-
Notifications
You must be signed in to change notification settings - Fork 0
/
bench.py
197 lines (162 loc) · 6.11 KB
/
bench.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
"""
The bench routine takes three parameters:
p : size of the base field
start : minimum degree (default 2)
stop : maximum degree (default 200)
and return a list of lists containing timings (in seconds) for
various operations (create, embed, project, iso) for composita of
degree n x (n+1) for n between start and stop.
Two optional parameters 'number' and 'repeat' allow influencing the
timeit machine (for lift and push only). See
sage: ?sage_timeit
"""
from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
from sage.rings.padics.factory import Zp
from sage.rings.finite_rings.finite_field_constructor import GF
from sage.misc.sage_timeit import sage_timeit
from sage.rings.arith import factor
from sage.rings.ff_compositum.all import *
from sage.misc.prandom import randrange
from sage.functions.other import ceil
################# Chebyshev
def _torsion_poly(ell, P=None):
"""
Computes the ell-th gauss period. If `P` is given, it must be a
polynomial ring into which the result is coerced.
This is my favourite equality:
sage: all(_torsion_poly(n)(I) == I^n*lucas_number2(n,1,-1) for n in range(1,10))
True
"""
if P is None:
P, R, = PolynomialRing(ZZ, 'x'), ZZ,
elif P.characteristic() == 0:
R = ZZ
else:
R = Zp(P.characteristic(), prec=1, type='capped-rel')
t = [1, 0]
for k in range(1, ell/2 + 1):
m = R(ell - 2*k + 2) * R(ell - 2*k + 1) / (R(ell - k) * R(k))
t.append(-t[-2] * m)
t.append(0)
return P(list(reversed(t))).shift(ell % 2 - 1)
# Montgomery ladder for Pell conics
def _pellmul(x, n):
# The zero point and ours
A, B = 2, x
for c in reversed(n.digits(2)):
if c == 0:
A, B = A**2 - 2, A*B - x
else:
A, B = A*B - x, B**2 - 2
return A
def cheby(K, ell, exp):
p = K.characteristic()
eta = K(1)
if p != 2:
o = (p + 1) // ell
while (eta**2 - 4).is_square() or _pellmul(eta, o) == 2:
eta = K.random_element()
P = PolynomialRing(K, 'x')
return _torsion_poly(ell**exp, P) - eta
############ Other irreducibles
def kummer(K, ell, exp):
eta = K.one()
try:
while eta.nth_root(ell):
eta += 1
except ValueError:
pass
return K.polynomial_ring().gen()**(ell**exp) - eta
def rand_irred(K, n):
return K.polynomial_ring().irreducible_element(n)
############ Combine them together
def comp_prod(P, Q):
n = Q.degree()
K = P.base_ring()
A = PolynomialRing(K, 'X')
X = A.gen()
AA = PolynomialRing(K, 'Y,Z')
Y, Z = AA.gens()
return P(Y).resultant(AA(Y**n * Q(Z/Y)), Y)(1,X)
def irred(K, n):
F = []
p = K.characteristic()
for ell, exp in factor(n):
if ell == 2:
F.append(rand_irred(K, ell**exp))
elif ell.divides(p-1):
F.append(kummer(K, ell, exp))
elif ell.divides(p+1):
F.append(cheby(K, ell, exp))
else:
F.append(rand_irred(K, ell**exp))
return reduce(comp_prod, F)
####
def test_irred(p, i1, i2, number=0, repeat=3):
K = GF(p)
P = FFDesc(p, irred(K, i1).list())
Q = FFDesc(p, irred(K, i2).list())
R = P.compositum(Q)
context = globals()
context.update(locals())
# must be done only once to avoid (dis)counting caching
tcomp = sage_timeit('P.compositum(Q)', context, number=1, repeat=1, seconds=True)
a = FFElt(P, [randrange(p) for i in range(i1)])
b = FFElt(Q, [randrange(p) for i in range(i2)])
c = FFElt(R, [randrange(p) for i in range(i1*i2)])
context = globals()
context.update(locals())
tembed_pre = sage_timeit('a.embed(b,R)', context, number=1, repeat=1, seconds=True)
tembed = sage_timeit('a.embed(b,R)', context, number=number, repeat=repeat, seconds=True)
# Burn R's precomputed polynomials
ab = a.embed(b,R)
ab.project(P,b)
ab = a.embed(b, R)
d = a.embed(b, R)
context = globals()
context.update(locals())
tproject_pre = sage_timeit('ab.project(P,b)', context, number=1, repeat=1, seconds=True)
tproject = sage_timeit('ab.project(P,b)', context, number=number, repeat=repeat, seconds=True)
tmono2dual = (sage_timeit('c.embed(P, P)', context, number=1, repeat=1, seconds=True) -
sage_timeit('c.embed(P, P)', context, number=1, repeat=1, seconds=True))
tmul = sage_timeit('c*c', context, number=number, repeat=repeat, seconds=True)
ttmul = sage_timeit('c*d', context, number=number, repeat=repeat, seconds=True)
tiso = sage_timeit('c.eltseq_dual_python(P,Q)', context, number=number, repeat=repeat, seconds=True)
tbsgs = sage_timeit('c.eltseq_dual_BSGS(P,Q)', context, number=number, repeat=repeat, seconds=True)
tmatrix = sage_timeit('c.eltseq_dual_matrix(P,Q)', context, number=number, repeat=repeat, seconds=True)
return tcomp, tembed_pre, tembed, tproject_pre, tproject, tmono2dual, tmul, ttmul, tiso, tbsgs, tmatrix
###
def test_python(p, i1, i2, number=0, repeat=3):
import compositum as c
K = GF(p)
P = K.extension(i1, 'x')
R, phi, phinv = c.ffext(P, i2)
a = P.random_element()
c = R.random_element()
d = R.random_element()
context = globals()
context.update(locals())
tembed = sage_timeit('phi(a)', context, number=number, repeat=repeat, seconds=True)
tproject = sage_timeit('phinv(c)', context, number=number, repeat=repeat, seconds=True)
tmul = sage_timeit('c*d', context, number=number, repeat=repeat, seconds=True)
return tembed, tproject, tmul
def bench(p, start=2, stop=200, routine=test_irred):
l = []
i = ZZ(start)
while i < stop:
print i,
try:
l.append((i, routine(p, i, i+1)))
except:
print "failed"
else:
print sum(l[-1][1])
i += ceil(i/10)
return l
def gplot_out(l):
s = "#\t" + "\t\t".join(('Comp\t', 'EmbedPre', 'Embed\t',
'ProjectPre', 'Project\t', 'M2D\t',
'Mulmod\t', 'Tmulmod\t', 'Iso\t', 'Bsgs\t', 'Matrix')) + "\n"
for i, t in l:
s += "%d\t%s\n" % (i, "\t".join(map(str, t)))
return s