bam2bcf.c

/*  bam2bcf.c -- variant calling.

    Copyright (C) 2010-2012 Broad Institute.
    Copyright (C) 2012-2024 Genome Research Ltd.

    Author: Heng Li <lh3@sanger.ac.uk>

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
DEALINGS IN THE SOFTWARE.  */

#include <math.h>
#include <stdint.h>
#include <assert.h>
#include <float.h>
#include <htslib/hts.h>
#include <htslib/sam.h>
#include <htslib/kstring.h>
#include <htslib/kfunc.h>
#include "bcftools.h"
#include "bam2bcf.h"

extern  void ks_introsort_uint32_t(size_t n, uint32_t a[]);

#define CALL_DEFTHETA 0.83
#define DEF_MAPQ 20

#define CAP_DIST 25

bcf_callaux_t *bcf_call_init(double theta, int min_baseQ, int max_baseQ,
                             int delta_baseQ)
{
    bcf_callaux_t *bca;
    if (theta <= 0.) theta = CALL_DEFTHETA;
    bca = (bcf_callaux_t*) calloc(1, sizeof(bcf_callaux_t));
    bca->capQ = 60;
    bca->openQ = 40; bca->extQ = 20; bca->tandemQ = 100;
    bca->min_baseQ = min_baseQ;
    bca->max_baseQ = max_baseQ;
    bca->delta_baseQ = delta_baseQ;
    bca->e = errmod_init(1. - theta);
    bca->min_frac = 0.002;
    bca->min_support = 1;
    bca->per_sample_flt = 0;
    bca->npos = 100;
    bca->ref_pos = (int*) malloc(bca->npos*sizeof(int));
    bca->alt_pos = (int*) malloc(bca->npos*sizeof(int));
    bca->iref_pos= (int*) malloc(bca->npos*sizeof(int));
    bca->ialt_pos= (int*) malloc(bca->npos*sizeof(int));
    bca->nqual = 60;
    bca->ref_mq  = (int*) malloc(bca->nqual*sizeof(int));
    bca->alt_mq  = (int*) malloc(bca->nqual*sizeof(int));
    bca->iref_mq = (int*) malloc(bca->nqual*sizeof(int));
    bca->ialt_mq = (int*) malloc(bca->nqual*sizeof(int));
    bca->ref_bq  = (int*) malloc(bca->nqual*sizeof(int));
    bca->alt_bq  = (int*) malloc(bca->nqual*sizeof(int));
    bca->fwd_mqs = (int*) malloc(bca->nqual*sizeof(int));
    bca->rev_mqs = (int*) malloc(bca->nqual*sizeof(int));
    return bca;
}

void bcf_iaux_destroy(bcf_callaux_t *bca);
void bcf_call_destroy(bcf_callaux_t *bca)
{
    if (bca == 0) return;
    bcf_iaux_destroy(bca);
    errmod_destroy(bca->e);
    if (bca->npos) {
        free(bca->ref_pos);  free(bca->alt_pos);
        free(bca->iref_pos); free(bca->ialt_pos);
        bca->npos = 0;
    }
    free(bca->ref_mq); free(bca->alt_mq);
    free(bca->iref_mq); free(bca->ialt_mq);
    free(bca->ref_bq); free(bca->alt_bq);
    free(bca->fwd_mqs); free(bca->rev_mqs);

    bca->nqual = 0;
    free(bca->bases); free(bca->inscns); free(bca);
}

static int get_aux_nm(const bam_pileup1_t *p, int32_t qpos, int is_ref)
{
    int64_t nm;
    const bam_pileup_cd *cd = &p->cd;

    if ( PLP_NM(cd) == -1 ) return -1;
    if ( PLP_NM(cd) == PLP_NM_UNSET )
    {
        // todo: make this localized to be useful for long reads as well
        bam1_t *rec = p->b;
        uint8_t *nm_tag = bam_aux_get(rec, "NM");
        if ( !nm_tag )
        {
            PLP_NM(cd) = -1;
            return -1;
        }
        nm = bam_aux2i(nm_tag);

        // Count indels as single events, not as the number of inserted/deleted
        // bases (which is what NM does). Add soft clips as mismatches.
        int i;
        for (i=0; i < rec->core.n_cigar; i++)
        {
            int val = bam_get_cigar(rec)[i] & BAM_CIGAR_MASK;
            if ( val==BAM_CSOFT_CLIP )
            {
                nm += bam_get_cigar(rec)[i] >> BAM_CIGAR_SHIFT;
            }
            else if ( val==BAM_CINS || val==BAM_CDEL )
            {
                val = bam_get_cigar(rec)[i] >> BAM_CIGAR_SHIFT;
                if ( val > 1 ) nm -= val - 1;
            }
        }
        PLP_NM(cd) = nm;
    }
    else
        nm = PLP_NM(cd);

    // Take into account MNPs, 2% of de novo SNVs appear within 20bp of another de novo SNV
    //      http://www.genome.org/cgi/doi/10.1101/gr.239756.118
    nm -= is_ref ? 1 : 2;

    if ( nm < 0 ) nm = 0;
    if ( nm >= B2B_N_NM ) nm = B2B_N_NM - 1;

    return nm;
}

// position in the sequence with respect to the aligned part of the read
static int get_position(const bam_pileup1_t *p, int *len,
                        int *sc_len, int *sc_dist) {
    int i, j, edist = p->qpos + 1;
    int sc_left = 0, sc_right = 0;
    int sc_left_dist = -1, sc_right_dist = -1;

    // left end
    for (i = 0; i < p->b->core.n_cigar; i++) {
        int cig  = bam_get_cigar(p->b)[i] & BAM_CIGAR_MASK;
        if (cig == BAM_CHARD_CLIP)
            continue;
        else if (cig == BAM_CSOFT_CLIP)
            sc_left += bam_get_cigar(p->b)[i] >> BAM_CIGAR_SHIFT;
        else
            break;
    }
    if (sc_left)
        sc_left_dist = p->qpos+1 - sc_left;
    edist -= sc_left;

    // right end
    for (j = p->b->core.n_cigar-1; j >= i; j--) {
        int cig  = bam_get_cigar(p->b)[j] & BAM_CIGAR_MASK;
        if (cig == BAM_CHARD_CLIP)
            continue;
        else if (cig == BAM_CSOFT_CLIP)
            sc_right += bam_get_cigar(p->b)[j] >> BAM_CIGAR_SHIFT;
        else
            break;
    }
    if (sc_right)
        sc_right_dist = p->b->core.l_qseq - sc_right - p->qpos;

    // Distance to nearest soft-clips and length of that clip.
    if (sc_left_dist >= 0) {
        if (sc_right_dist < 0 || sc_left_dist < sc_right_dist) {
            *sc_len  = sc_left;
            *sc_dist = sc_left_dist;
        }
    } else if (sc_right_dist >= 0) {
        *sc_len  = sc_right;
        *sc_dist = sc_right_dist;
    } else {
        *sc_len  = 0;
        *sc_dist = 0;
    }

    *len = p->b->core.l_qseq - sc_left - sc_right;
    return edist;
}

void bcf_callaux_clean(bcf_callaux_t *bca, bcf_call_t *call)
{
    memset(bca->ref_pos,0,sizeof(int)*bca->npos);
    memset(bca->alt_pos,0,sizeof(int)*bca->npos);
    memset(bca->iref_pos,0,sizeof(int)*bca->npos);
    memset(bca->ialt_pos,0,sizeof(int)*bca->npos);
    memset(bca->ref_mq,0,sizeof(int)*bca->nqual);
    memset(bca->alt_mq,0,sizeof(int)*bca->nqual);
    memset(bca->iref_mq,0,sizeof(int)*bca->nqual);
    memset(bca->ialt_mq,0,sizeof(int)*bca->nqual);
    memset(bca->ref_bq,0,sizeof(int)*bca->nqual);
    memset(bca->alt_bq,0,sizeof(int)*bca->nqual);
    memset(bca->fwd_mqs,0,sizeof(int)*bca->nqual);
    memset(bca->rev_mqs,0,sizeof(int)*bca->nqual);
    if ( call->ADF ) memset(call->ADF,0,sizeof(int32_t)*(call->n+1)*B2B_MAX_ALLELES);
    if ( call->ADR ) memset(call->ADR,0,sizeof(int32_t)*(call->n+1)*B2B_MAX_ALLELES);
    if ( call->SCR ) memset(call->SCR,0,sizeof(*call->SCR)*(call->n+1));
    if ( bca->fmt_flag&B2B_FMT_NMBZ )
    {
        memset(call->ref_nm,0,sizeof(*call->ref_nm)*(call->n+1)*B2B_N_NM);
        memset(call->alt_nm,0,sizeof(*call->alt_nm)*(call->n+1)*B2B_N_NM);
    }
    else
    {
        memset(call->ref_nm,0,sizeof(*call->ref_nm)*B2B_N_NM);
        memset(call->alt_nm,0,sizeof(*call->alt_nm)*B2B_N_NM);
    }
    if ( call->QM ) memset(call->QM,0,sizeof(*call->QM)*call->n*B2B_MAX_ALLELES);
    memset(call->QS,0,sizeof(*call->QS)*call->n*B2B_MAX_ALLELES);
    memset(bca->ref_scl,  0, 100*sizeof(int));
    memset(bca->alt_scl,  0, 100*sizeof(int));
    memset(bca->iref_scl, 0, 100*sizeof(int));
    memset(bca->ialt_scl, 0, 100*sizeof(int));
    int i;
    for (i=0; i<2; i++) bca->nnm[i] = 0;
    for (i=0; i<2; i++) bca->nm[i] = 0;
}

/*
    Notes:
    - Called from bam_plcmd.c by mpileup. Amongst other things, sets the bcf_callret1_t.QS frequencies
        which are carried over via bcf_call_combine and bcf_call2bcf to the output BCF as the INFO/QS and FMT/QS annotations.
        Later it's used for multiallelic calling by `call -m`, `call -mG` and `+trio-dnm`.
    - ref_base is the 4-bit representation of the reference base. It is negative if we are looking at an indel.
 */
/*
 * This function is called once for each sample.
 * _n is number of pilesups pl contributing reads to this sample
 * pl is pointer to array of _n pileups (one pileup per read)
 * ref_base is the 4-bit representation of the reference base. It is negative if we are looking at an indel.
 * bca is the settings to perform calls across all samples
 * r is the returned value of the call
 */
int bcf_call_glfgen(int _n, const bam_pileup1_t *pl, int ref_base, bcf_callaux_t *bca, bcf_callret1_t *r)
{
    int i, n, ref4, is_indel, ori_depth = 0;

#ifdef GLF_DEBUG
    fprintf(stderr, "Call GLFGEN\n");
#endif

    // clean from previous run
    r->ori_depth = 0;
    r->mq0 = 0;
    memset(r->anno,0,sizeof(double)*16);
    memset(r->p,0,sizeof(float)*25);
    if (r->QM) memset(r->QM,0,sizeof(*r->QM)*B2B_MAX_ALLELES);
    r->SCR = 0;

    if (ref_base >= 0) {
        ref4 = seq_nt16_int[ref_base];
        is_indel = 0;
    } else ref4 = 4, is_indel = 1;
    if (_n == 0) return -1;
    // enlarge the bases array if necessary
    if (bca->max_bases < _n) {
        bca->max_bases = _n;
        kroundup32(bca->max_bases);
        bca->bases = (uint16_t*)realloc(bca->bases, 2 * bca->max_bases);
    }

    // Detect if indel occurs anywhere in this sample
    int indel_in_sample = 0;
    if (bca->edlib) {
        for (i = n = 0; i < _n; ++i) {
            const bam_pileup1_t *p = pl + i;
            if (p->indel) indel_in_sample = 1;
        }
    }

    // fill the bases array
    double nqual_over_60 = bca->nqual / 60.0;
    int ADR_ref_missed[4] = {0};
    int ADF_ref_missed[4] = {0};
    for (i = n = 0; i < _n; ++i) {
        const bam_pileup1_t *p = pl + i;
        int b;          // the base or indel type
        int q;          // the base or indel quality used to calculate PL
        int seqQ;       // used to cap the indel quality given the sequence context
        int mapQ;       // to cap the quality for low MQ reads
        int baseQ;      // used only for supporting INFO annotations
        int is_diff;    // is this base or indel type different from the reference
        int min_dist;   // distance from the end, used for tail distance bias
        if ( bca->fmt_flag&(B2B_INFO_SCR|B2B_FMT_SCR) && PLP_HAS_SOFT_CLIP(&p->cd) ) r->SCR++;
        if (p->is_refskip || (p->b->core.flag&BAM_FUNMAP)) continue;

        // The meaning of the indel related variables:
        //  is_indel  .. is this position currently tested for an indel
        //  p->is_del .. is the current base a deletion in this read (unrelated to the tested indel)
        //  p->indel  .. is there an indel starting after this position (i.e. does this read have the tested indel)
        if (p->is_del && !is_indel) continue;   // not testing an indel and the read has a spanning deletion

        int inm = -1;

        ++ori_depth;
        if (is_indel)   // testing an indel position
        {
            b = p->aux>>16&0x3f;        // indel type
            seqQ = q = (p->aux & 0xff); // mp2 + builtin indel-bias

            if (bca->edlib) {
                if (indel_in_sample) {
                    seqQ = q = (p->aux & 0xff); // mp2 + builtin indel-bias
                } else if (p->aux & 0xff) {
                    // An indel in another sample, but not this.  So just use
                    // basic sequence confidences.
                    q = bam_get_qual(p->b)[p->qpos];
                    if (q > bca->max_baseQ) q = bca->max_baseQ;
                    seqQ = 99;
                }
            }

            if ( !bca->indels_v20 && !bca->edlib )
            {
                /*
                    This heuristics was introduced by e4e161068 and claims to fix #1446. However, we obtain
                    correct result on the provided test case even when this code is commented out, so this
                    may not be needed anymore. Leaving it in only for backward compatibility for now.
                    See mpileup-tests homdel-issue-1446 and CHM1_CHM13_2.45x-1-1701408 which work only when
                    this code is disabled.
                */
                if (p->indel == 0 && (q < _n/2 || _n > 20)) {
                    // high quality indel calls without p->indel set aren't
                    // particularly indicative of being a good REF match either,
                    // at least not in low coverage.  So require solid coverage
                    // before we start utilising such quals.
                    b = 0;
                    q = (int)bam_get_qual(p->b)[p->qpos];
                    seqQ = (3*seqQ + 2*q)/8;
                }
                if (_n > 20 && seqQ > 40) seqQ = 40;
            }

            is_diff = b ? 1 : 0;
            if ( bca->fmt_flag&(B2B_FMT_NMBZ|B2B_INFO_NMBZ|B2B_INFO_NM) )
            {
                inm = get_aux_nm(p,p->qpos,is_diff?0:1);
                if ( inm>=0 )
                {
                    bca->nnm[is_diff]++;
                    bca->nm[is_diff] += inm;
                }
            }

#ifdef GLF_DEBUG
            fprintf(stderr, "GLF %s\t%d\t%d\n", bam_get_qname(p->b),
                    bca->indel_types[b], q);
#endif
            if (q < bca->min_baseQ)
            {
                if (!p->indel && b < 4) // not an indel read
                {
                    if (bam_is_rev(p->b))
                        ADR_ref_missed[b]++;
                    else
                        ADF_ref_missed[b]++;
                }
                continue;
            }

#ifndef MIN
#define MIN(a,b) ((a)<(b)?(a):(b))
#endif

#ifndef MAX
#define MAX(a,b) ((a)>(b)?(a):(b))
#endif

#if 1 // TEST 6
            if (bca->edlib) {
                // Deeper data should rely more heavily on counts of data
                // than quality, as quality can be unreliable and prone to
                // miscalculations through BAQ, STR analysis, etc.
                // So we put a cap on how good seqQ can be.
                //
                // Is it simply the equivalent of increasing -F filter?
                // Not quite, as the latter removes many real variants upfront.
                // This calls them and then post-adjusts quality, potentially
                // dropping it later or changing genotype. So we still get
                // calls, but lower qual.
                seqQ = MIN(seqQ, bca->seqQ_offset-(MIN(20,_n)*5));

                if (indel_in_sample && p->indel == 0 && b != 0) {
                    // This read doesn't contain an indel in CIGAR, but it
                    // is assigned to an indel now (b != 0),  These are
                    // reads we've corrected with realignment, but they're
                    // also enriched for FPs so at high depth we reduce their
                    // confidence and let the depth do the talking.  If it's
                    // real and deep, then we don't need every read aligning.
                    // We also reduce base quality too to reflect the
                    // chance of our realignment being incorrect.

                    seqQ = MIN(seqQ, seqQ/2 + 5); // q2p5

                    // Finally reduce indel quality.
                    // This is a blend of indelQ and base QUAL.
                    q = MIN((int)bam_get_qual(p->b)[p->qpos]/4+10, q/4+1);
                }
            }
#endif

            // Note baseQ changes some output fields such as I16, but has no
            // significant affect on "call".
            baseQ  = p->aux>>8&0xff;
        }
        else
        {
            b = bam_seqi(bam_get_seq(p->b), p->qpos); // base
            b = seq_nt16_int[b? b : ref_base]; // b is the 2-bit base

            // Lowest of this and neighbour quality values
            uint8_t *qual = bam_get_qual(p->b);
            q = qual[p->qpos];
            if (p->qpos > 0 &&
                q > qual[p->qpos-1]+bca->delta_baseQ)
                q = qual[p->qpos-1]+bca->delta_baseQ;
            if (p->qpos+1 < p->b->core.l_qseq &&
                q > qual[p->qpos+1]+bca->delta_baseQ)
                q = qual[p->qpos+1]+bca->delta_baseQ;

            if (q < bca->min_baseQ) continue;
            if (q > bca->max_baseQ) q = bca->max_baseQ;
            baseQ = q;
            seqQ  = 99;
            is_diff = (ref4 < 4 && b == ref4)? 0 : 1;
            if ( bca->fmt_flag&(B2B_FMT_NMBZ|B2B_INFO_NMBZ|B2B_INFO_NM) )
            {
                inm = get_aux_nm(p,p->qpos,is_diff?0:1);
                if ( inm>=0 )
                {
                    bca->nnm[is_diff]++;
                    bca->nm[is_diff] += inm;
                }
            }
        }
        mapQ  = p->b->core.qual < 255? p->b->core.qual : DEF_MAPQ; // special case for mapQ==255
        if ( !mapQ ) r->mq0++;
#ifdef GLF_DEBUG
        fprintf(stderr, "GLF2 %s\t%d\t%d\t%d,%d\n",
                bam_get_qname(p->b), b, q,
                seqQ, mapQ);
#endif
        if (q > seqQ) q = seqQ;
        mapQ = mapQ < bca->capQ? mapQ : bca->capQ;
        if (q > mapQ) q = mapQ;
        if (q > 63) q = 63;
        if (q < 4) q = 4;       // MQ=0 reads count as BQ=4
        bca->bases[n++] = q<<5 | (int)bam_is_rev(p->b)<<4 | b;
        //if (is_indel) fprintf(stderr,"xx:base,q,strand\t%d\t%d\t%d\n",b,q,bam_is_rev(p->b)?0:1);

        // collect annotations
        if (b < 4)
        {
            if ( bca->fmt_flag&B2B_FMT_QM ) r->QM[b] += qual2err(q);
            r->QS[b] += q;
            if ( r->ADF )
            {
                if ( bam_is_rev(p->b) )
                    r->ADR[b]++;
                else
                    r->ADF[b]++;
            }
        }
        ++r->anno[0<<2|is_diff<<1|bam_is_rev(p->b)];
        min_dist = p->b->core.l_qseq - 1 - p->qpos;
        if (min_dist > p->qpos) min_dist = p->qpos;
        if (min_dist > CAP_DIST) min_dist = CAP_DIST;
        r->anno[1<<2|is_diff<<1|0] += baseQ;
        r->anno[1<<2|is_diff<<1|1] += baseQ * baseQ;
        r->anno[2<<2|is_diff<<1|0] += mapQ;
        r->anno[2<<2|is_diff<<1|1] += mapQ * mapQ;
        r->anno[3<<2|is_diff<<1|0] += min_dist;
        r->anno[3<<2|is_diff<<1|1] += min_dist * min_dist;

        // collect for bias tests
        if ( baseQ > 59 ) baseQ = 59;
        if ( mapQ > 59 ) mapQ = 59;
        int len, epos = 0, sc_len = 0, sc_dist = 0;
        if ( bca->fmt_flag & (B2B_INFO_RPBZ|B2B_INFO_VDB|B2B_INFO_SCBZ) )
        {
            int pos = get_position(p, &len, &sc_len, &sc_dist);
            epos = (double)pos/(len+1) * (bca->npos - 1);
            if (sc_len) {
                sc_len = 15.0*sc_len / (sc_dist+1);
                if (sc_len > 99) sc_len = 99;
            }
            assert( epos>=0 && epos<bca->npos );
            assert( sc_len>=0 && sc_len<bca->npos );
        }
        int imq  = mapQ * nqual_over_60;
        int ibq  = baseQ * nqual_over_60;

        if ( bam_is_rev(p->b) )
            bca->rev_mqs[imq]++;
        else
            bca->fwd_mqs[imq]++;

        if ( !is_diff )
        {
            bca->ref_pos[epos]++;
            bca->ref_bq[ibq]++;
            bca->ref_mq[imq]++;
            bca->ref_scl[sc_len]++;
            if ( inm>=0 )
            {
                bca->ref_nm[inm]++;
                if ( r->ref_nm ) r->ref_nm[inm]++;
            }
        }
        else
        {
            bca->alt_pos[epos]++;
            bca->alt_bq[ibq]++;
            bca->alt_mq[imq]++;
            bca->alt_scl[sc_len]++;
            if ( inm>=0 )
            {
                bca->alt_nm[inm]++;
                if ( r->alt_nm ) r->alt_nm[inm]++;
            }
        }
    }

    // Compensate for AD not being counted on low quality REF indel matches.
    if ( r->ADF && bca->ambig_reads==B2B_INC_AD0 )
    {
        for (i=0; i<4; i++)
        {
            r->ADR[0] += ADR_ref_missed[i];
            r->ADF[0] += ADF_ref_missed[i];
        }
    }
    else if ( r->ADF && bca->ambig_reads==B2B_INC_AD )
    {
        int dp = 0, dp_ambig = 0;
        for (i=0; i<4; i++) dp += r->ADR[i];
        for (i=0; i<4; i++) dp_ambig += ADR_ref_missed[i];
        if ( dp )
            for (i=0; i<4; i++) r->ADR[i] += lroundf((float)dp_ambig * r->ADR[i]/dp);
        dp = 0, dp_ambig = 0;
        for (i=0; i<4; i++) dp += r->ADF[i];
        for (i=0; i<4; i++) dp_ambig += ADF_ref_missed[i];
        if ( dp )
            for (i=0; i<4; i++) r->ADF[i] += lroundf((float)dp_ambig * r->ADF[i]/dp);
    }

    // Else consider downgrading bca->bases[] scores by AD vs AD_ref_missed
    // ratios.  This is detrimental on Illumina, but beneficial on PacBio CCS.
    // It's possibly related to the homopolyer error likelihoods or overall
    // Indel accuracy.  Maybe tie this in to the -h option?

    r->ori_depth = ori_depth;
    // glfgen
    errmod_cal(bca->e, n, 5, bca->bases, r->p); // calculate PL of each genotype

    // TODO: account for the number of unassigned reads.  If depth is 50,
    // but AD is 5,7 then it may look like a variant but it probably
    // should be low quality.

    return n;
}


/*
 *  calc_vdb() - returns value between zero (most biased) and one (no bias)
 *               on success, or HUGE_VAL when VDB cannot be calculated because
 *               of insufficient depth (<2x)
 *
 *  Variant Distance Bias tests if the variant bases are positioned within the
 *  reads with sufficient randomness. Unlike other tests, it looks only at
 *  variant reads and therefore gives different kind of information than Read
 *  Position Bias for instance. VDB was developed for detecting artefacts in
 *  RNA-seq calls where reads from spliced transcripts span splice site
 *  boundaries.  The current implementation differs somewhat from the original
 *  version described in supplementary material of PMID:22524474, but the idea
 *  remains the same. (Here the random variable tested is the average distance
 *  from the averaged position, not the average pairwise distance.)
 *
 *  For coverage of 2x, the calculation is exact but is approximated for the
 *  rest. The result is most accurate between 4-200x. For 3x or >200x, the
 *  reported values are slightly more favourable than those of a true random
 *  distribution.
 */
double calc_vdb(int *pos, int npos)
{
    // Note well: the parameters were obtained by fitting to simulated data of
    // 100bp reads. This assumes rescaling to 100bp in bcf_call_glfgen().
    const int readlen = 100;
    assert( npos==readlen );

    #define nparam 15
    const float param[nparam][3] = { {3,0.079,18}, {4,0.09,19.8}, {5,0.1,20.5}, {6,0.11,21.5},
        {7,0.125,21.6}, {8,0.135,22}, {9,0.14,22.2}, {10,0.153,22.3}, {15,0.19,22.8},
        {20,0.22,23.2}, {30,0.26,23.4}, {40,0.29,23.5}, {50,0.35,23.65}, {100,0.5,23.7},
        {200,0.7,23.7} };

    int i, dp = 0;
    float mean_pos = 0, mean_diff = 0;
    for (i=0; i<npos; i++)
    {
        if ( !pos[i] ) continue;
        dp += pos[i];
        mean_pos += pos[i]*i;
    }
    if ( dp<2 ) return HUGE_VAL;     // one or zero reads can be placed anywhere

    mean_pos /= dp;
    for (i=0; i<npos; i++)
    {
        if ( !pos[i] ) continue;
        mean_diff += pos[i] * fabs(i - mean_pos);
    }
    mean_diff /= dp;

    int ipos = mean_diff;   // tuned for float-to-int implicit conversion
    if ( dp==2 )
        return (2*readlen-2*(ipos+1)-1)*(ipos+1)/(readlen-1)/(readlen*0.5);

    if ( dp>=200 )
        i = nparam; // shortcut for big depths
    else
    {
        for (i=0; i<nparam; i++)
            if ( param[i][0]>=dp ) break;
    }
    float pshift, pscale;
    if ( i==nparam )
    {
        // the depth is too high, go with 200x
        pscale = param[nparam-1][1];
        pshift = param[nparam-1][2];
    }
    else if ( i>0 && param[i][0]!=dp )
    {
        // linear interpolation of parameters
        pscale = (param[i-1][1] + param[i][1])*0.5;
        pshift = (param[i-1][2] + param[i][2])*0.5;
    }
    else
    {
        pscale = param[i][1];
        pshift = param[i][2];
    }
    return 0.5*kf_erfc(-(mean_diff-pshift)*pscale);
}

double calc_chisq_bias(int *a, int *b, int n)
{
    int na = 0, nb = 0, i, ndf = n;
    for (i=0; i<n; i++) na += a[i];
    for (i=0; i<n; i++) nb += b[i];
    if ( !na || !nb ) return HUGE_VAL;

    double chisq = 0;
    for (i=0; i<n; i++)
    {
        if ( !a[i] && !b[i] ) ndf--;
        else
        {
            double tmp = a[i] - b[i];
            chisq += tmp*tmp/(a[i]+b[i]);
        }
    }
    /*
        kf_gammq: incomplete gamma function Q(a,x) = 1 - P(a,x) = Gamma(a,x)/Gamma(a)
        1 if the distributions are identical, 0 if very different
    */
    double prob = kf_gammaq(0.5*ndf, 0.5*chisq);
    return prob;
}

static double mann_whitney_1947_(int n, int m, int U)
{
     if (U<0) return 0;
     if (n==0||m==0) return U==0 ? 1 : 0;
    return (double)n/(n+m)*mann_whitney_1947_(n-1,m,U-m) + (double)m/(n+m)*mann_whitney_1947_(n,m-1,U);
}

double mann_whitney_1947(int n, int m, int U)
{
    #include "mw.h"

    assert(n >= 2 && m >= 2);

    return (n < 8 && m < 8 && U < 50)
        ? mw[n-2][m-2][U]
        : mann_whitney_1947_(n,m,U);
}

double mann_whitney_1947_cdf(int n, int m, int U)
{
    int i;
    double sum = 0;
    for (i=0; i<=U; i++)
        sum += mann_whitney_1947(n,m,i);
    return sum;
}

double calc_mwu_bias_cdf(int *a, int *b, int n)
{
    int na = 0, nb = 0, i;
    double U = 0;
    //double ties = 0;
    for (i=0; i<n; i++)
    {
        na += a[i];
        U  += a[i] * (nb + b[i]*0.5);
        nb += b[i];
        // if ( a[i] && b[i] )
        // {
        //     double tie = a[i] + b[i];
        //     ties += (tie*tie-1)*tie;
        // }
    }
    if ( !na || !nb ) return HUGE_VAL;

    // Always work with the smaller U
    double U_min = ((double)na * nb) - U;
    if ( U < U_min ) U_min = U;

    if ( na==1 ) return 2.0 * (floor(U_min)+1) / (nb+1);
    if ( nb==1 ) return 2.0 * (floor(U_min)+1) / (na+1);

    // Normal approximation, very good for na>=8 && nb>=8 and reasonable if na<8 or nb<8
    if ( na>=8 || nb>=8 )
    {
        double mean = ((double)na*nb)*0.5;
        // Correction for ties:
        //      double N = na+nb;
        //      double var2 = (N*N-1)*N-ties;
        //      if ( var2==0 ) return 1.0;
        //      var2 *= ((double)na*nb)/N/(N-1)/12.0;
        // No correction for ties:
        double var2 = ((double)na*nb)*(na+nb+1)/12.0;
        double z = (U_min - mean)/sqrt(2*var2);   // z is N(0,1)
        return 2.0 - kf_erfc(z);  // which is 1 + erf(z)
    }

    // Exact calculation
    double pval = 2*mann_whitney_1947_cdf(na,nb,U_min);
    return pval>1 ? 1 : pval;
}

double calc_mwu_bias(int *a, int *b, int n, int left)
{
    int na = 0, nb = 0, i;
    double U = 0;
    // double ties = 0;
    for (i=0; i<n; i++)
    {
        if (!a[i]) {
            if (!b[i]) continue;
            nb += b[i];
        } else if (!b[i]) {
            na += a[i];
            U  += a[i] * nb;
        } else {
            na += a[i];
            U  += a[i] * (nb + b[i]*0.5);
            nb += b[i];
            // double tie = a[i] + b[i];
            // ties += (tie*tie-1)*tie;
        }
    }
    if ( !na || !nb ) return HUGE_VAL;
    if ( na==1 || nb==1 ) return 1.0;       // Flat probability, all U values are equally likely

    double mean = ((double)na*nb)*0.5;
    if (left && U > mean) return 1; // for MQB which is asymmetrical
    if ( na==2 || nb==2 )
    {
        // Linear approximation
        return U>mean ? (2.0*mean-U)/mean : U/mean;
    }
    // Correction for ties:
    //      double N = na+nb;
    //      double var2 = (N*N-1)*N-ties;
    //      if ( var2==0 ) return 1.0;
    //      var2 *= ((double)na*nb)/N/(N-1)/12.0;
    // No correction for ties:
    double var2 = ((double)na*nb)*(na+nb+1)/12.0;
    if ( na>=8 || nb>=8 )
    {
        // Normal approximation, very good for na>=8 && nb>=8 and reasonable if na<8 or nb<8
        return exp(-0.5*(U-mean)*(U-mean)/var2);
    }

    // Exact calculation
    return mann_whitney_1947(na,nb,U) * sqrt(2*M_PI*var2);
}

// A Z-score version of the above function.
//
// See "Normal approximation and tie correction" at
// https://en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U_test
//
// The Z score is the number of standard deviations above or below the mean
// with 0 being equality of the two distributions and +ve/-ve from there.
//
// This is a more robust score to filter on.
// Refactored (by Claude Opus 5.5) to avoid the p^3-p step referred to in
// the Wikipedia page.
double calc_mwu_biasZ(int *a, int *b, int n, int left_only, int do_Z) {
    int i;

    // Optimisation: with no B values U is undefined.  (The old b_empty
    // branch computed na and t, but then always returned HUGE_VAL via !nb.)
    for (i = 0; i < n; i++)
        if (b[i])
            break;
    if (i == n)
        return HUGE_VAL;

    // Count equal (e) and less-than (l) permutations, plus the tie
    // adjustment.
    //
    // The standard tie-corrected variance is
    //     var = na*nb/12 * ((N+1) - sum(p^3-p) / (N*(N-1)))
    // with p = a[i]+b[i] and N = na+nb.  As sum(p) == N this simplifies to
    //     var = na*nb * (N^3 - sum(p^3)) / (12*N*(N-1))
    // N^3 - sum(p^3) is accumulated incrementally: adding a bin of size p
    // to a running total S contributes (S+p)^3 - S^3 - p^3 = 3*S*p*(S+p).
    // All terms are non-negative, so there is no integer overflow, no
    // cancellation, and a single occupied bin gives exactly zero.
    int64_t e = 0, l = 0, na = 0, nb = 0;
    double d = 0;   // N^3 - sum(p^3)
    for (i = n-1; i >= 0; i--) {
        // Combinations of a[i] and b[j] for i==j
        e += (int64_t)a[i]*b[i];

        // nb is running total of b[i+1]..b[n-1].
        // Therefore a[i]*nb is the number of combinations of a[i] and b[j]
        // for all i < j.
        l += a[i]*nb; // a<b

        int64_t S = na + nb, p = (int64_t)a[i] + b[i];
        d += 3.0 * S * p * (S + p);

        na += a[i];
        nb += b[i];
    }

    if (!na)
        return HUGE_VAL;

    double N = na + nb;             // >= 2 as na, nb >= 1
    double U = l + e*0.5;           // Mann-Whitney U score
    double m = (double)na*nb / 2.0;

    // With ties adjustment
    double var2 = (double)na*nb * d / (12.0 * N * (N-1));
    // var = na*nb*(na+nb+1)/12.0; // simpler; minus tie adjustment

    if (var2 <= 0)
        return do_Z ? 0 : 1;

    if (do_Z) {
        // S.D. normalised Z-score
        //Z = (U - m - (U-m >= 0 ? 0.5 : -0.5)) / sd; // gatk method?
        return (U - m) / sqrt(var2);
    }

    // Else U score, which can be asymmetric for some data types.
    if (left_only && U > m)
        return HUGE_VAL; // one-sided, +ve bias is OK, -ve is not.

    if (na >= 8 || nb >= 8) {
        // Normal approximation, very good for na>=8 && nb>=8 and
        // reasonable if na<8 or nb<8
        return exp(-0.5*(U-m)*(U-m)/var2);
    }

    // Exact calculation; na, nb < 8 here
    if (na==1 || nb == 1)
        return mann_whitney_1947_((int)na, (int)nb, U) * sqrt(2*M_PI*var2);
    else
        return mann_whitney_1947((int)na, (int)nb, U) * sqrt(2*M_PI*var2);
}

static inline double logsumexp2(double a, double b)
{
    if ( a>b )
        return log(1 + exp(b-a)) + a;
    else
        return log(1 + exp(a-b)) + b;
}

void calc_SegBias(const bcf_callret1_t *bcr, bcf_call_t *call)
{
    call->seg_bias = HUGE_VAL;
    if ( !bcr ) return;

    int nr = call->anno[2] + call->anno[3]; // number of observed non-reference reads
    if ( !nr ) return;

    int avg_dp = (call->anno[0] + call->anno[1] + nr) / call->n;    // average depth
    double M   = floor((double)nr / avg_dp + 0.5);   // an approximate number of variants samples in the population
    if ( M>call->n ) M = call->n;       // clamp M at the number of samples
    else if ( M==0 ) M = 1;
    double f = M / 2. / call->n;        // allele frequency
    double p = (double) nr / call->n;   // number of variant reads per sample expected if variant not real (poisson)
    double q = (double) nr / M;         // number of variant reads per sample expected if variant is real (poisson)
    double sum = 0;
    const double log2 = log(2.0);

    // fprintf(stderr,"M=%.1f  p=%e q=%e f=%f  dp=%d\n",M,p,q,f,avg_dp);
    int i;
    for (i=0; i<call->n; i++)
    {
        int oi = bcr[i].anno[2] + bcr[i].anno[3];       // observed number of non-ref reads
        double tmp;
        if ( oi )
        {
            // tmp = log(f) + oi*log(q/p) - q + log(2*(1-f) + f*pow(2,oi)*exp(-q)) + p; // this can under/overflow
            tmp = logsumexp2(log(2*(1-f)), log(f) + oi*log2 - q);
            tmp += log(f) + oi*log(q/p) - q + p;
        }
        else
            tmp = log(2*f*(1-f)*exp(-q) + f*f*exp(-2*q) + (1-f)*(1-f)) + p;
        sum += tmp;
        // fprintf(stderr,"oi=%d %e\n", oi,tmp);
    }
    call->seg_bias = sum;
}

/**
 *  bcf_call_combine() - sets the PL array and VDB, RPB annotations, finds the top two alleles
 *  @n:         number of samples
 *  @calls:     each sample's calls
 *  @bca:       auxiliary data structure for holding temporary values
 *  @ref_base:  the reference base
 *  @call:      filled with the annotations
 *
 *  Combines calls across the various samples being studied
 *  1. For each allele at each base across all samples the quality is summed so
 *     you end up with a set of quality sums for each allele present 2. The quality
 *     sums are sorted.
 *  3. Using the sorted quality sums we now create the allele ordering array
 *     A\subN. This is done by doing the following:
 *     a) If the reference allele is known it always comes first, otherwise N
 *        comes first.
 *     b) Then the rest of the alleles are output in descending order of quality
 *        sum (which we already know the qsum array was sorted).  Any allelles with
 *        qsum 0 will be excluded.
 *  4. Using the allele ordering array we create the genotype ordering array.
 *     In the worst case with an unknown reference this will be:  A0/A0 A1/A0 A1/A1
 *     A2/A0 A2/A1 A2/A2 A3/A0 A3/A1 A3/A2 A3/A3 A4/A0 A4/A1 A4/A2 A4/A3 A4/A4
 *  5. The genotype ordering array is then used to extract data from the error
 *     model 5*5 matrix and is used to produce a Phread likelihood array for each
 *     sample.
 */
int bcf_call_combine(int n, const bcf_callret1_t *calls, bcf_callaux_t *bca, int ref_base /*4-bit*/, bcf_call_t *call)
{
    int ref4, i, j;
    float qsum[B2B_MAX_ALLELES] = {0,0,0,0,0};
    if (ref_base >= 0) {
        call->ori_ref = ref4 = seq_nt16_int[ref_base];
        if (ref4 > 4) ref4 = 4;
    } else call->ori_ref = -1, ref4 = 0;

    // calculate qsum, this is done by summing normalized qsum across all samples,
    // to account for differences in coverage
    for (i = 0; i < n; ++i)
    {
        float sum = 0;
        for (j = 0; j < 4; ++j) sum += calls[i].QS[j];
        if ( sum )
            for (j = 0; j < 4; j++) qsum[j] += (float)calls[i].QS[j] / sum;
    }

    // sort qsum in ascending order (insertion sort)
    float *ptr[5], *tmp;
    for (i=0; i<5; i++) ptr[i] = &qsum[i];
    for (i=1; i<4; i++)
        for (j=i; j>0 && *ptr[j] < *ptr[j-1]; j--)
            tmp = ptr[j], ptr[j] = ptr[j-1], ptr[j-1] = tmp;

    // Set the reference allele and alternative allele(s)
    for (i=0; i<5; i++) call->a[i] = -1;
    for (i=0; i<B2B_MAX_ALLELES; i++) call->qsum[i] = 0;
    call->unseen = -1;
    call->a[0] = ref4;
    for (i=3, j=1; i>=0; i--)   // i: alleles sorted by QS; j, a[j]: output allele ordering
    {
        int ipos = ptr[i] - qsum;   // position in sorted qsum array
        if ( ipos==ref4 )
            call->qsum[0] = qsum[ipos];    // REF's qsum
        else
        {
            if ( !qsum[ipos] ) break;       // qsum is 0, this and consequent alleles are not seen in the pileup
            call->qsum[j] = qsum[ipos];
            call->a[j++]  = ipos;
        }
    }
    if (ref_base >= 0)
    {
        // for SNPs, find the "unseen" base
        if (((ref4 < 4 && j < 4) || (ref4 == 4 && j < 5)) && i >= 0)
            call->unseen = j, call->a[j++] = ptr[i] - qsum;
        call->n_alleles = j;
    }
    else
    {
        call->n_alleles = j;
        if (call->n_alleles == 1) return -1; // no reliable supporting read. stop doing anything
    }
    int has_alt = (call->n_alleles==2 && call->unseen!=-1) ? 0 : 1;
    /*
     * Set the phread likelihood array (call->PL) This array is 15 entries long
     * for each sample because that is size of an upper or lower triangle of a
     * worst case 5x5 matrix of possible genotypes. This worst case matrix will
     * occur when all 4 possible alleles are present and the reference allele
     * is unknown.  The sides of the matrix will correspond to the reference
     * allele (if known) followed by the alleles present in descending order of
     * quality sum
     */
    {
        int x, g[15], z;
        x = call->n_alleles * (call->n_alleles + 1) / 2;
        // get the possible genotypes
        // this is done by creating an ordered list of locations g for call (allele a, allele b) in the genotype likelihood matrix
        for (i = z = 0; i < call->n_alleles; ++i) {
            for (j = 0; j <= i; ++j) {
                g[z++] = call->a[j] * 5 + call->a[i];
            }
        }
        // for each sample calculate the PL
        for (i = 0; i < n; ++i)
        {
            int32_t *PL = call->PL + x * i;
            const bcf_callret1_t *r = calls + i;
            float min = FLT_MAX;
            for (j = 0; j < x; ++j) {
                if (min > r->p[g[j]]) min = r->p[g[j]];
            }
            for (j = 0; j < x; ++j) {
                int y;
                y = (int)(r->p[g[j]] - min + .499);   // .499 to ensure rounding to nearest int
                if (y > 255) y = 255;
                PL[j] = y;
            }
        }
        if ( call->DP4 )
        {
            for (i=0; i<n; i++)
            {
                call->DP4[4*i]   = calls[i].anno[0];
                call->DP4[4*i+1] = calls[i].anno[1];
                call->DP4[4*i+2] = calls[i].anno[2];
                call->DP4[4*i+3] = calls[i].anno[3];
            }
        }
        if ( call->SCR )
        {
            for (i=0; i<n; i++)
            {
                call->SCR[0]  += calls[i].SCR;
                call->SCR[1+i] = calls[i].SCR;
            }
        }
        if ( call->ADF )
        {
            assert( call->n_alleles<=B2B_MAX_ALLELES );   // this is always true for SNPs and so far for indels as well

            // reorder ADR,ADF to match the allele ordering at this site
            int32_t tmp[B2B_MAX_ALLELES];
            int32_t *adr = call->ADR + B2B_MAX_ALLELES, *adr_out = call->ADR + B2B_MAX_ALLELES;
            int32_t *adf = call->ADF + B2B_MAX_ALLELES, *adf_out = call->ADF + B2B_MAX_ALLELES;
            int32_t *adr_tot = call->ADR;   // the first bin stores total counts per site
            int32_t *adf_tot = call->ADF;
            for (i=0; i<n; i++)
            {
                for (j=0; j<call->n_alleles; j++)
                {
                    tmp[j] = adr[ call->a[j] ];
                    adr_tot[j] += tmp[j];
                }
                for (j=0; j<call->n_alleles; j++) adr_out[j] = tmp[j];
                for (j=0; j<call->n_alleles; j++)
                {
                    tmp[j] = adf[ call->a[j] ];
                    adf_tot[j] += tmp[j];
                }
                for (j=0; j<call->n_alleles; j++) adf_out[j] = tmp[j];
                adf_out += call->n_alleles;
                adr_out += call->n_alleles;
                adr += B2B_MAX_ALLELES;
                adf += B2B_MAX_ALLELES;
            }
        }
        if ( bca->fmt_flag & B2B_FMT_QS )
        {
            assert( call->n_alleles<=B2B_MAX_ALLELES );   // this is always true for SNPs and so far for indels as well

            // reorder QS to match the allele ordering at this site
            int32_t tmp[B2B_MAX_ALLELES];
            int32_t *qs = call->QS, *qs_out = call->QS;
            for (i=0; i<n; i++)
            {
                for (j=0; j<call->n_alleles; j++) tmp[j] = qs[ call->a[j] ];
                for (j=0; j<call->n_alleles; j++) qs_out[j] = tmp[j] < BCF_MAX_BT_INT32 ? tmp[j] : BCF_MAX_BT_INT32;
                qs_out += call->n_alleles;
                qs += B2B_MAX_ALLELES;
            }
        }
        if ( bca->fmt_flag & B2B_FMT_QM )
        {
            assert( call->n_alleles<=B2B_MAX_ALLELES );   // this is always true for SNPs and so far for indels as well

            // average and reorder QM to match the allele ordering at this site
            int32_t *qm  = call->QM;
            int32_t *adr = call->ADR + B2B_MAX_ALLELES;
            int32_t *adf = call->ADF + B2B_MAX_ALLELES;
            for (i=0; i<n; i++)
            {
                for (j=0; j<call->n_alleles; j++)   // j:reordered alleles
                {
                    int jold = call->a[j];
                    int dp = adr[j] + adf[j];
                    double val = dp ? -4.3429 * log(calls[i].QM[jold]/dp) : 0;
                    qm[j] = (int)(val + .499);  // 499 to ensure rounding to nearest int
                }
                adr += call->n_alleles; // adr,adf are overwritten with the new order and n_alleles!
                adf += call->n_alleles;
                qm  += call->n_alleles;
            }
        }

//      if (ref_base < 0) fprintf(stderr, "%d,%d,%f,%d\n", call->n_alleles, x, sum_min, call->unseen);
    }
    // combine annotations
    memset(call->anno, 0, 16 * sizeof(double));
    call->ori_depth = 0;
    call->depth     = 0;
    call->mq0       = 0;
    for (i = 0; i < n; ++i) {
        call->depth += calls[i].anno[0] + calls[i].anno[1] + calls[i].anno[2] + calls[i].anno[3];
        call->ori_depth += calls[i].ori_depth;
        call->mq0 += calls[i].mq0;
        for (j = 0; j < 16; ++j) call->anno[j] += calls[i].anno[j];
    }

    // No need to calculate MWU tests when there is no ALT allele, this should speed up things slightly
    if ( !has_alt ) return 0;

    if ( bca->fmt_flag & B2B_INFO_FS )
    {
        double left,right,two;
        call->strand_bias = kt_fisher_exact(call->anno[0], call->anno[1], call->anno[2], call->anno[3], &left, &right, &two);
    }
    if ( bca->fmt_flag & B2B_INFO_SGB ) calc_SegBias(calls, call);

    // calc_chisq_bias("XPOS", call->bcf_hdr->id[BCF_DT_CTG][call->tid].key, call->pos, bca->ref_pos, bca->alt_pos, bca->npos);
    // calc_chisq_bias("XMQ", call->bcf_hdr->id[BCF_DT_CTG][call->tid].key, call->pos, bca->ref_mq, bca->alt_mq, bca->nqual);
    // calc_chisq_bias("XBQ", call->bcf_hdr->id[BCF_DT_CTG][call->tid].key, call->pos, bca->ref_bq, bca->alt_bq, bca->nqual);

    // U z-normalised as +/- number of standard deviations from mean.
    if (call->ori_ref < 0) {    // indel
        if ( bca->fmt_flag & B2B_INFO_RPBZ )
            call->mwu_pos = calc_mwu_biasZ(bca->iref_pos, bca->ialt_pos, bca->npos, 0, 1);
        if ( bca->fmt_flag & B2B_INFO_MQBZ )
            call->mwu_mq  = calc_mwu_biasZ(bca->iref_mq,  bca->ialt_mq, bca->nqual,1,1);
        if ( bca->fmt_flag & B2B_INFO_SCBZ )
            call->mwu_sc  = calc_mwu_biasZ(bca->iref_scl, bca->ialt_scl, 100, 0,1);
    } else {
        if ( bca->fmt_flag & B2B_INFO_RPBZ )
            call->mwu_pos = calc_mwu_biasZ(bca->ref_pos, bca->alt_pos, bca->npos, 0, 1);
        if ( bca->fmt_flag & B2B_INFO_MQBZ )
            call->mwu_mq  = calc_mwu_biasZ(bca->ref_mq,  bca->alt_mq, bca->nqual,1,1);
        if ( bca->fmt_flag & B2B_INFO_BQBZ )
            call->mwu_bq  = calc_mwu_biasZ(bca->ref_bq,  bca->alt_bq, bca->nqual,0,1);
        if ( bca->fmt_flag & B2B_INFO_MQSBZ )
            call->mwu_mqs = calc_mwu_biasZ(bca->fwd_mqs, bca->rev_mqs, bca->nqual,0,1);
        if ( bca->fmt_flag & B2B_INFO_SCBZ )
            call->mwu_sc  = calc_mwu_biasZ(bca->ref_scl, bca->alt_scl, 100, 0,1);
    }
    if ( bca->fmt_flag & B2B_INFO_NMBZ )
        call->mwu_nm[0] = calc_mwu_biasZ(bca->ref_nm, bca->alt_nm, B2B_N_NM,0,1);
    if ( bca->fmt_flag & B2B_FMT_NMBZ )
    {
        for (i=0; i<n; i++)
        {
            float val = calc_mwu_biasZ(calls[i].ref_nm, calls[i].alt_nm, B2B_N_NM,0,1);
            call->mwu_nm[i+1] = val!=HUGE_VAL ? val : 0;
        }
    }
    if ( bca->fmt_flag & B2B_INFO_VDB )
        call->vdb = calc_vdb(bca->alt_pos, bca->npos);

    return 0;
}

int bcf_call2bcf(bcf_call_t *bc, bcf1_t *rec, bcf_callret1_t *bcr, int fmt_flag, const bcf_callaux_t *bca, const char *ref)
{
    extern double kt_fisher_exact(int n11, int n12, int n21, int n22, double *_left, double *_right, double *two);
    int i, j, nals = 1, has_alt = 0;

    bcf_hdr_t *hdr = bc->bcf_hdr;
    rec->rid  = bc->tid;
    rec->pos  = bc->pos;
    rec->qual = 0;

    bc->tmp.l = 0;
    if (bc->ori_ref < 0)    // indel
    {
        // REF
        kputc(ref[bc->pos], &bc->tmp);
        for (j = 0; j < bca->indelreg; ++j) kputc(ref[bc->pos+1+j], &bc->tmp);

        // ALT
        for (i=1; i<4; i++)
        {
            if (bc->a[i] < 0) break;
            kputc(',', &bc->tmp); kputc(ref[bc->pos], &bc->tmp);

            if (bca->indel_types[bc->a[i]] < 0) { // deletion
                for (j = -bca->indel_types[bc->a[i]]; j < bca->indelreg; ++j)
                    kputc(ref[bc->pos+1+j], &bc->tmp);
            } else { // insertion; cannot be a reference unless a bug
                char *inscns = &bca->inscns[bc->a[i] * bca->maxins];
                for (j = 0; j < bca->indel_types[bc->a[i]]; ++j)
                    kputc("ACGTN"[(int)inscns[j]], &bc->tmp);
                for (j = 0; j < bca->indelreg; ++j) kputc(ref[bc->pos+1+j], &bc->tmp);
            }
            nals++;
            has_alt = 1;
        }
    }
    else    // SNP
    {
        kputc("ACGTN"[bc->ori_ref], &bc->tmp);
        for (i=1; i<5; i++)
        {
            if (bc->a[i] < 0) break;
            kputc(',', &bc->tmp);
            if ( bc->unseen==i ) kputs("<*>", &bc->tmp);
            else
            {
                kputc("ACGT"[bc->a[i]], &bc->tmp);
                has_alt = 1;
            }
            nals++;
        }
    }
    bcf_update_alleles_str(hdr, rec, bc->tmp.s);

    bc->tmp.l = 0;

    // INFO
    if ( bc->ori_ref < 0 )
    {
        bcf_update_info_flag(hdr, rec, "INDEL", NULL, 1);
        uint32_t idv = bca->max_support;
        if ( fmt_flag&B2B_INFO_IMF) {
            float max_frac;
            // Recompute IDV and IMF based on alignment results for more
            // accurate counts, but only when in new "--indels-cns" mode.
            if (bc->ADF && bc->ADR && bca->edlib) {
                int max_ad = 0;
                for (int k = 1; k < rec->n_allele; k++) {
                    if (max_ad < bc->ADF[k] + bc->ADR[k])
                        max_ad = bc->ADF[k] + bc->ADR[k];
                }
                max_frac = (double)(max_ad) / bc->ori_depth;
                idv = max_ad;
            } else {
                max_frac = bca->max_frac;
            }
            // Copied here to maintain order for consistency of "make check"
            if ( fmt_flag&B2B_INFO_IDV )
                bcf_update_info_int32(hdr, rec, "IDV", &idv, 1);
            bcf_update_info_float(hdr, rec, "IMF", &max_frac, 1);
        } else {
            if ( fmt_flag&B2B_INFO_IDV )
                bcf_update_info_int32(hdr, rec, "IDV", &idv, 1);
        }
    }
    bcf_update_info_int32(hdr, rec, "DP", &bc->ori_depth, 1);
    if ( fmt_flag&B2B_INFO_ADF )
        bcf_update_info_int32(hdr, rec, "ADF", bc->ADF, rec->n_allele);
    if ( fmt_flag&B2B_INFO_ADR )
        bcf_update_info_int32(hdr, rec, "ADR", bc->ADR, rec->n_allele);
    if ( fmt_flag&(B2B_INFO_AD|B2B_INFO_DPR) )
    {
        for (i=0; i<rec->n_allele; i++) bc->ADF[i] += bc->ADR[i];
        if ( fmt_flag&B2B_INFO_AD )
            bcf_update_info_int32(hdr, rec, "AD", bc->ADF, rec->n_allele);
        if ( fmt_flag&B2B_INFO_DPR )
            bcf_update_info_int32(hdr, rec, "DPR", bc->ADF, rec->n_allele);
    }
    if ( fmt_flag&B2B_INFO_SCR )
        bcf_update_info_int32(hdr, rec, "SCR", bc->SCR, 1);

    float tmpf[16];
    for (i=0; i<16; i++) tmpf[i] = bc->anno[i];
    bcf_update_info_float(hdr, rec, "I16", tmpf, 16);
    bcf_update_info_float(hdr, rec, "QS", bc->qsum, nals);

    if ( has_alt )
    {
        if ( fmt_flag&B2B_INFO_VDB && bc->vdb != HUGE_VAL )
            bcf_update_info_float(hdr, rec, "VDB", &bc->vdb, 1);
        if ( fmt_flag&B2B_INFO_SGB && bc->seg_bias != HUGE_VAL )
            bcf_update_info_float(hdr, rec, "SGB", &bc->seg_bias, 1);
        if ( fmt_flag&B2B_INFO_NM && (bca->nnm[0] || bca->nnm[1]) )
        {
            for (i=0; i<2; i++) bc->nm[i] = bca->nnm[i] ? bca->nm[i]/bca->nnm[i] : 0;
            bcf_update_info_float(hdr, rec, "NM", bc->nm, 2);
        }

        if ( fmt_flag&B2B_INFO_RPBZ && bc->mwu_pos != HUGE_VAL )
            bcf_update_info_float(hdr, rec, "RPBZ", &bc->mwu_pos, 1);
        if ( fmt_flag&B2B_INFO_MQBZ && bc->mwu_mq != HUGE_VAL )
            bcf_update_info_float(hdr, rec, "MQBZ", &bc->mwu_mq, 1);
        if ( fmt_flag&B2B_INFO_MQSBZ && bc->mwu_mqs != HUGE_VAL )
            bcf_update_info_float(hdr, rec, "MQSBZ", &bc->mwu_mqs, 1);
        if ( fmt_flag&B2B_INFO_BQBZ && bc->mwu_bq != HUGE_VAL )
            bcf_update_info_float(hdr, rec, "BQBZ", &bc->mwu_bq, 1);
        if ( fmt_flag&B2B_INFO_NMBZ && bc->mwu_nm[0] != HUGE_VAL )
            bcf_update_info_float(hdr, rec, "NMBZ", bc->mwu_nm, 1);
        if ( fmt_flag&B2B_INFO_SCBZ && bc->mwu_sc != HUGE_VAL )
            bcf_update_info_float(hdr, rec, "SCBZ", &bc->mwu_sc, 1);
        if ( fmt_flag&B2B_INFO_FS && bc->strand_bias != HUGE_VAL )
            bcf_update_info_float(hdr, rec, "FS", &bc->strand_bias, 1);
    }

    tmpf[0] = bc->ori_depth ? (float)bc->mq0/bc->ori_depth : 0;
    if ( fmt_flag&B2B_INFO_MQ0F )
        bcf_update_info_float(hdr, rec, "MQ0F", tmpf, 1);

    // FORMAT
    rec->n_sample = bc->n;
    bcf_update_format_int32(hdr, rec, "PL", bc->PL, nals*(nals+1)/2 * rec->n_sample);
    if ( fmt_flag&B2B_FMT_DP )
    {
        int32_t *ptr = (int32_t*) bc->fmt_arr;
        for (i=0; i<bc->n; i++)
            ptr[i] = bc->DP4[4*i] + bc->DP4[4*i+1] + bc->DP4[4*i+2] + bc->DP4[4*i+3];
        bcf_update_format_int32(hdr, rec, "DP", bc->fmt_arr, rec->n_sample);
    }
    if ( fmt_flag&B2B_FMT_DV )
    {
        int32_t *ptr = (int32_t*) bc->fmt_arr;
        for (i=0; i<bc->n; i++)
            ptr[i] = bc->DP4[4*i+2] + bc->DP4[4*i+3];
        bcf_update_format_int32(hdr, rec, "DV", bc->fmt_arr, rec->n_sample);
    }
    if ( fmt_flag&B2B_FMT_SP )
    {
        int32_t *ptr = (int32_t*) bc->fmt_arr;
        for (i=0; i<bc->n; i++)
        {
            int fwd_ref = bc->DP4[4*i], rev_ref =  bc->DP4[4*i+1], fwd_alt = bc->DP4[4*i+2], rev_alt = bc->DP4[4*i+3];
            if ( fwd_ref+rev_ref<2 || fwd_alt+rev_alt<2 || fwd_ref+fwd_alt<2 || rev_ref+rev_alt<2 )
                ptr[i] = 0;
            else
            {
                double left, right, two;
                kt_fisher_exact(fwd_ref, rev_ref, fwd_alt, rev_alt, &left, &right, &two);
                int32_t x = (int)(-4.343 * log(two) + .499);
                if (x > 255) x = 255;
                ptr[i] = x;
            }
        }
        bcf_update_format_int32(hdr, rec, "SP", bc->fmt_arr, rec->n_sample);
    }
    if ( fmt_flag&B2B_FMT_DP4 )
        bcf_update_format_int32(hdr, rec, "DP4", bc->DP4, rec->n_sample*4);
    if ( fmt_flag&B2B_FMT_ADF )
        bcf_update_format_int32(hdr, rec, "ADF", bc->ADF+B2B_MAX_ALLELES, rec->n_sample*rec->n_allele);
    if ( fmt_flag&B2B_FMT_ADR )
        bcf_update_format_int32(hdr, rec, "ADR", bc->ADR+B2B_MAX_ALLELES, rec->n_sample*rec->n_allele);
    if ( fmt_flag&(B2B_FMT_AD|B2B_FMT_DPR) )
    {
        for (i=0; i<rec->n_sample*rec->n_allele; i++) bc->ADF[B2B_MAX_ALLELES+i] += bc->ADR[B2B_MAX_ALLELES+i];
        if ( fmt_flag&B2B_FMT_AD )
            bcf_update_format_int32(hdr, rec, "AD", bc->ADF+B2B_MAX_ALLELES, rec->n_sample*rec->n_allele);
        if ( fmt_flag&B2B_FMT_DPR )
            bcf_update_format_int32(hdr, rec, "DPR", bc->ADF+B2B_MAX_ALLELES, rec->n_sample*rec->n_allele);
    }
    if ( fmt_flag&B2B_FMT_SCR )
        bcf_update_format_int32(hdr, rec, "SCR", bc->SCR+1, rec->n_sample);
    if ( fmt_flag&B2B_FMT_QS )
        bcf_update_format_int32(hdr, rec, "QS", bc->QS, rec->n_sample*rec->n_allele);
    if ( fmt_flag&B2B_FMT_QM )
        bcf_update_format_int32(hdr, rec, "QM", bc->QM, rec->n_sample*rec->n_allele);

    if ( has_alt )
    {
        if ( fmt_flag&B2B_FMT_NMBZ )
            bcf_update_format_float(hdr, rec, "NMBZ", bc->mwu_nm+1, rec->n_sample);
    }

    return 0;
}