mirror of
https://github.com/zenorogue/hyperrogue.git
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586 lines
19 KiB
C++
586 lines
19 KiB
C++
// This generates the inverse geodesics tables.
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// Usage:
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// [executable] -geo sol -build -write solv-geodesics.dat
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// -geo 3:2 -build -write shyp-geodesics.dat
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// -geo 3:1/2 -build -write ssol-geodesics.dat
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// -exit
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// Loading generated tables and visualization:
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// [executable] /hyper -fsol [filename] -geo sol -visualize filename-%03d.png
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// You can also do -geo [...] -build to build and test the table
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// without writing it.
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// By default this generates 64x64x64 tables.
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// Add e.g. '-dim 128 128 128' before -write to generate
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// a more/less precise table.
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// # ./hyper -rk-steps 100 -geo Sol -iz-list -sn-unittest -build -write solv-geodesics-a.dat -visualize devmods/san1/solva-%04d.png -improve -write solv-geodesics.dat -visualize devmods/san1/solvb-%04d.png
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// # ./hyper -dim 32 32 32 -geo 3:1/2 -iz-list -sn-unittest -build -write ssol-geodesics-a.dat -visualize devmods/san1/ssola-%04d.png -improve -write ssol-geodesics.dat -visualize devmods/san1/ssolb-%04d.png
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// # ./hyper -dim 32 32 32 -geo 3:2 -iz-list -sn-unittest -build -write shyp-geodesics.dat -visualize devmods/san1/shypa-%04d.png
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#include "../hyper.h"
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#include <thread>
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#include <mutex>
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namespace hr {
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transmatrix parabolic1(ld u);
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namespace sn {
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template<class T> void parallelize(int threads, int Nmin, int Nmax, T action) {
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std::vector<std::thread> v;
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for(int k=0; k<threads; k++)
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v.emplace_back([&,k] () {
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for(int i=Nmin+k; i < Nmax; i += threads) action(k, i);
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});
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for(std::thread& t:v) t.join();
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}
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ld solerror(hyperpoint ok, hyperpoint chk) {
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auto zok = point3( x_to_ix(ok[0]), x_to_ix(ok[1]), z_to_iz(ok[2]) );
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auto zchk = point3( x_to_ix(chk[0]), x_to_ix(chk[1]), z_to_iz(chk[2]) );
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return hypot_d(3, zok - zchk);
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}
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int max_iter = 999999;
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hyperpoint fail(.1, .2, .3, .4);
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hyperpoint iterative_solve(hyperpoint xp, hyperpoint candidate, ld minerr, bool debug = false) {
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transmatrix T = Id; T[0][1] = 8; T[2][2] = 5;
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auto f = [&] (hyperpoint x) { return nisot::numerical_exp(x); }; // T * x; };
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auto ver = f(candidate);
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ld err = solerror(xp, ver);
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auto at = candidate;
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ld eps = 1e-6;
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hyperpoint c[3];
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for(int a=0; a<3; a++) c[a] = point3(a==0, a==1, a==2);
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int iter = 0;
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while(err > minerr) {
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iter++; if(iter > max_iter) return fail;
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if(debug) println(hlog, "\n\nf(", at, "?) = ", ver, " (error ", err, ")");
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array<hyperpoint, 3> pnear;
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for(int a=0; a<3; a++) {
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auto x = at + c[a] * eps;
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if(debug) println(hlog, "f(", x, ") = ", f(x), " = y + ", f(x)-ver );
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pnear[a] = (f(x) - ver) / eps; // (direct_exp(at + c[a] * eps, prec) - ver) / eps;
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}
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transmatrix U = Id;
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for(int a=0; a<3; a++)
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for(int b=0; b<3; b++)
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U[a][b] = pnear[b][a];
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hyperpoint diff = (xp - ver);
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hyperpoint bonus = inverse(U) * diff;
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if(hypot_d(3, bonus) > 0.1) bonus = bonus * 0.1 / hypot_d(3, bonus);
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int fixes = 0;
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if(debug)
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println(hlog, "\nU = ", U, "\ndiff = ", diff, "\nbonus = ", bonus, "\n");
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nextfix:
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hyperpoint next = at + bonus;
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hyperpoint nextver = f(next);
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ld nexterr = solerror(xp, nextver);
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if(debug) println(hlog, "f(", next, ") = ", nextver, ", error = ", nexterr);
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if(nexterr < err) {
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// println(hlog, "reduced error ", err, " to ", nexterr);
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at = next;
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ver = nextver;
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err = nexterr;
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continue;
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}
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else {
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bonus /= 2;
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fixes++;
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if(fixes > 10) {
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if(err > 999) {
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for(ld s = 1; abs(s) > 1e-9; s *= 0.5)
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for(int k=0; k<27; k++) {
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int kk = k;
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next = at;
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for(int i=0; i<3; i++) { if(kk%3 == 1) next[i] += s; if(kk%3 == 2) next[i] -= s; kk /= 3; }
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// next = at + c[k] * s;
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nextver = f(next);
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nexterr = solerror(xp, nextver);
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// println(hlog, "f(", next, ") = ", nextver, ", error = ", nexterr);
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if(nexterr < err) { at = next; ver = nextver; err = nexterr; goto nextiter; }
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}
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println(hlog, "cannot improve error ", err);
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exit(1);
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}
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return fail;
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}
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goto nextfix;
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}
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nextiter: ;
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}
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// println(hlog, "#it = ", iter);
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return at;
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}
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using ptlow = compressed_point;
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ptlow operator +(ptlow a, ptlow b) { return make_array<float>(a[0]+b[0], a[1]+b[1], a[2]+b[2]); }
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ptlow operator -(ptlow a, ptlow b) { return make_array<float>(a[0]-b[0], a[1]-b[1], a[2]-b[2]); }
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ptlow operator *(ptlow a, ld x) { return make_array<float>(a[0]*x, a[1]*x, a[2]*x); }
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void fint(FILE *f, int x) { fwrite(&x, sizeof(x), 1, f); }
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void ffloat(FILE *f, float x) { fwrite(&x, sizeof(x), 1, f); }
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void write_table(sn::tabled_inverses& tab, const char *fname) {
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FILE *f = fopen(fname, "wb");
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fint(f, tab.PRECX);
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fint(f, tab.PRECY);
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fint(f, tab.PRECZ);
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fwrite(&tab.tab[0], sizeof(ptlow) * tab.PRECX * tab.PRECY * tab.PRECZ, 1, f);
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fclose(f);
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}
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void alloc_table(sn::tabled_inverses& tab, int X, int Y, int Z) {
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tab.PRECX = X;
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tab.PRECY = Y;
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tab.PRECZ = Z;
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tab.tab.resize(X*Y*Z);
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}
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ld ptd(ptlow p) {
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return p[0]*p[0] + p[1]*p[1] + p[2] * p[2];
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}
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void fix_boundaries(sn::tabled_inverses& tab, int last_x, int last_y, int last_z) {
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int PRECX = tab.PRECX;
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int PRECY = tab.PRECY;
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int PRECZ = tab.PRECZ;
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for(int x=0; x<last_x; x++)
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for(int y=0; y<last_y; y++) {
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for(int z=last_z; z<PRECZ; z++)
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tab.get_int(x,y,z) = tab.get_int(x,y,z-1) * 2 - tab.get_int(x,y,z-2);
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if(nih)
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tab.get_int(x,y,0) = tab.get_int(x,y,1) * 2 - tab.get_int(x,y,2);
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}
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for(int x=0; x<last_x; x++)
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for(int y=last_y; y<PRECY; y++)
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for(int z=0; z<PRECZ; z++)
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tab.get_int(x,y,z) = tab.get_int(x,y-1,z) * 2 - tab.get_int(x,y-2,z);
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for(int x=last_x; x<PRECX; x++)
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for(int y=0; y<PRECY; y++)
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for(int z=0; z<PRECZ; z++)
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tab.get_int(x,y,z) = tab.get_int(x-1,y,z) * 2 - tab.get_int(x-2,y,z);
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}
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void build_sols(int PRECX, int PRECY, int PRECZ) {
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std::mutex file_mutex;
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ld max_err = 0;
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auto& tab = sn::get_tabled();
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alloc_table(tab, PRECX, PRECY, PRECZ);
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int last_x = PRECX-1, last_y = PRECY-1, last_z = PRECZ-1;
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auto act = [&] (int tid, int iz) {
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if((nih && iz == 0) || iz == PRECZ-1) return;
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auto solve_at = [&] (int ix, int iy) {
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// if(ix != 30 || iy <= 50 || iz) return;
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ld x = ix_to_x(ix / (PRECX-1.));
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ld y = ix_to_x(iy / (PRECY-1.));
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ld z = iz_to_z(iz / (PRECZ-1.));
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auto v = hyperpoint ({x,y,z,1});
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vector<hyperpoint> candidates;
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hyperpoint cand;
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candidates.push_back(point3(0,0,0));
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// sort(candidates.begin(), candidates.end(), [&] (hyperpoint a, hyperpoint b) { return solerror(v, direct_exp(a, prec)) > solerror(v, direct_exp(b, prec)); });
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// cand_best = candidates.back();
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vector<hyperpoint> solved_candidates;
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for(auto c: candidates) {
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auto solt = iterative_solve(v, c, 1e-6, false);
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solved_candidates.push_back(solt);
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if(solerror(v, nisot::numerical_exp(solt)) < 1e-9) break;
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}
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sort(solved_candidates.begin(), solved_candidates.end(), [&] (hyperpoint a, hyperpoint b) { return solerror(v, nisot::numerical_exp(a)) > solerror(v, nisot::numerical_exp(b)); });
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cand = solved_candidates.back();
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auto xerr = solerror(v, nisot::numerical_exp(cand));
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if(cand == fail) {
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println(hlog, format("[%2d %2d %2d] FAIL", iz, iy, ix));
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}
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else if(xerr > 1e-3) {
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println(hlog, format("[%2d %2d %2d] ", iz, iy, ix));
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println(hlog, "f(?) = ", v);
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println(hlog, "f(", cand, ") = ", nisot::numerical_exp(cand));
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println(hlog, "error = ", xerr);
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println(hlog, "canned = ", compress(azeq_to_table(cand)));
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max_err = xerr;
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return;
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}
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auto& so = tab.get_int(ix, iy, iz);
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so = compress(azeq_to_table(cand));
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for(int z=0; z<3; z++) if(isnan(so[z]) || isinf(so[z])) {
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println(hlog, cand, "canned to ", so);
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exit(4);
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}
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};
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for(int it=0; it<max(last_x, last_y); it++) {
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for(int a=0; a<it; a++) {
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if(it < last_x && a < last_y) solve_at(it, a);
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if(a < last_x && it < last_y) solve_at(a, it);
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}
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if(it < last_x && it < last_y) solve_at(it, it);
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std::lock_guard<std::mutex> fm(file_mutex);
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if(0) println(hlog, format("%2d: %2d", iz, it));
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}
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};
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parallelize(PRECZ, 0, PRECZ, act);
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fix_boundaries(tab, last_x, last_y, last_z);
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}
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std::mutex file_mutex_global;
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bool deb = false;
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hyperpoint find_optimal_geodesic(hyperpoint res) {
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auto p0 = point3(0, 0, 0);
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hyperpoint h = iterative_solve(res, p0, 100, 1e-9);
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if(h == fail) return fail;
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ld d = hypot_d(3, h);
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auto solve = [&] (hyperpoint m, pair<hyperpoint, hyperpoint> last) {
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hyperpoint t = // inverse_exp(m, iTable, false);
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iterative_solve(m, last.first, 100, 1e-9);
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hyperpoint u = // inverse_exp(inverse(nisot::translate(m)) * res, iTable, false);
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iterative_solve(inverse(nisot::translate(m)) * res, last.second, 100, 1e-6);
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return make_pair(t, u);
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};
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auto quality = [&] (pair<hyperpoint, hyperpoint> p) {
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return hypot_d(3, p.first) + hypot_d(3, p.second);
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};
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auto attempt = [&] (hyperpoint mid) {
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auto p = solve(mid, {p0, p0});
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ld qd = quality(p);
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if(true) {
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// println(hlog, "there is something better: ", qd, " vs ", d);
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bool found;
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bool failed = false;
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auto tryit = [&] (hyperpoint h) {
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auto p2 = solve(h, p);
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auto qd2 = quality(p2);
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if(p2.first == fail || p2.second == fail) failed = true;
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else if(qd2 < qd) {
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qd = qd2, p = p2, mid = h;
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found = true;
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return true;
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}
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return false;
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};
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ld delta = 1e-3;
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/*
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auto q_x = quality(solve(mid + point3(delta, 0, 0), p)) - qd;
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auto q_xx = quality(solve(mid + point3(delta+delta, 0, 0), p)) - qd - 2 * q_x;
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auto q_y = quality(solve(mid + point3(0, delta, 0), p)) - qd;
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auto q_yy = quality(solve(mid + point3(0, delta+delta, 0), p)) - qd - 2 * q_y;
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auto q_z = quality(solve(mid + point3(0, 0, delta), p)) - qd;
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auto q_zz = quality(solve(mid + point3(0, 0, delta+delta), p)) - qd - 2 * q_z;
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auto q_xy = quality(solve(mid + point3(delta, delta, 0), p)) - qd - q_x - q_y;
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auto q_xz = quality(solve(mid + point3(delta, 0, delta), p)) - qd - q_x - q_z;
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auto q_yz = quality(solve(mid + point3(0, delta, delta), p)) - qd - q_y - q_z;
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transmatrix T = build_matrix(
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hyperpoint(q_xx, q_xy, q_xz, 0),
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hyperpoint(q_xy, q_yy, q_yz, 0),
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hyperpoint(q_xz, q_yz, q_zz, 0),
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hyperpoint(0, 0, 0, 1)
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);
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hyperpoint q = hyperpoint(q_x, q_y, q_z, 0);
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*/
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int itera = 0;
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while(true) {
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itera++;
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if(itera % 1000 == 0) {
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std::lock_guard<std::mutex> fm(file_mutex_global);
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println(hlog, "itera = ", itera);
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if(itera >= 5000) return;
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}
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auto q_v = quality(solve(mid + point3(delta, -delta, 0), p)) - qd;
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auto q_vv = quality(solve(mid + point3(delta+delta, -delta-delta, 0), p)) - qd - 2 * q_v;
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auto q_z = quality(solve(mid + point3(0, 0, delta), p)) - qd;
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auto q_zz = quality(solve(mid + point3(0, 0, delta+delta), p)) - qd - 2 * q_z;
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auto q_vz = quality(solve(mid + point3(delta, -delta, delta), p)) - qd - q_v - q_z;
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ld d = q_vv * q_zz - q_vz * q_vz;
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if(d == 0 || isnan(d) || isinf(d)) {
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std::lock_guard<std::mutex> fm(file_mutex_global);
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println(hlog, "bad matrix in iteration #", itera);
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println(hlog, "p = ", p, " mid = ", mid);
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println(hlog, solve(mid, p));
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return;
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}
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transmatrix T = build_matrix(
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hyperpoint(q_vv, 0, q_vz, 0),
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hyperpoint(0, 1, 0, 0),
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hyperpoint(q_vz, 0, q_zz, 0),
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hyperpoint(0, 0, 0, 1)
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);
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hyperpoint q = hyperpoint(q_v, 0, q_z, 0);
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hyperpoint res = inverse(T) * -q;
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// println(hlog, "res = ", res);
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// println(hlog, "check = ", q + T * res);
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res[1] = -res[0];
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res = res * delta;
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res /= 10.;
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if(tryit(mid + res)) continue;
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if(tryit(mid + res/2)) continue;
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if(tryit(mid + res/4)) continue;
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break;
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}
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// q_x + q_xx * x + q_xy * y + q_xz * z == 0
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// q + Txyz == 0
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int it = 0;
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ld qd0 = qd;
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if(false) while(delta > 1e-6) {
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it++;
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// if(it % 1000 == 0) println(hlog, "iterations ", it);
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if(it > 1000) return;
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if(failed) return;
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found = false;
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while(tryit(mid + point3(delta, -delta, 0)));
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while(tryit(mid + point3(-delta, +delta, 0)));
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while(tryit(mid + point3(0, 0, delta)));
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while(tryit(mid + point3(0, 0, -delta)));
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// while(tryit(mid + point3(delta, delta, 0)));
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// while(tryit(mid + point3(-delta, -delta, 0)));
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if(found) println(hlog, "improved further from ", qd0, " to ", qd);
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if(!found) delta /= 2;
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}
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max_iter = 1000;
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auto h1 = iterative_solve(res, p.first * quality(p) / hypot_d(3, p.first), 100, 1e-6);
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if(deb) println(hlog, "h1 returns ", h1, " of length ", hypot_d(3, h1), " and error ", hypot_d(3, nisot::numerical_exp(h1) - res));
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if(h1 == fail) return;
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auto d1 = hypot_d(3, h1);
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if(d1 < d) h = h1, d = d1;
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}
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};
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hyperpoint old = h;
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attempt(point31(res[0], 0, res[2]/2));
|
|
attempt(point31(0, res[1], res[2]/2));
|
|
|
|
std::lock_guard<std::mutex> fm(file_mutex_global);
|
|
if(h != old && hypot_d(3, h) < hypot_d(3, old) - 1e-5)
|
|
println(hlog, "new = ", h, " vs old = ", old, " length ", hypot_d(3, h), " vs ", hypot_d(3, old));
|
|
else if(deb)
|
|
println(hlog, " not improved: ", old);
|
|
|
|
return h;
|
|
}
|
|
|
|
void fix_bugs(sn::tabled_inverses& tab) {
|
|
auto bug = compress(azeq_to_table(fail));
|
|
for(int iz=0; iz<tab.PRECZ; iz++)
|
|
for(int iy=0; iy<tab.PRECY; iy++)
|
|
for(int ix=0; ix<tab.PRECX; ix++) {
|
|
if(tab.get_int(ix, iy, iz) == bug)
|
|
for(int a=0; a<3; a++)
|
|
tab.get_int(ix, iy, iz)[a] = (tab.get_int(ix-1, iy, iz)[a]*2 - tab.get_int(ix-2, iy, iz)[a]);
|
|
}
|
|
}
|
|
|
|
void visualize_table(sn::tabled_inverses& tab, const string& s) {
|
|
renderbuffer rb(tab.PRECX, tab.PRECY, false);
|
|
rb.make_surface();
|
|
|
|
for(int iz=0; iz<tab.PRECZ; iz++) {
|
|
println(hlog, "iz=", iz);
|
|
for(int iy=0; iy<tab.PRECY; iy++)
|
|
for(int ix=0; ix<tab.PRECX; ix++) {
|
|
auto& p = qpixel(rb.srf, ix, iy);
|
|
if(ix == 52 && iy >= 30 && iy <= 40 && iz == 15)
|
|
println(hlog, "A ", tie(ix,iy,iz), " : ", tab.get_int(ix, iy, iz));
|
|
// println(hlog, ix, ", ", iy);
|
|
p = 0xFFFFFFFF;
|
|
for(int i=0; i<3; i++)
|
|
part(p, i) = 0x80 + 0x70 * tab.get_int(ix, iy, iz)[i];
|
|
}
|
|
SDL_SavePNG(rb.srf, format(s.c_str(), iz).c_str());
|
|
}
|
|
}
|
|
|
|
void improve(sn::tabled_inverses& tab) {
|
|
int PRECX = tab.PRECX;
|
|
int PRECY = tab.PRECY;
|
|
int PRECZ = tab.PRECZ;
|
|
int last_x = PRECX-1, last_y = PRECY-1, last_z = PRECZ-1;
|
|
|
|
max_iter = 1000;
|
|
auto act = [&] (int tid, int iz) {
|
|
if((nih && iz == 0) || iz == PRECZ-1) return;
|
|
for(int iy=0; iy<last_y; iy++)
|
|
for(int ix=0; ix<last_x; ix++) {
|
|
if(ix < 32 || iy < 32) continue;
|
|
if(deb) { if(ix < 50 || ix > 54 || iy != 46 || iz != 6) continue; }
|
|
if(deb) println(hlog, tie(ix, iy, iz), ":");
|
|
ld x = ix_to_x(ix / (PRECX-1.));
|
|
ld y = ix_to_x(iy / (PRECY-1.));
|
|
ld z = iz_to_z(iz / (PRECZ-1.));
|
|
hyperpoint p = point31(x, y, z);
|
|
// hyperpoint h1 = inverse_exp(p, iTable, false);
|
|
hyperpoint h2 = find_optimal_geodesic(p);
|
|
|
|
std::lock_guard<std::mutex> fm(file_mutex_global);
|
|
if(ix == last_x-1) println(hlog, "solved ", tie(ix, iy, iz));
|
|
|
|
if(h2 != fail) {
|
|
auto& so = tab.get_int(ix, iy, iz);
|
|
so = compress(azeq_to_table(h2));
|
|
}
|
|
}
|
|
};
|
|
max_iter = 1000000;
|
|
|
|
parallelize(PRECZ, 0, PRECZ, act);
|
|
if(deb) exit(7);
|
|
|
|
|
|
fix_boundaries(tab, last_x, last_y, last_z);
|
|
}
|
|
|
|
int dimX=64, dimY=64, dimZ=64;
|
|
|
|
EX hyperpoint recompress(hyperpoint h) { return decompress(compress(h)); }
|
|
|
|
int readArgs() {
|
|
using namespace arg;
|
|
|
|
if(0) ;
|
|
else if(argis("-dim")) {
|
|
PHASEFROM(2);
|
|
shift(); dimX = argi();
|
|
shift(); dimY = argi();
|
|
shift(); dimZ = argi();
|
|
}
|
|
else if(argis("-build")) {
|
|
PHASEFROM(2);
|
|
build_sols(dimX, dimY, dimZ);
|
|
}
|
|
else if(argis("-load-old")) {
|
|
sn::get_tabled().load();
|
|
}
|
|
else if(argis("-improve")) {
|
|
sn::get_tabled().load();
|
|
improve(sn::get_tabled());
|
|
}
|
|
else if(argis("-write")) {
|
|
shift();
|
|
write_table(sn::get_tabled(), argcs());
|
|
}
|
|
else if(argis("-fix-bugs")) {
|
|
sn::get_tabled().load();
|
|
fix_bugs(sn::get_tabled());
|
|
}
|
|
else if(argis("-iz-list")) {
|
|
sn::get_tabled().load();
|
|
for(int iz=0; iz<dimZ-1; iz++)
|
|
println(hlog, "iz=", iz, " z=", iz_to_z(iz / (dimZ-1.)));
|
|
}
|
|
else if(argis("-visualize")) {
|
|
shift();
|
|
sn::get_tabled().load();
|
|
visualize_table(sn::get_tabled(), argcs());
|
|
}
|
|
else if(argis("-sn-unittest")) {
|
|
println(hlog, "nih = ", (bool)nih);
|
|
ld maxerr;
|
|
auto test_result = [&maxerr] (ld a, ld b) { maxerr = max(maxerr, (a-b)); };
|
|
auto test_result_p = [&maxerr] (hyperpoint a, hyperpoint b) { maxerr = max(maxerr, hypot_d(3, a-b)); };
|
|
auto test = [&maxerr] (string s, reaction_t tester) {
|
|
maxerr = 0;
|
|
tester();
|
|
println(hlog, "unittest: ", s, " error = ", maxerr);
|
|
};
|
|
test("x_to_ix", [&] { for(ld a=0; a<=20; a+=.1) test_result(a, sn::ix_to_x(sn::x_to_ix(a))); });
|
|
test("z_to_iz", [&] { for(ld a=nih?-20:0; a<=20; a+=.1) test_result(a, sn::iz_to_z(sn::z_to_iz(a))); });
|
|
test("azeq_to_table", [&] { for(ld a=-5; a<=5; a++) for(ld b=-5; b<=5; b++) for(ld c=-5; c<=5; c++) { hyperpoint h = point3(a,b,c); test_result_p(h, sn::table_to_azeq(sn::azeq_to_table(h))); }});
|
|
test("azeq_to_table recompressed", [&] {
|
|
for(ld a=-5; a<=5; a++) for(ld b=-5; b<=5; b++) for(ld c=-5; c<=5; c++) {
|
|
hyperpoint h = point3(a,b,c); test_result_p(h, sn::table_to_azeq(recompress(sn::azeq_to_table(h))));
|
|
}
|
|
});
|
|
}
|
|
|
|
else return 1;
|
|
return 0;
|
|
}
|
|
|
|
auto hook = addHook(hooks_args, 100, readArgs);
|
|
|
|
}
|
|
}
|