/**
* @brief Update the MP version of the roots to the latest and greatest approximations.
*
* @param s A pointer to the current mps_context.
*/
MPS_PRIVATE void
mps_copy_roots (mps_context * s)
{
int i;
MPS_DEBUG_THIS_CALL (s);
switch (s->lastphase)
{
case no_phase:
mps_error (s, "Nothing to copy");
break;
case float_phase:
if (s->DOSORT)
mps_fsort (s);
for (i = 0; i < s->n; i++)
{
mpc_set_prec (s->root[i]->mvalue, DBL_MANT_DIG);
mpc_set_cplx (s->root[i]->mvalue, s->root[i]->fvalue);
rdpe_set_d (s->root[i]->drad, s->root[i]->frad);
}
break;
case dpe_phase:
if (s->DOSORT)
mps_dsort (s);
for (i = 0; i < s->n; i++)
{
mpc_set_prec (s->root[i]->mvalue, DBL_MANT_DIG);
mpc_set_cdpe (s->root[i]->mvalue, s->root[i]->dvalue);
}
break;
case mp_phase:
if (s->DOSORT)
mps_msort (s);
break;
}
}
void
mps_maberth_s_wl (mps_context * s, int j, mps_cluster * cluster, mpc_t abcorr,
pthread_mutex_t * aberth_mutexes)
{
int k;
mps_root * root;
cdpe_t z, temp;
mpc_t diff, mroot;
mpc_init2 (mroot, s->mpwp);
mpc_init2 (diff, s->mpwp);
pthread_mutex_lock (&aberth_mutexes[j]);
mpc_set (mroot, s->root[j]->mvalue);
pthread_mutex_unlock (&aberth_mutexes[j]);
cdpe_set (temp, cdpe_zero);
for (root = cluster->first; root != NULL; root = root->next)
{
k = root->k;
if (k == j)
continue;
pthread_mutex_lock (&aberth_mutexes[k]);
mpc_sub (diff, mroot, s->root[k]->mvalue);
pthread_mutex_unlock (&aberth_mutexes[k]);
mpc_get_cdpe (z, diff);
if (cdpe_eq_zero(z))
continue;
cdpe_inv_eq (z);
cdpe_add_eq (temp, z);
}
mpc_set_cdpe (abcorr, temp);
mpc_clear (mroot);
mpc_clear (diff);
}
/**
* @brief Compute Aberth correction for j-th root, without
* selective correction.
*/
void
mps_maberth (mps_context * s, mps_approximation * root, mpc_t abcorr)
{
int i;
cdpe_t z, temp;
mpc_t diff;
mpc_init2 (diff, s->mpwp);
cdpe_set (temp, cdpe_zero);
for (i = 0; i < s->n; i++)
{
if (s->root[i] == root)
continue;
mpc_sub (diff, root->mvalue, s->root[i]->mvalue);
mpc_get_cdpe (z, diff);
cdpe_inv_eq (z);
cdpe_add_eq (temp, z);
}
mpc_set_cdpe (abcorr, temp);
mpc_clear (diff);
}
/**
* @brief Compute Aberth correction for the j-th root,
* but only with other roots of the <code>jc</code>-th
* cluster.
*/
void
mps_maberth_s (mps_context * s, mps_approximation * ab_root, mps_cluster * cluster, mpc_t abcorr)
{
mps_root * root;
cdpe_t z, temp;
mpc_t diff;
mpc_init2 (diff, s->mpwp);
cdpe_set (temp, cdpe_zero);
for (root = cluster->first; root != NULL; root = root->next)
{
mps_approximation * appr = s->root[root->k];
if (appr == ab_root)
continue;
mpc_sub (diff, ab_root->mvalue, appr->mvalue);
mpc_get_cdpe (z, diff);
cdpe_inv_eq (z);
cdpe_add_eq (temp, z);
}
mpc_set_cdpe (abcorr, temp);
mpc_clear (diff);
}
/**
* @brief Check consistency of data and makes some basic adjustments.
*
* This routine check, for example, if there are zero roots in the polynomial
* (i.e. no costant term) and deflates the polynomial if necessary (shifting
* the coefficients).
*
* It sets the value of the parameter <code>which_case</code> to <code>'f'</code>
* if a floating point phase is enough, or to <code>'d'</code> if
* a <code>dpe</code> phase is needed.
*
* @param s The <code>mps_context</code> associated with the current computation.
* @param which_case the address of the variable which_case;
*/
MPS_PRIVATE void
mps_check_data (mps_context * s, char *which_case)
{
rdpe_t min_coeff, max_coeff, tmp;
mps_monomial_poly *p = NULL;
int i;
/* case of user-defined polynomial */
if (! MPS_IS_MONOMIAL_POLY (s->active_poly))
{
if (s->output_config->multiplicity)
mps_error (s,
"Multiplicity detection not yet implemented for user polynomial");
if (s->output_config->root_properties)
mps_error (s,
"Real/imaginary detection not yet implemented for user polynomial");
*which_case = 'd';
return;
}
else
p = MPS_MONOMIAL_POLY (s->active_poly);
/* Check consistency of input */
if (rdpe_eq (p->dap[s->n], rdpe_zero))
{
mps_warn (s, "The leading coefficient is zero");
do
(s->n)--;
while (rdpe_eq (p->dap[s->n], rdpe_zero));
MPS_POLYNOMIAL (p)->degree = s->n;
}
/* Compute min_coeff */
if (rdpe_lt (p->dap[0], p->dap[s->n]))
rdpe_set (min_coeff, p->dap[0]);
else
rdpe_set (min_coeff, p->dap[s->n]);
/* Compute max_coeff and its logarithm */
rdpe_set (max_coeff, p->dap[0]);
for (i = 1; i <= s->n; i++)
if (rdpe_lt (max_coeff, p->dap[i]))
rdpe_set (max_coeff, p->dap[i]);
s->lmax_coeff = rdpe_log (max_coeff);
/* Multiplicity and sep */
if (s->output_config->multiplicity)
{
if (MPS_STRUCTURE_IS_INTEGER (s->active_poly->structure))
{
mps_compute_sep (s);
}
else if (MPS_STRUCTURE_IS_RATIONAL (s->active_poly->structure))
{
mps_warn (s, "The multiplicity option has not been yet implemented");
s->sep = 0.0;
}
else
{
mps_warn (s, "The input polynomial has neither integer nor rational");
mps_warn (s, " coefficients: unable to compute multiplicities");
s->sep = 0.0;
}
}
/* Real/Imaginary detection */
if (s->output_config->root_properties ||
s->output_config->search_set == MPS_SEARCH_SET_REAL ||
s->output_config->search_set == MPS_SEARCH_SET_IMAG)
{
if (MPS_STRUCTURE_IS_INTEGER (s->active_poly->structure))
{
mps_compute_sep (s);
}
else if (MPS_STRUCTURE_IS_RATIONAL (s->active_poly->structure))
{
mps_error (s,
"The real/imaginary option has not been yet implemented for rational input");
return;
}
else
{
mps_error (s, "The input polynomial has neither integer nor rational "
"coefficients: unable to perform real/imaginary options");
return;
}
}
/* Select cases (dpe or floating point)
* First normalize the polynomial (only the float version) */
rdpe_div (tmp, max_coeff, min_coeff);
rdpe_mul_eq_d (tmp, (double)(s->n + 1));
rdpe_mul_eq (tmp, rdpe_mind);
rdpe_div_eq (tmp, rdpe_maxd);
if (rdpe_lt (tmp, rdpe_one))
{
mpc_t m_min_coeff;
cdpe_t c_min_coeff;
/* if (n+1)*max_coeff/min_coeff < dhuge/dtiny - float case */
*which_case = 'f';
rdpe_mul_eq (min_coeff, max_coeff);
rdpe_mul (tmp, rdpe_mind, rdpe_maxd);
rdpe_div (min_coeff, tmp, min_coeff);
rdpe_sqrt_eq (min_coeff);
rdpe_set (cdpe_Re (c_min_coeff), min_coeff);
rdpe_set (cdpe_Im (c_min_coeff), rdpe_zero);
mpc_init2 (m_min_coeff, mpc_get_prec (p->mfpc[0]));
mpc_set_cdpe (m_min_coeff, c_min_coeff);
/* min_coeff = sqrt(dhuge*dtiny/(min_coeff*max_coeff))
* NOTE: This is enabled for floating point polynomials only
* for the moment, but it may work nicely also for other representations. */
{
for (i = 0; i <= s->n; i++)
{
/* Multiply the MP leading coefficient */
mpc_mul_eq (p->mfpc[i], m_min_coeff);
rdpe_mul (tmp, p->dap[i], min_coeff);
rdpe_set (p->dap[i], tmp);
p->fap[i] = rdpe_get_d (tmp);
mpc_get_cdpe (p->dpc[i], p->mfpc[i]);
cdpe_get_x (p->fpc[i], p->dpc[i]);
}
}
mpc_clear (m_min_coeff);
}
else
*which_case = 'd';
}
/**
* @brief Main routine of the program that implements the algorithm
* in the standard polynomial version.
*
* The program is divided into many parts
* - Check the correctness of data, scale coefficients if
* needed, and select cases: the variable <code>which_case</code> is
* <code>'f'</code> or <code>'d'</code> according to float or dpe case.
* - Call msolve or dsolve according to the value of which_case.
* - Allocate MP variables mfpc, mroot, drad (if needed).
* - Start MPsolve loop
* - prepare data according to the current precision
* and to the data_type (density/sparsity/user)
* - Call msolve with the current precision
* - check for termination
*/
MPS_PRIVATE void
mps_standard_mpsolve (mps_context * s)
{
int i, nzc;
char which_case;
mps_boolean d_after_f, computed;
#ifndef DISABLE_DEBUG
clock_t *my_timer = mps_start_timer ();
#endif
mps_allocate_data (s);
if (s->DOLOG)
s->debug_level |= MPS_DEBUG_TRACE;
/* == 1 == Setup variables, i.e. copy coefficients
into dpr, dpc and similar. */
mps_setup (s);
s->lastphase = no_phase;
computed = false;
s->over_max = false;
/* == 2 == Resume from pre-computed roots */
if (s->resume)
{
mps_error (s, "Resume not supported yet");
#ifndef DISABLE_DEBUG
mps_stop_timer (my_timer);
#endif
return;
}
/* == 3 == Check data and get starting phase */
if (s->skip_float)
which_case = 'd';
else
which_case = 'f';
/* This variable is true if we need a dpe phase after the
* float phase */
d_after_f = false;
/* Check if a dpe phase is needed and deflate polynomial */
mps_check_data (s, &which_case);
/* Check for errors in check data */
if (mps_context_has_errors (s))
{
#ifndef DISABLE_DEBUG
mps_stop_timer (my_timer);
#endif
return;
}
rdpe_set_2dl (s->eps_out, 1.0, -s->output_config->prec);
if (s->DOLOG)
fprintf (s->logstr, "Which_case = %c, skip_float= %d\n", which_case,
s->skip_float);
/* == 4 == Float phase */
if (which_case == 'f')
{
if (s->DOLOG)
fprintf (s->logstr, "Float phase ...\n");
mps_fsolve (s, &d_after_f);
s->lastphase = float_phase;
if (s->DOLOG)
mps_dump (s);
computed = mps_check_stop (s);
if (computed && s->output_config->goal != MPS_OUTPUT_GOAL_APPROXIMATE)
goto exit_sub;
/* stop for COUNT and ISOLATE goals */
}
/* == 5 == DPE phase */
if (which_case == 'd' || d_after_f)
{ /* DPE phase */
if (s->DOLOG)
fprintf (s->logstr, "DPE phase ...\n");
/* If we are arriving from a float phase copy the floating points
* roots approximations in the DPE root approximations. */
if (d_after_f)
for (i = 0; i < s->n; i++)
{
rdpe_set_d (s->root[i]->drad, s->root[i]->frad);
cdpe_set_x (s->root[i]->dvalue, s->root[i]->fvalue);
}
s->lastphase = dpe_phase;
mps_dsolve (s, d_after_f);
if (s->DOLOG)
mps_dump (s);
computed = mps_check_stop (s);
if (computed && s->output_config->goal != MPS_OUTPUT_GOAL_APPROXIMATE)
goto exit_sub;
}
/* == 6 == Allocate MP variables mfpc, mroot, drad, mfppc, mfppc1
* (the real input case is not implemented yet ) */
MPS_DEBUG (s, "Starting MP phase");
s->lastphase = mp_phase;
/* ==== 6.1 initialize mp variables */
mps_mp_set_prec (s, 2 * DBL_MANT_DIG);
/* Prepare data according to the current working precision */
mps_prepare_data (s, s->mpwp);
/* ==== 6.2 set initial values for mp variables */
for (i = 0; i < s->n; i++)
{
if (which_case == 'd' || d_after_f)
mpc_set_cdpe (s->root[i]->mvalue, s->root[i]->dvalue);
else
{
mpc_set_cplx (s->root[i]->mvalue, s->root[i]->fvalue);
rdpe_set_d (s->root[i]->drad, s->root[i]->frad);
}
}
if (computed && s->output_config->goal == MPS_OUTPUT_GOAL_APPROXIMATE)
{
MPS_DEBUG (s, "Exiting since the approximation are computed and the goal is MPS_OUTPUT_GOAL_APPROXIMATE");
goto exit_sub;
}
MPS_DEBUG (s, "s->mpwp = %ld, s->mpwp_max = %ld", s->mpwp, s->mpwp_max);
MPS_DEBUG (s, "s->input_config->prec = %ld", s->active_poly->prec);
/* == 7 == Start MPSolve loop */
s->mpwp = mps_context_get_minimum_precision (s);
/* Poor man GMP - machine precision detection. We need that min_prec is contained
* in the interval [ DBL_MANT_DIG , 2 * DBL_MANT_DIG ]. This is probably true on most
* architectures with the instruction above, but we want to be sure. */
while (s->mpwp < DBL_MANT_DIG)
s->mpwp <<= 1;
while (s->mpwp > 2 * DBL_MANT_DIG)
s->mpwp >>= 1;
while (!computed && s->mpwp < s->mpwp_max)
{
s->mpwp *= 2;
if (s->mpwp > s->mpwp_max)
{
s->mpwp = s->mpwp_max;
s->over_max = true;
}
if (s->DOLOG)
fprintf (s->logstr, "MAIN: mp_loop: mpwp=%ld\n", s->mpwp);
/* == 7.1 == prepare data according to the current precision */
mps_mp_set_prec (s, s->mpwp);
mps_prepare_data (s, s->mpwp);
/* == 7.2 == Call msolve with the current precision */
if (s->DOLOG)
fprintf (s->logstr, "MAIN: now call msolve nclust=%ld\n", s->clusterization->n);
mps_msolve (s);
s->lastphase = mp_phase;
/* if (s->DOLOG) dump(logstr); */
if (s->DOLOG)
{ /* count isolated zeros */
nzc = 0;
for (i = 0; i < s->n; i++)
{
if (s->root[i]->status == MPS_ROOT_STATUS_ISOLATED ||
s->root[i]->status == MPS_ROOT_STATUS_APPROXIMATED)
nzc++;
}
fprintf (s->logstr, "MAIN: isolated %d roots\n", nzc);
fprintf (s->logstr, "MAIN: after msolve check stop\n");
}
/* == 7.3 == Check the stop condition */
computed = mps_check_stop (s);
mps_mmodify (s, true);
/* == 7.4 == reset the status vector */
for (i = 0; i < s->n; i++)
if (s->root[i]->status == MPS_ROOT_STATUS_NEW_CLUSTERED)
s->root[i]->status = MPS_ROOT_STATUS_CLUSTERED;
}
/* == 8 == Check for termination */
if (!computed)
{
if (s->over_max)
{
s->over_max = true;
/* mps_error (s, "Reached the maximum working precision"); */
MPS_DEBUG (s, "Reached the maximum working precision");
goto exit_sub;
}
else
{
/* mps_warn (s, "Reached the input precision"); */
MPS_DEBUG (s, "Reached the input precision");
goto exit_sub;
}
}
exit_sub:
/* == 9 == Check inclusion disks */
if (computed && s->clusterization->n < s->n)
if (!mps_inclusion (s))
{
mps_error (s, "Unable to compute inclusion disks");
return;
}
/* == 10 == Refine roots */
if (computed && !s->over_max && s->output_config->goal == MPS_OUTPUT_GOAL_APPROXIMATE)
{
s->lastphase = mp_phase;
mps_improve (s);
}
/* == 11 == Check inclusions */
/* This step is disabled since it cause problems with the lar* kind of polynomials.
* To be re-enabled a careful check of the necessary precision to avoid NULL DERIVATIVE
* warnings should be implemented.
* if (s->active_poly->prec > 0)
* mps_validate_inclusions (s);
*/
/* == 12 == Restore to highest used precision */
if (s->lastphase == mp_phase)
mps_restore_data (s);
#ifndef DISABLE_DEBUG
{
unsigned long time = mps_stop_timer (my_timer);
MPS_DEBUG (s, "Total time using MPSolve: %lu ms", time);
}
#endif
/* Finally copy the roots ready for output */
mps_copy_roots (s);
}