Abastro/mathematical-algorithms-cpp
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Normalize

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Abastro 2025-03-25 18:25:23 +09:00
parent 6e5f986c77
commit 8cc7ebd797
1 changed files with 23 additions and 10 deletions
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33
src/karatsuba.cpp
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@ -90,6 +90,16 @@ void sub_inplace(span<R> &a, span<R> &b, span<R> &result) {
result[i] = a[i] - b[i];
}
template <typename R>
vector<R> poly_normalize(vector<R> &a) {
int i;
for (i = a.size() - 1; i >= 0; i--) {
if (a[i] != 0)
break;
}
return vector(a.begin(), a.begin() + i + 1);
}
// Basic polynomial multiplication
template <typename R> vector<R> poly_mult_basic(vector<R> &a, vector<R> &b) {
if (a.size() == 0 && b.size() == 0)
@ -109,10 +119,6 @@ template <typename R> vector<R> poly_mult_basic(vector<R> &a, vector<R> &b) {
#define THRESHOLD 32
// TODO Reduce allocations
template <typename R> struct Karatsuba {
vector<R> result;
};
/**
* A step of the Karatsuba function.
* @param deg_bnd power-of-2 degree bound
@ -143,17 +149,19 @@ void poly_mult_Karatsuba_step(const size_t deg_bnd, span<R> &a, span<R> &b,
auto prod_add = buffer.subspan(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 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
poly_mult_Karatsuba_step(next_bnd, a0, b0, prod0, new_buffer); // need new_buffer to avoid rewrite; why?
poly_mult_Karatsuba_step(next_bnd, a1, b1, prod1, buffer_next);
poly_mult_Karatsuba_step(next_bnd, a1, b1, prod1, new_buffer);
add_inplace(a0, a1, a01);
add_inplace(b0, b1, b01);
poly_mult_Karatsuba_step(next_bnd, a01, b01, prod_add, buffer_next);
poly_mult_Karatsuba_step(next_bnd, a01, b01, prod_add, new_buffer);
// adjust prod_add
sub_inplace(prod_add, prod0, prod_add);
@ -190,16 +198,19 @@ void basic_vs_Karatsuba(size_t size) {
cout << "Degree " << size - 1 << endl;
auto begin = chrono::high_resolution_clock::now();
poly_mult_basic(p, q);
auto basic = poly_mult_basic(p, q);
auto end = chrono::high_resolution_clock::now();
auto spent = chrono::duration<double>(end - begin);
cout << "Basic took " << spent.count() << "s" << endl;
begin = chrono::high_resolution_clock::now();
poly_mult_Karatsuba(p, q);
auto karat = poly_mult_Karatsuba(p, q);
end = chrono::high_resolution_clock::now();
spent = chrono::duration<double>(end - begin);
cout << "Karatsuba took " << spent.count() << "s" << endl;
if (basic != karat)
cout << "Mismatch" << endl;
}
void only_Karatsuba(size_t size) {
@ -223,7 +234,9 @@ int main() {
cout << "Q: " << q << endl;
cout << "P + Q: " << poly_add(p, q) << endl;
cout << "basic P * Q: " << poly_mult_basic(p, q) << endl;
cout << "Karatsuba P * Q: " << poly_mult_Karatsuba(p, q) << endl;
auto karat = poly_mult_Karatsuba(p, q);
cout << "Karatsuba P * Q: " << karat << endl;
cout << "normalized: " << poly_normalize(karat) << endl;
cout << endl;
}