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pqc/external/flint-2.4.3/nmod_poly.h

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ALL: Add flint
2014-05-18 22:03:37 +00:00
/*=============================================================================
This file is part of FLINT.
FLINT is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
FLINT is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with FLINT; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2007, David Howden
Copyright (C) 2010, 2011 William Hart
Copyright (C) 2011 Sebastian Pancratz
Copyright (C) 2011 Fredrik Johansson
******************************************************************************/
#ifndef NMOD_POLY_H
#define NMOD_POLY_H
#undef ulong
#define ulong ulongxx /* interferes with system includes */
#include <stdio.h>
#undef ulong
#include <gmp.h>
#define ulong mp_limb_t
#include "flint.h"
#include "nmod_vec.h"
#include "nmod_mat.h"
#include "ulong_extras.h"
#include "fmpz.h"
#ifdef __cplusplus
extern "C" {
#endif
#define NMOD_DIVREM_DIVCONQUER_CUTOFF 300
#define NMOD_DIV_DIVCONQUER_CUTOFF 300 /* Must be <= NMOD_DIVREM_DIVCONQUER_CUTOFF */
#define NMOD_POLY_HGCD_CUTOFF 100 /* HGCD: Basecase -> Recursion */
#define NMOD_POLY_GCD_CUTOFF 340 /* GCD: Euclidean -> HGCD */
#define NMOD_POLY_SMALL_GCD_CUTOFF 200 /* GCD (small n): Euclidean -> HGCD */
static __inline__
slong NMOD_DIVREM_BC_ITCH(slong lenA, slong lenB, nmod_t mod)
{
const mp_bitcnt_t bits =
2 * (FLINT_BITS - mod.norm) + FLINT_BIT_COUNT(lenA - lenB + 1);
if (bits <= FLINT_BITS)
return lenA;
else if (bits <= 2 * FLINT_BITS)
return 2*(lenA + lenB - 1);
else
return 3*(lenA + lenB - 1);
}
static __inline__
slong NMOD_DIV_BC_ITCH(slong lenA, slong lenB, nmod_t mod)
{
const mp_bitcnt_t bits =
2 * (FLINT_BITS - mod.norm) + FLINT_BIT_COUNT(lenA - lenB + 1);
if (bits <= FLINT_BITS)
return lenA - lenB + 1;
else if (bits <= 2 * FLINT_BITS)
return 2*lenA;
else
return 3*lenA;
}
static __inline__
slong NMOD_DIVREM_DC_ITCH(slong lenB, nmod_t mod)
{
slong i = 0;
while (lenB > NMOD_DIVREM_DIVCONQUER_CUTOFF + i)
{
lenB = (lenB + 1)/2;
i++;
}
if (lenB > NMOD_DIVREM_DIVCONQUER_CUTOFF)
lenB = NMOD_DIVREM_DIVCONQUER_CUTOFF;
return NMOD_DIVREM_BC_ITCH(2*lenB - 1, lenB, mod) + 2*lenB - 1;
}
typedef struct
{
mp_ptr coeffs;
slong alloc;
slong length;
nmod_t mod;
} nmod_poly_struct;
typedef nmod_poly_struct nmod_poly_t[1];
/* zn_poly helper functions ************************************************
Copyright (C) 2007, 2008 David Harvey
*/
static __inline__
int signed_mpn_sub_n(mp_ptr res, mp_srcptr op1, mp_srcptr op2, slong n)
{
if (mpn_cmp(op1, op2, n) >= 0)
{
mpn_sub_n(res, op1, op2, n);
return 0;
}
else
{
mpn_sub_n(res, op2, op1, n);
return 1;
}
}
/* Memory management ********************************************************/
void nmod_poly_init(nmod_poly_t poly, mp_limb_t n);
void nmod_poly_init_preinv(nmod_poly_t poly, mp_limb_t n, mp_limb_t ninv);
void nmod_poly_init2(nmod_poly_t poly, mp_limb_t n, slong alloc);
void nmod_poly_init2_preinv(nmod_poly_t poly,
mp_limb_t n, mp_limb_t ninv, slong alloc);
void nmod_poly_realloc(nmod_poly_t poly, slong alloc);
void nmod_poly_clear(nmod_poly_t poly);
void nmod_poly_fit_length(nmod_poly_t poly, slong alloc);
static __inline__
void _nmod_poly_set_length(nmod_poly_t poly, slong len)
{
poly->length = len;
}
static __inline__
void _nmod_poly_normalise(nmod_poly_t poly)
{
while (poly->length && (poly->coeffs[poly->length - 1] == WORD(0)))
poly->length--;
}
/* Polynomial parameters ****************************************************/
static __inline__
slong nmod_poly_length(const nmod_poly_t poly)
{
return poly->length;
}
static __inline__
slong nmod_poly_degree(const nmod_poly_t poly)
{
return poly->length - 1;
}
static __inline__
mp_limb_t nmod_poly_modulus(const nmod_poly_t poly)
{
return poly->mod.n;
}
static __inline__
mp_bitcnt_t nmod_poly_max_bits(const nmod_poly_t poly)
{
return _nmod_vec_max_bits(poly->coeffs, poly->length);
}
static __inline__
mp_ptr nmod_poly_lead(const nmod_poly_t poly)
{
if (poly->length)
return poly->coeffs + (poly->length - 1);
else
return NULL;
}
/* Assignment and basic manipulation ****************************************/
static __inline__
void nmod_poly_set(nmod_poly_t a, const nmod_poly_t b)
{
if (a != b)
{
nmod_poly_fit_length(a, b->length);
flint_mpn_copyi(a->coeffs, b->coeffs, b->length);
a->length = b->length;
}
}
static __inline__
void nmod_poly_swap(nmod_poly_t poly1, nmod_poly_t poly2)
{
slong t;
mp_ptr tp;
t = poly1->alloc;
poly1->alloc = poly2->alloc;
poly2->alloc = t;
t = poly1->length;
poly1->length = poly2->length;
poly2->length = t;
tp = poly1->coeffs;
poly1->coeffs = poly2->coeffs;
poly2->coeffs = tp;
}
static __inline__
void nmod_poly_zero(nmod_poly_t res)
{
res->length = 0;
}
static __inline__
void nmod_poly_one(nmod_poly_t res)
{
nmod_poly_fit_length(res, 1);
res->length = 1;
res->coeffs[0] = 1;
}
static __inline__
void nmod_poly_truncate(nmod_poly_t poly, slong len)
{
if (poly->length > len)
{
poly->length = len;
_nmod_poly_normalise(poly);
}
}
void _nmod_poly_reverse(mp_ptr output, mp_srcptr input, slong len, slong m);
void nmod_poly_reverse(nmod_poly_t output, const nmod_poly_t input, slong m);
/* Comparison ***************************************************************/
static __inline__
int nmod_poly_equal(const nmod_poly_t a, const nmod_poly_t b)
{
if (a->length != b->length)
return 0;
if (a != b)
if (!_nmod_vec_equal(a->coeffs, b->coeffs, a->length))
return 0;
return 1;
}
static __inline__
int nmod_poly_is_zero(const nmod_poly_t poly)
{
return (poly->length == 0);
}
static __inline__ int
nmod_poly_is_one(const nmod_poly_t poly)
{
return (poly->length == 1) && (poly->coeffs[0] == 1);
}
/* Randomisation ************************************************************/
void nmod_poly_randtest(nmod_poly_t poly, flint_rand_t state, slong len);
static __inline__ void
nmod_poly_randtest_not_zero(nmod_poly_t poly, flint_rand_t state, slong len)
{
do {
nmod_poly_randtest(poly, state, len);
} while (nmod_poly_is_zero(poly));
}
void
nmod_poly_randtest_irreducible(nmod_poly_t poly, flint_rand_t state, slong len);
void
nmod_poly_randtest_monic(nmod_poly_t poly, flint_rand_t state, slong len);
void
nmod_poly_randtest_monic_irreducible(nmod_poly_t poly, flint_rand_t state, slong len);
void
nmod_poly_randtest_trinomial(nmod_poly_t poly, flint_rand_t state, slong len);
int
nmod_poly_randtest_trinomial_irreducible(nmod_poly_t poly, flint_rand_t state,
slong len, slong max_attempts);
void
nmod_poly_randtest_pentomial(nmod_poly_t poly, flint_rand_t state, slong len);
int
nmod_poly_randtest_pentomial_irreducible(nmod_poly_t poly, flint_rand_t state,
slong len, slong max_attempts);
void
nmod_poly_randtest_sparse_irreducible(nmod_poly_t poly, flint_rand_t state, slong len);
/* Getting and setting coefficients *****************************************/
static __inline__
ulong nmod_poly_get_coeff_ui(const nmod_poly_t poly, slong j)
{
return (j >= poly->length) ? 0 : poly->coeffs[j];
}
void nmod_poly_set_coeff_ui(nmod_poly_t poly, slong j, ulong c);
/* Input and output *********************************************************/
char * nmod_poly_get_str(const nmod_poly_t poly);
int nmod_poly_set_str(nmod_poly_t poly, const char * s);
static __inline__
int nmod_poly_print(const nmod_poly_t a)
{
size_t r;
slong i;
r = flint_printf("%wd %wu", a->length, a->mod.n);
if (a->length == 0)
return r;
else
if (r > 0)
r = flint_printf(" ");
for (i = 0; (r > 0) && (i < a->length); i++)
r = flint_printf(" %wu", a->coeffs[i]);
return (int) r;
}
int nmod_poly_fread(FILE * f, nmod_poly_t poly);
static __inline__
int nmod_poly_fprint(FILE * f, const nmod_poly_t poly)
{
char *s;
int r;
s = nmod_poly_get_str(poly);
r = fputs(s, f);
flint_free(s);
return (r < 0) ? r : 1;
}
static __inline__
int nmod_poly_read(nmod_poly_t poly)
{
return nmod_poly_fread(stdin, poly);
}
/* Shifting *****************************************************************/
void _nmod_poly_shift_left(mp_ptr res, mp_srcptr poly, slong len, slong k);
void nmod_poly_shift_left(nmod_poly_t res, const nmod_poly_t poly, slong k);
void _nmod_poly_shift_right(mp_ptr res, mp_srcptr poly, slong len, slong k);
void nmod_poly_shift_right(nmod_poly_t res, const nmod_poly_t poly, slong k);
/* Addition and subtraction *************************************************/
void _nmod_poly_add(mp_ptr res, mp_srcptr poly1, slong len1,
mp_srcptr poly2, slong len2, nmod_t mod);
void nmod_poly_add(nmod_poly_t res, const nmod_poly_t poly1,
const nmod_poly_t poly2);
void _nmod_poly_sub(mp_ptr res, mp_srcptr poly1, slong len1,
mp_srcptr poly2, slong len2, nmod_t mod);
void nmod_poly_sub(nmod_poly_t res, const nmod_poly_t poly1,
const nmod_poly_t poly2);
void nmod_poly_neg(nmod_poly_t res, const nmod_poly_t poly1);
/* Scalar multiplication and division ***************************************/
void nmod_poly_scalar_mul_nmod(nmod_poly_t res,
const nmod_poly_t poly1, mp_limb_t c);
void _nmod_poly_make_monic(mp_ptr output,
mp_srcptr input, slong len, nmod_t mod);
void nmod_poly_make_monic(nmod_poly_t output, const nmod_poly_t input);
/* Bit packing and unpacking aand reduction **********************************/
void _nmod_poly_KS2_pack1(mp_ptr res, mp_srcptr op, slong n, slong s,
ulong b, ulong k, slong r);
void _nmod_poly_KS2_pack(mp_ptr res, mp_srcptr op, slong n, slong s,
ulong b, ulong k, slong r);
void _nmod_poly_KS2_unpack1(mp_ptr res, mp_srcptr op, slong n, ulong b,
ulong k);
void _nmod_poly_KS2_unpack2(mp_ptr res, mp_srcptr op, slong n, ulong b,
ulong k);
void _nmod_poly_KS2_unpack3(mp_ptr res, mp_srcptr op, slong n, ulong b,
ulong k);
void _nmod_poly_KS2_unpack(mp_ptr res, mp_srcptr op, slong n, ulong b,
ulong k);
void _nmod_poly_KS2_reduce(mp_ptr res, slong s, mp_srcptr op,
slong n, ulong w, nmod_t mod);
void _nmod_poly_KS2_recover_reduce1(mp_ptr res, slong s, mp_srcptr op1,
mp_srcptr op2, slong n, ulong b, nmod_t mod);
void _nmod_poly_KS2_recover_reduce1(mp_ptr res, slong s, mp_srcptr op1,
mp_srcptr op2, slong n, ulong b, nmod_t mod);
void _nmod_poly_KS2_recover_reduce2(mp_ptr res, slong s, mp_srcptr op1,
mp_srcptr op2, slong n, ulong b, nmod_t mod);
void _nmod_poly_KS2_recover_reduce2b(mp_ptr res, slong s, mp_srcptr op1,
mp_srcptr op2, slong n, ulong b, nmod_t mod);
void _nmod_poly_KS2_recover_reduce(mp_ptr res, slong s, mp_srcptr op1,
mp_srcptr op2, slong n, ulong b, nmod_t mod);
void _nmod_poly_bit_pack(mp_ptr res, mp_srcptr poly,
slong len, mp_bitcnt_t bits);
void _nmod_poly_bit_unpack(mp_ptr res, slong len,
mp_srcptr mpn, mp_bitcnt_t bits, nmod_t mod);
void nmod_poly_bit_pack(fmpz_t f, const nmod_poly_t poly,
mp_bitcnt_t bit_size);
void
nmod_poly_bit_unpack(nmod_poly_t poly, const fmpz_t f, mp_bitcnt_t bit_size);
void
_nmod_poly_KS2_pack(mp_ptr res, mp_srcptr op, slong n, slong s,
ulong b, ulong k, slong r);
/* Multiplication ***********************************************************/
void _nmod_poly_mul_classical(mp_ptr res, mp_srcptr poly1, slong len1,
mp_srcptr poly2, slong len2, nmod_t mod);
void nmod_poly_mul_classical(nmod_poly_t res,
const nmod_poly_t poly1, const nmod_poly_t poly2);
void _nmod_poly_mullow_classical(mp_ptr res, mp_srcptr poly1, slong len1,
mp_srcptr poly2, slong len2, slong trunc, nmod_t mod);
void nmod_poly_mullow_classical(nmod_poly_t res,
const nmod_poly_t poly1, const nmod_poly_t poly2, slong trunc);
void _nmod_poly_mulhigh_classical(mp_ptr res, mp_srcptr poly1, slong len1,
mp_srcptr poly2, slong len2, slong start, nmod_t mod);
void nmod_poly_mulhigh_classical(nmod_poly_t res,
const nmod_poly_t poly1, const nmod_poly_t poly2, slong start);
void _nmod_poly_mul_KS(mp_ptr out, mp_srcptr in1, slong len1,
mp_srcptr in2, slong len2, mp_bitcnt_t bits, nmod_t mod);
void nmod_poly_mul_KS(nmod_poly_t res,
const nmod_poly_t poly1, const nmod_poly_t poly2, mp_bitcnt_t bits);
void _nmod_poly_mul_KS2(mp_ptr res, mp_srcptr op1, slong n1,
mp_srcptr op2, slong n2, nmod_t mod);
void nmod_poly_mul_KS2(nmod_poly_t res,
const nmod_poly_t poly1, const nmod_poly_t poly2);
void _nmod_poly_mul_KS4(mp_ptr res, mp_srcptr op1, slong n1,
mp_srcptr op2, slong n2, nmod_t mod);
void nmod_poly_mul_KS4(nmod_poly_t res,
const nmod_poly_t poly1, const nmod_poly_t poly2);
void _nmod_poly_mullow_KS(mp_ptr out, mp_srcptr in1, slong len1,
mp_srcptr in2, slong len2, mp_bitcnt_t bits, slong n, nmod_t mod);
void nmod_poly_mullow_KS(nmod_poly_t res, const nmod_poly_t poly1,
const nmod_poly_t poly2, mp_bitcnt_t bits, slong n);
void _nmod_poly_mul(mp_ptr res, mp_srcptr poly1, slong len1,
mp_srcptr poly2, slong len2, nmod_t mod);
void nmod_poly_mul(nmod_poly_t res,
const nmod_poly_t poly1, const nmod_poly_t poly2);
void _nmod_poly_mullow(mp_ptr res, mp_srcptr poly1, slong len1,
mp_srcptr poly2, slong len2, slong trunc, nmod_t mod);
void nmod_poly_mullow(nmod_poly_t res, const nmod_poly_t poly1,
const nmod_poly_t poly2, slong trunc);
void _nmod_poly_mulhigh(mp_ptr res, mp_srcptr poly1, slong len1,
mp_srcptr poly2, slong len2, slong n, nmod_t mod);
void nmod_poly_mulhigh(nmod_poly_t res, const nmod_poly_t poly1,
const nmod_poly_t poly2, slong n);
void _nmod_poly_mulmod(mp_ptr res, mp_srcptr poly1, slong len1,
mp_srcptr poly2, slong len2, mp_srcptr f,
slong lenf, nmod_t mod);
void nmod_poly_mulmod(nmod_poly_t res,
const nmod_poly_t poly1, const nmod_poly_t poly2, const nmod_poly_t f);
void _nmod_poly_mulmod_preinv(mp_ptr res, mp_srcptr poly1, slong len1,
mp_srcptr poly2, slong len2, mp_srcptr f,
slong lenf, mp_srcptr finv, slong lenfinv, nmod_t mod);
void
nmod_poly_mulmod_preinv(nmod_poly_t res, const nmod_poly_t poly1,
const nmod_poly_t poly2, const nmod_poly_t f,
const nmod_poly_t finv);
int _nmod_poly_invmod(mp_limb_t *A,
const mp_limb_t *B, slong lenB,
const mp_limb_t *P, slong lenP, const nmod_t mod);
int nmod_poly_invmod(nmod_poly_t A,
const nmod_poly_t B, const nmod_poly_t P);
/* Powering *****************************************************************/
void _nmod_poly_pow_binexp(mp_ptr res,
mp_srcptr poly, slong len, ulong e, nmod_t mod);
void nmod_poly_pow_binexp(nmod_poly_t res, const nmod_poly_t poly, ulong e);
void _nmod_poly_pow(mp_ptr res, mp_srcptr poly, slong len, ulong e, nmod_t mod);
void nmod_poly_pow(nmod_poly_t res, const nmod_poly_t poly, ulong e);
void _nmod_poly_pow_trunc_binexp(mp_ptr res, mp_srcptr poly,
ulong e, slong trunc, nmod_t mod);
void nmod_poly_pow_trunc_binexp(nmod_poly_t res,
const nmod_poly_t poly, ulong e, slong trunc);
void _nmod_poly_pow_trunc(mp_ptr res, mp_srcptr poly,
ulong e, slong trunc, nmod_t mod);
void nmod_poly_pow_trunc(nmod_poly_t res,
const nmod_poly_t poly, ulong e, slong trunc);
void
nmod_poly_powmod_ui_binexp(nmod_poly_t res,
const nmod_poly_t poly, ulong e,
const nmod_poly_t f);
void
_nmod_poly_powmod_ui_binexp(mp_ptr res, mp_srcptr poly,
ulong e, mp_srcptr f, slong lenf, nmod_t mod);
void
_nmod_poly_powmod_mpz_binexp(mp_ptr res, mp_srcptr poly,
mpz_srcptr e, mp_srcptr f,
slong lenf, nmod_t mod);
void
nmod_poly_powmod_mpz_binexp(nmod_poly_t res,
const nmod_poly_t poly, mpz_srcptr e,
const nmod_poly_t f);
void
_nmod_poly_powmod_ui_binexp_preinv (mp_ptr res, mp_srcptr poly,
ulong e, mp_srcptr f, slong lenf,
mp_srcptr finv, slong lenfinv, nmod_t mod);
void
nmod_poly_powmod_ui_binexp_preinv(nmod_poly_t res,
const nmod_poly_t poly, ulong e,
const nmod_poly_t f, const nmod_poly_t finv);
void
_nmod_poly_powmod_x_ui_preinv (mp_ptr res, ulong e, mp_srcptr f, slong lenf,
mp_srcptr finv, slong lenfinv, nmod_t mod);
void
nmod_poly_powmod_x_ui_preinv(nmod_poly_t res, ulong e, const nmod_poly_t f,
const nmod_poly_t finv);
void
_nmod_poly_powmod_mpz_binexp_preinv (mp_ptr res, mp_srcptr poly,
mpz_srcptr e, mp_srcptr f, slong lenf,
mp_srcptr finv, slong lenfinv, nmod_t mod);
void
nmod_poly_powmod_mpz_binexp_preinv(nmod_poly_t res,
const nmod_poly_t poly, mpz_srcptr e,
const nmod_poly_t f, const nmod_poly_t finv);
/* Division *****************************************************************/
void _nmod_poly_divrem_basecase(mp_ptr Q, mp_ptr R, mp_ptr W,
mp_srcptr A, slong A_len, mp_srcptr B, slong B_len, nmod_t mod);
void nmod_poly_divrem_basecase(nmod_poly_t Q, nmod_poly_t R,
const nmod_poly_t A, const nmod_poly_t B);
void _nmod_poly_divrem_divconquer_recursive(mp_ptr Q, mp_ptr BQ, mp_ptr W,
mp_ptr V, mp_srcptr A, mp_srcptr B, slong lenB, nmod_t mod);
void _nmod_poly_divrem_divconquer(mp_ptr Q, mp_ptr R,
mp_srcptr A, slong lenA, mp_srcptr B, slong lenB, nmod_t mod);
void nmod_poly_divrem_divconquer(nmod_poly_t Q, nmod_poly_t R,
const nmod_poly_t A, const nmod_poly_t B);
void _nmod_poly_divrem_q0(mp_ptr Q, mp_ptr R,
mp_srcptr A, mp_srcptr B, slong lenA, nmod_t mod);
void _nmod_poly_divrem_q1(mp_ptr Q, mp_ptr R,
mp_srcptr A, slong lenA, mp_srcptr B, slong lenB,
nmod_t mod);
void _nmod_poly_divrem(mp_ptr Q, mp_ptr R, mp_srcptr A, slong lenA,
mp_srcptr B, slong lenB, nmod_t mod);
void nmod_poly_divrem(nmod_poly_t Q, nmod_poly_t R,
const nmod_poly_t A, const nmod_poly_t B);
void _nmod_poly_div_basecase(mp_ptr Q, mp_ptr W, mp_srcptr A, slong A_len,
mp_srcptr B, slong B_len, nmod_t mod);
void nmod_poly_div_basecase(nmod_poly_t Q, const nmod_poly_t A,
const nmod_poly_t B);
void _nmod_poly_div_divconquer_recursive(mp_ptr Q, mp_ptr W, mp_ptr V,
mp_srcptr A, mp_srcptr B, slong lenB, nmod_t mod);
void _nmod_poly_div_divconquer(mp_ptr Q, mp_srcptr A, slong lenA,
mp_srcptr B, slong lenB, nmod_t mod);
void nmod_poly_div_divconquer(nmod_poly_t Q,
const nmod_poly_t A, const nmod_poly_t B);
void _nmod_poly_div(mp_ptr Q, mp_srcptr A, slong lenA,
mp_srcptr B, slong lenB, nmod_t mod);
void nmod_poly_div(nmod_poly_t Q, const nmod_poly_t A, const nmod_poly_t B);
void _nmod_poly_rem_basecase(mp_ptr R, mp_ptr W, mp_srcptr A, slong lenA,
mp_srcptr B, slong lenB, nmod_t mod);
void nmod_poly_rem_basecase(nmod_poly_t R, const nmod_poly_t A, const nmod_poly_t B);
void _nmod_poly_rem_q1(mp_ptr R,
mp_srcptr A, slong lenA, mp_srcptr B, slong lenB,
nmod_t mod);
void _nmod_poly_rem(mp_ptr R, mp_srcptr A, slong lenA,
mp_srcptr B, slong lenB, nmod_t mod);
void nmod_poly_rem(nmod_poly_t R, const nmod_poly_t A, const nmod_poly_t B);
void _nmod_poly_inv_series_basecase(mp_ptr Qinv,
mp_srcptr Q, slong n, nmod_t mod);
void nmod_poly_inv_series_basecase(nmod_poly_t Qinv,
const nmod_poly_t Q, slong n);
void _nmod_poly_inv_series_newton(mp_ptr Qinv,
mp_srcptr Q, slong n, nmod_t mod);
void nmod_poly_inv_series_newton(nmod_poly_t Qinv,
const nmod_poly_t Q, slong n);
static __inline__
void _nmod_poly_inv_series(mp_ptr Qinv, mp_srcptr Q, slong n, nmod_t mod)
{
_nmod_poly_inv_series_newton(Qinv, Q, n, mod);
}
static __inline__
void nmod_poly_inv_series(nmod_poly_t Qinv, const nmod_poly_t Q, slong n)
{
nmod_poly_inv_series_newton(Qinv, Q, n);
}
void _nmod_poly_div_series(mp_ptr Q, mp_srcptr A, mp_srcptr B,
slong n, nmod_t mod);
void nmod_poly_div_series(nmod_poly_t Q, const nmod_poly_t A,
const nmod_poly_t B, slong n);
void _nmod_poly_div_newton(mp_ptr Q, mp_srcptr A, slong Alen,
mp_srcptr B, slong Blen, nmod_t mod);
void nmod_poly_div_newton(nmod_poly_t Q, const nmod_poly_t A,
const nmod_poly_t B);
void _nmod_poly_divrem_newton(mp_ptr Q, mp_ptr R,
mp_srcptr A, slong Alen, mp_srcptr B, slong Blen, nmod_t mod);
void nmod_poly_divrem_newton(nmod_poly_t Q, nmod_poly_t R,
const nmod_poly_t A, const nmod_poly_t B);
void _nmod_poly_div_newton_n_preinv (mp_ptr Q, mp_srcptr A, slong lenA,
mp_srcptr B, slong lenB, mp_srcptr Binv, slong lenBinv, nmod_t mod);
void nmod_poly_div_newton_n_preinv (nmod_poly_t Q, const nmod_poly_t A,
const nmod_poly_t B, const nmod_poly_t Binv);
void _nmod_poly_divrem_newton_n_preinv (mp_ptr Q, mp_ptr R, mp_srcptr A,
slong lenA, mp_srcptr B, slong lenB, mp_srcptr Binv, slong lenBinv, nmod_t mod);
void nmod_poly_divrem_newton_n_preinv(nmod_poly_t Q, nmod_poly_t R,
const nmod_poly_t A, const nmod_poly_t B, const nmod_poly_t Binv);
mp_limb_t
_nmod_poly_div_root(mp_ptr Q, mp_srcptr A, slong len, mp_limb_t c, nmod_t mod);
mp_limb_t
nmod_poly_div_root(nmod_poly_t Q, const nmod_poly_t A, mp_limb_t c);
/* Derivative ***************************************************************/
void _nmod_poly_derivative(mp_ptr x_prime, mp_srcptr x, slong len, nmod_t mod);
void nmod_poly_derivative(nmod_poly_t x_prime, const nmod_poly_t x);
void _nmod_poly_integral(mp_ptr x_int, mp_srcptr x, slong len, nmod_t mod);
void nmod_poly_integral(nmod_poly_t x_int, const nmod_poly_t x);
/* Evaluation ***************************************************************/
void
_nmod_poly_evaluate_fmpz(fmpz_t rop, const mp_srcptr poly, const slong len, const fmpz_t c);
void
nmod_poly_evaluate_fmpz(fmpz_t rop, const nmod_poly_t poly, const fmpz_t c);
mp_limb_t _nmod_poly_evaluate_nmod(mp_srcptr poly,
slong len, mp_limb_t c, nmod_t mod);
mp_limb_t nmod_poly_evaluate_nmod(const nmod_poly_t poly, mp_limb_t c);
void _nmod_poly_evaluate_nmod_vec(mp_ptr ys, mp_srcptr coeffs, slong len,
mp_srcptr xs, slong n, nmod_t mod);
void nmod_poly_evaluate_nmod_vec(mp_ptr ys,
const nmod_poly_t poly, mp_srcptr xs, slong n);
void nmod_poly_evaluate_nmod_vec(mp_ptr ys, const nmod_poly_t poly,
mp_srcptr xs, slong n);
void _nmod_poly_evaluate_nmod_vec_iter(mp_ptr ys, mp_srcptr coeffs, slong len,
mp_srcptr xs, slong n, nmod_t mod);
void nmod_poly_evaluate_nmod_vec_iter(mp_ptr ys,
const nmod_poly_t poly, mp_srcptr xs, slong n);
void
_nmod_poly_evaluate_nmod_vec_fast_precomp(mp_ptr vs, mp_srcptr poly,
slong plen, const mp_ptr * tree, slong len, nmod_t mod);
void _nmod_poly_evaluate_nmod_vec_fast(mp_ptr ys, mp_srcptr coeffs, slong len,
mp_srcptr xs, slong n, nmod_t mod);
void nmod_poly_evaluate_nmod_vec_fast(mp_ptr ys,
const nmod_poly_t poly, mp_srcptr xs, slong n);
/* Subproduct tree **********************************************************/
mp_ptr * _nmod_poly_tree_alloc(slong len);
void _nmod_poly_tree_free(mp_ptr * tree, slong len);
void _nmod_poly_tree_build(mp_ptr * tree, mp_srcptr roots,
slong len, nmod_t mod);
/* Interpolation ************************************************************/
void _nmod_poly_interpolate_nmod_vec_newton(mp_ptr poly, mp_srcptr xs,
mp_srcptr ys, slong n, nmod_t mod);
void nmod_poly_interpolate_nmod_vec_newton(nmod_poly_t poly,
mp_srcptr xs, mp_srcptr ys, slong n);
void _nmod_poly_interpolate_nmod_vec_barycentric(mp_ptr poly, mp_srcptr xs,
mp_srcptr ys, slong n, nmod_t mod);
void nmod_poly_interpolate_nmod_vec_barycentric(nmod_poly_t poly,
mp_srcptr xs, mp_srcptr ys, slong n);
void _nmod_poly_interpolate_nmod_vec(mp_ptr poly, mp_srcptr xs,
mp_srcptr ys, slong n, nmod_t mod);
void nmod_poly_interpolate_nmod_vec(nmod_poly_t poly,
mp_srcptr xs, mp_srcptr ys, slong n);
void nmod_poly_interpolate_nmod_vec_fast(nmod_poly_t poly,
mp_srcptr xs, mp_srcptr ys, slong n);
void _nmod_poly_interpolate_nmod_vec_fast(mp_ptr poly,
mp_srcptr xs, mp_srcptr ys, slong len, nmod_t mod);
void
_nmod_poly_interpolate_nmod_vec_fast_precomp(mp_ptr poly, mp_srcptr ys,
const mp_ptr * tree, mp_srcptr weights, slong len, nmod_t mod);
void _nmod_poly_interpolation_weights(mp_ptr w, const mp_ptr * tree,
slong len, nmod_t mod);
/* Composition **************************************************************/
void _nmod_poly_compose_horner(mp_ptr res, mp_srcptr poly1,
slong len1, mp_srcptr poly2, slong len2, nmod_t mod);
void nmod_poly_compose_horner(nmod_poly_t res,
const nmod_poly_t poly1, const nmod_poly_t poly2);
void _nmod_poly_compose_divconquer(mp_ptr res, mp_srcptr poly1, slong len1,
mp_srcptr poly2, slong len2, nmod_t mod);
void nmod_poly_compose_divconquer(nmod_poly_t res,
const nmod_poly_t poly1, const nmod_poly_t poly2);
void _nmod_poly_compose(mp_ptr res, mp_srcptr poly1, slong len1,
mp_srcptr poly2, slong len2, nmod_t mod);
void nmod_poly_compose(nmod_poly_t res,
const nmod_poly_t poly1, const nmod_poly_t poly2);
/* Taylor shift *************************************************************/
void _nmod_poly_taylor_shift_horner(mp_ptr poly, mp_limb_t c,
slong len, nmod_t mod);
void nmod_poly_taylor_shift_horner(nmod_poly_t g,
const nmod_poly_t f, mp_limb_t c);
void _nmod_poly_taylor_shift_convolution(mp_ptr poly, mp_limb_t c,
slong len, nmod_t mod);
void nmod_poly_taylor_shift_convolution(nmod_poly_t g,
const nmod_poly_t f, mp_limb_t c);
void _nmod_poly_taylor_shift(mp_ptr poly, mp_limb_t c, slong len, nmod_t mod);
void nmod_poly_taylor_shift(nmod_poly_t g, const nmod_poly_t f, mp_limb_t c);
/* Modular composition ******************************************************/
void
_nmod_poly_compose_mod_brent_kung(mp_ptr res, mp_srcptr f, slong lenf,
mp_srcptr g, mp_srcptr h, slong lenh, nmod_t mod);
void
nmod_poly_compose_mod_brent_kung(nmod_poly_t res,
const nmod_poly_t f, const nmod_poly_t g,
const nmod_poly_t h);
void
_nmod_poly_reduce_matrix_mod_poly (nmod_mat_t A, const nmod_mat_t B,
const nmod_poly_t f);
void
_nmod_poly_precompute_matrix (nmod_mat_t A, mp_srcptr poly1, mp_srcptr poly2,
slong len2, mp_srcptr poly2inv, slong len2inv, nmod_t mod);
void
nmod_poly_precompute_matrix (nmod_mat_t A, const nmod_poly_t poly1,
const nmod_poly_t poly2, const nmod_poly_t poly2inv);
void
_nmod_poly_compose_mod_brent_kung_precomp_preinv(mp_ptr res, mp_srcptr poly1,
slong len1, const nmod_mat_t A, mp_srcptr poly3,
slong len3, mp_srcptr poly3inv, slong len3inv,
nmod_t mod);
void
nmod_poly_compose_mod_brent_kung_precomp_preinv(nmod_poly_t res,
const nmod_poly_t poly1, const nmod_mat_t A,
const nmod_poly_t poly3, const nmod_poly_t poly3inv);
void
_nmod_poly_compose_mod_brent_kung_preinv(mp_ptr res, mp_srcptr poly1, slong len1,
mp_srcptr poly2, mp_srcptr poly3, slong len3,
mp_srcptr poly3inv, slong len3inv, nmod_t mod);
void
nmod_poly_compose_mod_brent_kung_preinv(nmod_poly_t res,
const nmod_poly_t poly1, const nmod_poly_t poly2,
const nmod_poly_t poly3, const nmod_poly_t poly3inv);
void
_nmod_poly_compose_mod_horner(mp_ptr res,
mp_srcptr f, slong lenf, mp_srcptr g, mp_srcptr h, slong lenh, nmod_t mod);
void
nmod_poly_compose_mod_horner(nmod_poly_t res,
const nmod_poly_t f, const nmod_poly_t g,
const nmod_poly_t h);
void
_nmod_poly_compose_mod(mp_ptr res, mp_srcptr f, slong lenf,
mp_srcptr g,
mp_srcptr h, slong lenh, nmod_t mod);
void
nmod_poly_compose_mod(nmod_poly_t res,
const nmod_poly_t f, const nmod_poly_t g,
const nmod_poly_t h);
/* Power series composition and reversion ************************************/
void
_nmod_poly_compose_series_horner(mp_ptr res, mp_srcptr poly1, slong len1,
mp_srcptr poly2, slong len2, slong n, nmod_t mod);
void
nmod_poly_compose_series_horner(nmod_poly_t res,
const nmod_poly_t poly1, const nmod_poly_t poly2, slong n);
void
_nmod_poly_compose_series_brent_kung(mp_ptr res, mp_srcptr poly1, slong len1,
mp_srcptr poly2, slong len2, slong n, nmod_t mod);
void
nmod_poly_compose_series_brent_kung(nmod_poly_t res,
const nmod_poly_t poly1, const nmod_poly_t poly2, slong n);
void
_nmod_poly_compose_series(mp_ptr res, mp_srcptr poly1, slong len1,
mp_srcptr poly2, slong len2, slong n, nmod_t mod);
void
nmod_poly_compose_series(nmod_poly_t res,
const nmod_poly_t poly1, const nmod_poly_t poly2, slong n);
void
_nmod_poly_revert_series_lagrange(mp_ptr Qinv, mp_srcptr Q, slong n, nmod_t mod);
void
nmod_poly_revert_series_lagrange(nmod_poly_t Qinv,
const nmod_poly_t Q, slong n);
void
_nmod_poly_revert_series_lagrange_fast(mp_ptr Qinv, mp_srcptr Q,
slong n, nmod_t mod);
void
nmod_poly_revert_series_lagrange_fast(nmod_poly_t Qinv,
const nmod_poly_t Q, slong n);
void
_nmod_poly_revert_series_newton(mp_ptr Qinv, mp_srcptr Q, slong n, nmod_t mod);
void
nmod_poly_revert_series_newton(nmod_poly_t Qinv,
const nmod_poly_t Q, slong n);
void
_nmod_poly_revert_series(mp_ptr Qinv, mp_srcptr Q, slong n, nmod_t mod);
void
nmod_poly_revert_series(nmod_poly_t Qinv,
const nmod_poly_t Q, slong n);
void
_nmod_poly_compose_series_divconquer(mp_ptr res, mp_srcptr poly1, slong len1,
mp_srcptr poly2, slong len2,
slong N, nmod_t mod);
void
nmod_poly_compose_series_divconquer(nmod_poly_t res,
const nmod_poly_t poly1, const nmod_poly_t poly2, slong N);
/* Greatest common divisor **************************************************/
slong _nmod_poly_gcd_euclidean(mp_ptr G,
mp_srcptr A, slong lenA, mp_srcptr B, slong lenB, nmod_t mod);
void nmod_poly_gcd_euclidean(nmod_poly_t G,
const nmod_poly_t A, const nmod_poly_t B);
slong _nmod_poly_hgcd(mp_ptr *M, slong *lenM,
mp_ptr A, slong *lenA, mp_ptr B, slong *lenB,
mp_srcptr a, slong lena, mp_srcptr b, slong lenb,
nmod_t mod);
slong _nmod_poly_gcd_hgcd(mp_ptr G, mp_srcptr A, slong lenA,
mp_srcptr B, slong lenB, nmod_t mod);
void nmod_poly_gcd_hgcd(nmod_poly_t G, const nmod_poly_t A, const nmod_poly_t B);
slong _nmod_poly_gcd(mp_ptr G, mp_srcptr A, slong lenA,
mp_srcptr B, slong lenB, nmod_t mod);
void nmod_poly_gcd(nmod_poly_t G, const nmod_poly_t A, const nmod_poly_t B);
slong _nmod_poly_xgcd_euclidean(mp_ptr res, mp_ptr s, mp_ptr t,
mp_srcptr poly1, slong len1, mp_srcptr poly2, slong len2, nmod_t mod);
void nmod_poly_xgcd_euclidean(nmod_poly_t G, nmod_poly_t S, nmod_poly_t T,
const nmod_poly_t A, const nmod_poly_t B);
slong _nmod_poly_xgcd_hgcd(mp_ptr G, mp_ptr S, mp_ptr T,
mp_srcptr A, slong lenA, mp_srcptr B, slong lenB,
nmod_t mod);
void nmod_poly_xgcd_hgcd(nmod_poly_t G, nmod_poly_t S, nmod_poly_t T,
const nmod_poly_t A, const nmod_poly_t B);
slong _nmod_poly_xgcd(mp_ptr G, mp_ptr S, mp_ptr T,
mp_srcptr A, slong lenA, mp_srcptr B, slong lenB, nmod_t mod);
void nmod_poly_xgcd(nmod_poly_t G, nmod_poly_t S, nmod_poly_t T,
const nmod_poly_t A, const nmod_poly_t B);
mp_limb_t
_nmod_poly_resultant_euclidean(mp_srcptr poly1, slong len1,
mp_srcptr poly2, slong len2, nmod_t mod);
mp_limb_t
nmod_poly_resultant_euclidean(const nmod_poly_t f, const nmod_poly_t g);
static __inline__ mp_limb_t
_nmod_poly_resultant(mp_srcptr poly1, slong len1,
mp_srcptr poly2, slong len2, nmod_t mod)
{
return _nmod_poly_resultant_euclidean(poly1, len1, poly2, len2, mod);
}
static __inline__ mp_limb_t
nmod_poly_resultant(const nmod_poly_t f, const nmod_poly_t g)
{
return nmod_poly_resultant_euclidean(f, g);
}
slong _nmod_poly_gcdinv(mp_limb_t *G, mp_limb_t *S,
const mp_limb_t *A, slong lenA,
const mp_limb_t *B, slong lenB,
const nmod_t mod);
void nmod_poly_gcdinv(nmod_poly_t G, nmod_poly_t S,
const nmod_poly_t A, const nmod_poly_t B);
/* Square roots **************************************************************/
void _nmod_poly_invsqrt_series(mp_ptr g, mp_srcptr h, slong n, nmod_t mod);
void nmod_poly_invsqrt_series(nmod_poly_t g, const nmod_poly_t h, slong n);
void _nmod_poly_sqrt_series(mp_ptr g, mp_srcptr h, slong n, nmod_t mod);
void nmod_poly_sqrt_series(nmod_poly_t g, const nmod_poly_t h, slong n);
int _nmod_poly_sqrt(mp_ptr s, mp_srcptr p, slong len, nmod_t mod);
int nmod_poly_sqrt(nmod_poly_t b, const nmod_poly_t a);
/* Transcendental functions **************************************************/
void _nmod_poly_atan_series(mp_ptr g, mp_srcptr h, slong n, nmod_t mod);
void nmod_poly_atan_series(nmod_poly_t g, const nmod_poly_t h, slong n);
void _nmod_poly_tan_series(mp_ptr g, mp_srcptr h, slong n, nmod_t mod);
void nmod_poly_tan_series(nmod_poly_t g, const nmod_poly_t h, slong n);
void _nmod_poly_asin_series(mp_ptr g, mp_srcptr h, slong n, nmod_t mod);
void nmod_poly_asin_series(nmod_poly_t g, const nmod_poly_t h, slong n);
void _nmod_poly_sin_series(mp_ptr g, mp_srcptr h, slong n, nmod_t mod);
void nmod_poly_sin_series(nmod_poly_t g, const nmod_poly_t h, slong n);
void _nmod_poly_cos_series(mp_ptr g, mp_srcptr h, slong n, nmod_t mod);
void nmod_poly_cos_series(nmod_poly_t g, const nmod_poly_t h, slong n);
void _nmod_poly_asinh_series(mp_ptr g, mp_srcptr h, slong n, nmod_t mod);
void nmod_poly_asinh_series(nmod_poly_t g, const nmod_poly_t h, slong n);
void _nmod_poly_atanh_series(mp_ptr g, mp_srcptr h, slong n, nmod_t mod);
void nmod_poly_atanh_series(nmod_poly_t g, const nmod_poly_t h, slong n);
void _nmod_poly_sinh_series(mp_ptr g, mp_srcptr h, slong n, nmod_t mod);
void nmod_poly_sinh_series(nmod_poly_t g, const nmod_poly_t h, slong n);
void _nmod_poly_cosh_series(mp_ptr g, mp_srcptr h, slong n, nmod_t mod);
void nmod_poly_cosh_series(nmod_poly_t g, const nmod_poly_t h, slong n);
void _nmod_poly_tanh_series(mp_ptr g, mp_srcptr h, slong n, nmod_t mod);
void nmod_poly_tanh_series(nmod_poly_t g, const nmod_poly_t h, slong n);
void _nmod_poly_log_series_monomial_ui(mp_ptr res, mp_limb_t coeff,
ulong power, slong n, nmod_t mod);
void nmod_poly_log_series_monomial_ui(nmod_poly_t res, mp_limb_t coeff,
ulong power, slong n);
void _nmod_poly_log_series(mp_ptr res, mp_srcptr f, slong n, nmod_t mod);
void nmod_poly_log_series(nmod_poly_t res, const nmod_poly_t f, slong n);
void _nmod_poly_exp_series_monomial_ui(mp_ptr res, mp_limb_t coeff,
ulong power, slong n, nmod_t mod);
void nmod_poly_exp_series_monomial_ui(nmod_poly_t res, mp_limb_t coeff,
ulong power, slong n);
void
_nmod_poly_exp_series_basecase(mp_ptr f, mp_srcptr h,
slong hlen, slong n, nmod_t mod);
void nmod_poly_exp_series_basecase(nmod_poly_t f, const nmod_poly_t h, slong n);
void _nmod_poly_exp_expinv_series(mp_ptr f, mp_ptr g, mp_srcptr h, slong n, nmod_t mod);
void _nmod_poly_exp_series(mp_ptr f, mp_srcptr h, slong n, nmod_t mod);
void nmod_poly_exp_series(nmod_poly_t f, const nmod_poly_t h, slong n);
/* Products *****************************************************************/
void
nmod_poly_product_roots_nmod_vec(nmod_poly_t poly, mp_srcptr xs, slong n);
void
_nmod_poly_product_roots_nmod_vec(mp_ptr poly,
mp_srcptr xs, slong n, nmod_t mod);
/* Inflation and deflation ***************************************************/
ulong nmod_poly_deflation(const nmod_poly_t input);
void nmod_poly_deflate(nmod_poly_t result, const nmod_poly_t input,
ulong deflation);
void nmod_poly_inflate(nmod_poly_t result, const nmod_poly_t input,
ulong inflation);
#ifdef __cplusplus
}
#endif
#include "nmod_poly_factor.h"
#endif
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