symbols.update(locals())

	time = timeit.timeit("""generate(secret, args.k, args.n)""", number=1, globals=symbols)

	print("The generation took {0:.3}s, {1:.3}s per byte.".format(time, time/16))

	time = timeit.timeit("""reconstruct(*shares)""", number=1, globals=symbols)

	print("The reconstruction took {0:.3}s, {1:.3}s per byte.".format(time, time/16))

def profile(args):

	t = TestShamira()

def build_subparsers(parent):

	parent.set_defaults(func=lambda _: parent.error("missing command"))

	subparsers = parent.add_subparsers()

	profile_parser = subparsers.add_parser("profile")

	profile_parser.set_defaults(func=profile)

	measure_parser = subparsers.add_parser("measure")

	measure_parser.add_argument("-k", type=int, required=True)

	measure_parser.add_argument("-n", type=int, required=True)

import math

import cmath

import itertools

from .gf256 import gfmul, gfpow

# divisors of 255 and their factors in natural numbers

DIVISORS = [3, 5, 15, 17, 51, 85, 255]

FACTORS = {3: [3], 5: [5], 15: [3, 5], 17: [17], 51: [3, 17], 85: [5, 17], 255: [3, 5, 17]}

# values of n-th square roots in GF256

SQUARE_ROOTS = {3: 189, 5: 12, 15: 225, 17: 53, 51: 51, 85: 15, 255: 3}

def ceil_size(n):

	assert n <= DIVISORS[-1]

	for (i, ni) in enumerate(DIVISORS):

		if ni >= n:

			break

	return ni

def precompute_x(n):

	"""Return a geometric sequence [1, w, w**2, ..., w**(n-1)], where w**n==1.

	This can be done only for certain values of n."""

	assert n in SQUARE_ROOTS, n

	w = SQUARE_ROOTS[n]  # primitive N-th square root of 1

	return list(itertools.accumulate([1]+[w]*(n-1), gfmul))

def complex_dft(p):

	"""Quadratic formula from the definition. The basic case in complex numbers."""

	N = len(p)

	w = cmath.exp(-2*math.pi*1j/N)  # primitive N-th square root of 1

g = 3  # generator

E = [None]*256  # exponentials

L = [None]*256  # logarithms

acc = 1

for i in range(256):

	E[i] = acc

	L[acc] = i

	acc = _gfmul(acc, g)

L[1] = 0

INV = [E[255-L[i]] if i!=0 else None for i in range(256)]  # multiplicative inverse

def gfmul(a, b):

	"""Fast multiplication. Basic multiplication is expensive. a*b==g**(log(a)+log(b))"""

	assert 0<=a<=255, 0<=b<=255

	if a==0 or b==0: return 0

	t = L[a]+L[b]

	if t>255: t -= 255

	return E[t]

def gfpow(x, k):

	"""Compute x**k."""

	i = 1

	res = 1

	while i <= k:

		if k&i:

			res = gfmul(res, x)

		x = gfmul(x, x)

		i <<= 1

	return res