Improve isprime performance for 32-bit integers

[pabloferz]

As discussed here #11594 (mainly by @VicDrastik and @danaj). isprime has room for improvement. In particular this PR takes care only of the case of integers < 2^32. A version for 64-bit integers would require another strategy and should be done in another PR.

This version is much faster and uses less memory than the current implementation.

There is another possibility that was mentioned also in #11594, that is to use the algorithm due to Forišek and Jančina (which can be found here http://ceur-ws.org/Vol-1326/020-Forisek.pdf). @VicDrastik didn't seem to be fond of that solution but it is certainly faster than the one proposed here (although it uses a little more of memory 512 bytes, but we were already pre computing al primes up to 2^16, so this doesn't seem like much more.

I leave the code for that option below in case someone wants to consider it.

const bases = UInt16[15591,2018,166,7429,8064,16045,10503,4399,1949,1295,2776,3620,560,3128,5212,
2657,2300,2021,4652,1471,9336,4018,2398,20462,10277,8028,2213,6219,620,3763,4852,5012,3185,
1333,6227,5298,1074,2391,5113,7061,803,1269,3875,422,751,580,4729,10239,746,2951,556,2206,
3778,481,1522,3476,481,2487,3266,5633,488,3373,6441,3344,17,15105,1490,4154,2036,1882,1813,
467,3307,14042,6371,658,1005,903,737,1887,7447,1888,2848,1784,7559,3400,951,13969,4304,177,41,
19875,3110,13221,8726,571,7043,6943,1199,352,6435,165,1169,3315,978,233,3003,2562,2994,10587,
10030,2377,1902,5354,4447,1555,263,27027,2283,305,669,1912,601,6186,429,1930,14873,1784,1661,
524,3577,236,2360,6146,2850,55637,1753,4178,8466,222,2579,2743,2031,2226,2276,374,2132,813,
23788,1610,4422,5159,1725,3597,3366,14336,579,165,1375,10018,12616,9816,1371,536,1867,10864,
857,2206,5788,434,8085,17618,727,3639,1595,4944,2129,2029,8195,8344,6232,9183,8126,1870,3296,
7455,8947,25017,541,19115,368,566,5674,411,522,1027,8215,2050,6544,10049,614,774,2333,3007,
35201,4706,1152,1785,1028,1540,3743,493,4474,2521,26845,8354,864,18915,5465,2447,42,4511,
1660,166,1249,6259,2553,304,272,7286,73,6554,899,2816,5197,13330,7054,2818,3199,811,922,350,
7514,4452,3449,2663,4708,418,1621,1171,3471,88,11345,412,1559,194]

function witnesses(n::Union{UInt8,Int8,UInt16,Int16,UInt32,Int32})
    i = UInt64(n)
    i = ((i >> 16) $ i) * 0x45d9f3b
    i = ((i >> 16) $ i) * 0x45d9f3b
    i = ((i >> 16) $ i) & 255 + 1
    bases[i]
end

[kmsquire]

Is primes used in base? Should it be moved to a package?

[pabloferz]

Just for reference, the time it takes to check that all 32-bit the primes are primes is

635.517114 seconds (6.64 G allocations: 150.434 GB, 2.44% gc time) (master)
410.274658 seconds (2.73 G allocations: 89.169 GB, 2.15% gc time) (this PR)
309.419580 seconds (2.74 G allocations: 89.359 GB, 2.66% gc time) (Forišek and Jančina)

Also, checking whether or not each element of an array of 10^7 random UInt32s is prime, takes

4.734542 seconds (54.87 M allocations: 913.643 MB, 1.23% gc time) (master)
1.464444 seconds (1.85 M allocations: 28.153 MB, 0.07% gc time) (this PR)
1.188251 seconds (2.46 M allocations: 37.486 MB, 0.15% gc time) (Forišek and Jančina)

[pabloferz]

As far as i can see, none of the functions in primes.jl is used anywhere in base and I think all of them could be moved into a package. I don't know if there is a particular interest to keep them here.

[mschauer]

I think you can give a type hint

 for a in witnesses(n)::Tuple{Vararg{Int}}

making the witnesses stack allocated.

[JeffBezanson]

This should now be moved to https://github.com/JuliaMath/Primes.jl

@pabloferz Great work, thanks for this.

[pabloferz]

No problem. Moved over JuliaMath/Primes.jl#9