<filename>check_cycles.py
#
# check_cycles.py
# ===============
#

"""
Verify through brute-force checking that all prime numbers that are
greater than two and less than 2048 can be used to iterate through all
integer values modulo 2048 without any repetition.

Syntax:

  python3 check_cycles.py

"""

import sys

# Don't export anything
#
__all__ = []

#
# Prime number table
# ------------------
#
# Auto-generated by prime_table.py
#
primes = [
  3, 5, 7, 11, 13, 17, 19, 23, 29, 31,
  37, 41, 43, 47, 53, 59, 61, 67, 71, 73,
  79, 83, 89, 97, 101, 103, 107, 109, 113, 127,
  131, 137, 139, 149, 151, 157, 163, 167, 173, 179,
  181, 191, 193, 197, 199, 211, 223, 227, 229, 233,
  239, 241, 251, 257, 263, 269, 271, 277, 281, 283,
  293, 307, 311, 313, 317, 331, 337, 347, 349, 353,
  359, 367, 373, 379, 383, 389, 397, 401, 409, 419,
  421, 431, 433, 439, 443, 449, 457, 461, 463, 467,
  479, 487, 491, 499, 503, 509, 521, 523, 541, 547,
  557, 563, 569, 571, 577, 587, 593, 599, 601, 607,
  613, 617, 619, 631, 641, 643, 647, 653, 659, 661,
  673, 677, 683, 691, 701, 709, 719, 727, 733, 739,
  743, 751, 757, 761, 769, 773, 787, 797, 809, 811,
  821, 823, 827, 829, 839, 853, 857, 859, 863, 877,
  881, 883, 887, 907, 911, 919, 929, 937, 941, 947,
  953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019,
  1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087,
  1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153,
  1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229,
  1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297,
  1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381,
  1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453,
  1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523,
  1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597,
  1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663,
  1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741,
  1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823,
  1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901,
  1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993,
  1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039
]

#
# Program entrypoint
# ------------------
#

# Try out each prime
#
for p in primes:
  
  # Clear the bitmap for the 2048 values
  bm = [False for x in range(0, 2048)]
  
  # Start value at zero and set corresponding flag
  v = 0
  bm[0] = True
  
  # Keep generating successive entires, and check that they were not
  # already generated
  for i in range(1, 2048):
    # Update value
    v = (v + p) % 2048
    
    # Update bitmap and make sure not already set
    if bm[v]:
      print('Error: duplicate found!')
      sys.exit(1)
    else:
      bm[v] = True
    
  # Make sure all values have been set
  if False in bm:
    print('Error: not all values covered!')
    sys.exit(1)

# If we got here, all the checks worked
#
print('All checks passed.')

<filename>check_cycles.py
#
# check_cycles.py
# ===============
#

"""
Verify through brute-force checking that all prime numbers that are
greater than two and less than 2048 can be used to iterate through all
integer values modulo 2048 without any repetition.

Syntax:

  python3 check_cycles.py

"""

import sys

# Don't export anything
#
__all__ = []

#
# Prime number table
# ------------------
#
# Auto-generated by prime_table.py
#
primes = [
  3, 5, 7, 11, 13, 17, 19, 23, 29, 31,
  37, 41, 43, 47, 53, 59, 61, 67, 71, 73,
  79, 83, 89, 97, 101, 103, 107, 109, 113, 127,
  131, 137, 139, 149, 151, 157, 163, 167, 173, 179,
  181, 191, 193, 197, 199, 211, 223, 227, 229, 233,
  239, 241, 251, 257, 263, 269, 271, 277, 281, 283,
  293, 307, 311, 313, 317, 331, 337, 347, 349, 353,
  359, 367, 373, 379, 383, 389, 397, 401, 409, 419,
  421, 431, 433, 439, 443, 449, 457, 461, 463, 467,
  479, 487, 491, 499, 503, 509, 521, 523, 541, 547,
  557, 563, 569, 571, 577, 587, 593, 599, 601, 607,
  613, 617, 619, 631, 641, 643, 647, 653, 659, 661,
  673, 677, 683, 691, 701, 709, 719, 727, 733, 739,
  743, 751, 757, 761, 769, 773, 787, 797, 809, 811,
  821, 823, 827, 829, 839, 853, 857, 859, 863, 877,
  881, 883, 887, 907, 911, 919, 929, 937, 941, 947,
  953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019,
  1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087,
  1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153,
  1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229,
  1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297,
  1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381,
  1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453,
  1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523,
  1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597,
  1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663,
  1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741,
  1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823,
  1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901,
  1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993,
  1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039
]

#
# Program entrypoint
# ------------------
#

# Try out each prime
#
for p in primes:
  
  # Clear the bitmap for the 2048 values
  bm = [False for x in range(0, 2048)]
  
  # Start value at zero and set corresponding flag
  v = 0
  bm[0] = True
  
  # Keep generating successive entires, and check that they were not
  # already generated
  for i in range(1, 2048):
    # Update value
    v = (v + p) % 2048
    
    # Update bitmap and make sure not already set
    if bm[v]:
      print('Error: duplicate found!')
      sys.exit(1)
    else:
      bm[v] = True
    
  # Make sure all values have been set
  if False in bm:
    print('Error: not all values covered!')
    sys.exit(1)

# If we got here, all the checks worked
#
print('All checks passed.')

# # check_cycles.py # =============== # Verify through brute-force checking that all prime numbers that are greater than two and less than 2048 can be used to iterate through all integer values modulo 2048 without any repetition.  Syntax:    python3 check_cycles.py # Don't export anything # # # Prime number table # ------------------ # # Auto-generated by prime_table.py # # # Program entrypoint # ------------------ # # Try out each prime # # Clear the bitmap for the 2048 values # Start value at zero and set corresponding flag # Keep generating successive entires, and check that they were not # already generated # Update value # Update bitmap and make sure not already set # Make sure all values have been set # If we got here, all the checks worked #