NESC0843 RANDOM NUMBERS.

1. NAME OR DESIGNATION OF PROGRAM:  RANDOM NUMBERS.

3. DESCRIPTION OF PROBLEM OR FUNCTION

RANDOM NUMBERS is a data collection of almost 2.7 million 31-bit random numbers generated by  using a high resolution gas ionization detector chamber in conjunction with a 4096-channel multichannel analyzer to record the  radioactive decay of alpha particles from a U-235 source. The signals from the decaying alpha particles were fed to the 4096-channel analyzer, and for each channel the frequency of signals registered in a 20,000-microsecond interval was recorded. The parity bits of these frequency counts, 0 for an even count and 1 for and odd count, were then assembled in sequence to form 31-bit random numbers and transcribed onto magnetic tape. This cycle was repeated  to obtain the random numbers.

4. METHOD OF SOLUTION

The frequency distribution of counts from the device conforms to the Brockwell-Moyal distribution which takes into account the dead time of the counter. The count data were analyzed and tests for randomness on a sample indicate that the device is a highly reliable source of truly random numbers.

5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

The RANDOM NUMBERS tape contains 2,669,568 31-bit numbers.

6. TYPICAL RUNNING TIME

NEC0843/01: The program and number library have been implemented by  NEA-DB on an IBM 3090 computer.

7. UNUSUAL FEATURES OF THE PROGRAM:

8. RELATED AND AUXILIARY PROGRAMS

AFRAND, an auxiliary routine to retrieve the random numbers from the RANDOM NUMBERS tape, is in- cluded in the package, along with a test case to illustrate use of the RANDOM NUMBERS tape.

10. REFERENCES:

- N.A. Frigerio, L.P. Sanathanan, M. Morley, et al. :
  Random Numbers Spring from Alpha Decay
  ANL/ES-95 (May 1980)

11. MACHINE REQUIREMENTS

The auxiliary program AFRAND requires 55K bytes of memory for execution with the test case provided. Random numbers from the tape are read from tape unit 13.

13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:  OS/370.

14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS:

For better transportability, a formatted version of the random number library is distributed instead of the original binary  file. To re-generate the binary library, a conversion program is included.

15. NAME AND ESTABLISHMENT OF AUTHOR

         N.A. Frigerio, L.P. Sanathanan, M.Morley,
         and S.A. Tyler
         Division of Environmental Impact Studies
         N.A. Clark
         Applied Mathematics Division
         Argonne National Laboratory
         9700 South Cass Avenue
         Argonne, Illinois 60439

AFRAND   J. Wang
         Applied Mathematics Division
         Argonne National Laboratory

File name	File description	Records
NESC0843_01.001	INFORMATION FILE	94
NESC0843_01.002	EBCDIC TO BINARY CONVERSION PROGRAM	10
NESC0843_01.003	RANDOM FORTRAN SOURCE PROGRAM	39
NESC0843_01.004	DEMONSTRATION PROGRAM	15
NESC0843_01.005	DATA FILE WITH RANDOM NUMBERS	320000
NESC0843_01.006	JCL USED IN TESTING	117
NESC0843_01.007	JCL USED IN TESTING	145
NESC0843_01.008	JCL USED IN TESTING	37