/*
  Author:  Pate Williams (c) 1997

  "Algorithm 3.4.3 (Distinct Degree Factorization).
  Given a squarefree polynomial A contained in
  Fp[X], this algorithm finds for each d the
  polynomial A[d] which is the product of the
  irreducible factors of A of degree d." -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 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 zpoly_mul(long m, long n, verylong *za, verylong *zb,
               verylong *zc, long *p)
{
  long i, j, k;
  verylong zd = 0, zai = 0, zbk = 0, zsum = 0, zterm = 0;

  *p = m + n;
  for (k = 0; k <= *p; k++) {
    zzero(&zsum);
    for (i = 0; i <= k; i++) {
      j = k - i;
      if (i > m) zzero(&zai);
      else zcopy(za[i], &zai);
      if (j > n) zzero(&zbk);
      else zcopy(zb[j], &zbk);
      zmul(zai, zbk, &zterm);
      zcopy(zsum, &zd);
      zadd(zterm, zd, &zsum);
    }
    zcopy(zsum, &zc[k]);
  }
  zfree(&zd);
  zfree(&zai);
  zfree(&zbk);
  zfree(&zsum);
  zfree(&zterm);
}

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_pow(long degreeA, long degreem, verylong zn,
               verylong *zA, verylong *zm, verylong *zs,
               long *ds)
{
  long dp, dq, dx = degreeA, i;
  verylong za = 0, zb = 0, zp[POLY_SIZE], zq[POLY_SIZE],
           zx[POLY_SIZE], zy[POLY_SIZE];

  for (i = 0; i < POLY_SIZE; i++)
    zp[i] = zq[i] = zx[i] = zy[i] = 0;
  *ds = 0;
  zcopy(zn, &za);
  zone(&zs[0]);
  for (i = 0; i <= dx; i++) zcopy(zA[i], &zx[i]);
  while (zscompare(za, 0l) > 0) {
    if (zodd(za)) {
      /* s = (s * x) % m; */
      zpoly_mul(*ds, dx, zs, zx, zp, &dp);
      zpoly_div(dp, degreem, zp, zm, zq, zs, &dq, ds);
    }
    zcopy(za, &zb);
    zrshift(zb, 1l, &za);
    if (zscompare(za, 0l) > 0) {
      /* x = (x * x) % m; */
      for (i = 0; i <= dx; i++) zcopy(zx[i], &zy[i]);
      zpoly_mul(dx, dx, zx, zy, zp, &dp);
      zpoly_div(dp, degreem, zp, zm, zq, zx, &dq, &dx);
    }
  }
  zfree(&za);
  zfree(&zb);
  for (i = 0; i < POLY_SIZE; i++) {
    zfree(&zp[i]);
    zfree(&zq[i]);
    zfree(&zx[i]);
    zfree(&zy[i]);
  }
}

void zpoly_sub(long da, long db, verylong *za, verylong *zb,
               verylong *zc, long *dc)
/* c = a - b */
{
  long i;
  verylong zz = 0;

  zzero(&zz);
  if (da >= db) {
    for (i = 0; i <= db; i++)
      zsub(za[i], zb[i], &zc[i]);
    for (i = db + 1; i <= da; i++)
      zcopy(za[i], &zc[i]);
    *dc = da;
  }
  else {
    for (i = 0; i <= da; i++)
      zsub(za[i], zb[i], &zc[i]);
    for (i = da + 1; i <= db; i++)
      zsub(zz, zb[i], &zc[i]);
    *dc = db;
  }
  zfree(&zz);
}

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 distinct_degree(long dA, long p, verylong *zA,
                     verylong **zB, long *dB,
                     long *count)
/* distinct degree factorization */
{
  int zero;
  long d = 0, d1, dP, dR, dV = dA, dW = 1, e, e2, i;
  verylong za = 0, zp = 0;
  verylong zP[POLY_SIZE] = {0};
  verylong zR[POLY_SIZE] = {0};
  verylong zV[POLY_SIZE] = {0};
  verylong zW[POLY_SIZE] = {0};

  *count = 0;
  zintoz(p, &zp);
  for (i = 0; i <= dA; i++)
    zcopy(zA[i], &zV[i]);
  zzero(&zW[0]);
  zone(&zW[1]);
  L2:
  e = dV;
  d1 = d + 1;
  e2 = e / 2;
  if (d1 > e2) {
    if (e > 0) {
      monic(dV, p, zV);
      for (i = 0; i <= dV; i++)
        zcopy(zV[i], &zB[*count][i]);
      dB[*count] = dV;
      *count = *count + 1;
      for (i = d + 1; i <= e; i++) {
        zone(&zB[*count][0]);
        dB[*count] = 0;
        *count = *count + 1;
      }
    }
    zfree(&za);
    zfree(&zp);
    for (i = 0; i < POLY_SIZE; i++) {
      zfree(&zP[i]);
      zfree(&zR[i]);
      zfree(&zV[i]);
      zfree(&zW[i]);
    }
    return;
  }
  d++;
  zpoly_pow(dW, dV, zp, zW, zV, zP, &dP);
  for (i = 0; i <= dP; i++)
    zintoz(zsmod(zP[i], p), &zW[i]);
  dW = dP;
  zsadd(zW[1], - 1l, &za);
  zcopy(za, &zW[1]);
  zpoly_gcd(dW, dV, p, zW, zV, zB[*count], &dB[*count]);
  zero = 1;
  for (i = 1; zero && i <= dB[*count]; i++)
    zero = zscompare(zB[*count][i], 0l) == 0;
  monic(dB[*count], p, zB[*count]);
  if (!zero || (zero && zscompare(zB[*count][0], 1l) != 0)) {
    zpoly_div(dV, dB[*count], zV, zB[*count], zP, zR, &dP, &dR);
    for (i = 0; i <= dP; i++)
      zintoz(zsmod(zP[i], p), &zV[i]);
    dV = dP;
    zsadd(zW[1], + 1l, &za);
    zcopy(za, &zW[1]);
    zpoly_div(dW, dV, zW, zV, zP, zR, &dP, &dR);
    for (i = 0; i <= dR; i++)
      zintoz(zsmod(zR[i], p), &zW[i]);
    dW = dR;
  }
  #ifdef DEBUG
  zpoly_write("W = ", dW, zW);
  zpoly_write("V = ", dV, zV);
  zpoly_write("A = ", dB[*count], zB[*count]);
  #endif
  *count = *count + 1;
  goto L2;
}

int main(void)
{
  char answer[256];
  long count, dA, dB[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]);
    }
    distinct_degree(dA, p, zA, zB, dB, &count);
    for (i = 0; i < count; 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;
}