Reentrancy issue in sig_occurred()

[tornaria]

This is related but different from #215.

Reported sagemath/sage#38749 (comment) for a particular random seed, and after #216 it is permanent (see #181 (comment)).

Here's a log with sagemath 10.5 / python 3.13:

sage -t --long --warn-long 30.0 --random-seed=308265638168472780954235246279840024638 /usr/lib/python3.13/site-packages/sage/rings/integer.pyx
**********************************************************************
File "/usr/lib/python3.13/site-packages/sage/rings/integer.pyx", line 3074, in sage.rings.integer.Integer.divisors
Failed example:
    for i in range(20):           # long time                             # needs sage.libs.pari
        try:
            alarm(RDF.random_element(1e-3, 0.5))
            _ = n.divisors()
            cancel_alarm()  # we never get here
        except AlarmInterrupt:
            pass
Expected nothing
Got:
    Traceback (most recent call last):
      File "<frozen importlib._bootstrap>", line 653, in has_location
      File "signals.pyx", line 355, in cysignals.signals.python_check_interrupt
    cysignals.signals.AlarmInterrupt
    Exception ignored in: 'cysignals.signals.verify_exc_value'
    Traceback (most recent call last):
      File "<frozen importlib._bootstrap>", line 653, in has_location
      File "signals.pyx", line 355, in cysignals.signals.python_check_interrupt
    cysignals.signals.AlarmInterrupt: 
    Traceback (most recent call last):
      File "<frozen importlib._bootstrap>", line 653, in has_location
      File "signals.pyx", line 355, in cysignals.signals.python_check_interrupt
    cysignals.signals.AlarmInterrupt
    Exception ignored in: 'cysignals.signals.verify_exc_value'
    Traceback (most recent call last):
      File "<frozen importlib._bootstrap>", line 653, in has_location
      File "signals.pyx", line 355, in cysignals.signals.python_check_interrupt
    cysignals.signals.AlarmInterrupt: 
    Traceback (most recent call last):
      File "<frozen importlib._bootstrap>", line 653, in has_location
      File "signals.pyx", line 355, in cysignals.signals.python_check_interrupt
    cysignals.signals.AlarmInterrupt
    Exception ignored in: 'cysignals.signals.verify_exc_value'
    Traceback (most recent call last):
      File "<frozen importlib._bootstrap>", line 653, in has_location
      File "signals.pyx", line 355, in cysignals.signals.python_check_interrupt
    cysignals.signals.AlarmInterrupt: 
    Traceback (most recent call last):
      File "<frozen importlib._bootstrap>", line 653, in has_location
      File "signals.pyx", line 355, in cysignals.signals.python_check_interrupt
    cysignals.signals.AlarmInterrupt
    Exception ignored in: 'cysignals.signals.verify_exc_value'
    Traceback (most recent call last):
      File "<frozen importlib._bootstrap>", line 653, in has_location
      File "signals.pyx", line 355, in cysignals.signals.python_check_interrupt
    cysignals.signals.AlarmInterrupt: 
    Traceback (most recent call last):
      File "<frozen importlib._bootstrap>", line 653, in has_location
      File "signals.pyx", line 355, in cysignals.signals.python_check_interrupt
    cysignals.signals.AlarmInterrupt
    Exception ignored in: 'cysignals.signals.verify_exc_value'
    Traceback (most recent call last):
      File "<frozen importlib._bootstrap>", line 653, in has_location
      File "signals.pyx", line 355, in cysignals.signals.python_check_interrupt
    cysignals.signals.AlarmInterrupt: 
    Traceback (most recent call last):
      File "<frozen importlib._bootstrap>", line 653, in has_location
      File "signals.pyx", line 355, in cysignals.signals.python_check_interrupt
    cysignals.signals.AlarmInterrupt
    Exception ignored in: 'cysignals.signals.verify_exc_value'
    Traceback (most recent call last):
      File "<frozen importlib._bootstrap>", line 653, in has_location
      File "signals.pyx", line 355, in cysignals.signals.python_check_interrupt
    cysignals.signals.AlarmInterrupt: 
    Traceback (most recent call last):
      File "<frozen importlib._bootstrap>", line 653, in has_location
      File "signals.pyx", line 355, in cysignals.signals.python_check_interrupt
    cysignals.signals.AlarmInterrupt
    Exception ignored in: 'cysignals.signals.verify_exc_value'
    Traceback (most recent call last):
      File "<frozen importlib._bootstrap>", line 653, in has_location
      File "signals.pyx", line 355, in cysignals.signals.python_check_interrupt
    cysignals.signals.AlarmInterrupt: 
    Traceback (most recent call last):
      File "<frozen importlib._bootstrap>", line 653, in has_location
      File "signals.pyx", line 355, in cysignals.signals.python_check_interrupt
    cysignals.signals.AlarmInterrupt
    Exception ignored in: 'cysignals.signals.verify_exc_value'
    Traceback (most recent call last):
      File "<frozen importlib._bootstrap>", line 653, in has_location
      File "signals.pyx", line 355, in cysignals.signals.python_check_interrupt
    cysignals.signals.AlarmInterrupt: 
**********************************************************************

A minimal way to reproduce it with this file:

from math import prod
from sage.arith.misc import primes_first_n
from cysignals.alarm import alarm, AlarmInterrupt
from cysignals.tests import print_sig_occurred
from resource import getrusage, RUSAGE_SELF

def cputime():
    return sum(getrusage(RUSAGE_SELF)[:2])

n = prod(primes_first_n(25))

try:
    alarm(0.2)
    print(f"{cputime():5.2f}s first run")
    _ = n.divisors()
except AlarmInterrupt:
    print(f"{cputime():5.2f}s first alarm triggered")

try:
    alarm(0.04)
    print(f"{cputime():5.2f}s second run")
    _ = n.divisors()
except AlarmInterrupt:
    print(f"{cputime():5.2f}s second alarm triggered")

print(f"{cputime():5.2f}s done")

run from python as

$ python bug-sig_occurred.py 
 0.26s first run
 0.76s first alarm triggered
 0.76s second run
Traceback (most recent call last):
  File "<frozen importlib._bootstrap>", line 653, in has_location
  File "signals.pyx", line 355, in cysignals.signals.python_check_interrupt
cysignals.signals.AlarmInterrupt
Exception ignored in: 'cysignals.signals.verify_exc_value'
Traceback (most recent call last):
  File "<frozen importlib._bootstrap>", line 653, in has_location
  File "signals.pyx", line 355, in cysignals.signals.python_check_interrupt
cysignals.signals.AlarmInterrupt: 
 4.16s done

Note that the second alarm escapes; it is (printed and) ignored in verify_exc_value(), but the computation keeps going until the end.