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wolkentest.cpp
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/******************************************************/
/* */
/* wolkentest.cpp - test program */
/* */
/******************************************************/
/* Copyright 2019-2023 Pierre Abbat.
* This file is part of Wolkenbase.
*
* Wolkenbase 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.
*
* Wolkenbase 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 Wolkenbase. If not, see <http://www.gnu.org/licenses/>.
*/
#include <iostream>
#include <fstream>
#include <iomanip>
#include <algorithm>
#include <cstdlib>
#include <csignal>
#include <cfloat>
#include <cassert>
#include <cstring>
#include <vector>
#include <string>
#include "config.h"
#include "angle.h"
#include "octree.h"
#include "shape.h"
#include "testpattern.h"
#include "eisenstein.h"
#include "random.h"
#include "ldecimal.h"
#include "ps.h"
#include "freeram.h"
#include "flowsnake.h"
#include "peano.h"
#include "relprime.h"
#include "manysum.h"
#include "manygcd.h"
#include "matrix.h"
#include "leastsquares.h"
#define tassert(x) testfail|=(!(x))
//#define tassert(x) if (!(x)) {testfail=true; sleep(10);}
// so that tests still work in non-debug builds
using namespace std;
char hexdig[16]={'0','1','2','3','4','5','6','7','8','9','a','b','c','d','e','f'};
bool slowmanysum=false;
bool testfail=false;
vector<string> args;
xy randomInCircle()
{
int n=rng.usrandom();
double r=sqrt(n+0.5)/256;
return cossin((int)(n*PHITURN))*r;
}
void outsizeof(string typeName,int size)
{
cout<<"size of "<<typeName<<" is "<<size<<endl;
}
void testsizeof()
// This is not run as part of "make test".
{
outsizeof("LasPoint",sizeof(LasPoint));
outsizeof("OctBuffer",sizeof(OctBuffer));
/* LasPoint 104
* OctBuffer 152
*/
}
void testfreeram()
{
cout<<"Free RAM "<<freeRam()<<endl;
}
void testintegertrig()
{
double sinerror,coserror,ciserror,totsinerror,totcoserror,totciserror;
int i;
char bs=8;
for (totsinerror=totcoserror=totciserror=i=0;i<128;i++)
{
sinerror=sin(i<<24)+sin((i+64)<<24);
coserror=cos(i<<24)+cos((i+64)<<24);
ciserror=hypot(cos(i<<24),sin(i<<24))-1;
if (sinerror>0.04 || coserror>0.04 || ciserror>0.04)
{
printf("sin(%8x)=%a sin(%8x)=%a\n",i<<24,sin(i<<24),(i+64)<<24,sin((i+64)<<24));
printf("cos(%8x)=%a cos(%8x)=%a\n",i<<24,cos(i<<24),(i+64)<<24,cos((i+64)<<24));
printf("abs(cis(%8x))=%a\n",i<<24,hypot(cos(i<<24),sin(i<<24)));
}
totsinerror+=sinerror*sinerror;
totcoserror+=coserror*coserror;
totciserror+=ciserror*ciserror;
}
printf("total sine error=%e\n",totsinerror);
printf("total cosine error=%e\n",totcoserror);
printf("total cis error=%e\n",totciserror);
tassert(totsinerror+totcoserror+totciserror<2e-29);
//On Linux, the total error is 2e-38 and the M_PIl makes a big difference.
//On DragonFly BSD, the total error is 1.7e-29 and M_PIl is absent.
tassert(bintodeg(0)==0);
tassert(fabs(bintodeg(0x15555555)-60)<0.0000001);
tassert(fabs(bintomin(0x08000000)==1350));
tassert(fabs(bintosec(0x12345678)-184320)<0.001);
tassert(fabs(bintogon(0x1999999a)-80)<0.0000001);
tassert(fabs(bintorad(0x4f1bbcdd)-3.88322208)<0.00000001);
for (i=-2147400000;i<2147400000;i+=rng.usrandom()+18000)
{
cout<<setw(11)<<i<<bs<<bs<<bs<<bs<<bs<<bs<<bs<<bs<<bs<<bs<<bs;
cout.flush();
tassert(degtobin(bintodeg(i))==i);
tassert(mintobin(bintomin(i))==i);
tassert(sectobin(bintosec(i))==i);
tassert(gontobin(bintogon(i))==i);
tassert(radtobin(bintorad(i))==i);
tassert(foldangle(atan2i(cossin(i)))==foldangle(i));
}
tassert(sectobin(1295999.9999)==-2147483648);
tassert(sectobin(1296000.0001)==-2147483648);
tassert(sectobin(-1295999.9999)==-2147483648);
tassert(sectobin(-1296000.0001)==-2147483648);
cout<<" "<<bs<<bs<<bs<<bs<<bs<<bs<<bs<<bs<<bs<<bs<<bs;
cout<<"atan2a "<<0x40000<<' '<<ldecimal(atan2a(sin(0x40000),cos(0x40000)))<<' '<<ldecimal(tan(0x40000))<<endl;
cout<<"atan2a "<<0x80000<<' '<<ldecimal(atan2a(sin(0x80000),cos(0x80000)))<<' '<<ldecimal(tan(0x80000))<<endl;
cout<<"atan2i(0,0)="<<hex<<atan2i(0,0)<<dec<<endl;
}
void testflat()
{
ofstream dumpFile("flat.dump");
PostScript ps;
xy center=9*randomInCircle();
vector<int64_t> blocks;
vector<LasPoint> points;
int i;
Cylinder cyl(center,1);
setStorePoints(true);
flatScene(10,100);
blocks=octRoot.findBlocks(cyl);
cout<<"Blocks:";
for (i=0;i<blocks.size();i++)
cout<<' '<<blocks[i];
cout<<endl;
points=octStore.pointsIn(cyl);
cout<<points.size()<<" points in cylinder\n";
tassert(abs((int)points.size()-314)<8);
ps.open("flat.ps");
ps.setpaper(papersizes["A4 landscape"],0);
ps.prolog();
octStore.plot(ps);
octStore.dump(dumpFile);
}
xyz findIntersection(Shape &shape,xyz a,xyz b)
{
bool ain=shape.in(a),bin=shape.in(b),min;
xyz m;
assert(ain^bin);
while (true)
{
m=(a+b)/2;
if (a==m || m==b)
break;
min=shape.in(m);
if (min==ain)
a=m;
else
b=m;
}
return m;
}
void testparaboloid()
{
Paraboloid p1(xyz(0,0,13),13);
xyz v(0,0,13),a(5,0,12),b(5,2,12),c(13,13,0),d(-14,-12,0),e(9,16,0);
Cube l(v,1),m(b,0.1);
tassert(p1.in(v));
tassert(p1.in(a));
tassert(!p1.in(b));
tassert(p1.in(c));
tassert(!p1.in(d));
tassert(p1.in(e));
tassert(p1.intersect(l));
tassert(!p1.intersect(m));
}
void testsphere()
{
Sphere s1(xyz(100,200,300),89);
/* 89²=7921 is a square that can be expressed as the sum of three different
* positive squares in more than one way.
* 89²=15²+36²+80²=39²+48²+64²
*/
xyz cen(100,200,300),a(115,164,220),b(115,163,220),c(36,239,252),d(36,240,252);
xyz e(64,120,315),f(63,120,315),g(164,248,339),h(164,248,340);
tassert(s1.in(cen));
tassert(s1.in(a));
tassert(!s1.in(b));
tassert(s1.in(c));
tassert(!s1.in(d));
tassert(s1.in(e));
tassert(!s1.in(f));
tassert(s1.in(g));
tassert(!s1.in(h));
}
void testhyperboloid()
{
xyz ver(100,200,300),ocen1(100,200,228),ocen2(100,200,203);
xyz topEndCur(100.6,200.8,300),bottomEndCur(100.6,200.8,228);
xyz topEndAsy1(3000100,4000200,300),bottomEndAsy1(3000100,4000200,-4e9);
xyz topEndAsy2(6000100,8000200,300),bottomEndAsy2(6000100,8000200,-4e9);
double sint,hint,aint1,aint2;
Hyperboloid h1(ver,72,1);
/* 72²=5184 is a square that can be expressed as the difference of three different
* positive squares in more than one way.
* 72²=78²-18²-24²=97²-25²-60²
*/
Sphere s1(ocen1,72);
Hyperboloid h2(ver,97,2);
Sphere s2(ocen2,97);
xyz a(118,176,294),b(75,260,275);
xyz c(118,176,295),d(75,260,276);
xyz e(118,176,293),f(75,260,274);
tassert(h1.in(a));
tassert(h1.in(b));
tassert(!h1.in(c));
tassert(!h1.in(d));
tassert(h1.in(e));
tassert(h1.in(f));
sint=findIntersection(s1,topEndCur,bottomEndCur).getz();
hint=findIntersection(h1,topEndCur,bottomEndCur).getz();
cout<<"Sphere intersection "<<ldecimal(sint)<<" Hyperboloid intersection "<<ldecimal(hint)<<endl;
tassert(fabs(sint-hint)<1/sqr(72.)); // Check curvatures are equal. The actual difference is 1/(72**3*4).
aint1=findIntersection(h1,topEndAsy1,bottomEndAsy1).getz();
aint2=findIntersection(h1,topEndAsy2,bottomEndAsy2).getz();
cout<<"Asymptotic slope "<<ldecimal((aint1-aint2)/5e6)<<endl;
tassert(fabs(1-(aint1-aint2)/5e6)<1e-6);
sint=findIntersection(s2,topEndCur,bottomEndCur).getz();
hint=findIntersection(h2,topEndCur,bottomEndCur).getz();
cout<<"Sphere intersection "<<ldecimal(sint)<<" Hyperboloid intersection "<<ldecimal(hint)<<endl;
tassert(fabs(sint-hint)<1/sqr(97.));
aint1=findIntersection(h2,topEndAsy1,bottomEndAsy1).getz();
aint2=findIntersection(h2,topEndAsy2,bottomEndAsy2).getz();
cout<<"Asymptotic slope "<<ldecimal((aint1-aint2)/5e6)<<endl;
tassert(fabs(2-(aint1-aint2)/5e6)<1e-6);
}
void testcylinder()
{
Cylinder c1(xy(0,0),13);
xyz cen(0,0,13),a(5,12,0),b(5,13,4),c(-9,-9,-3),d(-11,-7,2);
Cube l(cen,1),m(a,0.1),n(d,1/16.),o(d,1/32.);
tassert(c1.in(cen));
tassert(c1.in(a));
tassert(!c1.in(b));
tassert(c1.in(c));
tassert(!c1.in(d));
tassert(c1.intersect(l));
tassert(c1.intersect(m));
tassert(c1.intersect(n));
tassert(!c1.intersect(o));
}
void knowndet(matrix &mat)
/* Sets mat to a triangular matrix with ones on the diagonal, which is known
* to have determinant 1, then permutes the rows and columns so that Gaussian
* elimination will mess up the entries.
*
* The number of rows should be 40 at most. More than that, and it will not
* be shuffled well.
*/
{
int i,j,ran,rr,rc,cc,flipcount,size,giveup;
mat.setidentity();
size=mat.getrows();
for (i=0;i<size;i++)
for (j=0;j<i;j++)
mat[i][j]=(rng.ucrandom()*2-255)/BYTERMS;
for (flipcount=giveup=0;(flipcount<2*size || (flipcount&1)) && giveup<10000;giveup++)
{ // If flipcount were odd, the determinant would be -1 instead of 1.
ran=rng.usrandom();
rr=ran%size;
ran/=size;
rc=ran%size;
ran/=size;
cc=ran%size;
if (rr!=rc)
{
flipcount++;
mat.swaprows(rr,rc);
}
if (rc!=cc)
{
flipcount++;
mat.swapcolumns(rc,cc);
}
}
}
void dumpknowndet(matrix &mat)
{
int i,j,byte;
for (i=0;i<mat.getrows();i++)
for (j=0;j<mat.getcolumns();j++)
{
if (mat[i][j]==0)
cout<<"z0";
else if (mat[i][j]==1)
cout<<"z1";
else
{
byte=rint(mat[i][j]*BYTERMS/2+127.5);
cout<<hexdig[byte>>4]<<hexdig[byte&15];
}
}
cout<<endl;
}
void loadknowndet(matrix &mat,string dump)
{
int i,j,byte;
string item;
for (i=0;i<mat.getrows();i++)
for (j=0;j<mat.getcolumns();j++)
{
item=dump.substr(0,2);
dump.erase(0,2);
if (item[0]=='z')
mat[i][j]=item[1]-'0';
else
{
byte=stoi(item,0,16);
mat[i][j]=(byte*2-255)/BYTERMS;
}
}
cout<<endl;
}
void testmatrix()
{
int i,j,chk2,chk3,chk4;
matrix m1(3,4),m2(4,3),m3(4,3),m4(4,3);
matrix t1(37,41),t2(41,43),t3(43,37),p1,p2,p3;
matrix t1t,t2t,t3t,p1t,p2t,p3t;
matrix hil(8,8),lih(8,8),hilprod;
matrix kd(7,7);
matrix r0,c0,p11;
matrix rs1(3,4),rs2,rs3,rs4;
vector<double> rv,cv;
double tr1,tr2,tr3,de1,de2,de3,tr1t,tr2t,tr3t;
double toler=1.2e-12;
double kde;
double lo,hi;
manysum lihsum;
m1[2][0]=5;
m1[1][3]=7;
tassert(m1[2][0]==5);
m2[2][0]=9;
m2[1][4]=6;
tassert(m2[2][0]==9);
for (i=0;i<4;i++)
for (j=0;j<3;j++)
{
m2[i][j]=rng.ucrandom();
m3[i][j]=rng.ucrandom();
}
for (chk2=chk3=i=0;i<4;i++)
for (j=0;j<3;j++)
{
chk2=(50*chk2+(int)m2[i][j])%83;
chk3=(50*chk3+(int)m3[i][j])%83;
}
m4=m2+m3;
for (chk4=i=0;i<4;i++)
for (j=0;j<3;j++)
chk4=(50*chk4+(int)m4[i][j])%83;
tassert(chk4==(chk2+chk3)%83);
m4=m2-m3;
for (chk4=i=0;i<4;i++)
for (j=0;j<3;j++)
chk4=(50*chk4+(int)m4[i][j]+332)%83;
tassert(chk4==(chk2-chk3+83)%83);
lo=INFINITY;
hi=0;
for (i=0;i<1;i++)
{
t1.randomize_c();
t2.randomize_c();
t3.randomize_c();
t1t=t1.transpose();
t2t=t2.transpose();
t3t=t3.transpose();
p1=t1*t2*t3;
p2=t2*t3*t1;
p3=t3*t1*t2;
p1t=t3t*t2t*t1t;
p2t=t1t*t3t*t2t;
p3t=t2t*t1t*t3t;
tr1=p1.trace();
tr2=p2.trace();
tr3=p3.trace();
tr1t=p1t.trace();
tr2t=p2t.trace();
tr3t=p3t.trace();
de1=p1.determinant();
de2=p2.determinant();
de3=p3.determinant();
cout<<"trace1 "<<ldecimal(tr1)
<<" trace2 "<<ldecimal(tr2)
<<" trace3 "<<ldecimal(tr3)<<endl;
tassert(fabs(tr1-tr2)<toler && fabs(tr2-tr3)<toler && fabs(tr3-tr1)<toler);
tassert(fabs(tr1-tr1t)<toler && fabs(tr2-tr2t)<toler && fabs(tr3-tr3t)<toler);
tassert(tr1!=0);
cout<<"det1 "<<de1
<<" det2 "<<de2
<<" det3 "<<de3<<endl;
tassert(fabs(de1)>1e80 && fabs(de2)<1e60 && fabs(de3)<1e52);
// de2 and de3 would actually be 0 with exact arithmetic.
if (fabs(de2)>hi)
hi=fabs(de2);
if (fabs(de2)<lo)
lo=fabs(de2);
}
cout<<"Lowest det2 "<<lo<<" Highest det2 "<<hi<<endl;
for (i=0;i<8;i++)
for (j=0;j<8;j++)
hil[i][j]=1./(i+j+1);
lih=invert(hil);
for (i=0;i<8;i++)
for (j=0;j<i;j++)
lihsum+=fabs(lih[i][j]-lih[j][i]);
cout<<"Total asymmetry of inverse of Hilbert matrix is "<<lihsum.total()<<endl;
hilprod=hil*lih;
lihsum.clear();
for (i=0;i<8;i++)
for (j=0;j<8;j++)
lihsum+=fabs(hilprod[i][j]-(i==j));
cout<<"Total error of Hilbert matrix * inverse is "<<lihsum.total()<<endl;
tassert(lihsum.total()<2e-5 && lihsum.total()>1e-15);
for (i=0;i<1;i++)
{
knowndet(kd);
//loadknowndet(kd,"z0z0z0z1c9dd28z0z1z03c46c35cz0z0z0z0z1z0z0aa74z169f635e3z0z0z0z003z0z1z0z0z0z0fcz146z160z000f50091");
//loadknowndet(kd,"a6z1fc7ce056d6d1z0z0z0z0z1b49ez0z0z1z02f53z1z0z0z0z0z0z0e2z0z097z1230488z0z19b25484e1ez0z0z0z0z0z1");
kd.dump();
dumpknowndet(kd);
kde=kd.determinant();
cout<<"Determinant of shuffled matrix is "<<ldecimal(kde)<<" diff "<<kde-1<<endl;
tassert(fabs(kde-1)<4e-12);
}
for (i=0;i<11;i++)
{
rv.push_back((i*i*i)%11);
cv.push_back((i*3+7)%11);
}
r0=rowvector(rv);
c0=columnvector(cv);
p1=r0*c0;
p11=c0*r0;
tassert(p1.trace()==253);
tassert(p11.trace()==253);
tassert(p1.determinant()==253);
tassert(p11.determinant()==0);
for (i=0;i<3;i++)
for (j=0;j<4;j++)
rs1[i][j]=(j+1.)/(i+1)-(i^j);
rs2=rs1;
rs2.resize(4,3);
rs3=rs1*rs2;
rs4=rs2*rs1;
for (i=0;i<3;i++)
for (j=0;j<3;j++)
tassert(rs1[i][j]==rs2[i][j]);
cout<<"det rs3="<<ldecimal(rs3.determinant())<<endl;
tassert(fabs(rs3.determinant()*9-100)<1e-12);
tassert(rs4.determinant()==0);
rs4[3][3]=1;
tassert(fabs(rs4.determinant()*9-100)<1e-12);
}
void testquaternion()
{
Quaternion q0(0,0,0,0),q1(1,0,0,0),qr2(0,1,0,0),qr3(0.5,0.5,0.5,0.5);
Quaternion qr5(M_1PHI/2+0.5,0.5,M_1PHI/2,0),qsum(1.5,0.5,0.5,0.5);
Quaternion qprod(-0.5,0,-M_1PHI/2,M_1PHI/2+0.5);
Quaternion qrste(-1/14.,5/14.,7/14.,11/14.);
xyz vec0(0,0.6,0.8),vec2,vec3,vec5;
xyz vec0m(0,0.0006,0.0008),vec016k(0,9600,12800);
xyz vec2r(0,-0.6,-0.8),vec3r(0.8,0,0.6),vec5r(0.3*M_1PHI+0.4,0.3-0.4/M_1PHI,0.3/M_1PHI+0.4*M_1PHI);
xyz vecste(0,0,-192);
/* qr2, qr3, and qr5 generate the group of order 120 which is the group
* of rotations of an icosahedron (or dodecahedron) times 2.
* The matrix of qr5 is
* 1-1/2φ² 1/2φ 1/2 0.809017 0.309017 0.500000
* 1/2φ 1/2 -1/2φ-1/2 0.309017 0.500000 -0.809017
* -1/2 1/2φ+1/2 1/2-1/2φ² -0.500000 0.809017 0.309017
*/
Quaternion op0,op1,res;
int i,j;
res=q1+qr3;
tassert(res==qsum);
tassert(res!=q0);
res=qr2*qr3*qr5; // 1/3 rotation about (0,1/φ,-φ)
for (j=0;j<4;j++)
cout<<setprecision(6)<<res.getcomp(j)<<' ';
cout<<endl;
tassert((qprod-res).norm()<1e-12);
res=q1;
for (i=0;i<10;i++)
{
res=res*qr5;
for (j=0;j<4;j++)
cout<<setprecision(6)<<res.getcomp(j)<<' ';
cout<<endl;
}
vec2=qr2.rotate(vec0);
vec3=qr3.rotate(vec0);
vec5=qr5.rotate(vec0);
cout<<vec2.getx()<<' '<<vec2.gety()<<' '<<vec2.getz()<<endl;
cout<<vec3.getx()<<' '<<vec3.gety()<<' '<<vec3.getz()<<endl;
cout<<vec5.getx()<<' '<<vec5.gety()<<' '<<vec5.getz()<<endl;
tassert((vec2-vec2r).length()<1e-15);
tassert((vec3-vec3r).length()<1e-15);
tassert((vec5-vec5r).length()<1e-15);
vec2=qrste.rotate(vecste);
cout<<vec2.getx()<<' '<<vec2.gety()<<' '<<vec2.getz()<<endl;
op0=versor(vec0,radtobin(0.0003));
op1=versor(vec0,radtobin(0.0007));
res=versor(vec0,radtobin(0.001));
tassert((op0*op1-res).norm()<1e-9);
op0=versor(vec0,0.0003);
op1=versor(vec0,0.0007);
res=versor(vec0,0.001);
tassert((op0*op1-res).norm()<1e-9);
op0=versor(vec0m);
tassert((op0-res).norm()<1e-9);
op0=versor(vec016k);
tassert((op0*res+1).norm()<1e-9);
op0=versor(xyz(4,0,0));
tassert(op0==qr2);
op0=versor(xyz(4/3.,4/3.,4/3.));
tassert((op0-qr3).norm()<1e-9);
}
void testrelprime()
{
tassert(relprime(987)==610);
tassert(relprime(610)==377);
tassert(relprime(377)==233);
tassert(relprime(233)==144);
tassert(relprime(144)==89);
tassert(relprime(89)==55);
tassert(relprime(55)==34);
tassert(relprime(100000)==61803);
tassert(relprime(100)==61);
tassert(relprime(0)==1);
tassert(relprime(1)==1);
tassert(relprime(2)==1);
tassert(relprime(3)==2);
tassert(relprime(4)==3);
tassert(relprime(5)==3);
tassert(relprime(6)==5);
}
void testmanygcd()
{
vector<double> numbers;
double g;
int i,n;
for (n=16384,i=14;i<32;i++,n*=2)
numbers.push_back(n/1e3);
for (n=19683,i=9;i<20;i++,n*=3)
numbers.push_back(n/1e3);
for (n=15625,i=6;i<14;i++,n*=5)
numbers.push_back(n/1e3);
for (n=16807,i=5;i<12;i++,n*=7)
numbers.push_back(n/1e3);
g=manygcd(numbers,1e-9);
cout<<"manygcd="<<ldecimal(g)<<endl;
tassert(fabs(g-0.001)<1e-9);
}
void testmanysum()
{
manysum ms,negms;
int i,j,h;
double x,naiveforwardsum,forwardsum,pairforwardsum,naivebackwardsum,backwardsum,pairbackwardsum;
vector<double> summands;
double odd[32];
long double oddl[32];
int pairtime=0;
//QTime starttime;
cout<<"manysum"<<endl;
for (i=0;i<32;i++)
oddl[i]=odd[i]=2*i+1;
for (i=0;i<32;i++)
{
tassert(pairwisesum(odd,i)==i*i);
tassert(pairwisesum(oddl,i)==i*i);
}
ms.clear();
summands.clear();
tassert(pairwisesum(summands)==0);
for (naiveforwardsum=i=0;i>-7;i--)
{
x=pow(1000,i);
for (j=0;j<(slowmanysum?1000000:100000);j++)
{
naiveforwardsum+=x;
ms+=x;
negms-=x;
summands.push_back(x);
}
}
ms.prune();
forwardsum=ms.total();
tassert(forwardsum==-negms.total());
//starttime.start();
pairforwardsum=pairwisesum(summands);
//pairtime+=starttime.elapsed();
ms.clear();
summands.clear();
for (naivebackwardsum=0,i=-6;i<1;i++)
{
x=pow(1000,i);
for (j=0;j<(slowmanysum?1000000:100000);j++)
{
naivebackwardsum+=x;
ms+=x;
summands.push_back(x);
}
}
ms.prune();
backwardsum=ms.total();
//starttime.start();
pairbackwardsum=pairwisesum(summands);
//pairtime+=starttime.elapsed();
cout<<"Forward: "<<ldecimal(naiveforwardsum)<<' '<<ldecimal(forwardsum)<<' '<<ldecimal(pairforwardsum)<<endl;
cout<<"Backward: "<<ldecimal(naivebackwardsum)<<' '<<ldecimal(backwardsum)<<' '<<ldecimal(pairbackwardsum)<<endl;
tassert(fabs((forwardsum-backwardsum)/(forwardsum+backwardsum))<DBL_EPSILON);
tassert(fabs((pairforwardsum-pairbackwardsum)/(pairforwardsum+pairbackwardsum))<DBL_EPSILON);
tassert(fabs((forwardsum-pairforwardsum)/(forwardsum+pairforwardsum))<DBL_EPSILON);
tassert(fabs((backwardsum-pairbackwardsum)/(backwardsum+pairbackwardsum))<DBL_EPSILON);
tassert(fabs((forwardsum-naiveforwardsum)/(forwardsum+naiveforwardsum))<1000000*DBL_EPSILON);
tassert(fabs((backwardsum-naivebackwardsum)/(backwardsum+naivebackwardsum))<1000*DBL_EPSILON);
tassert(fabs((naiveforwardsum-naivebackwardsum)/(naiveforwardsum+naivebackwardsum))>30*DBL_EPSILON);
ms.clear();
summands.clear();
h=slowmanysum?1:16;
for (naiveforwardsum=i=0;i>-0x360000;i-=h)
{
x=exp(i/65536.);
naiveforwardsum+=x;
ms+=x;
summands.push_back(x);
}
ms.prune();
forwardsum=ms.total();
//starttime.start();
pairforwardsum=pairwisesum(summands);
//pairtime+=starttime.elapsed();
ms.clear();
summands.clear();
for (naivebackwardsum=0,i=-0x35ffff&-h;i<1;i+=h)
{
x=exp(i/65536.);
naivebackwardsum+=x;
ms+=x;
summands.push_back(x);
}
ms.prune();
backwardsum=ms.total();
//starttime.start();
pairbackwardsum=pairwisesum(summands);
//pairtime+=starttime.elapsed();
cout<<"Forward: "<<ldecimal(naiveforwardsum)<<' '<<ldecimal(forwardsum)<<' '<<ldecimal(pairforwardsum)<<endl;
cout<<"Backward: "<<ldecimal(naivebackwardsum)<<' '<<ldecimal(backwardsum)<<' '<<ldecimal(pairbackwardsum)<<endl;
tassert(fabs((forwardsum-backwardsum)/(forwardsum+backwardsum))<DBL_EPSILON);
tassert(fabs((pairforwardsum-pairbackwardsum)/(pairforwardsum+pairbackwardsum))<DBL_EPSILON);
tassert(fabs((forwardsum-pairforwardsum)/(forwardsum+pairforwardsum))<DBL_EPSILON);
tassert(fabs((backwardsum-pairbackwardsum)/(backwardsum+pairbackwardsum))<DBL_EPSILON);
tassert(fabs((forwardsum-naiveforwardsum)/(forwardsum+naiveforwardsum))<1000000*DBL_EPSILON);
tassert(fabs((backwardsum-naivebackwardsum)/(backwardsum+naivebackwardsum))<1000*DBL_EPSILON);
tassert(fabs((naiveforwardsum-naivebackwardsum)/(naiveforwardsum+naivebackwardsum))>30*DBL_EPSILON);
//cout<<"Time in pairwisesum: "<<pairtime<<endl;
}
void testldecimal()
{
double d;
bool looptests=false;
cout<<ldecimal(1/3.)<<endl;
cout<<ldecimal(M_PI)<<endl;
cout<<ldecimal(-64664./65536,1./131072)<<endl;
/* This is a number from the Alaska geoid file, -0.9867, which was output
* as -.98669 when converting to GSF.
*/
if (looptests)
{
for (d=M_SQRT_3-20*DBL_EPSILON;d<=M_SQRT_3+20*DBL_EPSILON;d+=DBL_EPSILON)
cout<<ldecimal(d)<<endl;
for (d=1.25-20*DBL_EPSILON;d<=1.25+20*DBL_EPSILON;d+=DBL_EPSILON)
cout<<ldecimal(d)<<endl;
for (d=95367431640625;d>1e-14;d/=5)
cout<<ldecimal(d)<<endl;
for (d=123400000000000;d>3e-15;d/=10)
cout<<ldecimal(d)<<endl;
for (d=DBL_EPSILON;d<=1;d*=2)
cout<<ldecimal(M_SQRT_3,d)<<endl;
}
cout<<ldecimal(0)<<' '<<ldecimal(INFINITY)<<' '<<ldecimal(NAN)<<' '<<ldecimal(-5.67)<<endl;
cout<<ldecimal(3628800)<<' '<<ldecimal(1296000)<<' '<<ldecimal(0.000016387064)<<endl;
tassert(ldecimal(0)=="0");
tassert(ldecimal(1)=="1");
tassert(ldecimal(-1)=="-1");
tassert(isalpha(ldecimal(INFINITY)[0]));
tassert(isalpha(ldecimal(NAN)[1])); // on MSVC is negative, skip the minus sign
tassert(ldecimal(1.7320508)=="1.7320508");
tassert(ldecimal(1.7320508,0.0005)=="1.732");
tassert(ldecimal(-0.00064516)=="-.00064516");
tassert(ldecimal(3628800)=="3628800");
tassert(ldecimal(1296000)=="1296e3");
tassert(ldecimal(0.000016387064)=="1.6387064e-5");
tassert(ldecimal(-64664./65536,1./131072)=="-.9867");
}
void testleastsquares()
{
matrix a(3,2);
vector<double> b,x;
b.push_back(4);
b.push_back(1);
b.push_back(3);
a[0][0]=1;
a[0][1]=3; // http://ltcconline.net/greenl/courses/203/MatrixOnVectors/leastSquares.htm
a[1][0]=2;
a[1][1]=4;
a[2][0]=1;
a[2][1]=6;
x=linearLeastSquares(a,b);
cout<<"Least squares ("<<ldecimal(x[0])<<','<<ldecimal(x[1])<<")\n";
tassert(dist(xy(x[0],x[1]),xy(-29/77.,51/77.))<1e-9);
a.resize(2,3);
b.clear();
b.push_back(1);
b.push_back(0);
a[0][0]=1;
a[0][1]=1; // https://www.math.usm.edu/lambers/mat419/lecture15.pdf
a[0][2]=1;
a[1][0]=-1;
a[1][1]=-1;
a[1][2]=1;
x=minimumNorm(a,b);
cout<<"Minimum norm ("<<ldecimal(x[0])<<','<<ldecimal(x[1])<<','<<ldecimal(x[2])<<")\n";
tassert(dist(xyz(x[0],x[1],x[2]),xyz(0.25,0.25,0.5))<1e-9);
}
const int linearSize[]={1,2,3,9,24,65,171,454,1200,3176,8403,22234};
const int quadraticSize[]={0,3,24,171,1200,8403,58824,411771,2882400,20176803,141237624,988663371};
void testflowsnake()
{
PostScript ps;
Flowsnake fs;
double prog;
Cube cube(xyz(314159,271828,0),512);
Cylinder cyl;
int i,j,n;
int sz=6;
double squareSize=biggestSquare(sz);
Eisenstein e;
complex<double> z;
complex<double> corners[6];
vector<complex<double> > coast,side;
for (i=0;i<256;i++)
{
n=rng.usrandom()-32768;
tassert(baseSeven(baseFlow(n))==n);
}
corners[0]=complex<double>(0,M_SQRT_1_3)*pow(cFlowBase,sz);
for (i=1;i<6;i++)
corners[i]=corners[i-1]*(complex<double>)Eisenstein(1,1);
for (i=0;i<6;i++)
{
side=crinklyLine(corners[i],corners[(i+1)%6],0.5);
for (n=0;n<side.size();n++)
coast.push_back(side[n]);
}
ps.open("flowsnake.ps");
ps.setpaper(papersizes["A4 landscape"],0);
ps.prolog();
ps.startpage();
ps.setscale(-linearSize[sz],-linearSize[sz],linearSize[sz],linearSize[sz]);
ps.startline();
for (i=-quadraticSize[sz];i<=quadraticSize[sz];i++)
{
e=baseFlow(i);
z=e;
ps.lineto(xy(z.real(),z.imag()));
}
ps.endline();
ps.endpage();
ps.startpage();
ps.setscale(-linearSize[sz],-linearSize[sz],linearSize[sz],linearSize[sz]);
ps.setcolor(1,1,0);
ps.startline();
ps.lineto(xy(squareSize,squareSize));
ps.lineto(xy(-squareSize,squareSize));
ps.lineto(xy(-squareSize,-squareSize));
ps.lineto(xy(squareSize,-squareSize));
ps.endline(false,true);
ps.setcolor(0,0,0);
ps.startline();
for (i=loLim[sz];i<=hiLim[sz];i++)
{
e=toFlowsnake(i);
z=e;
ps.lineto(xy(z.real(),z.imag()));
}
ps.endline();
ps.setcolor(0,0,1);
ps.startline();
for (i=0;i<coast.size();i++)
ps.lineto(xy(coast[i].real(),coast[i].imag()));
ps.endline(true);
ps.endpage();
for (n=0;n<12;n++)
{
ps.startpage();
ps.setscale(-linearSize[n],-linearSize[n],linearSize[n],linearSize[n]);
corners[0]=complex<double>(0,M_SQRT_1_3)*pow(cFlowBase,n);
squareSize=biggestSquare(n);
for (i=1;i<6;i++)
corners[i]=corners[i-1]*(complex<double>)Eisenstein(1,1);
coast.clear();
for (i=0;i<6;i++)
{
side=crinklyLine(corners[i],corners[(i+1)%6],squareSize/1000);
for (j=0;j<side.size();j++)
coast.push_back(side[j]);
}
ps.setcolor(1,1,0);
ps.startline();
ps.lineto(xy(squareSize,squareSize));
ps.lineto(xy(-squareSize,squareSize));
ps.lineto(xy(-squareSize,-squareSize));
ps.lineto(xy(squareSize,-squareSize));
ps.endline(false,true);
if (n==0)
{
ps.setcolor(1,0.5,0.5);
ps.circle(xy(0.574918626350463586,0.07052452345448619644),0.01);
}
ps.setcolor(0,0,1);
ps.startline();
for (i=0;i<coast.size();i++)
ps.lineto(xy(coast[i].real(),coast[i].imag()));
ps.endline(true);
ps.endpage();
cout<<n<<" "<<ldecimal(2*squareSize)<<endl;
}
fs.setSize(cube,10);
ps.startpage();
ps.setscale(cube.minX(),cube.minY(),cube.maxX(),cube.maxY());
while (true)
{
prog=fs.progress();
cyl=fs.cyl(fs.next());
if (cyl.getRadius()==0)
break;
ps.setcolor(prog,prog,1-prog);
ps.circle(cyl.getCenter(),cyl.getRadius());
}
ps.endpage();
cout<<' ';
}
void testpeano()
{
unsigned i;
array<int,3> rec;
array<int,2> pnt;
char histo[36];
Peano pe;
PostScript ps;
memset(histo,0,36);
for (i=0;i<THREE20;i+=rec[2])
{
rec=peanoPoint(2,2,i);
cout<<setw(11)<<i<<' '<<rec[0]<<' '<<rec[1]<<endl;
}
for (i=0;i<THREE20;i+=rec[2])
{
rec=peanoPoint(5,7,i);
cout<<setw(11)<<i<<' '<<rec[0]<<' '<<rec[1]<<endl;
if (rec[0]<0)
histo[35]++;
else
histo[rec[0]*7+rec[1]]++;
}
for (i=0;i<35;i++)
tassert(histo[i]==1);
tassert(histo[i]==20);
ps.open("peano.ps");
ps.setpaper(papersizes["A4 landscape"],0);
ps.prolog();
ps.startpage();
ps.setscale(0,0,71,41);
ps.startline();
pe.resize(71,41);
for (i=0;i<71*41;i++)
{
pnt=pe.step();
ps.lineto(xy(pnt[0],pnt[1]));
}
ps.endline();
ps.endpage();
}
/* Files for testing block splitting:
* 719: 1, 710, 81
* 727: 1, 10, 100
* 5749: 1, 18, 324
* 5779: 1, 5762, 289
* The number of points in one octree block is 720, and in eight blocks is 5760.
* These numbers are the next primes above and below them. The numbers 710, 10,
* 18, and 5762 are primitive roots of the respective primes close to their
* positive or negative cube roots, for even distribution of points in the cube.
* The test showed that points were being lost when splitting a block.
*/
void test1splitfile(int p,int proot)
{
int i;
int zstep=(proot*proot)%p;
LasHeader lasHeader;
LasPoint pnt;
lasHeader.openWrite(to_string(p)+".las",SI_TEST);
lasHeader.setVersion(1,2);
lasHeader.setPointFormat(1);
lasHeader.setScale(xyz(0,0,0),xyz(1,1,1),xyz(1./p,1./p,1./p));
for (i=0;i<p;i++)
{
pnt.location=xyz((i+0.5)/p,((i*proot)%p+0.5)/p,((i*zstep)%p+0.5)/p);
pnt.returnNum=1;
pnt.gpsTime=i;
lasHeader.writePoint(pnt);
}
lasHeader.writeHeader();
}
void testsplitfile()
/* The two numbers are a prime near 1 or 8 times the number of records per
* block (see octree.h) and a primitive root near ± its cube root.
*/
{
test1splitfile(523,516);
test1splitfile(541,10);
test1splitfile(719,710);
test1splitfile(727,10);
test1splitfile(4289,17);
test1splitfile(4297,15);
test1splitfile(5749,18);
test1splitfile(5779,5762);
}
const short prec[7]=
{
1024,972,1000,1029,1089,1001,1071
};
/* The LCM of these numbers is 285290957952000, so the GCD of their reciprocals
* is too small to be used as a scale. This is to test setting the scale
* when combining several files into one point cloud.
*/
void testbigcloud()
/* Creates a big point cloud in seven files to test loading of big point clouds.
* The density is set so that, except at the edges, each cube containing
* points is a 1 meter cube.
* The total number of points is 7 million. This normally fits in RAM, but
* the program can be forced to swap by setting low RAM to all RAM.
*/
{
vector<long long> blocks;