status-im
/
research
mirror of https://github.com/status-im/research.git
2
0
Fork 0
Code Issues Projects Releases Wiki Activity

Added a bunch of C++ optimizations

This commit is contained in:
vub 2017-04-23 19:14:46 -04:00
parent 3397bd982e
commit 9721cf80eb
2 changed files with 170 additions and 33 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

198
erasure_code/ec65536/poly_utils.cpp
View File

@ -9,6 +9,8 @@ using namespace std;
vector<int> glogtable(65536, 0);
vector<int> gexptable(196608, 0);
const int ROOT_CUTOFF = 32;
void initialize_tables() {
int v = 1;
for (int i = 0; i < 65536; i++) {
@ -35,57 +37,189 @@ int eval_poly_at(vector<int> poly, int x) {
return y;
}
vector<int> lagrange_interp(vector<int> ys, vector<int> xs) {
int xs_size = xs.size();
vector<int> root(xs_size + 1);
root[xs_size] = 1;
for (int i = 0; i < xs_size; i++) {
int eval_log_poly_at(vector<int> poly, int x) {
if (x == 0)
return poly[0] == 65537 ? 0 : gexptable[poly[0]];
int logx = glogtable[x];
int y = 0;
for (int i = 0; i < poly.size(); i++) {
if (poly[i] != 65537)
y ^= gexptable[(logx * i + poly[i]) % 65535];
}
return y;
}
// Compute the product of two (equal length) polynomials. Takes ~O(N ** 1.59) time.
vector<int> karatsuba_mul(vector<int> p, vector<int> q) {
int L = p.size();
if (L <= 64) {
vector<int> o(L * 2);
for (int i = 0; i < L; i++) {
for (int j = 0; j < L; j++) {
if (p[i] && q[j])
o[i + j] ^= gexptable[glogtable[p[i]] + glogtable[q[j]]];
}
}
return o;
}
if (L % 2) {
L += 1;
p.push_back(0);
q.push_back(0);
}
int halflen = L / 2;
vector<int> low1 = vector<int>(p.begin(), p.begin() + halflen);
vector<int> low2 = vector<int>(q.begin(), q.begin() + halflen);
vector<int> high1 = vector<int>(p.begin() + halflen, p.end());
vector<int> high2 = vector<int>(q.begin() + halflen, q.end());
vector<int> sum1(halflen);
vector<int> sum2(halflen);
for (int i = 0; i < halflen; i++) {
sum1[i] = low1[i] ^ high1[i];
sum2[i] = low2[i] ^ high2[i];
}
vector<int> z0 = karatsuba_mul(low1, low2);
vector<int> z2 = karatsuba_mul(high1, high2);
vector<int> m = karatsuba_mul(sum1, sum2);
vector<int> o(L * 2);
for (int i = 0; i < L; i++) {
o[i] ^= z0[i];
o[i + halflen] ^= (m[i] ^ z0[i] ^ z2[i]);
o[i + L] ^= z2[i];
}
return o;
}
vector<int> mk_root(vector<int> xs) {
int L = xs.size();
if (L >= ROOT_CUTOFF) {
int halflen = L / 2;
vector<int> left = vector<int>(xs.begin(), xs.begin() + halflen);
vector<int> right = vector<int>(xs.begin() + halflen, xs.end());
vector<int> o = karatsuba_mul(mk_root(left), mk_root(right));
o.resize(L + 1);
return o;
}
vector<int> root(L + 1);
root[L] = 1;
for (int i = 0; i < L; i++) {
int logx = glogtable[xs[i]];
int offset = xs_size - i - 1;
int offset = L - i - 1;
root[offset] = 0;
for (int j = 0; j < i + 1; j++) {
if (root[j + 1 + offset] and xs[i])
root[j + offset] ^= gexptable[glogtable[root[j+1 + offset]] + logx];
}
}
vector<int> b(xs_size);
vector<int> output(root.size() - 1);
for (int i = 0; i < xs_size; i++) {
output[root.size() - 2] = 1;
int logx = glogtable[xs[i]];
for (int j = root.size() - 2; j > 0; j--) {
if (output[j] and xs[i])
output[j - 1] = root[j] ^ gexptable[glogtable[output[j]] + logx];
else
output[j - 1] = root[j];
}
int denom = eval_poly_at(output, xs[i]);
int log_yslice = glogtable[ys[i]] - glogtable[denom] + 65535;
for (int j = 0; j < xs_size; j++) {
if(output[j] and ys[i])
b[j] ^= gexptable[glogtable[output[j]] + log_yslice];
}
}
return b;
return root;
}
vector<int> subroot_linear_combination(vector<int> xs, vector<int> factors) {
int L = xs.size();
/*if (L <= ROOT_CUTOFF) {
vector<int> out(L + 1);
vector<int> root = mk_root(xs);
for (int i = 0; i < L; i++) {
vector<int> output(L + 1);
output[root.size() - 2] = 1;
int logx = glogtable[xs[i]];
if (factors[i]) {
int log_fac = glogtable[factors[i]];
for (int j = root.size() - 2; j > 0; j--) {
if (output[j] and xs[i])
output[j - 1] = root[j] ^ gexptable[glogtable[output[j]] + logx];
else
output[j - 1] = root[j];
out[j] ^= gexptable[glogtable[output[j]] + log_fac];
}
out[0] ^= gexptable[glogtable[output[0]] + log_fac];
}
}
return out;
}*/
if (L == 1) {
vector<int> o(2);
o[0] = factors[0];
return o;
}
int halflen = L / 2;
vector<int> xs_left = vector<int>(xs.begin(), xs.begin() + halflen);
vector<int> xs_right = vector<int>(xs.begin() + halflen, xs.end());
vector<int> factors_left = vector<int>(factors.begin(), factors.begin() + halflen);
vector<int> factors_right = vector<int>(factors.begin() + halflen, factors.end());
vector<int> R1 = mk_root(xs_left);
vector<int> R2 = mk_root(xs_right);
vector<int> o1 = karatsuba_mul(R1, subroot_linear_combination(xs_right, factors_right));
vector<int> o2 = karatsuba_mul(R2, subroot_linear_combination(xs_left, factors_left));
vector<int> o(L + 1);
for (int i = 0; i < L; i++) {
o[i] = o1[i] ^ o2[i];
}
return o;
}
vector<int> derivative(vector<int> p) {
vector<int> o(p.size() - 1);
for (int i = 0; i < o.size(); i+= 2) {
o[i] = p[i + 1];
}
return o;
}
vector<int> poly_to_logs(vector<int> p) {
vector<int> o(p.size());
for (int i = 0; i < p.size(); i++) {
if (p[i])
o[i] = glogtable[p[i]];
else
o[i] = 65537;
}
return o;
}
vector<int> lagrange_interp(vector<int> ys, vector<int> xs) {
int xs_size = xs.size();
vector<int> root = mk_root(xs);
vector<int> log_rootprime = poly_to_logs(derivative(root));
vector<int> factors(xs_size);
for (int i = 0; i < xs_size; i++) {
int denom = eval_log_poly_at(log_rootprime, xs[i]);
if (ys[i])
factors[i] = gexptable[glogtable[ys[i]] + 65535 - glogtable[denom]];
}
return subroot_linear_combination(xs, factors);
}
const int SIZE = 1024;
int main() {
initialize_tables();
//int myxs[] = {1, 2, 3, 4};
//std::vector<int> xs (myxs, myxs + sizeof(myxs) / sizeof(int) );
vector<int> xs(4096);
vector<int> ys(4096);
for (int v = 0; v < 4096; v++) {
xs[v] = v;
ys[v] = (v * v) % 65536;
vector<int> xs(SIZE);
vector<int> ys(SIZE);
for (int v = 0; v < SIZE; v++) {
ys[v] = v * 3;
xs[v] = 1000 + v * 7;
}
//vector<int> d = derivative(mk_root(xs));
//for (int i = 0; i < d.size(); i++) cout << d[i] << " ";
//cout << "\n";
/*vector<int> prod = mk_root(xs);
vector<int> prod = karatsuba_mul(xs, ys);
for (int i = 0; i < SIZE + 1; i++)
cout << prod[i] << " ";
cout << "\n";
cout << eval_poly_at(prod, 189) << " " << gexptable[glogtable[eval_poly_at(xs, 189)] + glogtable[eval_poly_at(ys, 189)]] << "\n";*/
vector<int> poly = lagrange_interp(ys, xs);
cout << eval_poly_at(poly, 1700) << "\n";
unsigned int o = 0;
for (int i = 4096; i < 8192; i++) {
for (int i = SIZE; i < SIZE * 2; i++) {
o += eval_poly_at(poly, i);
}
cout << o;
cout << o << "\n";
//cout << eval_poly_at(poly, 0) << " " << ys[0] << "\n";
//cout << eval_poly_at(poly, 134) << " " << ys[134] << "\n";
//cout << eval_poly_at(poly, 375) << " " << ys[375] << "\n";

5
erasure_code/ec65536/subquadratic_poly_utils.py
View File

@ -74,7 +74,10 @@ def lagrange_interp(pieces, xs):
# denoms = [eval_poly_at(d, xs[i]) for i in range(len(xs))]
# Generate output polynomial, which is the sum of the per-value numerator
# polynomials rescaled to have the right y values
return multi_root_derive(xs, [galois_div(p, d) for p, d in zip(pieces, denoms)])
factors = [galois_div(p, d) for p, d in zip(pieces, denoms)]
o = multi_root_derive(xs, factors)
print(o)
return o
def multi_root_derive(xs, muls):
if len(xs) == 1: