def nim_sum ( i, j ): #*****************************************************************************80 # ## NIM_SUM computes the Nim sum of two integers. # # Discussion: # # If K is the Nim sum of I and J, then each bit of K is the exclusive # OR of the corresponding bits of I and J. # # Example: # # I J K I base 2 J base 2 K base 2 # ---- ---- ---- ---------- ---------- ---------- # 0 0 0 0 0 0 # 1 0 1 1 0 1 # 1 1 0 1 1 0 # 2 7 5 10 111 101 # 11 28 23 1011 11100 10111 # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 26 May 2015 # # Author: # # John Burkardt # # Parameters: # # Input, integer I, J, the integers to be Nim-summed. # # Output, integer K, the Nim sum of I and J. # from ubvec_to_ui4 import ubvec_to_ui4 from ubvec_xor import ubvec_xor from ui4_to_ubvec import ui4_to_ubvec nbits = 32 ivec = ui4_to_ubvec ( i, nbits ) jvec = ui4_to_ubvec ( j, nbits ) kvec = ubvec_xor ( nbits, ivec, jvec ) k = ubvec_to_ui4 ( nbits, kvec ) return k
def nim_sum(i, j):
#*****************************************************************************80
#
## NIM_SUM computes the Nim sum of two integers.
#
# Discussion:
#
# If K is the Nim sum of I and J, then each bit of K is the exclusive
# OR of the corresponding bits of I and J.
#
# Example:
#
# I J K I base 2 J base 2 K base 2
# ---- ---- ---- ---------- ---------- ----------
# 0 0 0 0 0 0
# 1 0 1 1 0 1
# 1 1 0 1 1 0
# 2 7 5 10 111 101
# 11 28 23 1011 11100 10111
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 26 May 2015
#
# Author:
#
# John Burkardt
#
# Parameters:
#
# Input, integer I, J, the integers to be Nim-summed.
#
# Output, integer K, the Nim sum of I and J.
#
from ubvec_to_ui4 import ubvec_to_ui4
from ubvec_xor import ubvec_xor
from ui4_to_ubvec import ui4_to_ubvec
nbits = 32
ivec = ui4_to_ubvec(i, nbits)
jvec = ui4_to_ubvec(j, nbits)
kvec = ubvec_xor(nbits, ivec, jvec)
k = ubvec_to_ui4(nbits, kvec)
return k
def ubvec_xor_test():
#*****************************************************************************80
#
## UBVEC_XOR_TEST tests UBVEC_XOR;
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 26 May 2015
#
# Author:
#
# John Burkardt
#
from i4_uniform_ab import i4_uniform_ab
from ui4_to_ubvec import ui4_to_ubvec
from ubvec_to_ui4 import ubvec_to_ui4
n = 10
seed = 123456789
test_num = 10
print ''
print 'UBVEC_XOR_TEST'
print ' UBVEC_XOR exclusive-ors unsigned binary vectors representing'
print ' unsigned integers;'
print ''
print ' I J K = I XOR J'
print ''
for test in range(0, test_num):
i, seed = i4_uniform_ab(0, 100, seed)
j, seed = i4_uniform_ab(0, 100, seed)
bvec1 = ui4_to_ubvec(i, n)
bvec2 = ui4_to_ubvec(j, n)
bvec3 = ubvec_xor(n, bvec1, bvec2)
k = ubvec_to_ui4(n, bvec3)
print ' %8d %8d %8d' % (i, j, k)
#
# Terminate.
#
print ''
print 'UBVEC_XOR_TEST'
print ' Normal end of execution.'
return
def ubvec_xor_test ( ):
#*****************************************************************************80
#
## UBVEC_XOR_TEST tests UBVEC_XOR;
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 26 May 2015
#
# Author:
#
# John Burkardt
#
from i4_uniform_ab import i4_uniform_ab
from ui4_to_ubvec import ui4_to_ubvec
from ubvec_to_ui4 import ubvec_to_ui4
n = 10
seed = 123456789
test_num = 10
print ''
print 'UBVEC_XOR_TEST'
print ' UBVEC_XOR exclusive-ors unsigned binary vectors representing'
print ' unsigned integers;'
print ''
print ' I J K = I XOR J'
print ''
for test in range ( 0, test_num ):
i, seed = i4_uniform_ab ( 0, 100, seed )
j, seed = i4_uniform_ab ( 0, 100, seed )
bvec1 = ui4_to_ubvec ( i, n )
bvec2 = ui4_to_ubvec ( j, n )
bvec3 = ubvec_xor ( n, bvec1, bvec2 )
k = ubvec_to_ui4 ( n, bvec3 )
print ' %8d %8d %8d' % ( i, j, k )
#
# Terminate.
#
print ''
print 'UBVEC_XOR_TEST'
print ' Normal end of execution.'
return
def ui4_to_ubvec_test():
#*****************************************************************************80
#
## UI4_TO_UBVEC_TEST tests UI4_TO_UBVEC;
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 26 May 2015
#
# Author:
#
# John Burkardt
#
from ubvec_to_ui4 import ubvec_to_ui4
n = 10
print ''
print 'UI4_TO_UBVEC_TEST'
print ' UI4_TO_UBVEC converts an unsigned integer to an'
print ' unsigned binary vector;'
print ''
print ' UI4 --> UBVEC --> UI4'
print ''
for i in range(0, 11):
bvec = ui4_to_ubvec(i, n)
i2 = ubvec_to_ui4(n, bvec)
print ' %2d ' % (i),
for i in range(0, n):
print '%1d' % (bvec[i]),
print ' %2d' % (i2)
#
# Terminate.
#
print ''
print 'UI4_TO_UBVEC_TEST'
print ' Normal end of execution.'
return
def ui4_to_ubvec_test ( ):
#*****************************************************************************80
#
## UI4_TO_UBVEC_TEST tests UI4_TO_UBVEC;
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 26 May 2015
#
# Author:
#
# John Burkardt
#
from ubvec_to_ui4 import ubvec_to_ui4
n = 10
print ''
print 'UI4_TO_UBVEC_TEST'
print ' UI4_TO_UBVEC converts an unsigned integer to an'
print ' unsigned binary vector;'
print ''
print ' UI4 --> UBVEC --> UI4'
print ''
for i in range ( 0, 11 ):
bvec = ui4_to_ubvec ( i, n )
i2 = ubvec_to_ui4 ( n, bvec )
print ' %2d ' % ( i ),
for i in range ( 0, n ):
print '%1d' % ( bvec[i] ),
print ' %2d' % ( i2 )
#
# Terminate.
#
print ''
print 'UI4_TO_UBVEC_TEST'
print ' Normal end of execution.'
return
def subset_gray_rank(n, a):
#*****************************************************************************80
#
## SUBSET_GRAY_RANK ranks a subset of an N set, using the Gray code ordering.
#
# Example:
#
# N = 4
#
# A Rank
# ------- -----
#
# 0 0 0 0 1
# 1 0 0 0 2
# 1 1 0 0 3
# 0 1 0 0 4
# 0 1 1 0 5
# 1 1 1 0 6
# 1 0 1 0 7
# 0 0 1 0 8
# 0 0 1 1 9
# 1 0 1 1 10
# 1 1 1 1 11
# 0 1 1 1 12
# 0 1 0 1 13
# 1 1 0 1 14
# 1 0 0 1 15
# 0 0 0 1 16
#
# Licensing:
#
# This code is distributed under the GNU LGPL license.
#
# Modified:
#
# 31 May 2015
#
# Author:
#
# John Burkardt
#
# Parameters:
#
# Input, integer N, the order of the total set from which
# subsets will be drawn.
#
# Input, integer A(N); A(I) is 1 if element I is in the set,
# and 0 otherwise.
#
# Output, integer RANK, the rank of the subset in the Gray code ordering.
#
from gray_rank2 import gray_rank2
from ubvec_to_ui4 import ubvec_to_ui4
gray = ubvec_to_ui4(n, a)
rank = gray_rank2(gray)
rank = rank + 1
return rank
def subset_gray_rank ( n, a ): #*****************************************************************************80 # ## SUBSET_GRAY_RANK ranks a subset of an N set, using the Gray code ordering. # # Example: # # N = 4 # # A Rank # ------- ----- # # 0 0 0 0 1 # 1 0 0 0 2 # 1 1 0 0 3 # 0 1 0 0 4 # 0 1 1 0 5 # 1 1 1 0 6 # 1 0 1 0 7 # 0 0 1 0 8 # 0 0 1 1 9 # 1 0 1 1 10 # 1 1 1 1 11 # 0 1 1 1 12 # 0 1 0 1 13 # 1 1 0 1 14 # 1 0 0 1 15 # 0 0 0 1 16 # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 31 May 2015 # # Author: # # John Burkardt # # Parameters: # # Input, integer N, the order of the total set from which # subsets will be drawn. # # Input, integer A(N); A(I) is 1 if element I is in the set, # and 0 otherwise. # # Output, integer RANK, the rank of the subset in the Gray code ordering. # from gray_rank2 import gray_rank2 from ubvec_to_ui4 import ubvec_to_ui4 gray = ubvec_to_ui4 ( n, a ) rank = gray_rank2 ( gray ) rank = rank + 1 return rank
