示例#1
0
void mpfr_taylor_nat_log(mpfr_t R, mpfr_t x, mpz_t n)
{
	assert(mpz_cmp_ui(n, 0) > 0);
	assert(mpfr_cmp_ui(x, 0) > 0);

	mpfr_t a, t, tt;
	mpfr_exp_t b;
	mpz_t k;
	unsigned int f = 1000, F = 1000;

	mpfr_init(a);
	mpfr_frexp(&b, a, x, MPFR_RNDN);
	mpfr_ui_sub(a, 1, a, MPFR_RNDN);
	
	mpfr_init_set(t, a, MPFR_RNDN);
	mpfr_init(tt);
	mpfr_set(R, a, MPFR_RNDN);

	for(mpz_init_set_ui(k, 2); mpz_cmp(k, n) < 0; mpz_add_ui(k, k, 1))
	{
		mpfr_mul(t, t, a, MPFR_RNDN);
		mpfr_div_z(tt, t, k, MPFR_RNDN);
		mpfr_add(R, R, tt, MPFR_RNDN);
	}

	mpfr_mul_si(a, MPFR_NAT_LOG_2, b, MPFR_RNDN);
	mpfr_sub(R, a, R, MPFR_RNDN);
}
示例#2
0
文件: yn.c 项目: Kirija/XPIR
/* compute in s an approximation of S1 = sum((n-k)!/k!*y^k,k=0..n)
   return e >= 0 the exponent difference between the maximal value of |s|
   during the for loop and the final value of |s|.
*/
static mpfr_exp_t
mpfr_yn_s1 (mpfr_ptr s, mpfr_srcptr y, unsigned long n)
{
  unsigned long k;
  mpz_t f;
  mpfr_exp_t e, emax;

  mpz_init_set_ui (f, 1);
  /* we compute n!*S1 = sum(a[k]*y^k,k=0..n) where a[k] = n!*(n-k)!/k!,
     a[0] = (n!)^2, a[1] = n!*(n-1)!, ..., a[n-1] = n, a[n] = 1 */
  mpfr_set_ui (s, 1, MPFR_RNDN); /* a[n] */
  emax = MPFR_EXP(s);
  for (k = n; k-- > 0;)
    {
      /* a[k]/a[k+1] = (n-k)!/k!/(n-(k+1))!*(k+1)! = (k+1)*(n-k) */
      mpfr_mul (s, s, y, MPFR_RNDN);
      mpz_mul_ui (f, f, n - k);
      mpz_mul_ui (f, f, k + 1);
      /* invariant: f = a[k] */
      mpfr_add_z (s, s, f, MPFR_RNDN);
      e = MPFR_EXP(s);
      if (e > emax)
        emax = e;
    }
  /* now we have f = (n!)^2 */
  mpz_sqrt (f, f);
  mpfr_div_z (s, s, f, MPFR_RNDN);
  mpz_clear (f);
  return emax - MPFR_EXP(s);
}
示例#3
0
static void
_taylor_mpfr (gulong l, mpq_t q, mpfr_ptr res, mp_rnd_t rnd)
{
  NcmBinSplit **bs_ptr = _ncm_mpsf_sbessel_get_bs ();
  NcmBinSplit *bs = *bs_ptr;
  _binsplit_spherical_bessel *data = (_binsplit_spherical_bessel *) bs->userdata;
  gulong n;

  data->l = l;
  mpq_mul (data->mq2_2, q, q);
  mpq_neg (data->mq2_2, data->mq2_2);
  mpq_div_2exp (data->mq2_2, data->mq2_2, 1);

  //mpfr_printf ("# Taylor %ld %Qd | %Qd\n", l, q, data->mq2_2);

  ncm_binsplit_eval_prec (bs, binsplit_spherical_bessel_taylor, 10, mpfr_get_prec (res));

  //mpfr_printf ("# Taylor %ld %Qd | %Zd %Zd\n", l, q, bs->T, bs->Q);

  mpfr_set_q (res, q, rnd);
  mpfr_pow_ui (res, res, l, rnd);
  mpfr_mul_z (res, res, bs->T, rnd);
  mpfr_div_z (res, res, bs->Q, rnd);

  for (n = 1; n <= l; n++)
    mpfr_div_ui (res, res, 2L * n + 1, rnd);

  ncm_memory_pool_return (bs_ptr);
  return;
}
示例#4
0
/* computes S(n) = sum(n^k*(-1)^(k-1)/k!/k, k=1..ceil(4.319136566 * n))
   using binary splitting.
   We have S(n) = sum(f(k), k=1..N) with N=ceil(4.319136566 * n)
   and f(k) = n^k*(-1)*(k-1)/k!/k,
   thus f(k)/f(k-1) = -n*(k-1)/k^2
*/
static void
mpfr_const_euler_S2 (mpfr_t x, unsigned long n)
{
  mpz_t P, Q, T;
  unsigned long N = (unsigned long) (ALPHA * (double) n + 1.0);
  mpz_init (P);
  mpz_init (Q);
  mpz_init (T);
  mpfr_const_euler_S2_aux (P, Q, T, n, 1, N + 1, 0);
  mpfr_set_z (x, T, MPFR_RNDN);
  mpfr_div_z (x, x, Q, MPFR_RNDN);
  mpz_clear (P);
  mpz_clear (Q);
  mpz_clear (T);
}
示例#5
0
void mpfr_taylor_exp(mpfr_t R, mpfr_t x, mpz_t n)
{
	assert(mpz_cmp_ui(n, 0) >= 0);
	
	mpfr_t t;
	mpz_t k;
	
	mpfr_init_set_ui(t, 1, MPFR_RNDN);
	mpfr_set_ui(R, 1, MPFR_RNDN);
	
	for(mpz_init_set_ui(k, 1); mpz_cmp(k, n) < 0; mpz_add_ui(k, k, 1))
	{
		mpfr_mul(t, t, x, MPFR_RNDN);
		mpfr_div_z(t, t, k, MPFR_RNDN);
		mpfr_add(R, R, t, MPFR_RNDN);
	}
}
示例#6
0
void mpfr_naive_exp(mpfr_t R, mpfr_t x, mpz_t n)
{
	assert(mpz_cmp_ui(n, 0) >= 0);
	
	mpfr_t z;
	
	mpfr_init_set(z, x, MPFR_RNDN);
	mpfr_div_z(z, z, n, MPFR_RNDN);
	mpfr_add_ui(z, z, 1, MPFR_RNDN);
	
	if(mpfr_cmp_ui(z, 0) > 0)
		mpfr_squaring_int_exp(R, z, n);
	else
	{
		mpfr_neg(z, z, MPFR_RNDN);
		mpfr_squaring_int_exp(R, z, n);
		
		if(mpz_odd_p(n))
			mpfr_neg(R, R, MPFR_RNDN);
	}
}
示例#7
0
static PyObject *
GMPy_Real_FloorDiv(PyObject *x, PyObject *y, CTXT_Object *context)
{
    MPFR_Object *result;

    CHECK_CONTEXT(context);

    if (!(result = GMPy_MPFR_New(0, context))) {
        /* LCOV_EXCL_START */
        return NULL;
        /* LCOV_EXCL_STOP */
    }

    if (MPFR_Check(x)) {
        if (MPFR_Check(y)) {
            mpfr_clear_flags();

            result->rc = mpfr_div(result->f, MPFR(x), MPFR(y), GET_MPFR_ROUND(context));
            result->rc = mpfr_floor(result->f, result->f);
            goto done;
        }

        if (PyIntOrLong_Check(y)) {
            int error;
            long tempi = GMPy_Integer_AsLongAndError(y, &error);

            if (!error) {
                mpfr_clear_flags();

                result->rc = mpfr_div_si(result->f, MPFR(x), tempi, GET_MPFR_ROUND(context));
                result->rc = mpfr_floor(result->f, result->f);
                goto done;
            }
            else {
                mpz_set_PyIntOrLong(global.tempz, y);
                mpfr_clear_flags();

                result->rc = mpfr_div_z(result->f, MPFR(x), global.tempz, GET_MPFR_ROUND(context));
                result->rc = mpfr_floor(result->f, result->f);
                goto done;
            }
        }

        if (CHECK_MPZANY(y)) {
            mpfr_clear_flags();

            result->rc = mpfr_div_z(result->f, MPFR(x), MPZ(y), GET_MPFR_ROUND(context));
            result->rc = mpfr_floor(result->f, result->f);
            goto done;
        }

        if (IS_RATIONAL(y)) {
            MPQ_Object *tempy;

            if (!(tempy = GMPy_MPQ_From_Number(y, context))) {
                Py_DECREF((PyObject*)result);
                return NULL;
            }
            mpfr_clear_flags();

            result->rc = mpfr_div_q(result->f, MPFR(x), tempy->q, GET_MPFR_ROUND(context));
            result->rc = mpfr_floor(result->f, result->f);
            Py_DECREF((PyObject*)tempy);
            goto done;
        }

        if (PyFloat_Check(y)) {
            mpfr_clear_flags();

            result->rc = mpfr_div_d(result->f, MPFR(x), PyFloat_AS_DOUBLE(y), GET_MPFR_ROUND(context));
            result->rc = mpfr_floor(result->f, result->f);
            goto done;
        }
    }

    if (MPFR_Check(y)) {
        if (PyIntOrLong_Check(x)) {
            int error;
            long tempi = GMPy_Integer_AsLongAndError(x, &error);
            if (!error) {
                mpfr_clear_flags();

                result->rc = mpfr_si_div(result->f, tempi, MPFR(y), GET_MPFR_ROUND(context));
                result->rc = mpfr_floor(result->f, result->f);
                goto done;
            }
        }

        /* Since mpfr_z_div does not exist, this combination is handled at the
         * end by converting x to an mpfr. Ditto for rational.*/

        if (PyFloat_Check(x)) {
            mpfr_clear_flags();

            result->rc = mpfr_d_div(result->f, PyFloat_AS_DOUBLE(x), MPFR(y), GET_MPFR_ROUND(context));
            result->rc = mpfr_floor(result->f, result->f);
            goto done;
        }
    }

    /* Handle the remaining cases.
     * Note: verify that MPZ if converted at full precision! */

    if (IS_REAL(x) && IS_REAL(y)) {
        MPFR_Object *tempx, *tempy;

        tempx = GMPy_MPFR_From_Real(x, 1, context);
        tempy = GMPy_MPFR_From_Real(y, 1, context);
        if (!tempx || !tempy) {
            Py_XDECREF((PyObject*)tempx);
            Py_XDECREF((PyObject*)tempy);
            Py_DECREF((PyObject*)result);
            return NULL;
        }
        mpfr_clear_flags();

        result->rc = mpfr_div(result->f, MPFR(tempx), MPFR(tempy), GET_MPFR_ROUND(context));
        result->rc = mpfr_floor(result->f, result->f);
        Py_DECREF((PyObject*)tempx);
        Py_DECREF((PyObject*)tempy);
        goto done;
    }

    Py_DECREF((PyObject*)result);
    Py_RETURN_NOTIMPLEMENTED;

  done:
    _GMPy_MPFR_Cleanup(&result, context);
    return (PyObject*)result;
}
示例#8
0
文件: tgmpop.c 项目: Canar/mpfr
static void
special (void)
{
  mpfr_t x, y;
  mpq_t q;
  mpz_t z;
  int res = 0;

  mpfr_init (x);
  mpfr_init (y);
  mpq_init (q);
  mpz_init (z);

  /* cancellation in mpfr_add_q */
  mpfr_set_prec (x, 60);
  mpfr_set_prec (y, 20);
  mpz_set_str (mpq_numref (q), "-187207494", 10);
  mpz_set_str (mpq_denref (q), "5721", 10);
  mpfr_set_str_binary (x, "11111111101001011011100101100011011110010011100010000100001E-44");
  mpfr_add_q (y, x, q, MPFR_RNDN);
  CHECK_FOR ("cancelation in add_q", mpfr_cmp_ui_2exp (y, 256783, -64) == 0);

  mpfr_set_prec (x, 19);
  mpfr_set_str_binary (x, "0.1011110101110011100E0");
  mpz_set_str (mpq_numref (q), "187207494", 10);
  mpz_set_str (mpq_denref (q), "5721", 10);
  mpfr_set_prec (y, 29);
  mpfr_add_q (y, x, q, MPFR_RNDD);
  mpfr_set_prec (x, 29);
  mpfr_set_str_binary (x, "11111111101001110011010001001E-14");
  CHECK_FOR ("cancelation in add_q", mpfr_cmp (x,y) == 0);

  /* Inf */
  mpfr_set_inf (x, 1);
  mpz_set_str (mpq_numref (q), "395877315", 10);
  mpz_set_str (mpq_denref (q), "3508975966", 10);
  mpfr_set_prec (y, 118);
  mpfr_add_q (y, x, q, MPFR_RNDU);
  CHECK_FOR ("inf", mpfr_inf_p (y) && mpfr_sgn (y) > 0);
  mpfr_sub_q (y, x, q, MPFR_RNDU);
  CHECK_FOR ("inf", mpfr_inf_p (y) && mpfr_sgn (y) > 0);

  /* Nan */
  MPFR_SET_NAN (x);
  mpfr_add_q (y, x, q, MPFR_RNDU);
  CHECK_FOR ("nan", mpfr_nan_p (y));
  mpfr_sub_q (y, x, q, MPFR_RNDU);
  CHECK_FOR ("nan", mpfr_nan_p (y));

  /* Exact value */
  mpfr_set_prec (x, 60);
  mpfr_set_prec (y, 60);
  mpfr_set_str1 (x, "0.5");
  mpz_set_str (mpq_numref (q), "3", 10);
  mpz_set_str (mpq_denref (q), "2", 10);
  res = mpfr_add_q (y, x, q, MPFR_RNDU);
  CHECK_FOR ("0.5+3/2", mpfr_cmp_ui(y, 2)==0 && res==0);
  res = mpfr_sub_q (y, x, q, MPFR_RNDU);
  CHECK_FOR ("0.5-3/2", mpfr_cmp_si(y, -1)==0 && res==0);

  /* Inf Rationnal */
  mpq_set_ui (q, 1, 0);
  mpfr_set_str1 (x, "0.5");
  res = mpfr_add_q (y, x, q, MPFR_RNDN);
  CHECK_FOR ("0.5+1/0", mpfr_inf_p (y) && MPFR_IS_POS (y) && res == 0);
  res = mpfr_sub_q (y, x, q, MPFR_RNDN);
  CHECK_FOR ("0.5-1/0", mpfr_inf_p (y) && MPFR_IS_NEG (y) && res == 0);
  mpq_set_si (q, -1, 0);
  res = mpfr_add_q (y, x, q, MPFR_RNDN);
  CHECK_FOR ("0.5+ -1/0", mpfr_inf_p (y) && MPFR_IS_NEG (y) && res == 0);
  res = mpfr_sub_q (y, x, q, MPFR_RNDN);
  CHECK_FOR ("0.5- -1/0", mpfr_inf_p (y) && MPFR_IS_POS (y) && res == 0);
  res = mpfr_div_q (y, x, q, MPFR_RNDN);
  CHECK_FOR ("0.5 / (-1/0)", mpfr_zero_p (y) && MPFR_IS_NEG (y) && res == 0);
  mpq_set_ui (q, 1, 0);
  mpfr_set_inf (x, 1);
  res = mpfr_add_q (y, x, q, MPFR_RNDN);
  CHECK_FOR ("+Inf + +Inf", mpfr_inf_p (y) && MPFR_IS_POS (y) && res == 0);
  res = mpfr_sub_q (y, x, q, MPFR_RNDN);
  CHECK_FOR ("+Inf - +Inf", MPFR_IS_NAN (y) && res == 0);
  mpfr_set_inf (x, -1);
  res = mpfr_add_q (y, x, q, MPFR_RNDN);
  CHECK_FOR ("-Inf + +Inf", MPFR_IS_NAN (y) && res == 0);
  res = mpfr_sub_q (y, x, q, MPFR_RNDN);
  CHECK_FOR ("-Inf - +Inf", mpfr_inf_p (y) && MPFR_IS_NEG (y) && res == 0);
  mpq_set_si (q, -1, 0);
  mpfr_set_inf (x, 1);
  res = mpfr_add_q (y, x, q, MPFR_RNDN);
  CHECK_FOR ("+Inf + -Inf", MPFR_IS_NAN (y) && res == 0);
  res = mpfr_sub_q (y, x, q, MPFR_RNDN);
  CHECK_FOR ("+Inf - -Inf", mpfr_inf_p (y) && MPFR_IS_POS (y) && res == 0);
  mpfr_set_inf (x, -1);
  res = mpfr_add_q (y, x, q, MPFR_RNDN);
  CHECK_FOR ("-Inf + -Inf", mpfr_inf_p (y) && MPFR_IS_NEG (y) && res == 0);
  res = mpfr_sub_q (y, x, q, MPFR_RNDN);
  CHECK_FOR ("-Inf - -Inf", MPFR_IS_NAN (y) && res == 0);

  /* 0 */
  mpq_set_ui (q, 0, 1);
  mpfr_set_ui (x, 42, MPFR_RNDN);
  res = mpfr_add_q (y, x, q, MPFR_RNDN);
  CHECK_FOR ("42+0/1", mpfr_cmp_ui (y, 42) == 0 && res == 0);
  res = mpfr_sub_q (y, x, q, MPFR_RNDN);
  CHECK_FOR ("42-0/1", mpfr_cmp_ui (y, 42) == 0 && res == 0);
  res = mpfr_mul_q (y, x, q, MPFR_RNDN);
  CHECK_FOR ("42*0/1", mpfr_zero_p (y) && MPFR_IS_POS (y) && res == 0);
  mpfr_clear_flags ();
  res = mpfr_div_q (y, x, q, MPFR_RNDN);
  CHECK_FOR ("42/(0/1)", mpfr_inf_p (y) && MPFR_IS_POS (y) && res == 0
             && mpfr_divby0_p ());
  mpz_set_ui (z, 0);
  mpfr_clear_flags ();
  res = mpfr_div_z (y, x, z, MPFR_RNDN);
  CHECK_FORZ ("42/0", mpfr_inf_p (y) && MPFR_IS_POS (y) && res == 0
              && mpfr_divby0_p ());

  mpz_clear (z);
  mpq_clear (q);
  mpfr_clear (x);
  mpfr_clear (y);
}
示例#9
0
文件: tgmpop.c 项目: Canar/mpfr
static void
reduced_expo_range (void)
{
  mpfr_t x;
  mpz_t z;
  mpq_t q;
  mpfr_exp_t emin;
  int inex;

  emin = mpfr_get_emin ();
  set_emin (4);

  mpfr_init2 (x, 32);

  mpz_init (z);
  mpfr_clear_flags ();
  inex = mpfr_set_ui (x, 17, MPFR_RNDN);
  MPFR_ASSERTN (inex == 0);
  mpz_set_ui (z, 3);
  inex = mpfr_mul_z (x, x, z, MPFR_RNDN);
  if (inex != 0 || MPFR_IS_NAN (x) || mpfr_cmp_ui (x, 51) != 0)
    {
      printf ("Error 1 in reduce_expo_range: expected 51 with inex = 0,"
              " got\n");
      mpfr_out_str (stdout, 10, 0, x, MPFR_RNDN);
      printf ("with inex = %d\n", inex);
      exit (1);
    }
  inex = mpfr_div_z (x, x, z, MPFR_RNDN);
  if (inex != 0 || MPFR_IS_NAN (x) || mpfr_cmp_ui (x, 17) != 0)
    {
      printf ("Error 2 in reduce_expo_range: expected 17 with inex = 0,"
              " got\n");
      mpfr_out_str (stdout, 10, 0, x, MPFR_RNDN);
      printf ("with inex = %d\n", inex);
      exit (1);
    }
  inex = mpfr_add_z (x, x, z, MPFR_RNDN);
  if (inex != 0 || MPFR_IS_NAN (x) || mpfr_cmp_ui (x, 20) != 0)
    {
      printf ("Error 3 in reduce_expo_range: expected 20 with inex = 0,"
              " got\n");
      mpfr_out_str (stdout, 10, 0, x, MPFR_RNDN);
      printf ("with inex = %d\n", inex);
      exit (1);
    }
  inex = mpfr_sub_z (x, x, z, MPFR_RNDN);
  if (inex != 0 || MPFR_IS_NAN (x) || mpfr_cmp_ui (x, 17) != 0)
    {
      printf ("Error 4 in reduce_expo_range: expected 17 with inex = 0,"
              " got\n");
      mpfr_out_str (stdout, 10, 0, x, MPFR_RNDN);
      printf ("with inex = %d\n", inex);
      exit (1);
    }
  MPFR_ASSERTN (__gmpfr_flags == 0);
  if (mpfr_cmp_z (x, z) <= 0)
    {
      printf ("Error 5 in reduce_expo_range: expected a positive value.\n");
      exit (1);
    }
  mpz_clear (z);

  mpq_init (q);
  mpq_set_ui (q, 1, 1);
  mpfr_set_ui (x, 16, MPFR_RNDN);
  inex = mpfr_add_q (x, x, q, MPFR_RNDN);
  if (inex != 0 || MPFR_IS_NAN (x) || mpfr_cmp_ui (x, 17) != 0)
    {
      printf ("Error in reduce_expo_range for 16 + 1/1,"
              " got inex = %d and\nx = ", inex);
      mpfr_dump (x);
      exit (1);
    }
  inex = mpfr_sub_q (x, x, q, MPFR_RNDN);
  if (inex != 0 || MPFR_IS_NAN (x) || mpfr_cmp_ui (x, 16) != 0)
    {
      printf ("Error in reduce_expo_range for 17 - 1/1,"
              " got inex = %d and\nx = ", inex);
      mpfr_dump (x);
      exit (1);
    }
  mpq_clear (q);

  mpfr_clear (x);

  set_emin (emin);
}
示例#10
0
文件: yn.c 项目: Kirija/XPIR
/* compute in s an approximation of
   S3 = c*sum((h(k)+h(n+k))*y^k/k!/(n+k)!,k=0..infinity)
   where h(k) = 1 + 1/2 + ... + 1/k
   k=0: h(n)
   k=1: 1+h(n+1)
   k=2: 3/2+h(n+2)
   Returns e such that the error is bounded by 2^e ulp(s).
*/
static mpfr_exp_t
mpfr_yn_s3 (mpfr_ptr s, mpfr_srcptr y, mpfr_srcptr c, unsigned long n)
{
  unsigned long k, zz;
  mpfr_t t, u;
  mpz_t p, q; /* p/q will store h(k)+h(n+k) */
  mpfr_exp_t exps, expU;

  zz = mpfr_get_ui (y, MPFR_RNDU); /* y = z^2/4 */
  MPFR_ASSERTN (zz < ULONG_MAX - 2);
  zz += 2; /* z^2 <= 2^zz */
  mpz_init_set_ui (p, 0);
  mpz_init_set_ui (q, 1);
  /* initialize p/q to h(n) */
  for (k = 1; k <= n; k++)
    {
      /* p/q + 1/k = (k*p+q)/(q*k) */
      mpz_mul_ui (p, p, k);
      mpz_add (p, p, q);
      mpz_mul_ui (q, q, k);
    }
  mpfr_init2 (t, MPFR_PREC(s));
  mpfr_init2 (u, MPFR_PREC(s));
  mpfr_fac_ui (t, n, MPFR_RNDN);
  mpfr_div (t, c, t, MPFR_RNDN);    /* c/n! */
  mpfr_mul_z (u, t, p, MPFR_RNDN);
  mpfr_div_z (s, u, q, MPFR_RNDN);
  exps = MPFR_EXP (s);
  expU = exps;
  for (k = 1; ;k ++)
    {
      /* update t */
      mpfr_mul (t, t, y, MPFR_RNDN);
      mpfr_div_ui (t, t, k, MPFR_RNDN);
      mpfr_div_ui (t, t, n + k, MPFR_RNDN);
      /* update p/q:
         p/q + 1/k + 1/(n+k) = [p*k*(n+k) + q*(n+k) + q*k]/(q*k*(n+k)) */
      mpz_mul_ui (p, p, k);
      mpz_mul_ui (p, p, n + k);
      mpz_addmul_ui (p, q, n + 2 * k);
      mpz_mul_ui (q, q, k);
      mpz_mul_ui (q, q, n + k);
      mpfr_mul_z (u, t, p, MPFR_RNDN);
      mpfr_div_z (u, u, q, MPFR_RNDN);
      exps = MPFR_EXP (u);
      if (exps > expU)
        expU = exps;
      mpfr_add (s, s, u, MPFR_RNDN);
      exps = MPFR_EXP (s);
      if (exps > expU)
        expU = exps;
      if (MPFR_EXP (u) + (mpfr_exp_t) MPFR_PREC (u) < MPFR_EXP (s) &&
          zz / (2 * k) < k + n)
        break;
    }
  mpfr_clear (t);
  mpfr_clear (u);
  mpz_clear (p);
  mpz_clear (q);
  exps = expU - MPFR_EXP (s);
  /* the error is bounded by (6k^2+33/2k+11) 2^exps ulps
     <= 8*(k+2)^2 2^exps ulps */
  return 3 + 2 * MPFR_INT_CEIL_LOG2(k + 2) + exps;
}
示例#11
0
/*------------------------------------------------------------------------*/
int my_mpfr_beta (mpfr_t R, mpfr_t a, mpfr_t b, mpfr_rnd_t RND)
{
    mpfr_prec_t p_a = mpfr_get_prec(a), p_b = mpfr_get_prec(b);
    if(p_a < p_b) p_a = p_b;// p_a := max(p_a, p_b)
    if(mpfr_get_prec(R) < p_a)
	mpfr_prec_round(R, p_a, RND);// so prec(R) = max( prec(a), prec(b) )
    int ans;
    mpfr_t s; mpfr_init2(s, p_a);
#ifdef DEBUG_Rmpfr
    R_CheckUserInterrupt();
    int cc = 0;
#endif

    /* "FIXME": check each 'ans' below, and return when not ok ... */
    ans = mpfr_add(s, a, b, RND);

    if(mpfr_integer_p(s) && mpfr_sgn(s) <= 0) { // (a + b) is integer <= 0
	if(!mpfr_integer_p(a) && !mpfr_integer_p(b)) {
	    // but a,b not integer ==> R =  finite / +-Inf  = 0 :
	    mpfr_set_zero (R, +1);
	    mpfr_clear (s);
	    return ans;
	}// else: sum is integer; at least one {a,b} integer ==> both integer

	int sX = mpfr_sgn(a), sY = mpfr_sgn(b);
	if(sX * sY < 0) { // one negative, one positive integer
	    // ==> special treatment here :
	    if(sY < 0) // ==> sX > 0; swap the two
		mpfr_swap(a, b);
	    // now have --- a < 0 < b <= |a|  integer ------------------
	    /*              ================  and in this case:
	       B(a,b) = (-1)^b  B(1-a-b, b) = (-1)^b B(1-s, b)

		      = (1*2*..*b) / (-s-1)*(-s-2)*...*(-s-b)
	    */
	    /* where in the 2nd form, both numerator and denominator have exactly
	     * b integer factors. This is attractive {numerically & speed wise}
	     * for 'small' b */
#define b_large 100
#ifdef DEBUG_Rmpfr
	    Rprintf(" my_mpfr_beta(<neg int>): s = a+b= "); R_PRT(s);
	    Rprintf("\n   a = "); R_PRT(a);
	    Rprintf("\n   b = "); R_PRT(b); Rprintf("\n");
	    if(cc++ > 999) { mpfr_set_zero (R, +1); mpfr_clear (s); return ans; }
#endif
	    unsigned long b_ = 0;// -Wall
	    Rboolean
		b_fits_ulong = mpfr_fits_ulong_p(b, RND),
		small_b = b_fits_ulong &&  (b_ = mpfr_get_ui(b, RND)) < b_large;
	    if(small_b) {
#ifdef DEBUG_Rmpfr
		Rprintf("   b <= b_large = %d...\n", b_large);
#endif
		//----------------- small b ------------------
		// use GMP big integer arithmetic:
		mpz_t S; mpz_init(S); mpfr_get_z(S, s, RND); // S := s
		mpz_sub_ui (S, S, (unsigned long) 1); // S = s - 1 = (a+b-1)
		/* binomial coefficient choose(N, k) requires k a 'long int';
		 * here, b must fit into a long: */
		mpz_bin_ui (S, S, b_); // S = choose(S, b) = choose(a+b-1, b)
		mpz_mul_ui (S, S, b_); // S = S*b =  b * choose(a+b-1, b)
		// back to mpfr: R = 1 / S  = 1 / (b * choose(a+b-1, b))
		mpfr_set_ui(s, (unsigned long) 1, RND);
		mpfr_div_z(R, s, S, RND);
		mpz_clear(S);
	    }
	    else { // b is "large", use direct B(.,.) formula
#ifdef DEBUG_Rmpfr
		Rprintf("   b > b_large = %d...\n", b_large);
#endif
		// a := (-1)^b :
		// there is no  mpfr_si_pow(a, -1, b, RND);
		int neg; // := 1 ("TRUE") if (-1)^b = -1, i.e. iff  b is odd
		if(b_fits_ulong) { // (i.e. not very large)
		    neg = (b_ % 2); // 1 iff b_ is odd,  0 otherwise
		} else { // really large b; as we know it is integer, can still..
		    // b2 := b / 2
		    mpfr_t b2; mpfr_init2(b2, p_a);
		    mpfr_div_2ui(b2, b, 1, RND);
		    neg = !mpfr_integer_p(b2); // b is odd, if b/2 is *not* integer
#ifdef DEBUG_Rmpfr
		    Rprintf("   really large b; neg = ('b is odd') = %d\n", neg);
#endif
		}
		// s' := 1-s = 1-a-b
		mpfr_ui_sub(s, 1, s, RND);
#ifdef DEBUG_Rmpfr
		Rprintf("  neg = %d\n", neg);
		Rprintf("  s' = 1-a-b = "); R_PRT(s);
		Rprintf("\n  -> calling B(s',b)\n");
#endif
		// R := B(1-a-b, b) = B(s', b)
		if(small_b) {
		    my_mpfr_beta (R, s, b, RND);
		} else {
		    my_mpfr_lbeta (R, s, b, RND);
		    mpfr_exp(R, R, RND); // correct *if* beta() >= 0
		}
#ifdef DEBUG_Rmpfr
		Rprintf("  R' = beta(s',b) = "); R_PRT(R); Rprintf("\n");
#endif
		// Result = (-1)^b  B(1-a-b, b) = +/- s'
		if(neg) mpfr_neg(R, R, RND);
	    }
	    mpfr_clear(s);
	    return ans;
	}
   }

    ans = mpfr_gamma(s, s, RND);  /* s = gamma(a + b) */
#ifdef DEBUG_Rmpfr
    Rprintf("my_mpfr_beta(): s = gamma(a+b)= "); R_PRT(s);
    Rprintf("\n   a = "); R_PRT(a);
    Rprintf("\n   b = "); R_PRT(b);
#endif

    ans = mpfr_gamma(a, a, RND);
    ans = mpfr_gamma(b, b, RND);
    ans = mpfr_mul(b, b, a, RND); /* b' = gamma(a) * gamma(b) */

#ifdef DEBUG_Rmpfr
    Rprintf("\n    G(a) * G(b) = "); R_PRT(b); Rprintf("\n");
#endif

    ans = mpfr_div(R, b, s, RND);
    mpfr_clear (s);
    /* mpfr_free_cache() must be called in the caller !*/
    return ans;
}
示例#12
0
static void
_assympt_mpfr (gulong l, mpq_t q, mpfr_ptr res, mp_rnd_t rnd)
{
  NcmBinSplit **bs_ptr = _ncm_mpsf_sbessel_get_bs ();
  NcmBinSplit *bs = *bs_ptr;
  _binsplit_spherical_bessel *data = (_binsplit_spherical_bessel *) bs->userdata;
  gulong prec = mpfr_get_prec (res);
#define sin_x data->sin
#define cos_x data->cos
  mpfr_set_prec (sin_x, prec);
  mpfr_set_prec (cos_x, prec);

  mpfr_set_q (res, q, rnd);
  mpfr_sin_cos (sin_x, cos_x, res, rnd);

  switch (l % 4)
  {
    case 0:
      break;
    case 1:
      mpfr_swap (sin_x, cos_x);
      mpfr_neg (sin_x, sin_x, rnd);
      break;
    case 2:
      mpfr_neg (sin_x, sin_x, rnd);
      mpfr_neg (cos_x, cos_x, rnd);
      break;
    case 3:
      mpfr_swap (sin_x, cos_x);
      mpfr_neg (cos_x, cos_x, rnd);
      break;
  }

  if (l > 0)
  {
    mpfr_mul_ui (cos_x, cos_x, l * (l + 1), rnd);
    mpfr_div (cos_x, cos_x, res, rnd);
    mpfr_div (cos_x, cos_x, res, rnd);
    mpfr_div_2ui (cos_x, cos_x, 1, rnd);
  }

  mpfr_div (sin_x, sin_x, res, rnd);

  data->l = l;
  mpq_inv (data->mq2_2, q);
  mpq_mul (data->mq2_2, data->mq2_2, data->mq2_2);
  mpq_neg (data->mq2_2, data->mq2_2);
  mpq_div_2exp (data->mq2_2, data->mq2_2, 2);

  data->sincos = 0;
  binsplit_spherical_bessel_assympt (bs, 0, (l + 1) / 2 + (l + 1) % 2);
  mpfr_mul_z (sin_x, sin_x, bs->T, rnd);
  mpfr_div_z (sin_x, sin_x, bs->Q, rnd);

  data->sincos = 1;
  if (l > 0)
  {
    binsplit_spherical_bessel_assympt (bs, 0, l / 2 + l % 2);
    mpfr_mul_z (cos_x, cos_x, bs->T, rnd);
    mpfr_div_z (cos_x, cos_x, bs->Q, rnd);
    mpfr_add (res, sin_x, cos_x, rnd);
  }
  else
    mpfr_set (res, sin_x, rnd);

  ncm_memory_pool_return (bs_ptr);
  return;
}