multipole.h

/*******************************************************************************
 * This file is part of SWIFT.
 * Copyright (c) 2013 Pedro Gonnet (pedro.gonnet@durham.ac.uk)
 *               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_MULTIPOLE_H
#define SWIFT_MULTIPOLE_H

/* Config parameters. */
#include "../config.h"

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

/* Includes. */
#include "align.h"
#include "const.h"
#include "error.h"
#include "gravity.h"
#include "gravity_derivatives.h"
#include "gravity_properties.h"
#include "gravity_softened_derivatives.h"
#include "inline.h"
#include "kernel_gravity.h"
#include "part.h"
#include "periodic.h"
#include "vector_power.h"

#define multipole_align 128

struct grav_tensor {

  /* 0th order terms */
  float F_000;

#if SELF_GRAVITY_MULTIPOLE_ORDER > 0

  /* 1st order terms */
  float F_100, F_010, F_001;
#endif
#if SELF_GRAVITY_MULTIPOLE_ORDER > 1

  /* 2nd order terms */
  float F_200, F_020, F_002;
  float F_110, F_101, F_011;
#endif
#if SELF_GRAVITY_MULTIPOLE_ORDER > 2

  /* 3rd order terms */
  float F_300, F_030, F_003;
  float F_210, F_201;
  float F_120, F_021;
  float F_102, F_012;
  float F_111;
#endif
#if SELF_GRAVITY_MULTIPOLE_ORDER > 3

  /* 4th order terms */
  float F_400, F_040, F_004;
  float F_310, F_301;
  float F_130, F_031;
  float F_103, F_013;
  float F_220, F_202, F_022;
  float F_211, F_121, F_112;
#endif
#if SELF_GRAVITY_MULTIPOLE_ORDER > 4

  /* 5th order terms */
  float F_005, F_014, F_023;
  float F_032, F_041, F_050;
  float F_104, F_113, F_122;
  float F_131, F_140, F_203;
  float F_212, F_221, F_230;
  float F_302, F_311, F_320;
  float F_401, F_410, F_500;
#endif
#if SELF_GRAVITY_MULTIPOLE_ORDER > 5
#error "Missing implementation for order >5"
#endif
#ifdef SWIFT_DEBUG_CHECKS

  /* Total number of gpart this field tensor interacted with */
  long long num_interacted;

  /* Last time this tensor was zeroed */
  integertime_t ti_init;

#endif

  /* Has this tensor received any contribution? */
  char interacted;
};

struct multipole {

  /*! Bulk velocity */
  float vel[3];

  /*! Maximal velocity along each axis of all #gpart */
  float max_delta_vel[3];

  /*! Minimal velocity along each axis of all #gpart */
  float min_delta_vel[3];

  /*! Maximal co-moving softening of all the #gpart in the mulipole */
  float max_softening;

  /* 0th order term */
  float M_000;

#if SELF_GRAVITY_MULTIPOLE_ORDER > 0

  /* 1st order terms */
  float M_100, M_010, M_001;
#endif
#if SELF_GRAVITY_MULTIPOLE_ORDER > 1

  /* 2nd order terms */
  float M_200, M_020, M_002;
  float M_110, M_101, M_011;
#endif
#if SELF_GRAVITY_MULTIPOLE_ORDER > 2

  /* 3rd order terms */
  float M_300, M_030, M_003;
  float M_210, M_201;
  float M_120, M_021;
  float M_102, M_012;
  float M_111;
#endif
#if SELF_GRAVITY_MULTIPOLE_ORDER > 3

  /* 4th order terms */
  float M_400, M_040, M_004;
  float M_310, M_301;
  float M_130, M_031;
  float M_103, M_013;
  float M_220, M_202, M_022;
  float M_211, M_121, M_112;
#endif
#if SELF_GRAVITY_MULTIPOLE_ORDER > 4

  /* 5th order terms */
  float M_005, M_014, M_023;
  float M_032, M_041, M_050;
  float M_104, M_113, M_122;
  float M_131, M_140, M_203;
  float M_212, M_221, M_230;
  float M_302, M_311, M_320;
  float M_401, M_410, M_500;
#endif
#if SELF_GRAVITY_MULTIPOLE_ORDER > 5
#error "Missing implementation for order >5"
#endif

#ifdef SWIFT_DEBUG_CHECKS

  /* Total number of gpart in this multipole */
  long long num_gpart;

#endif
};

/**
 * @brief The multipole expansion of a mass distribution.
 */
struct gravity_tensors {

  union {

    /*! Linking pointer for "memory management". */
    struct gravity_tensors *next;

    /*! The actual content */
    struct {

      /*! Field tensor for the potential */
      struct grav_tensor pot;

      /*! Multipole mass */
      struct multipole m_pole;

      /*! Centre of mass of the matter dsitribution */
      double CoM[3];

      /*! Centre of mass of the matter dsitribution at the last rebuild */
      double CoM_rebuild[3];

      /*! Upper limit of the CoM<->gpart distance */
      double r_max;

      /*! Upper limit of the CoM<->gpart distance at the last rebuild */
      double r_max_rebuild;
    };
  };
} SWIFT_STRUCT_ALIGN;

#ifdef WITH_MPI
/* MPI datatypes for transfers */
extern MPI_Datatype multipole_mpi_type;
extern MPI_Op multipole_mpi_reduce_op;
void multipole_create_mpi_types(void);
#endif

/**
 * @brief Reset the data of a #multipole.
 *
 * @param m The #multipole.
 */
INLINE static void gravity_reset(struct gravity_tensors *m) {

  /* Just bzero the struct. */
  bzero(m, sizeof(struct gravity_tensors));
}

/**
 * @brief Drifts a #multipole forward in time.
 *
 * This uses a first-order approximation in time. We only move the CoM
 * using the bulk velocity measured at the last rebuild.
 *
 * @param m The #multipole.
 * @param dt The drift time-step.
 */
INLINE static void gravity_drift(struct gravity_tensors *m, double dt) {

  /* Motion of the centre of mass */
  const double dx = m->m_pole.vel[0] * dt;
  const double dy = m->m_pole.vel[1] * dt;
  const double dz = m->m_pole.vel[2] * dt;

  /* Move the whole thing according to bulk motion */
  m->CoM[0] += dx;
  m->CoM[1] += dy;
  m->CoM[2] += dz;

#ifdef SWIFT_DEBUG_CHECKS
  if (m->m_pole.vel[0] > m->m_pole.max_delta_vel[0] * 1.1)
    error("Invalid maximal velocity");
  if (m->m_pole.vel[0] < m->m_pole.min_delta_vel[0] * 1.1)
    error("Invalid minimal velocity");
  if (m->m_pole.vel[1] > m->m_pole.max_delta_vel[1] * 1.1)
    error("Invalid maximal velocity");
  if (m->m_pole.vel[1] < m->m_pole.min_delta_vel[1] * 1.1)
    error("Invalid minimal velocity");
  if (m->m_pole.vel[2] > m->m_pole.max_delta_vel[2] * 1.1)
    error("Invalid maximal velocity");
  if (m->m_pole.vel[2] < m->m_pole.min_delta_vel[2] * 1.1)
    error("Invalid minimal velocity");
#endif

  /* Maximal distance covered by any particle */
  float dv[3];
  dv[0] = max(m->m_pole.max_delta_vel[0] - m->m_pole.vel[0],
              m->m_pole.vel[0] - m->m_pole.min_delta_vel[0]);
  dv[1] = max(m->m_pole.max_delta_vel[1] - m->m_pole.vel[1],
              m->m_pole.vel[1] - m->m_pole.min_delta_vel[1]);
  dv[2] = max(m->m_pole.max_delta_vel[2] - m->m_pole.vel[2],
              m->m_pole.vel[2] - m->m_pole.min_delta_vel[2]);

  const float max_delta_vel =
      sqrt(dv[0] * dv[0] + dv[1] * dv[1] + dv[2] * dv[2]);
  const float x_diff = max_delta_vel * dt;

  /* Conservative change in maximal radius containing all gpart */
  m->r_max += x_diff;
}

/**
 * @brief Zeroes all the fields of a field tensor
 *
 * @param l The field tensor.
 * @param ti_current The current (integer) time (for debugging only).
 */
INLINE static void gravity_field_tensors_init(struct grav_tensor *l,
                                              integertime_t ti_current) {

  bzero(l, sizeof(struct grav_tensor));

#ifdef SWIFT_DEBUG_CHECKS
  l->ti_init = ti_current;
#endif
}

/**
 * @brief Adds a field tensor to another one (i.e. does la += lb).
 *
 * @param la The gravity tensors to add to.
 * @param lb The gravity tensors to add.
 */
INLINE static void gravity_field_tensors_add(
    struct grav_tensor *restrict la, const struct grav_tensor *restrict lb) {
#ifdef SWIFT_DEBUG_CHECKS
  if (lb->num_interacted == 0) error("Adding tensors that did not interact");
  la->num_interacted += lb->num_interacted;
#endif

  la->interacted = 1;

  /* Add 0th order terms */
  la->F_000 += lb->F_000;

#if SELF_GRAVITY_MULTIPOLE_ORDER > 0
  /* Add 1st order terms */
  la->F_100 += lb->F_100;
  la->F_010 += lb->F_010;
  la->F_001 += lb->F_001;
#endif
#if SELF_GRAVITY_MULTIPOLE_ORDER > 1
  /* Add 2nd order terms */
  la->F_200 += lb->F_200;
  la->F_020 += lb->F_020;
  la->F_002 += lb->F_002;
  la->F_110 += lb->F_110;
  la->F_101 += lb->F_101;
  la->F_011 += lb->F_011;
#endif
#if SELF_GRAVITY_MULTIPOLE_ORDER > 2
  /* Add 3rd order terms */
  la->F_300 += lb->F_300;
  la->F_030 += lb->F_030;
  la->F_003 += lb->F_003;
  la->F_210 += lb->F_210;
  la->F_201 += lb->F_201;
  la->F_120 += lb->F_120;
  la->F_021 += lb->F_021;
  la->F_102 += lb->F_102;
  la->F_012 += lb->F_012;
  la->F_111 += lb->F_111;
#endif
#if SELF_GRAVITY_MULTIPOLE_ORDER > 3
  /* Add 4th order terms */
  la->F_400 += lb->F_400;
  la->F_040 += lb->F_040;
  la->F_004 += lb->F_004;
  la->F_310 += lb->F_310;
  la->F_301 += lb->F_301;
  la->F_130 += lb->F_130;
  la->F_031 += lb->F_031;
  la->F_103 += lb->F_103;
  la->F_013 += lb->F_013;
  la->F_220 += lb->F_220;
  la->F_202 += lb->F_202;
  la->F_022 += lb->F_022;
  la->F_211 += lb->F_211;
  la->F_121 += lb->F_121;
  la->F_112 += lb->F_112;
#endif
#if SELF_GRAVITY_MULTIPOLE_ORDER > 4
  /* 5th order terms */
  la->F_005 += lb->F_005;
  la->F_014 += lb->F_014;
  la->F_023 += lb->F_023;
  la->F_032 += lb->F_032;
  la->F_041 += lb->F_041;
  la->F_050 += lb->F_050;
  la->F_104 += lb->F_104;
  la->F_113 += lb->F_113;
  la->F_122 += lb->F_122;
  la->F_131 += lb->F_131;
  la->F_140 += lb->F_140;
  la->F_203 += lb->F_203;
  la->F_212 += lb->F_212;
  la->F_221 += lb->F_221;
  la->F_230 += lb->F_230;
  la->F_302 += lb->F_302;
  la->F_311 += lb->F_311;
  la->F_320 += lb->F_320;
  la->F_401 += lb->F_401;
  la->F_410 += lb->F_410;
  la->F_500 += lb->F_500;
#endif
#if SELF_GRAVITY_MULTIPOLE_ORDER > 5
#error "Missing implementation for order >5"
#endif
}

/**
 * @brief Prints the content of a #grav_tensor to stdout.
 *
 * Note: Uses directly printf(), not a call to message().
 *
 * @param l The #grav_tensor to print.
 */
INLINE static void gravity_field_tensors_print(const struct grav_tensor *l) {

  printf("-------------------------\n");
  printf("Interacted: %d\n", l->interacted);
  printf("F_000= %12.5e\n", l->F_000);
#if SELF_GRAVITY_MULTIPOLE_ORDER > 0
  printf("-------------------------\n");
  printf("F_100= %12.5e F_010= %12.5e F_001= %12.5e\n", l->F_100, l->F_010,
         l->F_001);
#endif
#if SELF_GRAVITY_MULTIPOLE_ORDER > 1
  printf("-------------------------\n");
  printf("F_200= %12.5e F_020= %12.5e F_002= %12.5e\n", l->F_200, l->F_020,
         l->F_002);
  printf("F_110= %12.5e F_101= %12.5e F_011= %12.5e\n", l->F_110, l->F_101,
         l->F_011);
#endif
#if SELF_GRAVITY_MULTIPOLE_ORDER > 2
  printf("-------------------------\n");
  printf("F_300= %12.5e F_030= %12.5e F_003= %12.5e\n", l->F_300, l->F_030,
         l->F_003);
  printf("F_210= %12.5e F_201= %12.5e F_120= %12.5e\n", l->F_210, l->F_201,
         l->F_120);
  printf("F_021= %12.5e F_102= %12.5e F_012= %12.5e\n", l->F_021, l->F_102,
         l->F_012);
  printf("F_111= %12.5e\n", l->F_111);
#endif
#if SELF_GRAVITY_MULTIPOLE_ORDER > 3
  printf("-------------------------\n");
  printf("F_400= %12.5e F_040= %12.5e F_004= %12.5e\n", l->F_400, l->F_040,
         l->F_004);
  printf("F_310= %12.5e F_301= %12.5e F_130= %12.5e\n", l->F_310, l->F_301,
         l->F_130);
  printf("F_031= %12.5e F_103= %12.5e F_013= %12.5e\n", l->F_031, l->F_103,
         l->F_013);
  printf("F_220= %12.5e F_202= %12.5e F_022= %12.5e\n", l->F_220, l->F_202,
         l->F_022);
  printf("F_211= %12.5e F_121= %12.5e F_112= %12.5e\n", l->F_211, l->F_121,
         l->F_112);
#endif
  printf("-------------------------\n");
#if SELF_GRAVITY_MULTIPOLE_ORDER > 5
#error "Missing implementation for order >5"
#endif
}

/**
 * @brief Zeroes all the fields of a multipole.
 *
 * @param m The multipole
 */
INLINE static void gravity_multipole_init(struct multipole *m) {

  bzero(m, sizeof(struct multipole));
}

/**
 * @brief Prints the content of a #multipole to stdout.
 *
 * Note: Uses directly printf(), not a call to message().
 *
 * @param m The #multipole to print.
 */
INLINE static void gravity_multipole_print(const struct multipole *m) {

  printf("eps_max = %12.5e\n", m->max_softening);
  printf("Vel= [%12.5e %12.5e %12.5e]\n", m->vel[0], m->vel[1], m->vel[2]);
  printf("-------------------------\n");
  printf("M_000= %12.5e\n", m->M_000);
#if SELF_GRAVITY_MULTIPOLE_ORDER > 0
  printf("-------------------------\n");
  printf("M_100= %12.5e M_010= %12.5e M_001= %12.5e\n", m->M_100, m->M_010,
         m->M_001);
#endif
#if SELF_GRAVITY_MULTIPOLE_ORDER > 1
  printf("-------------------------\n");
  printf("M_200= %12.5e M_020= %12.5e M_002= %12.5e\n", m->M_200, m->M_020,
         m->M_002);
  printf("M_110= %12.5e M_101= %12.5e M_011= %12.5e\n", m->M_110, m->M_101,
         m->M_011);
#endif
#if SELF_GRAVITY_MULTIPOLE_ORDER > 2
  printf("-------------------------\n");
  printf("M_300= %12.5e M_030= %12.5e M_003= %12.5e\n", m->M_300, m->M_030,
         m->M_003);
  printf("M_210= %12.5e M_201= %12.5e M_120= %12.5e\n", m->M_210, m->M_201,
         m->M_120);
  printf("M_021= %12.5e M_102= %12.5e M_012= %12.5e\n", m->M_021, m->M_102,
         m->M_012);
  printf("M_111= %12.5e\n", m->M_111);
#endif
#if SELF_GRAVITY_MULTIPOLE_ORDER > 3
  printf("-------------------------\n");
  printf("M_400= %12.5e M_040= %12.5e M_004= %12.5e\n", m->M_400, m->M_040,
         m->M_004);
  printf("M_310= %12.5e M_301= %12.5e M_130= %12.5e\n", m->M_310, m->M_301,
         m->M_130);
  printf("M_031= %12.5e M_103= %12.5e M_013= %12.5e\n", m->M_031, m->M_103,
         m->M_013);
  printf("M_220= %12.5e M_202= %12.5e M_022= %12.5e\n", m->M_220, m->M_202,
         m->M_022);
  printf("M_211= %12.5e M_121= %12.5e M_112= %12.5e\n", m->M_211, m->M_121,
         m->M_112);
#endif
  printf("-------------------------\n");
#if SELF_GRAVITY_MULTIPOLE_ORDER > 5
#error "Missing implementation for order >5"
#endif
}

/**
 * @brief Adds a #multipole to another one (i.e. does ma += mb).
 *
 * @param ma The multipole to add to.
 * @param mb The multipole to add.
 */
INLINE static void gravity_multipole_add(struct multipole *restrict ma,
                                         const struct multipole *restrict mb) {

  /* Maximum of both softenings */
  ma->max_softening = max(ma->max_softening, mb->max_softening);

  /* Add 0th order term */
  ma->M_000 += mb->M_000;

#if SELF_GRAVITY_MULTIPOLE_ORDER > 0
  /* Add 1st order terms */
  ma->M_100 += mb->M_100;
  ma->M_010 += mb->M_010;
  ma->M_001 += mb->M_001;
#endif
#if SELF_GRAVITY_MULTIPOLE_ORDER > 1
  /* Add 2nd order terms */
  ma->M_200 += mb->M_200;
  ma->M_020 += mb->M_020;
  ma->M_002 += mb->M_002;
  ma->M_110 += mb->M_110;
  ma->M_101 += mb->M_101;
  ma->M_011 += mb->M_011;
#endif
#if SELF_GRAVITY_MULTIPOLE_ORDER > 2
  /* Add 3rd order terms */
  ma->M_300 += mb->M_300;
  ma->M_030 += mb->M_030;
  ma->M_003 += mb->M_003;
  ma->M_210 += mb->M_210;
  ma->M_201 += mb->M_201;
  ma->M_120 += mb->M_120;
  ma->M_021 += mb->M_021;
  ma->M_102 += mb->M_102;
  ma->M_012 += mb->M_012;
  ma->M_111 += mb->M_111;
#endif
#if SELF_GRAVITY_MULTIPOLE_ORDER > 3
  /* Add 4th order terms */
  ma->M_400 += mb->M_400;
  ma->M_040 += mb->M_040;
  ma->M_004 += mb->M_004;
  ma->M_310 += mb->M_310;
  ma->M_301 += mb->M_301;
  ma->M_130 += mb->M_130;
  ma->M_031 += mb->M_031;
  ma->M_103 += mb->M_103;
  ma->M_013 += mb->M_013;
  ma->M_220 += mb->M_220;
  ma->M_202 += mb->M_202;
  ma->M_022 += mb->M_022;
  ma->M_211 += mb->M_211;
  ma->M_121 += mb->M_121;
  ma->M_112 += mb->M_112;
#endif
#if SELF_GRAVITY_MULTIPOLE_ORDER > 4
  /* 5th order terms */
  ma->M_005 += mb->M_005;
  ma->M_014 += mb->M_014;
  ma->M_023 += mb->M_023;
  ma->M_032 += mb->M_032;
  ma->M_041 += mb->M_041;
  ma->M_050 += mb->M_050;
  ma->M_104 += mb->M_104;
  ma->M_113 += mb->M_113;
  ma->M_122 += mb->M_122;
  ma->M_131 += mb->M_131;
  ma->M_140 += mb->M_140;
  ma->M_203 += mb->M_203;
  ma->M_212 += mb->M_212;
  ma->M_221 += mb->M_221;
  ma->M_230 += mb->M_230;
  ma->M_302 += mb->M_302;
  ma->M_311 += mb->M_311;
  ma->M_320 += mb->M_320;
  ma->M_401 += mb->M_401;
  ma->M_410 += mb->M_410;
  ma->M_500 += mb->M_500;
#endif
#if SELF_GRAVITY_MULTIPOLE_ORDER > 5
#error "Missing implementation for order >5"
#endif

#ifdef SWIFT_DEBUG_CHECKS
  ma->num_gpart += mb->num_gpart;
#endif
}

/**
 * @brief Verifies whether two #multipole's are equal or not.
 *
 * @param ga The first #multipole.
 * @param gb The second #multipole.
 * @param tolerance The maximal allowed relative difference for the fields.
 * @return 1 if the multipoles are equal, 0 otherwise
 */
INLINE static int gravity_multipole_equal(const struct gravity_tensors *ga,
                                          const struct gravity_tensors *gb,
                                          double tolerance) {

  /* Check CoM */
  if (fabs(ga->CoM[0] - gb->CoM[0]) / fabs(ga->CoM[0] + gb->CoM[0]) >
      tolerance) {
    message("CoM[0] different");
    return 0;
  }
  if (fabs(ga->CoM[1] - gb->CoM[1]) / fabs(ga->CoM[1] + gb->CoM[1]) >
      tolerance) {
    message("CoM[1] different");
    return 0;
  }
  if (fabs(ga->CoM[2] - gb->CoM[2]) / fabs(ga->CoM[2] + gb->CoM[2]) >
      tolerance) {
    message("CoM[2] different");
    return 0;
  }

  /* Helper pointers */
  const struct multipole *ma = &ga->m_pole;
  const struct multipole *mb = &gb->m_pole;

  const double v2 = ma->vel[0] * ma->vel[0] + ma->vel[1] * ma->vel[1] +
                    ma->vel[2] * ma->vel[2];

  /* Check maximal softening */
  if (fabsf(ma->max_softening - mb->max_softening) /
          fabsf(ma->max_softening + mb->max_softening) >
      tolerance) {
    message("max softening different!");
    return 0;
  }

  /* Check bulk velocity (if non-zero and component > 1% of norm)*/
  if (fabsf(ma->vel[0] + mb->vel[0]) > 1e-10 &&
      (ma->vel[0] * ma->vel[0]) > 0.0001 * v2 &&
      fabsf(ma->vel[0] - mb->vel[0]) / fabsf(ma->vel[0] + mb->vel[0]) >
          tolerance) {
    message("v[0] different");
    return 0;
  }
  if (fabsf(ma->vel[1] + mb->vel[1]) > 1e-10 &&
      (ma->vel[1] * ma->vel[1]) > 0.0001 * v2 &&
      fabsf(ma->vel[1] - mb->vel[1]) / fabsf(ma->vel[1] + mb->vel[1]) >
          tolerance) {
    message("v[1] different");
    return 0;
  }
  if (fabsf(ma->vel[2] + mb->vel[2]) > 1e-10 &&
      (ma->vel[2] * ma->vel[2]) > 0.0001 * v2 &&
      fabsf(ma->vel[2] - mb->vel[2]) / fabsf(ma->vel[2] + mb->vel[2]) >
          tolerance) {
    message("v[2] different");
    return 0;
  }

  /* Manhattan Norm of 0th order terms */
  const float order0_norm = fabsf(ma->M_000) + fabsf(mb->M_000);

  /* Compare 0th order terms above 1% of norm */
  if (fabsf(ma->M_000 + mb->M_000) > 0.01f * order0_norm &&
      fabsf(ma->M_000 - mb->M_000) / fabsf(ma->M_000 + mb->M_000) > tolerance) {
    message("M_000 term different");
    return 0;
  }
#if SELF_GRAVITY_MULTIPOLE_ORDER > 0
  /* Manhattan Norm of 1st order terms */
  const float order1_norm = fabsf(ma->M_001) + fabsf(mb->M_001) +
                            fabsf(ma->M_010) + fabsf(mb->M_010) +
                            fabsf(ma->M_100) + fabsf(mb->M_100);

  /* Compare 1st order terms above 1% of norm */
  if (fabsf(ma->M_001 + mb->M_001) > 0.01f * order1_norm &&
      fabsf(ma->M_001 - mb->M_001) / fabsf(ma->M_001 + mb->M_001) > tolerance) {
    message("M_001 term different");
    return 0;
  }
  if (fabsf(ma->M_010 + mb->M_010) > 0.01f * order1_norm &&
      fabsf(ma->M_010 - mb->M_010) / fabsf(ma->M_010 + mb->M_010) > tolerance) {
    message("M_010 term different");
    return 0;
  }
  if (fabsf(ma->M_100 + mb->M_100) > 0.01f * order1_norm &&
      fabsf(ma->M_100 - mb->M_100) / fabsf(ma->M_100 + mb->M_100) > tolerance) {
    message("M_100 term different");
    return 0;
  }
#endif
#if SELF_GRAVITY_MULTIPOLE_ORDER > 1
  /* Manhattan Norm of 2nd order terms */
  const float order2_norm =
      fabsf(ma->M_002) + fabsf(mb->M_002) + fabsf(ma->M_011) +
      fabsf(mb->M_011) + fabsf(ma->M_020) + fabsf(mb->M_020) +
      fabsf(ma->M_101) + fabsf(mb->M_101) + fabsf(ma->M_110) +
      fabsf(mb->M_110) + fabsf(ma->M_200) + fabsf(mb->M_200);

  /* Compare 2nd order terms above 1% of norm */
  if (fabsf(ma->M_002 + mb->M_002) > 0.01f * order2_norm &&
      fabsf(ma->M_002 - mb->M_002) / fabsf(ma->M_002 + mb->M_002) > tolerance) {
    message("M_002 term different");
    return 0;
  }
  if (fabsf(ma->M_011 + mb->M_011) > 0.01f * order2_norm &&
      fabsf(ma->M_011 - mb->M_011) / fabsf(ma->M_011 + mb->M_011) > tolerance) {
    message("M_011 term different");
    return 0;
  }
  if (fabsf(ma->M_020 + mb->M_020) > 0.01f * order2_norm &&
      fabsf(ma->M_020 - mb->M_020) / fabsf(ma->M_020 + mb->M_020) > tolerance) {
    message("M_020 term different");
    return 0;
  }
  if (fabsf(ma->M_101 + mb->M_101) > 0.01f * order2_norm &&
      fabsf(ma->M_101 - mb->M_101) / fabsf(ma->M_101 + mb->M_101) > tolerance) {
    message("M_101 term different");
    return 0;
  }
  if (fabsf(ma->M_110 + mb->M_110) > 0.01f * order2_norm &&
      fabsf(ma->M_110 - mb->M_110) / fabsf(ma->M_110 + mb->M_110) > tolerance) {
    message("M_110 term different");
    return 0;
  }
  if (fabsf(ma->M_200 + mb->M_200) > 0.01f * order2_norm &&
      fabsf(ma->M_200 - mb->M_200) / fabsf(ma->M_200 + mb->M_200) > tolerance) {
    message("M_200 term different");
    return 0;
  }
#endif
  tolerance *= 10.;
#if SELF_GRAVITY_MULTIPOLE_ORDER > 2
  /* Manhattan Norm of 3rd order terms */
  const float order3_norm =
      fabsf(ma->M_003) + fabsf(mb->M_003) + fabsf(ma->M_012) +
      fabsf(mb->M_012) + fabsf(ma->M_021) + fabsf(mb->M_021) +
      fabsf(ma->M_030) + fabsf(mb->M_030) + fabsf(ma->M_102) +
      fabsf(mb->M_102) + fabsf(ma->M_111) + fabsf(mb->M_111) +
      fabsf(ma->M_120) + fabsf(mb->M_120) + fabsf(ma->M_201) +
      fabsf(mb->M_201) + fabsf(ma->M_210) + fabsf(mb->M_210) +
      fabsf(ma->M_300) + fabsf(mb->M_300);

  /* Compare 3rd order terms above 1% of norm */
  if (fabsf(ma->M_003 + mb->M_003) > 0.01f * order3_norm &&
      fabsf(ma->M_003 - mb->M_003) / fabsf(ma->M_003 + mb->M_003) > tolerance) {
    message("M_003 term different");
    return 0;
  }
  if (fabsf(ma->M_012 + mb->M_012) > 0.01f * order3_norm &&
      fabsf(ma->M_012 - mb->M_012) / fabsf(ma->M_012 + mb->M_012) > tolerance) {
    message("M_012 term different");
    return 0;
  }
  if (fabsf(ma->M_021 + mb->M_021) > 0.01f * order3_norm &&
      fabsf(ma->M_021 - mb->M_021) / fabsf(ma->M_021 + mb->M_021) > tolerance) {
    message("M_021 term different");
    return 0;
  }
  if (fabsf(ma->M_030 + mb->M_030) > 0.01f * order3_norm &&
      fabsf(ma->M_030 - mb->M_030) / fabsf(ma->M_030 + mb->M_030) > tolerance) {
    message("M_030 term different");
    return 0;
  }
  if (fabsf(ma->M_102 + mb->M_102) > 0.01f * order3_norm &&
      fabsf(ma->M_102 - mb->M_102) / fabsf(ma->M_102 + mb->M_102) > tolerance) {
    message("M_102 term different");
    return 0;
  }
  if (fabsf(ma->M_111 + mb->M_111) > 0.01f * order3_norm &&
      fabsf(ma->M_111 - mb->M_111) / fabsf(ma->M_111 + mb->M_111) > tolerance) {
    message("M_111 term different");
    return 0;
  }
  if (fabsf(ma->M_120 + mb->M_120) > 0.01f * order3_norm &&
      fabsf(ma->M_120 - mb->M_120) / fabsf(ma->M_120 + mb->M_120) > tolerance) {
    message("M_120 term different");
    return 0;
  }
  if (fabsf(ma->M_201 + mb->M_201) > 0.01f * order3_norm &&
      fabsf(ma->M_201 - mb->M_201) / fabsf(ma->M_201 + mb->M_201) > tolerance) {
    message("M_201 term different");
    return 0;
  }
  if (fabsf(ma->M_210 + mb->M_210) > 0.01f * order3_norm &&
      fabsf(ma->M_210 - mb->M_210) / fabsf(ma->M_210 + mb->M_210) > tolerance) {
    message("M_210 term different");
    return 0;
  }
  if (fabsf(ma->M_300 + mb->M_300) > 0.01f * order3_norm &&
      fabsf(ma->M_300 - mb->M_300) / fabsf(ma->M_300 + mb->M_300) > tolerance) {
    message("M_300 term different");
    return 0;
  }
#endif
#if SELF_GRAVITY_MULTIPOLE_ORDER > 3
  /* Manhattan Norm of 4th order terms */
  const float order4_norm =
      fabsf(ma->M_004) + fabsf(mb->M_004) + fabsf(ma->M_013) +
      fabsf(mb->M_013) + fabsf(ma->M_022) + fabsf(mb->M_022) +
      fabsf(ma->M_031) + fabsf(mb->M_031) + fabsf(ma->M_040) +
      fabsf(mb->M_040) + fabsf(ma->M_103) + fabsf(mb->M_103) +
      fabsf(ma->M_112) + fabsf(mb->M_112) + fabsf(ma->M_121) +
      fabsf(mb->M_121) + fabsf(ma->M_130) + fabsf(mb->M_130) +
      fabsf(ma->M_202) + fabsf(mb->M_202) + fabsf(ma->M_211) +
      fabsf(mb->M_211) + fabsf(ma->M_220) + fabsf(mb->M_220) +
      fabsf(ma->M_301) + fabsf(mb->M_301) + fabsf(ma->M_310) +
      fabsf(mb->M_310) + fabsf(ma->M_400) + fabsf(mb->M_400);

  /* Compare 4th order terms above 1% of norm */
  if (fabsf(ma->M_004 + mb->M_004) > 0.01f * order4_norm &&
      fabsf(ma->M_004 - mb->M_004) / fabsf(ma->M_004 + mb->M_004) > tolerance) {
    message("M_004 term different");
    return 0;
  }
  if (fabsf(ma->M_013 + mb->M_013) > 0.01f * order4_norm &&
      fabsf(ma->M_013 - mb->M_013) / fabsf(ma->M_013 + mb->M_013) > tolerance) {
    message("M_013 term different");
    return 0;
  }
  if (fabsf(ma->M_022 + mb->M_022) > 0.01f * order4_norm &&
      fabsf(ma->M_022 - mb->M_022) / fabsf(ma->M_022 + mb->M_022) > tolerance) {
    message("M_022 term different");
    return 0;
  }
  if (fabsf(ma->M_031 + mb->M_031) > 0.01f * order4_norm &&
      fabsf(ma->M_031 - mb->M_031) / fabsf(ma->M_031 + mb->M_031) > tolerance) {
    message("M_031 term different");
    return 0;
  }
  if (fabsf(ma->M_040 + mb->M_040) > 0.01f * order4_norm &&
      fabsf(ma->M_040 - mb->M_040) / fabsf(ma->M_040 + mb->M_040) > tolerance) {
    message("M_040 term different");
    return 0;
  }
  if (fabsf(ma->M_103 + mb->M_103) > 0.01f * order4_norm &&
      fabsf(ma->M_103 - mb->M_103) / fabsf(ma->M_103 + mb->M_103) > tolerance) {
    message("M_103 term different");
    return 0;
  }
  if (fabsf(ma->M_112 + mb->M_112) > 0.01f * order4_norm &&
      fabsf(ma->M_112 - mb->M_112) / fabsf(ma->M_112 + mb->M_112) > tolerance) {
    message("M_112 term different");
    return 0;
  }
  if (fabsf(ma->M_121 + mb->M_121) > 0.01f * order4_norm &&
      fabsf(ma->M_121 - mb->M_121) / fabsf(ma->M_121 + mb->M_121) > tolerance) {
    message("M_121 term different");
    return 0;
  }
  if (fabsf(ma->M_130 + mb->M_130) > 0.01f * order4_norm &&
      fabsf(ma->M_130 - mb->M_130) / fabsf(ma->M_130 + mb->M_130) > tolerance) {
    message("M_130 term different");
    return 0;
  }
  if (fabsf(ma->M_202 + mb->M_202) > 0.01f * order4_norm &&
      fabsf(ma->M_202 - mb->M_202) / fabsf(ma->M_202 + mb->M_202) > tolerance) {
    message("M_202 term different");
    return 0;
  }
  if (fabsf(ma->M_211 + mb->M_211) > 0.01f * order4_norm &&
      fabsf(ma->M_211 - mb->M_211) / fabsf(ma->M_211 + mb->M_211) > tolerance) {
    message("M_211 term different");
    return 0;
  }
  if (fabsf(ma->M_220 + mb->M_220) > 0.01f * order4_norm &&
      fabsf(ma->M_220 - mb->M_220) / fabsf(ma->M_220 + mb->M_220) > tolerance) {
    message("M_220 term different");
    return 0;
  }
  if (fabsf(ma->M_301 + mb->M_301) > 0.01f * order4_norm &&
      fabsf(ma->M_301 - mb->M_301) / fabsf(ma->M_301 + mb->M_301) > tolerance) {
    message("M_301 term different");
    return 0;
  }
  if (fabsf(ma->M_310 + mb->M_310) > 0.01f * order4_norm &&
      fabsf(ma->M_310 - mb->M_310) / fabsf(ma->M_310 + mb->M_310) > tolerance) {
    message("M_310 term different");
    return 0;
  }
  if (fabsf(ma->M_400 + mb->M_400) > 0.01f * order4_norm &&
      fabsf(ma->M_400 - mb->M_400) / fabsf(ma->M_400 + mb->M_400) > tolerance) {
    message("M_400 term different");
    return 0;
  }
#endif
#if SELF_GRAVITY_MULTIPOLE_ORDER > 4
  /* Manhattan Norm of 5th order terms */
  const float order5_norm =
      fabsf(ma->M_005) + fabsf(mb->M_005) + fabsf(ma->M_014) +
      fabsf(mb->M_014) + fabsf(ma->M_023) + fabsf(mb->M_023) +
      fabsf(ma->M_032) + fabsf(mb->M_032) + fabsf(ma->M_041) +
      fabsf(mb->M_041) + fabsf(ma->M_050) + fabsf(mb->M_050) +
      fabsf(ma->M_104) + fabsf(mb->M_104) + fabsf(ma->M_113) +
      fabsf(mb->M_113) + fabsf(ma->M_122) + fabsf(mb->M_122) +
      fabsf(ma->M_131) + fabsf(mb->M_131) + fabsf(ma->M_140) +
      fabsf(mb->M_140) + fabsf(ma->M_203) + fabsf(mb->M_203) +
      fabsf(ma->M_212) + fabsf(mb->M_212) + fabsf(ma->M_221) +
      fabsf(mb->M_221) + fabsf(ma->M_230) + fabsf(mb->M_230) +
      fabsf(ma->M_302) + fabsf(mb->M_302) + fabsf(ma->M_311) +
      fabsf(mb->M_311) + fabsf(ma->M_320) + fabsf(mb->M_320) +
      fabsf(ma->M_401) + fabsf(mb->M_401) + fabsf(ma->M_410) +
      fabsf(mb->M_410) + fabsf(ma->M_500) + fabsf(mb->M_500);

  /* Compare 5th order terms above 1% of norm */
  if (fabsf(ma->M_005 + mb->M_005) > 0.01f * order5_norm &&
      fabsf(ma->M_005 - mb->M_005) / fabsf(ma->M_005 + mb->M_005) > tolerance) {
    message("M_005 term different");
    return 0;
  }
  if (fabsf(ma->M_014 + mb->M_014) > 0.01f * order5_norm &&
      fabsf(ma->M_014 - mb->M_014) / fabsf(ma->M_014 + mb->M_014) > tolerance) {
    message("M_014 term different");
    return 0;
  }
  if (fabsf(ma->M_023 + mb->M_023) > 0.01f * order5_norm &&
      fabsf(ma->M_023 - mb->M_023) / fabsf(ma->M_023 + mb->M_023) > tolerance) {
    message("M_023 term different");
    return 0;
  }
  if (fabsf(ma->M_032 + mb->M_032) > 0.01f * order5_norm &&
      fabsf(ma->M_032 - mb->M_032) / fabsf(ma->M_032 + mb->M_032) > tolerance) {
    message("M_032 term different");
    return 0;
  }
  if (fabsf(ma->M_041 + mb->M_041) > 0.01f * order5_norm &&
      fabsf(ma->M_041 - mb->M_041) / fabsf(ma->M_041 + mb->M_041) > tolerance) {
    message("M_041 term different");
    return 0;
  }
  if (fabsf(ma->M_050 + mb->M_050) > 0.01f * order5_norm &&
      fabsf(ma->M_050 - mb->M_050) / fabsf(ma->M_050 + mb->M_050) > tolerance) {
    message("M_050 term different");
    return 0;
  }
  if (fabsf(ma->M_104 + mb->M_104) > 0.01f * order5_norm &&
      fabsf(ma->M_104 - mb->M_104) / fabsf(ma->M_104 + mb->M_104) > tolerance) {
    message("M_104 term different");
    return 0;
  }
  if (fabsf(ma->M_113 + mb->M_113) > 0.01f * order5_norm &&
      fabsf(ma->M_113 - mb->M_113) / fabsf(ma->M_113 + mb->M_113) > tolerance) {
    message("M_113 term different");
    return 0;
  }
  if (fabsf(ma->M_122 + mb->M_122) > 0.01f * order5_norm &&
      fabsf(ma->M_122 - mb->M_122) / fabsf(ma->M_122 + mb->M_122) > tolerance) {
    message("M_122 term different");
    return 0;
  }
  if (fabsf(ma->M_131 + mb->M_131) > 0.01f * order5_norm &&
      fabsf(ma->M_131 - mb->M_131) / fabsf(ma->M_131 + mb->M_131) > tolerance) {
    message("M_131 term different");
    return 0;
  }
  if (fabsf(ma->M_140 + mb->M_140) > 0.01f * order5_norm &&
      fabsf(ma->M_140 - mb->M_140) / fabsf(ma->M_140 + mb->M_140) > tolerance) {
    message("M_140 term different");
    return 0;
  }
  if (fabsf(ma->M_203 + mb->M_203) > 0.01f * order5_norm &&
      fabsf(ma->M_203 - mb->M_203) / fabsf(ma->M_203 + mb->M_203) > tolerance) {
    message("M_203 term different");
    return 0;
  }
  if (fabsf(ma->M_212 + mb->M_212) > 0.01f * order5_norm &&
      fabsf(ma->M_212 - mb->M_212) / fabsf(ma->M_212 + mb->M_212) > tolerance) {
    message("M_212 term different");
    return 0;
  }
  if (fabsf(ma->M_221 + mb->M_221) > 0.01f * order5_norm &&
      fabsf(ma->M_221 - mb->M_221) / fabsf(ma->M_221 + mb->M_221) > tolerance) {
    message("M_221 term different");
    return 0;
  }
  if (fabsf(ma->M_230 + mb->M_230) > 0.01f * order5_norm &&
      fabsf(ma->M_230 - mb->M_230) / fabsf(ma->M_230 + mb->M_230) > tolerance) {
    message("M_230 term different");
    return 0;
  }
  if (fabsf(ma->M_302 + mb->M_302) > 0.01f * order5_norm &&
      fabsf(ma->M_302 - mb->M_302) / fabsf(ma->M_302 + mb->M_302) > tolerance) {
    message("M_302 term different");
    return 0;
  }
  if (fabsf(ma->M_311 + mb->M_311) > 0.01f * order5_norm &&
      fabsf(ma->M_311 - mb->M_311) / fabsf(ma->M_311 + mb->M_311) > tolerance) {
    message("M_311 term different");
    return 0;