C------------------------------------------------------------------
C FORTRAN 77 program to test BESI0, BESEI0
C
C Method:
C
C Accuracy tests compare function values against values
C generated with the multiplication formula for small
C arguments and values generated from a Taylor's Series
C Expansion using Amos' Ratio Scheme for initial values
C for large arguments.
C
C Data required
C
C None
C
C Subprograms required from this package
C
C MACHAR - An environmental inquiry program providing
C information on the floating-point arithmetic
C system. Note that the call to MACHAR can
C be deleted provided the following five
C parameters are assigned the values indicated
C
C IBETA - the radix of the floating-point system
C IT - the number of base-IBETA digits in the
C significant of a floating-point number
C EPS - the smallest positive floating-point
C number such that 1.0+EPS .NE. 1.0
C XMIN - the smallest non-vanishing normalized
C floating-point power of the radix
C XMAX - the largest finite floating-point number
C
C REN(K) - a function subprogram returning random real
C numbers uniformly distributed over (0,1)
C
C
C Intrinsic functions required are:
C
C ABS, DBLE, INT, LOG, MAX, REAL, SQRT
C
C Reference: "Computation of Modified Bessel Functions and
C Their Ratios," D. E. Amos, Math. of Comp.,
C Volume 28, Number 24, January, 1974.
C
C "Performance evaluation of programs for certain
C Bessel functions", W. J. Cody and L. Stoltz,
C ACM Trans. on Math. Software, Vol. 15, 1989,
C pp 41-48.
C
C "Use of Taylor series to test accuracy of function
C programs," W. J. Cody and L. Stoltz, submitted
C for publication.
C
C Latest modification: May 30, 1989
C
C Authors: W. J. Cody and L. Stoltz
C Mathematics and Computer Science Division
C Argonne National Laboratory
C Argonne, IL 60439
C
C------------------------------------------------------------------
INTEGER I,IBETA,IEXP,II,IND,IOUT,IRND,IT,J,JT,J1,J2,K1,K2,K3,
1 MACHEP,MAXEXP,MB,MBORG,MINEXP,MB2,N,NEGEP,NGRD
CS REAL
CD DOUBLE PRECISION
1 A,AIT,AK,AKK,ALBETA,ARR,ATETEN,B,BESEI0,BESI0,BETA,BOT,C,
2 CONST,CONV,D,DEL,DELTA,E,EIGHT,EPS,EPSNEG,F,HALF,HUND,ONE,
3 OVRCHK,ONE28,REN,R6,R7,SIXTEN,SUM,TEMP,TOP,TWO,T1,T2,U,U2,
4 W,X,XA,XB,XBAD,XJ1,XL,XLAM,XLARGE,XMAX,XMB,XMIN,XN,XNINE,
5 X1,X99,Y,Z,ZERO,ZZ
DIMENSION ARR(8,6),U(560),U2(560)
CS DATA ZERO,HALF,ONE,TWO,EIGHT/0.0E0,0.5E0,1.0E0,2.0E0,8.0E0/,
CS 1 XNINE,SIXTEN,ATETEN,HUND/9.0E0,1.6E1,1.8E1,1.0E2/,
CS 2 ONE28,X99,XLAM,XLARGE/1.28E2,-999.0E0,1.03125E0,1.0E4/,
CS 3 C/0.9189385332E0/
CD DATA ZERO,HALF,ONE,TWO,EIGHT/0.0D0,0.5D0,1.0D0,2.0D0,8.0D0/,
CD 1 XNINE,SIXTEN,ATETEN,HUND/9.0D0,1.6D1,1.8D1,1.0D2/,
CD 2 ONE28,X99,XLAM,XLARGE/1.28D2,-999.0D0,1.03125D0,1.0D4/,
CD 3 C/0.9189385332D0/
CS DATA ARR/0.0E0,1.0E0,-1.0E0,1.0E0,-2.0E0,1.0E0,-3.0E0,1.0E0,
CS 1 -999.0E0,-999.0E0,-999.0E0,3.0E0,-12.0E0,9.0E0,-51.0E0,
CS 2 18.0E0,-5040.0E0,720.0E0,0.0E0,-999.0E0,-999.0E0,
CS 3 60.0E0,-360.0E0,345.0E0,-1320.0E0,192.0E0,-120.0E0,
CS 4 24.0E0,0.0E0,-999.0E0,-999.0E0,2520.0E0,-96.0E0,15.0E0,
CS 5 -33.0E0,7.0E0,-6.0E0,2.0E0,0.0E0,-999.0E0,-4.0E0,1.0E0,
CS 6 -3.0E0,1.0E0,-2.0E0,1.0E0,-1.0E0,1.0E0/
CD DATA ARR/0.0D0,1.0D0,-1.0D0,1.0D0,-2.0D0,1.0D0,-3.0D0,1.0D0,
CD 1 -999.0D0,-999.0D0,-999.0D0,3.0D0,-12.0D0,9.0D0,-51.0D0,
CD 2 18.0D0,-5040.0D0,720.0D0,0.0D0,-999.0D0,-999.0D0,
CD 3 60.0D0,-360.0D0,345.0D0,-1320.0D0,192.0D0,-120.0D0,
CD 4 24.0D0,0.0D0,-999.0D0,-999.0D0,2520.0D0,-96.0D0,15.0D0,
CD 5 -33.0D0,7.0D0,-6.0D0,2.0D0,0.0D0,-999.0D0,-4.0D0,1.0D0,
CD 6 -3.0D0,1.0D0,-2.0D0,1.0D0,-1.0D0,1.0D0/
DATA IOUT/6/
C------------------------------------------------------------------
C Define statement functions for conversions
C------------------------------------------------------------------
CS CONV(N) = REAL(N)
CD CONV(N) = DBLE(N)
TOP(X) = X - HALF*LOG(X) + LOG(ONE+(ONE/EIGHT-XNINE/
1 ONE28/X)/X)
BOT(X) = -(SIXTEN*X+ATETEN) / (((ONE28*X+SIXTEN)*X+
1 XNINE)*X) + ONE - HALF/X
C------------------------------------------------------------------
C Determine machine parameters and set constants
C------------------------------------------------------------------
CALL MACHAR(IBETA,IT,IRND,NGRD,MACHEP,NEGEP,IEXP,MINEXP,
1 MAXEXP,EPS,EPSNEG,XMIN,XMAX)
BETA = CONV(IBETA)
AIT = CONV(IT)
ALBETA = LOG(BETA)
A = ZERO
B = TWO
JT = 0
CONST = C + LOG(XMAX)
DELTA = XLAM - ONE
F = (XLAM-ONE) * (XLAM+ONE) * HALF
C-----------------------------------------------------------------
C Random argument accuracy tests
C-----------------------------------------------------------------
DO 300 J = 1, 4
C-------------------------------------------------------------------
C Calculate the number of terms needed for convergence of the
C series by using Newton's iteration on the asymptotic form of
C the multiplication theorem
C-------------------------------------------------------------------
XBAD = B
D = AIT * ALBETA - C + ONE
E = LOG(XBAD * F) + ONE
AKK = ONE
100 AK = AKK
Z = D + E*AK - (AK+HALF) * LOG(AK+ONE)
ZZ = E - (AK+HALF)/(AK+ONE) - LOG(AK+ONE)
AKK = AK - Z/ZZ
IF (ABS(AK-AKK) .GT. HUND*EPS*AK) GO TO 100
MBORG = INT(AKK) + 1
N = 2000
XN = CONV(N)
K1 = 0
K2 = 0
K3 = 0
X1 = ZERO
R6 = ZERO
R7 = ZERO
DEL = (B - A) / XN
XL = A
DO 200 I = 1, N
X = DEL * REN(JT) + XL
C------------------------------------------------------------------
C Carefully purify arguments
C------------------------------------------------------------------
IF (J .EQ. 1) THEN
Y = X/XLAM
ELSE
Y = X - DELTA
END IF
TEMP = SIXTEN * Y
T1 = TEMP + Y
T1 = TEMP + T1
Y = T1 - TEMP
Y = Y - TEMP
IF (J .EQ. 1) THEN
X = Y * XLAM
ELSE
X = Y + DELTA
END IF
C------------------------------------------------------------------
C Use Amos' Ratio Scheme
C------------------------------------------------------------------
D = F*Y
MB = MBORG + MBORG
MB2 = MB - 1
XMB = CONV(MB2)
TEMP = (XMB + ONE + HALF) * (XMB + ONE + HALF)
U2(MB) = Y / (XMB + HALF + SQRT(TEMP + Y*Y))
C------------------------------------------------------------------
C Generate ratios using recurrence
C------------------------------------------------------------------
DO 110 II = 2, MB
OVRCHK = XMB/(Y*HALF)
U2(MB2) = ONE / (OVRCHK + U2(MB2+1))
XMB = XMB - ONE
MB2 = MB2 - 1
110 CONTINUE
U(1) = BESI0(Y)
IF (J .EQ. 1) THEN
C------------------------------------------------------------------
C Accuracy test is based on the multiplication theorem
C------------------------------------------------------------------
MB = MB - MBORG
DO 120 II = 2, MB
U(II) = U(II-1) * U2(II-1)
120 CONTINUE
C------------------------------------------------------------------
C Accurate Summation
C------------------------------------------------------------------
MB = MB - 1
XMB = CONV(MB)
SUM = U(MB+1)
IND = MB
DO 155 II = 2, MB
SUM = SUM * D / XMB + U(IND)
IND = IND - 1
XMB = XMB - ONE
155 CONTINUE
ZZ = SUM * D + U(IND)
ELSE
C------------------------------------------------------------------
C Accuracy test is based on Taylor's Series Expansion
C------------------------------------------------------------------
U(2) = U(1) * U2(1)
MB = 8
J1 = MB
XJ1 = CONV(J1+1)
IEXP = 0
C------------------------------------------------------------------
C Accurate Summation
C------------------------------------------------------------------
DO 180 II = 1, MB
J2 = 1
160 J2 = J2 + 1
IF (ARR(J1,J2) .NE. X99) GO TO 160
J2 = J2 - 1
T1 = ARR(J1,J2)
J2 = J2 - 1
C------------------------------------------------------------------
C Group I0 terms in the derivative
C------------------------------------------------------------------
IF (J2 .EQ. 0) GO TO 168
165 T1 = T1 / (Y*Y) + ARR(J1,J2)
J2 = J2 - 1
IF (J2 .GE. 1) GO TO 165
168 IF (IEXP .EQ. 1) T1 = T1 / Y
J2 = 6
170 J2 = J2 - 1
IF (ARR(II,J2) .NE. X99) GO TO 170
J2 = J2 + 1
T2 = ARR(II,J2)
J2 = J2 + 1
IF (IEXP .EQ. 0) THEN
IEXP = 1
ELSE
IEXP = 0
END IF
C------------------------------------------------------------------
C Group I1 terms in the derivative
C------------------------------------------------------------------
IF (J2 .EQ. 7) GO TO 177
175 T2 = T2 / (Y*Y) + ARR(II,J2)
J2 = J2 + 1
IF (J2 .LE. 6) GO TO 175
177 IF (IEXP .EQ. 1) T2 = T2 / Y
IF (J1 .EQ. 8) THEN
SUM = U(1)*T1 + U(2)*T2
ELSE
SUM = SUM * (DELTA/XJ1) + (U(1)*T1 + U(2)*T2)
END IF
J1 = J1 - 1
XJ1 = CONV(J1+1)
180 CONTINUE
ZZ = SUM * DELTA + U(1)
END IF
Z = BESI0(X)
C------------------------------------------------------------------
C Accumulate Results
C------------------------------------------------------------------
W = (Z - ZZ) / Z
IF (W .GT. ZERO) THEN
K1 = K1 + 1
ELSE IF (W .LT. ZERO) THEN
K3 = K3 + 1
ELSE
K2 = K2 + 1
END IF
W = ABS(W)
IF (W .GT. R6) THEN
R6 = W
X1 = X
END IF
R7 = R7 + W * W
XL = XL + DEL
200 CONTINUE
C------------------------------------------------------------------
C Gather and print statistics for test
C------------------------------------------------------------------
N = K1 + K2 + K3
R7 = SQRT(R7/XN)
IF (J .EQ. 1) THEN
WRITE (IOUT,1000)
ELSE
WRITE (IOUT,1001)
END IF
WRITE (IOUT,1010) N,A,B
WRITE (IOUT,1011) K1,K2,K3
WRITE (IOUT,1020) IT,IBETA
IF (R6 .NE. ZERO) THEN
W = LOG(R6)/ALBETA
ELSE
W = X99
END IF
WRITE (IOUT,1021) R6,IBETA,W,X1
W = MAX(AIT+W,ZERO)
WRITE (IOUT,1022) IBETA,W
IF (R7 .NE. ZERO) THEN
W = LOG(R7)/ALBETA
ELSE
W = X99
END IF
WRITE (IOUT,1023) R7,IBETA,W
W = MAX(AIT+W,ZERO)
WRITE (IOUT,1022) IBETA,W
C------------------------------------------------------------------
C Initialize for next test
C------------------------------------------------------------------
A = B
B = B + B
IF (J .EQ. 1) B = B + B - HALF
300 CONTINUE
C-----------------------------------------------------------------
C Test of error returns
C
C Special tests
C-----------------------------------------------------------------
WRITE (IOUT,1030)
WRITE (IOUT,1031)
Y = BESI0(XMIN)
WRITE (IOUT,1032) Y
Y = BESI0(ZERO)
WRITE (IOUT,1033) 0,Y
X = -ONE * REN(JT)
Y = BESI0(X)
WRITE (IOUT,1034) X,Y
X = -X
Y = BESI0(X)
WRITE (IOUT,1034) X,Y
Y = BESEI0(XMAX)
WRITE (IOUT,1035) Y
C-----------------------------------------------------------------
C Determine largest safe argument for unscaled functions
C-----------------------------------------------------------------
WRITE (IOUT, 1036)
XA = LOG(XMAX)
330 XB = XA - (TOP(XA)-CONST) / BOT(XA)
IF (ABS(XB-XA)/XB .LE. EPS) THEN
GO TO 350
ELSE
XA = XB
GO TO 330
END IF
350 XLARGE = XB / XLAM
Y = BESI0(XLARGE)
WRITE (IOUT,1034) XLARGE,Y
XLARGE = XB * XLAM
Y = BESI0(XLARGE)
WRITE (IOUT,1034) XLARGE,Y
WRITE (IOUT, 1037)
STOP
C-----------------------------------------------------------------
1000 FORMAT('1Test of I0(X) vs Multiplication Theorem'//)
1001 FORMAT('1Test of I0(X) vs Taylor series'//)
1010 FORMAT(I7,' Random arguments were tested from the interval ',
1 '(',F5.2,',',F5.2,')'//)
1011 FORMAT(' I0(X) was larger',I6,' times,'/
1 10X,' agreed',I6,' times, and'/
1 6X,'was smaller',I6,' times.'//)
1020 FORMAT(' There are',I4,' base',I4,
1 ' significant digits in a floating-point number'//)
1021 FORMAT(' The maximum relative error of',E15.4,' = ',I4,' **',
1 F7.2/4X,'occurred for X =',E13.6)
1022 FORMAT(' The estimated loss of base',I4,
1 ' significant digits is',F7.2//)
1023 FORMAT(' The root mean square relative error was',E15.4,
1 ' = ',I4,' **',F7.2)
1030 FORMAT('1Special Tests'//)
1031 FORMAT(' Test with extreme arguments'/)
1032 FORMAT(' I0(XMIN) = ',E24.17/)
1033 FORMAT(' I0(',I1,') = ',E24.17/)
1034 FORMAT(' I0(',E24.17,' ) = ',E24.17/)
1035 FORMAT(' E**-X * I0(XMAX) = ',E24.17/)
1036 FORMAT(' Tests near the largest argument for unscaled functions'/)
1037 FORMAT(' This concludes the tests.')
C---------- Last line of BESI0 test program ----------
END
SUBROUTINE MACHAR(IBETA,IT,IRND,NGRD,MACHEP,NEGEP,IEXP,MINEXP,
1 MAXEXP,EPS,EPSNEG,XMIN,XMAX)
C----------------------------------------------------------------------
C This Fortran 77 subroutine is intended to determine the parameters
C of the floating-point arithmetic system specified below. The
C determination of the first three uses an extension of an algorithm
C due to M. Malcolm, CACM 15 (1972), pp. 949-951, incorporating some,
C but not all, of the improvements suggested by M. Gentleman and S.
C Marovich, CACM 17 (1974), pp. 276-277. An earlier version of this
C program was published in the book Software Manual for the
C Elementary Functions by W. J. Cody and W. Waite, Prentice-Hall,
C Englewood Cliffs, NJ, 1980.
C
C The program as given here must be modified before compiling. If
C a single (double) precision version is desired, change all
C occurrences of CS (CD) in columns 1 and 2 to blanks.
C
C Parameter values reported are as follows:
C
C IBETA - the radix for the floating-point representation
C IT - the number of base IBETA digits in the floating-point
C significand
C IRND - 0 if floating-point addition chops
C 1 if floating-point addition rounds, but not in the
C IEEE style
C 2 if floating-point addition rounds in the IEEE style
C 3 if floating-point addition chops, and there is
C partial underflow
C 4 if floating-point addition rounds, but not in the
C IEEE style, and there is partial underflow
C 5 if floating-point addition rounds in the IEEE style,
C and there is partial underflow
C NGRD - the number of guard digits for multiplication with
C truncating arithmetic. It is
C 0 if floating-point arithmetic rounds, or if it
C truncates and only IT base IBETA digits
C participate in the post-normalization shift of the
C floating-point significand in multiplication;
C 1 if floating-point arithmetic truncates and more
C than IT base IBETA digits participate in the
C post-normalization shift of the floating-point
C significand in multiplication.
C MACHEP - the largest negative integer such that
C 1.0+FLOAT(IBETA)**MACHEP .NE. 1.0, except that
C MACHEP is bounded below by -(IT+3)
C NEGEPS - the largest negative integer such that
C 1.0-FLOAT(IBETA)**NEGEPS .NE. 1.0, except that
C NEGEPS is bounded below by -(IT+3)
C IEXP - the number of bits (decimal places if IBETA = 10)
C reserved for the representation of the exponent
C (including the bias or sign) of a floating-point
C number
C MINEXP - the largest in magnitude negative integer such that
C FLOAT(IBETA)**MINEXP is positive and normalized
C MAXEXP - the smallest positive power of BETA that overflows
C EPS - FLOAT(IBETA)**MACHEP.
C EPSNEG - FLOAT(IBETA)**NEGEPS.
C XMIN - the smallest non-vanishing normalized floating-point
C power of the radix, i.e., XMIN = FLOAT(IBETA)**MINEXP
C XMAX - the largest finite floating-point number. In
C particular XMAX = (1.0-EPSNEG)*FLOAT(IBETA)**MAXEXP
C Note - on some machines XMAX will be only the
C second, or perhaps third, largest number, being
C too small by 1 or 2 units in the last digit of
C the significand.
C
C Latest modification: May 30, 1989
C
C Author: W. J. Cody
C Mathematics and Computer Science Division
C Argonne National Laboratory
C Argonne, IL 60439
C
C----------------------------------------------------------------------
INTEGER I,IBETA,IEXP,IRND,IT,ITEMP,IZ,J,K,MACHEP,MAXEXP,
1 MINEXP,MX,NEGEP,NGRD,NXRES
CS REAL
CD DOUBLE PRECISION
1 A,B,BETA,BETAIN,BETAH,CONV,EPS,EPSNEG,ONE,T,TEMP,TEMPA,
2 TEMP1,TWO,XMAX,XMIN,Y,Z,ZERO
C----------------------------------------------------------------------
CS CONV(I) = REAL(I)
CD CONV(I) = DBLE(I)
ONE = CONV(1)
TWO = ONE + ONE
ZERO = ONE - ONE
C----------------------------------------------------------------------
C Determine IBETA, BETA ala Malcolm.
C----------------------------------------------------------------------
A = ONE
10 A = A + A
TEMP = A+ONE
TEMP1 = TEMP-A
IF (TEMP1-ONE .EQ. ZERO) GO TO 10
B = ONE
20 B = B + B
TEMP = A+B
ITEMP = INT(TEMP-A)
IF (ITEMP .EQ. 0) GO TO 20
IBETA = ITEMP
BETA = CONV(IBETA)
C----------------------------------------------------------------------
C Determine IT, IRND.
C----------------------------------------------------------------------
IT = 0
B = ONE
100 IT = IT + 1
B = B * BETA
TEMP = B+ONE
TEMP1 = TEMP-B
IF (TEMP1-ONE .EQ. ZERO) GO TO 100
IRND = 0
BETAH = BETA / TWO
TEMP = A+BETAH
IF (TEMP-A .NE. ZERO) IRND = 1
TEMPA = A + BETA
TEMP = TEMPA+BETAH
IF ((IRND .EQ. 0) .AND. (TEMP-TEMPA .NE. ZERO)) IRND = 2
C----------------------------------------------------------------------
C Determine NEGEP, EPSNEG.
C----------------------------------------------------------------------
NEGEP = IT + 3
BETAIN = ONE / BETA
A = ONE
DO 200 I = 1, NEGEP
A = A * BETAIN
200 CONTINUE
B = A
210 TEMP = ONE-A
IF (TEMP-ONE .NE. ZERO) GO TO 220
A = A * BETA
NEGEP = NEGEP - 1
GO TO 210
220 NEGEP = -NEGEP
EPSNEG = A
C----------------------------------------------------------------------
C Determine MACHEP, EPS.
C----------------------------------------------------------------------
MACHEP = -IT - 3
A = B
300 TEMP = ONE+A
IF (TEMP-ONE .NE. ZERO) GO TO 320
A = A * BETA
MACHEP = MACHEP + 1
GO TO 300
320 EPS = A
C----------------------------------------------------------------------
C Determine NGRD.
C----------------------------------------------------------------------
NGRD = 0
TEMP = ONE+EPS
IF ((IRND .EQ. 0) .AND. (TEMP*ONE-ONE .NE. ZERO)) NGRD = 1
C----------------------------------------------------------------------
C Determine IEXP, MINEXP, XMIN.
C
C Loop to determine largest I and K = 2**I such that
C (1/BETA) ** (2**(I))
C does not underflow.
C Exit from loop is signaled by an underflow.
C----------------------------------------------------------------------
I = 0
K = 1
Z = BETAIN
T = ONE + EPS
NXRES = 0
400 Y = Z
Z = Y * Y
C----------------------------------------------------------------------
C Check for underflow here.
C----------------------------------------------------------------------
A = Z * ONE
TEMP = Z * T
IF ((A+A .EQ. ZERO) .OR. (ABS(Z) .GE. Y)) GO TO 410
TEMP1 = TEMP * BETAIN
IF (TEMP1*BETA .EQ. Z) GO TO 410
I = I + 1
K = K + K
GO TO 400
410 IF (IBETA .EQ. 10) GO TO 420
IEXP = I + 1
MX = K + K
GO TO 450
C----------------------------------------------------------------------
C This segment is for decimal machines only.
C----------------------------------------------------------------------
420 IEXP = 2
IZ = IBETA
430 IF (K .LT. IZ) GO TO 440
IZ = IZ * IBETA
IEXP = IEXP + 1
GO TO 430
440 MX = IZ + IZ - 1
C----------------------------------------------------------------------
C Loop to determine MINEXP, XMIN.
C Exit from loop is signaled by an underflow.
C----------------------------------------------------------------------
450 XMIN = Y
Y = Y * BETAIN
C----------------------------------------------------------------------
C Check for underflow here.
C----------------------------------------------------------------------
A = Y * ONE
TEMP = Y * T
IF (((A+A) .EQ. ZERO) .OR. (ABS(Y) .GE. XMIN)) GO TO 460
K = K + 1
TEMP1 = TEMP * BETAIN
IF ((TEMP1*BETA .NE. Y) .OR. (TEMP .EQ. Y)) THEN
GO TO 450
ELSE
NXRES = 3
XMIN = Y
END IF
460 MINEXP = -K
C----------------------------------------------------------------------
C Determine MAXEXP, XMAX.
C----------------------------------------------------------------------
IF ((MX .GT. K+K-3) .OR. (IBETA .EQ. 10)) GO TO 500
MX = MX + MX
IEXP = IEXP + 1
500 MAXEXP = MX + MINEXP
C----------------------------------------------------------------------
C Adjust IRND to reflect partial underflow.
C----------------------------------------------------------------------
IRND = IRND + NXRES
C----------------------------------------------------------------------
C Adjust for IEEE-style machines.
C----------------------------------------------------------------------
IF (IRND .GE. 2) MAXEXP = MAXEXP - 2
C----------------------------------------------------------------------
C Adjust for machines with implicit leading bit in binary
C significand, and machines with radix point at extreme
C right of significand.
C----------------------------------------------------------------------
I = MAXEXP + MINEXP
IF ((IBETA .EQ. 2) .AND. (I .EQ. 0)) MAXEXP = MAXEXP - 1
IF (I .GT. 20) MAXEXP = MAXEXP - 1
IF (A .NE. Y) MAXEXP = MAXEXP - 2
XMAX = ONE - EPSNEG
IF (XMAX*ONE .NE. XMAX) XMAX = ONE - BETA * EPSNEG
XMAX = XMAX / (BETA * BETA * BETA * XMIN)
I = MAXEXP + MINEXP + 3
IF (I .LE. 0) GO TO 520
DO 510 J = 1, I
IF (IBETA .EQ. 2) XMAX = XMAX + XMAX
IF (IBETA .NE. 2) XMAX = XMAX * BETA
510 CONTINUE
520 RETURN
C---------- Last line of MACHAR ----------
END
FUNCTION REN(K)
C---------------------------------------------------------------------
C Random number generator - based on Algorithm 266 by Pike and
C Hill (modified by Hansson), Communications of the ACM,
C Vol. 8, No. 10, October 1965.
C
C This subprogram is intended for use on computers with
C fixed point wordlength of at least 29 bits. It is
C best if the floating-point significand has at most
C 29 bits.
C
C Latest modification: May 30, 1989
C
C Author: W. J. Cody
C Mathematics and Computer Science Division
C Argonne National Laboratory
C Argonne, IL 60439
C
C---------------------------------------------------------------------
INTEGER IY,J,K
CS REAL CONV,C1,C2,C3,ONE,REN
CD DOUBLE PRECISION CONV,C1,C2,C3,ONE,REN
DATA IY/100001/
CS DATA ONE,C1,C2,C3/1.0E0,2796203.0E0,1.0E-6,1.0E-12/
CD DATA ONE,C1,C2,C3/1.0D0,2796203.0D0,1.0D-6,1.0D-12/
C---------------------------------------------------------------------
C Statement functions for conversion between integer and float
C---------------------------------------------------------------------
CS CONV(J) = REAL(J)
CD CONV(J) = DBLE(J)
C---------------------------------------------------------------------
J = K
IY = IY * 125
IY = IY - (IY/2796203) * 2796203
REN = CONV(IY) / C1 * (ONE + C2 + C3)
RETURN
C---------- Last card of REN ----------
END