# NAME

Math::Prime::Util::PrimeArray - A tied array for primes

# VERSION

Version 0.52

# SYNOPSIS

```
# Use package and create a tied variable
use Math::Prime::Util::PrimeArray;
tie my @primes, 'Math::Prime::Util::PrimeArray';
# or all in one (allowed: @primes, @prime, @pr, @p):
use Math::Prime::Util::PrimeArray '@primes';
# Use in a loop by index:
for my $n (0..9) {
print "prime $n = $primes[$n]\n";
}
# Use in a loop over array:
for my $p (@primes) {
last if $p > 1000; # stop sometime
print "$p\n";
}
# Use via array slice:
print join(",", @primes[0..49]), "\n";
# Use via each:
use 5.012;
while( my($index,$value) = each @primes ) {
last if $value > 1000; # stop sometime
print "The ${index}th prime is $value\n";
}
# Use with shift:
while ((my $p = shift @primes) < 1000) {
print "$p\n";
}
```

# DESCRIPTION

An array that acts like the infinite set of primes. This may be more convenient than using Math::Prime::Util directly, and in some cases it can be faster than calling `next_prime`

and `prev_prime`

.

If the access pattern is ascending or descending, then a window is sieved and results returned from the window as needed. If the access pattern is random, then `nth_prime`

is used.

Shifting acts like the array is losing elements at the front, so after two shifts, `$primes[0] == 5`

. Unshift will move the internal shift index back one, unless given an argument which is the number to move back. It will not shift past the beginning, so `unshift @primes, ~0`

is a useful way to reset from any shifts.

Example:

```
say shift @primes; # 2
say shift @primes; # 3
say shift @primes; # 5
say $primes[0]; # 7
unshift @primes; # back up one
say $primes[0]; # 5
unshift @primes, 2; # back up two
say $primes[0]; # 2
```

If you want sequential primes with low memory, I recommend using "forprimes" in Math::Prime::Util. It is much faster, as the tied array functionality in Perl is not high performance. It isn't as flexible as the prime array, but it is a very common pattern.

If you prefer an iterator pattern, I would recommend using "prime_iterator" in Math::Prime::Util. It will be a bit faster than using this tied array, but of course you don't get random access. If you find yourself using the `shift`

operation, consider the iterator.

# LIMITATIONS

The size of the array will always be shown as 2147483647 (IV32 max), even in a 64-bit environment where primes through `2^64`

are available.

Perl will mask all array arguments to 32-bit, making `2^32-1`

the maximum prime through the standard array interface. It will silently wrap after that. The only way around this is using the object interface:

```
use Math::Prime::Util::PrimeArray;
my $o = tie my @primes, 'Math::Prime::Util::PrimeArray';
say $o->FETCH(2**36);
```

Here we store the object returned by tie, allowing us to call its FETCH method directly. This is actually faster than using the array.

Some people find the idea of shifting a prime array abhorrent, as after two shifts, "the second prime is 7?!". If this bothers you, do not use `shift`

on the tied array.

# PERFORMANCE

```
sumprimes: sum_primes(nth_prime(100_000))
MPU forprimes: forprimes { $sum += $_ } nth_prime(100_000);
MPU iterator: my $it = prime_iterator; $sum += $it->() for 1..100000;
MPU array: $sum = vecsum( @{primes(nth_prime(100_000))} );
MPUPA: tie my @prime, ...; $sum += $prime[$_] for 0..99999;
MPUPA-FETCH: my $o=tie my @pr, ...; $sum += $o->FETCH($_) for 0..99999;
MNSP: my $seq = Math::NumSeq::Primes->new;
$sum += ($seq->next)[1] for 1..100000;
MPTA: tie my @prime, ...; $sum += $prime[$_] for 0..99999;
List::Gen $sum = primes->take(100000)->sum
```

Memory use is comparing the delta between just loading the module and running the test. Perl 5.20.0, Math::NumSeq v70, Math::Prime::TiedArray v0.04, List::Gen 0.974.

Summing the first 0.1M primes via walking the array:

```
.3ms 56k Math::Prime::Util sumprimes
4ms 56k Math::Prime::Util forprimes
4ms 4 MB Math::Prime::Util sum big array
31ms 0 Math::Prime::Util prime_iterator
68ms 644k MPU::PrimeArray using FETCH
101ms 644k MPU::PrimeArray array
95ms 1476k Math::NumSeq::Primes sequence iterator
4451ms 32 MB List::Gen sequence
6954ms 61 MB Math::Prime::TiedArray (extend 1k)
```

Summing the first 1M primes via walking the array:

```
0.005s 268k Math::Prime::Util sumprimes
0.05s 268k Math::Prime::Util forprimes
0.05s 41 MB Math::Prime::Util sum big array
0.3s 0 Math::Prime::Util prime_iterator
0.7s 644k MPU::PrimeArray using FETCH
1.0s 644k MPU::PrimeArray array
6.1s 2428k Math::NumSeq::Primes sequence iterator
106.0s 93 MB List::Gen sequence
98.1s 760 MB Math::Prime::TiedArray (extend 1k)
```

Summing the first 10M primes via walking the array:

```
0.07s 432k Math::Prime::Util sumprimes
0.5s 432k Math::Prime::Util forprimes
0.6s 394 MB Math::Prime::Util sum big array
3.2s 0 Math::Prime::Util prime_iterator
6.8s 772k MPU::PrimeArray using FETCH
10.2s 772k MPU::PrimeArray array
1046 s 11.1MB Math::NumSeq::Primes sequence iterator
6763 s 874 MB List::Gen sequence
>5000 MB Math::Primes::TiedArray (extend 1k)
```

Math::Prime::Util offers four obvious solutions: the `sum_primes`

function, a big array, an iterator, and the `forprimes`

construct. The big array is fast but uses a **lot** of memory, forcing the user to start programming segments. Using the iterator avoids all the memory use, but isn't as fast (this may improve in a later release, as this is a new feature). The `forprimes`

construct is both fast and low memory, but it isn't quite as flexible as the iterator (most notably there is no way to exit early, and it doesn't lend itself to wrapping inside a filter).

Math::NumSeq::Primes offers an iterator alternative, and works quite well as long as you don't need lots of primes. It does not support random access. It has reasonable performance for the first few hundred thousand, but each successive value takes much longer to generate, and once past 1 million it isn't very practical. Internally it is sieving all primes up to `n`

every time it makes a new segment which is why it slows down so much.

List::Gen includes a built-in prime sequence. It uses an inefficient Perl sieve for numbers below 10M, trial division past that. It uses too much time and memory to be practical for anything but very small inputs. It also gives incorrect results for large inputs (RT 105758).

Math::Primes::TiedArray is remarkably impractical for anything other than tiny numbers.

# SEE ALSO

This module uses Math::Prime::Util to do all the work. If you're doing anything but retrieving primes, you should examine that module to see if it has functionality you can use directly, as it may be a lot faster or easier.

Similar functionality can be had from Math::NumSeq and Math::Prime::TiedArray.

# AUTHORS

Dana Jacobsen <dana@acm.org>

# COPYRIGHT

Copyright 2012-2015 by Dana Jacobsen <dana@acm.org>

This program is free software; you can redistribute it and/or modify it under the same terms as Perl itself.