/*
Copyright 2016 Ian Jauslin

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

    http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*/

#include "zz_integral.h"


// I for z1-z2
int zz_I(mpfr_t out, mpfr_t p1, mpfr_t p2, mpfr_t q1, mpfr_t q2, mpfr_t F1, mpfr_t F2, mpfr_t t1, mpfr_t t2, mpfr_t phi, mpfr_t W, array_mpfr* tmps1, struct ss_cache cache){
  mpfr_t* tmps;

  // alloc tmps if needed
  array_mpfr_alloc_tmps(9, tmps1);

  tmps=tmps1->values;

  // tmps[0]=alpha1(p1,p2)
  zz_alpha1(tmps[0], p1, p2, cache, tmps[1]);
  // tmps[1]=m(p1,p2)
  zz_m(tmps[1], p1, p2, t2, phi, W, cache, tmps[2]);
  // tmps[2]=alpha1(q1,q2)
  zz_alpha1(tmps[2], q1, q2, cache, tmps[3]);
  // tmps[3]=m(q1,q2)
  zz_m(tmps[3], q1, q2, t2, phi, W, cache, tmps[4]);
  // tmps[4]=alpha1(F1,F2)
  zz_alpha1(tmps[4], F1, F2, cache, tmps[5]);
  // tmps[5]=m(F1,F2)
  zz_m(tmps[5], F1, F2, t2, phi, W, cache, tmps[6]);

  // tmps[6]=zeta(p)
  zz_zeta(tmps[6], tmps[0], t2, phi);
  // tmps[7]=zeta(q)
  zz_zeta(tmps[7], tmps[2], t2, phi);
  // tmps[8]=zeta(F)
  zz_zeta(tmps[8], tmps[4], t2, phi);
  // tmps[6]=Z=zeta(p)+zeta(q)-zeta(F)
  mpfr_add(tmps[6], tmps[6], tmps[7], MPFR_RNDN);
  mpfr_sub(tmps[6], tmps[6], tmps[8], MPFR_RNDN);

  // tmps[0]=xi(p)
  zz_xi(tmps[0], tmps[1], tmps[0], t1, tmps[7]);
  // tmps[2]=xi(q)
  zz_xi(tmps[2], tmps[3], tmps[2], t1, tmps[7]);
  // tmps[4]=xi(F)
  zz_xi(tmps[4], tmps[5], tmps[4], t1, tmps[7]);

  // tmps[1]=m(p)/xi(p)
  zz_mxi(tmps[1], tmps[1], tmps[0]);
  // tmps[3]=m(q)/xi(q)
  zz_mxi(tmps[3], tmps[3], tmps[2]);
  // tmps[5]=m(F)/xi(F)
  zz_mxi(tmps[5], tmps[5], tmps[4]);

  // I=(xip+xiq+xiF)*(mp/xip+mq/xiq-mF/xiF-mp*mq*mF/xip/xiq/xiF)*Z/(Z**2-(xip+xiq+xiF)**2)**2/108
  mpfr_add(tmps[0], tmps[0], tmps[2], MPFR_RNDN);
  mpfr_add(tmps[0], tmps[0], tmps[4], MPFR_RNDN);
  mpfr_add(tmps[2], tmps[1], tmps[3], MPFR_RNDN);
  mpfr_sub(tmps[2], tmps[2], tmps[5], MPFR_RNDN);
  mpfr_mul(tmps[1], tmps[1], tmps[3], MPFR_RNDN);
  mpfr_mul(tmps[1], tmps[1], tmps[5], MPFR_RNDN);
  mpfr_sub(tmps[1], tmps[2], tmps[1], MPFR_RNDN);
  mpfr_mul(tmps[1], tmps[0], tmps[1], MPFR_RNDN);
  mpfr_mul(tmps[1], tmps[1], tmps[6], MPFR_RNDN);
  mpfr_pow_ui(tmps[6], tmps[6], 2, MPFR_RNDN);
  mpfr_pow_ui(tmps[0], tmps[0], 2, MPFR_RNDN);
  mpfr_sub(tmps[0], tmps[6], tmps[0], MPFR_RNDN);
  mpfr_pow_ui(tmps[0], tmps[0], 2, MPFR_RNDN);
  mpfr_div(out, tmps[1], tmps[0], MPFR_RNDN);
  mpfr_div_ui(out, out, 108, MPFR_RNDN);

  return(0);
}


// I for z1+z2
int ZZ_I(mpfr_t out, mpfr_t p1, mpfr_t p2, mpfr_t q1, mpfr_t q2, mpfr_t F1, mpfr_t F2, mpfr_t t1, mpfr_t t2, mpfr_t phi, mpfr_t W, array_mpfr* tmps1, struct ss_cache cache){
  mpfr_t* tmps;

  // alloc tmps if needed
  array_mpfr_alloc_tmps(9, tmps1);

  tmps=tmps1->values;

  // tmps[0]=alpha1(p1,p2)
  zz_alpha1(tmps[0], p1, p2, cache, tmps[1]);
  // tmps[1]=m(p1,p2)
  zz_m(tmps[1], p1, p2, t2, phi, W, cache, tmps[2]);
  // tmps[2]=alpha1(q1,q2)
  zz_alpha1(tmps[2], q1, q2, cache, tmps[3]);
  // tmps[3]=m(q1,q2)
  zz_m(tmps[3], q1, q2, t2, phi, W, cache, tmps[4]);
  // tmps[4]=alpha1(F1,F2)
  zz_alpha1(tmps[4], F1, F2, cache, tmps[5]);
  // tmps[5]=m(F1,F2)
  zz_m(tmps[5], F1, F2, t2, phi, W, cache, tmps[6]);

  // tmps[6]=zeta(p)
  zz_zeta(tmps[6], tmps[0], t2, phi);
  // tmps[7]=zeta(q)
  zz_zeta(tmps[7], tmps[2], t2, phi);
  // tmps[8]=zeta(F)
  zz_zeta(tmps[8], tmps[4], t2, phi);
  // tmps[6]=Z**2=(zeta(p)+zeta(q)-zeta(F))**2
  mpfr_add(tmps[6], tmps[6], tmps[7], MPFR_RNDN);
  mpfr_sub(tmps[6], tmps[6], tmps[8], MPFR_RNDN);
  mpfr_pow_ui(tmps[6], tmps[6], 2, MPFR_RNDN);

  // tmps[0]=xi(p)
  zz_xi(tmps[0], tmps[1], tmps[0], t1, tmps[7]);
  // tmps[2]=xi(q)
  zz_xi(tmps[2], tmps[3], tmps[2], t1, tmps[7]);
  // tmps[4]=xi(F)
  zz_xi(tmps[4], tmps[5], tmps[4], t1, tmps[7]);

  // tmps[1]=m(p)/xi(p)
  zz_mxi(tmps[1], tmps[1], tmps[0]);
  // tmps[3]=m(q)/xi(q)
  zz_mxi(tmps[3], tmps[3], tmps[2]);
  // tmps[5]=m(F)/xi(F)
  zz_mxi(tmps[5], tmps[5], tmps[4]);

  // I=(1-mp*mF/xip/xiF-mq*mF/xiq/xiF+mp*mq/xip/xiq)*(Z**2+(xip+xiq+xiF)**2)/(Z**2-(xip+xiq+xiF)**2)**2/216
  mpfr_add(tmps[0], tmps[0], tmps[2], MPFR_RNDN);
  mpfr_add(tmps[0], tmps[0], tmps[4], MPFR_RNDN);
  mpfr_pow_ui(tmps[0], tmps[0], 2, MPFR_RNDN);
  mpfr_mul(tmps[2], tmps[1], tmps[3], MPFR_RNDN);
  mpfr_mul(tmps[4], tmps[3], tmps[5], MPFR_RNDN);
  mpfr_sub(tmps[2], tmps[2], tmps[4], MPFR_RNDN);
  mpfr_mul(tmps[4], tmps[1], tmps[5], MPFR_RNDN);
  mpfr_sub(tmps[2], tmps[2], tmps[4], MPFR_RNDN);
  mpfr_add_ui(out, tmps[2], 1, MPFR_RNDN);
  mpfr_add(tmps[1], tmps[6], tmps[0], MPFR_RNDN);
  mpfr_mul(out, out, tmps[1], MPFR_RNDN);
  mpfr_sub(tmps[0], tmps[6], tmps[0], MPFR_RNDN);
  mpfr_pow_ui(tmps[0], tmps[0], 2, MPFR_RNDN);
  mpfr_div(out, out, tmps[0], MPFR_RNDN);
  mpfr_div_ui(out, out, 216, MPFR_RNDN);

  return(0);
}

// zeta(k1,k2)
// requires m and alpha1 to be computed beforehand
int zz_zeta(mpfr_t zeta, mpfr_t alpha1, mpfr_t t2, mpfr_t phi){
  mpfr_cos(zeta, phi, MPFR_RNDN);
  mpfr_mul(zeta, zeta, t2, MPFR_RNDN);
  mpfr_mul_ui(zeta, zeta, 2, MPFR_RNDN);
  mpfr_mul(zeta, zeta, alpha1, MPFR_RNDN);
  return(0);
}
// xi(k1,k2)
// requires m and alpha1 to be computed beforehand
// requires one initialized tmp number
int zz_xi(mpfr_t xi, mpfr_t m, mpfr_t alpha1, mpfr_t t1, mpfr_t tmp){
  mpfr_pow_ui(tmp, m, 2, MPFR_RNDN);

  mpfr_mul(xi, alpha1, t1, MPFR_RNDN);
  mpfr_mul(xi, xi, t1, MPFR_RNDN);
  mpfr_mul_ui(xi, xi, 2, MPFR_RNDN);

  mpfr_add(xi, xi, tmp, MPFR_RNDN);
  mpfr_sqrt(xi, xi, MPFR_RNDN);
  return(0);
}
// m(k1,k2)
// requires two initialized tmp numbers
int zz_m(mpfr_t m, mpfr_t k1, mpfr_t k2, mpfr_t t2, mpfr_t phi, mpfr_t W, struct ss_cache cache, mpfr_t tmp1){
  zz_alpha2(m, k1, k2, cache, tmp1);
  mpfr_sin(tmp1, phi, MPFR_RNDN);
  mpfr_mul(m, m, tmp1, MPFR_RNDN);
  mpfr_mul(m, m, t2, MPFR_RNDN);
  mpfr_mul_ui(m, m, 2, MPFR_RNDN);
  mpfr_sub(m, W, m, MPFR_RNDN);
  return(0);
}
// m(k1,k2)/xi(k1,k2)
int zz_mxi(mpfr_t mxi, mpfr_t m, mpfr_t xi){
  // if xi=0, then return 0 (m/xi->0 at pF)
  if(mpfr_cmp_ui(xi,0)==0){
    mpfr_set_ui(mxi, 0, MPFR_RNDN);
    return(0);
  }
  mpfr_div(mxi, m, xi, MPFR_RNDN);

  return(0);
}

// alpha1(k1,k2)
// requires one initialized tmp number
int zz_alpha1(mpfr_t alpha1, mpfr_t k1, mpfr_t k2, struct ss_cache cache, mpfr_t tmp1){
  mpfr_mul(tmp1, k2, cache.pi, MPFR_RNDN);
  mpfr_div_ui(tmp1, tmp1, 3, MPFR_RNDN);
  mpfr_cos(tmp1, tmp1, MPFR_RNDN);
  
  mpfr_mul(alpha1, k1, cache.pi, MPFR_RNDN);
  mpfr_div(alpha1, alpha1, cache.sqrt3, MPFR_RNDN);
  mpfr_cos(alpha1, alpha1, MPFR_RNDN);

  mpfr_add(alpha1, alpha1, tmp1, MPFR_RNDN);
  mpfr_mul(alpha1, alpha1, tmp1, MPFR_RNDN);
  mpfr_mul_ui(alpha1, alpha1, 2, MPFR_RNDN);
  mpfr_add_d(alpha1, alpha1, 0.5, MPFR_RNDN);
  return(0);
}
// alpha2(k1,k2)
// requires one initialized tmp numbers
int zz_alpha2(mpfr_t alpha2, mpfr_t k1, mpfr_t k2, struct ss_cache cache, mpfr_t tmp1){
  mpfr_mul(tmp1, k2, cache.pi, MPFR_RNDN);
  mpfr_div_ui(tmp1, tmp1, 3, MPFR_RNDN);
  mpfr_cos(tmp1, tmp1, MPFR_RNDN);
  
  mpfr_mul(alpha2, k1, cache.pi, MPFR_RNDN);
  mpfr_div(alpha2, alpha2, cache.sqrt3, MPFR_RNDN);
  mpfr_cos(alpha2, alpha2, MPFR_RNDN);

  mpfr_sub(alpha2, alpha2, tmp1, MPFR_RNDN);

  mpfr_mul(tmp1, k2, cache.pi, MPFR_RNDN);
  mpfr_div_ui(tmp1, tmp1, 3, MPFR_RNDN);
  mpfr_sin(tmp1, tmp1, MPFR_RNDN);

  mpfr_mul(alpha2, alpha2, tmp1, MPFR_RNDN);
  mpfr_mul_ui(alpha2, alpha2, 2, MPFR_RNDN);
  return(0);
}