void mp_IinvC (mp_interval_t *rop, mpfr_t op) {
// CHECKS WHETHER op is 0
if (mpfr_cmp_si (op, 0) == 0) {
mpfr_set_str (rop->a, "nan", 10, MPFR_RNDD);
mpfr_set_str (rop->b, "nan", 10, MPFR_RNDU);
return;
}
// UP TO HERE, op is NOT ZERO
mpfr_si_div (rop->a, 1, op, MPFR_RNDD);
mpfr_si_div (rop->b, 1, op, MPFR_RNDU);
}
int
main (int argc, char *argv[])
{
mpfr_t x, z;
int y;
int i;
tests_start_mpfr ();
mpfr_inits2 (53, x, z, (mpfr_ptr) 0);
for(i = 0 ; i < numberof (tab) ; i++)
{
mpfr_set_str (x, tab[i].op1, 16, MPFR_RNDN);
y = tab[i].op2;
mpfr_add_si (z, x, y, MPFR_RNDZ);
if (mpfr_cmp_str (z, tab[i].res_add, 16, MPFR_RNDN))
ERROR1("add_si", i, z, tab[i].res_add);
mpfr_sub_si (z, x, y, MPFR_RNDZ);
if (mpfr_cmp_str (z, tab[i].res_sub, 16, MPFR_RNDN))
ERROR1("sub_si", i, z, tab[i].res_sub);
mpfr_si_sub (z, y, x, MPFR_RNDZ);
mpfr_neg (z, z, MPFR_RNDZ);
if (mpfr_cmp_str (z, tab[i].res_sub, 16, MPFR_RNDN))
ERROR1("si_sub", i, z, tab[i].res_sub);
mpfr_mul_si (z, x, y, MPFR_RNDZ);
if (mpfr_cmp_str (z, tab[i].res_mul, 16, MPFR_RNDN))
ERROR1("mul_si", i, z, tab[i].res_mul);
mpfr_div_si (z, x, y, MPFR_RNDZ);
if (mpfr_cmp_str (z, tab[i].res_div, 16, MPFR_RNDN))
ERROR1("div_si", i, z, tab[i].res_div);
}
mpfr_set_str1 (x, "1");
mpfr_si_div (z, 1024, x, MPFR_RNDN);
if (mpfr_cmp_str1 (z, "1024"))
ERROR1("si_div", i, z, "1024");
mpfr_si_div (z, -1024, x, MPFR_RNDN);
if (mpfr_cmp_str1 (z, "-1024"))
ERROR1("si_div", i, z, "-1024");
mpfr_clears (x, z, (mpfr_ptr) 0);
check_invert ();
test_generic_add_si (2, 200, 17);
test_generic_sub_si (2, 200, 17);
test_generic_mul_si (2, 200, 17);
test_generic_div_si (2, 200, 17);
tests_end_mpfr ();
return 0;
}
void mp_Iinv (mp_interval_t *rop, mp_interval_t op) {
// CHECK IF OP = [0,0]
if (mpfr_cmp_si (op.a, 0) == 0 && mpfr_cmp_si (op.b, 0) == 0) {
mpfr_set_str (rop->a, "nan", 10, MPFR_RNDD);
mpfr_set_str (rop->b, "nan", 10, MPFR_RNDU);
return;
}
// CHECKS WHETHER ZERO IS CONTAINED IN OP
if (mp_isZeroContained (op)) {
// IF ZERO IS LEFT BOUNDARY
if (mpfr_cmp_si (op.a, 0) == 0) {
mpfr_si_div (rop->a, 1, op.b, MPFR_RNDD);
mpfr_set_str (rop->b, "+inf", 10, MPFR_RNDU);
return;
}
// IF ZERO IS RIGHT BOUNDARY
if (mpfr_cmp_si (op.b, 0) == 0) {
mpfr_si_div (rop->b, 1, op.a, MPFR_RNDU);
mpfr_set_str (rop->a, "-inf", 10, MPFR_RNDD);
return;
}
// ZERO IS EXTRICTLY CONTAINED IN op
mpfr_set_str (rop->a, "-inf", 10, MPFR_RNDD);
mpfr_set_str (rop->b, "+inf", 10, MPFR_RNDU);
return;
}
// ZERO IS NOT IN op
mpfr_t ropA; mpfr_init (ropA);
mpfr_si_div (ropA, 1, op.b, MPFR_RNDD);
mpfr_si_div (rop->b, 1, op.a, MPFR_RNDU);
mpfr_set (rop->a, ropA, MPFR_RNDD);
mpfr_clear (ropA);
}
static int
mpfr_all_div (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t r)
{
mpfr_t a2;
unsigned int oldflags, newflags;
int inex, inex2;
oldflags = __gmpfr_flags;
inex = mpfr_div (a, b, c, r);
if (a == b || a == c)
return inex;
newflags = __gmpfr_flags;
mpfr_init2 (a2, MPFR_PREC (a));
if (mpfr_integer_p (b) && ! (MPFR_IS_ZERO (b) && MPFR_IS_NEG (b)))
{
/* b is an integer, but not -0 (-0 is rejected as
it becomes +0 when converted to an integer). */
if (mpfr_fits_ulong_p (b, MPFR_RNDA))
{
__gmpfr_flags = oldflags;
inex2 = mpfr_ui_div (a2, mpfr_get_ui (b, MPFR_RNDN), c, r);
MPFR_ASSERTN (SAME_SIGN (inex2, inex));
MPFR_ASSERTN (__gmpfr_flags == newflags);
check_equal (a, a2, "mpfr_ui_div", b, c, r);
}
if (mpfr_fits_slong_p (b, MPFR_RNDA))
{
__gmpfr_flags = oldflags;
inex2 = mpfr_si_div (a2, mpfr_get_si (b, MPFR_RNDN), c, r);
MPFR_ASSERTN (SAME_SIGN (inex2, inex));
MPFR_ASSERTN (__gmpfr_flags == newflags);
check_equal (a, a2, "mpfr_si_div", b, c, r);
}
}
if (mpfr_integer_p (c) && ! (MPFR_IS_ZERO (c) && MPFR_IS_NEG (c)))
{
/* c is an integer, but not -0 (-0 is rejected as
it becomes +0 when converted to an integer). */
if (mpfr_fits_ulong_p (c, MPFR_RNDA))
{
__gmpfr_flags = oldflags;
inex2 = mpfr_div_ui (a2, b, mpfr_get_ui (c, MPFR_RNDN), r);
MPFR_ASSERTN (SAME_SIGN (inex2, inex));
MPFR_ASSERTN (__gmpfr_flags == newflags);
check_equal (a, a2, "mpfr_div_ui", b, c, r);
}
if (mpfr_fits_slong_p (c, MPFR_RNDA))
{
__gmpfr_flags = oldflags;
inex2 = mpfr_div_si (a2, b, mpfr_get_si (c, MPFR_RNDN), r);
MPFR_ASSERTN (SAME_SIGN (inex2, inex));
MPFR_ASSERTN (__gmpfr_flags == newflags);
check_equal (a, a2, "mpfr_div_si", b, c, r);
}
}
mpfr_clear (a2);
return inex;
}
/* Implements asymptotic expansion for jn or yn (formulae 9.2.5 and 9.2.6
from Abramowitz & Stegun).
Assumes |z| > p log(2)/2, where p is the target precision
(z can be negative only for jn).
Return 0 if the expansion does not converge enough (the value 0 as inexact
flag should not happen for normal input).
*/
static int
FUNCTION (mpfr_ptr res, long n, mpfr_srcptr z, mpfr_rnd_t r)
{
mpfr_t s, c, P, Q, t, iz, err_t, err_s, err_u;
mpfr_prec_t w;
long k;
int inex, stop, diverge = 0;
mpfr_exp_t err2, err;
MPFR_ZIV_DECL (loop);
mpfr_init (c);
w = MPFR_PREC(res) + MPFR_INT_CEIL_LOG2(MPFR_PREC(res)) + 4;
MPFR_ZIV_INIT (loop, w);
for (;;)
{
mpfr_set_prec (c, w);
mpfr_init2 (s, w);
mpfr_init2 (P, w);
mpfr_init2 (Q, w);
mpfr_init2 (t, w);
mpfr_init2 (iz, w);
mpfr_init2 (err_t, 31);
mpfr_init2 (err_s, 31);
mpfr_init2 (err_u, 31);
/* Approximate sin(z) and cos(z). In the following, err <= k means that
the approximate value y and the true value x are related by
y = x * (1 + u)^k with |u| <= 2^(-w), following Higham's method. */
mpfr_sin_cos (s, c, z, MPFR_RNDN);
if (MPFR_IS_NEG(z))
mpfr_neg (s, s, MPFR_RNDN); /* compute jn/yn(|z|), fix sign later */
/* The absolute error on s/c is bounded by 1/2 ulp(1/2) <= 2^(-w-1). */
mpfr_add (t, s, c, MPFR_RNDN);
mpfr_sub (c, s, c, MPFR_RNDN);
mpfr_swap (s, t);
/* now s approximates sin(z)+cos(z), and c approximates sin(z)-cos(z),
with total absolute error bounded by 2^(1-w). */
/* precompute 1/(8|z|) */
mpfr_si_div (iz, MPFR_IS_POS(z) ? 1 : -1, z, MPFR_RNDN); /* err <= 1 */
mpfr_div_2ui (iz, iz, 3, MPFR_RNDN);
/* compute P and Q */
mpfr_set_ui (P, 1, MPFR_RNDN);
mpfr_set_ui (Q, 0, MPFR_RNDN);
mpfr_set_ui (t, 1, MPFR_RNDN); /* current term */
mpfr_set_ui (err_t, 0, MPFR_RNDN); /* error on t */
mpfr_set_ui (err_s, 0, MPFR_RNDN); /* error on P and Q (sum of errors) */
for (k = 1, stop = 0; stop < 4; k++)
{
/* compute next term: t(k)/t(k-1) = (2n+2k-1)(2n-2k+1)/(8kz) */
mpfr_mul_si (t, t, 2 * (n + k) - 1, MPFR_RNDN); /* err <= err_k + 1 */
mpfr_mul_si (t, t, 2 * (n - k) + 1, MPFR_RNDN); /* err <= err_k + 2 */
mpfr_div_ui (t, t, k, MPFR_RNDN); /* err <= err_k + 3 */
mpfr_mul (t, t, iz, MPFR_RNDN); /* err <= err_k + 5 */
/* the relative error on t is bounded by (1+u)^(5k)-1, which is
bounded by 6ku for 6ku <= 0.02: first |5 log(1+u)| <= |5.5u|
for |u| <= 0.15, then |exp(5.5u)-1| <= 6u for |u| <= 0.02. */
mpfr_mul_ui (err_t, t, 6 * k, MPFR_IS_POS(t) ? MPFR_RNDU : MPFR_RNDD);
mpfr_abs (err_t, err_t, MPFR_RNDN); /* exact */
/* the absolute error on t is bounded by err_t * 2^(-w) */
mpfr_abs (err_u, t, MPFR_RNDU);
mpfr_mul_2ui (err_u, err_u, w, MPFR_RNDU); /* t * 2^w */
mpfr_add (err_u, err_u, err_t, MPFR_RNDU); /* max|t| * 2^w */
if (stop >= 2)
{
/* take into account the neglected terms: t * 2^w */
mpfr_div_2ui (err_s, err_s, w, MPFR_RNDU);
if (MPFR_IS_POS(t))
mpfr_add (err_s, err_s, t, MPFR_RNDU);
else
mpfr_sub (err_s, err_s, t, MPFR_RNDU);
mpfr_mul_2ui (err_s, err_s, w, MPFR_RNDU);
stop ++;
}
/* if k is odd, add to Q, otherwise to P */
else if (k & 1)
{
/* if k = 1 mod 4, add, otherwise subtract */
if ((k & 2) == 0)
mpfr_add (Q, Q, t, MPFR_RNDN);
else
mpfr_sub (Q, Q, t, MPFR_RNDN);
/* check if the next term is smaller than ulp(Q): if EXP(err_u)
<= EXP(Q), since the current term is bounded by
err_u * 2^(-w), it is bounded by ulp(Q) */
if (MPFR_EXP(err_u) <= MPFR_EXP(Q))
stop ++;
else
stop = 0;
}
else
{
/* if k = 0 mod 4, add, otherwise subtract */
if ((k & 2) == 0)
mpfr_add (P, P, t, MPFR_RNDN);
else
mpfr_sub (P, P, t, MPFR_RNDN);
/* check if the next term is smaller than ulp(P) */
if (MPFR_EXP(err_u) <= MPFR_EXP(P))
stop ++;
else
stop = 0;
}
mpfr_add (err_s, err_s, err_t, MPFR_RNDU);
/* the sum of the rounding errors on P and Q is bounded by
err_s * 2^(-w) */
/* stop when start to diverge */
if (stop < 2 &&
((MPFR_IS_POS(z) && mpfr_cmp_ui (z, (k + 1) / 2) < 0) ||
(MPFR_IS_NEG(z) && mpfr_cmp_si (z, - ((k + 1) / 2)) > 0)))
{
/* if we have to stop the series because it diverges, then
increasing the precision will most probably fail, since
we will stop to the same point, and thus compute a very
similar approximation */
diverge = 1;
stop = 2; /* force stop */
}
}
/* the sum of the total errors on P and Q is bounded by err_s * 2^(-w) */
/* Now combine: the sum of the rounding errors on P and Q is bounded by
err_s * 2^(-w), and the absolute error on s/c is bounded by 2^(1-w) */
if ((n & 1) == 0) /* n even: P * (sin + cos) + Q (cos - sin) for jn
Q * (sin + cos) + P (sin - cos) for yn */
{
#ifdef MPFR_JN
mpfr_mul (c, c, Q, MPFR_RNDN); /* Q * (sin - cos) */
mpfr_mul (s, s, P, MPFR_RNDN); /* P * (sin + cos) */
#else
mpfr_mul (c, c, P, MPFR_RNDN); /* P * (sin - cos) */
mpfr_mul (s, s, Q, MPFR_RNDN); /* Q * (sin + cos) */
#endif
err = MPFR_EXP(c);
if (MPFR_EXP(s) > err)
err = MPFR_EXP(s);
#ifdef MPFR_JN
mpfr_sub (s, s, c, MPFR_RNDN);
#else
mpfr_add (s, s, c, MPFR_RNDN);
#endif
}
else /* n odd: P * (sin - cos) + Q (cos + sin) for jn,
Q * (sin - cos) - P (cos + sin) for yn */
{
#ifdef MPFR_JN
mpfr_mul (c, c, P, MPFR_RNDN); /* P * (sin - cos) */
mpfr_mul (s, s, Q, MPFR_RNDN); /* Q * (sin + cos) */
#else
mpfr_mul (c, c, Q, MPFR_RNDN); /* Q * (sin - cos) */
mpfr_mul (s, s, P, MPFR_RNDN); /* P * (sin + cos) */
#endif
err = MPFR_EXP(c);
if (MPFR_EXP(s) > err)
err = MPFR_EXP(s);
#ifdef MPFR_JN
mpfr_add (s, s, c, MPFR_RNDN);
#else
mpfr_sub (s, c, s, MPFR_RNDN);
#endif
}
if ((n & 2) != 0)
mpfr_neg (s, s, MPFR_RNDN);
if (MPFR_EXP(s) > err)
err = MPFR_EXP(s);
/* the absolute error on s is bounded by P*err(s/c) + Q*err(s/c)
+ err(P)*(s/c) + err(Q)*(s/c) + 3 * 2^(err - w - 1)
<= (|P|+|Q|) * 2^(1-w) + err_s * 2^(1-w) + 2^err * 2^(1-w),
since |c|, |old_s| <= 2. */
err2 = (MPFR_EXP(P) >= MPFR_EXP(Q)) ? MPFR_EXP(P) + 2 : MPFR_EXP(Q) + 2;
/* (|P| + |Q|) * 2^(1 - w) <= 2^(err2 - w) */
err = MPFR_EXP(err_s) >= err ? MPFR_EXP(err_s) + 2 : err + 2;
/* err_s * 2^(1-w) + 2^old_err * 2^(1-w) <= 2^err * 2^(-w) */
err2 = (err >= err2) ? err + 1 : err2 + 1;
/* now the absolute error on s is bounded by 2^(err2 - w) */
/* multiply by sqrt(1/(Pi*z)) */
mpfr_const_pi (c, MPFR_RNDN); /* Pi, err <= 1 */
mpfr_mul (c, c, z, MPFR_RNDN); /* err <= 2 */
mpfr_si_div (c, MPFR_IS_POS(z) ? 1 : -1, c, MPFR_RNDN); /* err <= 3 */
mpfr_sqrt (c, c, MPFR_RNDN); /* err<=5/2, thus the absolute error is
bounded by 3*u*|c| for |u| <= 0.25 */
mpfr_mul (err_t, c, s, MPFR_SIGN(c)==MPFR_SIGN(s) ? MPFR_RNDU : MPFR_RNDD);
mpfr_abs (err_t, err_t, MPFR_RNDU);
mpfr_mul_ui (err_t, err_t, 3, MPFR_RNDU);
/* 3*2^(-w)*|old_c|*|s| [see below] is bounded by err_t * 2^(-w) */
err2 += MPFR_EXP(c);
/* |old_c| * 2^(err2 - w) [see below] is bounded by 2^(err2-w) */
mpfr_mul (c, c, s, MPFR_RNDN); /* the absolute error on c is bounded by
1/2 ulp(c) + 3*2^(-w)*|old_c|*|s|
+ |old_c| * 2^(err2 - w) */
/* compute err_t * 2^(-w) + 1/2 ulp(c) = (err_t + 2^EXP(c)) * 2^(-w) */
err = (MPFR_EXP(err_t) > MPFR_EXP(c)) ? MPFR_EXP(err_t) + 1 : MPFR_EXP(c) + 1;
/* err_t * 2^(-w) + 1/2 ulp(c) <= 2^(err - w) */
/* now err_t * 2^(-w) bounds 1/2 ulp(c) + 3*2^(-w)*|old_c|*|s| */
err = (err >= err2) ? err + 1 : err2 + 1;
/* the absolute error on c is bounded by 2^(err - w) */
mpfr_clear (s);
mpfr_clear (P);
mpfr_clear (Q);
mpfr_clear (t);
mpfr_clear (iz);
mpfr_clear (err_t);
mpfr_clear (err_s);
mpfr_clear (err_u);
err -= MPFR_EXP(c);
if (MPFR_LIKELY (MPFR_CAN_ROUND (c, w - err, MPFR_PREC(res), r)))
break;
if (diverge != 0)
{
mpfr_set (c, z, r); /* will force inex=0 below, which means the
asymptotic expansion failed */
break;
}
MPFR_ZIV_NEXT (loop, w);
}
MPFR_ZIV_FREE (loop);
inex = (MPFR_IS_POS(z) || ((n & 1) == 0)) ? mpfr_set (res, c, r)
: mpfr_neg (res, c, r);
mpfr_clear (c);
return inex;
}
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;
}
int
mpfr_digamma (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
{
int inex;
MPFR_SAVE_EXPO_DECL (expo);
MPFR_LOG_FUNC
(("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec(x), mpfr_log_prec, x, rnd_mode),
("y[%Pu]=%.*Rg inexact=%d", mpfr_get_prec(y), mpfr_log_prec, y, inex));
if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(x)))
{
if (MPFR_IS_NAN(x))
{
MPFR_SET_NAN(y);
MPFR_RET_NAN;
}
else if (MPFR_IS_INF(x))
{
if (MPFR_IS_POS(x)) /* Digamma(+Inf) = +Inf */
{
MPFR_SET_SAME_SIGN(y, x);
MPFR_SET_INF(y);
MPFR_RET(0);
}
else /* Digamma(-Inf) = NaN */
{
MPFR_SET_NAN(y);
MPFR_RET_NAN;
}
}
else /* Zero case */
{
/* the following works also in case of overlap */
MPFR_SET_INF(y);
MPFR_SET_OPPOSITE_SIGN(y, x);
mpfr_set_divby0 ();
MPFR_RET(0);
}
}
/* Digamma is undefined for negative integers */
if (MPFR_IS_NEG(x) && mpfr_integer_p (x))
{
MPFR_SET_NAN(y);
MPFR_RET_NAN;
}
/* now x is a normal number */
MPFR_SAVE_EXPO_MARK (expo);
/* for x very small, we have Digamma(x) = -1/x - gamma + O(x), more precisely
-1 < Digamma(x) + 1/x < 0 for -0.2 < x < 0.2, thus:
(i) either x is a power of two, then 1/x is exactly representable, and
as long as 1/2*ulp(1/x) > 1, we can conclude;
(ii) otherwise assume x has <= n bits, and y has <= n+1 bits, then
|y + 1/x| >= 2^(-2n) ufp(y), where ufp means unit in first place.
Since |Digamma(x) + 1/x| <= 1, if 2^(-2n) ufp(y) >= 2, then
|y - Digamma(x)| >= 2^(-2n-1)ufp(y), and rounding -1/x gives the correct result.
If x < 2^E, then y > 2^(-E), thus ufp(y) > 2^(-E-1).
A sufficient condition is thus EXP(x) <= -2 MAX(PREC(x),PREC(Y)). */
if (MPFR_EXP(x) < -2)
{
if (MPFR_EXP(x) <= -2 * (mpfr_exp_t) MAX(MPFR_PREC(x), MPFR_PREC(y)))
{
int signx = MPFR_SIGN(x);
inex = mpfr_si_div (y, -1, x, rnd_mode);
if (inex == 0) /* x is a power of two */
{ /* result always -1/x, except when rounding down */
if (rnd_mode == MPFR_RNDA)
rnd_mode = (signx > 0) ? MPFR_RNDD : MPFR_RNDU;
if (rnd_mode == MPFR_RNDZ)
rnd_mode = (signx > 0) ? MPFR_RNDU : MPFR_RNDD;
if (rnd_mode == MPFR_RNDU)
inex = 1;
else if (rnd_mode == MPFR_RNDD)
{
mpfr_nextbelow (y);
inex = -1;
}
else /* nearest */
inex = 1;
}
MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, __gmpfr_flags);
goto end;
}
}
if (MPFR_IS_NEG(x))
inex = mpfr_digamma_reflection (y, x, rnd_mode);
/* if x < 1/2 we use the reflection formula */
else if (MPFR_EXP(x) < 0)
inex = mpfr_digamma_reflection (y, x, rnd_mode);
else
inex = mpfr_digamma_positive (y, x, rnd_mode);
end:
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (y, inex, rnd_mode);
}
void invert(ElementType &result, const ElementType& a) const
// we silently assume that a != 0. If it is, result is set to a^0, i.e. 1
{
mpfr_si_div(&result, 1, &a, GMP_RNDN);
}
void invert(elem &result, elem a) const { mpfr_si_div(&result, 1, &a, GMP_RNDN); }
int fractal_mpfr_calculate_line(image_info* img, int line)
{
int ret = 1;
int ix = 0;
int mx = 0;
int chk_px = ((rthdata*)img->rth_ptr)->check_stop_px;
int img_width = img->real_width;
int* raw_data = &img->raw_data[line * img_width];
depth_t depth = img->depth;
mpfr_t x, y;
mpfr_t x2, y2;
mpfr_t c_re, c_im;
/* working variables: */
mpfr_t wre, wim;
mpfr_t wre2, wim2;
mpfr_t frs_bail;
mpfr_t width, img_rw, img_xmin;
mpfr_t t1;
mpfr_init2(x, img->precision);
mpfr_init2(y, img->precision);
mpfr_init2(x2, img->precision);
mpfr_init2(y2, img->precision);
mpfr_init2(c_re, img->precision);
mpfr_init2(c_im, img->precision);
mpfr_init2(wre, img->precision);
mpfr_init2(wim, img->precision);
mpfr_init2(wre2, img->precision);
mpfr_init2(wim2, img->precision);
mpfr_init2(frs_bail,img->precision);
mpfr_init2(width, img->precision);
mpfr_init2(img_rw, img->precision);
mpfr_init2(img_xmin,img->precision);
mpfr_init2(t1, img->precision);
mpfr_set_si(frs_bail, 4, GMP_RNDN);
mpfr_set_si(img_rw, img_width, GMP_RNDN);
mpfr_set( img_xmin, img->xmin, GMP_RNDN);
mpfr_set( width, img->width, GMP_RNDN);
/* y = img->ymax - ((img->xmax - img->xmin)
/ (long double)img->real_width)
* (long double)img->lines_done; */
mpfr_div( t1, width, img_rw, GMP_RNDN);
mpfr_mul_si( t1, t1, line, GMP_RNDN);
mpfr_sub( y, img->ymax, t1, GMP_RNDN);
mpfr_mul( y2, y, y, GMP_RNDN);
while (ix < img_width)
{
mx += chk_px;
if (mx > img_width)
mx = img_width;
for (; ix < mx; ++ix, ++raw_data)
{
/* x = ((long double)ix / (long double)img->real_width)
* (img->xmax - img->xmin) + img->xmin; */
mpfr_si_div(t1, ix, img_rw, GMP_RNDN);
mpfr_mul(x, t1, width, GMP_RNDN);
mpfr_add(x, x, img_xmin, GMP_RNDN);
mpfr_mul( x2, x, x, GMP_RNDN);
mpfr_set( wre, x, GMP_RNDN);
mpfr_set( wim, y, GMP_RNDN);
mpfr_set( wre2, x2, GMP_RNDN);
mpfr_set( wim2, y2, GMP_RNDN);
switch (img->family)
{
case FAMILY_MANDEL:
mpfr_set(c_re, x, GMP_RNDN);
mpfr_set(c_im, y, GMP_RNDN);
break;
case FAMILY_JULIA:
mpfr_set(c_re, img->u.julia.c_re, GMP_RNDN);
mpfr_set(c_im, img->u.julia.c_im, GMP_RNDN);
break;
}
switch(img->fractal)
{
case BURNING_SHIP:
*raw_data = frac_burning_ship_mpfr(
depth, frs_bail,
wim, wre,
c_im, c_re,
wim2, wre2, t1);
break;
case GENERALIZED_CELTIC:
*raw_data = frac_generalized_celtic_mpfr(
depth, frs_bail,
wim, wre,
c_im, c_re,
wim2, wre2, t1);
break;
case VARIANT:
*raw_data = frac_variant_mpfr(
depth, frs_bail,
wim, wre,
c_im, c_re,
wim2, wre2, t1);
break;
case MANDELBROT:
default:
*raw_data = frac_mandel_mpfr(depth, frs_bail,
wim, wre,
c_im, c_re,
wim2, wre2, t1);
}
}
if (rth_render_should_stop((rthdata*)img->rth_ptr))
{
ret = 0;
break;
}
}
mpfr_clear(x);
mpfr_clear(y);
mpfr_clear(x2);
mpfr_clear(y2);
mpfr_clear(c_re);
mpfr_clear(c_im);
mpfr_clear(wre);
mpfr_clear(wim);
mpfr_clear(wre2);
mpfr_clear(wim2);
mpfr_clear(frs_bail);
mpfr_clear(width);
mpfr_clear(img_rw);
mpfr_clear(t1);
return ret;
}
