SUBROUTINE RANLUX(RVEC,LENV) C Subtract-and-borrow random number generator proposed by C Marsaglia and Zaman, implemented by F. James with the name C RCARRY in 1991, and later improved by Martin Luescher C in 1993 to produce "Luxury Pseudorandom Numbers". C Fortran 77 coded by F. James, 1993 C C references: C M. Luscher, Computer Physics Communications 79 (1994) 100 C F. James, Computer Physics Communications 79 (1994) 111 C C LUXURY LEVELS. C ------ ------ The available luxury levels are: C C level 0 (p=24): equivalent to the original RCARRY of Marsaglia C and Zaman, very long period, but fails many tests. C level 1 (p=48): considerable improvement in quality over level 0, C now passes the gap test, but still fails spectral test. C level 2 (p=97): passes all known tests, but theoretically still C defective. C level 3 (p=223): DEFAULT VALUE. Any theoretically possible C correlations have very small chance of being observed. C level 4 (p=389): highest possible luxury, all 24 bits chaotic. C C!!! ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ C!!! Calling sequences for RANLUX: ++ C!!! CALL RANLUX (RVEC, LEN) returns a vector RVEC of LEN ++ C!!! 32-bit random floating point numbers between ++ C!!! zero (not included) and one (also not incl.). ++ C!!! CALL RLUXGO(LUX,INT,K1,K2) initializes the generator from ++ C!!! one 32-bit integer INT and sets Luxury Level LUX ++ C!!! which is integer between zero and MAXLEV, or if ++ C!!! LUX .GT. 24, it sets p=LUX directly. K1 and K2 ++ C!!! should be set to zero unless restarting at a break++ C!!! point given by output of RLUXAT (see RLUXAT). ++ C!!! CALL RLUXAT(LUX,INT,K1,K2) gets the values of four integers++ C!!! which can be used to restart the RANLUX generator ++ C!!! at the current point by calling RLUXGO. K1 and K2++ C!!! specify how many numbers were generated since the ++ C!!! initialization with LUX and INT. The restarting ++ C!!! skips over K1+K2*E9 numbers, so it can be long.++ C!!! A more efficient but less convenient way of restarting is by: ++ C!!! CALL RLUXIN(ISVEC) restarts the generator from vector ++ C!!! ISVEC of 25 32-bit integers (see RLUXUT) ++ C!!! CALL RLUXUT(ISVEC) outputs the current values of the 25 ++ C!!! 32-bit integer seeds, to be used for restarting ++ C!!! ISVEC must be dimensioned 25 in the calling program ++ C!!! ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ DIMENSION RVEC(LENV) DIMENSION SEEDS(24), ISEEDS(24), ISDEXT(25) PARAMETER (MAXLEV=4, LXDFLT=3) DIMENSION NDSKIP(0:MAXLEV) DIMENSION NEXT(24) PARAMETER (TWOP12=4096., IGIGA=1000000000,JSDFLT=314159265) PARAMETER (ITWO24=2**24, ICONS=2147483563) SAVE NOTYET, I24, J24, CARRY, SEEDS, TWOM24, TWOM12, LUXLEV SAVE NSKIP, NDSKIP, IN24, NEXT, KOUNT, MKOUNT, INSEED INTEGER LUXLEV LOGICAL NOTYET DATA NOTYET, LUXLEV, IN24, KOUNT, MKOUNT /.TRUE., LXDFLT, 0,0,0/ DATA I24,J24,CARRY/24,10,0./ C default C Luxury Level 0 1 2 *3* 4 DATA NDSKIP/0, 24, 73, 199, 365 / Corresponds to p=24 48 97 223 389 C time factor 1 2 3 6 10 on slow workstation C 1 1.5 2 3 5 on fast mainframe C C NOTYET is .TRUE. if no initialization has been performed yet. C Default Initialization by Multiplicative Congruential IF (NOTYET) THEN NOTYET = .FALSE. JSEED = JSDFLT INSEED = JSEED WRITE(6,'(A,I12)') ' RANLUX DEFAULT INITIALIZATION: ',JSEED LUXLEV = LXDFLT NSKIP = NDSKIP(LUXLEV) LP = NSKIP + 24 IN24 = 0 KOUNT = 0 MKOUNT = 0 WRITE(6,'(A,I2,A,I4)') ' RANLUX DEFAULT LUXURY LEVEL = ', + LUXLEV,' p =',LP TWOM24 = 1. DO 25 I= 1, 24 TWOM24 = TWOM24 * 0.5 K = JSEED/53668 JSEED = 40014*(JSEED-K*53668) -K*12211 IF (JSEED .LT. 0) JSEED = JSEED+ICONS ISEEDS(I) = MOD(JSEED,ITWO24) 25 CONTINUE TWOM12 = TWOM24 * 4096. DO 50 I= 1,24 SEEDS(I) = REAL(ISEEDS(I))*TWOM24 NEXT(I) = I-1 50 CONTINUE NEXT(1) = 24 I24 = 24 J24 = 10 CARRY = 0. IF (SEEDS(24) .EQ. 0.) CARRY = TWOM24 ENDIF C C The Generator proper: "Subtract-with-borrow", C as proposed by Marsaglia and Zaman, C Florida State University, March, 1989 C DO 100 IVEC= 1, LENV UNI = SEEDS(J24) - SEEDS(I24) - CARRY IF (UNI .LT. 0.) THEN UNI = UNI + 1.0 CARRY = TWOM24 ELSE CARRY = 0. ENDIF SEEDS(I24) = UNI I24 = NEXT(I24) J24 = NEXT(J24) RVEC(IVEC) = UNI C small numbers (with less than 12 "significant" bits) are "padded". IF (UNI .LT. TWOM12) THEN RVEC(IVEC) = RVEC(IVEC) + TWOM24*SEEDS(J24) C and zero is forbidden in case someone takes a logarithm IF (RVEC(IVEC) .EQ. 0.) RVEC(IVEC) = TWOM24*TWOM24 ENDIF C Skipping to luxury. As proposed by Martin Luscher. IN24 = IN24 + 1 IF (IN24 .EQ. 24) THEN IN24 = 0 KOUNT = KOUNT + NSKIP DO 90 ISK= 1, NSKIP UNI = SEEDS(J24) - SEEDS(I24) - CARRY IF (UNI .LT. 0.) THEN UNI = UNI + 1.0 CARRY = TWOM24 ELSE CARRY = 0. ENDIF SEEDS(I24) = UNI I24 = NEXT(I24) J24 = NEXT(J24) 90 CONTINUE ENDIF 100 CONTINUE KOUNT = KOUNT + LENV IF (KOUNT .GE. IGIGA) THEN MKOUNT = MKOUNT + 1 KOUNT = KOUNT - IGIGA ENDIF RETURN C C Entry to input and float integer seeds from previous run ENTRY RLUXIN(ISDEXT) TWOM24 = 1. DO 195 I= 1, 24 NEXT(I) = I-1 195 TWOM24 = TWOM24 * 0.5 NEXT(1) = 24 TWOM12 = TWOM24 * 4096. WRITE(6,'(A)') ' FULL INITIALIZATION OF RANLUX WITH 25 INTEGERS:' WRITE(6,'(5X,5I12)') ISDEXT DO 200 I= 1, 24 SEEDS(I) = REAL(ISDEXT(I))*TWOM24 200 CONTINUE CARRY = 0. IF (ISDEXT(25) .LT. 0) CARRY = TWOM24 ISD = IABS(ISDEXT(25)) I24 = MOD(ISD,100) ISD = ISD/100 J24 = MOD(ISD,100) ISD = ISD/100 IN24 = MOD(ISD,100) ISD = ISD/100 LUXLEV = ISD IF (LUXLEV .LE. MAXLEV) THEN NSKIP = NDSKIP(LUXLEV) WRITE (6,'(A,I2)') ' RANLUX LUXURY LEVEL SET BY RLUXIN TO: ', + LUXLEV ELSE IF (LUXLEV .GE. 24) THEN NSKIP = LUXLEV - 24 WRITE (6,'(A,I5)') ' RANLUX P-VALUE SET BY RLUXIN TO:',LUXLEV ELSE NSKIP = NDSKIP(MAXLEV) WRITE (6,'(A,I5)') ' RANLUX ILLEGAL LUXURY RLUXIN: ',LUXLEV LUXLEV = MAXLEV ENDIF INSEED = -1 RETURN C C Entry to ouput seeds as integers ENTRY RLUXUT(ISDEXT) DO 300 I= 1, 24 ISDEXT(I) = INT(SEEDS(I)*TWOP12*TWOP12) 300 CONTINUE ISDEXT(25) = I24 + 100*J24 + 10000*IN24 + 1000000*LUXLEV IF (CARRY .GT. 0.) ISDEXT(25) = -ISDEXT(25) RETURN C C Entry to output the "convenient" restart point ENTRY RLUXAT(LOUT,INOUT,K1,K2) LOUT = LUXLEV INOUT = INSEED K1 = KOUNT K2 = MKOUNT RETURN C C Entry to initialize from one or three integers ENTRY RLUXGO(LUX,INS,K1,K2) IF (LUX .LT. 0) THEN LUXLEV = LXDFLT ELSE IF (LUX .LE. MAXLEV) THEN LUXLEV = LUX ELSE IF (LUX .LT. 24 .OR. LUX .GT. 2000) THEN LUXLEV = MAXLEV WRITE (6,'(A,I7)') ' RANLUX ILLEGAL LUXURY RLUXGO: ',LUX ELSE LUXLEV = LUX DO 310 ILX= 0, MAXLEV IF (LUX .EQ. NDSKIP(ILX)+24) LUXLEV = ILX 310 CONTINUE ENDIF IF (LUXLEV .LE. MAXLEV) THEN NSKIP = NDSKIP(LUXLEV) WRITE(6,'(A,I2,A,I4)') ' RANLUX LUXURY LEVEL SET BY RLUXGO :', + LUXLEV,' P=', NSKIP+24 ELSE NSKIP = LUXLEV - 24 WRITE (6,'(A,I5)') ' RANLUX P-VALUE SET BY RLUXGO TO:',LUXLEV ENDIF IN24 = 0 IF (INS .LT. 0) WRITE (6,'(A)') + ' Illegal initialization by RLUXGO, negative input seed' IF (INS .GT. 0) THEN JSEED = INS WRITE(6,'(A,3I12)') ' RANLUX INITIALIZED BY RLUXGO FROM SEEDS', + JSEED, K1,K2 ELSE JSEED = JSDFLT WRITE(6,'(A)')' RANLUX INITIALIZED BY RLUXGO FROM DEFAULT SEED' ENDIF INSEED = JSEED NOTYET = .FALSE. TWOM24 = 1. DO 325 I= 1, 24 TWOM24 = TWOM24 * 0.5 K = JSEED/53668 JSEED = 40014*(JSEED-K*53668) -K*12211 IF (JSEED .LT. 0) JSEED = JSEED+ICONS ISEEDS(I) = MOD(JSEED,ITWO24) 325 CONTINUE TWOM12 = TWOM24 * 4096. DO 350 I= 1,24 SEEDS(I) = REAL(ISEEDS(I))*TWOM24 NEXT(I) = I-1 350 CONTINUE NEXT(1) = 24 I24 = 24 J24 = 10 CARRY = 0. IF (SEEDS(24) .EQ. 0.) CARRY = TWOM24 C If restarting at a break point, skip K1 + IGIGA*K2 C Note that this is the number of numbers delivered to C the user PLUS the number skipped (if luxury .GT. 0). KOUNT = K1 MKOUNT = K2 IF (K1+K2 .NE. 0) THEN DO 500 IOUTER= 1, K2+1 INNER = IGIGA IF (IOUTER .EQ. K2+1) INNER = K1 DO 450 ISK= 1, INNER UNI = SEEDS(J24) - SEEDS(I24) - CARRY IF (UNI .LT. 0.) THEN UNI = UNI + 1.0 CARRY = TWOM24 ELSE CARRY = 0. ENDIF SEEDS(I24) = UNI I24 = NEXT(I24) J24 = NEXT(J24) 450 CONTINUE 500 CONTINUE C Get the right value of IN24 by direct calculation IN24 = MOD(KOUNT, NSKIP+24) IF (MKOUNT .GT. 0) THEN IZIP = MOD(IGIGA, NSKIP+24) IZIP2 = MKOUNT*IZIP + IN24 IN24 = MOD(IZIP2, NSKIP+24) ENDIF C Now IN24 had better be between zero and 23 inclusive IF (IN24 .GT. 23) THEN WRITE (6,'(A/A,3I11,A,I5)') + ' Error in RESTARTING with RLUXGO:',' The values', INS, + K1, K2, ' cannot occur at luxury level', LUXLEV IN24 = 0 ENDIF ENDIF RETURN END C +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ PROGRAM LUXTST C Exercise for the RANLUX Pseudorandom number generator. C DIMENSION RVEC(1000) DIMENSION ISDEXT(25) C C check that we get the right numbers (machine-indep.) WRITE (6,'(/A)') ' CALL RANLUX(RVEC,100)' CALL RANLUX(RVEC,100) WRITE (6,'(A/9X,5F12.8)') ' RANLUX default numbers 1- 5:', + (RVEC(L),L=1,5) CALL RANLUX(RVEC,100) WRITE (6,'(A/9X,5F12.8)') ' RANLUX default numbers 101-105:', + (RVEC(L),L=1,5) C WRITE (6,'(/A)') ' CALL RLUXGO(0,0,0,0)' CALL RLUXGO(0,0,0,0) CALL RANLUX(RVEC,100) WRITE (6,'(A/9X,5F12.8)') ' RANLUX luxury level 0, 1- 5:', + (RVEC(L),L=1,5) CALL RANLUX(RVEC,100) WRITE (6,'(A/9X,5F12.8)') ' RANLUX luxury level 0, 101-105:', + (RVEC(L),L=1,5) C WRITE (6,'(/A)') ' CALL RLUXGO(389,1,0,0)' CALL RLUXGO(389,1,0,0) CALL RANLUX(RVEC,100) WRITE (6,'(A/9X,5F12.8)') ' RANLUX luxury p=389, 1- 5:', + (RVEC(L),L=1,5) CALL RANLUX(RVEC,100) WRITE (6,'(A/9X,5F12.8)') ' RANLUX luxury p=389, 101-105:', + (RVEC(L),L=1,5) C WRITE (6,'(/A)') ' CALL RLUXGO(75,0,0,0)' CALL RLUXGO(75,0,0,0) CALL RANLUX(RVEC,100) WRITE (6,'(A/9X,5F12.8)') ' RANLUX luxury p= 75, 1- 5:', + (RVEC(L),L=1,5) CALL RANLUX(RVEC,100) WRITE (6,'(A/9X,5F12.8)') ' RANLUX luxury p= 75, 101-105:', + (RVEC(L),L=1,5) C WRITE (6,'(/A)') ' test restarting from the full vector' CALL RLUXUT(ISDEXT) WRITE (6,'(/A/(1X,5I14))') ' current RANLUX status saved:',ISDEXT CALL RANLUX(RVEC,100) WRITE (6,'(A/9X,5F12.8)') ' RANLUX numbers 1- 5:', + (RVEC(L),L=1,5) CALL RANLUX(RVEC,100) WRITE (6,'(A/9X,5F12.8)') ' RANLUX numbers 101-105:', + (RVEC(L),L=1,5) C WRITE (6,'(/A)') ' previous RANLUX status will be restored' CALL RLUXIN(ISDEXT) CALL RANLUX(RVEC,100) WRITE (6,'(A/9X,5F12.8)') ' RANLUX numbers 1- 5:', + (RVEC(L),L=1,5) CALL RANLUX(RVEC,100) WRITE (6,'(A/9X,5F12.8)') ' RANLUX numbers 101-105:', + (RVEC(L),L=1,5) C WRITE (6,'(/A)') ' test the restarting by skipping' CALL RLUXGO(4,7674985,0,0) CALL RLUXAT(I1,I2,I3,I4) WRITE (6,'(A,4I10)') ' RLUXAT values =',I1,I2,I3,I4 DO 150 LI= 1, 10 150 CALL RANLUX(RVEC,1000) CALL RLUXAT(I1,I2,I3,I4) WRITE (6,'(A,4I10)') ' RLUXAT values =',I1,I2,I3,I4 CALL RANLUX(RVEC,200) WRITE (6,'(A,2F10.6)') ' Next and 200th numbers are:', + RVEC(1), RVEC(200) CALL RLUXGO(I1,I2,I3,I4) CALL RANLUX(RVEC,200) WRITE (6,'(A,2F10.6)') ' Next and 200th numbers are:', + RVEC(1), RVEC(200) C WRITE (6,'(/A)') ' The following should provoke an error message' CALL RLUXGO(4,11111,31,0) STOP C C OUTPUT FROM THE ABOVE TEST PROGRAM SHOULD BE: C -------------------------------------------- C CALL RANLUX(RVEC,100) C RANLUX DEFAULT INITIALIZATION: 314159265 C RANLUX DEFAULT LUXURY LEVEL = 3 p = 223 C RANLUX default numbers 1- 5: C 0.53981817 0.76155043 0.06029940 0.79600263 0.30631220 C RANLUX default numbers 101-105: C 0.43156743 0.03774416 0.24897110 0.00147784 0.90274453 C C CALL RLUXGO(0,0,0,0) C RANLUX LUXURY LEVEL SET BY RLUXGO : 0 P= 24 C RANLUX INITIALIZED BY RLUXGO FROM DEFAULT SEED C RANLUX luxury level 0, 1- 5: C 0.53981817 0.76155043 0.06029940 0.79600263 0.30631220 C RANLUX luxury level 0, 101-105: C 0.41538775 0.05330932 0.58195311 0.91397446 0.67034441 C C CALL RLUXGO(389,1,0,0) C RANLUX LUXURY LEVEL SET BY RLUXGO : 4 P= 389 C RANLUX INITIALIZED BY RLUXGO FROM SEEDS 1 0 0 C RANLUX luxury p=389, 1- 5: C 0.94589490 0.47347850 0.95152789 0.42971975 0.09127384 C RANLUX luxury p=389, 101-105: C 0.02618265 0.03775346 0.97274780 0.13302165 0.43126065 C C CALL RLUXGO(75,0,0,0) C RANLUX P-VALUE SET BY RLUXGO TO: 75 C RANLUX INITIALIZED BY RLUXGO FROM DEFAULT SEED C RANLUX luxury p= 75, 1- 5: C 0.53981817 0.76155043 0.06029940 0.79600263 0.30631220 C RANLUX luxury p= 75, 101-105: C 0.25600731 0.23443210 0.59164381 0.59035838 0.07011414 C C test restarting from the full vector C C current RANLUX status saved: C 16156027 16534309 15243811 2751687 6002207 C 7979506 1301976 4567313 4305996 5872599 C 12003090 2146823 12606367 4111505 5979640 C 12739666 10489318 14036909 11729352 8061448 C 7832659 6069758 3197719 1832730 75080216 C RANLUX numbers 1- 5: C 0.22617835 0.60655993 0.86417443 0.43920082 0.23382509 C RANLUX numbers 101-105: C 0.08107197 0.21466845 0.84856731 0.94078046 0.85626233 C C previous RANLUX status will be restored C FULL INITIALIZATION OF RANLUX WITH 25 INTEGERS: C 16156027 16534309 15243811 2751687 6002207 C 7979506 1301976 4567313 4305996 5872599 C 12003090 2146823 12606367 4111505 5979640 C 12739666 10489318 14036909 11729352 8061448 C 7832659 6069758 3197719 1832730 75080216 C RANLUX P-VALUE SET BY RLUXIN TO: 75 C RANLUX numbers 1- 5: C 0.22617835 0.60655993 0.86417443 0.43920082 0.23382509 C RANLUX numbers 101-105: C 0.08107197 0.21466845 0.84856731 0.94078046 0.85626233 C C test the restarting by skipping C RANLUX LUXURY LEVEL SET BY RLUXGO : 4 P= 389 C RANLUX INITIALIZED BY RLUXGO FROM SEEDS 7674985 0 0 C RLUXAT values = 4 7674985 0 0 C RLUXAT values = 4 7674985 161840 0 C Next and 200th numbers are: 0.019648 0.590586 C RANLUX LUXURY LEVEL SET BY RLUXGO : 4 P= 389 C RANLUX INITIALIZED BY RLUXGO FROM SEEDS 7674985 161840 0 C Next and 200th numbers are: 0.019648 0.590586 C C The following should provoke an error message C RANLUX LUXURY LEVEL SET BY RLUXGO : 4 P= 389 C RANLUX INITIALIZED BY RLUXGO FROM SEEDS 11111 31 0 C Error in RESTARTING with RLUXGO: C The values 11111 31 0 cannot occur at luxury level 4 END ************************************************************************