def multicrunch(surfsums, varname=None):
"""
Given an iterable consisting of SURFSums, compute the rational function
given by their combined sum.
Note that this rational function necessarily has degree <= 0.
"""
surfsums = list(surfsums)
#
# Combine the various critical sets and construct a candidate denominator.
#
critical = set().union(*(Q._critical for Q in surfsums))
cand = dict()
for Q in surfsums:
E = Q._cand
for r in E:
if r not in cand or cand[r] < E[r]:
cand[r] = E[r]
if varname is None:
varname = 's'
R = QQ[varname]
s = R.gen(0)
g = R(prod((a * s - b)**e for ((a, b), e) in cand.items()))
m = g.degree()
logger.info('Total number of SURFs: %d' % sum(Q._count for Q in surfsums))
for Q in surfsums:
Q._file.flush()
logger.info('Combined size of data files: %s' %
readable_filesize(sum(os.path.getsize(Q._filename) for Q in surfsums)))
logger.info('Number of critical points: %d' % len(critical))
logger.info('Degree of candidate denominator: %d' % m)
#
# Construct m + 1 non-critical points for evaluation.
#
values = set()
while len(values) < m + 1:
x = QQ.random_element()
if x in critical:
continue
values.add(x)
values = list(values)
#
# Set up parallel computations.
#
# bucket_size = ceil(float(len(values)) / common.ncpus)
# this was unused
dat_filenames = [Q._filename for Q in surfsums]
res_names = []
val_names = []
value_batches = [values[j::common.ncpus] for j in range(common.ncpus)]
with TemporaryDirectory() as tmpdir:
for j, v in enumerate(value_batches):
if not v:
break
val_filename = os.path.join(tmpdir, 'values%d' % j)
val_names.append(val_filename)
res_names.append(os.path.join(tmpdir, 'results%d' % j))
with open(val_filename, 'w') as val_file:
val_file.write(str(len(v)) + '\n')
for x in v:
val_file.write(str(x) + '\n')
def fun(k):
ret = crunch(['crunch', val_names[k], res_names[k]] + dat_filenames)
if ret == 0:
logger.info('Cruncher #%d finished.' % k)
return ret
logger.info('Launching %d crunchers.' % len(res_names))
if not common.debug:
fun = parallel(ncpus=len(res_names))(fun)
for (arg, ret) in fun(list(range(len(res_names)))):
if ret == 'NO DATA':
raise RuntimeError('A parallel process died')
if ret != 0:
raise RuntimeError('crunch failed')
else:
for k in range(len(res_names)):
fun(k)
#
# Collect results
#
pairs = []
for j, rn in enumerate(res_names):
it_batch = iter(value_batches[j])
with open(rn, 'r') as res_file:
for line in res_file:
# We also need to evaluate the candidate denominator 'g'
# from above at the given random points.
x = QQ(next(it_batch))
pairs.append((x, g(x) * QQ(line)))
if len(values) != len(pairs):
raise RuntimeError('Length of results is off')
f = R.lagrange_polynomial(list(pairs))
res = SR(f / g)
return res.factor() if res else res
