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Commit 088c1b7

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6 files changed

+80
-84
lines changed

6 files changed

+80
-84
lines changed

‎README.txt‎

Lines changed: 0 additions & 4 deletions
Original file line numberDiff line numberDiff line change
@@ -103,10 +103,6 @@ Here are some points I consider working on at some point:
103103
- I have to implement the Montgomery algorithm for the algebraic square root computation.
104104
For the small numbers I have used my algorithm on, it is not a bottleneck yet.
105105

106-
- I have to optimize the Union-find algorithm for cycle detection, the version I have right now
107-
does not seem to be perfect, as I still do many operations to connect two distinct
108-
connected components.
109-
110106
- No matter how hard I tried, I am stuck on understanding the block Wiedemann algorithm. For
111107
now, the best I can do is the scalar one, with some optimizations. Namely, I use binary
112108
encoding of the blocks of vectors to compute matrix-vector product very efficiently.

‎config/config.ini‎

Lines changed: 3 additions & 3 deletions
Original file line numberDiff line numberDiff line change
@@ -5,10 +5,10 @@ lanczos=True
55
square_root_couveignes=False
66
large_primes_constant=100
77
block_size=8
8-
poly_search_nb_poly_coarse_eval=1000
9-
poly_search_nb_poly_precise_eval=200
8+
poly_search_nb_poly_coarse_eval=100
9+
poly_search_nb_poly_precise_eval=50
1010
poly_search_prime_bound=300
1111
poly_search_nb_roots=3
1212
poly_search_multiplier=1
1313
NB_CPU_POLY_SELECTION=4
14-
NB_CPU_SIEVE=1
14+
NB_CPU_SIEVE=4

‎src/compute_solutions.py‎

Lines changed: 1 addition & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -167,7 +167,7 @@ def compute_factors(pairs_used, vec, n, primes, f_x, g, g_prime, g_prime_sq, g_p
167167
else:
168168
x,y = create_solution(pairs_used,vec,n,len(primes),primes,g,g_prime,m0,m1,inert_set[-1],g_prime_sq,leading_coeff,g_prime_eval,2*M)
169169

170-
print(math.gcd(x-y,n), math.gcd(x+y,n))
170+
# print(math.gcd(x-y,n), math.gcd(x+y,n))
171171

172172
if x != y and math.gcd(x-y,n) != 1 and math.gcd(x+y,n) != 1:
173173
print_final_message(x, y, n, time_1, LOG_PATH)

‎src/mono_cpu_sieve.py‎

Lines changed: 3 additions & 5 deletions
Original file line numberDiff line numberDiff line change
@@ -13,9 +13,7 @@
1313
def find_relations(f_x, leading_coeff, g, primes, R_p, Q, B_prime, divide_leading, prod_primes, pow_div, pairs_used,
1414
const1, const2, logs, m0, m1, M, d, n, flag_use_batch_smooth_test, LOG_PATH):
1515
fp, pf = {}, {}
16-
connected_components_fp, connected_components_pf = {}, {}
17-
node_component_fp, node_component_pf = {}, {}
18-
index_component_fp, index_component_pf = 0, 0
16+
parent_fp, parent_pf = {}, {}
1917
full_found = 0
2018
partial_found_fp, partial_found_pf = 0, 0
2119
size_fp, size_pf = 0, 0
@@ -62,10 +60,10 @@ def find_relations(f_x, leading_coeff, g, primes, R_p, Q, B_prime, divide_leadin
6260
full_found += 1
6361

6462
elif z[4] > 1 and z[2] == 1:
65-
pairs_used, fp, graph_fp, size_fp, index_component_fp, cycle_len, full_found, partial_found_fp = handle_large_fp(tmp,z,pairs_used,fp,graph_fp,size_fp,connected_components_fp,node_component_fp,index_component_fp,g,divide_leading,cycle_len,full_found,partial_found_fp)
63+
pairs_used, fp, graph_fp, size_fp, parent_fp, cycle_len, full_found, partial_found_fp = handle_large_fp(tmp,z,pairs_used,fp,graph_fp,size_fp,parent_fp,g,divide_leading,cycle_len,full_found,partial_found_fp)
6664

6765
elif z[4] == 1 and z[2] > 1:
68-
pairs_used, pf, graph_pf, size_pf, index_component_pf, cycle_len, full_found, partial_found_pf = handle_large_pf(tmp, z, pairs_used, pf, graph_pf, size_pf, connected_components_pf, node_component_pf, index_component_pf, g, divide_leading, cycle_len, full_found, partial_found_pf)
66+
pairs_used, pf, graph_pf, size_pf, parent_pf, cycle_len, full_found, partial_found_pf = handle_large_pf(tmp, z, pairs_used, pf, graph_pf, size_pf, parent_pf, g, divide_leading, cycle_len, full_found, partial_found_pf)
6967

7068
sys.stdout.write('\r'+"b = "+str(b)+" "+str(len(pairs_used))+"/("+str(V)+"+10) ; full relations = "+str(full_found)+" | partial found fp = "+str(partial_found_fp)+" ("+str(size_fp)+") | partial found pf = "+str(partial_found_pf)+" ("+str(size_pf)+")")
7169
b += 1

‎src/multi_cpu_sieve.py‎

Lines changed: 3 additions & 5 deletions
Original file line numberDiff line numberDiff line change
@@ -45,9 +45,7 @@ def siever(b_queue, tmp_pairs, f_x, primes, R_p, prod_primes, m0, m1, d, b, M, l
4545
def find_relations(f_x, leading_coeff, g, primes, R_p, Q, B_prime, divide_leading, prod_primes, pow_div, pairs_used,
4646
const1, const2, logs, m0, m1, M, d, n, flag_use_batch_smooth_test, LOG_PATH, NB_CPU):
4747
fp, pf = {}, {}
48-
connected_components_fp, connected_components_pf = {}, {}
49-
node_component_fp, node_component_pf = {}, {}
50-
index_component_fp, index_component_pf = 0, 0
48+
parent_fp, parent_pf = {}, {}
5149
full_found = 0
5250
partial_found_fp, partial_found_pf = 0, 0
5351
size_fp, size_pf = 0, 0
@@ -100,10 +98,10 @@ def find_relations(f_x, leading_coeff, g, primes, R_p, Q, B_prime, divide_leadin
10098
full_found += 1
10199

102100
elif z[4] > 1 and z[2] == 1:
103-
pairs_used, fp, graph_fp, size_fp, index_component_fp, cycle_len, full_found, partial_found_fp = handle_large_fp(tmp,z,pairs_used,fp,graph_fp,size_fp,connected_components_fp,node_component_fp,index_component_fp,g,divide_leading,cycle_len,full_found,partial_found_fp)
101+
pairs_used, fp, graph_fp, size_fp, parent_fp, cycle_len, full_found, partial_found_fp = handle_large_fp(tmp,z,pairs_used,fp,graph_fp,size_fp,parent_fp,g,divide_leading,cycle_len,full_found,partial_found_fp)
104102

105103
elif z[4] == 1 and z[2] > 1:
106-
pairs_used, pf, graph_pf, size_pf, index_component_pf, cycle_len, full_found, partial_found_pf = handle_large_pf(tmp, z, pairs_used, pf, graph_pf, size_pf, connected_components_pf, node_component_pf, index_component_pf, g, divide_leading, cycle_len, full_found, partial_found_pf)
104+
pairs_used, pf, graph_pf, size_pf, parent_pf, cycle_len, full_found, partial_found_pf = handle_large_pf(tmp, z, pairs_used, pf, graph_pf, size_pf, parent_pf, g, divide_leading, cycle_len, full_found, partial_found_pf)
107105

108106
sys.stdout.write('\r'+"b = "+str(b)+" "+str(len(pairs_used))+"/("+str(V)+"+10) ; full relations = "+str(full_found)+" | partial found fp = "+str(partial_found_fp)+" ("+str(size_fp)+") | partial found pf = "+str(partial_found_pf)+" ("+str(size_pf)+")")
109107

‎src/relations.py‎

Lines changed: 70 additions & 66 deletions
Original file line numberDiff line numberDiff line change
@@ -85,7 +85,7 @@ def combine_fp(pair, pairs_used, fp, path, divide_leading, g):
8585
pairs_used.append(tmp)
8686

8787
# Master function, keeps the partial_relations and possible_smooth lists sorted, find the matching large primes, create the full relations from large primes
88-
def handle_large_fp(pair, large_primes, pairs_used, fp, graph_fp, size_fp, connected_components_fp, node_component_fp, index_component_fp, g, divide_leading, cycle_len, full_found, partial_found_fp):
88+
def handle_large_fp(pair, large_primes, pairs_used, fp, graph_fp, size_fp, parent_fp, g, divide_leading, cycle_len, full_found, partial_found_fp):
8989
pair[4] = [large_primes[3]]
9090

9191
if large_primes[3] == large_primes[4]:
@@ -94,98 +94,104 @@ def handle_large_fp(pair, large_primes, pairs_used, fp, graph_fp, size_fp, conne
9494

9595
elif not bool(fp):
9696
pair[4].append(large_primes[4])
97-
fp[large_primes[3]] = {}
98-
fp[large_primes[3]][large_primes[4]] = pair
9997

100-
graph_fp[large_primes[3]] = [large_primes[4]]
101-
graph_fp[large_primes[4]] = [large_primes[3]]
98+
small_p, big_p = large_primes[3], large_primes[4]
10299

103-
connected_components_fp[index_component_fp] = set((large_primes[3], large_primes[4]))
104-
node_component_fp[large_primes[3]] = index_component_fp
105-
node_component_fp[large_primes[4]] = index_component_fp
100+
fp[small_p] = {}
101+
fp[small_p][big_p] = pair
102+
103+
graph_fp[small_p] = [big_p]
104+
graph_fp[big_p] = [small_p]
105+
106+
parent_fp[small_p] = small_p
107+
parent_fp[big_p] = small_p
106108

107109
size_fp += 1
108-
index_component_fp += 1
109110

110111
else:
111-
flag_small_prime = large_primes[3] in graph_fp
112+
small_p, big_p = large_primes[3], large_primes[4]
113+
114+
flag_small_prime = small_p in graph_fp
112115

113116
# If the smallest prime has not already been seen
114117
if not flag_small_prime:
115-
graph_fp[large_primes[3]] = [large_primes[4]]
118+
graph_fp[small_p] = [big_p]
116119

117120
# Find where in partial relations it is needed to insert the new partial relation
118-
pair[4].append(large_primes[4])
119-
fp[large_primes[3]] = {}
120-
fp[large_primes[3]][large_primes[4]] = pair
121+
pair[4].append(big_p)
122+
123+
fp[small_p] = {}
124+
fp[small_p][big_p] = pair
121125

122126
size_fp += 1
123127

124128
# Find if largest prime has already been seen
125-
flag_big_prime = large_primes[4] in graph_fp
129+
flag_big_prime = big_p in graph_fp
126130

127131
if flag_big_prime: # if seen add the smallest prime to the list of links of the largest prime
128-
graph_fp[large_primes[4]].append(large_primes[3])
132+
graph_fp[big_p].append(small_p)
133+
134+
parent_fp[small_p] = parent_fp[big_p]
129135

130-
connected_components_fp[node_component_fp[large_primes[4]]].add(large_primes[3])
131-
node_component_fp[large_primes[3]] = node_component_fp[large_primes[4]]
132136
else: # If it has not been seen, append it
133-
graph_fp[large_primes[4]] = [large_primes[3]]
137+
graph_fp[big_p] = [small_p]
134138

135-
connected_components_fp[index_component_fp] = set((large_primes[3], large_primes[4]))
136-
node_component_fp[large_primes[3]] = index_component_fp
137-
node_component_fp[large_primes[4]] = index_component_fp
138-
index_component_fp += 1
139+
parent_fp[small_p] = small_p
140+
parent_fp[big_p] = small_p
139141

140142
# If the smallest prime has already been seen
141143
else:
142-
flag_big_prime = large_primes[4] in graph_fp
144+
flag_big_prime = big_p in graph_fp
143145

144146
# If big prime has not been seen
145147
if not flag_big_prime:
146-
graph_fp[large_primes[3]].append(large_primes[4]) # Append the largest prime to the list of links of the smallest prime
147-
graph_fp[large_primes[4]] = [large_primes[3]] # Create the large prime in the graph
148-
149-
connected_components_fp[node_component_fp[large_primes[3]]].add(large_primes[4])
150-
node_component_fp[large_primes[4]] = node_component_fp[large_primes[3]]
148+
graph_fp[small_p].append(big_p) # Append the largest prime to the list of links of the smallest prime
149+
graph_fp[big_p] = [small_p] # Create the large prime in the graph
151150

151+
parent_fp[big_p] = parent_fp[small_p]
152152

153-
pair[4].append(large_primes[4])
153+
pair[4].append(big_p)
154154
# Find where to insert the partial relation
155-
if large_primes[3] not in fp:
156-
fp[large_primes[3]] = {}
155+
if small_p not in fp:
156+
fp[small_p] = {}
157157

158-
fp[large_primes[3]][large_primes[4]] = pair
158+
fp[small_p][big_p] = pair
159159

160160
size_fp += 1
161161

162162
# If the largest prime has been seen, ie if both primes have already been seen
163163
else:
164-
if node_component_fp[large_primes[3]] != node_component_fp[large_primes[4]]:
165-
graph_fp[large_primes[3]].append(large_primes[4])
166-
graph_fp[large_primes[4]].append(large_primes[3])
167164

168-
connected_components_fp[node_component_fp[large_primes[3]]] = connected_components_fp[node_component_fp[large_primes[3]]].union(connected_components_fp[node_component_fp[large_primes[4]]])
165+
parent_small_p = parent_fp[small_p]
166+
while parent_fp[parent_small_p] != parent_small_p:
167+
parent_fp[parent_small_p], parent_small_p = parent_fp[parent_fp[parent_small_p]], parent_fp[parent_small_p]
169168

170-
for node in connected_components_fp[node_component_fp[large_primes[4]]]:
171-
node_component_fp[node] = node_component_fp[large_primes[3]]
169+
parent_big_p = parent_fp[big_p]
170+
while parent_fp[parent_big_p] != parent_big_p:
171+
parent_fp[parent_big_p], parent_big_p = parent_fp[parent_fp[parent_big_p]], parent_fp[parent_big_p]
172172

173-
pair[4].append(large_primes[4])
173+
if parent_small_p != parent_big_p:
174+
graph_fp[small_p].append(big_p)
175+
graph_fp[big_p].append(small_p)
176+
177+
parent_fp[parent_big_p] = parent_small_p
178+
179+
pair[4].append(big_p)
174180
# Find where to insert the partial relation
175-
if large_primes[3] not in fp:
176-
fp[large_primes[3]] = {}
181+
if small_p not in fp:
182+
fp[small_p] = {}
177183

178-
fp[large_primes[3]][large_primes[4]] = pair
184+
fp[small_p][big_p] = pair
179185

180186
size_fp += 1
181187
else:
182-
path_cycle = find_cycle_fp(graph_fp, large_primes[3:5])
188+
path_cycle = find_cycle_fp(graph_fp, [small_p, big_p])
183189
if len(path_cycle) < 11: cycle_len[len(path_cycle)-2] += 1
184190
else: cycle_len[-1] += 1
185191
combine_fp(pair,pairs_used,fp,path_cycle,divide_leading,g)
186192
partial_found_fp += 1
187193

188-
return pairs_used, fp, graph_fp, size_fp, index_component_fp, cycle_len, full_found, partial_found_fp
194+
return pairs_used, fp, graph_fp, size_fp, parent_fp, cycle_len, full_found, partial_found_fp
189195

190196
def find_cycle_pf(graph, init):
191197
if init[0] == (1, 1): return DFS_pf(graph, init)
@@ -278,7 +284,7 @@ def combine_pf(pair, pairs_used, pf, path, divide_leading, g):
278284

279285
pairs_used.append(tmp)
280286

281-
def handle_large_pf(pair, large_primes, pairs_used, pf, graph_pf, size_pf, connected_components_pf, node_component_pf, index_component_pf, g, divide_leading, cycle_len, full_found, partial_found_pf):
287+
def handle_large_pf(pair, large_primes, pairs_used, pf, graph_pf, size_pf, parent_pf, g, divide_leading, cycle_len, full_found, partial_found_pf):
282288
if large_primes[1] == 1:
283289
tmp = (1, 1) # [smallest_prime, r_smallest]
284290
pair[2] = [tmp]
@@ -303,10 +309,8 @@ def handle_large_pf(pair, large_primes, pairs_used, pf, graph_pf, size_pf, conne
303309
graph_pf[tmp2] = {}
304310
graph_pf[tmp2][tmp[0]] = [tmp]
305311

306-
connected_components_pf[index_component_pf] = set((tmp, tmp2))
307-
node_component_pf[tmp] = index_component_pf
308-
node_component_pf[tmp2] = index_component_pf
309-
index_component_pf += 1
312+
parent_pf[tmp] = tmp
313+
parent_pf[tmp2] = tmp
310314

311315
else:
312316
flag_small_prime = tmp in graph_pf
@@ -329,17 +333,14 @@ def handle_large_pf(pair, large_primes, pairs_used, pf, graph_pf, size_pf, conne
329333
else:
330334
graph_pf[tmp2][tmp[0]] = [tmp]
331335

332-
connected_components_pf[node_component_pf[tmp2]].add(tmp)
333-
node_component_pf[tmp] = node_component_pf[tmp2]
336+
parent_pf[tmp] = tmp2
334337

335338
else: # If it has not been seen, create it in the graph
336339
graph_pf[tmp2] = {}
337340
graph_pf[tmp2][tmp[0]] = [tmp]
338-
339-
connected_components_pf[index_component_pf] = set((tmp, tmp2))
340-
node_component_pf[tmp] = index_component_pf
341-
node_component_pf[tmp2] = index_component_pf
342-
index_component_pf += 1
341+
342+
parent_pf[tmp] = tmp
343+
parent_pf[tmp2] = tmp
343344

344345
# If [smallest_prime, r_smallest] has already be seen
345346
# We look for [largest_prime, r_largest]
@@ -355,8 +356,7 @@ def handle_large_pf(pair, large_primes, pairs_used, pf, graph_pf, size_pf, conne
355356
graph_pf[tmp2] = {}
356357
graph_pf[tmp2][tmp[0]] = [tmp] # Create the large prime in the graph
357358

358-
connected_components_pf[node_component_pf[tmp]].add(tmp2)
359-
node_component_pf[tmp2] = node_component_pf[tmp]
359+
parent_pf[tmp2] = tmp
360360

361361
pair[2].append(tmp2)
362362
# Find where to insert the partial relation
@@ -368,7 +368,15 @@ def handle_large_pf(pair, large_primes, pairs_used, pf, graph_pf, size_pf, conne
368368
size_pf += 1
369369

370370
else:
371-
if node_component_pf[tmp] != node_component_pf[tmp2]:
371+
parent_tmp = parent_pf[tmp]
372+
while parent_pf[parent_tmp] != parent_tmp:
373+
parent_pf[parent_tmp], parent_tmp = parent_pf[parent_pf[parent_tmp]], parent_pf[parent_tmp]
374+
375+
parent_tmp2 = parent_pf[tmp2]
376+
while parent_pf[parent_tmp2] != parent_tmp2:
377+
parent_pf[parent_tmp2], parent_tmp2 = parent_pf[parent_pf[parent_tmp2]], parent_pf[parent_tmp2]
378+
379+
if parent_tmp != parent_tmp2:
372380
if tmp2[0] in graph_pf[tmp]:
373381
graph_pf[tmp][tmp2[0]].append(tmp2)
374382
else:
@@ -379,10 +387,7 @@ def handle_large_pf(pair, large_primes, pairs_used, pf, graph_pf, size_pf, conne
379387
else:
380388
graph_pf[tmp2][tmp[0]] = [tmp]
381389

382-
connected_components_pf[node_component_pf[tmp]] = connected_components_pf[node_component_pf[tmp]].union(connected_components_pf[node_component_pf[tmp2]])
383-
384-
for node in connected_components_pf[node_component_pf[tmp2]]:
385-
node_component_pf[node] = node_component_pf[tmp]
390+
parent_pf[parent_tmp2] = parent_tmp
386391

387392
pair[2].append(tmp2)
388393

@@ -395,10 +400,9 @@ def handle_large_pf(pair, large_primes, pairs_used, pf, graph_pf, size_pf, conne
395400

396401
else:
397402
path_cycle = find_cycle_pf(graph_pf, [tmp, tmp2])
398-
#path_cycle = DFS_pf(graph_pf,[tmp, tmp2])
399403
if len(path_cycle) < 11: cycle_len[len(path_cycle)-2] += 1
400404
else: cycle_len[-1] += 1
401405
combine_pf(pair,pairs_used,pf,path_cycle,divide_leading,g)
402406
partial_found_pf += 1
403407

404-
return pairs_used, pf, graph_pf, size_pf, index_component_pf, cycle_len, full_found, partial_found_pf
408+
return pairs_used, pf, graph_pf, size_pf, parent_pf, cycle_len, full_found, partial_found_pf

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