def test_ellrains(pbound = 2**62, nbound = 100):
import sys
from sage.sets.primes import Primes
for p in Primes():
if p < 4:
continue
if p > pbound:
break
for n in xrange(2, nbound):
k = GF(p**n, name='z')
K = FiniteField_flint_fq_nmod(p, k.modulus(), name='z')
try:
a, b = find_gens(K, K)
print "Testing p = {} and n = {}".format(p, n)
print "Computing minpol...",
sys.stdout.flush()
f = a.minpoly()
assert f.degree() == n
g = b.minpoly()
assert f == g
print "done"
except RuntimeError:
pass
def benchmark(pbound=[3, 2**10],
nbound=[3, 2**8],
cbound=[1, Infinity],
obound=[1, Infinity],
loops=10,
tloop=Infinity,
tmax=Infinity,
prime=False,
even=False,
check=False,
fname=None,
write=False,
overwrite=False,
verbose=True,
skip_pari=False,
skip_magma=False,
skip_rains=False,
skip_kummer=False):
if write:
mode = 'w' if overwrite else 'a'
f = open(fname, mode, 0)
else:
f = sys.stdout
pmin, pmax = pbound
nmin, nmax = nbound
omin, omax = obound
cmin, cmax = cbound
M = Magma()
for p in xrange(pmin, pmax):
p = ZZ(p)
if not p.is_prime():
continue
for n in xrange(nmin, nmax):
n = ZZ(n)
if (prime == 1 and not is_prime(n)) or (prime == 2
and not is_prime_power(n)):
continue
if n < 2:
continue
if n % p == 0:
continue
if (not even) and (n % 2 == 0):
continue
o, G = find_root_order(p, [n, n], n, verbose=False)
m = G[0][0].parent().order()
c = Mod(p, n).multiplicative_order()
if verbose:
sys.stdout.write("\r" + " " * 79)
print("\rp = {}, n = {}, (o = {}, c = {})".format(p, n, o, c))
if verbose:
t = mytime()
sys.stdout.write("Constructing fields ({})".format(
time.strftime("%c")))
sys.stdout.flush()
q = p**n
k = GF(q, name='z')
k_rand = GF(q, modulus='random', name='z')
k_flint = GF_flint(p, k.modulus(), name='z')
if verbose > 1:
sys.stdout.write("\ntotal: {}s\n".format(mytime(t)))
sys.stdout.flush()
# Magma
if verbose:
sys.stdout.write("\r" + " " * 79)
sys.stdout.write("\rMagma ({})".format(time.strftime("%c")))
sys.stdout.flush()
tloops = 0
for l in xrange(loops):
if skip_magma:
break
if (o > omax) or (o == p):
break
# let's assume that launching a new Magma instance is cheaper
# than computing random irreducible polynomials
try:
M._start()
except OSError as err:
# but it can also cause fork issues...
# let's accept this
# and fail as the situation will only worsen
# unless it is "just" a memory issue
# which should be mitigated by COW but is not
#print(err)
if err.errno == errno.ENOMEM:
break
else:
raise
try:
k_magma = M(k)
k_rand_magma = M(k_rand)
if tloop is not Infinity:
alarm(tloop)
t = mytime()
k_magma.Embed(k_rand_magma, nvals=0)
#M._eval_line("Embed(k_magma, k_rand_magma);", wait_for_prompt=False)
tloops += mytime(t)
except TypeError:
# sage/magma interface sometimes gets confused
pass
except (KeyboardInterrupt, AlarmInterrupt):
# sage interface eats KeyboardInterrupt
# and AlarmInterrupt derives from it
tloops = 0
break
finally:
if tloop is not Infinity:
cancel_alarm()
M.quit()
# sage pexpect interface leaves zombies around
try:
while os.waitpid(-1, os.WNOHANG)[0]:
pass
# but sometimes every child is already buried
# and we get an ECHILD error...
except OSError:
pass
if tloops > tmax:
break
tmagma = tloops / (l + 1)
if verbose > 1:
sys.stdout.write("\ntotal: {}s, per loop: {}s\n".format(
tloops, tloops / (l + 1)))
sys.stdout.flush()
# Rains algorithms
if verbose:
sys.stdout.write("\r" + " " * 79)
sys.stdout.write("\rCyclotomic Rains ({})".format(
time.strftime("%c")))
sys.stdout.flush()
trains = []
tloops = 0
for l in xrange(loops):
if skip_rains:
break
if (o > omax) or (o == p):
break
try:
if tloop is not Infinity:
alarm(tloop)
t = mytime()
a, b = find_gens_cyclorains(k_flint,
k_flint,
use_lucas=False)
tloops += mytime(t)
except (KeyboardInterrupt, AlarmInterrupt):
tloops = 0
break
finally:
if tloop is not Infinity:
cancel_alarm()
if check and (l == 0 or check > 1):
g = a.minpoly()
if g.degree() != n:
raise RuntimeError("wrong degree")
if g != b.minpoly():
raise RuntimeError("different minpolys")
if tloops > tmax:
break
trains.append(tloops / (l + 1))
if verbose > 1:
sys.stdout.write("\ntotal: {}s, per loop: {}s\n".format(
tloops, tloops / (l + 1)))
sys.stdout.flush()
# Conic Rains
if verbose:
sys.stdout.write("\r" + " " * 79)
sys.stdout.write("\rConic Rains ({})".format(
time.strftime("%c")))
sys.stdout.flush()
tloops = 0
for l in xrange(loops):
if skip_rains:
break
if (o != 2) or (o > omax) or (o == p):
break
try:
if tloop is not Infinity:
alarm(tloop)
t = mytime()
a, b = find_gens_cyclorains(k_flint,
k_flint,
use_lucas=True)
tloops += mytime(t)
except (KeyboardInterrupt, AlarmInterrupt):
tloops = 0
break
finally:
if tloop is not Infinity:
cancel_alarm()
if check and (l == 0 or check > 1):
g = a.minpoly()
if g.degree() != n:
raise RuntimeError("wrong degree")
if g != b.minpoly():
raise RuntimeError("different minpolys")
if tloops > tmax:
break
trains.append(tloops / (l + 1))
if verbose > 1:
sys.stdout.write("\ntotal: {}s, per loop: {}s\n".format(
tloops, tloops / (l + 1)))
sys.stdout.flush()
# Elliptic Rains
if verbose:
sys.stdout.write("\r" + " " * 79)
sys.stdout.write("\rElliptic Rains ({})".format(
time.strftime("%c")))
sys.stdout.flush()
tloops = 0
for l in xrange(loops):
if skip_rains:
break
try:
if tloop is not Infinity:
alarm(tloop)
t = mytime()
a, b = find_gens_ellrains(k_flint, k_flint)
tloops += mytime(t)
except RuntimeError:
# sometimes no suitable elliptic curve exists
pass
except (KeyboardInterrupt, AlarmInterrupt):
tloops = 0
break
finally:
if tloop is not Infinity:
cancel_alarm()
if check and (l == 0 or check > 1):
g = a.minpoly()
if g.degree() != n:
raise RuntimeError("wrong degree")
if g != b.minpoly():
raise RuntimeError("different minpolys")
if tloops > tmax:
break
trains.append(tloops / (l + 1))
if verbose > 1:
sys.stdout.write("\ntotal: {}s, per loop: {}s\n".format(
tloops, tloops / (l + 1)))
sys.stdout.flush()
# PARI/GP
if verbose:
sys.stdout.write("\r" + " " * 79)
sys.stdout.write("\rPARI/GP ({})".format(time.strftime("%c")))
sys.stdout.flush()
tloops = 0
for l in xrange(loops):
if skip_pari:
break
if c < cmin or c > cmax:
break
try:
if tloop is not Infinity:
alarm(tloop)
t = mytime()
a, b = find_gens_pari(k, k)
tloops += mytime(t)
except (KeyboardInterrupt, AlarmInterrupt):
tloops = 0
break
finally:
if tloop is not Infinity:
cancel_alarm()
if check and (l == 0 or check > 1):
g = a.minpoly()
if g.degree() != n:
raise RuntimeError("wrong degree")
if g != b.minpoly():
raise RuntimeError("different minpolys")
if tloops > tmax:
break
tpari = tloops / (l + 1)
# Kummer algorithms
tkummer = []
# only linalg and modcomp implemented for c==1
for i, algo in enumerate(kummer_algolist[2 * (c == 1):-2 *
(c == 1) - 1]):
if verbose:
sys.stdout.write("\r" + " " * 79)
sys.stdout.write("\rKummer {} ({})".format(
kummer_namelist[2 * (c == 1) + i],
time.strftime("%c")))
sys.stdout.flush()
tloops = 0
for l in xrange(loops):
if skip_kummer:
break
if c < cmin or c > cmax:
break
try:
if tloop is not Infinity:
alarm(tloop)
t = mytime()
a, b = find_gens_kummer(k_flint, k_flint, n, algo)
tloops += mytime(t)
except (KeyboardInterrupt, AlarmInterrupt):
tloops = 0
break
finally:
if tloop is not Infinity:
cancel_alarm()
if check and (l == 0 or check > 1):
g = a.minpoly()
if g.degree() != n:
raise RuntimeError("wrong degree")
if g != b.minpoly():
raise RuntimeError("different minpolys")
if tloops > tmax:
break
tkummer.append(tloops / (l + 1))
if verbose > 1:
sys.stdout.write("\ntotal: {}s, per loop: {}s\n".format(
tloops, tloops / (l + 1)))
sys.stdout.flush()
tkummer = 2 * (c == 1) * [0] + tkummer + 2 * (c == 1) * [0]
if verbose:
sys.stdout.write("\r")
sys.stdout.flush()
f.write(("{} {} ({}, {})" + " {}" + " {}" * len(trains) + " {}" +
" {}" * len(tkummer) + "\n").format(
p, n, o, c, *([tmagma] + trains + [tpari] + tkummer)))
if write:
f.close()
def benchmark(pbound = [3, 2**10], nbound = [3, 2**8], cbound = [1, Infinity], obound = [1, Infinity], loops = 10, tloop = Infinity, tmax = Infinity, prime = False, even = False, check = False, fname = None, write = False, overwrite = False, verbose = True, skip_pari = False, skip_magma = False, skip_rains = False, skip_kummer = False):
if write:
mode = 'w' if overwrite else 'a'
f = open(fname, mode, 0)
else:
f = sys.stdout
pmin, pmax = pbound
nmin, nmax = nbound
omin, omax = obound
cmin, cmax = cbound
M = Magma()
for p in xrange(pmin, pmax):
p = ZZ(p)
if not p.is_prime():
continue
for n in xrange(nmin, nmax):
n = ZZ(n)
if (prime == 1 and not is_prime(n)) or (prime == 2 and not is_prime_power(n)):
continue
if n < 2:
continue
if n % p == 0:
continue
if (not even) and (n % 2 == 0):
continue
o, G = find_root_order(p, [n, n], n, verbose=False)
m = G[0][0].parent().order()
c = Mod(p,n).multiplicative_order()
if verbose:
sys.stdout.write("\r"+" "*79)
print("\rp = {}, n = {}, (o = {}, c = {})".format(p, n, o, c))
if verbose:
t = mytime()
sys.stdout.write("Constructing fields ({})".format(time.strftime("%c")))
sys.stdout.flush()
q = p**n
k = GF(q, name='z')
k_rand = GF(q, modulus='random', name='z')
k_flint = GF_flint(p, k.modulus(), name='z')
if verbose > 1:
sys.stdout.write("\ntotal: {}s\n".format(mytime(t)))
sys.stdout.flush()
# Magma
if verbose:
sys.stdout.write("\r"+" "*79)
sys.stdout.write("\rMagma ({})".format(time.strftime("%c")))
sys.stdout.flush()
tloops = 0
for l in xrange(loops):
if skip_magma:
break
if (o > omax) or (o == p):
break
# let's assume that launching a new Magma instance is cheaper
# than computing random irreducible polynomials
try:
M._start()
except OSError as err:
# but it can also cause fork issues...
# let's accept this
# and fail as the situation will only worsen
# unless it is "just" a memory issue
# which should be mitigated by COW but is not
#print(err)
if err.errno == errno.ENOMEM:
break
else:
raise
try:
k_magma = M(k)
k_rand_magma = M(k_rand)
if tloop is not Infinity:
alarm(tloop)
t = mytime()
k_magma.Embed(k_rand_magma, nvals=0)
#M._eval_line("Embed(k_magma, k_rand_magma);", wait_for_prompt=False)
tloops += mytime(t)
except TypeError:
# sage/magma interface sometimes gets confused
pass
except (KeyboardInterrupt, AlarmInterrupt):
# sage interface eats KeyboardInterrupt
# and AlarmInterrupt derives from it
tloops = 0
break
finally:
if tloop is not Infinity:
cancel_alarm()
M.quit()
# sage pexpect interface leaves zombies around
try:
while os.waitpid(-1, os.WNOHANG)[0]:
pass
# but sometimes every child is already buried
# and we get an ECHILD error...
except OSError:
pass
if tloops > tmax:
break
tmagma = tloops / (l+1)
if verbose > 1:
sys.stdout.write("\ntotal: {}s, per loop: {}s\n".format(tloops, tloops/(l+1)))
sys.stdout.flush()
# Rains algorithms
if verbose:
sys.stdout.write("\r"+" "*79)
sys.stdout.write("\rCyclotomic Rains ({})".format(time.strftime("%c")))
sys.stdout.flush()
trains = []
tloops = 0
for l in xrange(loops):
if skip_rains:
break
if (o > omax) or (o == p):
break
try:
if tloop is not Infinity:
alarm(tloop)
t = mytime()
a, b = find_gens_cyclorains(k_flint, k_flint, use_lucas = False)
tloops += mytime(t)
except (KeyboardInterrupt, AlarmInterrupt):
tloops = 0
break
finally:
if tloop is not Infinity:
cancel_alarm()
if check and (l == 0 or check > 1):
g = a.minpoly()
if g.degree() != n:
raise RuntimeError("wrong degree")
if g != b.minpoly():
raise RuntimeError("different minpolys")
if tloops > tmax:
break
trains.append(tloops / (l+1))
if verbose > 1:
sys.stdout.write("\ntotal: {}s, per loop: {}s\n".format(tloops, tloops/(l+1)))
sys.stdout.flush()
# Conic Rains
if verbose:
sys.stdout.write("\r"+" "*79)
sys.stdout.write("\rConic Rains ({})".format(time.strftime("%c")))
sys.stdout.flush()
tloops = 0
for l in xrange(loops):
if skip_rains:
break
if (o != 2) or (o > omax) or (o == p):
break
try:
if tloop is not Infinity:
alarm(tloop)
t = mytime()
a, b = find_gens_cyclorains(k_flint, k_flint, use_lucas = True)
tloops += mytime(t)
except (KeyboardInterrupt, AlarmInterrupt):
tloops = 0
break
finally:
if tloop is not Infinity:
cancel_alarm()
if check and (l == 0 or check > 1):
g = a.minpoly()
if g.degree() != n:
raise RuntimeError("wrong degree")
if g != b.minpoly():
raise RuntimeError("different minpolys")
if tloops > tmax:
break
trains.append(tloops / (l+1))
if verbose > 1:
sys.stdout.write("\ntotal: {}s, per loop: {}s\n".format(tloops, tloops/(l+1)))
sys.stdout.flush()
# Elliptic Rains
if verbose:
sys.stdout.write("\r"+" "*79)
sys.stdout.write("\rElliptic Rains ({})".format(time.strftime("%c")))
sys.stdout.flush()
tloops = 0
for l in xrange(loops):
if skip_rains:
break
try:
if tloop is not Infinity:
alarm(tloop)
t = mytime()
a, b = find_gens_ellrains(k_flint, k_flint)
tloops += mytime(t)
except RuntimeError:
# sometimes no suitable elliptic curve exists
pass
except (KeyboardInterrupt, AlarmInterrupt):
tloops = 0
break
finally:
if tloop is not Infinity:
cancel_alarm()
if check and (l == 0 or check > 1):
g = a.minpoly()
if g.degree() != n:
raise RuntimeError("wrong degree")
if g != b.minpoly():
raise RuntimeError("different minpolys")
if tloops > tmax:
break
trains.append(tloops / (l+1))
if verbose > 1:
sys.stdout.write("\ntotal: {}s, per loop: {}s\n".format(tloops, tloops/(l+1)))
sys.stdout.flush()
# PARI/GP
if verbose:
sys.stdout.write("\r"+" "*79)
sys.stdout.write("\rPARI/GP ({})".format(time.strftime("%c")))
sys.stdout.flush()
tloops = 0
for l in xrange(loops):
if skip_pari:
break
if c < cmin or c > cmax:
break
try:
if tloop is not Infinity:
alarm(tloop)
t = mytime()
a, b = find_gens_pari(k, k)
tloops += mytime(t)
except (KeyboardInterrupt, AlarmInterrupt):
tloops = 0
break
finally:
if tloop is not Infinity:
cancel_alarm()
if check and (l == 0 or check > 1):
g = a.minpoly()
if g.degree() != n:
raise RuntimeError("wrong degree")
if g != b.minpoly():
raise RuntimeError("different minpolys")
if tloops > tmax:
break
tpari = tloops / (l+1)
# Kummer algorithms
tkummer = []
# only linalg and modcomp implemented for c==1
for i, algo in enumerate(kummer_algolist[2*(c==1):-2*(c==1)-1]):
if verbose:
sys.stdout.write("\r"+" "*79)
sys.stdout.write("\rKummer {} ({})".format(kummer_namelist[2*(c==1)+i], time.strftime("%c")))
sys.stdout.flush()
tloops = 0
for l in xrange(loops):
if skip_kummer:
break
if c < cmin or c > cmax:
break
try:
if tloop is not Infinity:
alarm(tloop)
t = mytime()
a, b = find_gens_kummer(k_flint, k_flint, n, algo)
tloops += mytime(t)
except (KeyboardInterrupt, AlarmInterrupt):
tloops = 0
break
finally:
if tloop is not Infinity:
cancel_alarm()
if check and (l == 0 or check > 1):
g = a.minpoly()
if g.degree() != n:
raise RuntimeError("wrong degree")
if g != b.minpoly():
raise RuntimeError("different minpolys")
if tloops > tmax:
break
tkummer.append(tloops / (l+1))
if verbose > 1:
sys.stdout.write("\ntotal: {}s, per loop: {}s\n".format(tloops, tloops/(l+1)))
sys.stdout.flush()
tkummer = 2*(c == 1)*[0] + tkummer + 2*(c == 1)*[0]
if verbose:
sys.stdout.write("\r")
sys.stdout.flush()
f.write(("{} {} ({}, {})" + " {}" + " {}"*len(trains) + " {}" + " {}"*len(tkummer)+"\n").format(p, n, o, c, *([tmagma] + trains + [tpari] + tkummer)))
if write:
f.close()
