Fastest method to generate big random string with lower Latin letters

performance, python, python-3.x, random, stdin

Solution

Here's Python 3 code that generates 1000000 "random" lowercase letters in `0.28` seconds (see also `0.11`-seconds solution at the end; @Ashwini Chaudhary's code from the question takes `0.55` seconds on my machine, @Markku K.'s code -- `0.53`):

#!/usr/bin/env python3
import os
import sys

def write_random_lowercase(n):
    min_lc = ord(b'a')
    len_lc = 26
    ba = bytearray(os.urandom(n))
    for i, b in enumerate(ba):
        ba[i] = min_lc + b % len_lc # convert 0..255 to 97..122
    sys.stdout.buffer.write(ba)

write_random_lowercase(1000000)

`% len_lc` skews the distribution (see at the end on how to fix it) though It still satisfies the conditions (ascii, lowercase, frequencies of 1, 2, 3 letter sequences):

$ python3 generate-random.py | python3 check-seq.py

where `check-seq.py`:

#!/usr/bin/env python3
import sys
from collections import Counter
from string import ascii_lowercase

def main():
    limits = [40000, 2000, 100]

    s = sys.stdin.buffer.readline() # a single line
    assert 1000000 <= len(s) <= 1000002 # check length +/- newline
    s.decode('ascii','strict') # check ascii
    assert set(s) == set(ascii_lowercase.encode('ascii')) # check lowercase

    for n, lim in enumerate(limits, start=1):
        freq = Counter(tuple(s[i:i+n]) for i in range(len(s)))
        assert max(freq.values()) <= lim, freq

main()

Note: on acm.timus.ru `generate-random.py` gives "Output limit exceeded".

To improve performance, you could use `bytes.translate()` method (`0.11` seconds):

#!/usr/bin/env python3
import os
import sys

# make translation table from 0..255 to 97..122
tbl = bytes.maketrans(bytearray(range(256)),
                      bytearray([ord(b'a') + b % 26 for b in range(256)]))
# generate random bytes and translate them to lowercase ascii
sys.stdout.buffer.write(os.urandom(1000000).translate(tbl))

How to fix `% len_lc` skew

`256` (number of bytes) is not evenly divisible by `26` (number of lower Latin letters) therefore the formula `min_lc + b % len_lc` makes some values appear less often than others e.g.:

#!/usr/bin/env python3
"""Find out skew: x = 97 + y % 26 where y is uniform from [0, 256) range."""
from collections import Counter, defaultdict

def find_skew(random_bytes):
    char2freq = Counter(chr(ord(b'a') + b % 26) for b in random_bytes)
    freq2char = defaultdict(set)
    for char, freq in char2freq.items():
        freq2char[freq].add(char)
    return {f: ''.join(sorted(c)) for f, c in freq2char.items()}

print(find_skew(range(256)))
# -> {9: 'wxyz', 10: 'abcdefghijklmnopqrstuv'}

Here, the input `range(256)` is uniformly distributed (each byte occurs exactly once) but `'wxyz'` letters in the output are less often then the rest `9` vs. `10` occurrences. To fix it, unaligned bytes could be dropped:

print(find_skew(range(256 - (256 % 26))))
# -> {9: 'abcdefghijklmnopqrstuvwxyz'}

Here, the input is uniformly distributed bytes in the range `[0, 234)` the output is uniformly distributed ascii lowercase letters.

`bytes.translate()` accepts the second argument to specify bytes to delete:

#!/usr/bin/env python3
import os
import sys

nbytes = 256
nletters = 26
naligned = nbytes - (nbytes % nletters)
tbl = bytes.maketrans(bytearray(range(naligned)),
                      bytearray([ord(b'a') + b % nletters
                                 for b in range(naligned)]))
bytes2delete = bytearray(range(naligned, nbytes))
R = lambda n: os.urandom(n).translate(tbl, bytes2delete)

def write_random_ascii_lowercase_letters(write, n):
    """*write* *n* random ascii lowercase letters."""    
    while n > 0:
        # R(n) expected to drop `(nbytes - nletters) / nbytes` bytes
        # to compensate, increase the initial size        
        n -= write(memoryview(R(n * nbytes // naligned + 1))[:n])

write = sys.stdout.buffer.write
write_random_ascii_lowercase_letters(write, 1000000)

If the random generator (`os.urandom` here) produces long sequences of the bytes that are outside of the aligned range (`>=234`) then the `while` loop may execute many times.

The time performance can be improved by another order of magnitude if `random.getrandbits(8*n).to_bytes(n, 'big')` is used instead of `os.urandom(n)`. The former uses Mersenne Twister as the core generator that may be faster than `os.urandom()` that uses sources provided by the operating system. The latter is more secure if you use the random string for secrets.

Problem

Original source