#!/usr/bin/env python
"""Simple example implementations of the Sieve of Erathostenes."""
__author__ = "Fernando Perez <Fernando.Perez@colorado.edu>"
import sys
import math
import numpy as N
def sieve(nmax):
"""Return a list of prime numbers up to nmax, using Erathostenes' sieve.
This is a more efficient implementation than the naive one: we combine a
set with an auxiliary list (kept sorted)."""
# Sanity checks
assert nmax>1, "nmax must be > 1"
if nmax == 2: return [2]
# For nmax>3, do full sieve
primes_head = [2]
first = 3
# The primes tail will be kept both as a set and as a sorted list
primes_tail_lst = range(first,nmax+1,2)
primes_tail_set = set(primes_tail_lst)
# optimize a couple of name lookups from loops
tail_remove = primes_tail_set.remove
head_append = primes_head.append
sqrt = math.sqrt
# Now do the actual sieve
while first <= round(sqrt(primes_tail_lst[-1])):
# Move the first leftover prime from the set to the head list
first = primes_tail_lst[0]
tail_remove(first) # remove it from the set
head_append(first) # and store it in the head list
# Now, remove from the primes tail all non-primes. For us to be able
# to break as soon as a key is not found, it's crucial that the tail
# list is always sorted.
for next_candidate in primes_tail_lst:
try:
tail_remove(first*next_candidate)
except KeyError:
break
# Build a new sorted tail list with the leftover keys
primes_tail_lst = list(primes_tail_set)
primes_tail_lst.sort()
return primes_head + primes_tail_lst
