Bell Labs)
C           Hall, A. D., (Bell Labs)
C           Schryer, N. L., (Bell Labs)
C***DESCRIPTION
C
C   I1MACH can be used to obtain machine-dependent parameters for the
C   local machine environment.  It is a function subprogram with one
C   (input) argument and can be referenced as follows:
C
C        K = I1MACH(I)
C
C   where I=1,...,16.  The (output) value of K above is determined by
C   the (input) value of I.  The results for various values of I are
C   discussed below.
C
C   I/O unit numbers:
C     I1MACH( 1) = the standard input unit.
C     I1MACH( 2) = the standard output unit.
C     I1MACH( 3) = the standard punch unit.
C     I1MACH( 4) = the standard error message unit.
C
C   Words:
C     I1MACH( 5) = the number of bits per integer storage unit.
C     I1MACH( 6) = the number of characters per integer storage unit.
C
C   Integers:
C     assume integers are represented in the S-digit, base-A form
C
C                sign ( X(S-1)*A**(S-1) + ... + X(1)*A + X(0) )
C
C                where 0 .LE. X(I) .LT. A for I=0,...,S-1.
C     I1MACH( 7) = A, the base.
C     I1MACH( 8) = S, the number of base-A digits.
C     I1MACH( 9) = A**S - 1, the largest magnitude.
C
C   Floating-Point Numbers:
C     Assume floating-point numbers are represented in the T-digit,
C     base-B form
C                sign (B**E)*( (X(1)/B) + ... + (X(T)/B**T) )
C
C                where 0 .LE. X(I) .LT. B for I=1,...,T,
C                0 .LT. X(1), and EMIN .LE. E .LE. EMAX.
C     I1MACH(10) = B, the base.
C
C   Single-Precision:
C     I1MACH(11) = T, the number of base-B digits.
C     I1MACH(12) = EMIN, the smallest exponent E.
C     I1MACH(13) = EMAX, the largest exponent E.
C
C   Double-Precision:
C     I1MACH(14) = T, the number of base-B digits.
C     I1MACH(15) = EMIN, the smallest exponent E.
C     I1MACH(16) = EMAX, the largest exponent E.
C
C   To alter this function for a particular environment, the desired
C   set of DATA statements should be activated by removing the C from
C   column 1.  Also, the values of I1MACH(1) - I1MACH(4) should be
C   checked for consistency with the local operating system.
C
C***REFERENCES  P. A. Fox, A. D. Hall and N. L. Schryer, Framework for
C                 a portable library, ACM Transactions on Mathematical
C                 Software 4, 2 (June 1978), pp. 177-188.
C***ROUTINES CALLED  (NONE)
C***REVISION HISTORY  (YYMMDD)
C   750101  DATE WRITTEN
C   891012  Added VAX G-floating constants.  (WRB)
C   891012  REVISION DATE from Version 3.2
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C   900618  Added DEC RISC constants.  (WRB)
C   900723  Added IBM RS 6000 constants.  (WRB)
C   901009  Correct I1MACH(7) for IBM Mainframes. Should be 2 not 16.
C           (RWC)
C   910710  Added HP 730 constants.  (SMR)
C   911114  Added Convex IEEE constants.  (WRB)
C   920121  Added SUN -r8 compiler option constants.  (WRB)
C   920229  Added Touchstone Delta i860 constants.  (WRB)
C   920501  Reformatted the REFERENCES section.  (WRB)
C   920625  Added Convex -p8 and -pd8 compiler option constants.
C           (BKS, WRB)
C   930201  Added DEC Alpha and SGI constants.  (RWC and WRB)
C   930618  Corrected I1MACH(5) for Convex -p8 and -pd8 compiler
C           options.  (DWL, RWC and WRB).
C   010817  Elevated IEEE to highest importance; see next set of
C           comments below.  (DWL)
C***END PROLOGUE  I1MACH
C
C Initial data here correspond to the IEEE standard.  If one of the
C sets of initial data below is preferred, do the necessary commenting
C and uncommenting. (DWL)
      INTEGER imach(16),output
      DATA imach( 1) /          5 /
      DATA imach( 2) /          6 /
      DATA imach( 3) /          6 /
      DATA imach( 4) /          6 /
      DATA imach( 5) /         32 /
      DATA imach( 6) /          4 /
      DATA imach( 7) /          2 /
      DATA imach( 8) /         31 /
      DATA imach( 9) / 2147483647 /
      DATA imach(10) /          2 /
      DATA imach(11) /         24 /
      DATA imach(12) /       -126 /
      DATA imach(13) /        127 /
      DATA imach(14) /         53 /
      DATA imach(15) /      -1022 /
      DATA imach(16) /       1023 /
      SAVE imach
cc      EQUIVALENCE (IMACH(4),OUTPUT)
C
C     MACHINE CONSTANTS FOR THE AMIGA
C     ABSOFT COMPILER
C
C     DATA IMACH( 1) /          5 /
C     DATA IMACH( 2) /          6 /
C     DATA IMACH( 3) /          5 /
C     DATA IMACH( 4) /          6 /
C     DATA IMACH( 5) /         32 /
C     DATA IMACH( 6) /          4 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         31 /
C     DATA IMACH( 9) / 2147483647 /
C     DATA IMACH(10) /          2 /
C     DATA IMACH(11) /         24 /
C     DATA IMACH(12) /       -126 /
C     DATA IMACH(13) /        127 /
C     DATA IMACH(14) /         53 /
C     DATA IMACH(15) /      -1022 /
C     DATA IMACH(16) /       1023 /
C
C     MACHINE CONSTANTS FOR THE APOLLO
C
C     DATA IMACH( 1) /          5 /
C     DATA IMACH( 2) /          6 /
C     DATA IMACH( 3) /          6 /
C     DATA IMACH( 4) /          6 /
C     DATA IMACH( 5) /         32 /
C     DATA IMACH( 6) /          4 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         31 /
C     DATA IMACH( 9) / 2147483647 /
C     DATA IMACH(10) /          2 /
C     DATA IMACH(11) /         24 /
C     DATA IMACH(12) /       -125 /
C     DATA IMACH(13) /        129 /
C     DATA IMACH(14) /         53 /
C     DATA IMACH(15) /      -1021 /
C     DATA IMACH(16) /       1025 /
C
C     MACHINE CONSTANTS FOR THE BURROUGHS 1700 SYSTEM
C
C     DATA IMACH( 1) /          7 /
C     DATA IMACH( 2) /          2 /
C     DATA IMACH( 3) /          2 /
C     DATA IMACH( 4) /          2 /
C     DATA IMACH( 5) /         36 /
C     DATA IMACH( 6) /          4 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         33 /
C     DATA IMACH( 9) / Z1FFFFFFFF /
C     DATA IMACH(10) /          2 /
C     DATA IMACH(11) /         24 /
C     DATA IMACH(12) /       -256 /
C     DATA IMACH(13) /        255 /
C     DATA IMACH(14) /         60 /
C     DATA IMACH(15) /       -256 /
C     DATA IMACH(16) /        255 /
C
C     MACHINE CONSTANTS FOR THE BURROUGHS 5700 SYSTEM
C
C     DATA IMACH( 1) /          5 /
C     DATA IMACH( 2) /          6 /
C     DATA IMACH( 3) /          7 /
C     DATA IMACH( 4) /          6 /
C     DATA IMACH( 5) /         48 /
C     DATA IMACH( 6) /          6 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         39 /
C     DATA IMACH( 9) / O0007777777777777 /
C     DATA IMACH(10) /          8 /
C     DATA IMACH(11) /         13 /
C     DATA IMACH(12) /        -50 /
C     DATA IMACH(13) /         76 /
C     DATA IMACH(14) /         26 /
C     DATA IMACH(15) /        -50 /
C     DATA IMACH(16) /         76 /
C
C     MACHINE CONSTANTS FOR THE BURROUGHS 6700/7700 SYSTEMS
C
C     DATA IMACH( 1) /          5 /
C     DATA IMACH( 2) /          6 /
C     DATA IMACH( 3) /          7 /
C     DATA IMACH( 4) /          6 /
C     DATA IMACH( 5) /         48 /
C     DATA IMACH( 6) /          6 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         39 /
C     DATA IMACH( 9) / O0007777777777777 /
C     DATA IMACH(10) /          8 /
C     DATA IMACH(11) /         13 /
C     DATA IMACH(12) /        -50 /
C     DATA IMACH(13) /         76 /
C     DATA IMACH(14) /         26 /
C     DATA IMACH(15) /     -32754 /
C     DATA IMACH(16) /      32780 /
C
C     MACHINE CONSTANTS FOR THE CDC 170/180 SERIES USING NOS/VE
C
C     DATA IMACH( 1) /          5 /
C     DATA IMACH( 2) /          6 /
C     DATA IMACH( 3) /          7 /
C     DATA IMACH( 4) /          6 /
C     DATA IMACH( 5) /         64 /
C     DATA IMACH( 6) /          8 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         63 /
C     DATA IMACH( 9) / 9223372036854775807 /
C     DATA IMACH(10) /          2 /
C     DATA IMACH(11) /         47 /
C     DATA IMACH(12) /      -4095 /
C     DATA IMACH(13) /       4094 /
C     DATA IMACH(14) /         94 /
C     DATA IMACH(15) /      -4095 /
C     DATA IMACH(16) /       4094 /
C
C     MACHINE CONSTANTS FOR THE CDC 6000/7000 SERIES
C
C     DATA IMACH( 1) /          5 /
C     DATA IMACH( 2) /          6 /
C     DATA IMACH( 3) /          7 /
C     DATA IMACH( 4) /    6LOUTPUT/
C     DATA IMACH( 5) /         60 /
C     DATA IMACH( 6) /         10 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         48 /
C     DATA IMACH( 9) / 00007777777777777777B /
C     DATA IMACH(10) /          2 /
C     DATA IMACH(11) /         47 /
C     DATA IMACH(12) /       -929 /
C     DATA IMACH(13) /       1070 /
C     DATA IMACH(14) /         94 /
C     DATA IMACH(15) /       -929 /
C     DATA IMACH(16) /       1069 /
C
C     MACHINE CONSTANTS FOR THE CELERITY C1260
C
C     DATA IMACH( 1) /          5 /
C     DATA IMACH( 2) /          6 /
C     DATA IMACH( 3) /          6 /
C     DATA IMACH( 4) /          0 /
C     DATA IMACH( 5) /         32 /
C     DATA IMACH( 6) /          4 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         31 /
C     DATA IMACH( 9) / Z'7FFFFFFF' /
C     DATA IMACH(10) /          2 /
C     DATA IMACH(11) /         24 /
C     DATA IMACH(12) /       -126 /
C     DATA IMACH(13) /        127 /
C     DATA IMACH(14) /         53 /
C     DATA IMACH(15) /      -1022 /
C     DATA IMACH(16) /       1023 /
C
C     MACHINE CONSTANTS FOR THE CONVEX
C     USING THE -fn COMPILER OPTION
C
C     DATA IMACH( 1) /          5 /
C     DATA IMACH( 2) /          6 /
C     DATA IMACH( 3) /          7 /
C     DATA IMACH( 4) /          6 /
C     DATA IMACH( 5) /         32 /
C     DATA IMACH( 6) /          4 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         31 /
C     DATA IMACH( 9) / 2147483647 /
C     DATA IMACH(10) /          2 /
C     DATA IMACH(11) /         24 /
C     DATA IMACH(12) /       -127 /
C     DATA IMACH(13) /        127 /
C     DATA IMACH(14) /         53 /
C     DATA IMACH(15) /      -1023 /
C     DATA IMACH(16) /       1023 /
C
C     MACHINE CONSTANTS FOR THE CONVEX
C     USING THE -fi COMPILER OPTION
C
C     DATA IMACH( 1) /          5 /
C     DATA IMACH( 2) /          6 /
C     DATA IMACH( 3) /          7 /
C     DATA IMACH( 4) /          6 /
C     DATA IMACH( 5) /         32 /
C     DATA IMACH( 6) /          4 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         31 /
C     DATA IMACH( 9) / 2147483647 /
C     DATA IMACH(10) /          2 /
C     DATA IMACH(11) /         24 /
C     DATA IMACH(12) /       -125 /
C     DATA IMACH(13) /        128 /
C     DATA IMACH(14) /         53 /
C     DATA IMACH(15) /      -1021 /
C     DATA IMACH(16) /       1024 /
C
C     MACHINE CONSTANTS FOR THE CONVEX
C     USING THE -p8 COMPILER OPTION
C
C     DATA IMACH( 1) /          5 /
C     DATA IMACH( 2) /          6 /
C     DATA IMACH( 3) /          7 /
C     DATA IMACH( 4) /          6 /
C     DATA IMACH( 5) /         64 /
C     DATA IMACH( 6) /          4 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         63 /
C     DATA IMACH( 9) / 9223372036854775807 /
C     DATA IMACH(10) /          2 /
C     DATA IMACH(11) /         53 /
C     DATA IMACH(12) /      -1023 /
C     DATA IMACH(13) /       1023 /
C     DATA IMACH(14) /        113 /
C     DATA IMACH(15) /     -16383 /
C     DATA IMACH(16) /      16383 /
C
C     MACHINE CONSTANTS FOR THE CONVEX
C     USING THE -pd8 COMPILER OPTION
C
C     DATA IMACH( 1) /          5 /
C     DATA IMACH( 2) /          6 /
C     DATA IMACH( 3) /          7 /
C     DATA IMACH( 4) /          6 /
C     DATA IMACH( 5) /         64 /
C     DATA IMACH( 6) /          4 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         63 /
C     DATA IMACH( 9) / 9223372036854775807 /
C     DATA IMACH(10) /          2 /
C     DATA IMACH(11) /         53 /
C     DATA IMACH(12) /      -1023 /
C     DATA IMACH(13) /       1023 /
C     DATA IMACH(14) /         53 /
C     DATA IMACH(15) /      -1023 /
C     DATA IMACH(16) /       1023 /
C
C     MACHINE CONSTANTS FOR THE CRAY
C     USING THE 46 BIT INTEGER COMPILER OPTION
C
C     DATA IMACH( 1) /        100 /
C     DATA IMACH( 2) /        101 /
C     DATA IMACH( 3) /        102 /
C     DATA IMACH( 4) /        101 /
C     DATA IMACH( 5) /         64 /
C     DATA IMACH( 6) /          8 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         46 /
C     DATA IMACH( 9) / 1777777777777777B /
C     DATA IMACH(10) /          2 /
C     DATA IMACH(11) /         47 /
C     DATA IMACH(12) /      -8189 /
C     DATA IMACH(13) /       8190 /
C     DATA IMACH(14) /         94 /
C     DATA IMACH(15) /      -8099 /
C     DATA IMACH(16) /       8190 /
C
C     MACHINE CONSTANTS FOR THE CRAY
C     USING THE 64 BIT INTEGER COMPILER OPTION
C
C     DATA IMACH( 1) /        100 /
C     DATA IMACH( 2) /        101 /
C     DATA IMACH( 3) /        102 /
C     DATA IMACH( 4) /        101 /
C     DATA IMACH( 5) /         64 /
C     DATA IMACH( 6) /          8 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         63 /
C     DATA IMACH( 9) / 777777777777777777777B /
C     DATA IMACH(10) /          2 /
C     DATA IMACH(11) /         47 /
C     DATA IMACH(12) /      -8189 /
C     DATA IMACH(13) /       8190 /
C     DATA IMACH(14) /         94 /
C     DATA IMACH(15) /      -8099 /
C     DATA IMACH(16) /       8190 /
C
C     MACHINE CONSTANTS FOR THE DATA GENERAL ECLIPSE S/200
C
C     DATA IMACH( 1) /         11 /
C     DATA IMACH( 2) /         12 /
C     DATA IMACH( 3) /          8 /
C     DATA IMACH( 4) /         10 /
C     DATA IMACH( 5) /         16 /
C     DATA IMACH( 6) /          2 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         15 /
C     DATA IMACH( 9) /      32767 /
C     DATA IMACH(10) /         16 /
C     DATA IMACH(11) /          6 /
C     DATA IMACH(12) /        -64 /
C     DATA IMACH(13) /         63 /
C     DATA IMACH(14) /         14 /
C     DATA IMACH(15) /        -64 /
C     DATA IMACH(16) /         63 /
C
C     MACHINE CONSTANTS FOR THE DEC ALPHA
C     USING G_FLOAT
C
C     DATA IMACH( 1) /          5 /
C     DATA IMACH( 2) /          6 /
C     DATA IMACH( 3) /          5 /
C     DATA IMACH( 4) /          6 /
C     DATA IMACH( 5) /         32 /
C     DATA IMACH( 6) /          4 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         31 /
C     DATA IMACH( 9) / 2147483647 /
C     DATA IMACH(10) /          2 /
C     DATA IMACH(11) /         24 /
C     DATA IMACH(12) /       -127 /
C     DATA IMACH(13) /        127 /
C     DATA IMACH(14) /         53 /
C     DATA IMACH(15) /      -1023 /
C     DATA IMACH(16) /       1023 /
C
C     MACHINE CONSTANTS FOR THE DEC ALPHA
C     USING IEEE_FLOAT
C
C     DATA IMACH( 1) /          5 /
C     DATA IMACH( 2) /          6 /
C     DATA IMACH( 3) /          6 /
C     DATA IMACH( 4) /          6 /
C     DATA IMACH( 5) /         32 /
C     DATA IMACH( 6) /          4 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         31 /
C     DATA IMACH( 9) / 2147483647 /
C     DATA IMACH(10) /          2 /
C     DATA IMACH(11) /         24 /
C     DATA IMACH(12) /       -125 /
C     DATA IMACH(13) /        128 /
C     DATA IMACH(14) /         53 /
C     DATA IMACH(15) /      -1021 /
C     DATA IMACH(16) /       1024 /
C
C     MACHINE CONSTANTS FOR THE DEC RISC
C
C     DATA IMACH( 1) /          5 /
C     DATA IMACH( 2) /          6 /
C     DATA IMACH( 3) /          6 /
C     DATA IMACH( 4) /          6 /
C     DATA IMACH( 5) /         32 /
C     DATA IMACH( 6) /          4 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         31 /
C     DATA IMACH( 9) / 2147483647 /
C     DATA IMACH(10) /          2 /
C     DATA IMACH(11) /         24 /
C     DATA IMACH(12) /       -125 /
C     DATA IMACH(13) /        128 /
C     DATA IMACH(14) /         53 /
C     DATA IMACH(15) /      -1021 /
C     DATA IMACH(16) /       1024 /
C
C     MACHINE CONSTANTS FOR THE DEC VAX
C     USING D_FLOATING
C
C     DATA IMACH( 1) /          5 /
C     DATA IMACH( 2) /          6 /
C     DATA IMACH( 3) /          5 /
C     DATA IMACH( 4) /          6 /
C     DATA IMACH( 5) /         32 /
C     DATA IMACH( 6) /          4 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         31 /
C     DATA IMACH( 9) / 2147483647 /
C     DATA IMACH(10) /          2 /
C     DATA IMACH(11) /         24 /
C     DATA IMACH(12) /       -127 /
C     DATA IMACH(13) /        127 /
C     DATA IMACH(14) /         56 /
C     DATA IMACH(15) /       -127 /
C     DATA IMACH(16) /        127 /
C
C     MACHINE CONSTANTS FOR THE DEC VAX
C     USING G_FLOATING
C
C     DATA IMACH( 1) /          5 /
C     DATA IMACH( 2) /          6 /
C     DATA IMACH( 3) /          5 /
C     DATA IMACH( 4) /          6 /
C     DATA IMACH( 5) /         32 /
C     DATA IMACH( 6) /          4 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         31 /
C     DATA IMACH( 9) / 2147483647 /
C     DATA IMACH(10) /          2 /
C     DATA IMACH(11) /         24 /
C     DATA IMACH(12) /       -127 /
C     DATA IMACH(13) /        127 /
C     DATA IMACH(14) /         53 /
C     DATA IMACH(15) /      -1023 /
C     DATA IMACH(16) /       1023 /
C
C     MACHINE CONSTANTS FOR THE ELXSI 6400
C
C     DATA IMACH( 1) /          5 /
C     DATA IMACH( 2) /          6 /
C     DATA IMACH( 3) /          6 /
C     DATA IMACH( 4) /          6 /
C     DATA IMACH( 5) /         32 /
C     DATA IMACH( 6) /          4 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         32 /
C     DATA IMACH( 9) / 2147483647 /
C     DATA IMACH(10) /          2 /
C     DATA IMACH(11) /         24 /
C     DATA IMACH(12) /       -126 /
C     DATA IMACH(13) /        127 /
C     DATA IMACH(14) /         53 /
C     DATA IMACH(15) /      -1022 /
C     DATA IMACH(16) /       1023 /
C
C     MACHINE CONSTANTS FOR THE HARRIS 220
C
C     DATA IMACH( 1) /          5 /
C     DATA IMACH( 2) /          6 /
C     DATA IMACH( 3) /          0 /
C     DATA IMACH( 4) /          6 /
C     DATA IMACH( 5) /         24 /
C     DATA IMACH( 6) /          3 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         23 /
C     DATA IMACH( 9) /    8388607 /
C     DATA IMACH(10) /          2 /
C     DATA IMACH(11) /         23 /
C     DATA IMACH(12) /       -127 /
C     DATA IMACH(13) /        127 /
C     DATA IMACH(14) /         38 /
C     DATA IMACH(15) /       -127 /
C     DATA IMACH(16) /        127 /
C
C     MACHINE CONSTANTS FOR THE HONEYWELL 600/6000 SERIES
C
C     DATA IMACH( 1) /          5 /
C     DATA IMACH( 2) /          6 /
C     DATA IMACH( 3) /         43 /
C     DATA IMACH( 4) /          6 /
C     DATA IMACH( 5) /         36 /
C     DATA IMACH( 6) /          6 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         35 /
C     DATA IMACH( 9) / O377777777777 /
C     DATA IMACH(10) /          2 /
C     DATA IMACH(11) /         27 /
C     DATA IMACH(12) /       -127 /
C     DATA IMACH(13) /        127 /
C     DATA IMACH(14) /         63 /
C     DATA IMACH(15) /       -127 /
C     DATA IMACH(16) /        127 /
C
C     MACHINE CONSTANTS FOR THE HP 730
C
C     DATA IMACH( 1) /          5 /
C     DATA IMACH( 2) /          6 /
C     DATA IMACH( 3) /          6 /
C     DATA IMACH( 4) /          6 /
C     DATA IMACH( 5) /         32 /
C     DATA IMACH( 6) /          4 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         31 /
C     DATA IMACH( 9) / 2147483647 /
C     DATA IMACH(10) /          2 /
C     DATA IMACH(11) /         24 /
C     DATA IMACH(12) /       -125 /
C     DATA IMACH(13) /        128 /
C     DATA IMACH(14) /         53 /
C     DATA IMACH(15) /      -1021 /
C     DATA IMACH(16) /       1024 /
C
C     MACHINE CONSTANTS FOR THE HP 2100
C     3 WORD DOUBLE PRECISION OPTION WITH FTN4
C
C     DATA IMACH( 1) /          5 /
C     DATA IMACH( 2) /          6 /
C     DATA IMACH( 3) /          4 /
C     DATA IMACH( 4) /          1 /
C     DATA IMACH( 5) /         16 /
C     DATA IMACH( 6) /          2 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         15 /
C     DATA IMACH( 9) /      32767 /
C     DATA IMACH(10) /          2 /
C     DATA IMACH(11) /         23 /
C     DATA IMACH(12) /       -128 /
C     DATA IMACH(13) /        127 /
C     DATA IMACH(14) /         39 /
C     DATA IMACH(15) /       -128 /
C     DATA IMACH(16) /        127 /
C
C     MACHINE CONSTANTS FOR THE HP 2100
C     4 WORD DOUBLE PRECISION OPTION WITH FTN4
C
C     DATA IMACH( 1) /          5 /
C     DATA IMACH( 2) /          6 /
C     DATA IMACH( 3) /          4 /
C     DATA IMACH( 4) /          1 /
C     DATA IMACH( 5) /         16 /
C     DATA IMACH( 6) /          2 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         15 /
C     DATA IMACH( 9) /      32767 /
C     DATA IMACH(10) /          2 /
C     DATA IMACH(11) /         23 /
C     DATA IMACH(12) /       -128 /
C     DATA IMACH(13) /        127 /
C     DATA IMACH(14) /         55 /
C     DATA IMACH(15) /       -128 /
C     DATA IMACH(16) /        127 /
C
C     MACHINE CONSTANTS FOR THE HP 9000
C
C     DATA IMACH( 1) /          5 /
C     DATA IMACH( 2) /          6 /
C     DATA IMACH( 3) /          6 /
C     DATA IMACH( 4) /          7 /
C     DATA IMACH( 5) /         32 /
C     DATA IMACH( 6) /          4 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         32 /
C     DATA IMACH( 9) / 2147483647 /
C     DATA IMACH(10) /          2 /
C     DATA IMACH(11) /         24 /
C     DATA IMACH(12) /       -126 /
C     DATA IMACH(13) /        127 /
C     DATA IMACH(14) /         53 /
C     DATA IMACH(15) /      -1015 /
C     DATA IMACH(16) /       1017 /
C
C     MACHINE CONSTANTS FOR THE IBM 360/370 SERIES,
C     THE XEROX SIGMA 5/7/9, THE SEL SYSTEMS 85/86, AND
C     THE PERKIN ELMER (INTERDATA) 7/32.
C
C     DATA IMACH( 1) /          5 /
C     DATA IMACH( 2) /          6 /
C     DATA IMACH( 3) /          7 /
C     DATA IMACH( 4) /          6 /
C     DATA IMACH( 5) /         32 /
C     DATA IMACH( 6) /          4 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         31 /
C     DATA IMACH( 9) /  Z7FFFFFFF /
C     DATA IMACH(10) /         16 /
C     DATA IMACH(11) /          6 /
C     DATA IMACH(12) /        -64 /
C     DATA IMACH(13) /         63 /
C     DATA IMACH(14) /         14 /
C     DATA IMACH(15) /        -64 /
C     DATA IMACH(16) /         63 /
C
C     MACHINE CONSTANTS FOR THE IBM PC
C
C     DATA IMACH( 1) /          5 /
C     DATA IMACH( 2) /          6 /
C     DATA IMACH( 3) /          0 /
C     DATA IMACH( 4) /          0 /
C     DATA IMACH( 5) /         32 /
C     DATA IMACH( 6) /          4 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         31 /
C     DATA IMACH( 9) / 2147483647 /
C     DATA IMACH(10) /          2 /
C     DATA IMACH(11) /         24 /
C     DATA IMACH(12) /       -125 /
C     DATA IMACH(13) /        127 /
C     DATA IMACH(14) /         53 /
C     DATA IMACH(15) /      -1021 /
C     DATA IMACH(16) /       1023 /
C
C     MACHINE CONSTANTS FOR THE IBM RS 6000
C
C     DATA IMACH( 1) /          5 /
C     DATA IMACH( 2) /          6 /
C     DATA IMACH( 3) /          6 /
C     DATA IMACH( 4) /          0 /
C     DATA IMACH( 5) /         32 /
C     DATA IMACH( 6) /          4 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         31 /
C     DATA IMACH( 9) / 2147483647 /
C     DATA IMACH(10) /          2 /
C     DATA IMACH(11) /         24 /
C     DATA IMACH(12) /       -125 /
C     DATA IMACH(13) /        128 /
C     DATA IMACH(14) /         53 /
C     DATA IMACH(15) /      -1021 /
C     DATA IMACH(16) /       1024 /
C
C     MACHINE CONSTANTS FOR THE INTEL i860
C
C     DATA IMACH( 1) /          5 /
C     DATA IMACH( 2) /          6 /
C     DATA IMACH( 3) /          6 /
C     DATA IMACH( 4) /          6 /
C     DATA IMACH( 5) /         32 /
C     DATA IMACH( 6) /          4 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         31 /
C     DATA IMACH( 9) / 2147483647 /
C     DATA IMACH(10) /          2 /
C     DATA IMACH(11) /         24 /
C     DATA IMACH(12) /       -125 /
C     DATA IMACH(13) /        128 /
C     DATA IMACH(14) /         53 /
C     DATA IMACH(15) /      -1021 /
C     DATA IMACH(16) /       1024 /
C
C     MACHINE CONSTANTS FOR THE PDP-10 (KA PROCESSOR)
C
C     DATA IMACH( 1) /          5 /
C     DATA IMACH( 2) /          6 /
C     DATA IMACH( 3) /          5 /
C     DATA IMACH( 4) /          6 /
C     DATA IMACH( 5) /         36 /
C     DATA IMACH( 6) /          5 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         35 /
C     DATA IMACH( 9) / "377777777777 /
C     DATA IMACH(10) /          2 /
C     DATA IMACH(11) /         27 /
C     DATA IMACH(12) /       -128 /
C     DATA IMACH(13) /        127 /
C     DATA IMACH(14) /         54 /
C     DATA IMACH(15) /       -101 /
C     DATA IMACH(16) /        127 /
C
C     MACHINE CONSTANTS FOR THE PDP-10 (KI PROCESSOR)
C
C     DATA IMACH( 1) /          5 /
C     DATA IMACH( 2) /          6 /
C     DATA IMACH( 3) /          5 /
C     DATA IMACH( 4) /          6 /
C     DATA IMACH( 5) /         36 /
C     DATA IMACH( 6) /          5 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         35 /
C     DATA IMACH( 9) / "377777777777 /
C     DATA IMACH(10) /          2 /
C     DATA IMACH(11) /         27 /
C     DATA IMACH(12) /       -128 /
C     DATA IMACH(13) /        127 /
C     DATA IMACH(14) /         62 /
C     DATA IMACH(15) /       -128 /
C     DATA IMACH(16) /        127 /
C
C     MACHINE CONSTANTS FOR PDP-11 FORTRAN SUPPORTING
C     32-BIT INTEGER ARITHMETIC.
C
C     DATA IMACH( 1) /          5 /
C     DATA IMACH( 2) /          6 /
C     DATA IMACH( 3) /          5 /
C     DATA IMACH( 4) /          6 /
C     DATA IMACH( 5) /         32 /
C     DATA IMACH( 6) /          4 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         31 /
C     DATA IMACH( 9) / 2147483647 /
C     DATA IMACH(10) /          2 /
C     DATA IMACH(11) /         24 /
C     DATA IMACH(12) /       -127 /
C     DATA IMACH(13) /        127 /
C     DATA IMACH(14) /         56 /
C     DATA IMACH(15) /       -127 /
C     DATA IMACH(16) /        127 /
C
C     MACHINE CONSTANTS FOR PDP-11 FORTRAN SUPPORTING
C     16-BIT INTEGER ARITHMETIC.
C
C     DATA IMACH( 1) /          5 /
C     DATA IMACH( 2) /          6 /
C     DATA IMACH( 3) /          5 /
C     DATA IMACH( 4) /          6 /
C     DATA IMACH( 5) /         16 /
C     DATA IMACH( 6) /          2 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         15 /
C     DATA IMACH( 9) /      32767 /
C     DATA IMACH(10) /          2 /
C     DATA IMACH(11) /         24 /
C     DATA IMACH(12) /       -127 /
C     DATA IMACH(13) /        127 /
C     DATA IMACH(14) /         56 /
C     DATA IMACH(15) /       -127 /
C     DATA IMACH(16) /        127 /
C
C     MACHINE CONSTANTS FOR THE SILICON GRAPHICS
C
C     DATA IMACH( 1) /          5 /
C     DATA IMACH( 2) /          6 /
C     DATA IMACH( 3) /          6 /
C     DATA IMACH( 4) /          6 /
C     DATA IMACH( 5) /         32 /
C     DATA IMACH( 6) /          4 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         31 /
C     DATA IMACH( 9) / 2147483647 /
C     DATA IMACH(10) /          2 /
C     DATA IMACH(11) /         24 /
C     DATA IMACH(12) /       -125 /
C     DATA IMACH(13) /        128 /
C     DATA IMACH(14) /         53 /
C     DATA IMACH(15) /      -1021 /
C     DATA IMACH(16) /       1024 /
C
C     MACHINE CONSTANTS FOR THE SUN
C
C     DATA IMACH( 1) /          5 /
C     DATA IMACH( 2) /          6 /
C     DATA IMACH( 3) /          6 /
C     DATA IMACH( 4) /          6 /
C     DATA IMACH( 5) /         32 /
C     DATA IMACH( 6) /          4 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         31 /
C     DATA IMACH( 9) / 2147483647 /
C     DATA IMACH(10) /          2 /
C     DATA IMACH(11) /         24 /
C     DATA IMACH(12) /       -125 /
C     DATA IMACH(13) /        128 /
C     DATA IMACH(14) /         53 /
C     DATA IMACH(15) /      -1021 /
C     DATA IMACH(16) /       1024 /
C
C     MACHINE CONSTANTS FOR THE SUN
C     USING THE -r8 COMPILER OPTION
C
C     DATA IMACH( 1) /          5 /
C     DATA IMACH( 2) /          6 /
C     DATA IMACH( 3) /          6 /
C     DATA IMACH( 4) /          6 /
C     DATA IMACH( 5) /         32 /
C     DATA IMACH( 6) /          4 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         31 /
C     DATA IMACH( 9) / 2147483647 /
C     DATA IMACH(10) /          2 /
C     DATA IMACH(11) /         53 /
C     DATA IMACH(12) /      -1021 /
C     DATA IMACH(13) /       1024 /
C     DATA IMACH(14) /        113 /
C     DATA IMACH(15) /     -16381 /
C     DATA IMACH(16) /      16384 /
C
C     MACHINE CONSTANTS FOR THE UNIVAC 1100 SERIES FTN COMPILER
C
C     DATA IMACH( 1) /          5 /
C     DATA IMACH( 2) /          6 /
C     DATA IMACH( 3) /          1 /
C     DATA IMACH( 4) /          6 /
C     DATA IMACH( 5) /         36 /
C     DATA IMACH( 6) /          4 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         35 /
C     DATA IMACH( 9) / O377777777777 /
C     DATA IMACH(10) /          2 /
C     DATA IMACH(11) /         27 /
C     DATA IMACH(12) /       -128 /
C     DATA IMACH(13) /        127 /
C     DATA IMACH(14) /         60 /
C     DATA IMACH(15) /      -1024 /
C     DATA IMACH(16) /       1023 /
C
C     MACHINE CONSTANTS FOR THE Z80 MICROPROCESSOR
C
C     DATA IMACH( 1) /          1 /
C     DATA IMACH( 2) /          1 /
C     DATA IMACH( 3) /          0 /
C     DATA IMACH( 4) /          1 /
C     DATA IMACH( 5) /         16 /
C     DATA IMACH( 6) /          2 /
C     DATA IMACH( 7) /          2 /
C     DATA IMACH( 8) /         15 /
C     DATA IMACH( 9) /      32767 /
C     DATA IMACH(10) /          2 /
C     DATA IMACH(11) /         24 /
C     DATA IMACH(12) /       -127 /
C     DATA IMACH(13) /        127 /
C     DATA IMACH(14) /         56 /
C     DATA IMACH(15) /       -127 /
C     DATA IMACH(16) /        127 /
C
C***FIRST EXECUTABLE STATEMENT  I1MACH
      IF (i .LT. 1  .OR.  i .GT. 16) GO TO 10
C
      i1mach = imach(i)
      RETURN
C
   10 CONTINUE
      WRITE (unit = output, fmt = 9000)
 9000 FORMAT ('1ERROR    1 IN I1MACH - I OUT OF BOUNDS')
C
C     CALL FDUMP
C
      stop

j4save()

function j4save	(		IWHICH,
			IVALUE,
		logical	ISET
	)

C***BEGIN PROLOGUE  J4SAVE
C***SUBSIDIARY
C***PURPOSE  Save or recall global variables needed by error
C            handling routines.
C***LIBRARY   SLATEC (XERROR)
C***TYPE      INTEGER (J4SAVE-I)
C***KEYWORDS  ERROR MESSAGES, ERROR NUMBER, RECALL, SAVE, XERROR
C***AUTHOR  Jones, R. E., (SNLA)
C***DESCRIPTION
C
C     Abstract
C        J4SAVE saves and recalls several global variables needed
C        by the library error handling routines.
C
C     Description of Parameters
C      --Input--
C        IWHICH - Index of item desired.
C                = 1 Refers to current error number.
C                = 2 Refers to current error control flag.
C                = 3 Refers to current unit number to which error
C                    messages are to be sent.  (0 means use standard.)
C                = 4 Refers to the maximum number of times any
C                     message is to be printed (as set by XERMAX).
C                = 5 Refers to the total number of units to which
C                     each error message is to be written.
C                = 6 Refers to the 2nd unit for error messages
C                = 7 Refers to the 3rd unit for error messages
C                = 8 Refers to the 4th unit for error messages
C                = 9 Refers to the 5th unit for error messages
C        IVALUE - The value to be set for the IWHICH-th parameter,
C                 if ISET is .TRUE. .
C        ISET   - If ISET=.TRUE., the IWHICH-th parameter will BE
C                 given the value, IVALUE.  If ISET=.FALSE., the
C                 IWHICH-th parameter will be unchanged, and IVALUE
C                 is a dummy parameter.
C      --Output--
C        The (old) value of the IWHICH-th parameter will be returned
C        in the function value, J4SAVE.
C
C***SEE ALSO  XERMSG
C***REFERENCES  R. E. Jones and D. K. Kahaner, XERROR, the SLATEC
C                 Error-handling Package, SAND82-0800, Sandia
C                 Laboratories, 1982.
C***ROUTINES CALLED  (NONE)
C***REVISION HISTORY  (YYMMDD)
C   790801  DATE WRITTEN
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C   900205  Minor modifications to prologue.  (WRB)
C   900402  Added TYPE section.  (WRB)
C   910411  Added KEYWORDS section.  (WRB)
C   920501  Reformatted the REFERENCES section.  (WRB)
C***END PROLOGUE  J4SAVE
      LOGICAL iset
      INTEGER iparam(9)
      SAVE iparam
      DATA iparam(1),iparam(2),iparam(3),iparam(4)/0,2,0,10/
      DATA iparam(5)/1/
      DATA iparam(6),iparam(7),iparam(8),iparam(9)/0,0,0,0/
C***FIRST EXECUTABLE STATEMENT  J4SAVE
      j4save = iparam(iwhich)
      IF (iset) iparam(iwhich) = ivalue
      RETURN

xercnt()

subroutine xercnt	(	character*(*)	LIBRAR,
		character*(*)	SUBROU,
		character*(*)	MESSG,
			NERR,
			LEVEL,
			KONTRL
	)

C***BEGIN PROLOGUE  XERCNT
C***SUBSIDIARY
C***PURPOSE  Allow user control over handling of errors.
C***LIBRARY   SLATEC (XERROR)
C***CATEGORY  R3C
C***TYPE      ALL (XERCNT-A)
C***KEYWORDS  ERROR, XERROR
C***AUTHOR  Jones, R. E., (SNLA)
C***DESCRIPTION
C
C     Abstract
C        Allows user control over handling of individual errors.
C        Just after each message is recorded, but before it is
C        processed any further (i.e., before it is printed or
C        a decision to abort is made), a call is made to XERCNT.
C        If the user has provided his own version of XERCNT, he
C        can then override the value of KONTROL used in processing
C        this message by redefining its value.
C        KONTRL may be set to any value from -2 to 2.
C        The meanings for KONTRL are the same as in XSETF, except
C        that the value of KONTRL changes only for this message.
C        If KONTRL is set to a value outside the range from -2 to 2,
C        it will be moved back into that range.
C
C     Description of Parameters
C
C      --Input--
C        LIBRAR - the library that the routine is in.
C        SUBROU - the subroutine that XERMSG is being called from
C        MESSG  - the first 20 characters of the error message.
C        NERR   - same as in the call to XERMSG.
C        LEVEL  - same as in the call to XERMSG.
C        KONTRL - the current value of the control flag as set
C                 by a call to XSETF.
C
C      --Output--
C        KONTRL - the new value of KONTRL.  If KONTRL is not
C                 defined, it will remain at its original value.
C                 This changed value of control affects only
C                 the current occurrence of the current message.
C
C***REFERENCES  R. E. Jones and D. K. Kahaner, XERROR, the SLATEC
C                 Error-handling Package, SAND82-0800, Sandia
C                 Laboratories, 1982.
C***ROUTINES CALLED  (NONE)
C***REVISION HISTORY  (YYMMDD)
C   790801  DATE WRITTEN
C   861211  REVISION DATE from Version 3.2
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C   900206  Routine changed from user-callable to subsidiary.  (WRB)
C   900510  Changed calling sequence to include LIBRARY and SUBROUTINE
C           names, changed routine name from XERCTL to XERCNT.  (RWC)
C   920501  Reformatted the REFERENCES section.  (WRB)
C***END PROLOGUE  XERCNT
      CHARACTER*(*) librar, subrou, messg
C***FIRST EXECUTABLE STATEMENT  XERCNT
      RETURN

xerhlt()

subroutine xerhlt

(

character*(*)

MESSG

)

C***BEGIN PROLOGUE  XERHLT
C***SUBSIDIARY
C***PURPOSE  Abort program execution and print error message.
C***LIBRARY   SLATEC (XERROR)
C***CATEGORY  R3C
C***TYPE      ALL (XERHLT-A)
C***KEYWORDS  ABORT PROGRAM EXECUTION, ERROR, XERROR
C***AUTHOR  Jones, R. E., (SNLA)
C***DESCRIPTION
C
C     Abstract
C        ***Note*** machine dependent routine
C        XERHLT aborts the execution of the program.
C        The error message causing the abort is given in the calling
C        sequence, in case one needs it for printing on a dayfile,
C        for example.
C
C     Description of Parameters
C        MESSG is as in XERMSG.
C
C***REFERENCES  R. E. Jones and D. K. Kahaner, XERROR, the SLATEC
C                 Error-handling Package, SAND82-0800, Sandia
C                 Laboratories, 1982.
C***ROUTINES CALLED  (NONE)
C***REVISION HISTORY  (YYMMDD)
C   790801  DATE WRITTEN
C   861211  REVISION DATE from Version 3.2
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C   900206  Routine changed from user-callable to subsidiary.  (WRB)
C   900510  Changed calling sequence to delete length of character
C           and changed routine name from XERABT to XERHLT.  (RWC)
C   920501  Reformatted the REFERENCES section.  (WRB)
C***END PROLOGUE  XERHLT
      CHARACTER*(*) messg
C***FIRST EXECUTABLE STATEMENT  XERHLT
      stop

xermsg()

subroutine xermsg	(	character*(*)	LIBRAR,
		character*(*)	SUBROU,
		character*(*)	MESSG,
			NERR,
			LEVEL
	)

C***BEGIN PROLOGUE  XERMSG
C***PURPOSE  Process error messages for SLATEC and other libraries.
C***LIBRARY   SLATEC (XERROR)
C***CATEGORY  R3C
C***TYPE      ALL (XERMSG-A)
C***KEYWORDS  ERROR MESSAGE, XERROR
C***AUTHOR  Fong, Kirby, (NMFECC at LLNL)
C***DESCRIPTION
C
C   XERMSG processes a diagnostic message in a manner determined by the
C   value of LEVEL and the current value of the library error control
C   flag, KONTRL.  See subroutine XSETF for details.
C
C    LIBRAR   A character constant (or character variable) with the name
C             of the library.  This will be 'SLATEC' for the SLATEC
C             Common Math Library.  The error handling package is
C             general enough to be used by many libraries
C             simultaneously, so it is desirable for the routine that
C             detects and reports an error to identify the library name
C             as well as the routine name.
C
C    SUBROU   A character constant (or character variable) with the name
C             of the routine that detected the error.  Usually it is the
C             name of the routine that is calling XERMSG.  There are
C             some instances where a user callable library routine calls
C             lower level subsidiary routines where the error is
C             detected.  In such cases it may be more informative to
C             supply the name of the routine the user called rather than
C             the name of the subsidiary routine that detected the
C             error.
C
C    MESSG    A character constant (or character variable) with the text
C             of the error or warning message.  In the example below,
C             the message is a character constant that contains a
C             generic message.
C
C                   CALL XERMSG ('SLATEC', 'MMPY',
C                  *'THE ORDER OF THE MATRIX EXCEEDS THE ROW DIMENSION',
C                  *3, 1)
C
C             It is possible (and is sometimes desirable) to generate a
C             specific message--e.g., one that contains actual numeric
C             values.  Specific numeric values can be converted into
C             character strings using formatted WRITE statements into
C             character variables.  This is called standard Fortran
C             internal file I/O and is exemplified in the first three
C             lines of the following example.  You can also catenate
C             substrings of characters to construct the error message.
C             Here is an example showing the use of both writing to
C             an internal file and catenating character strings.
C
C                   CHARACTER*5 CHARN, CHARL
C                   WRITE (CHARN,10) N
C                   WRITE (CHARL,10) LDA
C                10 FORMAT(I5)
C                   CALL XERMSG ('SLATEC', 'MMPY', 'THE ORDER'//CHARN//
C                  *   ' OF THE MATRIX EXCEEDS ITS ROW DIMENSION OF'//
C                  *   CHARL, 3, 1)
C
C             There are two subtleties worth mentioning.  One is that
C             the // for character catenation is used to construct the
C             error message so that no single character constant is
C             continued to the next line.  This avoids confusion as to
C             whether there are trailing blanks at the end of the line.
C             The second is that by catenating the parts of the message
C             as an actual argument rather than encoding the entire
C             message into one large character variable, we avoid
C             having to know how long the message will be in order to
C             declare an adequate length for that large character
C             variable.  XERMSG calls XERPRN to print the message using
C             multiple lines if necessary.  If the message is very long,
C             XERPRN will break it into pieces of 72 characters (as
C             requested by XERMSG) for printing on multiple lines.
C             Also, XERMSG asks XERPRN to prefix each line with ' *  '
C             so that the total line length could be 76 characters.
C             Note also that XERPRN scans the error message backwards
C             to ignore trailing blanks.  Another feature is that
C             the substring '$$' is treated as a new line sentinel
C             by XERPRN.  If you want to construct a multiline
C             message without having to count out multiples of 72
C             characters, just use '$$' as a separator.  '$$'
C             obviously must occur within 72 characters of the
C             start of each line to have its intended effect since
C             XERPRN is asked to wrap around at 72 characters in
C             addition to looking for '$$'.
C
C    NERR     An integer value that is chosen by the library routine's
C             author.  It must be in the range -99 to 999 (three
C             printable digits).  Each distinct error should have its
C             own error number.  These error numbers should be described
C             in the machine readable documentation for the routine.
C             The error numbers need be unique only within each routine,
C             so it is reasonable for each routine to start enumerating
C             errors from 1 and proceeding to the next integer.
C
C    LEVEL    An integer value in the range 0 to 2 that indicates the
C             level (severity) of the error.  Their meanings are
C
C            -1  A warning message.  This is used if it is not clear
C                that there really is an error, but the user's attention
C                may be needed.  An attempt is made to only print this
C                message once.
C
C             0  A warning message.  This is used if it is not clear
C                that there really is an error, but the user's attention
C                may be needed.
C
C             1  A recoverable error.  This is used even if the error is
C                so serious that the routine cannot return any useful
C                answer.  If the user has told the error package to
C                return after recoverable errors, then XERMSG will
C                return to the Library routine which can then return to
C                the user's routine.  The user may also permit the error
C                package to terminate the program upon encountering a
C                recoverable error.
C
C             2  A fatal error.  XERMSG will not return to its caller
C                after it receives a fatal error.  This level should
C                hardly ever be used; it is much better to allow the
C                user a chance to recover.  An example of one of the few
C                cases in which it is permissible to declare a level 2
C                error is a reverse communication Library routine that
C                is likely to be called repeatedly until it integrates
C                across some interval.  If there is a serious error in
C                the input such that another step cannot be taken and
C                the Library routine is called again without the input
C                error having been corrected by the caller, the Library
C                routine will probably be called forever with improper
C                input.  In this case, it is reasonable to declare the
C                error to be fatal.
C
C    Each of the arguments to XERMSG is input; none will be modified by
C    XERMSG.  A routine may make multiple calls to XERMSG with warning
C    level messages; however, after a call to XERMSG with a recoverable
C    error, the routine should return to the user.  Do not try to call
C    XERMSG with a second recoverable error after the first recoverable
C    error because the error package saves the error number.  The user
C    can retrieve this error number by calling another entry point in
C    the error handling package and then clear the error number when
C    recovering from the error.  Calling XERMSG in succession causes the
C    old error number to be overwritten by the latest error number.
C    This is considered harmless for error numbers associated with
C    warning messages but must not be done for error numbers of serious
C    errors.  After a call to XERMSG with a recoverable error, the user
C    must be given a chance to call NUMXER or XERCLR to retrieve or
C    clear the error number.
C***REFERENCES  R. E. Jones and D. K. Kahaner, XERROR, the SLATEC
C                 Error-handling Package, SAND82-0800, Sandia
C                 Laboratories, 1982.
C***ROUTINES CALLED  FDUMP, J4SAVE, XERCNT, XERHLT, XERPRN, XERSVE
C***REVISION HISTORY  (YYMMDD)
C   880101  DATE WRITTEN
C   880621  REVISED AS DIRECTED AT SLATEC CML MEETING OF FEBRUARY 1988.
C           THERE ARE TWO BASIC CHANGES.
C           1.  A NEW ROUTINE, XERPRN, IS USED INSTEAD OF XERPRT TO
C               PRINT MESSAGES.  THIS ROUTINE WILL BREAK LONG MESSAGES
C               INTO PIECES FOR PRINTING ON MULTIPLE LINES.  '$$' IS
C               ACCEPTED AS A NEW LINE SENTINEL.  A PREFIX CAN BE
C               ADDED TO EACH LINE TO BE PRINTED.  XERMSG USES EITHER
C               ' ***' OR ' *  ' AND LONG MESSAGES ARE BROKEN EVERY
C               72 CHARACTERS (AT MOST) SO THAT THE MAXIMUM LINE
C               LENGTH OUTPUT CAN NOW BE AS GREAT AS 76.
C           2.  THE TEXT OF ALL MESSAGES IS NOW IN UPPER CASE SINCE THE
C               FORTRAN STANDARD DOCUMENT DOES NOT ADMIT THE EXISTENCE
C               OF LOWER CASE.
C   880708  REVISED AFTER THE SLATEC CML MEETING OF JUNE 29 AND 30.
C           THE PRINCIPAL CHANGES ARE
C           1.  CLARIFY COMMENTS IN THE PROLOGUES
C           2.  RENAME XRPRNT TO XERPRN
C           3.  REWORK HANDLING OF '$$' IN XERPRN TO HANDLE BLANK LINES
C               SIMILAR TO THE WAY FORMAT STATEMENTS HANDLE THE /
C               CHARACTER FOR NEW RECORDS.
C   890706  REVISED WITH THE HELP OF FRED FRITSCH AND REG CLEMENS TO
C           CLEAN UP THE CODING.
C   890721  REVISED TO USE NEW FEATURE IN XERPRN TO COUNT CHARACTERS IN
C           PREFIX.
C   891013  REVISED TO CORRECT COMMENTS.
C   891214  Prologue converted to Version 4.0 format.  (WRB)
C   900510  Changed test on NERR to be -9999999 < NERR < 99999999, but
C           NERR .ne. 0, and on LEVEL to be -2 < LEVEL < 3.  Added
C           LEVEL=-1 logic, changed calls to XERSAV to XERSVE, and
C           XERCTL to XERCNT.  (RWC)
C   920501  Reformatted the REFERENCES section.  (WRB)
C***END PROLOGUE  XERMSG
      CHARACTER*(*) librar, subrou, messg
      CHARACTER*8 xlibr, xsubr
      CHARACTER*72  temp
      CHARACTER*20  lfirst
C***FIRST EXECUTABLE STATEMENT  XERMSG
      lkntrl = j4save(2, 0, .false.)
      maxmes = j4save(4, 0, .false.)
C
C       LKNTRL IS A LOCAL COPY OF THE CONTROL FLAG KONTRL.
C       MAXMES IS THE MAXIMUM NUMBER OF TIMES ANY PARTICULAR MESSAGE
C          SHOULD BE PRINTED.
C
C       WE PRINT A FATAL ERROR MESSAGE AND TERMINATE FOR AN ERROR IN
C          CALLING XERMSG.  THE ERROR NUMBER SHOULD BE POSITIVE,
C          AND THE LEVEL SHOULD BE BETWEEN 0 AND 2.
C
      IF (nerr.LT.-9999999 .OR. nerr.GT.99999999 .OR. nerr.EQ.0 .OR.
     *   level.LT.-1 .OR. level.GT.2) THEN
         CALL xerprn (' ***', -1, 'FATAL ERROR IN...$$ ' //
     *      'XERMSG -- INVALID ERROR NUMBER OR LEVEL$$ '//
     *      'JOB ABORT DUE TO FATAL ERROR.', 72)
         CALL xersve (' ', ' ', ' ', 0, 0, 0, kdummy)
         CALL xerhlt (' ***XERMSG -- INVALID INPUT')
         RETURN
      ENDIF
C
C       RECORD THE MESSAGE.
C
      i = j4save(1, nerr, .true.)
      CALL xersve (librar, subrou, messg, 1, nerr, level, kount)
C
C       HANDLE PRINT-ONCE WARNING MESSAGES.
C
      IF (level.EQ.-1 .AND. kount.GT.1) RETURN
C
C       ALLOW TEMPORARY USER OVERRIDE OF THE CONTROL FLAG.
C
      xlibr  = librar
      xsubr  = subrou
      lfirst = messg
      lerr   = nerr
      llevel = level
      CALL xercnt (xlibr, xsubr, lfirst, lerr, llevel, lkntrl)
C
      lkntrl = max(-2, min(2,lkntrl))
      mkntrl = abs(lkntrl)
C
C       SKIP PRINTING IF THE CONTROL FLAG VALUE AS RESET IN XERCNT IS
C       ZERO AND THE ERROR IS NOT FATAL.
C
      IF (level.LT.2 .AND. lkntrl.EQ.0) GO TO 30
      IF (level.EQ.0 .AND. kount.GT.maxmes) GO TO 30
      IF (level.EQ.1 .AND. kount.GT.maxmes .AND. mkntrl.EQ.1) GO TO 30
      IF (level.EQ.2 .AND. kount.GT.max(1,maxmes)) GO TO 30
C
C       ANNOUNCE THE NAMES OF THE LIBRARY AND SUBROUTINE BY BUILDING A
C       MESSAGE IN CHARACTER VARIABLE TEMP (NOT EXCEEDING 66 CHARACTERS)
C       AND SENDING IT OUT VIA XERPRN.  PRINT ONLY IF CONTROL FLAG
C       IS NOT ZERO.
C
      IF (lkntrl .NE. 0) THEN
         temp(1:21) = 'MESSAGE FROM ROUTINE '
         i = min(len(subrou), 16)
         temp(22:21+i) = subrou(1:i)
         temp(22+i:33+i) = ' IN LIBRARY '
         ltemp = 33 + i
         i = min(len(librar), 16)
         temp(ltemp+1:ltemp+i) = librar(1:i)
         temp(ltemp+i+1:ltemp+i+1) = '.'
         ltemp = ltemp + i + 1
         CALL xerprn (' ***', -1, temp(1:ltemp), 72)
      ENDIF
C
C       IF LKNTRL IS POSITIVE, PRINT AN INTRODUCTORY LINE BEFORE
C       PRINTING THE MESSAGE.  THE INTRODUCTORY LINE TELLS THE CHOICE
C       FROM EACH OF THE FOLLOWING THREE OPTIONS.
C       1.  LEVEL OF THE MESSAGE
C              'INFORMATIVE MESSAGE'
C              'POTENTIALLY RECOVERABLE ERROR'
C              'FATAL ERROR'
C       2.  WHETHER CONTROL FLAG WILL ALLOW PROGRAM TO CONTINUE
C              'PROG CONTINUES'
C              'PROG ABORTED'
C       3.  WHETHER OR NOT A TRACEBACK WAS REQUESTED.  (THE TRACEBACK
C           MAY NOT BE IMPLEMENTED AT SOME SITES, SO THIS ONLY TELLS
C           WHAT WAS REQUESTED, NOT WHAT WAS DELIVERED.)
C              'TRACEBACK REQUESTED'
C              'TRACEBACK NOT REQUESTED'
C       NOTICE THAT THE LINE INCLUDING FOUR PREFIX CHARACTERS WILL NOT
C       EXCEED 74 CHARACTERS.
C       WE SKIP THE NEXT BLOCK IF THE INTRODUCTORY LINE IS NOT NEEDED.
C
      IF (lkntrl .GT. 0) THEN
C
C       THE FIRST PART OF THE MESSAGE TELLS ABOUT THE LEVEL.
C
         IF (level .LE. 0) THEN
            temp(1:20) = 'INFORMATIVE MESSAGE,'
            ltemp = 20
         ELSEIF (level .EQ. 1) THEN
            temp(1:30) = 'POTENTIALLY RECOVERABLE ERROR,'
            ltemp = 30
         ELSE
            temp(1:12) = 'FATAL ERROR,'
            ltemp = 12
         ENDIF
C
C       THEN WHETHER THE PROGRAM WILL CONTINUE.
C
         IF ((mkntrl.EQ.2 .AND. level.GE.1) .OR.
     *       (mkntrl.EQ.1 .AND. level.EQ.2)) THEN
            temp(ltemp+1:ltemp+14) = ' PROG ABORTED,'
            ltemp = ltemp + 14
         ELSE
            temp(ltemp+1:ltemp+16) = ' PROG CONTINUES,'
            ltemp = ltemp + 16
         ENDIF
C
C       FINALLY TELL WHETHER THERE SHOULD BE A TRACEBACK.
C
         IF (lkntrl .GT. 0) THEN
            temp(ltemp+1:ltemp+20) = ' TRACEBACK REQUESTED'
            ltemp = ltemp + 20
         ELSE
            temp(ltemp+1:ltemp+24) = ' TRACEBACK NOT REQUESTED'
            ltemp = ltemp + 24
         ENDIF
         CALL xerprn (' ***', -1, temp(1:ltemp), 72)
      ENDIF
C
C       NOW SEND OUT THE MESSAGE.
C
      CALL xerprn (' *  ', -1, messg, 72)
C
C       IF LKNTRL IS POSITIVE, WRITE THE ERROR NUMBER AND REQUEST A
C          TRACEBACK.
C
      IF (lkntrl .GT. 0) THEN
         WRITE (temp, '(''ERROR NUMBER = '', I8)') nerr
         DO 10 i=16,22
            IF (temp(i:i) .NE. ' ') GO TO 20
   10    CONTINUE
C
   20    CALL xerprn (' *  ', -1, temp(1:15) // temp(i:23), 72)
         CALL fdump
      ENDIF
C
C       IF LKNTRL IS NOT ZERO, PRINT A BLANK LINE AND AN END OF MESSAGE.
C
      IF (lkntrl .NE. 0) THEN
         CALL xerprn (' *  ', -1, ' ', 72)
         CALL xerprn (' ***', -1, 'END OF MESSAGE', 72)
         CALL xerprn ('    ',  0, ' ', 72)
      ENDIF
C
C       IF THE ERROR IS NOT FATAL OR THE ERROR IS RECOVERABLE AND THE
C       CONTROL FLAG IS SET FOR RECOVERY, THEN RETURN.
C
   30 IF (level.LE.0 .OR. (level.EQ.1 .AND. mkntrl.LE.1)) RETURN
C
C       THE PROGRAM WILL BE STOPPED DUE TO AN UNRECOVERED ERROR OR A
C       FATAL ERROR.  PRINT THE REASON FOR THE ABORT AND THE ERROR
C       SUMMARY IF THE CONTROL FLAG AND THE MAXIMUM ERROR COUNT PERMIT.
C
      IF (lkntrl.GT.0 .AND. kount.LT.max(1,maxmes)) THEN
         IF (level .EQ. 1) THEN
            CALL xerprn
     *         (' ***', -1, 'JOB ABORT DUE TO UNRECOVERED ERROR.', 72)
         ELSE
            CALL xerprn(' ***', -1, 'JOB ABORT DUE TO FATAL ERROR.', 72)
         ENDIF
         CALL xersve (' ', ' ', ' ', -1, 0, 0, kdummy)
         CALL xerhlt (' ')
      ELSE
         CALL xerhlt (messg)
      ENDIF
      RETURN

xerprn()

subroutine xerprn	(	character*(*)	PREFIX,
		integer	NPREF,
		character*(*)	MESSG,
		integer	NWRAP
	)

C***BEGIN PROLOGUE  XERPRN
C***SUBSIDIARY
C***PURPOSE  Print error messages processed by XERMSG.
C***LIBRARY   SLATEC (XERROR)
C***CATEGORY  R3C
C***TYPE      ALL (XERPRN-A)
C***KEYWORDS  ERROR MESSAGES, PRINTING, XERROR
C***AUTHOR  Fong, Kirby, (NMFECC at LLNL)
C***DESCRIPTION
C
C This routine sends one or more lines to each of the (up to five)
C logical units to which error messages are to be sent.  This routine
C is called several times by XERMSG, sometimes with a single line to
C print and sometimes with a (potentially very long) message that may
C wrap around into multiple lines.
C
C PREFIX  Input argument of type CHARACTER.  This argument contains
C         characters to be put at the beginning of each line before
C         the body of the message.  No more than 16 characters of
C         PREFIX will be used.
C
C NPREF   Input argument of type INTEGER.  This argument is the number
C         of characters to use from PREFIX.  If it is negative, the
C         intrinsic function LEN is used to determine its length.  If
C         it is zero, PREFIX is not used.  If it exceeds 16 or if
C         LEN(PREFIX) exceeds 16, only the first 16 characters will be
C         used.  If NPREF is positive and the length of PREFIX is less
C         than NPREF, a copy of PREFIX extended with blanks to length
C         NPREF will be used.
C
C MESSG   Input argument of type CHARACTER.  This is the text of a
C         message to be printed.  If it is a long message, it will be
C         broken into pieces for printing on multiple lines.  Each line
C         will start with the appropriate prefix and be followed by a
C         piece of the message.  NWRAP is the number of characters per
C         piece; that is, after each NWRAP characters, we break and
C         start a new line.  In addition the characters '$$' embedded
C         in MESSG are a sentinel for a new line.  The counting of
C         characters up to NWRAP starts over for each new line.  The
C         value of NWRAP typically used by XERMSG is 72 since many
C         older error messages in the SLATEC Library are laid out to
C         rely on wrap-around every 72 characters.
C
C NWRAP   Input argument of type INTEGER.  This gives the maximum size
C         piece into which to break MESSG for printing on multiple
C         lines.  An embedded '$$' ends a line, and the count restarts
C         at the following character.  If a line break does not occur
C         on a blank (it would split a word) that word is moved to the
C         next line.  Values of NWRAP less than 16 will be treated as
C         16.  Values of NWRAP greater than 132 will be treated as 132.
C         The actual line length will be NPREF + NWRAP after NPREF has
C         been adjusted to fall between 0 and 16 and NWRAP has been
C         adjusted to fall between 16 and 132.
C
C***REFERENCES  R. E. Jones and D. K. Kahaner, XERROR, the SLATEC
C                 Error-handling Package, SAND82-0800, Sandia
C                 Laboratories, 1982.
C***ROUTINES CALLED  I1MACH, XGETUA
C***REVISION HISTORY  (YYMMDD)
C   880621  DATE WRITTEN
C   880708  REVISED AFTER THE SLATEC CML SUBCOMMITTEE MEETING OF
C           JUNE 29 AND 30 TO CHANGE THE NAME TO XERPRN AND TO REWORK
C           THE HANDLING OF THE NEW LINE SENTINEL TO BEHAVE LIKE THE
C           SLASH CHARACTER IN FORMAT STATEMENTS.
C   890706  REVISED WITH THE HELP OF FRED FRITSCH AND REG CLEMENS TO
C           STREAMLINE THE CODING AND FIX A BUG THAT CAUSED EXTRA BLANK
C           LINES TO BE PRINTED.
C   890721  REVISED TO ADD A NEW FEATURE.  A NEGATIVE VALUE OF NPREF
C           CAUSES LEN(PREFIX) TO BE USED AS THE LENGTH.
C   891013  REVISED TO CORRECT ERROR IN CALCULATING PREFIX LENGTH.
C   891214  Prologue converted to Version 4.0 format.  (WRB)
C   900510  Added code to break messages between words.  (RWC)
C   920501  Reformatted the REFERENCES section.  (WRB)
C***END PROLOGUE  XERPRN
      CHARACTER*(*) prefix, messg
      INTEGER npref, nwrap
      CHARACTER*148 cbuff
      INTEGER iu(5), nunit
      CHARACTER*2 newlin
      parameter(newlin = '$$')
C***FIRST EXECUTABLE STATEMENT  XERPRN
      CALL xgetua(iu,nunit)
C
C       A ZERO VALUE FOR A LOGICAL UNIT NUMBER MEANS TO USE THE STANDARD
C       ERROR MESSAGE UNIT INSTEAD.  I1MACH(4) RETRIEVES THE STANDARD
C       ERROR MESSAGE UNIT.
C
      n = i1mach(4)
      DO 10 i=1,nunit
         IF (iu(i) .EQ. 0) iu(i) = n
   10 CONTINUE
C
C       LPREF IS THE LENGTH OF THE PREFIX.  THE PREFIX IS PLACED AT THE
C       BEGINNING OF CBUFF, THE CHARACTER BUFFER, AND KEPT THERE DURING
C       THE REST OF THIS ROUTINE.
C
      IF ( npref .LT. 0 ) THEN
         lpref = len(prefix)
      ELSE
         lpref = npref
      ENDIF
      lpref = min(16, lpref)
      IF (lpref .NE. 0) cbuff(1:lpref) = prefix
C
C       LWRAP IS THE MAXIMUM NUMBER OF CHARACTERS WE WANT TO TAKE AT ONE
C       TIME FROM MESSG TO PRINT ON ONE LINE.
C
      lwrap = max(16, min(132, nwrap))
C
C       SET LENMSG TO THE LENGTH OF MESSG, IGNORE ANY TRAILING BLANKS.
C
      lenmsg = len(messg)
      n = lenmsg
      DO 20 i=1,n
         IF (messg(lenmsg:lenmsg) .NE. ' ') GO TO 30
         lenmsg = lenmsg - 1
   20 CONTINUE
   30 CONTINUE
C
C       IF THE MESSAGE IS ALL BLANKS, THEN PRINT ONE BLANK LINE.
C
      IF (lenmsg .EQ. 0) THEN
         cbuff(lpref+1:lpref+1) = ' '
         DO 40 i=1,nunit
            WRITE(iu(i), '(A)') cbuff(1:lpref+1)
   40    CONTINUE
         RETURN
      ENDIF
C
C       SET NEXTC TO THE POSITION IN MESSG WHERE THE NEXT SUBSTRING
C       STARTS.  FROM THIS POSITION WE SCAN FOR THE NEW LINE SENTINEL.
C       WHEN NEXTC EXCEEDS LENMSG, THERE IS NO MORE TO PRINT.
C       WE LOOP BACK TO LABEL 50 UNTIL ALL PIECES HAVE BEEN PRINTED.
C
C       WE LOOK FOR THE NEXT OCCURRENCE OF THE NEW LINE SENTINEL.  THE
C       INDEX INTRINSIC FUNCTION RETURNS ZERO IF THERE IS NO OCCURRENCE
C       OR IF THE LENGTH OF THE FIRST ARGUMENT IS LESS THAN THE LENGTH
C       OF THE SECOND ARGUMENT.
C
C       THERE ARE SEVERAL CASES WHICH SHOULD BE CHECKED FOR IN THE
C       FOLLOWING ORDER.  WE ARE ATTEMPTING TO SET LPIECE TO THE NUMBER
C       OF CHARACTERS THAT SHOULD BE TAKEN FROM MESSG STARTING AT
C       POSITION NEXTC.
C
C       LPIECE .EQ. 0   THE NEW LINE SENTINEL DOES NOT OCCUR IN THE
C                       REMAINDER OF THE CHARACTER STRING.  LPIECE
C                       SHOULD BE SET TO LWRAP OR LENMSG+1-NEXTC,
C                       WHICHEVER IS LESS.
C
C       LPIECE .EQ. 1   THE NEW LINE SENTINEL STARTS AT MESSG(NEXTC:
C                       NEXTC).  LPIECE IS EFFECTIVELY ZERO, AND WE
C                       PRINT NOTHING TO AVOID PRODUCING UNNECESSARY
C                       BLANK LINES.  THIS TAKES CARE OF THE SITUATION
C                       WHERE THE LIBRARY ROUTINE HAS A MESSAGE OF
C                       EXACTLY 72 CHARACTERS FOLLOWED BY A NEW LINE
C                       SENTINEL FOLLOWED BY MORE CHARACTERS.  NEXTC
C                       SHOULD BE INCREMENTED BY 2.
C
C       LPIECE .GT. LWRAP+1  REDUCE LPIECE TO LWRAP.
C
C       ELSE            THIS LAST CASE MEANS 2 .LE. LPIECE .LE. LWRAP+1
C                       RESET LPIECE = LPIECE-1.  NOTE THAT THIS
C                       PROPERLY HANDLES THE END CASE WHERE LPIECE .EQ.
C                       LWRAP+1.  THAT IS, THE SENTINEL FALLS EXACTLY
C                       AT THE END OF A LINE.
C
      nextc = 1
   50 lpiece = index(messg(nextc:lenmsg), newlin)
      IF (lpiece .EQ. 0) THEN
C
C       THERE WAS NO NEW LINE SENTINEL FOUND.
C
         idelta = 0
         lpiece = min(lwrap, lenmsg+1-nextc)
         IF (lpiece .LT. lenmsg+1-nextc) THEN
            DO 52 i=lpiece+1,2,-1
               IF (messg(nextc+i-1:nextc+i-1) .EQ. ' ') THEN
                  lpiece = i-1
                  idelta = 1
                  GOTO 54
               ENDIF
   52       CONTINUE
         ENDIF
   54    cbuff(lpref+1:lpref+lpiece) = messg(nextc:nextc+lpiece-1)
         nextc = nextc + lpiece + idelta
      ELSEIF (lpiece .EQ. 1) THEN
C
C       WE HAVE A NEW LINE SENTINEL AT MESSG(NEXTC:NEXTC+1).
C       DON'T PRINT A BLANK LINE.
C
         nextc = nextc + 2
         GO TO 50
      ELSEIF (lpiece .GT. lwrap+1) THEN
C
C       LPIECE SHOULD BE SET DOWN TO LWRAP.
C
         idelta = 0
         lpiece = lwrap
         DO 56 i=lpiece+1,2,-1
            IF (messg(nextc+i-1:nextc+i-1) .EQ. ' ') THEN
               lpiece = i-1
               idelta = 1
               GOTO 58
            ENDIF
   56    CONTINUE
   58    cbuff(lpref+1:lpref+lpiece) = messg(nextc:nextc+lpiece-1)
         nextc = nextc + lpiece + idelta
      ELSE
C
C       IF WE ARRIVE HERE, IT MEANS 2 .LE. LPIECE .LE. LWRAP+1.
C       WE SHOULD DECREMENT LPIECE BY ONE.
C
         lpiece = lpiece - 1
         cbuff(lpref+1:lpref+lpiece) = messg(nextc:nextc+lpiece-1)
         nextc  = nextc + lpiece + 2
      ENDIF
C
C       PRINT
C
      DO 60 i=1,nunit
         WRITE(iu(i), '(A)') cbuff(1:lpref+lpiece)
   60 CONTINUE
C
      IF (nextc .LE. lenmsg) GO TO 50
      RETURN

xersve()

subroutine xersve	(	character*(*)	LIBRAR,
		character*(*)	SUBROU,
		character*(*)	MESSG,
			KFLAG,
			NERR,
			LEVEL,
			ICOUNT
	)

C***BEGIN PROLOGUE  XERSVE
C***SUBSIDIARY
C***PURPOSE  Record that an error has occurred.
C***LIBRARY   SLATEC (XERROR)
C***CATEGORY  R3
C***TYPE      ALL (XERSVE-A)
C***KEYWORDS  ERROR, XERROR
C***AUTHOR  Jones, R. E., (SNLA)
C***DESCRIPTION
C
C *Usage:
C
C        INTEGER  KFLAG, NERR, LEVEL, ICOUNT
C        CHARACTER * (len) LIBRAR, SUBROU, MESSG
C
C        CALL XERSVE (LIBRAR, SUBROU, MESSG, KFLAG, NERR, LEVEL, ICOUNT)
C
C *Arguments:
C
C        LIBRAR :IN    is the library that the message is from.
C        SUBROU :IN    is the subroutine that the message is from.
C        MESSG  :IN    is the message to be saved.
C        KFLAG  :IN    indicates the action to be performed.
C                      when KFLAG > 0, the message in MESSG is saved.
C                      when KFLAG=0 the tables will be dumped and
C                      cleared.
C                      when KFLAG < 0, the tables will be dumped and
C                      not cleared.
C        NERR   :IN    is the error number.
C        LEVEL  :IN    is the error severity.
C        ICOUNT :OUT   the number of times this message has been seen,
C                      or zero if the table has overflowed and does not
C                      contain this message specifically.  When KFLAG=0,
C                      ICOUNT will not be altered.
C
C *Description:
C
C   Record that this error occurred and possibly dump and clear the
C   tables.
C
C***REFERENCES  R. E. Jones and D. K. Kahaner, XERROR, the SLATEC
C                 Error-handling Package, SAND82-0800, Sandia
C                 Laboratories, 1982.
C***ROUTINES CALLED  I1MACH, XGETUA
C***REVISION HISTORY  (YYMMDD)
C   800319  DATE WRITTEN
C   861211  REVISION DATE from Version 3.2
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C   900413  Routine modified to remove reference to KFLAG.  (WRB)
C   900510  Changed to add LIBRARY NAME and SUBROUTINE to calling
C           sequence, use IF-THEN-ELSE, make number of saved entries
C           easily changeable, changed routine name from XERSAV to
C           XERSVE.  (RWC)
C   910626  Added LIBTAB and SUBTAB to SAVE statement.  (BKS)
C   920501  Reformatted the REFERENCES section.  (WRB)
C***END PROLOGUE  XERSVE
      parameter(lentab=10)
      INTEGER lun(5)
      CHARACTER*(*) librar, subrou, messg
      CHARACTER*8  libtab(lentab), subtab(lentab), lib, sub
      CHARACTER*20 mestab(lentab), mes
      dimension nertab(lentab), levtab(lentab), kount(lentab)
      SAVE libtab, subtab, mestab, nertab, levtab, kount, kountx, nmsg
      DATA kountx/0/, nmsg/0/
C***FIRST EXECUTABLE STATEMENT  XERSVE
C
      IF (kflag.LE.0) THEN
C
C        Dump the table.
C
         IF (nmsg.EQ.0) RETURN
C
C        Print to each unit.
C
         CALL xgetua (lun, nunit)
         DO 20 kunit = 1,nunit
            iunit = lun(kunit)
            IF (iunit.EQ.0) iunit = i1mach(4)
C
C           Print the table header.
C
            WRITE (iunit,9000)
C
C           Print body of table.
C
            DO 10 i = 1,nmsg
               WRITE (iunit,9010) libtab(i), subtab(i), mestab(i),
     *            nertab(i),levtab(i),kount(i)
   10       CONTINUE
C
C           Print number of other errors.
C
            IF (kountx.NE.0) WRITE (iunit,9020) kountx
            WRITE (iunit,9030)
   20    CONTINUE
C
C        Clear the error tables.
C
         IF (kflag.EQ.0) THEN
            nmsg = 0
            kountx = 0
         ENDIF
      ELSE
C
C        PROCESS A MESSAGE...
C        SEARCH FOR THIS MESSG, OR ELSE AN EMPTY SLOT FOR THIS MESSG,
C        OR ELSE DETERMINE THAT THE ERROR TABLE IS FULL.
C
         lib = librar
         sub = subrou
         mes = messg
         DO 30 i = 1,nmsg
            IF (lib.EQ.libtab(i) .AND. sub.EQ.subtab(i) .AND.
     *         mes.EQ.mestab(i) .AND. nerr.EQ.nertab(i) .AND.
     *         level.EQ.levtab(i)) THEN
                  kount(i) = kount(i) + 1
                  icount = kount(i)
                  RETURN
            ENDIF
   30    CONTINUE
C
         IF (nmsg.LT.lentab) THEN
C
C           Empty slot found for new message.
C
            nmsg = nmsg + 1
            libtab(i) = lib
            subtab(i) = sub
            mestab(i) = mes
            nertab(i) = nerr
            levtab(i) = level
            kount(i) = 1
            icount    = 1
         ELSE
C
C           Table is full.
C
            kountx = kountx+1
            icount = 0
         ENDIF
      ENDIF
      RETURN
C
C     Formats.
C
 9000 FORMAT ('0          ERROR MESSAGE SUMMARY' /
     +   ' LIBRARY    SUBROUTINE MESSAGE START             NERR',
     +   '     LEVEL     COUNT')
 9010 FORMAT (1x,a,3x,a,3x,a,3i10)
 9020 FORMAT ('0OTHER ERRORS NOT INDIVIDUALLY TABULATED = ', i10)
 9030 FORMAT (1x)

xgetua()

subroutine xgetua	(	dimension(5)	IUNITA,
			N
	)

C***BEGIN PROLOGUE  XGETUA
C***PURPOSE  Return unit number(s) to which error messages are being
C            sent.
C***LIBRARY   SLATEC (XERROR)
C***CATEGORY  R3C
C***TYPE      ALL (XGETUA-A)
C***KEYWORDS  ERROR, XERROR
C***AUTHOR  Jones, R. E., (SNLA)
C***DESCRIPTION
C
C     Abstract
C        XGETUA may be called to determine the unit number or numbers
C        to which error messages are being sent.
C        These unit numbers may have been set by a call to XSETUN,
C        or a call to XSETUA, or may be a default value.
C
C     Description of Parameters
C      --Output--
C        IUNIT - an array of one to five unit numbers, depending
C                on the value of N.  A value of zero refers to the
C                default unit, as defined by the I1MACH machine
C                constant routine.  Only IUNIT(1),...,IUNIT(N) are
C                defined by XGETUA.  The values of IUNIT(N+1),...,
C                IUNIT(5) are not defined (for N .LT. 5) or altered
C                in any way by XGETUA.
C        N     - the number of units to which copies of the
C                error messages are being sent.  N will be in the
C                range from 1 to 5.
C
C***REFERENCES  R. E. Jones and D. K. Kahaner, XERROR, the SLATEC
C                 Error-handling Package, SAND82-0800, Sandia
C                 Laboratories, 1982.
C***ROUTINES CALLED  J4SAVE
C***REVISION HISTORY  (YYMMDD)
C   790801  DATE WRITTEN
C   861211  REVISION DATE from Version 3.2
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C   920501  Reformatted the REFERENCES section.  (WRB)
C***END PROLOGUE  XGETUA
      dimension iunita(5)
C***FIRST EXECUTABLE STATEMENT  XGETUA
      n = j4save(5,0,.false.)
      DO 30 i=1,n
         index = i+4
         IF (i.EQ.1) index = 3
         iunita(i) = j4save(index,0,.false.)
   30 CONTINUE
      RETURN