quiz_01_solution.py

# python 3 + numpy

from numpy import iinfo, int64

# iinfo(int64).max will give the maximum value of an 8-byte precision integer, 
# which should be 2^63 - 1 = 9223372036854775807
# (there is one bit for the sign, and a shift by 1 because of zero)

# The trick is that a 8-byte float uses 11 bits for the exponent
# which leaves 63 - 11 = 52 for the significand, 
# but it's first digit is implicitly a 1, so 53
# Thus, dividing by 2**10 brings it to the largest integer such that
# it and any smaller integer can be represented exactly as a float
# Actually, that number minus 1, due to the -1 above and rounding down.
q = iinfo(int64).max // 2**10

# This just sents a limit that's a bit higher than q,
# which won't be reached because of precision loss (see later)
q_lim = q + 3

# This loop will print "hello" several times 
# and then terminate if q increases enough, but it won't.
while q < q_lim:
	print('hello')
  # Because we used `1.`, q will be converted to a double precision float.
  # But it will have the highest possible exact value.
  # Increasing the value by 1 will result in it not being exactly represented
  # and as such rounded (down). Thus, q will stay the same.
	q += 1.

# So this program will run forever (or more likely, until you terminate it).

# As a bonus, note that `iinfo(int64).max // 2**10` is NOT the highest integer
# exactly represented as a float64, it's just the highest where all lower 
# integers can also be represented.
# In fact, every higher number that can be represented as a float64 is an integer,
# because there isn't enough precision for decimals.