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#include "../../../include/odfaeg/Network/bigInt.hpp"
using namespace std;
namespace odfaeg {
unsigned int BigInt::cmpt = 0;
BigInt::BigInt(const std::string& number) {
base = 10;
positif = (number.at(number.length()-1) != '-') ? true : false;
nbChiffres = (positif) ? number.length() : number.length() - 1;
for (unsigned int i = 0; i < nbChiffres; i++) {
unsigned int c = number.at(i) - 48;
if (c >= 0 && c < 10)
chiffres.push_back(c);
}
}
BigInt::BigInt(unsigned long long integer, bool positif, unsigned int b) {
this->positif = positif;
this->base = b;
nbChiffres = 0;
if (integer > 0) {
if (base < std::numeric_limits<unsigned int>::max()) {
unsigned long long int max = 1LL;
while (integer >= max)
max *= base;
max /= base;
while (max > 0) {
unsigned long long int c;
c = integer / max;
computeNbC(c);
chiffres.push_back(c);
integer %= max;
max /= b;
}
} else {
unsigned long long int c = integer / base;
computeNbC(c);
chiffres.push_back(c);
integer %= base;
computeNbC(integer);
chiffres.push_back(integer);
}
}
}
void BigInt::computeNbC (unsigned long long int c) {
unsigned int nb = base;
unsigned int i = 1;
while (c >= nb) {
nb *= base;
i++;
}
nbChiffres += i;
}
unsigned int BigInt::getNbChiffres() {
return nbChiffres;
}
BigInt BigInt::generate (int nbBits, unsigned int base) {
unsigned int nearestPowerOfTwo = math::Math::logn(base, 2);
base = math::Math::power(2, nearestPowerOfTwo);
BigInt n;
n.nbChiffres = (nearestPowerOfTwo == 1) ? base : nbBits / base * nearestPowerOfTwo;
do {
for (int i = 0; i < n.nbChiffres; i++) {
unsigned int c = math::Math::random(base-1);
n.insert(c, 0);
}
} while (n.isNull());
n.shorten();
return n;
}
bool BigInt::isPositif () {
return positif;
}
void BigInt::shorten () {
vector<unsigned int>::iterator it;
for (it = chiffres.begin(); it != chiffres.end(); ) {
if (*it == 0) {
it = chiffres.erase(it);
nbChiffres--;
} else
break;
}
}
void BigInt::clear()
{
chiffres.clear();
}
bool BigInt::isNull() const {
return chiffres.empty();
}
unsigned int BigInt::size() const {
return chiffres.size();
}
unsigned int BigInt::operator[] ( unsigned int i ) const {
return ( i<0 || i>=chiffres.size() ? 0 : chiffres[i] );
}
BigInt BigInt::operator++ (int i) {
for(int i= chiffres.size() - 1; i>= 0; i-- ) {
if (chiffres[i] == base -1)
chiffres[i]= 0;
else {
++(chiffres[i]);
return *this;
}
}
insert (1, 0);
return *this;
}
void BigInt::insert(unsigned int c, int pos) {
if (pos <= size()) {
BigInt result(0, true, base);
result.chiffres.resize(size() + 1, 0);
for (int i = 0, j = 0; i <= size(); i++, j++) {
if (i != pos) {
result.chiffres[i] = chiffres[j];
} else {
j--;
}
}
result.chiffres[pos] = c;
computeNbC(c);
*this = result;
}
}
BigInt BigInt::operator-- (int i) {
bool ok = false;
for(int i=chiffres.size() - 1; i>=0; i--)
if (chiffres[i] == 0)
chiffres[i]= base - 1;
else {
--(chiffres[i]);
shorten();
ok = true;
}
if (!ok)
cerr<<"Error : negative number"<<endl;
return *this;
}
int BigInt::comparaison (const BigInt &b) const {
if ( chiffres.size() > b.chiffres.size() )
return +1;
if ( chiffres.size() < b.chiffres.size() )
return -1;
for(unsigned int i= 0; i < chiffres.size(); i++) {
if ( chiffres[i] > b.chiffres[i] )
return +1;
if ( chiffres[i] < b.chiffres[i] )
return -1;
}
return 0;
}
bool BigInt::operator== ( const BigInt& a ) const {
return ( comparaison(a) == 0 );
}
bool BigInt::operator!= ( const BigInt& a) const {
return ( comparaison(a) != 0 );
}
bool BigInt::operator< ( const BigInt& a ) const {
return ( comparaison(a) < 0 );
}
bool BigInt::operator<= ( const BigInt& a ) const {
return ( comparaison(a) <= 0 );
}
bool BigInt::operator> ( const BigInt& a) const {
return ( comparaison(a) > 0 );
}
bool BigInt::operator>= ( const BigInt& a) const {
return ( comparaison(a) >= 0 );
}
BigInt BigInt::operator-() const {
BigInt result = *this;
result.positif = !positif;
return result;
}
BigInt BigInt::add (const BigInt& bi) const {
if (isNull())
return bi;
if (bi.isNull())
return *this;
BigInt somme(0, true, base);
somme.clear();
unsigned int taille = max(this->size(), bi.size())+1;
somme.chiffres.resize( taille, 0);
unsigned int retenue= 0;
int i, j;
for(i=size() - 1, j = bi.size() - 1; i >= 0; i--, j--) {
unsigned long long int temp = (unsigned long long int) (*this)[i] + (unsigned long long int) bi[j] + (unsigned long long int) retenue;
if ( temp < base) {
somme.chiffres[i] = (unsigned int) temp;
retenue = 0;
}
else {
somme.chiffres[i]= (unsigned int) temp - base;
retenue = 1;
}
}
while (retenue != 0) {
if (i >= 0) {
unsigned long long int temp = (unsigned long long int) (*this)[i] + (unsigned long long int) bi[i] + (unsigned long long int) retenue;
if ( temp < base) {
somme.chiffres[i] = (unsigned int) temp;
retenue = 0;
} else {
somme.chiffres[i]= (unsigned int) temp - base;
}
i--;
} else {
somme.insert(retenue, 0);
retenue = 0;
}
}
somme.shorten();
return somme;
}
BigInt BigInt::operator+ (const BigInt &bi) const {
BigInt a = *this;
BigInt b = bi;
BigInt result(0, true, base);
if (positif && bi.positif) {
if (bi.size() > size()) {
a = bi;
b = *this;
}
result = a.add(b);
} else if (!positif && bi.positif) {
if (*this >= bi) {
result = a.sub(b);
result.positif = false;
} else {
result = b.sub(a);
}
} else if (positif && !bi.positif) {
if (*this >= bi) {
result = a.sub(b);
} else {
result = b.sub(a);
result.positif = false;
}
} else {
if (bi.size() > size()) {
a = bi;
b = *this;
}
result = a.add(b);
result.positif = false;
}
return result;
}
BigInt BigInt::operator+= (const BigInt &bi) {
*this = *this + bi;
return *this;
}
BigInt BigInt::sub (const BigInt &bi) const {
BigInt diff(0, true, this->base);
diff.clear();
if (bi.isNull())
return *this;
unsigned int taille= max( this->size(), bi.size() );
diff.chiffres.resize( taille, 0);
// Calculer la somme chiffre par chiffre en tenant compte des retenues
unsigned int retenue= 0;
int i, j;
for(i=size() - 1, j = bi.size() - 1; i>=0; i--, j--) {
long long temp = (long long) ((unsigned long long int) (*this)[i] - (unsigned long long int) bi[j] - (unsigned long long int) retenue);
if ( temp >= 0 ) {
diff.chiffres[i]= (unsigned int) temp;
retenue = 0;
}
else {
diff.chiffres[i]= (unsigned int) (temp + base);
retenue = 1;
}
}
while (retenue > 0) {
long long int temp = (long long int) ((unsigned long long int) (*this)[i] - (unsigned long long int) retenue);
if ( temp >= 0 ) {
diff.chiffres[i]= (unsigned int) temp;
retenue = 0;
}
else {
//std::cout<<*this<<" "<<bi<<" "<<diff.size()<<" "<<i<<std::endl;
diff.chiffres[i]= (unsigned int) (temp + base);
}
i--;
}
diff.shorten();
return diff;
}
BigInt BigInt::operator- (const BigInt &bi) const {
BigInt result(0, true, base);
BigInt a = *this;
BigInt b = bi;
if (positif && bi.positif) {
if (*this >= bi) {
result = a.sub(b);
} else {
result = b.sub(a);
result.positif = false;
}
} else if (!positif && bi.positif) {
if (bi.size() > size()) {
a = bi;
b = *this;
}
result = a.add(b);
result.positif = false;
} else if (positif && !bi.positif) {
if (bi.size() > size()) {
a = bi;
b = *this;
}
result = a.add(b);
} else {
if (*this >= bi) {
result = a.sub(b);
result.positif = false;
} else {
result.positif = true;
result = b.sub(a);
}
}
return result;
}
BigInt BigInt::operator-= (const BigInt &bi) {
*this = *this - bi;
return *this;
}
BigInt BigInt::addZeros (unsigned int n) {
if (n < 0)
return *this;
if (isNull())
return *this;
BigInt result(0, positif, base);
result.chiffres.resize(size() + n, 0);
nbChiffres += n;
for (int i = 0; i < size(); i++) {
result.chiffres[i] = chiffres[i];
}
return result;
}
BigInt BigInt::multiply (const BigInt &bi) const {
BigInt produit(0, true, this->base);
produit.clear();
if ( this->size() == 0 || bi.size() == 0 ) {
return produit;
}
int i = 0, j = bi.size() - 1;
produit = scaleUp(bi.chiffres[i]).addZeros(j);
while ( j > 0)
{
i++; j--;
produit += scaleUp (bi.chiffres[i]).addZeros(j);
}
produit.shorten();
return produit;
}
BigInt BigInt::karatsuba (const BigInt &bi) const {
if (size() >= bi.size()) {
unsigned int n = size() / 2;
BigInt a = arraySub(0, size() - n);
BigInt b = arraySub(size() - n, n);
if (bi.size() > n) {
BigInt c = bi.arraySub(0, bi.size() - n);
BigInt d = bi.arraySub(bi.size() - n, n);
BigInt ac = a * c;
BigInt bd = b * d;
BigInt ad_bc = (a + b) * (c + d) - ac - bd;
ac = ac.addZeros(2*n);
ad_bc = ad_bc.addZeros(n);
return ac + ad_bc + bd;
} else {
BigInt aq = a * bi;
BigInt bq = b * bi;
aq = aq.addZeros(n);
return aq + bq;
}
}
return *this;
}
BigInt BigInt::operator* (const BigInt &bi) const {
// D´el´eguer les petites multiplications `a la m´ethode scolaire
BigInt result(0, true, base);
if (size() < bi.size())
result = bi * *this;
else if (bi.size() < karatsuba_treshold)
result = multiply(bi);
else
result = karatsuba(bi);
if (!positif && bi.positif || positif && !bi.positif)
result.positif = false;
else
result.positif = true;
return result;
}
BigInt BigInt::operator*= (const BigInt &bi) {
*this = *this * bi;
return *this;
}
BigInt BigInt::operator/ (const BigInt &bi) const {
if (bi == 0) {
cerr<<"Error : b is null!";
return 0;
}
if (bi > *this) {
std::cout<<"greater!"<<std::endl;
return 0;
}
cmpt = 0;
BigInt result(0, true, base);
BigInt reste(0, true, base);
result = burnikel_ziegler(bi, reste);
if (!positif && bi.positif || positif && !bi.positif)
result.positif = false;
else
result.positif = true;
return result;
}
BigInt BigInt::operator/= (const BigInt &bi) {
*this = *this / bi;
return *this;
}
BigInt BigInt::operator% (const BigInt& bi) const {
if (bi == BigInt(0)) {
cerr<<"Error : b is null!";
return 0;
}
if (bi > *this)
return *this;
BigInt reste(0, true, base);
burnikel_ziegler(bi, reste);
reste.shorten();
if (!positif && bi.positif || positif && !bi.positif)
reste.positif = false;
else
reste.positif = true;
return reste;
}
BigInt BigInt::pow (BigInt exp) {
BigInt un(1, true, base);
BigInt deux (2, true, base);
if (exp.isNull()) {
return un;
} else if (exp % deux == 0) {
BigInt a = pow(exp / deux);
return (a * a);
} else {
return (*this) * pow (exp - un);
}
}
BigInt BigInt::prodMod (const BigInt &b, const BigInt &n) const {
if(isNull()) {
return 0;
} else {
// a = 2 * q + e
BigInt q = *this / BigInt(2);
BigInt e = *this % BigInt(2);
BigInt r = BigInt(2) * q.prodMod(b, n) % n;
return e == 0 ? r : (r + b) % n;
}
}
BigInt BigInt::modOfPow (const BigInt exp, const BigInt mod) const {
BigInt result = 1;
BigInt e = exp, bs;
bs = *this;
while (e > 0) {
if (e % 2 == 1)
result = result * bs % mod;
e /= 2;
bs = bs * bs % mod;
}
return result;
}
BigInt BigInt::operator%= (const BigInt &bi) {
*this = *this % bi;
return *this;
}
BigInt BigInt::arraySub (int n, int length) const {
BigInt result(0, true, this->base);
if (n >= 0 && n + length < size() && length > 0) {
result.chiffres.resize(length, 0);
for (int i = n, j = 0; j < length; i++, j++) {
result.chiffres[j] = chiffres[i];
}
}
result.shorten();
return result;
}
BigInt BigInt::operator<< (int n) const {
if (n < 0)
return *this;
if (isNull())
return *this;
BigInt result(0, true, base);
result.chiffres.resize(size() + n, 0);
for (int i = 0; i < size(); i++) {
result.chiffres.push_back(chiffres[i]);
}
return result;
}
BigInt BigInt::operator>> (int n) const {
if (n < 0)
return *this;
if (isNull())
return *this;
if (n > size())
n = size();
BigInt result (0, true, base);
result.chiffres.resize(size() - n, 0);
for (int i = 0; i < result.size(); i++)
result.chiffres[i] = chiffres[i];
return result;
}
BigInt BigInt::operator& (int n) const {
BigInt a, b, bi(n);
if (size() > bi.size()) {
b = bi<<(size() - bi.size() - 1);
a = *this;
} else if (size() < bi.size()) {
a = *this<<(bi.size() - size() - 1);
b = bi;
} else {
a = *this;
b = bi;
}
BigInt result (0, true, base);
result.chiffres.resize(a.size(), 0);
for (int i = 0; i < a.size(); i++) {
result.chiffres[i] = chiffres[i] & b.chiffres[i];
}
result.shorten();
return result;
}
BigInt BigInt::scaleUp (unsigned int n) const {
unsigned long long int accu = 0;
unsigned int retenue = 0;
BigInt result(0, true, base);
result.chiffres.resize(size() + 1, 0);
BigInt bs = BigInt(base, true, base);
BigInt ni(n);
if (ni >= 0 && ni < bs) {
if (n == 0)
return 0;
for (int i = size(); i > 0; i--) {
accu = (unsigned long long) chiffres[i-1] * n + (unsigned long long) retenue;
result.chiffres[i] = (unsigned int) (accu % base);
retenue = (unsigned int) (accu / base);
}
result.chiffres[0] = retenue;
if (retenue == 0)
result.shorten();
}
return result;
}
BigInt BigInt::scaleDown (unsigned long long int n, BigInt& r) const {
unsigned long long int accu = 0;
unsigned int retenue = 0;
BigInt result = *this;
if (n >= 0 && n < base * base) {
for (unsigned int i = 0; i < size(); i++) {
accu = (unsigned long long) chiffres[i] + (unsigned long long int) retenue * base;
result.chiffres[i] = (unsigned int) (accu / n);
retenue = (unsigned int) (accu % n);
}
}
if((int) chiffres.size() -1 > 0 && result.chiffres[0] == 0)
result.arraySub(1,chiffres.size()-1);
r = BigInt(retenue, true, base);
result.shorten();
return result;
}
BigInt BigInt::burnikel_ziegler(const BigInt &bi, BigInt &r) const {
BigInt q(0, true, base);
if (bi.size() <= 2) {
unsigned long long int b2 = (bi.size() < 2) ? bi.chiffres[0] : bi.chiffres[0] * base + bi.chiffres[1];
q = scaleDown(b2, r);
r.shorten();
std::cout<<r<<std::endl;
return q;
}
unsigned int n = (bi.size() - 1) / 2;
// D´ecouper a et b en deux moiti´es
BigInt a0, a1;
a0 = arraySub(size() - n, n);
a1 = arraySub(0, size() - n);
if (a1 >= bi) {
BigInt q1, r1, q0, r0;
q1 = a1.burnikel_ziegler (bi, r1);
r1 = r1.addZeros(n);
q0 = (r1 + a0).burnikel_ziegler (bi, r0);
r = r0;
std::cout<<r<<std::endl;
q1 = q1.addZeros(n);
return q1 + q0;
} else {
BigInt b0, b1, q1, r1, a0_r1, b0_q1;
b0 = bi.arraySub(bi.size() - n, n);
b1 = bi.arraySub(0, bi.size() - n);
q1 = a1.burnikel_ziegler(b1, r1);
r1 = r1.addZeros(n);
a0_r1 = r1 + a0;
b0_q1 = b0 * q1;
if (a0_r1 >= b0_q1) {
r = a0_r1 - b0_q1;
std::cout<<r<<std::endl;
return q1;
} else {
BigInt minus_x = b0_q1 - a0_r1;
r = bi - minus_x;
std::cout<<r<<std::endl;
return q1 - BigInt(1, true, base);
}
}
}
// Op´erateur de sortie (afficher les chiffres, ou bien "0" pour une suite vide)
ostream& operator<< ( ostream& out, const BigInt& bi) {
if ( bi.size()== 0 ) return ( out << 0 );
if (!bi.positif)
out<<"-";
for( int i = 0; i < bi.size(); i++) {
out<<bi.chiffres[i];
if (i != bi.size()-1)
out<<".";
}
return out;
}
} |
Problème de récursion
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