Abastro/mathematical-algorithms-cpp
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Trimmed allocations

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Abastro 2025-03-24 21:14:35 +09:00
parent 33b0b78238
commit 08239b005c
1 changed files with 67 additions and 39 deletions
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106
src/karatsuba.cpp
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@ -1,3 +1,4 @@
#include <algorithm>
#include <chrono> #include <chrono>
#include <complex> #include <complex>
#include <iostream> #include <iostream>
@ -21,6 +22,14 @@ 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) {
for (auto x : v) {
os << x << " ";
}
return os;
}
vector<int> random_int_vector(size_t size) { vector<int> random_int_vector(size_t size) {
auto result = vector<int>(); auto result = vector<int>();
for (size_t i = 0; i < size; i++) { for (size_t i = 0; i < size; i++) {
@ -97,66 +106,62 @@ template <typename R> vector<R> poly_mult_basic(vector<R> &a, vector<R> &b) {
return res; return res;
} }
#define THRESHOLD 1 #define THRESHOLD 32
// TODO Reduce allocations // TODO Reduce allocations
template <typename R> template <typename R> struct Karatsuba {
struct Karatsuba {
vector<R> result; vector<R> result;
}; };
/** /**
* A step of the Karatsuba function. * A step of the Karatsuba function.
* @param deg_bnd power-of-2 degree bound * @param deg_bnd power-of-2 degree bound
* @param buffer the buffer which is used only throughout the invocation
*/ */
template <typename R> template <typename R>
vector<R> poly_mult_Karatsuba_step(const size_t deg_bnd, span<R> &a, void poly_mult_Karatsuba_step(const size_t deg_bnd, span<R> &a, span<R> &b,
span<R> &b) { span<R> &result, span<R> &buffer) {
if (deg_bnd <= THRESHOLD) { if (deg_bnd <= THRESHOLD) {
auto vec_a = vector(a.begin(), a.end()); auto vec_a = vector(a.begin(), a.end());
auto vec_b = vector(b.begin(), b.end()); auto vec_b = vector(b.begin(), b.end());
return poly_mult_basic(vec_a, vec_b); auto result_vec = poly_mult_basic(vec_a, vec_b);
copy(result_vec.begin(), result_vec.end(), result.begin());
return;
} }
auto result = vector<R>(deg_bnd << 1, 0);
const auto next_bnd = deg_bnd >> 1; const auto next_bnd = deg_bnd >> 1;
auto a0 = span(a.begin(), next_bnd); auto a0 = a.subspan(0, next_bnd);
auto a1 = span(a.begin() + next_bnd, next_bnd); auto a1 = a.subspan(next_bnd, next_bnd);
auto b0 = span(b.begin(), next_bnd); auto b0 = b.subspan(0, next_bnd);
auto b1 = span(b.begin() + next_bnd, next_bnd); auto b1 = b.subspan(next_bnd, next_bnd);
auto a01 = vector<R>(next_bnd);
auto b01 = vector<R>(next_bnd); auto a01 = buffer.subspan(0, next_bnd);
auto span_a01 = span(a01); auto b01 = buffer.subspan(next_bnd, next_bnd);
auto span_b01 = span(b01);
auto prod0 = poly_mult_Karatsuba_step(next_bnd, a0, b0); auto prod0 = result.subspan(0, deg_bnd);
auto prod1 = poly_mult_Karatsuba_step(next_bnd, a1, b1); auto prod1 = result.subspan(deg_bnd, deg_bnd);
add_inplace(a0, a1, span_a01); auto prod_add = buffer.subspan(2 * next_bnd, deg_bnd);
add_inplace(b0, b1, span_b01);
auto prod_add = poly_mult_Karatsuba_step(next_bnd, span_a01, span_b01);
auto span_prod0 = span(prod0); // Buffer which does not overlap with currently used memory
auto span_prod1 = span(prod1); auto buffer_next = buffer.subspan(4 * next_bnd, 4 * next_bnd);
auto span_prod_add = span(prod_add); auto new_buffer_vec = vector<R>(4 * next_bnd);
auto new_buffer = span(new_buffer_vec);
// 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);
add_inplace(a0, a1, a01);
add_inplace(b0, b1, b01);
poly_mult_Karatsuba_step(next_bnd, a01, b01, prod_add, buffer_next);
// adjust prod_add // adjust prod_add
sub_inplace(span_prod_add, span_prod0, span_prod_add); sub_inplace(prod_add, prod0, prod_add);
sub_inplace(span_prod_add, span_prod1, span_prod_add); sub_inplace(prod_add, prod1, prod_add);
// Add high term at X^deg_bnd position
auto span_result_high = span(result.begin() + deg_bnd, prod1.size());
add_inplace(span_prod1, span_result_high, span_result_high);
// Add middle term at X^next_bnd position // Add middle term at X^next_bnd position
auto span_result_mid = span(result.begin() + next_bnd, span_prod_add.size()); auto result_mid = result.subspan(next_bnd, deg_bnd);
add_inplace(span_prod_add, span_result_mid, span_result_mid); add_inplace(prod_add, result_mid, result_mid);
// Add low term at X^0 position
auto span_result_low = span(result.begin(), prod0.size());
add_inplace(span_prod0, span_result_low, span_result_low);
return result;
} }
template <typename R> template <typename R>
@ -167,9 +172,15 @@ vector<R> poly_mult_Karatsuba(vector<R> &a, vector<R> &b) {
a.resize(deg_bound); a.resize(deg_bound);
b.resize(deg_bound); b.resize(deg_bound);
auto result = vector<R>(deg_bound << 1);
auto buffer = vector<R>(deg_bound * 4);
auto span_a = span(a); auto span_a = span(a);
auto span_b = span(b); auto span_b = span(b);
return poly_mult_Karatsuba_step(deg_bound, span_a, span_b); auto span_result = span(result);
auto span_buffer = span(buffer);
poly_mult_Karatsuba_step(deg_bound, span_a, span_b, span_result, span_buffer);
return result;
} }
void basic_vs_Karatsuba(size_t size) { void basic_vs_Karatsuba(size_t size) {
@ -191,6 +202,19 @@ void basic_vs_Karatsuba(size_t size) {
cout << "Karatsuba took " << spent.count() << "s" << endl; cout << "Karatsuba took " << spent.count() << "s" << endl;
} }
void only_Karatsuba(size_t size) {
auto p = random_int_vector(size);
auto q = random_int_vector(size);
cout << "Degree " << size - 1 << endl;
auto begin = chrono::high_resolution_clock::now();
poly_mult_Karatsuba(p, q);
auto end = chrono::high_resolution_clock::now();
auto spent = chrono::duration<double>(end - begin);
cout << "Karatsuba took " << spent.count() << "s" << endl;
}
int main() { int main() {
{ {
auto p = vector<int>{1, 2}; auto p = vector<int>{1, 2};
@ -220,6 +244,10 @@ 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(65536);
only_Karatsuba(131072);
// { // {
// auto p = random_real_vector(4000); // auto p = random_real_vector(4000);