/*******************************************************************************
 * This file is part of SWIFT.
 * Coypright (c) 2016 Matthieu Schaller (matthieu.schaller@durham.ac.uk)
 *
 * This program is free software: you can redistribute it and/or modify
 * it under the terms of the GNU Lesser General Public License as published
 * by the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * This program 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 Lesser General Public License
 * along with this program.  If not, see <http://www.gnu.org/licenses/>.
 *
 ******************************************************************************/
#ifndef SWIFT_EAGLE_STARS_IMF_H
#define SWIFT_EAGLE_STARS_IMF_H

/* Some standard headers. */
#include <string.h>

/* Local includes. */
#include "exp10.h"
#include "inline.h"
#include "interpolate.h"
#include "minmax.h"
#include "yield_tables.h"

/**
 * @brief the different weightings allowed for the IMF integration
 */
enum eagle_imf_integration_type {
  eagle_imf_integration_no_weight,   /*<! No weighting */
  eagle_imf_integration_mass_weight, /*<! Weighted by mass */
  eagle_imf_integration_yield_weight /*<! Weigthed by stellar yields */
} __attribute__((packed));

/**
 * @brief determine which IMF mass bins the upper and lower input mass bounds
 * belong to
 *
 * @param log10_min_mass Lower mass bound
 * @param log10_max_mass Upper mass bound
 * @param i_min (return) Index of IMF mass bin containing log10_min_mass
 * @param i_max (return) Index of IMF mass bin containing log10_max_mass
 * @param feedback_props the #feedback_props data struct
 */
INLINE static void determine_imf_bins(
    double log10_min_mass, double log10_max_mass, int *i_min, int *i_max,
    const struct feedback_props *feedback_props) {

#ifdef SWIFT_DEBUG_CHECKS
  if (log10_min_mass > log10_max_mass)
    error("Lower bound higher than larger bound.");
#endif

  const int N_bins = eagle_feedback_N_imf_bins;
  const double *const imf_bins_log10 = feedback_props->imf_mass_bin_log10;

  /* Check whether lower mass is within the IMF mass bin range */
  log10_min_mass = max(log10_min_mass, imf_bins_log10[0]);
  log10_min_mass = min(log10_min_mass, imf_bins_log10[N_bins - 1]);

  /* Check whether upper mass is within the IMF mass bin range */
  log10_max_mass = max(log10_max_mass, imf_bins_log10[0]);
  log10_max_mass = min(log10_max_mass, imf_bins_log10[N_bins - 1]);

  *i_min = 0;
  while ((*i_min < N_bins - 2) && imf_bins_log10[*i_min + 1] < log10_min_mass) {
    (*i_min)++;
  }

  *i_max = 1;
  while ((*i_max < N_bins - 1) && imf_bins_log10[*i_max] < log10_max_mass) {
    (*i_max)++;
  }
}

/**
 * @brief Integrate the IMF between a minimum and maximum mass using the
 * trapezoidal rule. The IMF may be weighted by various quantities, as specified
 * by the variable, mode, including an input array, stellar_yields.
 *
 * @param log10_min_mass log10 mass lower integration bound
 * @param log10_max_mass log10 mass upper integration bound
 * @param mode Type of weighting for the IMF integration.
 * @param stellar_yields Array of weights based on yields. Used only for
 * yield-weighted integration.
 * @param feedback_props the #feedback_props data structure
 */
INLINE static double integrate_imf(
    const double log10_min_mass, const double log10_max_mass,
    const enum eagle_imf_integration_type mode,
    const double stellar_yields[eagle_feedback_N_imf_bins],
    const struct feedback_props *feedback_props) {

  /* Pull out some common terms */
  const double *imf = feedback_props->imf;
  const double *imf_mass_bin = feedback_props->imf_mass_bin;
  const double *imf_mass_bin_log10 = feedback_props->imf_mass_bin_log10;

  /* IMF mass bin spacing in log10 space. Assumes uniform spacing. */
  const double imf_log10_mass_bin_size =
      imf_mass_bin_log10[1] - imf_mass_bin_log10[0];

  /* Determine bins to integrate over based on integration bounds */
  int i_min, i_max;
  determine_imf_bins(log10_min_mass, log10_max_mass, &i_min, &i_max,
                     feedback_props);

  /* Array for the integrand */
  double integrand[eagle_feedback_N_imf_bins];

  /* Add up the contribution from each of the IMF mass bins */
  switch (mode) {

    case eagle_imf_integration_no_weight:

      /* Integrate IMF on its own */
      for (int i = i_min; i < i_max + 1; i++) {
        integrand[i] = imf[i] * imf_mass_bin[i];
      }
      break;

    case eagle_imf_integration_mass_weight:

      /* Integrate IMF weighted by mass */
      for (int i = i_min; i < i_max + 1; i++) {
        integrand[i] = imf[i] * imf_mass_bin[i] * imf_mass_bin[i];
      }
      break;

    case eagle_imf_integration_yield_weight:

#ifdef SWIFT_DEBUG_CHECKS
      if (stellar_yields == NULL)
        error(
            "Yield array not passed in despite asking for yield-weighted IMf "
            "integration.");
#endif

      /* Integrate IMF weighted by yields */
      for (int i = i_min; i < i_max + 1; i++) {
        integrand[i] = stellar_yields[i] * imf[i] * imf_mass_bin[i];
      }
      break;

    default:
      error("Invalid mode for IMF integration");
  }

  /* Integrate using trapezoidal rule */
  double result = 0.;
  for (int i = i_min; i < i_max + 1; i++) {
    result += integrand[i];
  }

  /* Update end bins since contribution was overcounted when summing up all
   * entries */
  result -= 0.5 * (integrand[i_min] + integrand[i_max]);

  /* Correct first bin */
  const double first_bin_offset =
      (log10_min_mass - imf_mass_bin_log10[i_min]) / imf_log10_mass_bin_size;

  if (first_bin_offset < 0.5) {
    result -= first_bin_offset * integrand[i_min];
  } else {
    result -= 0.5 * integrand[i_min];
    result -= (first_bin_offset - 0.5) * integrand[i_min + 1];
  }

  /* Correct last bin */
  const double last_bin_offset =
      (log10_max_mass - imf_mass_bin_log10[i_max - 1]) /
      imf_log10_mass_bin_size;

  if (last_bin_offset < 0.5) {
    result -= 0.5 * integrand[i_max];
    result -= (0.5 - last_bin_offset) * integrand[i_max - 1];
  } else {
    result -= (1.0 - last_bin_offset) * integrand[i_max];
  }

  /* The IMF is tabulated in log10, multiply by log10(mass bin size) to get
   * result of integrating IMF */
  return result * imf_log10_mass_bin_size * M_LN10;
}

/**
 * @brief Allocate space for IMF table and compute values to populate this
 * table.
 *
 * @param feedback_props #feedback_props data structure
 */
INLINE static void init_imf(struct feedback_props *feedback_props) {

  /* Compute size of mass bins in log10 space */
  const double imf_log10_mass_bin_size =
      (feedback_props->log10_imf_max_mass_msun -
       feedback_props->log10_imf_min_mass_msun) /
      (double)(eagle_feedback_N_imf_bins - 1);

  /* Allocate IMF array */
  if (swift_memalign("imf-tables", (void **)&feedback_props->imf,
                     SWIFT_STRUCT_ALIGNMENT,
                     eagle_feedback_N_imf_bins * sizeof(double)) != 0)
    error("Failed to allocate IMF bins table");

  /* Allocate array to store IMF mass bins */
  if (swift_memalign("imf-tables", (void **)&feedback_props->imf_mass_bin,
                     SWIFT_STRUCT_ALIGNMENT,
                     eagle_feedback_N_imf_bins * sizeof(double)) != 0)
    error("Failed to allocate IMF bins table");

  /* Allocate array to store IMF mass bins in log10 space */
  if (swift_memalign("imf-tables", (void **)&feedback_props->imf_mass_bin_log10,
                     SWIFT_STRUCT_ALIGNMENT,
                     eagle_feedback_N_imf_bins * sizeof(double)) != 0)
    error("Failed to allocate IMF bins table");

  /* Set IMF from Chabrier 2003, PASP, 115, 763
   * Eq. 17 with values from table 1 */
  for (int i = 0; i < eagle_feedback_N_imf_bins; i++) {

    /* Logarithmically-spaced bins in units of solar masses */
    const double log10_mass_msun =
        feedback_props->log10_imf_min_mass_msun + i * imf_log10_mass_bin_size;

    const double mass_msun = exp10(log10_mass_msun);

    feedback_props->imf_mass_bin[i] = mass_msun;
    feedback_props->imf_mass_bin_log10[i] = log10_mass_msun;

    if (mass_msun > 1.0) {

      /* High-mass end */
      feedback_props->imf[i] = 0.237912 * pow(mass_msun, -2.3);
    } else {

      /* Low-mass end */
      feedback_props->imf[i] =
          0.852464 *
          exp((log10_mass_msun - log10(0.079)) *
              (log10_mass_msun - log10(0.079)) / (-2.0 * 0.69 * 0.69)) /
          mass_msun;
    }
  }

  /* Normalize the IMF */
  const float norm = integrate_imf(feedback_props->log10_imf_min_mass_msun,
                                   feedback_props->log10_imf_max_mass_msun,
                                   eagle_imf_integration_mass_weight,
                                   /*(stellar_yields=)*/ NULL, feedback_props);

  for (int i = 0; i < eagle_feedback_N_imf_bins; i++)
    feedback_props->imf[i] /= norm;
}

/**
 * @brief Calculate mass (in solar masses) of stars that died from the star
 * particle's birth up to its current age (in Gyr).
 *
 * Calculation uses the tables of Portinari et al. 1998, A&A, 334, 505
 *
 * @param age_Gyr age of star in Gyr.
 * @param Z Star's metallicity (metal mass fraction).
 * @param feedback_props the #feedback_props data structure.
 * @return Mass of stars died up to that age in solar masses.
 */
INLINE static double dying_mass_msun(
    const double age_Gyr, const double Z,
    const struct feedback_props *feedback_props) {

  /* Pull out some common terms */
  const double *lifetime_Z = feedback_props->lifetimes.metallicity;
  const double *lifetime_m = feedback_props->lifetimes.mass;
  double **const dying_times = feedback_props->lifetimes.dyingtime;
  const int n_Z = eagle_feedback_lifetime_N_metals;
  const int n_m = eagle_feedback_lifetime_N_masses;

  /* Early abort? */
  if (age_Gyr <= 0.) {
    return feedback_props->imf_max_mass_msun;
  }

  const double log10_age_yr = log10(age_Gyr * 1.0e9);

  /* Calculate index along the metallicity axis */
  int Z_index;
  double Z_offset;
  if (Z <= lifetime_Z[0]) {

    /* Before start of the table */
    Z_index = 0;
    Z_offset = 0.;

  } else if (Z >= lifetime_Z[n_Z - 1]) {

    /* After end of the table */
    Z_index = n_Z - 2;
    Z_offset = 1.;

  } else {

    /* Normal case: Somewhere inside the table */
    Z_index = 0;
    while (Z_index < n_Z - 1 && lifetime_Z[Z_index + 1] <= Z) {
      Z_index++;
    }

#ifdef SWIFT_DEBUG_CHECKS
    if (Z_index >= n_Z) error("Z_index is beyond the range  of the table");
#endif

    Z_offset = (Z - lifetime_Z[Z_index]) /
               (lifetime_Z[Z_index + 1] - lifetime_Z[Z_index]);
  }

  /* Check whether we are not beyond the age table for the low metallicity end
   */
  int time_index_lowZ = -1;
  double time_offset_lowZ = 0.;
  if (log10_age_yr >= dying_times[Z_index][0]) {

    /* Before start of the table */
    time_index_lowZ = 0;
    time_offset_lowZ = 0.;

  } else if (log10_age_yr <= dying_times[Z_index][n_m - 1]) {

    /* After end of the table */
    time_index_lowZ = n_m - 2;
    time_offset_lowZ = 1.;
  }

  /* Check whether we are not beyond the age table for the high metallicity end
   */
  int time_index_highZ = -1;
  double time_offset_highZ = 0.;
  if (log10_age_yr >= dying_times[Z_index + 1][0]) {

    /* Before start of the table */
    time_index_highZ = 0;
    time_offset_highZ = 0.;

  } else if (log10_age_yr <= dying_times[Z_index + 1][n_m - 1]) {

    /* After end of the table */
    time_index_highZ = n_m - 2;
    time_offset_highZ = 1.0;
  }

  /* Search the table starting from the largest times until we reach
     a solution for the low-metallicity bound */
  int i = n_m - 1;
  while (i >= 0 && time_index_lowZ == -1) {

    if (dying_times[Z_index][i] >= log10_age_yr && time_index_lowZ == -1) {

      /* record index */
      time_index_lowZ = i;

      /* record distance from table element */
      time_offset_lowZ =
          (log10_age_yr - dying_times[Z_index][time_index_lowZ]) /
          (dying_times[Z_index][time_index_lowZ + 1] -
           dying_times[Z_index][time_index_lowZ]);

      break;
    }
    i--;
  }

#ifdef SWIFT_DEBUG_CHECKS
  if (time_index_lowZ == -1) error("Could not find low-metallicity bound!");
#endif

  /* Search the table starting from the largest times until we reach
     a solution for the high-metallicity bound */
  i = n_m - 1;
  while (i >= 0 && time_index_highZ == -1) {

    if (dying_times[Z_index + 1][i] >= log10_age_yr && time_index_highZ == -1) {

      /* record index */
      time_index_highZ = i;

      /* record distance from table element */
      time_offset_highZ =
          (log10_age_yr - dying_times[Z_index + 1][time_index_highZ]) /
          (dying_times[Z_index + 1][time_index_highZ + 1] -
           dying_times[Z_index + 1][time_index_highZ]);

      break;
    }
    i--;
  }

#ifdef SWIFT_DEBUG_CHECKS
  if (time_index_highZ == -1) error("Could not find high-metallicity bound!");
#endif

  /* And now interpolate the solution */
  const double mass_low_Z =
      interpolate_1d(lifetime_m, time_index_lowZ, time_offset_lowZ);
  const double mass_high_Z =
      interpolate_1d(lifetime_m, time_index_highZ, time_offset_highZ);

  double mass = (1. - Z_offset) * mass_low_Z + Z_offset * mass_high_Z;

  /* Check that we haven't killed too many stars */
  mass = min(mass, feedback_props->imf_max_mass_msun);

  return mass;
}

/**
 * @brief Calculate lifetime of stellar population in Gyr for a given mass.
 *
 * Calculation uses the tables of Portinari et al. 1998, A&A, 334, 505
 *
 * @param mass in solar masses.
 * @param Z Metallicity (metal mass fraction).
 * @param feedback_props the #feedback_props data structure.
 * @return The life time in Giga-years.
 */
INLINE static float lifetime_in_Gyr(
    const float mass, const float Z,
    const struct feedback_props *feedback_props) {

  /* Pull out some common terms */
  const double *lifetime_Z = feedback_props->lifetimes.metallicity;
  const double *lifetime_m = feedback_props->lifetimes.mass;
  double **const dying_times = feedback_props->lifetimes.dyingtime;
  const int n_Z = eagle_feedback_lifetime_N_metals;
  const int n_m = eagle_feedback_lifetime_N_masses;

  /* Calculate index along the mass axis */
  int m_index;
  float m_offset;
  if (mass <= lifetime_m[0]) {

    /* Before start of the table */
    m_index = 0;
    m_offset = 0.f;

  } else if (mass >= lifetime_m[n_m - 1]) {

    /* After end of the table */
    m_index = n_m - 2;
    m_offset = 1.f;

  } else {

    /* Normal case: Somewhere inside the table */
    for (m_index = 0; m_index < n_m - 1; m_index++)
      if (lifetime_m[m_index + 1] > mass) break;

    m_offset = (mass - lifetime_m[m_index]) /
               (lifetime_m[m_index + 1] - lifetime_m[m_index]);
  }

  /* Calculate index along the metallicity axis */
  int Z_index;
  float Z_offset;
  if (Z <= lifetime_Z[0]) {

    /* Before start of the table */
    Z_index = 0;
    Z_offset = 0.f;

  } else if (Z >= lifetime_Z[n_Z - 1]) {

    /* After end of the table */
    Z_index = n_Z - 2;
    Z_offset = 1.f;

  } else {

    for (Z_index = 0; Z_index < n_Z - 1; Z_index++)
      if (lifetime_Z[Z_index + 1] > Z) break;

    /* Normal case: Somewhere inside the table */
    Z_offset = (Z - lifetime_Z[Z_index]) /
               (lifetime_Z[Z_index + 1] - lifetime_Z[Z_index]);
  }

  /* Interpolation of the table to get the time */
  const float log_time_years =
      interpolate_2d(dying_times, Z_index, m_index, Z_offset, m_offset);

  /* Convert to Giga-years */
  const float time_Gyr = exp10f(log_time_years - 9.f);

  return time_Gyr;
}

#endif
