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/*
* Normaliz
* Copyright (C) 2007-2014 Winfried Bruns, Bogdan Ichim, Christof Soeger
* This 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.
*
* This program 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 this program. If not, see <http://www.gnu.org/licenses/>.
*
* As an exception, when this program is distributed through (i) the App Store
* by Apple Inc.; (ii) the Mac App Store by Apple Inc.; or (iii) Google Play
* by Google Inc., then that store may impose any digital rights management,
* device limits and/or redistribution restrictions that are required by its
* terms of service.
*/
//---------------------------------------------------------------------------
#include <iostream>
#include <string>
#include <algorithm>
#include <list>
#include "libnormaliz/integer.h"
#include "libnormaliz/vector_operations.h"
#include "libnormaliz/matrix.h"
//---------------------------------------------------------------------------
namespace libnormaliz {
using namespace std;
//---------------------------------------------------------------------------
template<typename Integer>
Integer v_scalar_product(const vector<Integer>& av,const vector<Integer>& bv){
//loop stretching ; brings some small speed improvement
Integer ans = 0;
size_t i,n=av.size();
#ifdef __MIC__
// this version seems to be better vectorizable on the mic
for (i=0; i<n; ++i)
ans += av[i]*bv[i];
#else // __MIC__
typename vector<Integer>::const_iterator a=av.begin(), b=bv.begin();
if( n >= 16 )
{
for( i = 0; i < ( n >> 4 ); ++i, a += 16, b +=16 ){
ans += a[0] * b[0];
ans += a[1] * b[1];
ans += a[2] * b[2];
ans += a[3] * b[3];
ans += a[4] * b[4];
ans += a[5] * b[5];
ans += a[6] * b[6];
ans += a[7] * b[7];
ans += a[8] * b[8];
ans += a[9] * b[9];
ans += a[10] * b[10];
ans += a[11] * b[11];
ans += a[12] * b[12];
ans += a[13] * b[13];
ans += a[14] * b[14];
ans += a[15] * b[15];
}
n -= i<<4;
}
if( n >= 8)
{
ans += a[0] * b[0];
ans += a[1] * b[1];
ans += a[2] * b[2];
ans += a[3] * b[3];
ans += a[4] * b[4];
ans += a[5] * b[5];
ans += a[6] * b[6];
ans += a[7] * b[7];
n -= 8;
a += 8;
b += 8;
}
if( n >= 4)
{
ans += a[0] * b[0];
ans += a[1] * b[1];
ans += a[2] * b[2];
ans += a[3] * b[3];
n -= 4;
a += 4;
b += 4;
}
if( n >= 2)
{
ans += a[0] * b[0];
ans += a[1] * b[1];
n -= 2;
a += 2;
b += 2;
}
if(n>0)
ans += a[0]*b[0];
#endif // __MIC__
if(!check_range(ans)){
#pragma omp atomic
GMP_scal_prod++;
// cout << "av " << av;
// cout << "bv " << bv;
vector<mpz_class> mpz_a(av.size()), mpz_b(bv.size());
convert(mpz_a, av);
convert(mpz_b, bv);
convert(ans, v_scalar_product(mpz_a,mpz_b));
}
return ans;
}
//---------------------------------------------------------------------------
template<typename Integer>
Integer v_scalar_product_unequal_vectors_end(const vector<Integer>& a,const vector<Integer>& b){
Integer ans = 0;
size_t i,n=a.size(),m=b.size();
for (i = 1; i <= n; i++) {
ans+=a[n-i]*b[m-i];
}
return ans;
}
//---------------------------------------------------------------------------
/*
* template<typename Integer>
vector<Integer> v_add_overflow_check(const vector<Integer>& a,const vector<Integer>& b){
size_t i,s=a.size();
Integer test;
vector<Integer> d(s);
for (i = 0; i <s; i++) {
d[i]=a[i]+b[i];
test=(a[i]%overflow_test_modulus + b[i]%overflow_test_modulus); // %overflow_test_modulus;
if((d[i]-test) % overflow_test_modulus !=0){
errorOutput()<<"Arithmetic failure in vector addition. Moat likely arithmetic overflow.\n";
throw ArithmeticException();
}
}
return d;
}
*/
//---------------------------------------------------------------------------
template<typename Integer>
vector<Integer> v_add(const vector<Integer>& a,const vector<Integer>& b){
assert(a.size() == b.size());
size_t i,s=a.size();
vector<Integer> d(s);
for (i = 0; i <s; i++) {
d[i]=a[i]+b[i];
}
return d;
}
//---------------------------------------------------------------------------
template<typename Integer>
void v_add_result(vector<Integer>& result, const size_t s, const vector<Integer>& a,const vector<Integer>& b){
assert(a.size() == b.size() && a.size() == result.size());
size_t i;
// vector<Integer> d(s);
for (i = 0; i <s; i++) {
result[i]=a[i]+b[i];
}
// return d;
}
//---------------------------------------------------------------------------
template<typename Integer>
vector<Integer>& v_add_to_mod(vector<Integer>& a, const vector<Integer>& b, const Integer& m) {
// assert(a.size() == b.size());
size_t i, s=a.size();
for (i = 0; i <s; i++) {
// a[i] = (a[i]+b[i])%m;
if ((a[i] += b[i]) >= m) {
a[i] -= m;
}
}
return a;
}
//---------------------------------------------------------------------------
template<typename Integer>
vector<Integer>& v_abs(vector<Integer>& v){
size_t i, size=v.size();
for (i = 0; i < size; i++) {
if (v[i]<0) v[i] = Iabs(v[i]);
}
return v;
}
//---------------------------------------------------------------------------
template<typename Integer>
vector<Integer> v_abs_value(vector<Integer>& v){
size_t i, size=v.size();
vector<Integer> w=v;
for (i = 0; i < size; i++) {
if (v[i]<0) w[i] = Iabs(v[i]);
}
return w;
}
//---------------------------------------------------------------------------
template<typename Integer>
Integer v_gcd(const vector<Integer>& v){
size_t i, size=v.size();
Integer g=0;
for (i = 0; i < size; i++) {
g=libnormaliz::gcd(g,v[i]);
if (g==1) {
return 1;
}
}
return g;
}
//---------------------------------------------------------------------------
template<typename Integer>
Integer v_lcm(const vector<Integer>& v){
size_t i,size=v.size();
Integer g=1;
for (i = 0; i < size; i++) {
g=libnormaliz::lcm(g,v[i]);
if (g==0) {
return 0;
}
}
return g;
}
//---------------------------------------------------------------------------
template<typename Integer>
Integer v_make_prime(vector<Integer>& v){
size_t i, size=v.size();
Integer g=v_gcd(v);
if (g!=0) {
for (i = 0; i < size; i++) {
v[i] /= g;
}
}
return g;
}
//---------------------------------------------------------------------------
template<typename Integer>
bool v_scalar_mult_mod_inner(vector<Integer>& w, const vector<Integer>& v, const Integer& scalar, const Integer& modulus){
size_t i,size=v.size();
Integer test;
for (i = 0; i <size; i++) {
test=v[i]*scalar;
if(!check_range(test)){
return false;
}
w[i]=test % modulus;
if(w[i]<0)
w[i]+=modulus;
}
return true;
}
//---------------------------------------------------------------------------
template<typename Integer>
vector<Integer> v_scalar_mult_mod(const vector<Integer>& v, const Integer& scalar, const Integer& modulus){
vector<Integer> w(v.size());
if(v_scalar_mult_mod_inner(w,v,scalar,modulus))
return w;
#pragma omp atomic
GMP_scal_prod++;
vector<mpz_class> x,y(v.size());
convert(x,v);
v_scalar_mult_mod_inner(y,x,convertTo<mpz_class>(scalar),convertTo<mpz_class>(modulus));
return convertTo<vector<Integer>>(y);
}
//---------------------------------------------------------------------------
template<typename Integer>
void v_scalar_division(vector<Integer>& v, const Integer& scalar){
size_t i,size=v.size();
for (i = 0; i <size; i++) {
assert(v[i]%scalar == 0);
v[i] /= scalar;
}
}
//---------------------------------------------------------------------------
template<typename Integer>
void v_reduction_modulo(vector<Integer>& v, const Integer& modulo){
size_t i,size=v.size();
for (i = 0; i <size; i++) {
v[i]=v[i]%modulo;
if (v[i]<0) {
v[i]=v[i]+modulo;
}
}
}
//---------------------------------------------------------------------------
template<typename Integer>
bool v_test_scalar_product(const vector<Integer>& av,const vector<Integer>& bv, const Integer& result, const long& m){
Integer ans = 0;
size_t i,n=av.size();
typename vector<Integer>::const_iterator a=av.begin(),b=bv.begin();
if( n >= 16 )
{
for( i = 0; i < ( n >> 4 ); ++i, a += 16, b += 16 ){
ans += a[0] * b[0];
ans += a[1] * b[1];
ans += a[2] * b[2];
ans += a[3] * b[3];
ans %= m;
ans += a[4] * b[4];
ans += a[5] * b[5];
ans += a[6] * b[6];
ans += a[7] * b[7];
ans %= m;
ans += a[8] * b[8];
ans += a[9] * b[9];
ans += a[10] * b[10];
ans += a[11] * b[11];
ans %= m;
ans += a[12] * b[12];
ans += a[13] * b[13];
ans += a[14] * b[14];
ans += a[15] * b[15];
ans %= m;
}
n -= i << 4;
}
if( n >= 8)
{
ans += a[0] * b[0];
ans += a[1] * b[1];
ans += a[2] * b[2];
ans += a[3] * b[3];
ans %= m;
ans += a[4] * b[4];
ans += a[5] * b[5];
ans += a[6] * b[6];
ans += a[7] * b[7];
ans %= m;
n -= 8;
a += 8;
b += 8;
}
if( n >= 4)
{
ans += a[0] * b[0];
ans += a[1] * b[1];
ans += a[2] * b[2];
ans += a[3] * b[3];
ans %= m;
n -= 4;
a += 4;
b += 4;
}
if( n >= 2)
{
ans += a[0] * b[0];
ans += a[1] * b[1];
n -= 2;
a += 2;
b += 2;
}
if(n>0)
ans += a[0]*b[0];
ans %= m;
if (((result-ans) % m)!=0) {
return false;
}
return true;
}
//---------------------------------------------------------------------------
template<typename T>
vector<T> v_merge(const vector<T>& a, const T& b) {
size_t s=a.size();
vector<T> c(s+1);
for (size_t i = 0; i < s; i++) {
c[i]=a[i];
}
c[s] = b;
return c;
}
//---------------------------------------------------------------------------
template<typename T>
vector<T> v_merge(const vector<T>& a,const vector<T>& b){
size_t s1=a.size(), s2=b.size(), i;
vector<T> c(s1+s2);
for (i = 0; i < s1; i++) {
c[i]=a[i];
}
for (i = 0; i < s2; i++) {
c[s1+i]=b[i];
}
return c;
}
//---------------------------------------------------------------------------
template<typename T>
vector<T> v_cut_front(const vector<T>& v, size_t size){
size_t s,k;
vector<T> tmp(size);
s=v.size()-size;
for (k = 0; k < size; k++) {
tmp[k]=v[s+k];
}
return tmp;
}
//---------------------------------------------------------------------------
template<typename Integer>
vector<key_t> v_non_zero_pos(const vector<Integer>& v){
vector<key_t> key;
size_t size=v.size();
key.reserve(size);
for (key_t i = 0; i <size; i++) {
if (v[i]!=0) {
key.push_back(i);
}
}
return key;
}
//---------------------------------------------------------------------------
template<typename Integer>
bool v_is_zero(const vector<Integer>& v) {
for (size_t i = 0; i < v.size(); ++i) {
if (v[i] != 0) return false;
}
return true;
}
//---------------------------------------------------------------------------
template<typename Integer>
void v_el_trans(const vector<Integer>& av,vector<Integer>& bv, const Integer& F, const size_t& start){
size_t i,n=av.size();
typename vector<Integer>::const_iterator a=av.begin();
typename vector<Integer>::iterator b=bv.begin();
a += start;
b += start;
n -= start;
if( n >= 8 )
{
for( i = 0; i < ( n >> 3 ); ++i, a += 8, b += 8 ){
b[0] += F*a[0];
b[1] += F*a[1];
b[2] += F*a[2];
b[3] += F*a[3];
b[4] += F*a[4];
b[5] += F*a[5];
b[6] += F*a[6];
b[7] += F*a[7];
}
n -= i << 3;
}
if( n >= 4)
{
b[0] += F*a[0];
b[1] += F*a[1];
b[2] += F*a[2];
b[3] += F*a[3];
n -=4;
a +=4;
b +=4;
}
if( n >= 2)
{
b[0] += F*a[0];
b[1] += F*a[1];
n -=2;
a +=2;
b +=2;
}
if(n>0)
b[0] += F*a[0];
}
//---------------------------------------------------------------
vector<bool> v_bool_andnot(const vector<bool>& a, const vector<bool>& b) {
assert(a.size() == b.size());
vector<bool> result(a);
for (size_t i=0; i<b.size(); ++i) {
if (b[i])
result[i]=false;
}
return result;
}
// swaps entry i and j of the vector<bool> v
void v_bool_entry_swap(vector<bool>& v, size_t i, size_t j) {
if (v[i] != v[j]) {
v[i].flip();
v[j].flip();
}
}
//---------------------------------------------------------------
// computes approximating lattice simplex using the A_n dissection of the unit cube
// q is a rational vector with the denominator in the FIRST component q[0]
template<typename Integer>
void approx_simplex(const vector<Integer>& q, std::list<vector<Integer> >& approx, const long k){
//cout << "approximate the point " << q;
long dim=q.size();
long l=k;
//if (k>q[0]) l=q[0]; // approximating on level q[0](=grading) is the best we can do
// TODO in this case, skip the rest and just approximate on q[0]
Matrix<Integer> quot = Matrix<Integer>(l,dim);
Matrix<Integer> remain=Matrix<Integer>(l,dim);
for(long j=0;j<l;j++){
for(long i=0;i<dim;++i){
quot[j][i]=(q[i]*(j+1))/q[0]; // write q[i]=quot*q[0]+remain
//quot[j][0] = 1;
remain[j][i]=(q[i]*(j+1))%q[0]; // with 0 <= remain < q[0]
if(remain[j][i]<0){
remain[j][i]+=q[0];
quot[j][i]--;
}
}
v_make_prime(quot[j]);
remain[j][0]=q[0]; // helps to avoid special treatment of i=0
}
// choose best level
//cout << "this is the qout matrix" << endl;
//quot.pretty_print(cout);
//cout << "this is the remain matrix" << endl;
//remain.pretty_print(cout);
long best_level=l-1;
vector<long> nr_zeros(l);
for(long j=l-1;j>=0;j--){
for(long i=0;i<dim;++i){
if(remain[j][i]==0) nr_zeros[j]++;
}
if (nr_zeros[j]>nr_zeros[best_level]) best_level=j;
}
//cout << "the best level is " << (best_level+1) << endl;
//now we proceed as before
vector<pair<Integer,size_t>> best_remain(dim);
for(long i=0;i<dim;i++){
best_remain[i].first = remain[best_level][i];
best_remain[i].second = i; // after sorting we must lnow where elements come from
}
sort(best_remain.begin(),best_remain.end());
reverse(best_remain.begin(),best_remain.end()); // we sort remain into descending order
/*for(long i=0;i<dim;++i){
cout << remain[i].first << " " << remain[i].second << endl;
} */
for(long i=1;i<dim;++i){
if(best_remain[i].first<best_remain[i-1].first)
{
approx.push_back(quot[best_level]);
//cout << "add the point " << quot[best_level];
// cout << i << " + " << remain[i].first << " + " << quot << endl;
}
quot[best_level][best_remain[i].second]++;
}
if(best_remain[dim-1].first > 0){
// cout << "E " << quot << endl;
approx.push_back(quot[best_level]);
//cout << "add the point " << quot[best_level];
}
}
vector<key_t> identity_key(size_t n){
vector<key_t> key(n);
for(size_t k=0;k<n;++k)
key[k]=k;
return key;
}
//---------------------------------------------------------------
// Sorting
template <typename T>
void order_by_perm(vector<T>& v, const vector<key_t>& permfix){
vector<key_t> perm=permfix; // we may want to use permfix a second time
vector<key_t> inv(perm.size());
for(key_t i=0;i<perm.size();++i)
inv[perm[i]]=i;
for(key_t i=0;i<perm.size();++i){
key_t j=perm[i];
swap(v[i],v[perm[i]]);
swap(perm[i],perm[inv[i]]);
swap(inv[i],inv[j]);
}
}
// vector<bool> is special
template <>
void order_by_perm(vector<bool>& v, const vector<key_t>& permfix){
vector<key_t> perm=permfix; // we may want to use permfix a second time
vector<key_t> inv(perm.size());
for(key_t i=0;i<perm.size();++i)
inv[perm[i]]=i;
for(key_t i=0;i<perm.size();++i){
key_t j=perm[i];
// v.swap(v[i],v[perm[i]]);
v_bool_entry_swap(v,i,perm[i]);
swap(perm[i],perm[inv[i]]);
swap(inv[i],inv[j]);
}
}
template long v_make_prime(vector<long >&);
template long long v_make_prime(vector<long long>&);
template mpz_class v_make_prime(vector<mpz_class>&);
template void v_add_result<long >(vector<long >&, size_t, const vector<long >&, const vector<long >&);
template void v_add_result<long long>(vector<long long>&, size_t, const vector<long long>&, const vector<long long>&);
template void v_add_result<mpz_class>(vector<mpz_class>&, size_t, const vector<mpz_class>&, const vector<mpz_class>&);
} // end namespace libnormaliz
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