text: #include <math.h>
  #include <stdlib.h>
  #include <string.h>
  #include <stdio.h>
  #include <errno.h>
  #include <assert.h>
  #include <limits.h>
  #include <zlib.h>
  #include "prob1.h"
  #include "kstring.h"
  
  #include "kseq.h"
  KSTREAM_INIT(gzFile, gzread, 16384)
  
  #define MC_MAX_EM_ITER 16
  #define MC_EM_EPS 1e-5
  #define MC_DEF_INDEL 0.15
  
  gzFile bcf_p1_fp_lk;
  
  unsigned char seq_nt4_table[256] = {
  	4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4, 
  	4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4, 
  	4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4,  4, 4 /*'-'*/, 4, 4,
  	4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4, 
  	4, 0, 4, 1,  4, 4, 4, 2,  4, 4, 4, 4,  4, 4, 4, 4, 
  	4, 4, 4, 4,  3, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4, 
  	4, 0, 4, 1,  4, 4, 4, 2,  4, 4, 4, 4,  4, 4, 4, 4, 
  	4, 4, 4, 4,  3, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4, 
  	4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4, 
  	4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4, 
  	4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4, 
  	4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4, 
  	4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4, 
  	4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4, 
  	4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4, 
  	4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4,  4, 4, 4, 4
  };
  
  struct __bcf_p1aux_t {
  	int n, M, n1, is_indel;
  	uint8_t *ploidy; // haploid or diploid ONLY
  	float *lk;
  	double *q2p, *pdg; // pdg -> P(D|g)
  	double *phi, *phi_indel;
  	double *z, *zswap; // aux for afs
  	double *z1, *z2, *phi1, *phi2; // only calculated when n1 is set
  	double **hg; // hypergeometric distribution
  	double *lf; // log factorial
  	double t, t1, t2;
  	double *afs, *afs1; // afs: accumulative AFS; afs1: site posterior distribution
  	const uint8_t *PL; // point to PL
  	int PL_len;
  };
  
  void bcf_p1_indel_prior(bcf_p1aux_t *ma, double x)
  {
  	int i;
  	for (i = 0; i < ma->M; ++i)
  		ma->phi_indel[i] = ma->phi[i] * x;
  	ma->phi_indel[ma->M] = 1. - ma->phi[ma->M] * x;
  }
  
  static void init_prior(int type, double theta, int M, double *phi)
  {
  	int i;
  	if (type == MC_PTYPE_COND2) {
  		for (i = 0; i <= M; ++i)
  			phi[i] = 2. * (i + 1) / (M + 1) / (M + 2);
  	} else if (type == MC_PTYPE_FLAT) {
  		for (i = 0; i <= M; ++i)
  			phi[i] = 1. / (M + 1);
  	} else {
  		double sum;
  		for (i = 0, sum = 0.; i < M; ++i)
  			sum += (phi[i] = theta / (M - i));
  		phi[M] = 1. - sum;
  	}
  }
  
  void bcf_p1_init_prior(bcf_p1aux_t *ma, int type, double theta)
  {
  	init_prior(type, theta, ma->M, ma->phi);
  	bcf_p1_indel_prior(ma, MC_DEF_INDEL);
  }
  
  void bcf_p1_init_subprior(bcf_p1aux_t *ma, int type, double theta)
  {
  	if (ma->n1 <= 0 || ma->n1 >= ma->M) return;
  	init_prior(type, theta, 2*ma->n1, ma->phi1);
  	init_prior(type, theta, 2*(ma->n - ma->n1), ma->phi2);
  }
  
  int bcf_p1_read_prior(bcf_p1aux_t *ma, const char *fn)
  {
  	gzFile fp;
  	kstring_t s;
  	kstream_t *ks;
  	long double sum;
  	int dret, k;
  	memset(&s, 0, sizeof(kstring_t));
  	fp = strcmp(fn, "-")? gzopen(fn, "r") : gzdopen(fileno(stdin), "r");
  	ks = ks_init(fp);
  	memset(ma->phi, 0, sizeof(double) * (ma->M + 1));
  	while (ks_getuntil(ks, '\n', &s, &dret) >= 0) {
  		if (strstr(s.s, "[afs] ") == s.s) {
  			char *p = s.s + 6;
  			for (k = 0; k <= ma->M; ++k) {
  				int x;
  				double y;
  				x = strtol(p, &p, 10);
  				if (x != k && (errno == EINVAL || errno == ERANGE)) return -1;
  				++p;
  				y = strtod(p, &p);
  				if (y == 0. && (errno == EINVAL || errno == ERANGE)) return -1;
  				ma->phi[ma->M - k] += y;
  			}
  		}
  	}
  	ks_destroy(ks);
  	gzclose(fp);
  	free(s.s);
  	for (sum = 0., k = 0; k <= ma->M; ++k) sum += ma->phi[k];
  	fprintf(stderr, "[prior]");
  	for (k = 0; k <= ma->M; ++k) ma->phi[k] /= sum;
  	for (k = 0; k <= ma->M; ++k) fprintf(stderr, " %d:%.3lg", k, ma->phi[ma->M - k]);
  	fputc('\n', stderr);
  	for (sum = 0., k = 1; k < ma->M; ++k) sum += ma->phi[ma->M - k] * (2.* k * (ma->M - k) / ma->M / (ma->M - 1));
  	fprintf(stderr, "[%s] heterozygosity=%lf, ", __func__, (double)sum);
  	for (sum = 0., k = 1; k <= ma->M; ++k) sum += k * ma->phi[ma->M - k] / ma->M;
  	fprintf(stderr, "theta=%lf\n", (double)sum);
  	bcf_p1_indel_prior(ma, MC_DEF_INDEL);
  	return 0;
  }
  
  bcf_p1aux_t *bcf_p1_init(int n, uint8_t *ploidy)
  {
  	bcf_p1aux_t *ma;
  	int i;
  	ma = calloc(1, sizeof(bcf_p1aux_t));
  	ma->n1 = -1;
  	ma->n = n; ma->M = 2 * n;
  	if (ploidy) {
  		ma->ploidy = malloc(n);
  		memcpy(ma->ploidy, ploidy, n);
  		for (i = 0, ma->M = 0; i < n; ++i) ma->M += ploidy[i];
  		if (ma->M == 2 * n) {
  			free(ma->ploidy);
  			ma->ploidy = 0;
  		}
  	}
  	ma->q2p = calloc(256, sizeof(double));
  	ma->pdg = calloc(3 * ma->n, sizeof(double));
  	ma->phi = calloc(ma->M + 1, sizeof(double));
  	ma->phi_indel = calloc(ma->M + 1, sizeof(double));
  	ma->phi1 = calloc(ma->M + 1, sizeof(double));
  	ma->phi2 = calloc(ma->M + 1, sizeof(double));
  	ma->z = calloc(ma->M + 1, sizeof(double));
  	ma->zswap = calloc(ma->M + 1, sizeof(double));
  	ma->z1 = calloc(ma->M + 1, sizeof(double)); // actually we do not need this large
  	ma->z2 = calloc(ma->M + 1, sizeof(double));
  	ma->afs = calloc(ma->M + 1, sizeof(double));
  	ma->afs1 = calloc(ma->M + 1, sizeof(double));
  	ma->lf = calloc(ma->M + 1, sizeof(double));
  	ma->lk = calloc(ma->M + 1, sizeof(float));
  	for (i = 0; i < 256; ++i)
  		ma->q2p[i] = pow(10., -i / 10.);
  	for (i = 0; i <= ma->M; ++i) ma->lf[i] = lgamma(i + 1);
  	bcf_p1_init_prior(ma, MC_PTYPE_FULL, 1e-3); // the simplest prior
  	return ma;
  }
  
  int bcf_p1_get_M(bcf_p1aux_t *b) { return b->M; }
  
  int bcf_p1_set_n1(bcf_p1aux_t *b, int n1)
  {
  	if (n1 == 0 || n1 >= b->n) return -1;
  	if (b->M != b->n * 2) {
  		fprintf(stderr, "[%s] unable to set `n1' when there are haploid samples.\n", __func__);
  		return -1;
  	}
  	b->n1 = n1;
  	return 0;
  }
  
  void bcf_p1_set_ploidy(bcf1_t *b, bcf_p1aux_t *ma)
  {
      // bcf_p1aux_t fields are not visible outside of prob1.c, hence this wrapper.
      // Ideally, this should set ploidy per site to allow pseudo-autosomal regions
      b->ploidy = ma->ploidy;
  }
  
  void bcf_p1_destroy(bcf_p1aux_t *ma)
  {
  	if (ma) {
  		int k;
  		free(ma->lf);
  		if (ma->hg && ma->n1 > 0) {
  			for (k = 0; k <= 2*ma->n1; ++k) free(ma->hg[k]);
  			free(ma->hg);
  		}
  		free(ma->ploidy); free(ma->q2p); free(ma->pdg);
  		free(ma->phi); free(ma->phi_indel); free(ma->phi1); free(ma->phi2);
  		free(ma->z); free(ma->zswap); free(ma->z1); free(ma->z2);
  		free(ma->afs); free(ma->afs1);
  		free(ma->lk);
  		free(ma);
  	}
  }
  
  extern double kf_gammap(double s, double z);
  int test16(bcf1_t *b, anno16_t *a);
  
  // Wigginton 2005, PMID: 15789306
  // written by Jan Wigginton
  double calc_hwe(int obs_hom1, int obs_hom2, int obs_hets)
  {
      if (obs_hom1 + obs_hom2 + obs_hets == 0 ) return 1;
  
      assert(obs_hom1 >= 0 && obs_hom2 >= 0 && obs_hets >= 0);
  
      int obs_homc = obs_hom1 < obs_hom2 ? obs_hom2 : obs_hom1;
      int obs_homr = obs_hom1 < obs_hom2 ? obs_hom1 : obs_hom2;
  
      int rare_copies = 2 * obs_homr + obs_hets;
      int genotypes   = obs_hets + obs_homc + obs_homr;
  
      double *het_probs = (double*) calloc(rare_copies+1, sizeof(double));
  
      /* start at midpoint */
      int mid = rare_copies * (2 * genotypes - rare_copies) / (2 * genotypes);
  
      /* check to ensure that midpoint and rare alleles have same parity */
      if ((rare_copies & 1) ^ (mid & 1)) mid++;
  
      int curr_hets = mid;
      int curr_homr = (rare_copies - mid) / 2;
      int curr_homc = genotypes - curr_hets - curr_homr;
  
      het_probs[mid] = 1.0;
      double sum = het_probs[mid];
      for (curr_hets = mid; curr_hets > 1; curr_hets -= 2)
      {
          het_probs[curr_hets - 2] = het_probs[curr_hets] * curr_hets * (curr_hets - 1.0) / (4.0 * (curr_homr + 1.0) * (curr_homc + 1.0));
          sum += het_probs[curr_hets - 2];
  
          /* 2 fewer heterozygotes for next iteration -> add one rare, one common homozygote */
          curr_homr++;
          curr_homc++;
      }
  
      curr_hets = mid;
      curr_homr = (rare_copies - mid) / 2;
      curr_homc = genotypes - curr_hets - curr_homr;
      for (curr_hets = mid; curr_hets <= rare_copies - 2; curr_hets += 2)
      {
          het_probs[curr_hets + 2] = het_probs[curr_hets] * 4.0 * curr_homr * curr_homc /((curr_hets + 2.0) * (curr_hets + 1.0));
          sum += het_probs[curr_hets + 2];
  
          /* add 2 heterozygotes for next iteration -> subtract one rare, one common homozygote */
          curr_homr--;
          curr_homc--;
      }
      int i;
      for (i = 0; i <= rare_copies; i++) het_probs[i] /= sum;
  
      /*  p-value calculation for p_hwe  */
      double p_hwe = 0.0;
      for (i = 0; i <= rare_copies; i++)
      {
          if (het_probs[i] > het_probs[obs_hets])
              continue;
          p_hwe += het_probs[i];
      }
  
      p_hwe = p_hwe > 1.0 ? 1.0 : p_hwe;
      free(het_probs);
      return p_hwe;
  
  }
  
  
  static void _bcf1_set_ref(bcf1_t *b, int idp)
  {
      kstring_t s;
      int old_n_gi = b->n_gi;
      s.m = b->m_str; s.l = b->l_str - 1; s.s = b->str;
      kputs(":GT", &s); kputc('\0', &s);
      b->m_str = s.m; b->l_str = s.l; b->str = s.s;
      bcf_sync(b);
  
      // Call GTs
      int isample, an = 0;
      for (isample = 0; isample < b->n_smpl; isample++) 
      {
          if ( idp>=0 && ((uint16_t*)b->gi[idp].data)[isample]==0 )
              ((uint8_t*)b->gi[old_n_gi].data)[isample] = 1<<7;
          else
          {
              ((uint8_t*)b->gi[old_n_gi].data)[isample] = 0;
              an += b->ploidy ? b->ploidy[isample] : 2;
          }
      }
      bcf_fit_alt(b,1);
      b->qual = 999;
  
      // Prepare BCF for output: ref, alt, filter, info, format
      memset(&s, 0, sizeof(kstring_t)); kputc('\0', &s); 
      kputs(b->ref, &s); kputc('\0', &s);
      kputs(b->alt, &s); kputc('\0', &s); kputc('\0', &s);
      {
          ksprintf(&s, "AN=%d;", an);
          kputs(b->info, &s); 
          anno16_t a;
          int has_I16 = test16(b, &a) >= 0? 1 : 0;
          if (has_I16 )
          {
              if ( a.is_tested) ksprintf(&s, ";PV4=%.2g,%.2g,%.2g,%.2g", a.p[0], a.p[1], a.p[2], a.p[3]);
              ksprintf(&s, ";DP4=%d,%d,%d,%d;MQ=%d", a.d[0], a.d[1], a.d[2], a.d[3], a.mq);
          }
          kputc('\0', &s);
          rm_info(&s, "I16=");
          rm_info(&s, "QS=");
      }
      kputs(b->fmt, &s); kputc('\0', &s);
      free(b->str);
      b->m_str = s.m; b->l_str = s.l; b->str = s.s;
      bcf_sync(b);
  }
  
  int call_multiallelic_gt(bcf1_t *b, bcf_p1aux_t *ma, double threshold, int var_only)
  {
      int nals = 1;
      char *p;
      for (p=b->alt; *p; p++)
      {
          if ( *p=='X' || p[0]=='.' ) break;
          if ( p[0]==',' ) nals++;
      }
      if ( b->alt[0] && !*p ) nals++;
  
      if ( nals>4 )
      {
          if ( *b->ref=='N' ) return 0;
          fprintf(stderr,"Not ready for this, more than 4 alleles at %d: %s, %s\n", b->pos+1, b->ref,b->alt); 
          exit(1);
      }
  
      // find PL, DV and DP FORMAT indexes
      uint8_t *pl = NULL;
      int i, npl = 0, idp = -1, idv = -1;
      for (i = 0; i < b->n_gi; ++i) 
      {
          if (b->gi[i].fmt == bcf_str2int("PL", 2)) 
          {
              pl  = (uint8_t*)b->gi[i].data;
              npl = b->gi[i].len;
          }
          else if (b->gi[i].fmt == bcf_str2int("DP", 2))  idp=i;
          else if (b->gi[i].fmt == bcf_str2int("DV", 2))  idv=i;
      }
      if ( nals==1 ) 
      {
          if ( !var_only ) _bcf1_set_ref(b, idp);
          return 1;
      }
      if ( !pl ) return -1;
  
      assert(ma->q2p[0] == 1);
  
      // Init P(D|G)
      int npdg = nals*(nals+1)/2;
      double *pdg,*_pdg;
      _pdg = pdg = malloc(sizeof(double)*ma->n*npdg);
      for (i=0; i<ma->n; i++)
      {
          int j; 
          double sum = 0;
          for (j=0; j<npdg; j++)
          {
              //_pdg[j] = pow(10,-0.1*pl[j]); 
              _pdg[j] = ma->q2p[pl[j]];
              sum += _pdg[j];
          }
          if ( sum )
              for (j=0; j<npdg; j++) _pdg[j] /= sum;
          _pdg += npdg;
          pl += npl;
      }
  
      if ((p = strstr(b->info, "QS=")) == 0) { fprintf(stderr,"INFO/QS is required with -m, exiting\n"); exit(1); }
      double qsum[4];
      if ( sscanf(p+3,"%lf,%lf,%lf,%lf",&qsum[0],&qsum[1],&qsum[2],&qsum[3])!=4 ) { fprintf(stderr,"Could not parse %s\n",p); exit(1); }
  
  
      // Calculate the most likely combination of alleles, remembering the most and second most likely set
      int ia,ib,ic, max_als=0, max_als2=0;
      double ref_lk = 0, max_lk = INT_MIN, max_lk2 = INT_MIN, lk_sum = INT_MIN, lk_sums[3];
      for (ia=0; ia<nals; ia++)
      {
          double lk_tot = 0;
          int iaa = (ia+1)*(ia+2)/2-1;
          int isample;
          for (isample=0; isample<ma->n; isample++)
          {
              double *p = pdg + isample*npdg;
              // assert( log(p[iaa]) <= 0 );
              lk_tot += log(p[iaa]);
          }
          if ( ia==0 ) ref_lk = lk_tot;
          if ( max_lk<lk_tot ) { max_lk2 = max_lk; max_als2 = max_als; max_lk = lk_tot; max_als = 1<<ia; }
          else if ( max_lk2<lk_tot ) { max_lk2 = lk_tot; max_als2 = 1<<ia; }
          lk_sum = lk_tot>lk_sum ? lk_tot + log(1+exp(lk_sum-lk_tot)) : lk_sum + log(1+exp(lk_tot-lk_sum));
      }
      lk_sums[0] = lk_sum;
      if ( nals>1 )
      {
          for (ia=0; ia<nals; ia++)
          {
              if ( qsum[ia]==0 ) continue;
              int iaa = (ia+1)*(ia+2)/2-1;
              for (ib=0; ib<ia; ib++)
              {
                  if ( qsum[ib]==0 ) continue;
                  double lk_tot = 0;
                  double fa  = qsum[ia]/(qsum[ia]+qsum[ib]);
                  double fb  = qsum[ib]/(qsum[ia]+qsum[ib]);
                  double fab = 2*fa*fb; fa *= fa; fb *= fb;
                  int isample, ibb = (ib+1)*(ib+2)/2-1, iab = iaa - ia + ib;
                  for (isample=0; isample<ma->n; isample++)
                  {
                      double *p = pdg + isample*npdg;
                      //assert( log(fa*p[iaa] + fb*p[ibb] + fab*p[iab]) <= 0 );
                      if ( b->ploidy && b->ploidy[isample]==1 )
                          lk_tot +=  log(fa*p[iaa] + fb*p[ibb]);
                      else 
                          lk_tot +=  log(fa*p[iaa] + fb*p[ibb] + fab*p[iab]);
                  }
                  if ( max_lk<lk_tot ) { max_lk2 = max_lk; max_als2 = max_als; max_lk = lk_tot; max_als = 1<<ia|1<<ib; }
                  else if ( max_lk2<lk_tot ) { max_lk2 = lk_tot; max_als2 = 1<<ia|1<<ib; }
                  lk_sum = lk_tot>lk_sum ? lk_tot + log(1+exp(lk_sum-lk_tot)) : lk_sum + log(1+exp(lk_tot-lk_sum));
              }
          }
          lk_sums[1] = lk_sum;
      }
      if ( nals>2 )
      {
          for (ia=0; ia<nals; ia++)
          {
              if ( qsum[ia]==0 ) continue;
              int iaa = (ia+1)*(ia+2)/2-1;
              for (ib=0; ib<ia; ib++)
              {
                  if ( qsum[ib]==0 ) continue;
                  int ibb = (ib+1)*(ib+2)/2-1; 
                  int iab = iaa - ia + ib;
                  for (ic=0; ic<ib; ic++)
                  {
                      if ( qsum[ic]==0 ) continue;
                      double lk_tot = 0;
                      double fa  = qsum[ia]/(qsum[ia]+qsum[ib]+qsum[ic]);
                      double fb  = qsum[ib]/(qsum[ia]+qsum[ib]+qsum[ic]);
                      double fc  = qsum[ic]/(qsum[ia]+qsum[ib]+qsum[ic]);
                      double fab = 2*fa*fb, fac = 2*fa*fc, fbc = 2*fb*fc; fa *= fa; fb *= fb; fc *= fc;
                      int isample, icc = (ic+1)*(ic+2)/2-1;
                      int iac = iaa - ia + ic, ibc = ibb - ib + ic;
                      for (isample=0; isample<ma->n; isample++)
                      {
                          double *p = pdg + isample*npdg;
                          //assert( log(fa*p[iaa] + fb*p[ibb] + fc*p[icc] + fab*p[iab] + fac*p[iac] + fbc*p[ibc]) <= 0 );
                          if ( b->ploidy && b->ploidy[isample]==1 ) 
                              lk_tot += log(fa*p[iaa] + fb*p[ibb] + fc*p[icc]);
                          else
                              lk_tot += log(fa*p[iaa] + fb*p[ibb] + fc*p[icc] + fab*p[iab] + fac*p[iac] + fbc*p[ibc]);
                      }
                      if ( max_lk<lk_tot ) { max_lk2 = max_lk; max_als2 = max_als; max_lk = lk_tot; max_als = 1<<ia|1<<ib|1<<ic; }
                      else if ( max_lk2<lk_tot ) { max_lk2 = lk_tot; max_als2 = 1<<ia|1<<ib|1<<ic; }
                      lk_sum = lk_tot>lk_sum ? lk_tot + log(1+exp(lk_sum-lk_tot)) : lk_sum + log(1+exp(lk_tot-lk_sum));
                  }
              }
          }
          lk_sums[2] = lk_sum;
      }
  
      // Should we add another allele, does it increase the likelihood significantly?
      int n1=0, n2=0;
      for (i=0; i<nals; i++) if ( max_als&1<<i) n1++;
      for (i=0; i<nals; i++) if ( max_als2&1<<i) n2++;
      if ( n2<n1 && kf_gammap(1,2.0*(max_lk-max_lk2))<threshold )
      {
          // the threshold not exceeded, use the second most likely set with fewer alleles
          max_lk  = max_lk2;
          max_als = max_als2;
          n1 = n2;
      }
      lk_sum = lk_sums[n1-1];
  
      // Get the BCF record ready for GT and GQ
      kstring_t s;
      int old_n_gi = b->n_gi;
      s.m = b->m_str; s.l = b->l_str - 1; s.s = b->str;
      kputs(":GT:GQ", &s); kputc('\0', &s);
      b->m_str = s.m; b->l_str = s.l; b->str = s.s;
      bcf_sync(b);
  
      // Call GTs
      int isample, gts=0, ac[4] = {0,0,0,0};
      int nRR = 0, nAA = 0, nRA = 0, max_dv = 0;
      for (isample = 0; isample < b->n_smpl; isample++) 
      {
          int ploidy = b->ploidy ? b->ploidy[isample] : 2;
          double *p = pdg + isample*npdg;
          int ia, als = 0;
          double lk = 0, lk_s = 0;
          for (ia=0; ia<nals; ia++)
          {
              if ( !(max_als&1<<ia) ) continue;
              int iaa = (ia+1)*(ia+2)/2-1;
              double _lk = p[iaa]*qsum[ia]*qsum[ia];
              if ( _lk > lk ) { lk = _lk; als = ia<<3 | ia; }
              lk_s += _lk;
          }
          if ( ploidy==2 ) 
          {
              for (ia=0; ia<nals; ia++)
              {
                  if ( !(max_als&1<<ia) ) continue;
                  int iaa = (ia+1)*(ia+2)/2-1;
                  for (ib=0; ib<ia; ib++)
                  {
                      if ( !(max_als&1<<ib) ) continue;
                      int iab = iaa - ia + ib;
                      double _lk = 2*qsum[ia]*qsum[ib]*p[iab];
                      if ( _lk > lk ) { lk = _lk; als = ib<<3 | ia; }
                      lk_s += _lk;
                  }
              }
          }
          lk = -log(1-lk/lk_s)/0.2302585;
          int dp = 0;
          if ( idp>=0 && (dp=((uint16_t*)b->gi[idp].data)[isample])==0 )
          {
              // no coverage
              ((uint8_t*)b->gi[old_n_gi].data)[isample]   = 1<<7;
              ((uint8_t*)b->gi[old_n_gi+1].data)[isample] = 0;
              continue;
          }
          if ( lk>99 ) lk = 99;
          ((uint8_t*)b->gi[old_n_gi].data)[isample]   = als;
          ((uint8_t*)b->gi[old_n_gi+1].data)[isample] = (int)lk;
  
          // For MDV annotation
          int dv;
          if ( als && idv>=0 && (dv=((uint16_t*)b->gi[idv].data)[isample]) )
          {
              if ( max_dv < dv ) max_dv = dv;
          }
  
          // For HWE annotation; multiple ALT alleles treated as one
          if ( !als ) nRR++;
          else if ( !(als>>3&7) || !(als&7) ) nRA++;
          else nAA++;
  
          gts |= 1<<(als>>3&7) | 1<<(als&7);
          ac[ als>>3&7 ]++;
          ac[ als&7 ]++;
      }
      free(pdg);
      bcf_fit_alt(b,max_als);
  
      // The VCF spec is ambiguous about QUAL: is it the probability of anything else
      //  (that is QUAL(non-ref) = P(ref)+P(any non-ref other than ALT)) or is it
      //  QUAL(non-ref)=P(ref) and QUAL(ref)=1-P(ref)? Assuming the latter.
      b->qual = gts>1 ? -4.343*(ref_lk - lk_sum) : -4.343*log(1-exp(ref_lk - lk_sum));
      if ( b->qual>999 ) b->qual = 999;
  
      // Prepare BCF for output: ref, alt, filter, info, format
      memset(&s, 0, sizeof(kstring_t)); kputc('\0', &s); 
      kputs(b->ref, &s); kputc('\0', &s);
      kputs(b->alt, &s); kputc('\0', &s); kputc('\0', &s);
      {
          int an=0, nalts=0;
          for (i=0; i<nals; i++)
          {
              an += ac[i];
              if ( i>0 && ac[i] ) nalts++;
          }
          ksprintf(&s, "AN=%d;", an);
          if ( nalts )
          {
              kputs("AC=", &s);
              for (i=1; i<nals; i++)
              {
                  if ( !(gts&1<<i) ) continue;
                  nalts--;
                  ksprintf(&s,"%d", ac[i]);
                  if ( nalts>0 ) kputc(',', &s);
              }
              kputc(';', &s);
          }
          kputs(b->info, &s); 
          anno16_t a;
          int has_I16 = test16(b, &a) >= 0? 1 : 0;
          if (has_I16 )
          {
              if ( a.is_tested) ksprintf(&s, ";PV4=%.2g,%.2g,%.2g,%.2g", a.p[0], a.p[1], a.p[2], a.p[3]);
              ksprintf(&s, ";DP4=%d,%d,%d,%d;MQ=%d", a.d[0], a.d[1], a.d[2], a.d[3], a.mq);
              ksprintf(&s, ";QBD=%e", b->qual/(a.d[0] + a.d[1] + a.d[2] + a.d[3]));
              if ( max_dv ) ksprintf(&s, ";MDV=%d", max_dv);
          }
          if ( nAA+nRA )
          {
              double hwe = calc_hwe(nAA, nRR, nRA);
              ksprintf(&s, ";HWE=%e", hwe);
          }
          kputc('\0', &s);
          rm_info(&s, "I16=");
          rm_info(&s, "QS=");
      }
      kputs(b->fmt, &s); kputc('\0', &s);
      free(b->str);
      b->m_str = s.m; b->l_str = s.l; b->str = s.s;
      bcf_sync(b);
  
      return gts;
  }
  
  static int cal_pdg(const bcf1_t *b, bcf_p1aux_t *ma)
  {
      int i, j;
      long *p, tmp;
      p = alloca(b->n_alleles * sizeof(long));
      memset(p, 0, sizeof(long) * b->n_alleles);
      for (j = 0; j < ma->n; ++j) {
          const uint8_t *pi = ma->PL + j * ma->PL_len;
          double *pdg = ma->pdg + j * 3;
          pdg[0] = ma->q2p[pi[2]]; pdg[1] = ma->q2p[pi[1]]; pdg[2] = ma->q2p[pi[0]];
          for (i = 0; i < b->n_alleles; ++i)
              p[i] += (int)pi[(i+1)*(i+2)/2-1];
      }
      for (i = 0; i < b->n_alleles; ++i) p[i] = p[i]<<4 | i;
      for (i = 1; i < b->n_alleles; ++i) // insertion sort
          for (j = i; j > 0 && p[j] < p[j-1]; --j)
              tmp = p[j], p[j] = p[j-1], p[j-1] = tmp;
      for (i = b->n_alleles - 1; i >= 0; --i)
          if ((p[i]&0xf) == 0) break;
      return i;
  }
  
  
  int bcf_p1_call_gt(const bcf_p1aux_t *ma, double f0, int k)
  {
  	double sum, g[3];
  	double max, f3[3], *pdg = ma->pdg + k * 3;
  	int q, i, max_i, ploidy;
  	ploidy = ma->ploidy? ma->ploidy[k] : 2;
  	if (ploidy == 2) {
  		f3[0] = (1.-f0)*(1.-f0); f3[1] = 2.*f0*(1.-f0); f3[2] = f0*f0;
  	} else {
  		f3[0] = 1. - f0; f3[1] = 0; f3[2] = f0;
  	}
  	for (i = 0, sum = 0.; i < 3; ++i)
  		sum += (g[i] = pdg[i] * f3[i]);
  	for (i = 0, max = -1., max_i = 0; i < 3; ++i) {
  		g[i] /= sum;
  		if (g[i] > max) max = g[i], max_i = i;
  	}
  	max = 1. - max;
  	if (max < 1e-308) max = 1e-308;
  	q = (int)(-4.343 * log(max) + .499);
  	if (q > 99) q = 99;
  	return q<<2|max_i;
  }
  
  #define TINY 1e-20
  
  static void mc_cal_y_core(bcf_p1aux_t *ma, int beg)
  {
  	double *z[2], *tmp, *pdg;
  	int _j, last_min, last_max;
  	assert(beg == 0 || ma->M == ma->n*2);
  	z[0] = ma->z;
  	z[1] = ma->zswap;
  	pdg = ma->pdg;
  	memset(z[0], 0, sizeof(double) * (ma->M + 1));
  	memset(z[1], 0, sizeof(double) * (ma->M + 1));
  	z[0][0] = 1.;
  	last_min = last_max = 0;
  	ma->t = 0.;
  	if (ma->M == ma->n * 2) {
  		int M = 0;
  		for (_j = beg; _j < ma->n; ++_j) {
  			int k, j = _j - beg, _min = last_min, _max = last_max, M0;
  			double p[3], sum;
  			M0 = M; M += 2;
  			pdg = ma->pdg + _j * 3;
  			p[0] = pdg[0]; p[1] = 2. * pdg[1]; p[2] = pdg[2];
  			for (; _min < _max && z[0][_min] < TINY; ++_min) z[0][_min] = z[1][_min] = 0.;
  			for (; _max > _min && z[0][_max] < TINY; --_max) z[0][_max] = z[1][_max] = 0.;
  			_max += 2;
  			if (_min == 0) k = 0, z[1][k] = (M0-k+1) * (M0-k+2) * p[0] * z[0][k];
  			if (_min <= 1) k = 1, z[1][k] = (M0-k+1) * (M0-k+2) * p[0] * z[0][k] + k*(M0-k+2) * p[1] * z[0][k-1];
  			for (k = _min < 2? 2 : _min; k <= _max; ++k)
  				z[1][k] = (M0-k+1)*(M0-k+2) * p[0] * z[0][k] + k*(M0-k+2) * p[1] * z[0][k-1] + k*(k-1)* p[2] * z[0][k-2];
  			for (k = _min, sum = 0.; k <= _max; ++k) sum += z[1][k];
  			ma->t += log(sum / (M * (M - 1.)));
  			for (k = _min; k <= _max; ++k) z[1][k] /= sum;
  			if (_min >= 1) z[1][_min-1] = 0.;
  			if (_min >= 2) z[1][_min-2] = 0.;
  			if (j < ma->n - 1) z[1][_max+1] = z[1][_max+2] = 0.;
  			if (_j == ma->n1 - 1) { // set pop1; ma->n1==-1 when unset
  				ma->t1 = ma->t;
  				memcpy(ma->z1, z[1], sizeof(double) * (ma->n1 * 2 + 1));
  			}
  			tmp = z[0]; z[0] = z[1]; z[1] = tmp;
  			last_min = _min; last_max = _max;
  		}
  		//for (_j = 0; _j < last_min; ++_j) z[0][_j] = 0.; // TODO: are these necessary?
  		//for (_j = last_max + 1; _j < ma->M; ++_j) z[0][_j] = 0.;
  	} else { // this block is very similar to the block above; these two might be merged in future
  		int j, M = 0;
  		for (j = 0; j < ma->n; ++j) {
  			int k, M0, _min = last_min, _max = last_max;
  			double p[3], sum;
  			pdg = ma->pdg + j * 3;
  			for (; _min < _max && z[0][_min] < TINY; ++_min) z[0][_min] = z[1][_min] = 0.;
  			for (; _max > _min && z[0][_max] < TINY; --_max) z[0][_max] = z[1][_max] = 0.;
  			M0 = M;
  			M += ma->ploidy[j];
  			if (ma->ploidy[j] == 1) {
  				p[0] = pdg[0]; p[1] = pdg[2];
  				_max++;
  				if (_min == 0) k = 0, z[1][k] = (M0+1-k) * p[0] * z[0][k];
  				for (k = _min < 1? 1 : _min; k <= _max; ++k)
  					z[1][k] = (M0+1-k) * p[0] * z[0][k] + k * p[1] * z[0][k-1];
  				for (k = _min, sum = 0.; k <= _max; ++k) sum += z[1][k];
  				ma->t += log(sum / M);
  				for (k = _min; k <= _max; ++k) z[1][k] /= sum;
  				if (_min >= 1) z[1][_min-1] = 0.;
  				if (j < ma->n - 1) z[1][_max+1] = 0.;
  			} else if (ma->ploidy[j] == 2) {
  				p[0] = pdg[0]; p[1] = 2 * pdg[1]; p[2] = pdg[2];
  				_max += 2;
  				if (_min == 0) k = 0, z[1][k] = (M0-k+1) * (M0-k+2) * p[0] * z[0][k];
  				if (_min <= 1) k = 1, z[1][k] = (M0-k+1) * (M0-k+2) * p[0] * z[0][k] + k*(M0-k+2) * p[1] * z[0][k-1];
  				for (k = _min < 2? 2 : _min; k <= _max; ++k)
  					z[1][k] = (M0-k+1)*(M0-k+2) * p[0] * z[0][k] + k*(M0-k+2) * p[1] * z[0][k-1] + k*(k-1)* p[2] * z[0][k-2];
  				for (k = _min, sum = 0.; k <= _max; ++k) sum += z[1][k];
  				ma->t += log(sum / (M * (M - 1.)));
  				for (k = _min; k <= _max; ++k) z[1][k] /= sum;
  				if (_min >= 1) z[1][_min-1] = 0.;
  				if (_min >= 2) z[1][_min-2] = 0.;
  				if (j < ma->n - 1) z[1][_max+1] = z[1][_max+2] = 0.;
  			}
  			tmp = z[0]; z[0] = z[1]; z[1] = tmp;
  			last_min = _min; last_max = _max;
  		}
  	}
  	if (z[0] != ma->z) memcpy(ma->z, z[0], sizeof(double) * (ma->M + 1));
  	if (bcf_p1_fp_lk) {
  		int k;
  		long double sum = 0.;
  		for (k = 0; k <= ma->M; ++k) {
  			ma->zswap[k] = ma->z[k] > 1e-10? ma->z[k] : 0;
  			sum += ma->zswap[k];
  		}
  		sum = 1. / sum;
  		for (k = 0; k <= ma->M; ++k)
  			ma->lk[k] = (float)(ma->zswap[k] * sum);
  		gzwrite(bcf_p1_fp_lk, ma->lk, sizeof(float) * (ma->M + 1));
  	}
  }
  
  static void mc_cal_y(bcf_p1aux_t *ma)
  {
  	if (ma->n1 > 0 && ma->n1 < ma->n && ma->M == ma->n * 2) { // NB: ma->n1 is ineffective when there are haploid samples
  		int k;
  		long double x;
  		memset(ma->z1, 0, sizeof(double) * (2 * ma->n1 + 1));
  		memset(ma->z2, 0, sizeof(double) * (2 * (ma->n - ma->n1) + 1));
  		ma->t1 = ma->t2 = 0.;
  		mc_cal_y_core(ma, ma->n1);
  		ma->t2 = ma->t;
  		memcpy(ma->z2, ma->z, sizeof(double) * (2 * (ma->n - ma->n1) + 1));
  		mc_cal_y_core(ma, 0);
  		// rescale z
  		x = expl(ma->t - (ma->t1 + ma->t2));
  		for (k = 0; k <= ma->M; ++k) ma->z[k] *= x;
  	} else mc_cal_y_core(ma, 0);
  }
  
  #define CONTRAST_TINY 1e-30
  
  extern double kf_gammaq(double s, double z); // incomplete gamma function for chi^2 test
  
  static inline double chi2_test(int a, int b, int c, int d)
  {
  	double x, z;
  	x = (double)(a+b) * (c+d) * (b+d) * (a+c);
  	if (x == 0.) return 1;
  	z = a * d - b * c;
  	return kf_gammaq(.5, .5 * z * z * (a+b+c+d) / x);
  }
  
  // chi2=(a+b+c+d)(ad-bc)^2/[(a+b)(c+d)(a+c)(b+d)]
  static inline double contrast2_aux(const bcf_p1aux_t *p1, double sum, int k1, int k2, double x[3])
  {
  	double p = p1->phi[k1+k2] * p1->z1[k1] * p1->z2[k2] / sum * p1->hg[k1][k2];
  	int n1 = p1->n1, n2 = p1->n - p1->n1;
  	if (p < CONTRAST_TINY) return -1;
  	if (.5*k1/n1 < .5*k2/n2) x[1] += p;
  	else if (.5*k1/n1 > .5*k2/n2) x[2] += p;
  	else x[0] += p;
  	return p * chi2_test(k1, k2, (n1<<1) - k1, (n2<<1) - k2);
  }
  
  static double contrast2(bcf_p1aux_t *p1, double ret[3])
  {
  	int k, k1, k2, k10, k20, n1, n2;
  	double sum;
  	// get n1 and n2
  	n1 = p1->n1; n2 = p1->n - p1->n1;
  	if (n1 <= 0 || n2 <= 0) return 0.;
  	if (p1->hg == 0) { // initialize the hypergeometric distribution
  		/* NB: the hg matrix may take a lot of memory when there are many samples. There is a way
  		   to avoid precomputing this matrix, but it is slower and quite intricate. The following
  		   computation in this block can be accelerated with a similar strategy, but perhaps this
  		   is not a serious concern for now. */
  		double tmp = lgamma(2*(n1+n2)+1) - (lgamma(2*n1+1) + lgamma(2*n2+1));
  		p1->hg = calloc(2*n1+1, sizeof(void*));
  		for (k1 = 0; k1 <= 2*n1; ++k1) {
  			p1->hg[k1] = calloc(2*n2+1, sizeof(double));
  			for (k2 = 0; k2 <= 2*n2; ++k2)
  				p1->hg[k1][k2] = exp(lgamma(k1+k2+1) + lgamma(p1->M-k1-k2+1) - (lgamma(k1+1) + lgamma(k2+1) + lgamma(2*n1-k1+1) + lgamma(2*n2-k2+1) + tmp));
  		}
  	}
  	{ // compute
  		long double suml = 0;
  		for (k = 0; k <= p1->M; ++k) suml += p1->phi[k] * p1->z[k];
  		sum = suml;
  	}
  	{ // get the max k1 and k2
  		double max;
  		int max_k;
  		for (k = 0, max = 0, max_k = -1; k <= 2*n1; ++k) {
  			double x = p1->phi1[k] * p1->z1[k];
  			if (x > max) max = x, max_k = k;
  		}
  		k10 = max_k;
  		for (k = 0, max = 0, max_k = -1; k <= 2*n2; ++k) {
  			double x = p1->phi2[k] * p1->z2[k];
  			if (x > max) max = x, max_k = k;
  		}
  		k20 = max_k;
  	}
  	{ // We can do the following with one nested loop, but that is an O(N^2) thing. The following code block is much faster for large N.
  		double x[3], y;
  		long double z = 0., L[2];
  		x[0] = x[1] = x[2] = 0; L[0] = L[1] = 0;
  		for (k1 = k10; k1 >= 0; --k1) {
  			for (k2 = k20; k2 >= 0; --k2) {
  				if ((y = contrast2_aux(p1, sum, k1, k2, x)) < 0) break;
  				else z += y;
  			}
  			for (k2 = k20 + 1; k2 <= 2*n2; ++k2) {
  				if ((y = contrast2_aux(p1, sum, k1, k2, x)) < 0) break;
  				else z += y;
  			}
  		}
  		ret[0] = x[0]; ret[1] = x[1]; ret[2] = x[2];
  		x[0] = x[1] = x[2] = 0;
  		for (k1 = k10 + 1; k1 <= 2*n1; ++k1) {
  			for (k2 = k20; k2 >= 0; --k2) {
  				if ((y = contrast2_aux(p1, sum, k1, k2, x)) < 0) break;
  				else z += y;
  			}
  			for (k2 = k20 + 1; k2 <= 2*n2; ++k2) {
  				if ((y = contrast2_aux(p1, sum, k1, k2, x)) < 0) break;
  				else z += y;
  			}
  		}
  		ret[0] += x[0]; ret[1] += x[1]; ret[2] += x[2];
  		if (ret[0] + ret[1] + ret[2] < 0.95) { // in case of bad things happened
  			ret[0] = ret[1] = ret[2] = 0; L[0] = L[1] = 0;
  			for (k1 = 0, z = 0.; k1 <= 2*n1; ++k1)
  				for (k2 = 0; k2 <= 2*n2; ++k2)
  					if ((y = contrast2_aux(p1, sum, k1, k2, ret)) >= 0) z += y;
  			if (ret[0] + ret[1] + ret[2] < 0.95) // It seems that this may be caused by floating point errors. I do not really understand why...
  				z = 1.0, ret[0] = ret[1] = ret[2] = 1./3;
  		}
  		return (double)z;
  	}
  }
  
  static double mc_cal_afs(bcf_p1aux_t *ma, double *p_ref_folded, double *p_var_folded)
  {
  	int k;
  	long double sum = 0., sum2;
  	double *phi = ma->is_indel? ma->phi_indel : ma->phi;
  	memset(ma->afs1, 0, sizeof(double) * (ma->M + 1));
  	mc_cal_y(ma);
  	// compute AFS
  	for (k = 0, sum = 0.; k <= ma->M; ++k)
  		sum += (long double)phi[k] * ma->z[k];
  	for (k = 0; k <= ma->M; ++k) {
  		ma->afs1[k] = phi[k] * ma->z[k] / sum;
  		if (isnan(ma->afs1[k]) || isinf(ma->afs1[k])) return -1.;
  	}
  	// compute folded variant probability
  	for (k = 0, sum = 0.; k <= ma->M; ++k)
  		sum += (long double)(phi[k] + phi[ma->M - k]) / 2. * ma->z[k];
  	for (k = 1, sum2 = 0.; k < ma->M; ++k)
  		sum2 += (long double)(phi[k] + phi[ma->M - k]) / 2. * ma->z[k];
  	*p_var_folded = sum2 / sum;
  	*p_ref_folded = (phi[k] + phi[ma->M - k]) / 2. * (ma->z[ma->M] + ma->z[0]) / sum;
  	// the expected frequency
  	for (k = 0, sum = 0.; k <= ma->M; ++k) {
  		ma->afs[k] += ma->afs1[k];
  		sum += k * ma->afs1[k];
  	}
  	return sum / ma->M;
  }
  
  int bcf_p1_cal(const bcf1_t *b, int do_contrast, bcf_p1aux_t *ma, bcf_p1rst_t *rst)
  {
  	int i, k;
  	long double sum = 0.;
  	ma->is_indel = bcf_is_indel(b);
  	rst->perm_rank = -1;
  	// set PL and PL_len
  	for (i = 0; i < b->n_gi; ++i) {
  		if (b->gi[i].fmt == bcf_str2int("PL", 2)) {
  			ma->PL = (uint8_t*)b->gi[i].data;
  			ma->PL_len = b->gi[i].len;
  			break;
  		}
  	}
  	if (i == b->n_gi) return -1; // no PL
  	if (b->n_alleles < 2) return -1; // FIXME: find a better solution
  	// 
  	rst->rank0 = cal_pdg(b, ma);
  	rst->f_exp = mc_cal_afs(ma, &rst->p_ref_folded, &rst->p_var_folded);
  	rst->p_ref = ma->afs1[ma->M];
  	for (k = 0, sum = 0.; k < ma->M; ++k)
  		sum += ma->afs1[k];
  	rst->p_var = (double)sum;
  	{ // compute the allele count
  		double max = -1;
  		rst->ac = -1;
  		for (k = 0; k <= ma->M; ++k)
  			if (max < ma->z[k]) max = ma->z[k], rst->ac = k;
  		rst->ac = ma->M - rst->ac;
  	}
  	// calculate f_flat and f_em
  	for (k = 0, sum = 0.; k <= ma->M; ++k)
  		sum += (long double)ma->z[k];
  	rst->f_flat = 0.;
  	for (k = 0; k <= ma->M; ++k) {
  		double p = ma->z[k] / sum;
  		rst->f_flat += k * p;
  	}
  	rst->f_flat /= ma->M;
  	{ // estimate equal-tail credible interval (95% level)
  		int l, h;
  		double p;
  		for (i = 0, p = 0.; i <= ma->M; ++i)
  			if (p + ma->afs1[i] > 0.025) break;
  			else p += ma->afs1[i];
  		l = i;
  		for (i = ma->M, p = 0.; i >= 0; --i)
  			if (p + ma->afs1[i] > 0.025) break;
  			else p += ma->afs1[i];
  		h = i;
  		rst->cil = (double)(ma->M - h) / ma->M; rst->cih = (double)(ma->M - l) / ma->M;
  	}
  	if (ma->n1 > 0) { // compute LRT
  		double max0, max1, max2;
  		for (k = 0, max0 = -1; k <= ma->M; ++k)
  			if (max0 < ma->z[k]) max0 = ma->z[k];
  		for (k = 0, max1 = -1; k <= ma->n1 * 2; ++k)
  			if (max1 < ma->z1[k]) max1 = ma->z1[k];
  		for (k = 0, max2 = -1; k <= ma->M - ma->n1 * 2; ++k)
  			if (max2 < ma->z2[k]) max2 = ma->z2[k];
  		rst->lrt = log(max1 * max2 / max0);
  		rst->lrt = rst->lrt < 0? 1 : kf_gammaq(.5, rst->lrt);
  	} else rst->lrt = -1.0;
  	rst->cmp[0] = rst->cmp[1] = rst->cmp[2] = rst->p_chi2 = -1.0;
  	if (do_contrast && rst->p_var > 0.5) // skip contrast2() if the locus is a strong non-variant
  		rst->p_chi2 = contrast2(ma, rst->cmp);
  	return 0;
  }
  
  void bcf_p1_dump_afs(bcf_p1aux_t *ma)
  {
  	int k;
  	fprintf(stderr, "[afs]");
  	for (k = 0; k <= ma->M; ++k)
  		fprintf(stderr, " %d:%.3lf", k, ma->afs[ma->M - k]);
  	fprintf(stderr, "\n");
  	memset(ma->afs, 0, sizeof(double) * (ma->M + 1));
  }
  