#include <assert.h>
#include "qpms_specfunc.h"
#include <stdlib.h>
#include <stddef.h>
#include <string.h>
#include "kahansum.h"
#include <gsl/gsl_sf_bessel.h>
#include <complex.h>
#include "qpms_error.h"
#include <camos.h>
#include <math.h>

#ifndef M_LN2
#define M_LN2   0.69314718055994530942  /* log_e 2 */
#endif

static inline complex double ipow(int x) {
  return cpow(I,x);
}

#if 0
// Inspired by scipy/special/_spherical_bessel.pxd
static inline complex double spherical_jn(qpms_l_t l, complex double z) {
  if (isnan(creal(z)) || isnan(cimag(z))) return NAN+I*NAN;
  if (l < 0) QPMS_WTF;
  if (fpclassify(creal(z)) == FP_INFINITE) 
    if(0 == cimag(z))
      return 0;
    else
      return INFINITY + I * INFINITY;
  if (z == 0)
    if (l == 0) return 1;
    else return 0;
  return csqrt(M_PI_2/z) * zbesj(l + .5, z);
}

static inline complex double spherical_yn(qpms_l_t l, complex double z) {
  if (isnan(creal(z)) || isnan(cimag(z))) return NAN+I*NAN;
  if (l < 0) QPMS_WTF;
  if (fpclassify(creal(z)) == FP_INFINITE) 
    if(0 == cimag(z))
      return 0;
    else
      return INFINITY + I * INFINITY;
  if (z == 0)
    return NAN;
  return csqrt(M_PI_2/z) * zbesy(l + .5, z);
}
#endif 

// There is a big issue with gsl's precision of spherical bessel function; these have to be implemented differently
qpms_errno_t qpms_sph_bessel_realx_fill(qpms_bessel_t typ, qpms_l_t lmax, double x, complex double *result_array) {
  int retval;
  double tmparr[lmax+1];
  switch(typ) {
    case QPMS_BESSEL_REGULAR:
      retval = gsl_sf_bessel_jl_steed_array(lmax, x, tmparr);
      for (int l = 0; l <= lmax; ++l) result_array[l] = tmparr[l];
      return retval;
      break;
    case QPMS_BESSEL_SINGULAR: //FIXME: is this precise enough? Would it be better to do it one-by-one?
      retval = gsl_sf_bessel_yl_array(lmax,x,tmparr);
      for (int l = 0; l <= lmax; ++l) result_array[l] = tmparr[l];
      return retval;
      break;
    case QPMS_HANKEL_PLUS:
    case QPMS_HANKEL_MINUS:
      retval = gsl_sf_bessel_jl_steed_array(lmax, x, tmparr);
      for (int l = 0; l <= lmax; ++l) result_array[l] = tmparr[l];
      if(retval) return retval;
      retval = gsl_sf_bessel_yl_array(lmax, x, tmparr);
      if (typ==QPMS_HANKEL_PLUS)
        for (int l = 0; l <= lmax; ++l) result_array[l] += I * tmparr[l];
      else 
        for (int l = 0; l <= lmax; ++l) result_array[l] +=-I * tmparr[l];
      return retval;
      break;
    default:
      abort();
      //return GSL_EDOM;
  }
  assert(0);
}

// TODO DOC
qpms_errno_t qpms_sph_bessel_fill(qpms_bessel_t typ, qpms_l_t lmax, complex double x, complex double *res) {
  if(!cimag(x))
    return qpms_sph_bessel_realx_fill(typ, lmax, creal(x), res);
  else if (isnan(creal(x)) || isnan(cimag(x))) 
    for(qpms_l_t l = 0; l <= lmax; ++l) res[l] = NAN + I*NAN;
  else if (lmax < 0) QPMS_WTF;
  else if (fpclassify(creal(x)) == FP_INFINITE) 
    for(qpms_l_t l = 0; l <= lmax; ++l) res[l] = INFINITY + I * INFINITY;
  else {
try_again: ;
    int retry_counter = 0;
    const double zr = creal(x), zi = cimag(x), fnu = 0.5;
    const int n = lmax + 1, kode = 1 /* No exponential scaling */;
    double cyr[n], cyi[n];
    int ierr, nz;
    unsigned int kindchar; // Only for error output
    const complex double prefac = csqrt(M_PI_2/x);
    switch(typ) {
      case QPMS_BESSEL_REGULAR:
        kindchar = 'j';
        ierr = camos_zbesj(zr, zi, fnu, kode, n, cyr, cyi, &nz);
        break;
      case QPMS_BESSEL_SINGULAR:
        kindchar = 'y';
        {
          double cwrkr[lmax + 1], cwrki[lmax + 1];
          ierr = camos_zbesy(zr, zi, fnu, kode, n, cyr, cyi, &nz, cwrkr, cwrki);
        }
        break;
      case QPMS_HANKEL_PLUS:
      case QPMS_HANKEL_MINUS: 
        kindchar = 'h';
        {
          const int m = (typ == QPMS_HANKEL_PLUS) ? 1 : 2;
          ierr = camos_zbesh(zr, zi, fnu, kode, m, n, cyr, cyi, &nz);
        }
        break;
      default:
        QPMS_WTF;
    }
    // TODO check for underflows? (nz != 0)
    if (ierr == 0 || ierr == 3) {
      for (qpms_l_t l = 0; l <= lmax; ++l)
        res[l] = prefac * (cyr[l] + I * cyi[l]);
      if (ierr == 3) 
        QPMS_WARN("Amos's zbes%c computation done but losses of significance "
            "by argument reduction produce less than half of machine accuracy.", 
            kindchar);
      return QPMS_SUCCESS; //TODO maybe something else if ierr == 3
    }
    else {
      if (retry_counter < 5) {
        QPMS_WARN("Amos's zbes%c failed with ierr == %d (lMax = %d, x = %+.16g%+.16gi). Retrying.\n",
           kindchar, (int) ierr, lmax, creal(x), cimag(x));
        ++retry_counter;
        goto try_again;
      } else QPMS_PR_ERROR("Amos's zbes%c failed with ierr == %d (lMax = %d, x = %+.16g%+.16gi).",
           kindchar, (int) ierr, lmax, creal(x), cimag(x));
    }
  }
  return QPMS_SUCCESS;
}

static inline ptrdiff_t akn_index(qpms_l_t n, qpms_l_t k) {
  assert(k <= n);
  return ((ptrdiff_t) n + 1) * n / 2 + k;
}
static inline ptrdiff_t bkn_index(qpms_l_t n, qpms_l_t k) {
  assert(k <= n+1);
  return ((ptrdiff_t) n + 2) * (n + 1) / 2 - 1 + k;
}

static inline qpms_errno_t qpms_sbessel_calculator_ensure_lMax(qpms_sbessel_calculator_t *c, qpms_l_t lMax) {
  if (lMax <= c->lMax)
    return QPMS_SUCCESS;
  else {
    if ( NULL == (c->akn = realloc(c->akn, sizeof(double) * akn_index(lMax + 2, 0))))
      abort();
    //if ( NULL == (c->bkn = realloc(c->bkn, sizeof(complex double) * bkn_index(lMax + 1, 0))))
    //	abort();
    for(qpms_l_t n = c->lMax+1; n <= lMax + 1; ++n)
      for(qpms_l_t k = 0; k <= n; ++k)
        c->akn[akn_index(n,k)] = exp(lgamma(n + k + 1) - k*M_LN2 - lgamma(k + 1) - lgamma(n - k + 1));
    // ... TODO derivace
    c->lMax = lMax;
    return QPMS_SUCCESS;
  }
}

complex double qpms_sbessel_calc_h1(qpms_sbessel_calculator_t *c, qpms_l_t n, complex double x) {
  if(QPMS_SUCCESS != qpms_sbessel_calculator_ensure_lMax(c, n))
    abort();
  complex double z = I/x; 
  complex double result = 0;
  for (qpms_l_t k = n; k >= 0; --k) 
    // can we use fma for complex?
    //result = fma(result, z, c->akn(n, k));
    result = result * z + c->akn[akn_index(n,k)];
  result *= z * ipow(-n-2) * cexp(I * x);
  return result;
}

qpms_errno_t qpms_sbessel_calc_h1_fill(qpms_sbessel_calculator_t * const c,
    const qpms_l_t lMax, const complex double x, complex double * const target) {
  if(QPMS_SUCCESS != qpms_sbessel_calculator_ensure_lMax(c, lMax))
    abort();
  memset(target, 0, sizeof(complex double) * lMax);
  complex double kahancomp[lMax];
  memset(kahancomp, 0, sizeof(complex double) * lMax);
  for(qpms_l_t k = 0; k <= lMax; ++k){
    double xp = cpow(x, -k-1);
    for(qpms_l_t l = k; l <= lMax; ++l)
      ckahanadd(target + l, kahancomp + l, c->akn[akn_index(l,k)] * xp * ipow(k-l-1));
  }
  complex double eix = cexp(I * x);
  for (qpms_l_t l = 0; l <= lMax; ++l)
    target[l] *= eix; 
  return QPMS_SUCCESS;
}

qpms_sbessel_calculator_t *qpms_sbessel_calculator_init() {
  qpms_sbessel_calculator_t *c = malloc(sizeof(qpms_sbessel_calculator_t));
  c->akn = NULL;
  //c->bkn = NULL;
  c->lMax = -1;
  return c;
}

void qpms_sbessel_calculator_pfree(qpms_sbessel_calculator_t *c) {
  if(c->akn) free(c->akn);
  //if(c->bkn) free(c->bkn);
  free(c);
}