diff --git a/ASCPU.txt b/ASCPU.txt
new file mode 100644
index 0000000..763c7cb
--- /dev/null
+++ b/ASCPU.txt
@@ -0,0 +1 @@
+AMD Opteron(tm) Processor 3380
diff --git a/CMakeLists.txt b/CMakeLists.txt
index 187be4b..acc2d7d 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -7,6 +7,7 @@ SET(EXECUTABLE_OUTPUT_PATH ${PROJECT_BINARY_DIR}/bin)
SUBDIRS(src test app)
set(CMAKE_CXX_FLAGS "-O9 -Wall")
+#set(CMAKE_CXX_FLAGS "-g -O0 -Wall")
# add a target to generate API documentation with Doxygen
find_package(Doxygen)
diff --git a/TODO b/TODO
index 9d446bb..1a5bd75 100644
--- a/TODO
+++ b/TODO
@@ -12,8 +12,36 @@
+ átállitani integer programozásra az optimalizálást
+ induláskor mérjen le 10-et és az alapján irja ki a várható befejezési időt és a végén meg a teljes futái időt (elég egyet is)
+ grafikonokat készíteni a célfüggvény értékéről illetve a változások arányáról a megtett lépések függvényében
-- tudjon a progi megszakítás után elmentett állapotból folytatni
++ tudjon a progi megszakítás után elmentett állapotból folytatni
++ megnézni, hogy a BKZ_QP1 mennyivel gyorsabb mint a BKZ_XD és kipróbálni, hogy lehet-e csak az első körben XD-t használni a többiben meg QP-t (már egy LLL is szépen lecsökkenti a számokat) - viszont ha ez működik, akkor már biztos benne van az NTL-ben (BKZ-t futtattam és LLL hibaüzenetet kaptam), ha meg nem akkor nem akarok ezzel kockáztatni 3 hónapnyi számitást)
++ hogyan lehet helyesen és statisztikailag relevánsan mérni az időket? (magas dimenzióban nincs sok lehetőség a BKZ-t lemérni úgyhogy halottnak tűnik az ötlet)
++ a timingben darmstadt challange-s latticekkel teszteljen ne pedig cjloss-al (a generátor viszonylag egyszerű NTL-es cuccokat használ), mégsem, magas dimenzióban sokkal jobb ha a konkrét lattice-t kezdi el darálni
++ boundtoolba betenni a darmstadt challange-es alapértelmezett korlátot
++ implementálni a konkrét lattice-s timing-ot
++ boundary kimenetet pontosságát maximumra venni
++ lépésközt állithatóra venni
++ valamelyikbe ellenőrzést implementálni: számolja teljesen végig a pruned enumerationt és dobjon egy grafikonfilet az összehasonlitásról
++ végiggondolni hogyan kell helyesen randomizálni a bázist, kell-e javitani rajta
++ az aritmetikát mindenhol ahol kell átirni RR-re (pl gh számitás gyanús, hogy kelleni fog) (100-as challange-el tesztelni)
++ kis progi ami kigenerálja
+ + full
+ + linear
+ + a schneider
++ boundtoolba új funkció: bemeneti fájlban kapott boundary-ról kiirja a várható időtartamot és a sikeresélyt
++ letesztelni, hogy LLL-XD followed by BKZ-FP blocksize 40 mennyivel gyorsabb mint a BKZ-XD simán... (kezdve valamilyen alacsonyabb blokkmérettel pl 30)
++ összevonni a timing-ot és a preprocesst
+- egy 110 dimenziós boundary-t számolni és összevetni phong-éval (vagy a Schneider félével, mert ebben e dimenzióban mindkettő ugyanaz)
+- átirni a psuccexpet randomra
+- megnézni, hogy az psuccexp-ben jó lambdát adok-e meg neki vagy egyel nagyobbat
+- a verify-ba olyan opciót, hogy csak a predictiont csinálja meg, ne kelljen várni az enumeration-re
+- a végén kiirni az eredmény hermite faktorát (végiggondolni, hogy az utsó sorban valóban a hermite faktorok vannak-e
+- állitható gh approx faktort irni a boundary keresőhöz
+- a boundary generatort kiegésziteni a schnorr- hörnerrel
+
+
+Majd egyszer:
+- a verify programot integrálni az eprune-ba
******** Itt lesz kész az extreme pruning *****
- Megnézni az early termination-ös cikkeket, hogy milyen blokkméretet lenne érdemes használni egy 128 dimenziós bázis előfeldolgozásához
- Megirni a pruningos BKZ-t, enumerationt külön függvénybe tenni
diff --git a/app/CMakeLists.txt b/app/CMakeLists.txt
index 6a57689..bab1b2b 100644
--- a/app/CMakeLists.txt
+++ b/app/CMakeLists.txt
@@ -2,6 +2,8 @@ SET(TARGET1 timing)
SET(TARGET2 boundtool)
SET(TARGET3 genlattice)
SET(TARGET4 eprune)
+SET(TARGET5 verify)
+SET(TARGET6 genbound)
INCLUDE_DIRECTORIES(${PROJECT_SOURCE_DIR}/include)
LINK_DIRECTORIES(${LIBRARY_OUTPUT_PATH})
@@ -16,3 +18,9 @@ TARGET_LINK_LIBRARIES(${TARGET3} cleanbkz ntl)
ADD_EXECUTABLE(${TARGET4} eprune.cpp)
TARGET_LINK_LIBRARIES(${TARGET4} cleanbkz ntl)
+
+ADD_EXECUTABLE(${TARGET5} verify.cpp)
+TARGET_LINK_LIBRARIES(${TARGET5} cleanbkz ntl)
+
+ADD_EXECUTABLE(${TARGET6} genbound.cpp)
+TARGET_LINK_LIBRARIES(${TARGET6} cleanbkz ntl)
diff --git a/app/boundtool.cpp b/app/boundtool.cpp
index 19e0c32..ab81c8f 100644
--- a/app/boundtool.cpp
+++ b/app/boundtool.cpp
@@ -30,7 +30,9 @@
using namespace std;
// Defined in boundary.cpp
-extern double ball_vol(int k, double r);
+extern RR ball_vol_RR(int k, RR r);
+extern void init_factorials(int up_to);
+extern RR RR_PI;
// Defined in tools.cpp
char* get_cmd_option(char** begin, char** end, const string& option);
@@ -40,11 +42,14 @@ bool cmd_option_exists(char** begin, char** end, const string& option);
int main(int argc, char** argv) {
double t_node= 0;
double t_reduc= 0;
- double delta= 1e-1;
unsigned long iterations= 1000;
mat_ZZ basis;
+ int dim;
+ double* boundary;
ZZ v;
v= 0;
+ ZZ delta;
+ delta= 1;
stringstream ss;
char* act_arg;
@@ -56,28 +61,33 @@ int main(int argc, char** argv) {
<< "\t-n n\t\tThe (avarage) time the enumeration algorithm takes to process a single node. (required)" << endl
<< "\t-r n\t\tThe (avarege) running time of the preprocessing reduction algorithm. (required)" << endl
<< "\t-c n\t\tNumber of random changes to make during the numerical optimization. (default: 1000)" << endl
- << "\t-d n\t\tThe size of the single random changes to meke during the optimization. (default: 0.1)" << endl
- << "\t-l n\t\tOptimize for shortest vector with length square root of n. (the Gaussian heuristic is default)" << endl;
+ << "\t-d n\t\tThe size of the single random changes to meke during the optimization. (default: 1)" << endl
+ << "\t-l n\t\tOptimize for shortest vector with length square root of n. (the Gaussian heuristic is default)" << endl
+ << "\t-o n\t\tThe name of the file containing the information about previous computation that has to be continued. Just the -c switch can be used in this case." << endl;
return 0;
}
- if (!cmd_option_exists(argv, argv+argc, "-f")) {
- cout << "Input basis is missing. Run again with -h for help." << endl;
+ if (!cmd_option_exists(argv, argv+argc, "-f") && !cmd_option_exists(argv, argv+argc, "-o")) {
+ cout << "Input basis information is missing. Run again with -h for help." << endl;
return 0;
}
- if (!cmd_option_exists(argv, argv+argc, "-n")) {
+ if (!cmd_option_exists(argv, argv+argc, "-n") && !cmd_option_exists(argv, argv+argc, "-o")) {
cout << "Parameter t_node is missing. Run again with -h for help." << endl;
return 0;
}
- if (!cmd_option_exists(argv, argv+argc, "-r")) {
+ if (!cmd_option_exists(argv, argv+argc, "-r") && !cmd_option_exists(argv, argv+argc, "-o")) {
cout << "Parameter t_reduc is missing. Run again with -h for help." << endl;
return 0;
}
act_arg= get_cmd_option(argv, argv + argc, "-n");
if (act_arg) {
+ if(cmd_option_exists(argv, argv+argc, "-o")){
+ cerr << "ERROR: invalid switch. In the presence of the -o switch the only other switch allowed is the -c" << endl;
+ return 1;
+ }
ss << act_arg;
ss >> t_node;
ss.clear();
@@ -89,6 +99,10 @@ int main(int argc, char** argv) {
act_arg= get_cmd_option(argv, argv + argc, "-r");
if (act_arg) {
+ if(cmd_option_exists(argv, argv+argc, "-o")){
+ cerr << "ERROR: invalid switch. In the presence of the -o switch the only other switch allowed is the -c" << endl;
+ return 1;
+ }
ss << act_arg;
ss >> t_reduc;
ss.clear();
@@ -100,10 +114,14 @@ int main(int argc, char** argv) {
act_arg= get_cmd_option(argv, argv + argc, "-d");
if (act_arg) {
+ if(cmd_option_exists(argv, argv+argc, "-o")){
+ cerr << "ERROR: invalid switch. In the presence of the -o switch the only other switch allowed is the -c" << endl;
+ return 1;
+ }
ss << act_arg;
ss >> delta;
ss.clear();
- if(delta <= 0) {
+ if(delta < 1) {
cerr << "ERROR: invalid delta. The optimization step should be greater than zero. Aborting." << endl;
return 1;
}
@@ -122,6 +140,10 @@ int main(int argc, char** argv) {
act_arg= get_cmd_option(argv, argv + argc, "-l");
if (act_arg) {
+ if(cmd_option_exists(argv, argv+argc, "-o")){
+ cerr << "ERROR: invalid switch. In the presence of the -o switch the only other switch allowed is the -c" << endl;
+ return 1;
+ }
ss << act_arg;
ss >> v;
ss.clear();
@@ -131,9 +153,23 @@ int main(int argc, char** argv) {
}
}
+ act_arg= get_cmd_option(argv, argv + argc, "-o");
+ if (act_arg) {
+ ifstream infile(act_arg);
+ if (infile.is_open()) {
+ continue_boundary_gen(infile, iterations, &boundary, dim);
+ } else {
+ cerr << "ERROR: can't open input file: '" << act_arg << "'. Aborting." << endl;
+ return 1;
+ }
+ }
act_arg= get_cmd_option(argv, argv + argc, "-f");
if (act_arg) {
+ if(cmd_option_exists(argv, argv+argc, "-o")){
+ cerr << "ERROR: invalid switch. In the presence of the -o switch the only other switch allowed is the -c" << endl;
+ return 1;
+ }
ifstream basis_file(act_arg);
if (basis_file.is_open())
basis_file >> basis;
@@ -143,54 +179,64 @@ int main(int argc, char** argv) {
}
}
- mat_RR mu1;
- vec_RR c1;
- ComputeGS(basis,mu1,c1);
-
- //lengths of the GS basis vectors
- RR* c= new RR[mu1.NumRows()];
- for(int i= 0; i < mu1.NumRows(); i++) {
- c[i]= SqrRoot(c1[i]);
- c[i].SetPrecision(RR_PRECISION);
- }
- int dim= mu1.NumRows();
- double* boundary= new double[dim];
-
cout << "# Generated with cleanbkz " << CBKZ_VERSION << endl
<< "# Copyright (C) 2014 Janos Follath" << endl
<< "# This is free software with ABSOLUTELY NO WARRANTY." << endl << "#" << endl;
- //length of the shortest vector in the cjloss lattice
- if(v>0) {
- //v= sqrt(v);
- cout << "# Using supplied lambda square: " << v << endl;
- }
- else {
- double tmp,gh= 1;
- double* gsghs= new double[dim];
+ if(!cmd_option_exists(argv, argv+argc, "-o")){
+ mat_RR mu1;
+ vec_RR c1;
+ ComputeGS(basis,mu1,c1);
+
+ //lengths of the GS basis vectors
+ RR* c= new RR[mu1.NumRows()];
for(int i= 0; i < mu1.NumRows(); i++) {
- conv(tmp, c[i]);
- gh*= tmp;
- gsghs[i]= pow(gh/ball_vol(i+1, 1),1.0/(i+1));
+ c[i].SetPrecision(RR_PRECISION);
+ c[i]= SqrRoot(c1[i]);
+ }
+
+ dim= mu1.NumRows();
+ boundary= new double[dim];
+
+ //length of the shortest vector in the cjloss lattice
+ if(v>0) {
+ //v= sqrt(v);
+ cout << "# Using supplied lambda square: " << v << endl;
+ }
+ else {
+ RR_PI.SetPrecision(RR_PRECISION);
+ RR_PI= ComputePi_RR();
+ init_factorials(2*dim+1);
+ RR one,gh,exp;
+ one.SetPrecision(RR_PRECISION);
+ gh.SetPrecision(RR_PRECISION);
+ exp.SetPrecision(RR_PRECISION);
+ gh= one= 1;
+ for(int i= 0; i < mu1.NumRows(); i++) {
+ gh*= sqrt(c1[i]);
+ }
+ exp= 1.0/dim;
+ pow(gh, gh/ball_vol_RR(dim, one), exp);
+ gh*= 1.05;
+ conv(v, gh*gh);
+ cout << "# No lambda square supplied, using Gaussian heuristic: " << gh << endl;
}
- delete gsghs;
- gh= pow(gh/ball_vol(dim, 1),1.0/dim);
- v= gh*gh;
- cout << "# No lambda square supplied, using Gaussian heuristic: " << v << endl;
- }
+ double p_succ;
+ double t_enum;
+ //NOTE: gs vector lengths and wanted vector length given
+
+ generate_boundary(c, t_node, t_reduc, dim, boundary, v, delta, iterations, p_succ, t_enum, false);
- double p_succ;
- double t_enum;
- //NOTE: gs vector lengths and wanted vector length given
- generate_boundary(c, t_node, t_reduc, dim, boundary, v, delta, iterations, p_succ, t_enum, false);
+ cout << "# basis: '" << act_arg << "' " << endl
+ << "# estimated enumeration time: " << t_enum << endl
+ << "# success probability: " << p_succ << endl;
+ }
- cout << "# basis: '" << act_arg << "' " << endl
- << "# estimated enumeration time: " << t_enum << endl
- << "# success probability: " << p_succ << endl
- << "# boudary function: " << endl;
+ cout << "# boudary function: " << endl;
+
vec_RR out;
out.SetLength(dim);
@@ -198,8 +244,10 @@ int main(int argc, char** argv) {
out[i]= boundary[i];
cout << "# " << out << endl << endl;
- for(int i= 0; i < dim; i++)
- cout << i << " " << boundary[i] << endl;
+ for(int i= 0; i < dim; i++) {
+ out[i].SetOutputPrecision(RR_PRECISION);
+ cout << i << " " << out[i] << endl;
+ }
cout << endl;
return 0;
diff --git a/app/eprune.cpp b/app/eprune.cpp
index c7000fa..7b969a4 100644
--- a/app/eprune.cpp
+++ b/app/eprune.cpp
@@ -33,6 +33,8 @@ extern void enumerate_epr(double** mu, double *b, double* Rvec, int n, vec_RR& r
extern void profile_enumerate_epr(double** mu, double *b, double* Rvec, int n, vec_RR& result);
+// The maximum of the coefficients of the random unimodular matrix
+#define UNIMOD_SIZE 100
mat_ZZ unimod(int dim){
mat_ZZ L, U;
L.SetDims(dim, dim);
@@ -43,8 +45,8 @@ mat_ZZ unimod(int dim){
for(int i= 0; i < dim; i++)
for(int j= i+1; j < dim; j++) {
- U[i][j]= RandomBnd(2);
- L[j][i]= RandomBnd(2);
+ U[i][j]= RandomBnd(UNIMOD_SIZE);
+ L[j][i]= RandomBnd(UNIMOD_SIZE);
}
return L*U;
@@ -60,7 +62,7 @@ int main(int argc, char** argv) {
if (argc==1 || cmd_option_exists(argv, argv+argc, "-h")) {
cout << "This program performs lattice enumeration with extreme pruning:" << endl
<< "\t-h \t\tPrint this help." << endl
- << "\t-v \t\tPerforms a single enumeration round and compares the nodes to the prediction." << endl
+ //<< "\t-v \t\tPerforms a single enumeration round and compares the nodes to the prediction." << endl
<< "\t-l filename\tReads the lattice from the file filename. (This option is mandatory)" << endl
<< "\t-b filename\tReads the boundary function from the file filename. (This option is mandatory)" << endl;
return 0;
@@ -119,7 +121,7 @@ int main(int argc, char** argv) {
double* boundary= new double[basis.NumRows()];
for(int i= 0; i < basis.NumRows(); i++){
conv(boundary[i], bnd[i]);
- boundary[i]*= boundary[i];
+ //boundary[i]*= boundary[i];
}
vec_RR solution;
@@ -147,7 +149,8 @@ int main(int argc, char** argv) {
begin= clock();
basis= basis*unimod(basis.NumRows());
- BKZ_QP1(basis, 0.99, beta);
+ LLL_XD(basis, 0.99);
+ BKZ_FP(basis, 0.99, beta);
ComputeGS(basis,mu1,c1);
@@ -192,7 +195,7 @@ int main(int argc, char** argv) {
for(int i= 0; i< basis.NumRows(); i++)
sqrdLength+= sol[i]*sol[i];
- cout << "Squared length of the shortest vector: " << sqrdLength << endl << endl;
+ cout << "Length of the shortest vector: " << sqrt(sqrdLength) << endl << endl;
cout << "Time spent with enumeration: " << t_all/CLOCKS_PER_SEC << endl;
cout << "Time spent with reduction: " << t_reduc/CLOCKS_PER_SEC << endl;
diff --git a/app/genbound.cpp b/app/genbound.cpp
new file mode 100644
index 0000000..cc98385
--- /dev/null
+++ b/app/genbound.cpp
@@ -0,0 +1,238 @@
+/*
+ Copyright (C) 2014 Janos Follath.
+
+ This file is part of cleanbkz.
+
+ cleanbkz is free software: you can redistribute it and/or modify
+ it under the terms of the GNU General Public License as published by
+ the Free Software Foundation, either version 3 of the License, or
+ (at your option) any later version.
+
+ cleanbkz is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ GNU General Public License for more details.
+
+ You should have received a copy of the GNU General Public License
+ along with cleanbkz. If not, see .
+
+*/
+
+#include
+#include
+#include
+#include
+#include
+#include
+#include
+#include
+
+using namespace std;
+
+// Defined in boundary.cpp
+extern RR ball_vol_RR(int k, RR r);
+extern void init_factorials(int up_to);
+extern RR RR_PI;
+extern RR t_extreme_RR(RR Rvec[], RR b_star_norm[], double t_node, double t_reduc, int n);
+extern RR p_succ(RR Rvec[], int n);
+
+// Defined in tools.cpp
+char* get_cmd_option(char** begin, char** end, const string& option);
+bool cmd_option_exists(char** begin, char** end, const string& option);
+
+
+int main(int argc, char** argv) {
+ mat_ZZ basis;
+ int dim;
+ double* boundary;
+ ZZ R2;
+ R2= 0;
+ double t_node, t_reduc;
+ t_node= t_reduc= 0;
+
+ stringstream ss;
+ char* act_arg;
+
+ if (argc==1 || cmd_option_exists(argv, argv+argc, "-h")) {
+ cout << "This program generates boundary functions for full enumeration, linear pruning and Schneider's polynomial pruning. A preprocessed basis of the lattice is required. Options -f -d and -s are mutually exclusive. Program options:" << endl
+ << "\t-h \t\tPrint this help." << endl
+ << "\t-l n\t\tThe name of the file containing the preprocessed lattice basis. (required)" << endl
+ << "\t-f n\t\tGenerate boundary without pruning" << endl
+ << "\t-d n\t\tGenerate double step linear boundary" << endl
+ << "\t-s n\t\tGenerate Schneiders boundary function (default)" << endl
+ << "\t-n n\t\tThe (avarage) time the enumeration algorithm takes to process a single node. (optional)" << endl
+ << "\t-r n\t\tThe (avarege) running time of the preprocessing reduction algorithm. (optional)" << endl;
+ return 0;
+ }
+
+ act_arg= get_cmd_option(argv, argv + argc, "-n");
+ if (act_arg) {
+ ss << act_arg;
+ ss >> t_node;
+ ss.clear();
+ if(t_node < 0) {
+ cerr << "ERROR: invalid t_node. The running time should be greater than or equal to zero. Aborting." << endl;
+ return 1;
+ }
+ }
+
+ act_arg= get_cmd_option(argv, argv + argc, "-r");
+ if (act_arg) {
+ ss << act_arg;
+ ss >> t_reduc;
+ ss.clear();
+ if(t_reduc < 0) {
+ cerr << "ERROR: invalid t_reduc. The running time should be greater than or equal to zero. Aborting." << endl;
+ return 1;
+ }
+ }
+
+ if (!cmd_option_exists(argv, argv+argc, "-l")) {
+ cout << "Input basis information is missing. Run again with -h for help." << endl;
+ return 0;
+ }
+
+ if ((cmd_option_exists(argv, argv+argc, "-s") && cmd_option_exists(argv, argv+argc, "-d")) || (cmd_option_exists(argv, argv+argc, "-s") && cmd_option_exists(argv, argv+argc, "-f")) || (cmd_option_exists(argv, argv+argc, "-f") && cmd_option_exists(argv, argv+argc, "-d")) ) {
+ cout << "Options -f -d and -s are mutually exclusive. Run again with -h for help." << endl;
+ return 0;
+ }
+
+ act_arg= get_cmd_option(argv, argv + argc, "-l");
+ if (act_arg) {
+ ifstream basis_file(act_arg);
+ if (basis_file.is_open())
+ basis_file >> basis;
+ else {
+ cerr << "ERROR: can't open input file: '" << act_arg << "'. Aborting." << endl;
+ return 1;
+ }
+ }
+
+
+ cout << "# Generated with cleanbkz " << CBKZ_VERSION << endl
+ << "# Copyright (C) 2014 Janos Follath" << endl
+ << "# This is free software with ABSOLUTELY NO WARRANTY." << endl << "#" << endl;
+
+ mat_RR mu1;
+ vec_RR c1;
+ ComputeGS(basis,mu1,c1);
+
+ //lengths of the GS basis vectors
+ RR* c= new RR[mu1.NumRows()];
+ for(int i= 0; i < mu1.NumRows(); i++) {
+ c[i].SetPrecision(RR_PRECISION);
+ c[i]= SqrRoot(c1[i]);
+ }
+
+ dim= mu1.NumRows();
+ //dim=110;
+ boundary= new double[dim];
+
+ RR_PI.SetPrecision(RR_PRECISION);
+ RR_PI= ComputePi_RR();
+ init_factorials(2*dim+1);
+ RR one,gh,exp;
+ one.SetPrecision(RR_PRECISION);
+ gh.SetPrecision(RR_PRECISION);
+ exp.SetPrecision(RR_PRECISION);
+ gh= one= 1;
+ for(int i= 0; i < mu1.NumRows(); i++) {
+ gh*= sqrt(c1[i]);
+ }
+ exp= 1.0/dim;
+ pow(gh, gh/ball_vol_RR(dim, one), exp);
+ gh*= 1.05;
+ conv(R2, gh*gh);
+ cout << "# Using Darmstadt bound (Gaussian heuristic times 1.05): " << gh << endl;
+ cout << "# basis: '" << act_arg << "' " << endl;
+
+ if(cmd_option_exists(argv, argv+argc, "-f")) {
+ ZZ* act= new ZZ[dim];
+ act[0]= act[1]= (2*R2)/dim;
+ for(int i= 2; i < dim; i+=2) {
+ act[i]= act[i+1]= act[i-1]+act[0];
+ //cout << act[i] << endl;
+ }
+ act[dim-1]= R2;
+ if(dim%2==0)
+ act[dim-2]= R2;
+
+ for(int i= 0; i < dim; i++)
+ conv(boundary[i],act[i]);
+ } else if (cmd_option_exists(argv, argv+argc, "-d")) {
+ for(int i= 0; i < dim; i++)
+ conv(boundary[i],R2);
+ } else {
+ /*double coeffs[]= {9.1e-4, 4e-2, -4e-3, 2.3e-4, -6.9e-6, 1.21e-7, -1.2e-9, 6.2e-12, -1.29e-14};
+ for(int i= 1; i<=dim; i++) {
+ boundary[i-1]= 0;
+ for(int j= 0; j<=8; j++)
+ //boundary[i-1]+= pow(i*110/dim,j)*coeffs[j];
+ boundary[i-1]+= pow(1.0*i/dim,j)*coeffs[j];
+ //boundary[i-1]*=110/dim;*/
+ double div = (double) dim;
+ double y,scale;
+ conv(scale,R2);
+ for (double x = 1; x<=dim; x+=1){
+ y = x/div;
+ boundary[int(x)] = min( -276.919520419850*pow(y,8) \
+ +1208.33321732860 *pow(y,7) \
+ -2128.79627565000 *pow(y,6) \
+ +1952.22801180000 *pow(y,5) \
+ -1012.11476080000 *pow(y,4) \
+ + 305.211610000000*pow(y,3) \
+ - 51.347076000000*pow(y,2) \
+ + 4.408932000000*pow(y,1) \
+ + 0.000914465000, 1.0);
+ boundary[int(x)]*= scale;
+ }
+
+ for(int i= 0; i< dim; i+=2)
+ boundary[i]= boundary[i+1]= floor(boundary[i+1]);
+
+ for(int i= 1; i< dim-1; i+=2)
+ if(boundary[i]>boundary[i+1])
+ for(int j= i; j >= 0; j--)
+ if(boundary[j] > boundary[i+1])
+ boundary[j]= boundary[i+1];
+
+
+
+ }
+
+ RR* act= new RR[dim];
+ for(int i= 0; i< dim; i++)
+ conv(act[i],boundary[i]);
+
+ RR p_succ_r;
+ RR t_enum;
+ if((t_node!=0)&&(t_reduc!=0))
+ t_enum= t_extreme_RR(act, c, t_node, t_reduc, dim);
+
+
+ RR* mod_f= new RR[dim];
+ for(int j= 0; j < dim; j++) {
+ conv(mod_f[j], act[j]);
+ mod_f[j]= sqrt(mod_f[j]);
+ }
+ p_succ_r= p_succ(mod_f, dim);
+
+ cout << "# estimated enumeration time: " << t_enum << endl;
+ cout << "# success probability: " << p_succ_r << endl;
+ cout << "# boudary function: " << endl;
+
+
+ vec_RR out;
+ out.SetLength(dim);
+ for(int i= 0; i < dim; i++)
+ out[i]= boundary[i];
+ cout << "# " << out << endl << endl;
+
+ for(int i= 0; i < dim; i++) {
+ out[i].SetOutputPrecision(RR_PRECISION);
+ cout << i << " " << out[i] << endl;
+ }
+ cout << endl;
+
+ return 0;
+}
diff --git a/app/genlattice.cpp b/app/genlattice.cpp
index a50ff55..f25b56c 100644
--- a/app/genlattice.cpp
+++ b/app/genlattice.cpp
@@ -19,6 +19,7 @@
*/
#include
+#include
#include
#include
#include
@@ -28,7 +29,15 @@
using namespace std;
-//TODO: refaktorálni a paraméterfeldolgozást: csinálni hozzá int és double változatot, hibaüzenetekkel és kivételkezeléssel
+// Defined in boundary.cpp
+extern RR ball_vol_RR(int k, RR r);
+extern void init_factorials(int up_to);
+extern RR RR_PI;
+extern void enumerate_epr(double** mu, double *b, double* Rvec, int n, vec_RR& result,
+ unsigned long &termination, double &time);
+
+
+void measure_epr(mat_ZZ& basis, int beta, unsigned long termination, double& t_node, double& t_reduc);
void gen_randlat(mat_ZZ& basis, ZZ determinant, int dim) {
basis.SetDims(dim, dim);
@@ -62,16 +71,18 @@ int main(int argc, char** argv) {
<< "\t-m n\t\tGenerates a random lattice with entries of length at most n. It is ignored when -c is given." << endl
<< "\t-h \t\tPrint this help." << endl
<< "\t-s n\t\tUse n as the seed of the pseudorandom generator." << endl
+ << "\t-p filename\tPreprocess an existing lattice basis" << endl
+ << "\t-t \t\tMeasure and output enumeration timing information" << endl
<< "\t-k n\t\tReduces the generated basis with blocksize of n." << endl;
return 0;
}
- if (!cmd_option_exists(argv, argv+argc, "-d")) {
+ if (!cmd_option_exists(argv, argv+argc, "-d") && !cmd_option_exists(argv, argv+argc, "-p")) {
cout << "Lattice dimension is missing. Run again with -h for help." << endl;
return 0;
}
- if (!cmd_option_exists(argv, argv+argc, "-m") && !cmd_option_exists(argv, argv+argc, "-c")) {
+ if (!cmd_option_exists(argv, argv+argc, "-m") && !cmd_option_exists(argv, argv+argc, "-c") && !cmd_option_exists(argv, argv+argc, "-p")) {
cout << "ERROR: neither maximum size of entries nor density is provided. Aborting." << endl;
return 0;
}
@@ -161,11 +172,100 @@ int main(int argc, char** argv) {
GenPrime(determinant,maxsize);
gen_randlat(m,determinant,dim);
}
+ else if (cmd_option_exists(argv, argv+argc, "-p")) {
+ act_arg= get_cmd_option(argv, argv + argc, "-p");
+ ifstream basis_file(act_arg);
+ if (basis_file.is_open())
+ basis_file >> m;
+ else {
+ cerr << "ERROR: can't open input file: '" << act_arg << "'. Aborting." << endl;
+ return 1;
+ }
+ }
- if(beta > 1 && !(cmd_option_exists(argv, argv+argc, "-c")))
- BKZ_QP1(m, 0.99, beta);
+ double t_node, t_reduc;
+ if(beta > 1 && !(cmd_option_exists(argv, argv+argc, "-c"))) {
+
+ if(cmd_option_exists(argv, argv+argc, "-t")) {
+ measure_epr(m, beta, 10000000, t_node, t_reduc);
+ }else{
+ LLL_XD(m, 0.99);
+ BKZ_FP(m, 0.99, beta);
+ }
+ }
- cout << m << endl << beta;
+ cout << m << endl << beta << endl;
+ if(cmd_option_exists(argv, argv+argc, "-t")) {
+ cout << t_node << endl;
+ cout << t_reduc << endl;
+ }
return 0;
}
+
+void measure_epr(mat_ZZ& basis, int beta, unsigned long termination, double& t_node, double& t_reduc) {
+ double enu_time= 0;
+ mat_RR mu1;
+ vec_RR c1;
+ clock_t begin, end;
+ vec_RR result;
+ unsigned long nodes;
+
+ t_node= t_reduc= 0;
+
+ int dimension= basis.NumRows();
+
+ double** mu= new double*[dimension];
+ for(int i= 0; i < dimension; i++)
+ mu[i]= new double[dimension];
+
+ double* c= new double[dimension];
+
+ begin= clock();
+ LLL_XD(basis, 0.99);
+ BKZ_FP(basis, 0.99, beta);
+ end= clock();
+
+ ComputeGS(basis,mu1,c1);
+
+ for(int i= 0; i < dimension; i++)
+ for(int j= 0; j < dimension; j++)
+ conv(mu[i][j], mu1[i][j]);
+
+ for(int i= 0; i < dimension; i++)
+ conv(c[i], c1[i]);
+
+
+ RR_PI.SetPrecision(RR_PRECISION);
+ RR_PI= ComputePi_RR();
+ init_factorials(2*dimension+1);
+ RR one,gh,exp;
+ one.SetPrecision(RR_PRECISION);
+ gh.SetPrecision(RR_PRECISION);
+ exp.SetPrecision(RR_PRECISION);
+ gh= one= 1;
+ for(int i= 0; i < mu1.NumRows(); i++) {
+ gh*= sqrt(c1[i]);
+ }
+ exp= 1.0/dimension;
+ pow(gh, gh/ball_vol_RR(dimension, one), exp);
+ gh*= 1.05;
+
+ //cout << "Using Darmstadt bound: " << gh << endl;
+
+ double* Rvec= new double[dimension];
+ for(int i= 0; i < dimension; i++)
+ conv(Rvec[i], gh*gh);
+
+ t_reduc= (double)(end - begin) / CLOCKS_PER_SEC;
+ nodes= termination;
+ enumerate_epr(mu, c, Rvec, dimension, result, nodes, enu_time);
+
+ /*if(enu_time < 1.0/CLOCKS_PER_SEC/termination)
+ cerr << "Warning! Zero enumeration time!" << endl;
+ else if (nodes!=0)
+ cerr << "Warning! Nodes traversed: " << (termination-nodes) << endl;*/
+ t_node= enu_time;
+
+}
+
diff --git a/app/timing.cpp b/app/timing.cpp
index 755f1d7..f123906 100644
--- a/app/timing.cpp
+++ b/app/timing.cpp
@@ -19,10 +19,12 @@
*/
#include
+#include
#include
#include
#include
#include
+#include
#include
#include
@@ -34,6 +36,13 @@ using namespace NTL;
void measure_epr(int dimension, int beta, unsigned long samples, unsigned long termination,
double& t_node, double& t_reduc, unsigned long& zeroes, unsigned long& bias);
+void measure_epr(mat_ZZ basis, int beta, unsigned long termination, double& t_node, double& t_reduc);
+
+// Defined in boundary.cpp
+extern RR ball_vol_RR(int k, RR r);
+extern void init_factorials(int up_to);
+extern RR RR_PI;
+
int main(int argc, char** argv) {
int dimension= 0;
int bkz_blocksize= 2;
@@ -48,6 +57,7 @@ int main(int argc, char** argv) {
if (argc==1 || cmd_option_exists(argv, argv+argc, "-h")) {
cout << "This program uses cjloss lattices to measure the parameters t_node and t_reduc required for the computation of boundary functions. These are the running time of the enumeration and reduction algorithms on the current platform (in the case the cjloss lattices the dimension of the preprocessing is one higher than the enumeration). Program options:" << endl
<< "\t-h \t\tPrint this help." << endl
+ << "\t-l filename\tPerform tests on the given lattice. (no other switch is allowed just the -b and the -k)" << endl
<< "\t-d n\t\tMeasure running times in dimension n." << endl
<< "\t-s n\t\tStart the measurements in dimension n. It is ignored when -d is given." << endl
<< "\t-e n\t\tContinue measuring in all dimensions until dimension n with a step five. It is ignored when -d is given." << endl
@@ -72,6 +82,10 @@ int main(int argc, char** argv) {
act_arg= get_cmd_option(argv, argv + argc, "-d");
if (act_arg) {
+ if(cmd_option_exists(argv, argv+argc, "-l")){
+ cerr << "ERROR: invalid switch. In the presence of the -l switch the only other switch allowed is the -b and the -k" << endl;
+ return 1;
+ }
ss << act_arg;
ss >> dimension;
ss.clear();
@@ -83,6 +97,10 @@ int main(int argc, char** argv) {
act_arg= get_cmd_option(argv, argv + argc, "-n");
if (act_arg) {
+ if(cmd_option_exists(argv, argv+argc, "-l")){
+ cerr << "ERROR: invalid switch. In the presence of the -l switch the only other switch allowed is the -b and the -k" << endl;
+ return 1;
+ }
ss << act_arg;
ss >> samples;
ss.clear();
@@ -105,6 +123,10 @@ int main(int argc, char** argv) {
act_arg= get_cmd_option(argv, argv + argc, "-s");
if (act_arg) {
+ if(cmd_option_exists(argv, argv+argc, "-l")){
+ cerr << "ERROR: invalid switch. In the presence of the -l switch the only other switch allowed is the -b and the -k" << endl;
+ return 1;
+ }
ss << act_arg;
ss >> start;
ss.clear();
@@ -116,6 +138,10 @@ int main(int argc, char** argv) {
act_arg= get_cmd_option(argv, argv + argc, "-e");
if (act_arg) {
+ if(cmd_option_exists(argv, argv+argc, "-l")){
+ cerr << "ERROR: invalid switch. In the presence of the -l switch the only other switch allowed is the -b and the -k" << endl;
+ return 1;
+ }
ss << act_arg;
ss >> end;
ss.clear();
@@ -125,6 +151,18 @@ int main(int argc, char** argv) {
}
}
+ mat_ZZ basis;
+ act_arg= get_cmd_option(argv, argv + argc, "-l");
+ if (act_arg) {
+ ifstream basis_file(act_arg);
+ if (basis_file.is_open())
+ basis_file >> basis;
+ else {
+ cerr << "ERROR: can't open input file: '" << act_arg << "'. Aborting." << endl;
+ return 1;
+ }
+ }
+
cout << "cleanbkz " << CBKZ_VERSION << endl
<< "Copyright (C) 2014 Janos Follath" << endl
<< "This is free software with ABSOLUTELY NO WARRANTY." << endl << endl;
@@ -145,8 +183,14 @@ int main(int argc, char** argv) {
cout << "t_node= " << t_node << endl;
cout << "t_reduc= " << t_reduc << endl;
cout << "biased/zeroes: " << bias << "/" << zeroes << endl << endl;
- }
- else {
+ } else if(cmd_option_exists(argv, argv+argc, "-l")){
+ cout << "Measuring timing for: " << get_cmd_option(argv, argv + argc, "-l") << endl;
+
+ measure_epr(basis, bkz_blocksize, nodes, t_node, t_reduc);
+
+ cout << "t_node= " << t_node << endl;
+ cout << "t_reduc= " << t_reduc << endl;
+ } else {
if (cmd_option_exists(argv, argv+argc, "-t")) {
unsigned long int total= 0;
for(int i= start; i <= end; i+=5) {
@@ -168,11 +212,11 @@ int main(int argc, char** argv) {
cout << "t_reduc= " << t_reduc << endl;
cout << "biased/zeroes: " << bias << "/" << zeroes << endl << endl;
}
- }
- cout << "(Sometimes the enumeration doesn't have to inspect the prescribed number of nodes or even nodes enough "
+ cout << "(Sometimes the enumeration doesn't have to inspect the prescribed number of nodes or even nodes enough "
<< "to make the runing time measureable, the number of these cases are in the \"biased/zeroes\" line."
<< "The first number measures only the biased cases with nonzero running time.)" << endl << endl;
+ }
return 0;
}
@@ -209,7 +253,8 @@ void measure_epr(int dimension, int beta, unsigned long samples, unsigned long t
tmp= lattice->get_basis(0);
begin= clock();
- BKZ_QP1(tmp, 0.99, beta);
+ LLL_XD(tmp, 0.99);
+ BKZ_FP(tmp, 0.99, beta);
end= clock();
t_reduc+= (double)(end - begin) / CLOCKS_PER_SEC;
@@ -243,3 +288,69 @@ void measure_epr(int dimension, int beta, unsigned long samples, unsigned long t
t_reduc/= samples;
}
+void measure_epr(mat_ZZ basis, int beta, unsigned long termination, double& t_node, double& t_reduc) {
+ double enu_time= 0;
+ mat_RR mu1;
+ vec_RR c1;
+ clock_t begin, end;
+ vec_RR result;
+ unsigned long nodes;
+
+ t_node= t_reduc= 0;
+
+ int dimension= basis.NumRows();
+
+ double** mu= new double*[dimension];
+ for(int i= 0; i < dimension; i++)
+ mu[i]= new double[dimension];
+
+ double* c= new double[dimension];
+
+ begin= clock();
+ LLL_XD(basis, 0.99);
+ BKZ_FP(basis, 0.99, beta);
+ end= clock();
+
+ ComputeGS(basis,mu1,c1);
+
+ for(int i= 0; i < dimension; i++)
+ for(int j= 0; j < dimension; j++)
+ conv(mu[i][j], mu1[i][j]);
+
+ for(int i= 0; i < dimension; i++)
+ conv(c[i], c1[i]);
+
+
+ RR_PI.SetPrecision(RR_PRECISION);
+ RR_PI= ComputePi_RR();
+ init_factorials(2*dimension+1);
+ RR one,gh,exp;
+ one.SetPrecision(RR_PRECISION);
+ gh.SetPrecision(RR_PRECISION);
+ exp.SetPrecision(RR_PRECISION);
+ gh= one= 1;
+ for(int i= 0; i < mu1.NumRows(); i++) {
+ gh*= sqrt(c1[i]);
+ }
+ exp= 1.0/dimension;
+ pow(gh, gh/ball_vol_RR(dimension, one), exp);
+ gh*= 1.05;
+
+ cout << "Using Darmstadt bound: " << gh << endl;
+
+ double* Rvec= new double[dimension];
+ for(int i= 0; i < dimension; i++)
+ conv(Rvec[i], gh*gh);
+
+ t_reduc= (double)(end - begin) / CLOCKS_PER_SEC;
+ nodes= termination;
+ enumerate_epr(mu, c, Rvec, dimension, result, nodes, enu_time);
+
+ if(enu_time < 1.0/CLOCKS_PER_SEC/termination)
+ cerr << "Warning! Zero enumeration time!" << endl;
+ else if (nodes!=0)
+ cerr << "Warning! Nodes traversed: " << (termination-nodes) << endl;
+ t_node= enu_time;
+
+}
+
diff --git a/app/verify.cpp b/app/verify.cpp
new file mode 100644
index 0000000..cf7cd2d
--- /dev/null
+++ b/app/verify.cpp
@@ -0,0 +1,128 @@
+/*
+ Copyright (C) 2014 Janos Follath.
+
+ This file is part of cleanbkz.
+
+ cleanbkz is free software: you can redistribute it and/or modify
+ it under the terms of the GNU General Public License as published by
+ the Free Software Foundation, either version 3 of the License, or
+ (at your option) any later version.
+
+ cleanbkz is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ GNU General Public License for more details.
+
+ You should have received a copy of the GNU General Public License
+ along with cleanbkz. If not, see .
+
+*/
+
+#define MIN(X,Y) ((X) < (Y) ? (X) : (Y))
+
+#include
+#include
+#include
+#include
+#include
+#include
+#include
+#include
+
+using namespace std;
+
+extern void init_factorials(int);
+
+extern void predict_nodes_RR(RR Rvec[], double b_star_norm[], int n);
+
+extern double ball_vol(int k, double r);
+
+extern void profile_enumerate_epr(double** mu, double *b, double* Rvec, int n, vec_RR& result);
+
+void gen_randlat(mat_ZZ& basis, ZZ determinant, int dim);
+
+int main(int argc, char** argv) {
+ int dim;
+ mat_ZZ basis;
+ vec_ZZ boundary;
+ char* act_arg;
+
+ if (argc==1 || cmd_option_exists(argv, argv+argc, "-h")) {
+ cout << "This program verifies the node prediction." << endl
+ << "\t-h \t\tPrint this help." << endl
+ << "\t-l n\t\tThe name of the file containing the preprocessed lattice basis. (required)" << endl
+ << "\t-b n\t\tThe name of the file containing the boundary function. (required)" << endl;
+ return 0;
+ }
+
+ act_arg= get_cmd_option(argv, argv + argc, "-b");
+ if (act_arg) {
+ ifstream basis_file(act_arg);
+ if (basis_file.is_open()) {
+ basis_file >> boundary;
+ cout << "# Bounding function: " << endl << "# " << boundary << endl;
+ } else {
+ cerr << "ERROR: can't open input file: '" << act_arg << "'. Aborting." << endl;
+ return 1;
+ }
+ }
+
+ act_arg= get_cmd_option(argv, argv + argc, "-l");
+ if (act_arg) {
+ ifstream basis_file(act_arg);
+ if (basis_file.is_open()){
+ basis_file >> basis;
+ } else {
+ cerr << "ERROR: can't open input file: '" << act_arg << "'. Aborting." << endl;
+ return 1;
+ }
+ }
+
+ dim= basis.NumRows();
+
+ mat_RR mu1;
+ vec_RR c1;
+ ComputeGS(basis,mu1,c1);
+
+ double* c= new double[mu1.NumRows()];
+ for(int i= 0; i < mu1.NumRows(); i++)
+ conv(c[i], c1[i]);
+
+
+ double** mu= new double*[mu1.NumRows()];
+ for(int i= 0; i < mu1.NumRows(); i++)
+ mu[i]= new double[mu1.NumCols()];
+ for(int i= 0; i < mu1.NumRows(); i++)
+ for(int j= 0; j < mu1.NumCols(); j++)
+ conv(mu[i][j], mu1[i][j]);
+
+// Gaussian heuristic
+ double gh= 1;
+ for(int i= 0; i < mu1.NumRows(); i++)
+ gh*= sqrt(c[i]);
+ gh= 1.05* pow(gh/ball_vol(dim, 1),1.0/dim);
+ cout << "# Darmstadt bound: " << gh << endl;
+
+// Enumeration
+ double* act= new double[dim];
+ for(int i= 0; i data/svpchallengedim80seed0red20.lat
+./bin/timing -l data/svpchallengedim80seed0.lat -k 20
+./bin/boundtool -f data/svpchallengedim80seed0red20.lat -n 8e-08 -r 9.74 -c 300 -d 100000
+
+
diff --git a/debug.sh b/debug.sh
index 4ec444e..15d64dc 100755
--- a/debug.sh
+++ b/debug.sh
@@ -5,8 +5,8 @@ extension="${filename##*.}"
filename="${filename%.*}"
# gnuplot -p -e "set terminal pdf;set output '$filename.pdf';unset key;set yrange [0:*];plot '$1'"
-gnuplot -p -e "set terminal pdf;set output '$filename.pdf';set yrange [0:*]; plot '$1' i 0 u 1:2 w lines title columnheader(1), '$1' i 1 u 1:2 w lines title columnheader(1)"
-#gnuplot -p -e "set terminal pdf;set output '$filename.pdf';set yrange [1:*];set logscale y; plot '$1' i 0 u 1:2 w dots title columnheader(1), '$1' i 1 u 1:2 w dots title columnheader(1)"
+#gnuplot -p -e "set terminal pdf;set output '$filename.pdf';set yrange [0:*]; plot '$1' i 0 u 1:2 w lines title columnheader(1), '$1' i 1 u 1:2 w lines title columnheader(1)"
+gnuplot -p -e "set terminal pdf;set output '$filename.pdf';set yrange [1:*];set logscale y; plot '$1' i 0 u 1:2 w dots title columnheader(1), '$1' i 1 u 1:2 w dots title columnheader(1)"
#gnuplot -p -e "set terminal pdf;set output '$filename.pdf';set yrange [1:*];set logscale y; plot '$1' i 0 u 1:2 w dots title columnheader(1), '$1' i 1 u 1:2 w dots title columnheader(1)"
#gnuplot -p -e "set terminal pdf;set output '$filename.pdf';set yrange [1:1.21e+24];set logscale y; set ytics(1.02e+03,1.05e+06,1.07e+09,1.1e+12,1.13e+15,1.15e+18,1.18e+21,1.21e+24);plot '$1' i 0 u 1:2 title columnheader(1)"
#gnuplot -p -e "set terminal pdf;set output '$filename.pdf';set yrange [1:*];set logscale y; plot '$1' i 0 u 1:2 w dots title columnheader(1), '$1' i 1 u 1:2 w dots title columnheader(1), '$1' i 2 u 1:2 w dots title columnheader(1)"
diff --git a/include/cleanbkz/boundary.hpp b/include/cleanbkz/boundary.hpp
index 16153de..8bf46fe 100644
--- a/include/cleanbkz/boundary.hpp
+++ b/include/cleanbkz/boundary.hpp
@@ -55,11 +55,19 @@ void generate_boundary(
int n, //!< The dimension of the lattice
double Rvec[], //!< Container with enough space reserved for the result (n double values)
NTL::ZZ R, //!< The square length of the vector the enumeration is looking for
- double delta, //!< The step of the random modifications
+ ZZ delta, //!< The step of the random modifications
unsigned long iterations, //!< The number of random modifications to test
double& p_succ, //!< Container for the success probability of the resulting function
double& t_enum, //!< Container for the estimated running time of the resulting function
bool quiet //!< Set this false if you do not want this function to print on the standard output
);
+/** Continues a previously started boundary function optimization for enumeration with extreme pruning. Uses numerical optimization with random changes as briefly explained in: Nicolas Gama, Phong Q. Nguyen and Oded Regev "Lattice Enumeration using Extreme Pruning", Advances in Cryptology – EUROCRYPT 2010 Lecture Notes in Computer Science Volume 6110, 2010, pp 257-278. */
+void continue_boundary_gen(
+ std::ifstream& infile, //!< Reference to the input file stream containing the information about the previous computation
+ unsigned long iterations, //!< The number of random modifications to test
+ double** Rvec, //!< This parameter will hold the result
+ int& dim //!< This parameter will hold the length of the result
+ );
+
#endif
diff --git a/newCPU.txt b/newCPU.txt
new file mode 100644
index 0000000..023aa48
--- /dev/null
+++ b/newCPU.txt
@@ -0,0 +1,17 @@
+http://www.cpubenchmark.net/high_end_cpus.html
+Intel Core i7-4790K @ 4.00GHz - 300USD (11,290)
+Intel Core i7-5820K @ 3.30GHz - 375USD (12,952)
+Intel Core i7-5930K @ 3.50GHz - 550USD (13,493)
+
+Intel Xeon E5-1650 v2 @ 3.20GHz - 560USD (12,495)
+
+
+----------------------------------------------------------------------------
+Xeon vs i7
+
+The current line of Xeons are based on the same architecture as the i7. The difference is usually that the Xeons are the cream of the crop. They run cooler and at lower voltages and are spec'd for 24/7 continuous usage. Otherwise, performance is usually identical. Xeons are able to be used in multi-socket motherboards, where i7s are not (which is why the Mac Pros use them).
+
+Xeons are also usually the first to be updated. There are 6-core Xeons, but not i7s yet, though they are still based on the same architecture.
+
+The additional reliability of the Xeons is very important in servers, especially rackmount and blade-enclosed servers where the lower heat dissipation and power consumption are essential. These benefits usually don't mean too much to all but the most extreme overclockers though, so people in the desktop segment usually ignore it due to the enormous difference in the price of both the CPU and the motherboards needed to support them.
+
diff --git a/plot_boundary.sh b/plot_boundary.sh
new file mode 100755
index 0000000..cd35f8d
--- /dev/null
+++ b/plot_boundary.sh
@@ -0,0 +1,7 @@
+#!/bin/sh
+
+filename=$(basename "$1")
+extension="${filename##*.}"
+filename="${filename%.*}"
+
+gnuplot -p -e "set terminal pdf;set output '$filename.pdf';unset key;set yrange [0:*];plot '$1'"
diff --git a/plot_nodes.sh b/plot_nodes.sh
new file mode 100755
index 0000000..15d64dc
--- /dev/null
+++ b/plot_nodes.sh
@@ -0,0 +1,12 @@
+#!/bin/sh
+
+filename=$(basename "$1")
+extension="${filename##*.}"
+filename="${filename%.*}"
+
+# gnuplot -p -e "set terminal pdf;set output '$filename.pdf';unset key;set yrange [0:*];plot '$1'"
+#gnuplot -p -e "set terminal pdf;set output '$filename.pdf';set yrange [0:*]; plot '$1' i 0 u 1:2 w lines title columnheader(1), '$1' i 1 u 1:2 w lines title columnheader(1)"
+gnuplot -p -e "set terminal pdf;set output '$filename.pdf';set yrange [1:*];set logscale y; plot '$1' i 0 u 1:2 w dots title columnheader(1), '$1' i 1 u 1:2 w dots title columnheader(1)"
+#gnuplot -p -e "set terminal pdf;set output '$filename.pdf';set yrange [1:*];set logscale y; plot '$1' i 0 u 1:2 w dots title columnheader(1), '$1' i 1 u 1:2 w dots title columnheader(1)"
+#gnuplot -p -e "set terminal pdf;set output '$filename.pdf';set yrange [1:1.21e+24];set logscale y; set ytics(1.02e+03,1.05e+06,1.07e+09,1.1e+12,1.13e+15,1.15e+18,1.18e+21,1.21e+24);plot '$1' i 0 u 1:2 title columnheader(1)"
+#gnuplot -p -e "set terminal pdf;set output '$filename.pdf';set yrange [1:*];set logscale y; plot '$1' i 0 u 1:2 w dots title columnheader(1), '$1' i 1 u 1:2 w dots title columnheader(1), '$1' i 2 u 1:2 w dots title columnheader(1)"
diff --git a/plot_progress.sh b/plot_progress.sh
new file mode 100755
index 0000000..4ec444e
--- /dev/null
+++ b/plot_progress.sh
@@ -0,0 +1,12 @@
+#!/bin/sh
+
+filename=$(basename "$1")
+extension="${filename##*.}"
+filename="${filename%.*}"
+
+# gnuplot -p -e "set terminal pdf;set output '$filename.pdf';unset key;set yrange [0:*];plot '$1'"
+gnuplot -p -e "set terminal pdf;set output '$filename.pdf';set yrange [0:*]; plot '$1' i 0 u 1:2 w lines title columnheader(1), '$1' i 1 u 1:2 w lines title columnheader(1)"
+#gnuplot -p -e "set terminal pdf;set output '$filename.pdf';set yrange [1:*];set logscale y; plot '$1' i 0 u 1:2 w dots title columnheader(1), '$1' i 1 u 1:2 w dots title columnheader(1)"
+#gnuplot -p -e "set terminal pdf;set output '$filename.pdf';set yrange [1:*];set logscale y; plot '$1' i 0 u 1:2 w dots title columnheader(1), '$1' i 1 u 1:2 w dots title columnheader(1)"
+#gnuplot -p -e "set terminal pdf;set output '$filename.pdf';set yrange [1:1.21e+24];set logscale y; set ytics(1.02e+03,1.05e+06,1.07e+09,1.1e+12,1.13e+15,1.15e+18,1.18e+21,1.21e+24);plot '$1' i 0 u 1:2 title columnheader(1)"
+#gnuplot -p -e "set terminal pdf;set output '$filename.pdf';set yrange [1:*];set logscale y; plot '$1' i 0 u 1:2 w dots title columnheader(1), '$1' i 1 u 1:2 w dots title columnheader(1), '$1' i 2 u 1:2 w dots title columnheader(1)"
diff --git a/ratio.tmp b/ratio.tmp
index 745bc2e..0f219c0 100644
--- a/ratio.tmp
+++ b/ratio.tmp
@@ -1 +1 @@
-2 13 69 339 1355 4788 14545 39469 95677 201819 412763 819609 1676146 3101275 4998689 7436042 10740473 13423824 15591263 17141409 17619306 16238926 14688734 12495592 10446876 8711786 6795375 4899701 3329245 2157371 1343679 742077 440010 256421 137334 66845 29540 12577 5305 1978 720 304 100 27 13 5 2 2 2 2
\ No newline at end of file
+3 8 30 98 271 652 1702 3832 9545 19088 33302 53278 75818 103773 188586 269434 343133 404652 695414 945785 1088151 1106141 1421885 1506474 2250998 2514364 2403021 2154305 2633790 2476946 3421878 3800470 4588395 4574138 5128969 4479082 5593639 5394202 6790987 6764986 7350251 6177154 6524585 5578909 6842017 6552596 6709821 5502239 5892175 5036320 5197335 4252727 4689694 4222734 4219745 3322200 3194977 2318880 2210445 1768962 1458399 999343 751817 499596 392694 254070 179656 101933 57388 27289 13388 5374 2083 807 268 77 22 7 1 1
\ No newline at end of file
diff --git a/src/boundary.cpp b/src/boundary.cpp
index a1b9814..f7dd7f8 100644
--- a/src/boundary.cpp
+++ b/src/boundary.cpp
@@ -79,6 +79,8 @@ RR ball_vol_RR(int k, RR r) {
exp.SetPrecision(RR_PRECISION);
pipow.SetPrecision(RR_PRECISION);
+ //cout << "Ball vol: k= " << k << ", r= " << r << endl;
+
exp= k;
pow(pwr, r, exp);
@@ -179,7 +181,7 @@ RR integral_odd_RR(int h, int l, RR tvec[], RR vvec[]) {
tmp= (2*h+1)/2.0;
- /******** Debug ***************
+ //******** Debug ***************
if(1-tvec[l-h]<0) {
cout << "tvec[" << (l-h) << "]== " << tvec[l-h] << endl;
@@ -310,7 +312,7 @@ RR ci_prob_RR(RR Rvec[], int k) {
bounds[i]= Rvec[2*i]*Rvec[2*i]/(Rvec[k-1]*Rvec[k-1]);
//bounds[i]= Rvec[2*i]*Rvec[2*i]/(Rvec[k-1]*Rvec[k-1]);
- /******** Debug ***************
+ //******** Debug ***************
if(bounds[i]>1) {
cout << "k: " << k << "\ti: " << i << "\tl: " << l << endl;
@@ -529,9 +531,8 @@ void predict_nodes_RR(RR Rvec[], double b_star_norm[], int n) {
cout << "# Measured nodes: " << sum << endl;
}
-
static
-void generate_boundary_step(RR b_star_norm[], double t_node, double t_reduc, int n, ZZ* act, double delta, unsigned long iterations, RR& t_enum, int& changes) {
+void generate_boundary_step(RR b_star_norm[], double t_node, double t_reduc, int n, ZZ* act, ZZ delta, unsigned long iterations, RR& t_enum, int& changes, RR* values_init, double* ratios_init, unsigned int oldits) {
ZZ* mod= new ZZ[n];
RR* mod_f= new RR[n];
time_t currentTime;
@@ -559,13 +560,6 @@ void generate_boundary_step(RR b_star_norm[], double t_node, double t_reduc, int
cerr << "Estimated end of computation: " << asctime(localTime);
}
- if(i%10==0) {
- values[stat_ctr]= t_enum;
- ratios[stat_ctr]= ((float) (changes-oldchanges))/10;
- stat_ctr++;
- oldchanges= changes;
- }
-
do {
if(n%2==0)
change= 2*(rand()%(n/2-1));
@@ -586,9 +580,13 @@ void generate_boundary_step(RR b_star_norm[], double t_node, double t_reduc, int
/*if((change==0) && (mod[change]+sign*delta<=0))
flag= true;*/
- } while((mod[change]+sign < 1) || (mod[change]+sign > mod[n-1]));
+ } while( ((sign<0) && (mod[change] == 1)) || ((sign>0) && (mod[change] == mod[n-1])) );
- mod[change]= mod[change+1]+= sign;
+ mod[change]= mod[change+1]+= sign*delta;
+ if(mod[change]<1)
+ mod[change]= mod[change+1]= 1;
+ if(mod[change]>mod[n-1])
+ mod[change]= mod[change+1]= mod[n-1];
// Ensuring monotonity
//if((change < n-2) && mod[change] > mod[change+2])
@@ -603,7 +601,7 @@ void generate_boundary_step(RR b_star_norm[], double t_node, double t_reduc, int
if(mod[j] < mod[change])
mod[j]= mod[change];
- if(t_enum == -1) {
+ if(i == 0) {
for(int j= 0; j < n; j++) {
conv(mod_f[j], act[j]);
mod_f[j]= sqrt(mod_f[j]);
@@ -632,27 +630,97 @@ void generate_boundary_step(RR b_star_norm[], double t_node, double t_reduc, int
} else
for(int j= 0; j < n; j++)
mod[j]= act[j];
-
+
+ if(i%10==0) {
+ values[stat_ctr]= t_enum;
+ ratios[stat_ctr]= ((float) (changes-oldchanges))/10;
+ stat_ctr++;
+ oldchanges= changes;
+ }
+
+
}
time( ¤tTime );
localTime = localtime( ¤tTime );
cerr << "Computation finished: " << asctime(localTime) << endl;
- // Output statistics
-
+ // Output dump data
+
ofstream stat_out;
stat_out.open ("optistat.dat");
+ // timing and delta
+ stat_out << "# " << t_node << " " << t_reduc << " " << delta << endl;
+
+ // dimension
+ stat_out << "# " << n << endl;
+
+ // GS vectors
+ stat_out << "# ";
+ for(int j= 0; j < n; j++) {
+ b_star_norm[j].SetOutputPrecision(RR_PRECISION);
+ stat_out << b_star_norm[j] << " ";
+ }
+ stat_out << endl;
+
+ // last boundary
+ stat_out << "# ";
+ for(int j= 0; j < n; j++)
+ stat_out << act[j] << " ";
+ stat_out << endl;
+
+ // statistics
+ int s1= 0;
+ unsigned int s2= 1;
+ /*unsigned int s2= 0;
+ if(oldits==0)
+ s2= 1;*/
+
+ stat_out << "# " << oldits + iterations/10-1 << endl << "# ";
+ for(unsigned int i= s1; i0)
+ scale= values_init[0];
+ else if (iterations/10>0)
+ scale= values[0];
+ else
+ scale= 1;
+
+
stat_out << "\"Change ratios\"" << endl;
- for(unsigned int i= 1; i> tmp;
+ infile >> t_node;
+ infile >> t_reduc;
+ infile >> delta;
+
+ infile >> tmp;
+ infile >> n;
+
+ b_star_norm= new RR[n];
+ infile >> tmp;
+ for(int i= 0; i> b_star_norm[i];
+ }
+
+ act= new ZZ[n];
+ infile >> tmp;
+ for(int i= 0; i> act[i];
+
+ infile >> tmp;
+ infile >> oldits;
+
+ values_init= new RR[oldits];
+ infile >> tmp;
+ for(unsigned int i= 0; i> values_init[i];
+ }
+
+ ratios_init= new double[oldits];
+ infile >> tmp;
+ /*string line;
+ while ( getline (infile,line) ) {
+ cout << line << '\n';
+ }
+ infile.close();
+ exit(0);*/
+ for(unsigned int i= 0; i> ratios_init[i];
+
+
+ /* Debug/ellenőrzés
+ cout << n << " " << t_node << " " << t_reduc << endl;
+ for(int j= 0; j < n; j++) {
+ b_star_norm[j].SetOutputPrecision(RR_PRECISION);
+ cout << b_star_norm[j] << " ";
+ }
+ cout << endl;
+ cout << oldits << endl;
+ for(unsigned int i= 0; irvec[k+1]?rvec[k]:rvec[k+1];
for(int i= rvec[k+1]; i>k; i--)
diff --git a/test/CMakeLists.txt b/test/CMakeLists.txt
index 2463388..f096d3a 100644
--- a/test/CMakeLists.txt
+++ b/test/CMakeLists.txt
@@ -1,7 +1,7 @@
SET(TARGET_NAME1 unit_tests)
SET(TARGET_NAME2 act_test)
SET(TARGET_NAME3 performance_test)
-#SET(TARGET_NAME4 detprofile)
+SET(TARGET_NAME4 psucc_exp)
INCLUDE_DIRECTORIES(${PROJECT_SOURCE_DIR}/include)
LINK_DIRECTORIES(${LIBRARY_OUTPUT_PATH})
@@ -14,5 +14,5 @@ TARGET_LINK_LIBRARIES(${TARGET_NAME2} cleanbkz ntl)
ADD_EXECUTABLE(${TARGET_NAME3} performance_test.cpp)
TARGET_LINK_LIBRARIES(${TARGET_NAME3} cleanbkz ntl)
-#ADD_EXECUTABLE(${TARGET_NAME4} detprofile.cpp)
-#TARGET_LINK_LIBRARIES(${TARGET_NAME4} cleanbkz ntl)
+ADD_EXECUTABLE(${TARGET_NAME4} psucc_exp.cpp)
+TARGET_LINK_LIBRARIES(${TARGET_NAME4} cleanbkz ntl)
diff --git a/test/act_test.cpp b/test/act_test.cpp
index ba4d504..9a8343f 100644
--- a/test/act_test.cpp
+++ b/test/act_test.cpp
@@ -87,7 +87,7 @@ int main(int argc, char** argv) {
gh*= c[i];
gsghs[i]= pow(gh/ball_vol(i+1, 1),1.0/(i+1));
}
- gh= pow(gh/ball_vol(dim, 1),1.0/dim);
+ gh= 1.05* pow(gh/ball_vol(dim, 1),1.0/dim);
if(l_cjloss)
cout << "# Shortest vector length: " << sqrt(dim) << endl;
cout << "# Gaussian heuristic: " << gh << endl;
diff --git a/test/psucc_exp.cpp b/test/psucc_exp.cpp
new file mode 100644
index 0000000..12b074e
--- /dev/null
+++ b/test/psucc_exp.cpp
@@ -0,0 +1,262 @@
+/*
+ Copyright (C) 2014 Janos Follath.
+
+ This file is part of cleanbkz.
+
+ cleanbkz is free software: you can redistribute it and/or modify
+ it under the terms of the GNU General Public License as published by
+ the Free Software Foundation, either version 3 of the License, or
+ (at your option) any later version.
+
+ cleanbkz is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ GNU General Public License for more details.
+
+ You should have received a copy of the GNU General Public License
+ along with cleanbkz. If not, see .
+
+*/
+
+#define MIN(X,Y) ((X) < (Y) ? (X) : (Y))
+
+#include
+#include
+#include
+#include
+#include
+#include
+#include
+#include
+
+using namespace std;
+
+extern RR p_succ(RR Rvec[], int n);
+extern void init_factorials(int);
+extern RR RR_PI;
+extern void enumerate_epr(double** mu, double *b, double* Rvec, int n, vec_RR& result, unsigned long &termination, double &time);
+
+extern void predict_nodes_RR(RR Rvec[], double b_star_norm[], int n);
+
+extern void predict_nodes(double Rvec[], double b_star_norm[], int n);
+extern double ball_vol(int k, double r);
+extern void profile_enumerate_epr(double** mu, double *b, double* Rvec, int n, vec_RR& result);
+
+void gen_randlat(mat_ZZ& basis, ZZ determinant, int dim);
+
+// The maximum of the coefficients of the random unimodular matrix
+#define UNIMOD_SIZE 100
+mat_ZZ unimod(int dim){
+ mat_ZZ L, U;
+ L.SetDims(dim, dim);
+ U.SetDims(dim, dim);
+
+ for(int i= 0; i < dim; i++)
+ L[i][i]= U[i][i]= 1;
+
+ for(int i= 0; i < dim; i++)
+ for(int j= i+1; j < dim; j++) {
+ U[i][j]= RandomBnd(UNIMOD_SIZE);
+ L[j][i]= RandomBnd(UNIMOD_SIZE);
+ }
+
+ return L*U;
+}
+
+
+int main(int argc, char** argv) {
+ int dim, bsize= 2;
+ stringstream ss;
+ mat_ZZ basis;
+ int lattices, bases;
+ int* seeds;
+ int* lsucc;
+ int* psucc;
+
+ // dimension
+ ss << argv[1];
+ ss >> dim;
+ ss.clear();
+
+ // number of random lattices
+ ss << argv[2];
+ ss >> lattices;
+ ss.clear();
+ seeds= new int[lattices];
+ lsucc= new int[lattices];
+ psucc= new int[lattices];
+
+ // number of bases per lattice
+ ss << argv[3];
+ ss >> bases;
+ ss.clear();
+
+ // reduction blocksize
+ if(argc>4) {
+ ss << argv[4];
+ ss >> bsize;
+ ss.clear();
+ }
+
+ double* polybound= new double[dim];
+ double* linbound= new double[dim];
+
+ // Schneider's polynomial approximation boundary function
+ double div = (double) dim;
+ double y,scale;
+ scale= dim;
+ for (double x = 1; x<=dim; x+=1){
+ y = x/div;
+ polybound[int(x)] = min( -276.919520419850*pow(y,8) \
+ +1208.33321732860 *pow(y,7) \
+ -2128.79627565000 *pow(y,6) \
+ +1952.22801180000 *pow(y,5) \
+ -1012.11476080000 *pow(y,4) \
+ + 305.211610000000*pow(y,3) \
+ - 51.347076000000*pow(y,2) \
+ + 4.408932000000*pow(y,1) \
+ + 0.000914465000, 1.0);
+ polybound[int(x)]*= scale;
+ }
+
+ for(int i= 0; i< dim; i+=2)
+ polybound[i]= polybound[i+1]= floor(polybound[i+1]);
+
+ for(int i= 1; i< dim-1; i+=2)
+ if(polybound[i]>polybound[i+1])
+ for(int j= i; j >= 0; j--)
+ if(polybound[j] > polybound[i+1])
+ polybound[j]= polybound[i+1];
+
+ // linear boudary function
+ ZZ* act= new ZZ[dim];
+ ZZ R2;
+ conv(R2, dim);
+ act[0]= act[1]= (2*R2)/dim;
+ for(int i= 2; i < dim; i+=2) {
+ act[i]= act[i+1]= act[i-1]+act[0];
+ }
+ act[dim-1]= R2;
+ if(dim%2==0)
+ act[dim-2]= R2;
+
+ for(int i= 0; i < dim; i++)
+ conv(linbound[i],act[i]);
+
+
+ // Computing success probabilities
+ RR_PI.SetPrecision(RR_PRECISION);
+ RR_PI= ComputePi_RR();
+ init_factorials(2*dim+2);
+ RR* mod_f= new RR[dim];
+ cout << "Linear boundary: " << endl;
+ for(int j= 0; j < dim; j++) {
+ cout << linbound[j] << " ";
+ conv(mod_f[j], linbound[j]);
+ mod_f[j]= sqrt(mod_f[j]);
+ }
+ cout << endl << "Linear success rate: " << p_succ(mod_f, dim) << endl;
+
+ cout << "Polynomial boundary: " << endl;
+ for(int j= 0; j < dim; j++) {
+ cout << polybound[j] << " ";
+ conv(mod_f[j], polybound[j]);
+ mod_f[j]= sqrt(mod_f[j]);
+ }
+ cout << endl << "Polynomial success rate: " << p_succ(mod_f, dim) << endl;
+
+
+ // Performing randomization followed by enumeration
+ unsigned long termination= 0;
+ mat_RR mu1;
+ vec_RR c1;
+ vec_RR solution;
+ double* c= new double[dim];
+ double** mu= new double*[dim];
+ double t_enum;
+
+ for(int i= 0; i>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
+**************************************************************************
+>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
+
+yanesca@peace:~/workspace/cleanbkz$ ./bin/boundtool -f data/svpchallengedim100seed0red20.lat -n 8e-08 -r 36.39 -c 300 -d 100000
+Starting time: Mon Nov 24 13:35:22 2014
+Estimated end of computation: Mon Nov 24 13:52:01 2014
+
+---------------------------------------------------------------------------
+---------------------------------------------------------------------------
+---------------------------------------------------------------------------
+
+d80k20 -> 20 min
+d100k20 -> 2 years (lehet, hogy nem volt rendesen optimalizálva sem)
+d100k30 -> 24 days
diff --git a/tmp b/tmp
new file mode 100644
index 0000000..cfbc621
--- /dev/null
+++ b/tmp
@@ -0,0 +1,102 @@
+[[51 -384 278 -300 117 -151 717 5 202 -417 -161 139 -145 292 -42 115 520 296 -450 -27 -198 -147 301 193 -335 -267 127 248 -76 -636 -324 586 233 -745 -84 -227 -77 178 494 221 376 795 -256 -447 771 480 106 102 -500 915 28 400 -69 -439 447 409 -332 -2 -543 664 664 -337 513 52 -93 349 -313 43 301 166 -675 -26 10 -772 105 -216 -191 124 298 -76 -340 99 491 -395 226 16 573 -126 -376 293 32 17 -968 360 -663 -89 105 383 622 135]
+[743 299 -366 148 222 -270 426 -408 -218 114 859 -58 -263 -313 -342 115 -237 -101 -423 -208 298 -180 105 -280 -662 497 22 381 132 382 -443 128 -316 409 650 248 403 396 61 160 -170 -758 295 150 -179 -221 36 215 -850 -899 -154 133 -238 373 127 -382 -369 203 280 -110 -290 220 76 384 371 -367 23 -633 320 -74 214 -136 438 142 -104 211 351 1007 197 692 -373 -211 50 284 -146 9 -518 -187 -123 -172 62 -473 921 -585 -275 -400 -44 838 -381 -74]
+[-226 -885 -569 28 -300 56 -498 333 511 309 -266 -185 -57 629 69 87 -697 488 -586 351 412 -11 -359 350 -44 -41 -94 -448 2 679 -18 -594 -4 -744 113 -117 -444 -3 182 -134 636 367 -472 223 -275 -300 -229 118 346 327 414 111 -125 -295 -607 677 243 705 -101 427 129 142 141 225 -46 898 -6 -2 273 -383 -134 252 -451 304 -261 252 205 -965 -347 -271 130 -303 169 -665 45 -349 651 392 670 -284 361 -373 -278 655 636 507 162 -130 -19 -163]
+[-264 282 225 -395 117 -158 619 302 721 -405 -1292 172 587 -71 -569 146 376 -469 92 -783 -341 141 57 -405 173 -498 399 362 -13 -1204 448 662 273 -234 -395 -637 -390 191 -386 281 169 439 504 338 344 -433 83 -576 386 519 -271 -698 -319 385 551 623 -85 -82 -781 -82 -179 -219 -309 -768 62 -18 532 99 -484 399 -56 407 294 312 311 -201 -117 117 265 -368 -333 471 521 79 138 -86 -184 -46 -352 885 -609 498 -225 139 -448 -221 -539 -199 695 252]
+[99 -135 244 -250 -23 -9 -242 4 -467 -467 -452 322 -420 324 689 -550 194 407 -188 1046 210 -662 293 212 -373 152 -94 -111 -86 346 -309 394 -503 -615 -311 333 -429 534 4 42 -151 213 -600 -451 64 41 34 -250 -460 264 -46 150 487 -436 447 45 -439 497 -62 -127 196 -75 34 527 -223 109 -687 297 268 857 141 328 -337 -648 1 -73 -566 -293 167 -54 645 651 322 -615 79 -165 188 -65 110 -511 924 132 -575 118 554 -326 214 606 -677 163]
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