def get_max_cheby_minus_x_phi_over_coprimes(x, q):
phi_q, coprime_list = eul_totie(q)
# cheby_mod_list will be list of list, 2D array
cheby_mod_list = []
# let's calculate cheby_lst_for_a mod(q) 1st
for a in range(q):
# only calculate when a and q is coprime, this is needed, because
# only these choice will get something similar to x/phi_q
if a in coprime_list:
# we use the cheby_fun_q_a_integer_use_saved_von_mang() instead of the following function
# to speed up calculation.
# cheby_list_for_a = cheby_fun_q_a_integer(x, q, a) # calculate von_mang every time.
cheby_list_for_a = cheby_fun_q_a_integer_use_saved_von_mang(x, q, a) # use cached von_mang
tmp = deepcopy(cheby_list_for_a)
cheby_mod_list.append(tmp)
num_of_coprimes = len(coprime_list)
cheby_minus_x_phi_max = []
for i in range(x):
# initialize largest for each a, in the follow, i is actual x in
# analytic formula, we just need to do (i+1) because array count start from 0
x_phi_q = float(i + 1)/phi_q
largest = np.absolute(cheby_mod_list[0][i] - x_phi_q )
# loop for 1<= a <= q, (a, q) = 1
for a in range(num_of_coprimes):
tmp = np.absolute(cheby_mod_list[a][i] - x_phi_q)
if(tmp > largest):
largest = tmp
cheby_minus_x_phi_max.append(largest)
return cheby_minus_x_phi_max
def get_max_cheby_minus_x_phi_fast_simulation(x, q):
print 'get_max_cheby_minus_x_phi use fast simulation. x = %d, q = %d'%(x, q)
phi_q, coprime_list = eul_totie(q)
a = 1
cheby_list_for_a = cheby_fun_q_a_integer_use_saved_von_mang(x, q, a)
cheby_minus_x_phi_max = []
for i in range(x):
# initialize largest for each a, in the follow, i is actual x in
# analytic formula, we just need to do (i+1) because array count start from 0
x_phi_q = float(i + 1)/phi_q
largest = np.absolute(cheby_list_for_a[i] - x_phi_q )
cheby_minus_x_phi_max.append(largest)
return cheby_minus_x_phi_max
