Crashes in SISLattice

[lenerd]

I was playing around with the estimator for SIS and noticed crashes for certain parameters (see below for examples) in the cost_zeta method of SISLattice when searching for beta.

lattice-estimator/estimator/sis_lattice.py

Lines 231 to 239 in dfbc622

	# step 1. optimize β
	with local_minimum(
	40, baseline_cost["beta"] + 1, precision=2, log_level=log_level + 1
	) as it:
	for beta in it:
	it.update(f(beta))
	for beta in it.neighborhood:
	it.update(f(beta))
	cost = it.y

1. If baseline_cost["beta"] + 1 is smaller than 40, we get a ValueError because we try to search in an empty range.
2. If baseline_cost["beta"] + 1 is equal to 41, we get a TypeError: Because precision is set to 2, the start and stop parameters of local_minimum are divided by two, resulting in an empty range [20,20) due to rounding and no neighborhood can be computed.

Maybe the SIS parameters in the examples below are obviously stupid for a lattice expert, but it would be nicer to have a helpful error message that explains what went wrong and maybe indicates how to change the parameters to obtain useful results.

---

Examples Code and Stack Traces

from estimator import *

# results in `ValueError: Incorrect bounds 20 > 10`
params = SIS.Parameters(n=1, q=2^1000, length_bound=2^100, norm=oo)
est = SIS.lattice(params)

Traceback (most recent call last):
  File "/home/lennart/dev/lattice-estimator/test.sage.py", line 11, in <module>
    est = SIS.lattice(params)
          ^^^^^^^^^^^^^^^^^^^
  File "/home/lennart/dev/lattice-estimator/estimator/sis_lattice.py", line 329, in __call__
    f(
  File "/home/lennart/dev/lattice-estimator/estimator/sis_lattice.py", line 232, in cost_zeta
    with local_minimum(
         ^^^^^^^^^^^^^^
  File "/home/lennart/dev/lattice-estimator/estimator/util.py", line 256, in __init__
    local_minimum_base.__init__(self, start, stop, smallerf, suppress_bounds_warning, log_level)
  File "/home/lennart/dev/lattice-estimator/estimator/util.py", line 97, in __init__
    raise ValueError(f"Incorrect bounds {start} > {stop}.")
ValueError: Incorrect bounds 20 > 10.

from estimator import *

# results in `TypeError: unsupported operand type(s) for *: 'NoneType' and 'int'`
params = SIS.Parameters(n=1, q=2^10000, length_bound=2^100, norm=oo)
est = SIS.lattice(params)

Traceback (most recent call last):
  File "/home/lennart/dev/lattice-estimator/test.sage.py", line 15, in <module>
    est = SIS.lattice(params)
          ^^^^^^^^^^^^^^^^^^^
  File "/home/lennart/dev/lattice-estimator/estimator/sis_lattice.py", line 329, in __call__
    f(
  File "/home/lennart/dev/lattice-estimator/estimator/sis_lattice.py", line 237, in cost_zeta
    for beta in it.neighborhood:
                ^^^^^^^^^^^^^^^
  File "/home/lennart/dev/lattice-estimator/estimator/util.py", line 273, in neighborhood
    start = max(start_bound, self.x - self._precision)
                             ^^^^^^
  File "/home/lennart/dev/lattice-estimator/estimator/util.py", line 264, in x
    return self._best.low * self._precision
           ~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~
TypeError: unsupported operand type(s) for *: 'NoneType' and 'int'