MATRMUL0 - Matrix Multiplication 2K

Consider the following C++ code, it constructs n×n matrices A,B and vector V from matrix C=A×B which you need to calculate.

uint32_t n, i, j, d1, p1, r1, m1, d2, p2, m2, A[n][n], B[n][n];
uint64_t C[n][n], V[n];
//here you need to read n, p1, d1, r1, m1, p2, d2, r2, m2 from input.
for (i=0; i<n; ++i)
    for (j=0; j<n; ++j) {
        d1 = d1 * p1 + r1;
        d2 = d2 * p2 + r2;
        A[i][j] = d1 >> (32 - m1);
        B[i][j] = d2 >> (32 - m2);
    }
//here you need to calculate C=A*B
for (i=0; i<n; ++i) {
    V[i] = 0;
    for (j=0; j<n; ++j)
        V[i] ^= C[i][j];
}
//here you need to output V[0], V[1], ..., V[n-1], separated by spaces.

Input

You are given integers n, p1, d1, r1, m1, p2, d2, r2, m2, separated by spaces.

1≤n≤2048, 1≤m1,m2≤26, 0≤p1,d1,r1,p2,d2,r2<232.

Output

You need to output V[0], ..., V[n-1], separated by spaces.

Example

Input:
4 1664525 0 1013904223 26 1664525 1 1013904223 26
Output:
3929555766216722 770418013451752 7738542081270672 4286515685761206

P.S.

There are 4 tests with n≈2048. My best solution time — ~3.2s (~0.8s per test) which is 20 times faster than time limit.

Also try the challenge MATRMUL, to get AC there your time here should be less than 14s for cubic algorithm and 16s for Strassen's.


Added by:Michael Kharitonov
Date:2017-04-09
Time limit:16s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All
Resource:fastcomputing.org

hide comments
2023-04-03 06:53:27 Ishan
I have been hearing from my ECE friends that cache misses cost a lot more than ALU operations these days. This is probably the first time m trying to experience it firsthand. Good that you created a problem with one of the most important topics in CS research in modern times.
2017-12-31 12:18:07 Michael Kharitonov
tip: use Function Attributes or Function Specific Option Pragmas:
https://gcc.gnu.org/onlinedocs/gcc/Common-Function-Attributes.html
https://gcc.gnu.org/onlinedocs/gcc/Function-Specific-Option-Pragmas.html


Last edit: 2018-07-25 23:23:41
2017-09-21 19:38:20 Sushant Moon
I need some hints for this problem. Please if anyone has any it would be a very much helpful Thank You
http://discuss.spoj.com/t/needed-some-help-with-matrmul0-problem/24667

Last edit: 2017-12-31 12:18:35
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