/*
  Author:  Pate Williams (c) 1997

  "Algorithm 3.4.2 (Squarefree Factorization). Let
  A is contained in Fp[X] be a monic polynomial and
  let A = product(i >= 1, A[i] ^ i) be its square-
  free factorization, where the A[i] are squarefree
  and pairwise coprime." -Henri Cohen- See "A Course
  in Computational Algebraic Number Theory" by Henri
  Cohen page 126.
*/

#include <ctype.h>
#include <stdio.h>
#include <stdlib.h>
#include "lip.h"

#define DEBUG
#define POLY_SIZE 256

void error(char *message)
{
  fprintf(stderr, "%s", message);
  exit(1);
}

verylong **allocate_very_matrix(long m, long n)
{
  long i;
  verylong **matrix = calloc(m, sizeof(verylong *));

  if (!matrix)
    error("Failure in allocate_very_matrix.");
  for (i = 0; i < m; i++) {
    matrix[i] = calloc(n, sizeof(verylong));
    if (!matrix[i])
      error("Failure in allocate_very_matrix.");
  }
  return matrix;
}

void free_very_matrix(verylong **zm, long m, long n)
{
  long i, j;

  for (i = 0; i < m; i++) {
    for (j = 0; j < n; j++)
      zfree(&zm[i][j]);
    free(zm[i]);
  }
  free(zm);
}

void zspow(verylong za, long n, verylong *zb)
{
  int c = zscompare(za, 0l);
  verylong zc = 0;

  if (c > 0)
    zsexp(za, n, zb);
  else if (c < 0) {
    zcopy(za, &zc);
    zabs(&zc);
    zsexp(zc, n, zb);
    if (n & 1) znegate(zb);
  }
  else
    zzero(zb);
  zfree(&zc);
}

void zpoly_div(long m, long n, verylong *zu, verylong *zv,
               verylong *zq, verylong *zr, long *p, long *s)
{
  long j, jk, k, nk;
  verylong za = 0, zb = 0, zvn = 0;

  zcopy(zv[n], &zvn);
  for (j = 0; j <= m; j++)
    zcopy(zu[j], &zr[j]);
  if (m < n) {
    *p = 0, *s = m;
    zzero(&zq[0]);
  }
  else {
    *p = m - n, *s = n - 1;
    for (k = *p; k >= 0; k--) {
      nk = n + k;
      zspow(zvn, k, &za);
      zmul(zr[nk], za, &zq[k]);
      for (j = nk - 1; j >= 0; j--) {
        jk = j - k;
        if (jk >= 0) {
          zmul(zvn, zr[j], &za);
          zmul(zr[nk], zv[jk], &zb);
          zsub(za, zb, &zr[j]);
        }
        else {
          zcopy(zr[j], &za);
          zmul(zvn, za, &zr[j]);
        }
      }
    }
    while (*p > 0 && zscompare(zq[*p], 0l) == 0) *p = *p - 1;
    while (*s > 0 && zscompare(zr[*s], 0l) == 0) *s = *s - 1;
  }
  zfree(&za);
  zfree(&zb);
  zfree(&zvn);
}

void zpoly_gcd(long degreeA, long degreeB, long p,
               verylong *zA, verylong *zB, verylong *za,
               long *da)
{
  int nonzero = 0, zero;
  long db, dq, dr, i;
  verylong zc = 0, zp = 0;
  verylong zb[POLY_SIZE], zq[POLY_SIZE], zr[POLY_SIZE];

  for (i = 0; i < POLY_SIZE; i++)
    zb[i] = zq[i] = zr[i] = 0;
  if (degreeA > degreeB) {
    *da = degreeA;
    db = degreeB;
    for (i = 0; i <= *da; i++) zcopy(zA[i], &za[i]);
    for (i = 0; i <= db; i++) zcopy(zB[i], &zb[i]);
  }
  else {
    *da = degreeB;
    db = degreeA;
    for (i = 0; i <= *da; i++) zcopy(zB[i], &za[i]);
    for (i = 0; i <= db; i++) zcopy(zA[i], &zb[i]);
  }
  for (i = 0; i <= db && !nonzero; i++)
    nonzero = zscompare(zb[i], 0l) != 0;
  while (nonzero) {
    zpoly_div(*da, db, za, zb, zq, zr, &dq, &dr);
    zintoz(p, &zp);
    for (i = 0; i <= dr; i++) {
      zcopy(zr[i], &zc);
      zmod(zc, zp, &zr[i]);
    }
    zero = 1;
    for (i = dr; i >= 0 && zero; i--) {
      zero = zscompare(zr[i], 0l) == 0;
      if (zero && dr > 0) dr--;
    }
    for (i = 0; i <= db; i++) zcopy(zb[i], &za[i]);
    *da = db;
    for (i = 0; i <= dr; i++) zcopy(zr[i], &zb[i]);
    db = dr;
    nonzero = 0;
    for (i = 0; i <= db && !nonzero; i++)
      nonzero = zscompare(zb[i], 0l) != 0;
  }
  zfree(&zc);
  zfree(&zp);
  for (i = 0; i < POLY_SIZE; i++) {
    zfree(&zb[i]);
    zfree(&zq[i]);
    zfree(&zr[i]);
  }
}

void zpoly_write(char *label, long dA, verylong *zA)
{
  long i;

  printf("%s", label);
  for (i = dA; i >= 0; i--) {
    zwrite(zA[i]);
    printf(" ");
  }
  printf("\n");
}

void monic(long dA, long p, verylong *zA)
{
  long i;
  verylong za = 0, zi = 0, zp = 0;

  zintoz(p, &zp);
  zinvmod(zA[dA], zp, &zi);
  zone(&zA[dA]);
  for (i = 0; i < dA; i++) {
    zmulmod(zA[i], zi, zp, &za);
    zcopy(za, &zA[i]);
  }
  zfree(&za);
  zfree(&zi);
  zfree(&zp);
}

void square_free(long dA, long p,
                 verylong *zA, verylong **zB,
                 long *dB, long *expB, long *count)
/* factors A into the matrix B */
{
  int zero;
  long dP, dR, dT, dT0, dT0p, dV, dW, e = 1, i, j, k;
  verylong za = 0;
  verylong zP[POLY_SIZE], zR[POLY_SIZE];
  verylong zT[POLY_SIZE], zV[POLY_SIZE];
  verylong zW[POLY_SIZE];
  verylong zT0[POLY_SIZE], zT0p[POLY_SIZE];

  *count = 0;
  for (i = 0; i < POLY_SIZE; i++) {
    zP[i] = zT[i] = zR[i] = zV[i] = zW[i];
    zT0[i] = zT0p[i] = 0;
  }
  for (i = 0; i <= dA; i++)
    zcopy(zA[i], &zT0[i]);
  dT0 = dA;
  L2:
  zero = 1;
  for (i = 1; zero && i <= dT0; i++)
    zero = zscompare(zT0[i], 0l) == 0;
  if (zero) {
    zfree(&za);
    for (i = 0; i < POLY_SIZE; i++) {
      zfree(&zP[i]);
      zfree(&zR[i]);
      zfree(&zT[i]);
      zfree(&zV[i]);
      zfree(&zW[i]);
      zfree(&zT0[i]);
      zfree(&zT0p[i]);
    }
    return;
  }
  /* calculate derivative of T0 */
  for (i = 1; i <= dT0; i++) {
    zsmul(zT0[i], i, &za);
    zintoz(zsmod(za, p), &zT0p[i - 1]);
  }
  dT0p = dT0 - 1;
  zero = 1;
  for (i = dT0p; zero && i >= 0; i--) {
    zero = zscompare(zT0p[i], 0l) == 0;
    if (zero) dT0p--;
  }
  if (dT0p == - 1) dT0p++;
  zpoly_gcd(dT0, dT0p, p, zT0, zT0p, zT, &dT);
  zpoly_div(dT0, dT, zT0, zT, zV, zR, &dV, &dR);
  for (i = 0; i <= dT; i++)
    zintoz(zsmod(zT[i], p), &zT[i]);
  k = 0;
  L3:
  for (i = 0; i <= dV; i++)
    zintoz(zsmod(zV[i], p), &zV[i]);
  #ifdef DEBUG
  zpoly_write("T0  = ", dT0, zT0);
  zpoly_write("T0' = ", dT0p, zT0p);
  zpoly_write("T   = ", dT, zT);
  zpoly_write("V   = ", dV, zV);
  #endif
  zero = 1;
  for (i = 1; zero && i <= dV; i++)
    zero = zscompare(zV[i], 0l) == 0;
  if (zero) {
    dT0 = - 1;
    for (j = 0; j <= dT / p; j++) {
      if (j % p == 0) {
        dT0++;
        zcopy(zT[j], &zT0[j / p]);
      }
    }
    if (dT0 == - 1) dT0++;
    e *= p;
    goto L2;
  }
  k++;
  if (k % p == 0) {
    zpoly_div(dT, dV, zT, zV, zP, zR, &dP, &dR);
    for (i = 0; i <= dP; i++)
      zintoz(zsmod(zP[i], p), &zT[i]);
    dT = dP;
    k++;
  }
  zpoly_gcd(dT, dV, p, zT, zV, zW, &dW);
  zpoly_div(dV, dW, zV, zW, zB[*count], zR, &dB[*count], &dR);
  for (i = 0; i <= dB[*count]; i++)
    zintoz(zsmod(zB[*count][i], p), &zB[*count][i]);
  zero = 1;
  for (i = dB[*count]; zero && i >= 0; i--) {
    zero = zscompare(zB[*count][i], 0l) == 0;
    if (zero) dB[*count]--;
  }
  monic(dB[*count], p, zB[*count]);
  #ifdef DEBUG
  zpoly_write("W = ", dW, zW);
  zpoly_write("A = ", dB[*count], zB[*count]);
  #endif
  for (i = 0; i <= dW; i++)
    zcopy(zW[i], &zV[i]);
  dV = dW;
  zpoly_div(dT, dV, zT, zV, zP, zR, &dP, &dR);
  for (i = 0; i <= dP; i++)
    zintoz(zsmod(zP[i], p), &zT[i]);
  dT = dP;
  if (dB[*count] != dA) {
    zero = 1;
    for (i = 1; zero && i <= dB[*count]; i++)
      zero = zscompare(zB[*count][i], 0l) == 0;
    if (dB[*count] > 0 && !zero) {
       expB[*count] = e * k;
      *count = *count + 1;
    }
  }
  goto L3;
}

int main(void)
{
  char answer[256];
  long count, dA, dB[32], expB[32], i, m = 32, p;
  verylong zA[POLY_SIZE] = {0};
  verylong **zB = allocate_very_matrix(m, POLY_SIZE);

  do {
    printf("degree of polynomial = ");
    scanf("%d", &dA);
    printf("modulus = ");
    scanf("%d", &p);
    for (i = 0; i <= dA; i++) {
      printf("A[%ld] = ", i);
      zread(&zA[i]);
    }
    square_free(dA, p, zA, zB, dB, expB, &count);
    for (i = 0; i < count; i++) {
      printf("exponent = %ld ", expB[i]);
      zpoly_write("factor = ", dB[i], zB[i]);
    }
    printf("another polynomial (n or y)? ");
    scanf("%s", answer);
  } while (tolower(answer[0]) == 'y');
  for (i = 0; i <= dA; i++) zfree(&zA[i]);
  free_very_matrix(zB, m, POLY_SIZE);
  return 0;
}