#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
	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));
	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);
	}
}

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)
		gzwrite(bcf_p1_fp_lk, ma->z, sizeof(double) * (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));
}