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main.cpp
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main.cpp
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/******************************************************/
/* */
/* main.cpp - main program */
/* */
/******************************************************/
/* Copyright 2014,2016,2018-2021,2023 Pierre Abbat.
* This file is part of the Quadlods program.
*
* The Quadlods program 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.
*
* Quadlods 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 and Lesser General Public License
* for more details.
*
* You should have received a copy of the GNU General Public License
* and Lesser General Public License along with Quadlods. If not, see
* <http://www.gnu.org/licenses/>.
*/
#include <iostream>
#include <iomanip>
#include <bitset>
#include <set>
#include <ctime>
#include <cassert>
#include <cmath>
#include <boost/program_options.hpp>
#include "main.h"
#include "config.h"
#include "hstep.h"
#include "ps.h"
#include "threads.h"
#include "random.h"
#include "circletest.h"
#include "filltest.h"
#include "contfrac.h"
#include "ldecimal.h"
#include "histogram.h"
#include "manysum.h"
#include "flowertest.h"
#include "fourier.h"
#include "plot.h"
#include "pairpoint.h"
#include "matrix.h"
#include "interact.h"
#include "discrepancy.h"
#define tassert(x) testfail|=(!(x))
using namespace std;
using namespace quadlods;
namespace po=boost::program_options;
struct command
{
std::string word;
void (*fun)();
std::string desc;
command(std::string w,void (*f)(),std::string d)
{
word=w;
fun=f;
desc=d;
}
};
vector<command> commands;
Quadlods cirquads;
map<int,Quadlods> quads;
bool testfail=false;
char rpint[][2]=
{ // relatively prime integers whose sum of squares is less than 100
{1,1},{1,2},{1,3},{1,4},{2,3},{1,5},{1,6},{2,5},
{3,4},{1,7},{3,5},{1,8},{2,7},{4,5},{2,9},{3,8},
{4,7},{5,6},{5,7},{4,9},{5,8},{6,7}
};
map<double,int> singleq;
int minlargerp;
PostScript ps;
string resstr;
double resolution;
string primestr;
vector<int> primelist;
string scramblestr;
int ndims,niter,scramble;
string filename;
bool useMinMax=false,disc2d=false;
int maxStairStep;
void listCommands()
{
int i;
cout<<"Quadlods version "<<VERSION<<" © "<<COPY_YEAR<<" Pierre Abbat\n"<<
"Quadratic-irrational (Richtmyer) and Halton low-discrepancy sequences\n"<<
"Distributed under GPL v3 or later; library distributed under LGPL.\n"<<
"This is free software with no warranty.\n";
cout<<"Commands:\n";
for (i=0;i<commands.size();i++)
cout<<setw(15)<<left<<commands[i].word<<commands[i].desc<<'\n';
}
int parseInt(string intstr)
{
int ret;
size_t idx;
ret=stoi(intstr,&idx);
if (idx<intstr.length())
throw(invalid_argument("parseInt"));
return ret;
}
double parseDouble(string intstr)
{
double ret;
size_t idx;
ret=stod(intstr,&idx);
if (idx<intstr.length())
throw(invalid_argument("parseDouble"));
return ret;
}
bool isValidPrime(int n)
{
int i;
bool ret=n>1 && n<65522 && (n==2 || (n&1));
for (i=3;ret && i*i<=n;i+=2)
if (n>i && (n%i==0))
ret=false;
return ret;
}
void testContinuedFraction()
{
ContinuedFraction cf2,cf3,cf5,cf7;
cout<<"Continued fraction unit test\n";
cf2.terms.push_back(1);
cf2.terms.push_back(2);
cf2.period=1;
cf3.terms.push_back(1);
cf3.terms.push_back(1);
cf3.terms.push_back(2);
cf3.period=2;
cf5.terms.push_back(1);
cf5.period=1;
cf7.terms.push_back(2);
cf7.terms.push_back(1);
cf7.terms.push_back(1);
cf7.terms.push_back(1);
cf7.terms.push_back(4);
cf7.period=4;
tassert(fabs(cf3.averageTerm()-cf7.averageTerm())<1e-15);
tassert(cf3.maximumTerm()<cf7.maximumTerm());
tassert(cf2.averageTerm()==2);
tassert(cf2.maximumTerm()==2);
tassert(cf5.averageTerm()==1);
tassert(cf5.maximumTerm()==1);
}
void testReverseScramble()
{
int i,j;
cout<<"Reverse scramble unit test\n";
fillReverseScrambleTable(5,QL_SCRAMBLE_NONE);
fillReverseScrambleTable(5,QL_SCRAMBLE_POWER);
tassert(reverseScrambleTable[(QL_SCRAMBLE_NONE<<16)+5][10646]==5638);
tassert(reverseScrambleTable[(QL_SCRAMBLE_POWER<<16)+5][10646]==5642);
for (i=2;i<12;i++)
{
for (j=0;j<i;j++)
cout<<faureperm(j,i)<<' ';
cout<<endl;
}
}
vector<int> factor(int n)
{
vector<int> ret;
int i,p;
for (i=0;i<QL_MAX_DIMS && n>1;i++)
{
p=nthprime(i);
while (n%p==0)
{
ret.push_back(p);
n/=p;
}
}
return ret;
}
bool parsePrimeList()
{
string numstr;
int num;
size_t pos;
bool ret=true;
while (primestr.length())
{
pos=primestr.find_first_of(", ");
numstr=primestr.substr(0,pos);
if (pos<=primestr.length())
pos++;
primestr.erase(0,pos);
if (numstr.length())
{
if (numstr.find_first_not_of("0123456789")>numstr.length())
{
try
{
num=parseInt(numstr);
if (isValidPrime(num))
primelist.push_back(num);
else
{
cerr<<num<<" is not a prime less than 65535\n";
ret=false;
}
}
catch (...)
{
cerr<<numstr<<" is out of range for an int\n";
ret=false;
}
}
else
{
cerr<<numstr<<" is not a positive integer\n";
ret=false;
}
}
}
return ret;
}
array<short,676> digraphs(string word)
{
int l0,l1,i;
array<short,676> ret;
for (i=0;i<676;i++)
ret[i]=0;
for (i=0;i+1<word.length();i++)
{
l0=tolower(word[i]);
l1=tolower(word[i+1]);
if (l0>='a' && l0<='z' && l1>='a' && l1<='z')
ret[(l0-'a')*26+(l1-'a')]++;
}
return ret;
}
int parseScramble(string scramblestr)
{
vector<array<short,676> > digs;
array<short,676> digj=digraphs(scramblestr);
vector<int> match;
int i,j,ret,maxmatch=-1,nmatch=0;
digs.push_back(digraphs("None"));
digs.push_back(digraphs("Third"));
digs.push_back(digraphs("Thue-Morse"));
digs.push_back(digraphs("Gray"));
digs.push_back(digraphs("Power"));
digs.push_back(digraphs("Faure"));
digs.push_back(digraphs("tipwitch"));
digs.push_back(digraphs("default"));
match.resize(digs.size());
for (i=0;i<676;i++)
for (j=0;j<digs.size();j++)
match[j]+=digs[j][i]*digj[i];
for (i=0;i<match.size();i++)
if (match[i]>maxmatch)
maxmatch=match[i];
if (match[0]==maxmatch)
{
nmatch++;
ret=QL_SCRAMBLE_NONE;
}
if (match[1]==maxmatch)
{
nmatch++;
ret=QL_SCRAMBLE_THIRD;
}
if (match[2]==maxmatch)
{
nmatch++;
ret=QL_SCRAMBLE_THUEMORSE;
}
if (match[3]==maxmatch)
{
nmatch++;
ret=QL_SCRAMBLE_GRAY;
}
if (match[4]==maxmatch)
{
nmatch++;
ret=QL_SCRAMBLE_POWER;
}
if (match[5]==maxmatch)
{
nmatch++;
ret=QL_SCRAMBLE_FAURE;
}
if (match[6]==maxmatch)
{
nmatch++;
ret=QL_SCRAMBLE_TIPWITCH;
}
if (match[7]==maxmatch)
{
nmatch++;
ret=QL_SCRAMBLE_DEFAULT;
}
if (nmatch>1)
{
ret=-1;
}
return ret;
}
double parseResolution(string resstr)
{
size_t rest;
double ret;
try
{
ret=stod(resstr,&rest);
if (rest<resstr.length())
ret=-1;
}
catch (...)
{
int i;
string lower;
for (i=0;i<resstr.length();i++)
lower+=tolower(resstr[i]);
if (lower==string("halton").substr(0,lower.length()) && lower.length()>0)
ret=0;
else
ret=-1;
}
return ret;
}
void plotxy(Quadlods& quad,int xdim,int ydim,int inx,int allinx)
{
int i;
double x,y;
time_t now,then;
char buf[24];
vector<double> point;
Quadlods sel2;
PairCompressor pc;
vector<int> pinx2;
pinx2.push_back(xdim);
pinx2.push_back(ydim);
sel2=select(quad,pinx2);
ps.startpage();
ps.setscale(0,0,1,1);
// (2,5) and (7,2) ((2,0) and (5,2)) look splotchy at 30000, but fill in well at 100000.
sprintf(buf,"%d %d",sel2.getprime(0),sel2.getprime(1));
ps.write(0,1,buf);
for (i=0;i<niter;i++)
{
point=sel2.dgen();
x=point[0];
y=point[1];
pc.insert(xy(x,y));
now=time(nullptr);
if (now!=then)
{
cout<<rint((inx+(double)i/niter)/allinx*100)<<"% \r";
cout.flush();
then=now;
}
}
ps.draw(pc);
ps.endpage();
}
void testcoverage()
/* Cycle sizes: 408, 571, 377.
* Total cycle size: 87828936 (LCM).
* Remaining factor: 1.
*/
{
int i,x,y,z,inx;
Quadlods cov;
bitset<87828936> *histo;
vector<mpq_class> point;
vector<int> p235; // since sorting the primes, the list begins 5,3,2
cout<<"Testing coverage\n";
p235.push_back(2);
p235.push_back(3);
p235.push_back(5);
cov.init(p235,370);
cov.setscramble(scramble);
histo=new bitset<87828936>;
for (i=0;i<87828936;i++)
{
point=cov.gen();
x=mpz_class(point[0]*408).get_si();
y=mpz_class(point[1]*571).get_si();
z=mpz_class(point[2]*377).get_si();
inx=x+408*(y+571*z);
histo->set(inx);
if (i%878290==0)
{
cout<<setw(2)<<i/878290<<"%\b\b\b";
cout.flush();
}
}
cout<<histo->count()<<endl;
if (histo->count()==87828936)
cout<<"Complete coverage\n";
else
{
testfail=true;
cout<<"Coverage test failed\n";
}
delete histo;
}
void test2quads(double q0,double q1,double toler)
{
int i,a=0,b=0;
int p0,p1;
double diff;
for (i=0;i<sizeof(rpint)/sizeof(rpint[0]);i++)
{
a=rpint[i][0];
b=rpint[i][1];
diff=a*q0-b*q1;
diff-=rint(diff);
if (fabs(diff)<toler)
break;
a=-a;
diff=a*q0-b*q1;
diff-=rint(diff);
if (fabs(diff)<toler)
break;
if (i==0)
continue;
swap(a,b);
diff=a*q0-b*q1;
diff-=rint(diff);
if (fabs(diff)<toler)
break;
b=-b;
diff=a*q0-b*q1;
diff-=rint(diff);
if (fabs(diff)<toler)
break;
a=b=0;
}
if (a)
{
p0=singleq[q0];
p1=singleq[q1];
cout<<"Close quads are "<<a<<'*'<<q0<<" ("<<p0<<") and "<<b<<'*'<<q1<<" ("<<p1<<")."<<endl;
if (p0<p1)
swap(p0,p1);
if (p0<minlargerp)
minlargerp=p0;
}
}
void findclosequad()
{
map<double,int>::iterator j;
vector<double> qlist;
int i,k,p;
double q;
singleq.clear();
minlargerp=65536;
for (i=0;i<QL_MAX_DIMS;i++)
{
p=nthprime(i);
q=nthquad(i);
singleq[q]=p;
}
for (j=singleq.begin();j!=singleq.end();++j)
qlist.push_back(j->first);
for (i=0;i<QL_MAX_DIMS;i++)
for (k=0;k<i;k++)
test2quads(qlist[i],qlist[k],2e-9);
cout<<"Use primes below "<<minlargerp<<endl;
}
/* Some bad pairs of primes for Richtmyer:
* 65027,65029
* 59053,59051
* 13691,13693
* A set that is somewhat bad:
* 5,4933,42533,57713 (CF expansions all begin n;1,1,1,1,1,1,1,1)
* 42533,57713 is bad, but not as bad as 65027,65029.
* Twin primes, 2 and 4 more than a square:
* 3,5 227,229 1091,1093 2027,2029 3251,3253
* 13691,13693 21611,21613 59051,59053 65027,65029.
* All these have CF expansions of the form a;(a,b) and c;(a)
* where b=2a and a=2c-1.
* Any large enough pair of twin primes is bad for Halton, and even
* when Faure-scrambled, such pairs as 21839,21841 (close to 65536/3)
* are bad. So are pairs whose ratio is close to 2, such as 63277,31643.
*
* 44741,63277 is a good pair for Faure; their ratio is very nearly √2.
*/
void testCircle()
{
if (niter>0 && (ndims>0 || primelist.size()))
{
ps.open(filename.length()?filename:"circle.ps");
quads[0].init(ndims,resolution);
quads[0].init(primelist,resolution);
quads[0].setscramble(scramble);
quads[0].advance(-1);
circletest(quads[0],niter,ps);
ps.trailer();
ps.close();
}
if (niter<=0)
cerr<<"Please specify number of iterations with -n\n";
if (ndims<=0 && primelist.size()==0)
cerr<<"Please specify number of dimensions with -d or primes with -p\n";
}
void testScatter()
{
int i,j,inx,allinx;
time_t now,then;
if (niter>0 && (ndims>0 || primelist.size()))
{
ps.open(filename.length()?filename:"scatter.ps");
ps.prolog();
quads[0].init(ndims,resolution);
quads[0].init(primelist,resolution);
quads[0].setscramble(scramble);
quads[0].advance(-1);
allinx=quads[0].size()*(quads[0].size()-1)/2;
//for (i=0;resolution && i<quads[0].size();i++)
//cout<<quads[0].getnum(i)<<'/'<<quads[0].getdenom(i)<<' '<<quads[0].getacc(i)<<endl;
for (i=0;i<quads[0].size();i++)
for (j=0;j<i;j++)
{
inx=i*(i-1)/2+j;
plotxy(quads[0],i,j,inx,allinx);
now=time(nullptr);
if (now!=then)
{
cout<<rint((double)inx/allinx*100)<<"% \r";
cout.flush();
then=now;
}
}
ps.trailer();
ps.close();
}
if (niter<=0)
cerr<<"Please specify number of iterations with -n\n";
if (ndims<=0 && primelist.size()==0)
cerr<<"Please specify number of dimensions with -d or primes with -p\n";
}
void testFill()
{
if (niter>0 && (ndims>0 || primelist.size()))
{
ps.open(filename.length()?filename:"fill.ps");
quads[0].init(ndims,resolution);
quads[0].init(primelist,resolution);
quads[0].setscramble(scramble);
quads[0].advance(-1);
filltest(quads[0],niter,ps);
ps.trailer();
ps.close();
}
if (niter<=0)
cerr<<"Please specify number of iterations with -n\n";
if (ndims<=0 && primelist.size()==0)
cerr<<"Please specify number of dimensions with -d or primes with -p\n";
}
void testFlower()
{
if (niter>0 && (ndims>0 || primelist.size()))
{
ps.open(filename.length()?filename:"flower.ps");
quads[0].init(ndims,resolution);
quads[0].init(primelist,resolution);
quads[0].setscramble(scramble);
quads[0].advance(-1);
flowertest(quads[0],niter,ps,disc2d);
ps.trailer();
ps.close();
}
if (niter<=0)
cerr<<"Please specify number of iterations with -n\n";
if (ndims<=0 && primelist.size()==0)
cerr<<"Please specify number of dimensions with -d or primes with -p\n";
}
void testFourier()
{
if (niter>0 && (ndims>0 || primelist.size()))
{
ps.open(filename.length()?filename:"fourier.ps");
quads[0].init(ndims,resolution);
quads[0].init(primelist,resolution);
quads[0].setscramble(scramble);
quads[0].advance(-1);
fouriertest(quads[0],niter,ps);
ps.trailer();
ps.close();
}
if (niter<=0)
cerr<<"Please specify number of iterations with -n\n";
if (ndims<=0 && primelist.size()==0)
cerr<<"Please specify number of dimensions with -d or primes with -p\n";
}
void quadPlot()
{
ps.open(filename.length()?filename:"quadplot.ps");
quads[0].init(ndims,resolution);
quads[0].init(primelist,resolution);
quads[0].setscramble(scramble);
quads[0].advance(-1);
quadplot(ps);
ps.trailer();
ps.close();
}
void testRandom()
{
int hist[256],i;
int done=0,max,min,maxstep=0;
memset(hist,0,sizeof(hist));
while (!done)
{
hist[rng.ucrandom()]++;
for (max=i=0,min=16777777;i<256;i++)
{
if (hist[i]>max)
max=hist[i];
if (hist[i]<min)
min=hist[i];
}
if (max>16777215)
done=-1;
if (max-min>1.1*pow(max,1/3.) && max-min<0.9*pow(max,2/3.))
done=1;
if (max-maxstep>=16384)
{
maxstep=max;
//cout<<max<<' '<<min<<endl;
}
}
tassert(done==1);
cout<<"Random test: max "<<max<<" min "<<min<<endl;
done=maxstep=0;
memset(hist,0,sizeof(hist));
while (!done)
{
hist[rng.rangerandom(251)]++;
for (max=i=0,min=16777777;i<251;i++)
{
if (hist[i]>max)
max=hist[i];
if (hist[i]<min)
min=hist[i];
}
if (max>16777215)
done=-1;
if (max-min>1.1*pow(max,1/3.) && max-min<0.9*pow(max,2/3.))
done=1;
if (max-maxstep>=16384)
{
maxstep=max;
//cout<<max<<' '<<min<<endl;
}
}
tassert(done==1);
cout<<"Range random test: max "<<max<<" min "<<min<<endl;
done=maxstep=0;
memset(hist,0,sizeof(hist));
while (!done)
{
hist[rng.frandom(mpq_class(1,3))]++;
for (max=i=0,min=16777777;i<2;i++)
{
if (hist[i]*(1+i)>max)
max=hist[i]*(1+i);
if (hist[i]*(1+i)<min)
min=hist[i]*(1+i);
}
if (max>16777215)
done=-1;
if (min>256 && max-min>1.1*pow(max,1/3.) && max-min<0.9*pow(max,2/3.))
done=1;
if (max-maxstep>=16384)
{
maxstep=max;
//cout<<max<<' '<<min<<endl;
}
}
tassert(done==1);
cout<<"Fractional random test: "<<hist[0]<<" zeros "<<hist[1]<<" ones\n";
}
void testSeed()
{
int n,i,j,seedlen;
vector<double> point;
char *seedbuf;
time_t now;
quads[0].init(5,1e10);
quads[1].init(5,0);
for (n=0;n<2;n++)
{
seedlen=quads[n].seedsize();
cout<<seedlen<<" bytes needed to seed"<<endl;
seedbuf=new char[seedlen];
now=time(NULL);
for (i=0;i<sizeof(time_t) && i<seedlen;i++)
seedbuf[i]=now>>(8*i);
for (;i<seedlen;i++)
seedbuf[i]=seedbuf[i-1]+seedbuf[i-sizeof(time_t)];
quads[n].seed(seedbuf,seedlen);
for (i=0;i<30;i++)
{
point=quads[n].dgen();
for (j=0;j<point.size();j++)
cout<<point[j]<<' ';
cout<<endl;
}
delete[] seedbuf;
}
}
void testNegativeHalton()
{
int i,j;
vector<double> point,sum;
quads[0].init(5,0,QL_SCRAMBLE_NONE);
quads[0].advance(-16);
sum.resize(5,0);
cout<<"Negative Halton test\n";
for (i=0;i<30;i++)
{
point=quads[0].dgen();
for (j=0;j<point.size();j++)
{
sum[j]+=point[j];
cout<<point[j]<<' ';
}
cout<<endl;
}
for (j=0;j<sum.size();j++)
{
tassert(fabs(sum[j]-15)<1e-12);
}
}
array<double,3> spherePoint(double x0,double x1)
{
array<double,3> ret;
double r;
ret[2]=2*x1-1;
r=sqrt(1-sqr(ret[2]));
ret[1]=r*sin(x0*2*M_PI);
ret[0]=r*cos(x0*2*M_PI);
return ret;
}
double upperDiff(int n)
/* For a six-dimensional integration, the error in the sum should be bounded
* by the sixth power of the logarithm. For small n, though, it isn't.
*/
{
return pow(log(n),6)/5e4+pow(log(n),4)/180+pow(log(n),3)/128+log(n)*2.22;
}
void testuvmatrix()
// Calculate the distribution of the determinant of three unit 3-vectors
{
int i,j,k;
double det,reldiff,maxreldiff=0;
time_t now,then;
bool analyze=false;
vector<double> allsqdet;
double absdiff,minabsdiff,maxabsdiff;
double hi=-INFINITY,lo=INFINITY,scale;
manysum sumsqdet;
histogram hist(-1,1);
matrix mat(3,3);
array<double,3> row;
array<double,4> vline;
vector<array<double,4> > vlines;
vector<double> point;
if (niter==0)
{
analyze=true;
niter=7776000;
}
quads[0].init(6,resolution);
quads[0].setscramble(scramble);
cout<<"Calculating determinants of 3×3 unit vector matrices\n";
for (i=0;i<niter;i++)
{
point=quads[0].dgen();
row=spherePoint(point[0],point[1]);
for (j=0;j<3;j++)
mat[0][j]=row[j];
row=spherePoint(point[2],point[3]);
for (j=0;j<3;j++)
mat[1][j]=row[j];
row=spherePoint(point[4],point[5]);
for (j=0;j<3;j++)
mat[2][j]=row[j];
det=mat.determinant();
now=time(nullptr);
if (now!=then)
{
cout<<rint((double)i/niter*100)<<"% \r";
cout.flush();
reldiff=fabs(sumsqdet.total()-i*6./27.)/pow(log(i),6);
if (reldiff>maxreldiff)
maxreldiff=reldiff;
then=now;
}
hist<<det;
sumsqdet+=det*det;
if (analyze)
allsqdet.push_back(det*det);
}
ps.open(filename.length()?filename:"uvmatrix.ps");
ps.setpaper(a4land,0);
ps.prolog();
ps.startpage();
ps.setscale(0,-1,3,1);
hist.plot(ps,HISTO_LINEAR);
ps.endpage();
cout<<niter<<" iterations, average square determinant is "<<sumsqdet.total()/niter<<endl;
//cout<<"compare "<<sumsqdet.total()-niter*6./27.<<' '<<upperDiff(niter)<<endl;
if (niter<2)
cout<<"Please increase the number of iterations with -n\n";
else if (fabs(sumsqdet.total()-niter*6./27.)>upperDiff(niter))
{
cout<<"Test failed, average square determinant should be 6/27\n";
// 6/27 is 3!/3^3
testfail=true;
}
//cout<<"Maximum relative difference is "<<maxreldiff<<endl;
if (analyze)
{
for (i=2;i<2;i++)
{
minabsdiff=INFINITY;
maxabsdiff=0;
if (niter%i==0)
{
for (j=0;j<niter;j+=i)
{
sumsqdet.clear();
for (k=0;k<i;k++)
sumsqdet+=allsqdet[j+k];
absdiff=fabs(sumsqdet.total()-i*6./27.);
if (absdiff<minabsdiff)
minabsdiff=absdiff;
if (absdiff>maxabsdiff)
maxabsdiff=absdiff;
}
cout<<i<<' '<<minabsdiff<<'-'<<maxabsdiff<<" < "<<upperDiff(i)<<endl;
vline[0]=log(i);
vline[1]=log(minabsdiff);
vline[2]=maxabsdiff;
vline[3]=upperDiff(i);
vlines.push_back(vline);
for (k=1;k<4;k++)
{
if (vline[k]>hi)
hi=vline[k];
if (vline[k]<lo)
lo=vline[k];
}
}
}
if (vlines.size())
{
ps.startpage();
ps.setscale(0,-1,3,1);
scale=(hi-lo)/2;
ps.startline();
ps.lineto(0,-1);
ps.lineto(3,-1);
ps.lineto(3,1);
ps.lineto(0,1);
ps.endline(true);
ps.setcolor(0,0,1);
for (i=0;i<vlines.size();i++)
ps.line2p(xy(vlines[i][0]/log(niter)*3,(vlines[i][1]-lo)/scale-1),
xy(vlines[i][0]/log(niter)*3,(vlines[i][2]-lo)/scale-1));
ps.setcolor(1,0,0);
ps.startline();
for (i=0;i<vlines.size();i++)
ps.lineto(vlines[i][0]/log(niter)*3,(vlines[i][3]-lo)/scale-1);
ps.endline();
ps.endpage();
}
niter=0;
}
ps.close();
}
void outHaltonAccumulators(vector<unsigned short> terHacc,vector<unsigned short> quinHacc,vector<unsigned short> septHacc,bool sign)
{
int i;
for (i=terHacc.size()-1;i>=0;i--)
cout<<terHacc[i]<<' ';
cout<<endl<<haccValue(terHacc,59049,sign)<<endl;
for (i=quinHacc.size()-1;i>=0;i--)
cout<<quinHacc[i]<<' ';
cout<<endl<<haccValue(quinHacc,15625,sign)<<endl;
for (i=septHacc.size()-1;i>=0;i--)
cout<<septHacc[i]<<' ';
cout<<endl<<haccValue(septHacc,16807,sign)<<endl;
}
void testHaltonAccumulator()
{
vector<unsigned short> terHacc,quinHacc,septHacc;
int i;
mpz_class inc;
bool sign=false,newsign;
cout<<"Halton accumulator test\n";
newsign=incHacc(terHacc,59049,496125,0,sign);
tassert(!newsign);
newsign=incHacc(quinHacc,15625,496125,0,sign);
tassert(!newsign);
newsign=incHacc(septHacc,16807,496125,0,sign);
tassert(!newsign);
outHaltonAccumulators(terHacc,quinHacc,septHacc,newsign);
sign=newsign;
newsign=incHacc(terHacc,59049,-524288,0,sign);
tassert(newsign);
newsign=incHacc(quinHacc,15625,-524288,0,sign);
tassert(newsign);
newsign=incHacc(septHacc,16807,-524288,0,sign);
tassert(newsign);
outHaltonAccumulators(terHacc,quinHacc,septHacc,newsign);
sign=newsign;
for (inc=1,i=0;i<41;i++)
inc*=41;
newsign=incHacc(terHacc,59049,inc,sign);
tassert(!newsign);
newsign=incHacc(quinHacc,15625,inc,sign);
tassert(!newsign);
newsign=incHacc(septHacc,16807,inc,sign);
tassert(!newsign);
outHaltonAccumulators(terHacc,quinHacc,septHacc,newsign);
tassert(terHacc[0]==41670);
tassert(terHacc.size()==14);
tassert(terHacc.back()==12542);
tassert(quinHacc[0]==3603);
tassert(quinHacc.size()==16);
tassert(quinHacc.back()==1647);
tassert(septHacc[0]==4036);
tassert(septHacc.size()==16);
tassert(septHacc.back()==551);
}
void test1AreaInCircle(double minx,double miny,double maxx,double maxy,double rightArea)
{
double area=areaInCircle(minx,miny,maxx,maxy);
cout<<"Area="<<ldecimal(area);
if (rightArea>=0)
{
cout<<", should be "<<ldecimal(rightArea);
tassert(fabs(area-rightArea)<1e-9);
}
cout<<endl;
}
void test4AreaInCircle(double x0,double x1,double x2,double y0,double y1,double y2)
{
double area[5];
double diff;
int i;
if (x0>x1)
swap(x0,x1);
if (x1>x2)
swap(x1,x2);
if (x0>x1)
swap(x0,x1);
if (y0>y1)
swap(y0,y1);