Convert mpz to heap type

[skirpichev]

Closes #351

[skirpichev]

Benchmark	3.13-ref	3.13-patch
(mpz(1<<7))**2	273 ns	330 ns: 1.21x slower
(mpz(1<<38))**2	274 ns	326 ns: 1.19x slower
(mpz(1<<300))**2	340 ns	392 ns: 1.15x slower
(mpz(1<<3000))**2	3.75 us	3.92 us: 1.05x slower
Geometric mean	(ref)	1.15x slower

Benchmark	3.14-ref	3.14-patch
(mpz(1<<7))**2	254 ns	315 ns: 1.24x slower
(mpz(1<<38))**2	254 ns	315 ns: 1.24x slower
(mpz(1<<300))**2	323 ns	381 ns: 1.18x slower
(mpz(1<<3000))**2	3.82 us	3.96 us: 1.03x slower
Geometric mean	(ref)	1.17x slower

Details

$ echo $CFLAGS 
-std=c11 -Wall -Wpedantic -Werror -O3
$ python3.13 -c "import sysconfig; print(sysconfig.get_config_var('CONFIG_ARGS'))"
'--enable-optimizations' '--with-system-libmpdec'

# bench.py
from operator import mul

import gmp
import pyperf


runner = pyperf.Runner()
for v in ["1<<7", "1<<38", "1<<300", "1<<3000"]:
    i = eval(v)
    bn = "(mpz("+v+"))**2"
    x = gmp.mpz(i)
    runner.bench_func(bn, mul, x, x)

[skirpichev]

Another benchmark:

Benchmark	ref	heap-type
collatz(97)	124 us	169 us: 1.37x slower
collatz(871)	186 us	255 us: 1.37x slower
Geometric mean	(ref)	1.37x slower

# bench.py
import pyperf
from gmp import mpz

zero = mpz(0)
one = mpz(1)
two = mpz(2)
three = mpz(3)

# https://en.wikipedia.org/wiki/Collatz_conjecture
def collatz(n):
    total = zero
    n = mpz(n)
    while n > 1:
        n = n*three + one if n & one else n//two
        total += one
    return total

runner = pyperf.Runner()
for i in [97, 871]:
    h = f"collatz({i})"
    runner.bench_func(h, collatz, i)

[skirpichev]

It's worse on PyPy as well, with bench/collatz.py:

collatz0(97): Mean +- std dev: [ref] 356 us +- 58 us -> [heap] 423 us +- 59 us: 1.19x slower
collatz0(871): Mean +- std dev: [ref] 539 us +- 90 us -> [heap] 648 us +- 94 us: 1.20x slower
collatz0((1<<128)+31): Mean +- std dev: [ref] 2.59 ms +- 0.45 ms -> [heap] 3.22 ms +- 0.48 ms: 1.25x slower
collatz1(97): Mean +- std dev: [ref] 547 us +- 75 us -> [heap] 662 us +- 79 us: 1.21x slower
collatz1(871): Mean +- std dev: [ref] 808 us +- 82 us -> [heap] 1.05 ms +- 0.13 ms: 1.30x slower
collatz1((1<<128)+31): Mean +- std dev: [ref] 4.05 ms +- 0.71 ms -> [heap] 5.01 ms +- 0.72 ms: 1.24x slower
collatz2(97): Mean +- std dev: [ref] 398 us +- 58 us -> [heap] 486 us +- 63 us: 1.22x slower
collatz2(871): Mean +- std dev: [ref] 613 us +- 94 us -> [heap] 727 us +- 95 us: 1.19x slower
collatz2((1<<128)+31): Mean +- std dev: [ref] 2.99 ms +- 0.49 ms -> [heap] 3.65 ms +- 0.51 ms: 1.22x slower

Geometric mean: 1.22x slower