Abastro/mathematical-algorithms-cpp
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Corrected code

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Abastro 2025-03-25 21:50:33 +09:00
parent 8cc7ebd797
commit 6f30ac9341
1 changed files with 20 additions and 22 deletions
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42
src/karatsuba.cpp
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@ -22,7 +22,6 @@ template <typename T> ostream &operator<<(ostream &os, const vector<T> &v) {
return os; return os;
} }
template <typename T> ostream &operator<<(ostream &os, const span<T> &v) { template <typename T> ostream &operator<<(ostream &os, const span<T> &v) {
for (auto x : v) { for (auto x : v) {
os << x << " "; os << x << " ";
@ -90,8 +89,7 @@ void sub_inplace(span<R> &a, span<R> &b, span<R> &result) {
result[i] = a[i] - b[i]; result[i] = a[i] - b[i];
} }
template <typename R> template <typename R> vector<R> poly_normalize(vector<R> &a) {
vector<R> poly_normalize(vector<R> &a) {
int i; int i;
for (i = a.size() - 1; i >= 0; i--) { for (i = a.size() - 1; i >= 0; i--) {
if (a[i] != 0) if (a[i] != 0)
@ -140,28 +138,22 @@ void poly_mult_Karatsuba_step(const size_t deg_bnd, span<R> &a, span<R> &b,
auto a1 = a.subspan(next_bnd, next_bnd); auto a1 = a.subspan(next_bnd, next_bnd);
auto b0 = b.subspan(0, next_bnd); auto b0 = b.subspan(0, next_bnd);
auto b1 = b.subspan(next_bnd, next_bnd); auto b1 = b.subspan(next_bnd, next_bnd);
auto a01 = buffer.subspan(0, next_bnd); auto store = vector<R>(next_bnd * 4);
auto b01 = buffer.subspan(next_bnd, next_bnd); auto a01 = span(store.begin() + 0, next_bnd);
auto b01 = span(store.begin() + next_bnd, next_bnd);
auto prod0 = result.subspan(0, deg_bnd); auto prod0 = result.subspan(0, deg_bnd);
auto prod1 = result.subspan(deg_bnd, deg_bnd); auto prod1 = result.subspan(deg_bnd, deg_bnd);
auto prod_add = buffer.subspan(2 * next_bnd, deg_bnd); auto prod_add = span(store.begin() + 2 * next_bnd, deg_bnd);
// Buffer which does not overlap with currently used memory
// auto buffer_next = buffer.subspan(4 * next_bnd, 4 * next_bnd);
auto new_buffer_vec = vector<R>(4 * next_bnd);
auto new_buffer = span(new_buffer_vec);
auto new_buffer_2 = vector<R>(4 * next_bnd);
auto new_buffer_2 = span(new_buffer_2)
// correctly put into prod0 and prod1 position // correctly put into prod0 and prod1 position
poly_mult_Karatsuba_step(next_bnd, a0, b0, prod0, new_buffer); // need new_buffer to avoid rewrite; why? poly_mult_Karatsuba_step(next_bnd, a0, b0, prod0, buffer);
poly_mult_Karatsuba_step(next_bnd, a1, b1, prod1, new_buffer); poly_mult_Karatsuba_step(next_bnd, a1, b1, prod1, buffer);
add_inplace(a0, a1, a01); add_inplace(a0, a1, a01);
add_inplace(b0, b1, b01); add_inplace(b0, b1, b01);
poly_mult_Karatsuba_step(next_bnd, a01, b01, prod_add, new_buffer); poly_mult_Karatsuba_step(next_bnd, a01, b01, prod_add, buffer);
// adjust prod_add // adjust prod_add
sub_inplace(prod_add, prod0, prod_add); sub_inplace(prod_add, prod0, prod_add);
@ -209,8 +201,11 @@ void basic_vs_Karatsuba(size_t size) {
spent = chrono::duration<double>(end - begin); spent = chrono::duration<double>(end - begin);
cout << "Karatsuba took " << spent.count() << "s" << endl; cout << "Karatsuba took " << spent.count() << "s" << endl;
if (basic != karat) if (poly_normalize(basic) == poly_normalize(karat))
cout << "Mismatch" << endl; cout << "+ Match" << endl;
else
cout << "- Mismatch" << endl;
cout << endl;
} }
void only_Karatsuba(size_t size) { void only_Karatsuba(size_t size) {
@ -245,8 +240,11 @@ int main() {
auto q = random_int_vector(8); auto q = random_int_vector(8);
cout << "P: " << p << endl; cout << "P: " << p << endl;
cout << "Q: " << q << endl; cout << "Q: " << q << endl;
cout << "basic P * Q: " << poly_mult_basic(p, q) << endl; auto basic = poly_mult_basic(p, q);
cout << "Karatsuba P * Q: " << poly_mult_Karatsuba(p, q) << endl; cout << "basic P * Q: " << basic << endl;
auto karat = poly_mult_Karatsuba(p, q);
cout << "Karatsuba P * Q: " << karat << endl;
cout << endl;
} }
basic_vs_Karatsuba(128); basic_vs_Karatsuba(128);
@ -257,7 +255,7 @@ int main() {
basic_vs_Karatsuba(4096); basic_vs_Karatsuba(4096);
basic_vs_Karatsuba(8192); basic_vs_Karatsuba(8192);
basic_vs_Karatsuba(16384); basic_vs_Karatsuba(16384);
only_Karatsuba(32768); only_Karatsuba(32768);
only_Karatsuba(65536); only_Karatsuba(65536);
only_Karatsuba(131072); only_Karatsuba(131072);