C------------------------------------------------------------------ C FORTRAN 77 program to test BESI1, BESEI1 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 References: "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,B,BESEI1,BESI1,BETA,BOT,C,CONST,CONV, 2 D,DEL,DELTA,E,EIGHT,EPS,EPSNEG,F,HALF,HUND,ONE,OVRCHK,REN,R6, 3 R7,SIXTEN,SUM,TEMP,THREE,TOP,T1,T2,U,U2,W,X,XA,XB,XBAD,XJ1, 4 XL,XLAM,XLARGE,XMAX,XMB,XMIN,XN,X1,X99,Y,Z,ZERO,ZZ DIMENSION ARR(8,7),U(560),U2(560) CS DATA ZERO,HALF,ONE,THREE,EIGHT/0.0E0,0.5E0,1.0E0,3.0E0,8.0E0/, CS 1 SIXTEN,HUND,X99,XLAM/1.6E1,1.0E2,-999.0E0,1.03125E0/, CS 2 XLARGE,C/1.0E4,0.9189385332E0/ CD DATA ZERO,HALF,ONE,THREE,EIGHT/0.0D0,0.5D0,1.0D0,3.0D0,8.0D0/, CD 1 SIXTEN,HUND,X99,XLAM/1.6D1,1.0D2,-999.0D0,1.03125D0/, CD 2 XLARGE,C/1.0D4,0.9189385332D0/ CS DATA ARR/1.0E0,-1.0E0,1.0E0,-2.0E0,1.0E0,-3.0E0,1.0E0,-4.0E0, CS 1 -999.0E0,-999.0E0,3.0E0,-12.0E0,9.0E0,-51.0E0,18.0E0, CS 2 -132.0E0,40320.0E0,0.0E0,-999.0E0,-999.0E0,60.0E0, CS 3 -360.0E0,345.0E0,-2700.0E0,10440.0E0,-5040.0E0,720.0E0, CS 4 0.0E0,-999.0E0,-999.0E0,2520.0E0,-20160.0E0,729.0E0, CS 5 -1320.0E0,192.0E0,-120.0E0,24.0E0,0.0E0,-999.0E0, CS 6 -999.0E0,26.0E0,-96.0E0,15.0E0,-33.0E0,7.0E0,-6.0E0, CS 7 2.0E0,0.0E0,1.0E0,-4.0E0,1.0E0,-3.0E0,1.0E0,-2.0E0, CS 8 1.0E0,-1.0E0/ CD DATA ARR/1.0D0,-1.0D0,1.0D0,-2.0D0,1.0D0,-3.0D0,1.0D0,-4.0D0, CD 1 -999.0D0,-999.0D0,3.0D0,-12.0D0,9.0D0,-51.0D0,18.0D0, CD 2 -132.0D0,40320.0D0,0.0D0,-999.0D0,-999.0D0,60.0D0, CD 3 -360.0D0,345.0D0,-2700.0D0,10440.0D0,-5040.0D0,720.0D0, CD 4 0.0D0,-999.0D0,-999.0D0,2520.0D0,-20160.0D0,729.0D0, CD 5 -1320.0D0,192.0D0,-120.0D0,24.0D0,0.0D0,-999.0D0, CD 6 -999.0D0,26.0D0,-96.0D0,15.0D0,-33.0D0,7.0D0,-6.0D0, CD 7 2.0D0,0.0D0,1.0D0,-4.0D0,1.0D0,-3.0D0,1.0D0,-2.0D0, CD 8 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-THREE/(EIGHT*X)) BOT(X) = THREE / ((EIGHT*X-THREE)*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 = ONE 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 W = SIXTEN * Y T1 = W + Y T1 = W + T1 Y = T1 - W Y = Y - W 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(2) = BESI1(Y) U(1) = U(2) / U2(1) IF (J .EQ. 1) THEN C------------------------------------------------------------------ C Accuracy test is based on the multiplication theorem C------------------------------------------------------------------ MB = MB - MBORG DO 120 II = 3, MB U(II) = U(II-1) * U2(II-1) 120 CONTINUE C------------------------------------------------------------------ C Accurate Summation C------------------------------------------------------------------ MB = MB - 1 XMB = CONV(MB-1) 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 = XLAM * SUM ELSE C------------------------------------------------------------------ C Accuracy test is based on Taylor's Series Expansion C------------------------------------------------------------------ MB = 8 J1 = MB XJ1 = CONV(J1+1) IEXP = 1 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 = 7 170 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. 8) GO TO 177 175 T2 = T2 / (Y*Y) + ARR(II,J2) J2 = J2 + 1 IF (J2 .LE. 7) 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(2) END IF Z = BESI1(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 + THREE + HALF 300 CONTINUE C----------------------------------------------------------------- C Test of error returns C C Special tests C----------------------------------------------------------------- WRITE (IOUT,1030) WRITE (IOUT,1031) Y = BESI1(XMIN) WRITE (IOUT,1032) Y Y = BESI1(ZERO) WRITE (IOUT,1033) 0,Y X = -ONE * REN(JT) Y = BESI1(X) WRITE (IOUT,1034) X,Y X = -X Y = BESI1(X) WRITE (IOUT,1034) X,Y Y = BESEI1(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 = BESI1(XLARGE) WRITE (IOUT,1034) XLARGE,Y XLARGE = XB * XLAM Y = BESI1(XLARGE) WRITE (IOUT,1034) XLARGE,Y WRITE (IOUT, 1037) STOP C----------------------------------------------------------------- 1000 FORMAT('1Test of I1(X) vs Multiplication Theorem'//) 1001 FORMAT('1Test of I1(X) vs Taylor series'//) 1010 FORMAT(I7,' Random arguments were tested from the interval ', 1 '(',F5.2,',',F5.2,')'//) 1011 FORMAT(' I1(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(' I1(XMIN) = ',E24.17/) 1033 FORMAT(' I1(',I1,') = ',E24.17/) 1034 FORMAT(' I1(',E24.17,' ) = ',E24.17/) 1035 FORMAT(' E**-X * I1(XMAX) = ',E24.17/) 1036 FORMAT(' Tests near the largest argument for unscaled functions'/) 1037 FORMAT(' This concludes the tests.') C ---------- Last line of BESI1 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