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// THTCONST.CC: Test program for Silverman & CPS height bounds
//////////////////////////////////////////////////////////////////////////
//
// Copyright 1990-2012 John Cremona
//
// This file is part of the eclib package.
//
// eclib 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 2 of the License, or (at your
// option) any later version.
//
// eclib 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 eclib; if not, write to the Free Software Foundation,
// Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA
//
//////////////////////////////////////////////////////////////////////////
//
#include <eclib/points.h> // from qcurves library
#include <eclib/sieve_search.h>
#include <eclib/cperiods.h>
#include <eclib/elog.h>
#include <eclib/egr.h>
#include <eclib/htconst.h>
bigint a1,a2,a3,a4,a6;
Curve C;
Curvedata CD;
vector<Point> plist;
const double margin = 0.01;
int getcurve(void)
{
// cout << "Enter curve coefficients a1,a2,a3,a4,a6: " << endl;
cin >> C;
// cout<<C<<endl;
if(C.isnull()) return 0; // quitting condition
// cin >> a1 >> a2 >> a3 >> a4 >> a6;
// C = Curve(a1,a2,a3,a4,a6);
CD = Curvedata(C,0); // "1" means minimise
// cout<<CD<<endl;
return 1;
}
int main()
{
#ifdef MPFP
set_precision(100);
#endif
initprimes("PRIMES",0);
cin.flags( cin.flags() | ios::dec );
long nsilverbetter=0, ncpsbetter=0, n=0;
double silvertotal=0, cpstotal=0, cps2total=0;
long kkmintotal=0;
while (getcurve())
{
cout<<endl;
if(C!=(Curve)CD)
{
cout<<"Input curve "<<C<<", ";
cout<<"Working with minimal curve "<<CD<<":\t";
}
else
cout << "Curve "<< C <<":\t";
double silver = silverman_bound(CD);
cout << "Silverman bound = " << silver << "\t";
double cps = cps_bound(CD);
cout << "CPS bound = " << cps << "\n";
double egr_bound = egr_height_constant(CD);
cout << "egr bound = " << egr_bound << "\n";
bigint k;
Curvedata CD2=opt_x_shift(CD,k);
double cps2 = cps_bound(CD2);
cout << "Shift by "<<k<<": "<< (Curve)CD2 <<":\t";
cout << "CPS bound 2 = " << cps2 << "\n";
bigint kmin=k; double cpsmin=cps2; long kkmin=0;
Curvedata CDup=CD2;
CDup.transform(BIGINT(1),BIGINT(0),BIGINT(0));
double cpsup = cps_bound(CDup);
cout << "Shift by "<<(k+1)<<" (up by 1): "<< (Curve)CDup <<":\t";
cout << "CPS bound = " << cpsup << "\n";
Curvedata CDdown=CD2;
CDdown.transform(BIGINT(-1),BIGINT(0),BIGINT(0));
double cpsdown = cps_bound(CDdown);
cout << "Shift by "<<(k-1)<<" (down by 1): "<< (Curve)CDdown <<":\t";
cout << "CPS bound = " << cpsdown << "\n";
long kk=0, kd=0;
if(cpsup<cps2-margin)
{cout<<"Up looks better\n"; kd=+1;}
else
if(cpsdown<cps2-margin)
{cout<<"Down looks better\n"; kd=-1;}
if(kd==0)
{
kkmintotal+=kkmin;
cout<<"No significant improvement (margin of "<<margin<<")!\n";
cout << "Best shift by "<<k<<": ";
cout << "Best CPS bound = " << cps2 << "\n";
}
else
{
double cpsk, lastcps=cps2;
for(kk=kd; ; kk+=kd)
{
Curvedata CDk=CD2;
CDk.transform(BIGINT(kk),BIGINT(0),BIGINT(0));
cpsk = cps_bound(CDk);
cout << "Shift by "<<(k+kk)<<" (relative "<<kk<<"): "<< (Curve)CDk <<":\t";
cout << "CPS bound = " << cpsk << "\n";
if(lastcps<cpsk+margin)
{
cout<<"not getting significantly better, stopping."<<endl;
break;
}
lastcps=cpsk;
if(cpsk<cpsmin) {cpsmin=cpsk; kmin=k+kk; kkmin=kk;}
}
cps2=cpsmin; kkmintotal+=kkmin;
cout << "Best shift by "<<k+kkmin<<": ";
cout << "Best CPS bound = " << cps2 << "\n";
}
if (silver<cps) nsilverbetter++; else ncpsbetter++;
silvertotal+=silver;
cpstotal+=cps;
cps2total+=cps2;
n++;
if(n%100==0)
cout<<"So far, CPS is better for "<<ncpsbetter
<<" curves out of "<<n<<endl;
// double best = height_constant(CD);
// cout << "Best = " << best << "\n";
}
cout<<"Overall, CPS is better for "<<ncpsbetter
<<" curves out of "<<n<<endl;
double rate = (100.0*ncpsbetter)/n;
cout << "For " << rate << "% of curves the new bound is better."<<endl;
cout << "Average difference (silverman-cps) = "<<(silvertotal-cpstotal)/n<<endl;
cout << "Average difference (silverman-cps2) = "<<(silvertotal-cps2total)/n<<endl;
cout << "Silverman average = "<<silvertotal/n<<endl;
cout << "CPS 1 average = "<<cpstotal/n<<endl;
cout << "CPS 2 average = "<<cps2total/n<<endl;
cout << "Average offset = "<<(double)kkmintotal/n << endl;
}
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