// clang time.c LagCoef.o M.o -O3
#include <stdio.h>
#include <stdlib.h>
typedef long unsigned int L;
typedef L ft(L);
extern ft * T[256]; // in M.c
typedef unsigned char uc;
void LagCoef(int n, uc r, uc av[n], uc coef[n]);
static L ru(){return (L)arc4random()<<32 | arc4random();}
int main(){L * area = malloc((11+3+3+1)*512*sizeof(L));
  if(!area) exit(printf("No space\n"));
  L * base = (L *)((L)(area+511)&(-1L<<12)); // 17 aligned pages.
  for(int j=0; j<11*512; ++j) base[j] = ru(); // generate the asset.
  uc av[11]; for(int j=0; j<11; ++j) av[j]=j;
  // page number is portion argument for both asset and aux.
  for(int j=11; j<11+3; ++j) { // generate each aux page.
    uc coe[11]; LagCoef(11, j, av, coe);
    for(int n=0; n<512; ++n) base[(j<<9)+n] = 0;
    for(int k=0; k<11; ++k) {ft * m = T[coe[k]];
      for(int n=0; n<512; ++n) base[(j<<9)+n] ^= (*m)(base[(k<<9)+n]);}}
  if(0) for(int y=0; y<13; ++y) printf("%016lx\n", base[(11<<9)+y]);
  // We have now constructed the 3 auxiliaries.
  uc sur[11] = {1, 2, 4, 5, 7, 8, 9, 10, 11, 12, 13};
  uc lost[3] = {0, 3, 6};
  for(int n=0; n<3; ++n) for(int k=0; k<512; ++k) // copy the three lost pages.
     base[((14+n)<<9)+k] = base[(lost[n]<<9)+k];
// reconstruct the three lost pages.
  for(int cc=0; cc<10000; ++cc) { // .... timing
  for(int n=0; n<3; ++n) for(int k=0; k<512; ++k) base[(lost[n]<<9)+k] = 0;
  for(int n=0; n<3; ++n) {uc coe[11]; LagCoef(11, lost[n], sur, coe);
    for(int j=0; j<11; ++j) { // consult each surviving page.
      ft * m = T[coe[j]];
      for(int k=0; k<512; ++k)
        base[(lost[n]<<9)+k] ^= (*m)(base[(sur[j]<<9)+k]);}}}
  // Now the asset should be like new.
  for(int n = 0; n<3; n++) { // verify each page.
    for(int k=0; k<512; ++k)
      if(base[(lost[n]<<9)+k] ^ base[((14+n)<<9)+k]) exit(printf("Bad!!\n"));}
  return 0;}