bwamem.c

#include <stdlib.h>
#include <string.h>
#include <stdio.h>
#include <assert.h>
#include <limits.h>
#include <math.h>
#ifdef HAVE_PTHREAD
#include <pthread.h>
#endif

#include "kstring.h"
#include "bwamem.h"
#include "bntseq.h"
#include "ksw.h"
#include "kvec.h"
#include "ksort.h"
#include "utils.h"

#ifdef USE_MALLOC_WRAPPERS
#  include "malloc_wrap.h"
#endif

/* Theory on probability and scoring *ungapped* alignment
 *
 * s'(a,b) = log[P(b|a)/P(b)] = log[4P(b|a)], assuming uniform base distribution
 * s'(a,a) = log(4), s'(a,b) = log(4e/3), where e is the error rate
 *
 * Scale s'(a,b) to s(a,a) s.t. s(a,a)=x. Then s(a,b) = x*s'(a,b)/log(4), or conversely: s'(a,b)=s(a,b)*log(4)/x
 *
 * If the matching score is x and mismatch penalty is -y, we can compute error rate e:
 *   e = .75 * exp[-log(4) * y/x]
 *
 * log P(seq) = \sum_i log P(b_i|a_i) = \sum_i {s'(a,b) - log(4)}
 *   = \sum_i { s(a,b)*log(4)/x - log(4) } = log(4) * (S/x - l)
 *
 * where S=\sum_i s(a,b) is the alignment score. Converting to the phred scale:
 *   Q(seq) = -10/log(10) * log P(seq) = 10*log(4)/log(10) * (l - S/x) = 6.02 * (l - S/x)
 *
 *
 * Gap open (zero gap): q' = log[P(gap-open)], r' = log[P(gap-ext)] (see Durbin et al. (1998) Section 4.1)
 * Then q = x*log[P(gap-open)]/log(4), r = x*log[P(gap-ext)]/log(4)
 *
 * When there are gaps, l should be the length of alignment matches (i.e. the M operator in CIGAR)
 */

static const bntseq_t *global_bns = 0; // for debugging only

mem_opt_t *mem_opt_init()
{
  mem_opt_t *o;
  o = calloc(1, sizeof(mem_opt_t));
  o->flag = 0;
  o->a = 1; o->b = 4;
  o->o_del = o->o_ins = 6;
  o->e_del = o->e_ins = 1;
  o->w = 100;
  o->T = 30;
  o->zdrop = 100;
  o->pen_unpaired = 17;
  o->pen_clip5 = o->pen_clip3 = 5;

  o->max_mem_intv = 20;

  o->min_seed_len = 19;
  o->split_width = 10;
  o->max_occ = 500;
  o->max_chain_gap = 10000;
  o->max_ins = 10000;
  o->mask_level = 0.50;
  o->drop_ratio = 0.50;
  o->XA_drop_ratio = 0.80;
  o->split_factor = 1.5;
  o->chunk_size = 10000000;
  o->n_threads = 1;
  o->max_XA_hits = 5;
  o->max_XA_hits_alt = 200;
  o->max_matesw = 50;
  o->mask_level_redun = 0.95;
  o->min_chain_weight = 0;
  o->max_chain_extend = 1<<30;
  o->mapQ_coef_len = 50; o->mapQ_coef_fac = log(o->mapQ_coef_len);
  bwa_fill_scmat(o->a, o->b, o->mat);
  return o;
}

/***************************
 * Collection SA invervals *
 ***************************/

#define intv_lt(a, b) ((a).readBegin == (b).readBegin ? (a).readEnd<(b).readEnd : (a).readBegin<(b).readBegin)
KSORT_INIT(mem_intv, bwtintv_t, intv_lt)

typedef struct {
  bwtintv_v mem, mem1, *tmpv[2];
} smem_aux_t;

static smem_aux_t *smem_aux_init()
{
  smem_aux_t *a;
  a = calloc(1, sizeof(smem_aux_t));
  a->tmpv[0] = calloc(1, sizeof(bwtintv_v));
  a->tmpv[1] = calloc(1, sizeof(bwtintv_v));
  return a;
}

static void smem_aux_destroy(smem_aux_t *a)
{	
  free(a->tmpv[0]->a); free(a->tmpv[0]);
  free(a->tmpv[1]->a); free(a->tmpv[1]);
  free(a->mem.a); free(a->mem1.a);
  free(a);
}

static void mem_collect_intv(const mem_opt_t *opt, const lbwt_t *lbwt, int len, const uint8_t *seq, smem_aux_t *a)
{
  int i, k, x = 0, old_n;
  int start_width = 1;
  int split_len = (int)(opt->min_seed_len * opt->split_factor + .499);
  a->mem.n = 0;
  // first pass: find all SMEMs
  while (x < len) {
    if (seq[x] < 4) {
      x = bwt_smem1(lbwt, len, seq, x, start_width, &a->mem1, a->tmpv);
      for (i = 0; i < a->mem1.n; ++i) {
	bwtintv_t *p = &a->mem1.a[i];
	int slen = p->readEnd-p->readBegin;//(uint32_t)p->info - (p->info>>32); // seed length
	if (slen >= opt->min_seed_len)
	  kv_push(bwtintv_t, a->mem, *p);
      }
    } else ++x;
  }
  // second pass: find MEMs inside a long SMEM
  old_n = a->mem.n;
  for (k = 0; k < old_n; ++k) {
    bwtintv_t *p = &a->mem.a[k];
    //int start = p->info>>32, end = (int32_t)p->info;
    uint32_t start=p->readBegin,end=p->readEnd;
    if (end - start < split_len || p->len > opt->split_width) continue;
    bwt_smem1(lbwt, len, seq, (start + end)>>1, p->len+1, &a->mem1, a->tmpv);
    for (i = 0; i < a->mem1.n; ++i)
      if (a->mem1.a[i].readEnd - (a->mem1.a[i].readBegin) >= opt->min_seed_len)
  	kv_push(bwtintv_t, a->mem, a->mem1.a[i]);
  }
  // third pass: LAST-like
  if (opt->max_mem_intv > 0) {
    x = 0;
    while (x < len) {
      if (seq[x] < 4) {
	bwtintv_t m;
	x = bwt_seed_strategy1(lbwt, len, seq, x, opt->min_seed_len, opt->max_mem_intv, &m);
	if (m.len > 0) kv_push(bwtintv_t, a->mem, m);
      } else ++x;
    }
  }
  // sort
  ks_introsort(mem_intv, a->mem.n, a->mem.a);
}

/************
 * Chaining *
 ************/

typedef struct {
  uint64_t rbeg;
  int32_t qbeg, len;
  int score;
} mem_seed_t; // unaligned memory

typedef struct {
  int n, m, first, rid;
  uint32_t w:29, kept:2, is_alt:1;
  float frac_rep;
  int64_t pos;
  mem_seed_t *seeds;
} mem_chain_t;

typedef struct { size_t n, m; mem_chain_t *a;  } mem_chain_v;

#include "kbtree.h"

#define chain_cmp(a, b) (((b).pos < (a).pos) - ((a).pos < (b).pos))
KBTREE_INIT(chn, mem_chain_t, chain_cmp)

// return 1 if the seed is merged into the chain
static int test_and_merge(const mem_opt_t *opt, int64_t l_pac, mem_chain_t *c, const mem_seed_t *p, int seed_rid)
{
  int64_t qend, rend, x, y;
  const mem_seed_t *last = &c->seeds[c->n-1];
  qend = last->qbeg + last->len;
  rend = last->rbeg + last->len;
  if (seed_rid != c->rid) return 0; // different chr; request a new chain
  if (p->qbeg >= c->seeds[0].qbeg && p->qbeg + p->len <= qend && p->rbeg >= c->seeds[0].rbeg && p->rbeg + p->len <= rend)
    return 1; // contained seed; do nothing
  if ((last->rbeg < l_pac || c->seeds[0].rbeg < l_pac) && p->rbeg >= l_pac) return 0; // don't chain if on different strand
  x = p->qbeg - last->qbeg; // always non-negtive
  y = p->rbeg - last->rbeg;
  if (y >= 0 && x - y <= opt->w && y - x <= opt->w && x - last->len < opt->max_chain_gap && y - last->len < opt->max_chain_gap) { // grow the chain
    if (c->n == c->m) {
      c->m <<= 1;
      c->seeds = realloc(c->seeds, c->m * sizeof(mem_seed_t));
    }
    c->seeds[c->n++] = *p;
    return 1;
  }
  return 0; // request to add a new chain
}

int mem_chain_weight(const mem_chain_t *c)
{
  int64_t end;
  int j, w = 0, tmp;
  for (j = 0, end = 0; j < c->n; ++j) {
    const mem_seed_t *s = &c->seeds[j];
    if (s->qbeg >= end) w += s->len;
    else if (s->qbeg + s->len > end) w += s->qbeg + s->len - end;
    end = end > s->qbeg + s->len? end : s->qbeg + s->len;
  }
  tmp = w; w = 0;
  for (j = 0, end = 0; j < c->n; ++j) {
    const mem_seed_t *s = &c->seeds[j];
    if (s->rbeg >= end) w += s->len;
    else if (s->rbeg + s->len > end) w += s->rbeg + s->len - end;
    end = end > s->rbeg + s->len? end : s->rbeg + s->len;
  }
  w = w < tmp? w : tmp;
  return w < 1<<30? w : (1<<30)-1;
}

void mem_print_chain(const bntseq_t *bns, mem_chain_v *chn)
{
  int i, j;
  for (i = 0; i < chn->n; ++i) {
    mem_chain_t *p = &chn->a[i];
    err_printf("* Found CHAIN(%d): n=%d; weight=%d", i, p->n, mem_chain_weight(p));
    for (j = 0; j < p->n; ++j) {
      bwtint_t pos;
      int is_rev;
      pos = bns_depos(bns, p->seeds[j].rbeg, &is_rev);
      if (is_rev) pos -= p->seeds[j].len - 1;
      err_printf("\t%d;%d;%d,%ld(%s:%c%ld)", p->seeds[j].score, p->seeds[j].len, p->seeds[j].qbeg, (long)p->seeds[j].rbeg, bns->anns[p->rid].name, "+-"[is_rev], (long)(pos - bns->anns[p->rid].offset) + 1);
    }
    err_putchar('\n');
  }
}
#define _get_sahigh2(sahigh2,l) (((sahigh2)[(l)>>4]>>(((~(l))&15)<<1))&3)
mem_chain_v mem_chain(const mem_opt_t *opt, const lbwt_t *lbwt, const bntseq_t *bns, int len, const uint8_t *seq, void *buf)
{
  int i, b, e, l_rep;
  int64_t l_pac = bns->l_pac;
  mem_chain_v chain;
  kbtree_t(chn) *tree;
  smem_aux_t *aux;

  kv_init(chain);
  if (len < opt->min_seed_len) return chain; // if the query is shorter than the seed length, no match
  tree = kb_init(chn, KB_DEFAULT_SIZE);

  aux = buf? (smem_aux_t*)buf : smem_aux_init();
  mem_collect_intv(opt, lbwt, len, seq, aux);
  for (i = 0, b = e = l_rep = 0; i < aux->mem.n; ++i) { // compute frac_rep
    bwtintv_t *p = &aux->mem.a[i];
    int sb=p->readBegin,se=p->readEnd;
    if (p->len <= opt->max_occ) continue;
    if (sb > e) l_rep += e - b, b = sb, e = se;
    else e = e > se? e : se;
  }
  l_rep += e - b;
  for (i = 0; i < aux->mem.n; ++i) {
    bwtintv_t *p = &aux->mem.a[i];
    int step, count, slen = p->readEnd-p->readBegin; // seed length
    int64_t k;
    // if (slen < opt->min_seed_len) continue; // ignore if too short or too repetitive
    step = p->len > opt->max_occ? p->len / opt->max_occ : 1;
    for (k = count = 0; k < p->len && count < opt->max_occ; k += step, ++count) {
      mem_chain_t tmp, *lower, *upper;
      mem_seed_t s;
      int rid, to_add = 0;
      s.rbeg=tmp.pos=lbwt->sa_low32[p->fs+k]+((3ull&_get_sahigh2(lbwt->sa_high2,p->fs+k))<<32);// this is the base coordinate in the forward-reverse reference
      s.qbeg = p->readBegin;
      s.score= s.len = slen;
      if(s.rbeg+p->readEnd-p->readBegin>2*lbwt->refLen) continue; //condition: cycle rotation, out of boundary
      rid = bns_intv2rid(bns, s.rbeg, s.rbeg + s.len);
      if (rid < 0) continue; // bridging multiple reference sequences or the forward-reverse boundary; TODO: split the seed; don't discard it!!!
      if (kb_size(tree)) {
	kb_intervalp(chn, tree, &tmp, &lower, &upper); // find the closest chain
	if (!lower || !test_and_merge(opt, l_pac, lower, &s, rid)) to_add = 1;
      } else to_add = 1;
      if (to_add) { // add the seed as a new chain
	tmp.n = 1; tmp.m = 4;
	tmp.seeds = calloc(tmp.m, sizeof(mem_seed_t));
	tmp.seeds[0] = s;
	tmp.rid = rid;
	tmp.is_alt = !!bns->anns[rid].is_alt;
	kb_putp(chn, tree, &tmp);
      }
    }
  }
  if (buf == 0) smem_aux_destroy(aux);

  kv_resize(mem_chain_t, chain, kb_size(tree));

#define traverse_func(p_) (chain.a[chain.n++] = *(p_))
  __kb_traverse(mem_chain_t, tree, traverse_func);
#undef traverse_func

  for (i = 0; i < chain.n; ++i) chain.a[i].frac_rep = (float)l_rep / len;
  if (bwa_verbose >= 4) printf("* fraction of repetitive seeds: %.3f\n", (float)l_rep / len);

  kb_destroy(chn, tree);
  return chain;
}

/********************
 * Filtering chains *
 ********************/

#define chn_beg(ch) ((ch).seeds->qbeg)
#define chn_end(ch) ((ch).seeds[(ch).n-1].qbeg + (ch).seeds[(ch).n-1].len)

#define flt_lt(a, b) ((a).w > (b).w)
KSORT_INIT(mem_flt, mem_chain_t, flt_lt)

int mem_chain_flt(const mem_opt_t *opt, int n_chn, mem_chain_t *a)
{
  int i, k;
  kvec_t(int) chains = {0,0,0}; // this keeps int indices of the non-overlapping chains
  if (n_chn == 0) return 0; // no need to filter
  // compute the weight of each chain and drop chains with small weight
  for (i = k = 0; i < n_chn; ++i) {
    mem_chain_t *c = &a[i];
    c->first = -1; c->kept = 0;
    c->w = mem_chain_weight(c);
    if (c->w < opt->min_chain_weight) free(c->seeds);
    else a[k++] = *c; // this line free the chain with small weight
  }
  n_chn = k;
  ks_introsort(mem_flt, n_chn, a);//sort chains use chain.weight
  // pairwise chain comparisons
  a[0].kept = 3;
  kv_push(int, chains, 0);// push the 0-th chain
  for (i = 1; i < n_chn; ++i) {
    int large_ovlp = 0;
    for (k = 0; k < chains.n; ++k) {// k must small than or equal to i 
      int j = chains.a[k];
      int b_max = chn_beg(a[j]) > chn_beg(a[i])? chn_beg(a[j]) : chn_beg(a[i]);
      int e_min = chn_end(a[j]) < chn_end(a[i])? chn_end(a[j]) : chn_end(a[i]);
      if (e_min > b_max && (!a[j].is_alt || a[i].is_alt)) { // have overlap; don't consider ovlp where the kept chain is ALT while the current chain is primary
	int li = chn_end(a[i]) - chn_beg(a[i]);
	int lj = chn_end(a[j]) - chn_beg(a[j]);
	int min_l = li < lj? li : lj;
	if (e_min - b_max >= min_l * opt->mask_level && min_l < opt->max_chain_gap) { // significant overlap
	  large_ovlp = 1;
	  if (a[j].first < 0) a[j].first = i; // keep the first shadowed hit s.t. mapq can be more accurate
	  if (a[i].w < a[j].w * opt->drop_ratio && a[j].w - a[i].w >= opt->min_seed_len<<1)
	    break;
	}//else no overlap
      }
    }
    if (k == chains.n) {
      kv_push(int, chains, i);// push the i-th chain
      a[i].kept = large_ovlp? 2 : 3;
    }
  }
  for (i = 0; i < chains.n; ++i) {
    mem_chain_t *c = &a[chains.a[i]];
    if (c->first >= 0) a[c->first].kept = 1;
  }
  free(chains.a);
  for (i = k = 0; i < n_chn; ++i) { // don't extend more than opt->max_chain_extend .kept=1/2 chains
    if (a[i].kept == 0 || a[i].kept == 3) continue;
    if (++k >= opt->max_chain_extend) break;
  }
  for (; i < n_chn; ++i)
    if (a[i].kept < 3) a[i].kept = 0;
  for (i = k = 0; i < n_chn; ++i) { // free discarded chains
    mem_chain_t *c = &a[i];
    if (c->kept == 0) free(c->seeds);
    else a[k++] = a[i];
  }
  return k;
}

/******************************
 * De-overlap single-end hits *
 ******************************/

#define alnreg_slt2(a, b) ((a).re < (b).re)
KSORT_INIT(mem_ars2, mem_alnreg_t, alnreg_slt2)

#define alnreg_slt(a, b) ((a).score > (b).score || ((a).score == (b).score && ((a).rb < (b).rb || ((a).rb == (b).rb && (a).qb < (b).qb))))
KSORT_INIT(mem_ars, mem_alnreg_t, alnreg_slt)

#define alnreg_hlt(a, b)  ((a).score > (b).score || ((a).score == (b).score && ((a).is_alt < (b).is_alt || ((a).is_alt == (b).is_alt && (a).hash < (b).hash))))
KSORT_INIT(mem_ars_hash, mem_alnreg_t, alnreg_hlt)

#define alnreg_hlt2(a, b) ((a).is_alt < (b).is_alt || ((a).is_alt == (b).is_alt && ((a).score > (b).score || ((a).score == (b).score && (a).hash < (b).hash))))
KSORT_INIT(mem_ars_hash2, mem_alnreg_t, alnreg_hlt2)

#define PATCH_MAX_R_BW 0.05f
#define PATCH_MIN_SC_RATIO 0.90f

int mem_patch_reg(const mem_opt_t *opt, const bntseq_t *bns, const uint8_t *pac, uint8_t *query, const mem_alnreg_t *a, const mem_alnreg_t *b, int *_w)
{
  int w, score, q_s, r_s;
  double r;
  if (bns == 0 || pac == 0 || query == 0) return 0;
  assert(a->rid == b->rid && a->rb <= b->rb);
  if (a->rb < bns->l_pac && b->rb >= bns->l_pac) return 0; // on different strands
  if (a->qb >= b->qb || a->qe >= b->qe || a->re >= b->re) return 0; // not colinear
  w = (a->re - b->rb) - (a->qe - b->qb); // required bandwidth
  w = w > 0? w : -w; // l = abs(l)
  r = (double)(a->re - b->rb) / (b->re - a->rb) - (double)(a->qe - b->qb) / (b->qe - a->qb); // relative bandwidth
  r = r > 0.? r : -r; // r = fabs(r)
  if (bwa_verbose >= 4)
    printf("* potential hit merge between [%d,%d)<=>[%ld,%ld) and [%d,%d)<=>[%ld,%ld), @ %s; w=%d, r=%.4g\n",
	   a->qb, a->qe, (long)a->rb, (long)a->re, b->qb, b->qe, (long)b->rb, (long)b->re, bns->anns[a->rid].name, w, r);
  if (a->re < b->rb || a->qe < b->qb) { // no overlap on query or on ref
    if (w > opt->w<<1 || r >= PATCH_MAX_R_BW) return 0; // the bandwidth or the relative bandwidth is too large
  } else if (w > opt->w<<2 || r >= PATCH_MAX_R_BW*2) return 0; // more permissive if overlapping on both ref and query
  // global alignment
  w += a->w + b->w;
  w = w < opt->w<<2? w : opt->w<<2;
  if (bwa_verbose >= 4) printf("* test potential hit merge with global alignment; w=%d\n", w);
  bwa_gen_cigar2(opt->mat, opt->o_del, opt->e_del, opt->o_ins, opt->e_ins, w, bns->l_pac, pac, b->qe - a->qb, query + a->qb, a->rb, b->re, &score, 0, 0);
  q_s = (int)((double)(b->qe - a->qb) / ((b->qe - b->qb) + (a->qe - a->qb)) * (b->score + a->score) + .499); // predicted score from query
  r_s = (int)((double)(b->re - a->rb) / ((b->re - b->rb) + (a->re - a->rb)) * (b->score + a->score) + .499); // predicted score from ref
  if (bwa_verbose >= 4) printf("* score=%d;(%d,%d)\n", score, q_s, r_s);
  if ((double)score / (q_s > r_s? q_s : r_s) < PATCH_MIN_SC_RATIO) return 0;
  *_w = w;
  return score;
}

int mem_sort_dedup_patch(const mem_opt_t *opt, const bntseq_t *bns, const uint8_t *pac, uint8_t *query, int n, mem_alnreg_t *a)
{
  int m, i, j;
  if (n <= 1) return n;
  ks_introsort(mem_ars2, n, a); // sort by the END position, not START!
  for (i = 0; i < n; ++i) a[i].n_comp = 1;
  for (i = 1; i < n; ++i) {
    mem_alnreg_t *p = &a[i];
    if (p->rid != a[i-1].rid || p->rb >= a[i-1].re + opt->max_chain_gap) continue; // then no need to go into the loop below
    for (j = i - 1; j >= 0 && p->rid == a[j].rid && p->rb < a[j].re + opt->max_chain_gap; --j) {
      mem_alnreg_t *q = &a[j];
      int64_t or, oq, mr, mq;
      int score, w;
      if (q->qe == q->qb) continue; // a[j] has been excluded
      or = q->re - p->rb; // overlap length on the reference
      oq = q->qb < p->qb? q->qe - p->qb : p->qe - q->qb; // overlap length on the query
      mr = q->re - q->rb < p->re - p->rb? q->re - q->rb : p->re - p->rb; // min ref len in alignment
      mq = q->qe - q->qb < p->qe - p->qb? q->qe - q->qb : p->qe - p->qb; // min qry len in alignment
      if (or > opt->mask_level_redun * mr && oq > opt->mask_level_redun * mq) { // one of the hits is redundant
	if (p->score < q->score) {
	  p->qe = p->qb;
	  break;
	} else q->qe = q->qb;
      } else if (q->rb < p->rb && (score = mem_patch_reg(opt, bns, pac, query, q, p, &w)) > 0) { // then merge q into p
	p->n_comp += q->n_comp + 1;
	p->seedcov = p->seedcov > q->seedcov? p->seedcov : q->seedcov;
	p->sub = p->sub > q->sub? p->sub : q->sub;
	p->csub = p->csub > q->csub? p->csub : q->csub;
	p->qb = q->qb, p->rb = q->rb;
	p->truesc = p->score = score;
	p->w = w;
	q->qb = q->qe;
      }
    }
  }
  for (i = 0, m = 0; i < n; ++i) // exclude identical hits
    if (a[i].qe > a[i].qb) {
      if (m != i) a[m++] = a[i];
      else ++m;
    }
  n = m;
  ks_introsort(mem_ars, n, a);
  for (i = 1; i < n; ++i) { // mark identical hits
    if (a[i].score == a[i-1].score && a[i].rb == a[i-1].rb && a[i].qb == a[i-1].qb)
      a[i].qe = a[i].qb;
  }
  for (i = 1, m = 1; i < n; ++i) // exclude identical hits
    if (a[i].qe > a[i].qb) {
      if (m != i) a[m++] = a[i];
      else ++m;
    }
  return m;
}

typedef kvec_t(int) int_v;

static void mem_mark_primary_se_core(const mem_opt_t *opt, int n, mem_alnreg_t *a, int_v *z)
{ // similar to the loop in mem_chain_flt()
  int i, k, tmp;
  tmp = opt->a + opt->b;
  tmp = opt->o_del + opt->e_del > tmp? opt->o_del + opt->e_del : tmp;
  tmp = opt->o_ins + opt->e_ins > tmp? opt->o_ins + opt->e_ins : tmp;
  z->n = 0;
  kv_push(int, *z, 0);
  for (i = 1; i < n; ++i) {
    for (k = 0; k < z->n; ++k) {
      int j = z->a[k];
      int b_max = a[j].qb > a[i].qb? a[j].qb : a[i].qb;
      int e_min = a[j].qe < a[i].qe? a[j].qe : a[i].qe;
      if (e_min > b_max) { // have overlap
	int min_l = a[i].qe - a[i].qb < a[j].qe - a[j].qb? a[i].qe - a[i].qb : a[j].qe - a[j].qb;
	if (e_min - b_max >= min_l * opt->mask_level) { // significant overlap
	  if (a[j].sub == 0) a[j].sub = a[i].score;
	  if (a[j].score - a[i].score <= tmp && (a[j].is_alt || !a[i].is_alt))
	    ++a[j].sub_n;
	  break;
	}
      }
    }
    if (k == z->n) kv_push(int, *z, i);
    else a[i].secondary = z->a[k];
  }
}

int mem_mark_primary_se(const mem_opt_t *opt, int n, mem_alnreg_t *a, int64_t id)
{
  int i, n_pri;
  int_v z = {0,0,0};
  if (n == 0) return 0;
  for (i = n_pri = 0; i < n; ++i) {
    a[i].sub = a[i].alt_sc = 0, a[i].secondary = a[i].secondary_all = -1, a[i].hash = hash_64(id+i);
    if (!a[i].is_alt) ++n_pri;
  }
  ks_introsort(mem_ars_hash, n, a);
  mem_mark_primary_se_core(opt, n, a, &z);
  for (i = 0; i < n; ++i) {
    mem_alnreg_t *p = &a[i];
    p->secondary_all = i; // keep the rank in the first round
    if (!p->is_alt && p->secondary >= 0 && a[p->secondary].is_alt)
      p->alt_sc = a[p->secondary].score;
  }
  if (n_pri >= 0 && n_pri < n) {
    kv_resize(int, z, n);
    if (n_pri > 0) ks_introsort(mem_ars_hash2, n, a);
    for (i = 0; i < n; ++i) z.a[a[i].secondary_all] = i;
    for (i = 0; i < n; ++i) {
      if (a[i].secondary >= 0) {
	a[i].secondary_all = z.a[a[i].secondary];
	if (a[i].is_alt) a[i].secondary = INT_MAX;
      } else a[i].secondary_all = -1;
    }
    if (n_pri > 0) { // mark primary for hits to the primary assembly only
      for (i = 0; i < n_pri; ++i) a[i].sub = 0, a[i].secondary = -1;
      mem_mark_primary_se_core(opt, n_pri, a, &z);
    }
  } else {
    for (i = 0; i < n; ++i)
      a[i].secondary_all = a[i].secondary;
  }
  free(z.a);
  return n_pri;
}

/*********************************
 * Test if a seed is good enough *
 *********************************/

#define MEM_SHORT_EXT 50
#define MEM_SHORT_LEN 200

#define MEM_HSP_COEF 1.1f
#define MEM_MINSC_COEF 5.5f
#define MEM_SEEDSW_COEF 0.05f

int mem_seed_sw(const mem_opt_t *opt, const bntseq_t *bns, const uint8_t *pac, int l_query, const uint8_t *query, const mem_seed_t *s)
{
  int qb, qe, rid;
  int64_t rb, re, mid, l_pac = bns->l_pac;
  uint8_t *rseq = 0;
  kswr_t x;

  if (s->len >= MEM_SHORT_LEN) return -1; // the seed is longer than the max-extend; no need to do SW
  qb = s->qbeg, qe = s->qbeg + s->len;
  rb = s->rbeg, re = s->rbeg + s->len;
  mid = (rb + re) >> 1;
  qb -= MEM_SHORT_EXT; qb = qb > 0? qb : 0;
  qe += MEM_SHORT_EXT; qe = qe < l_query? qe : l_query;
  rb -= MEM_SHORT_EXT; rb = rb > 0? rb : 0;
  re += MEM_SHORT_EXT; re = re < l_pac<<1? re : l_pac<<1;
  if (rb < l_pac && l_pac < re) {
    if (mid < l_pac) re = l_pac;
    else rb = l_pac;
  }
  if (qe - qb >= MEM_SHORT_LEN || re - rb >= MEM_SHORT_LEN) return -1; // the seed seems good enough; no need to do SW

  rseq = bns_fetch_seq(bns, pac, &rb, mid, &re, &rid);
  x = ksw_align2(qe - qb, (uint8_t*)query + qb, re - rb, rseq, 5, opt->mat, opt->o_del, opt->e_del, opt->o_ins, opt->e_ins, KSW_XSTART, 0);
  free(rseq);
  return x.score;
}

void mem_flt_chained_seeds(const mem_opt_t *opt, const bntseq_t *bns, const uint8_t *pac, int l_query, const uint8_t *query, int n_chn, mem_chain_t *a)
{
  double min_l = opt->min_chain_weight? MEM_HSP_COEF * opt->min_chain_weight : MEM_MINSC_COEF * log(l_query);
  int i, j, k, min_HSP_score = (int)(opt->a * min_l + .499);
  if (min_l > MEM_SEEDSW_COEF * l_query) return; // don't run the following for short reads
  for (i = 0; i < n_chn; ++i) {
    mem_chain_t *c = &a[i];
    for (j = k = 0; j < c->n; ++j) {
      mem_seed_t *s = &c->seeds[j];
      s->score = mem_seed_sw(opt, bns, pac, l_query, query, s);
      if (s->score < 0 || s->score >= min_HSP_score) {
	s->score = s->score < 0? s->len * opt->a : s->score;
	c->seeds[k++] = *s;
      }
    }
    c->n = k;
  }
}

/****************************************
 * Construct the alignment from a chain *
 ****************************************/

static inline int cal_max_gap(const mem_opt_t *opt, int qlen)
{
  int l_del = (int)((double)(qlen * opt->a - opt->o_del) / opt->e_del + 1.);
  int l_ins = (int)((double)(qlen * opt->a - opt->o_ins) / opt->e_ins + 1.);
  int l = l_del > l_ins? l_del : l_ins;
  l = l > 1? l : 1;
  return l < opt->w<<1? l : opt->w<<1;
}

#define MAX_BAND_TRY  2

void mem_chain2aln(const mem_opt_t *opt, const bntseq_t *bns, const uint8_t *pac, int l_query, const uint8_t *query, const mem_chain_t *c, mem_alnreg_v *av)
{
  int i, k, rid, max_off[2], aw[2]; // aw: actual bandwidth used in extension
  int64_t l_pac = bns->l_pac, rmax[2], tmp, max = 0;
  const mem_seed_t *s;
  uint8_t *rseq = 0;
  uint64_t *srt;

  if (c->n == 0) return;
  // get the max possible span
  rmax[0] = l_pac<<1; rmax[1] = 0;
  for (i = 0; i < c->n; ++i) {
    int64_t b, e;
    const mem_seed_t *t = &c->seeds[i];
    b = t->rbeg - (t->qbeg + cal_max_gap(opt, t->qbeg));
    e = t->rbeg + t->len + ((l_query - t->qbeg - t->len) + cal_max_gap(opt, l_query - t->qbeg - t->len));
    rmax[0] = rmax[0] < b? rmax[0] : b;
    rmax[1] = rmax[1] > e? rmax[1] : e;
    if (t->len > max) max = t->len;
  }
  rmax[0] = rmax[0] > 0? rmax[0] : 0;
  rmax[1] = rmax[1] < l_pac<<1? rmax[1] : l_pac<<1;
  if (rmax[0] < l_pac && l_pac < rmax[1]) { // crossing the forward-reverse boundary; then choose one side
    if (c->seeds[0].rbeg < l_pac) rmax[1] = l_pac; // this works because all seeds are guaranteed to be on the same strand
    else rmax[0] = l_pac;
  }
  // retrieve the reference sequence
  rseq = bns_fetch_seq(bns, pac, &rmax[0], c->seeds[0].rbeg, &rmax[1], &rid);
  assert(c->rid == rid);

  srt = malloc(c->n * 8);
  for (i = 0; i < c->n; ++i)
    srt[i] = (uint64_t)c->seeds[i].score<<32 | i;
  ks_introsort_64(c->n, srt);

  for (k = c->n - 1; k >= 0; --k) {
    mem_alnreg_t *a;
    s = &c->seeds[(uint32_t)srt[k]];// to select highest score seeds among the seed that not be choosed 

    for (i = 0; i < av->n; ++i) { // test whether extension has been made before
      mem_alnreg_t *p = &av->a[i];
      int64_t rd;
      int qd, w, max_gap;
      if (s->rbeg < p->rb || s->rbeg + s->len > p->re || s->qbeg < p->qb || s->qbeg + s->len > p->qe) continue; // not fully contained
      if (s->len - p->seedlen0 > .1 * l_query) continue; // this seed may give a better alignment
      // qd: distance ahead of the seed on query; rd: on reference
      qd = s->qbeg - p->qb; rd = s->rbeg - p->rb;
      max_gap = cal_max_gap(opt, qd < rd? qd : rd); // the maximal gap allowed in regions ahead of the seed
      w = max_gap < p->w? max_gap : p->w; // bounded by the band width
      if (qd - rd < w && rd - qd < w) break; // the seed is "around" a previous hit
      // similar to the previous four lines, but this time we look at the region behind
      qd = p->qe - (s->qbeg + s->len); rd = p->re - (s->rbeg + s->len);
      max_gap = cal_max_gap(opt, qd < rd? qd : rd);
      w = max_gap < p->w? max_gap : p->w;
      if (qd - rd < w && rd - qd < w) break;
    }
    if (i < av->n) { // the seed is (almost) contained in an existing alignment; further testing is needed to confirm it is not leading to a different aln
      if (bwa_verbose >= 4)
	printf("** Seed(%d) [%ld;%ld,%ld] is almost contained in an existing alignment [%d,%d) <=> [%ld,%ld)\n",
	       k, (long)s->len, (long)s->qbeg, (long)s->rbeg, av->a[i].qb, av->a[i].qe, (long)av->a[i].rb, (long)av->a[i].re);
      for (i = k + 1; i < c->n; ++i) { // check overlapping seeds in the same chain
	const mem_seed_t *t;
	if (srt[i] == 0) continue;
	t = &c->seeds[(uint32_t)srt[i]];
	if (t->len < s->len * .95) continue; // only check overlapping if t is long enough; TODO: more efficient by early stopping
	if (s->qbeg <= t->qbeg && s->qbeg + s->len - t->qbeg >= s->len>>2 && t->qbeg - s->qbeg != t->rbeg - s->rbeg) break;
	if (t->qbeg <= s->qbeg && t->qbeg + t->len - s->qbeg >= s->len>>2 && s->qbeg - t->qbeg != s->rbeg - t->rbeg) break;
      }
      if (i == c->n) { // no overlapping seeds; then skip extension
	srt[k] = 0; // mark that seed extension has not been performed
	continue;
      }
      if (bwa_verbose >= 4)
	printf("** Seed(%d) might lead to a different alignment even though it is contained. Extension will be performed.\n", k);
    }

    a = kv_pushp(mem_alnreg_t, *av);
    memset(a, 0, sizeof(mem_alnreg_t));
    a->w = aw[0] = aw[1] = opt->w;
    a->score = a->truesc = -1;
    a->rid = c->rid;

    if (bwa_verbose >= 4) err_printf("** ---> Extending from seed(%d) [%ld;%ld,%ld] @ %s <---\n", k, (long)s->len, (long)s->qbeg, (long)s->rbeg, bns->anns[c->rid].name);
    if (s->qbeg) { // left extension
      uint8_t *rs, *qs;
      int qle, tle, gtle, gscore;
      qs = malloc(s->qbeg);
      for (i = 0; i < s->qbeg; ++i) qs[i] = query[s->qbeg - 1 - i];
      tmp = s->rbeg - rmax[0];
      rs = malloc(tmp);
      for (i = 0; i < tmp; ++i) rs[i] = rseq[tmp - 1 - i];
      if (bwa_verbose >= 4) {
	int j;
	printf("*** Left ref:   "); for (j = 0; j < tmp; ++j) putchar("ACGTN"[(int)rs[j]]); putchar('\n');
	printf("*** Left query: "); for (j = 0; j < s->qbeg; ++j) putchar("ACGTN"[(int)qs[j]]); putchar('\n');
      }
      a->score = ksw_extend2(s->qbeg, qs, tmp, rs, 5, opt->mat, opt->o_del, opt->e_del, opt->o_ins, opt->e_ins, aw[0], opt->pen_clip5, opt->zdrop, s->len * opt->a, &qle, &tle, &gtle, &gscore, &max_off[0]);
      if (bwa_verbose >= 4) { printf("*** Left extension: prev_score=%d; score=%d; qle=%d; tle=%d; gtle=%d; gscore=%d; bandwidth=%d; max_off_diagonal_dist=%d\n", s->len*opt->a, a->score, qle, tle, gtle, gscore, aw[0], max_off[0]); fflush(stdout); }
      // check whether we prefer to reach the end of the query
      if (gscore <= 0 || gscore <= a->score - opt->pen_clip5) { // local extension
	a->qb = s->qbeg - qle, a->rb = s->rbeg - tle;
	a->truesc = a->score;
      } else { // to-end extension
	a->qb = 0, a->rb = s->rbeg - gtle;
	a->truesc = gscore;
      }
      free(qs); free(rs);
    } else a->score = a->truesc = s->len * opt->a, a->qb = 0, a->rb = s->rbeg;

    if (s->qbeg + s->len != l_query) { // right extension
      int qle, tle, qe, re, gtle, gscore, sc0 = a->score;
      qe = s->qbeg + s->len;
      re = s->rbeg + s->len - rmax[0];
      assert(re >= 0);
      if (bwa_verbose >= 4) {
	int j;
	printf("*** Right ref:   "); for (j = 0; j < rmax[1] - rmax[0] - re; ++j) putchar("ACGTN"[(int)rseq[re+j]]); putchar('\n');
	printf("*** Right query: "); for (j = 0; j < l_query - qe; ++j) putchar("ACGTN"[(int)query[qe+j]]); putchar('\n');
      }
      a->score = ksw_extend2(l_query - qe, query + qe, rmax[1] - rmax[0] - re, rseq + re, 5, opt->mat, opt->o_del, opt->e_del, opt->o_ins, opt->e_ins, aw[1], opt->pen_clip3, opt->zdrop, sc0, &qle, &tle, &gtle, &gscore, &max_off[1]);
      if (bwa_verbose >= 4) { printf("*** Right extension: prev_score=%d; score=%d; qle=%d; tle=%d; gtle=%d; gscore=%d; bandwidth=%d; max_off_diagonal_dist=%d\n", sc0, a->score, qle, tle, gtle, gscore, aw[1], max_off[1]); fflush(stdout); }
      // similar to the above
      if (gscore <= 0 || gscore <= a->score - opt->pen_clip3) { // local extension
	a->qe = qe + qle, a->re = rmax[0] + re + tle;
	a->truesc += a->score - sc0;
      } else { // to-end extension
	a->qe = l_query, a->re = rmax[0] + re + gtle;
	a->truesc += gscore - sc0;
      }
    } else a->qe = l_query, a->re = s->rbeg + s->len;
    if (bwa_verbose >= 4) printf("*** Added alignment region: [%d,%d) <=> [%ld,%ld); score=%d; {left,right}_bandwidth={%d,%d}\n", a->qb, a->qe, (long)a->rb, (long)a->re, a->score, aw[0], aw[1]);

    // compute seedcov
    for (i = 0, a->seedcov = 0; i < c->n; ++i) {
      const mem_seed_t *t = &c->seeds[i];
      if (t->qbeg >= a->qb && t->qbeg + t->len <= a->qe && t->rbeg >= a->rb && t->rbeg + t->len <= a->re) // seed fully contained
	a->seedcov += t->len; // this is not very accurate, but for approx. mapQ, this is good enough
    }
    a->w = aw[0] > aw[1]? aw[0] : aw[1];
    a->seedlen0 = s->len;

    a->frac_rep = c->frac_rep;
  }
  free(srt); free(rseq);
}

/*****************************
 * Basic hit->SAM conversion *
 *****************************/

static inline int infer_bw(int l1, int l2, int score, int a, int q, int r)
{
  int w;
  if (l1 == l2 && l1 * a - score < (q + r - a)<<1) return 0; // to get equal alignment length, we need at least two gaps
  w = ((double)((l1 < l2? l1 : l2) * a - score - q) / r + 2.);
  if (w < abs(l1 - l2)) w = abs(l1 - l2);
  return w;
}

static inline int get_rlen(int n_cigar, const uint32_t *cigar)
{
  int k, l;
  for (k = l = 0; k < n_cigar; ++k) {
    int op = cigar[k]&0xf;
    if (op == 0 || op == 2)
      l += cigar[k]>>4;
  }
  return l;
}

static inline void add_cigar(const mem_opt_t *opt, mem_aln_t *p, kstring_t *str, int which)
{
  int i;
  if (p->n_cigar) { // aligned
    for (i = 0; i < p->n_cigar; ++i) {
      int c = p->cigar[i]&0xf;
      if (!(opt->flag&MEM_F_SOFTCLIP) && !p->is_alt && (c == 3 || c == 4))
	c = which? 4 : 3; // use hard clipping for supplementary alignments
      kputw(p->cigar[i]>>4, str); kputc("MIDSH"[c], str);
    }
  } else kputc('*', str); // having a coordinate but unaligned (e.g. when copy_mate is true)
}

void mem_aln2sam(const mem_opt_t *opt, const bntseq_t *bns, kstring_t *str, bseq1_t *s, int n, const mem_aln_t *list, int which, const mem_aln_t *m_)
{
  int i, l_name;
  mem_aln_t ptmp = list[which], *p = &ptmp, mtmp, *m = 0; // make a copy of the alignment to convert

  if (m_) mtmp = *m_, m = &mtmp;
  // set flag
  p->flag |= m? 0x1 : 0; // is paired in sequencing
  p->flag |= p->rid < 0? 0x4 : 0; // is mapped
  p->flag |= m && m->rid < 0? 0x8 : 0; // is mate mapped
  if (p->rid < 0 && m && m->rid >= 0) // copy mate to alignment
    p->rid = m->rid, p->pos = m->pos, p->is_rev = m->is_rev, p->n_cigar = 0;
  if (m && m->rid < 0 && p->rid >= 0) // copy alignment to mate
    m->rid = p->rid, m->pos = p->pos, m->is_rev = p->is_rev, m->n_cigar = 0;
  p->flag |= p->is_rev? 0x10 : 0; // is on the reverse strand
  p->flag |= m && m->is_rev? 0x20 : 0; // is mate on the reverse strand

  // print up to CIGAR
  l_name = strlen(s->name);
  ks_resize(str, str->l + s->l_seq + l_name + (s->qual? s->l_seq : 0) + 20);
  kputsn(s->name, l_name, str); kputc('\t', str); // QNAME
  kputw((p->flag&0xffff) | (p->flag&0x10000? 0x100 : 0), str); kputc('\t', str); // FLAG
  if (p->rid >= 0) { // with coordinate
    kputs(bns->anns[p->rid].name, str); kputc('\t', str); // RNAME
    kputl(p->pos + 1, str); kputc('\t', str); // POS
    kputw(p->mapq, str); kputc('\t', str); // MAPQ
    add_cigar(opt, p, str, which);
  } else kputsn("*\t0\t0\t*", 7, str); // without coordinte
  kputc('\t', str);

  // print the mate position if applicable
  if (m && m->rid >= 0) {
    if (p->rid == m->rid) kputc('=', str);
    else kputs(bns->anns[m->rid].name, str);
    kputc('\t', str);
    kputl(m->pos + 1, str); kputc('\t', str);
    if (p->rid == m->rid) {
      int64_t p0 = p->pos + (p->is_rev? get_rlen(p->n_cigar, p->cigar) - 1 : 0);
      int64_t p1 = m->pos + (m->is_rev? get_rlen(m->n_cigar, m->cigar) - 1 : 0);
      if (m->n_cigar == 0 || p->n_cigar == 0) kputc('0', str);
      else kputl(-(p0 - p1 + (p0 > p1? 1 : p0 < p1? -1 : 0)), str);
    } else kputc('0', str);
  } else kputsn("*\t0\t0", 5, str);
  kputc('\t', str);

  // print SEQ and QUAL
  if (p->flag & 0x100) { // for secondary alignments, don't write SEQ and QUAL
    kputsn("*\t*", 3, str);
  } else if (!p->is_rev) { // the forward strand
    int i, qb = 0, qe = s->l_seq;
    if (p->n_cigar && which && !(opt->flag&MEM_F_SOFTCLIP) && !p->is_alt) { // have cigar && not the primary alignment && not softclip all
      if ((p->cigar[0]&0xf) == 4 || (p->cigar[0]&0xf) == 3) qb += p->cigar[0]>>4;
      if ((p->cigar[p->n_cigar-1]&0xf) == 4 || (p->cigar[p->n_cigar-1]&0xf) == 3) qe -= p->cigar[p->n_cigar-1]>>4;
    }
    ks_resize(str, str->l + (qe - qb) + 1);
    for (i = qb; i < qe; ++i) str->s[str->l++] = "ACGTN"[(int)s->seq[i]];
    kputc('\t', str);
    if (s->qual) { // printf qual
      ks_resize(str, str->l + (qe - qb) + 1);
      for (i = qb; i < qe; ++i) str->s[str->l++] = s->qual[i];
      str->s[str->l] = 0;
    } else kputc('*', str);
  } else { // the reverse strand
    int i, qb = 0, qe = s->l_seq;
    if (p->n_cigar && which && !(opt->flag&MEM_F_SOFTCLIP) && !p->is_alt) {
      if ((p->cigar[0]&0xf) == 4 || (p->cigar[0]&0xf) == 3) qe -= p->cigar[0]>>4;
      if ((p->cigar[p->n_cigar-1]&0xf) == 4 || (p->cigar[p->n_cigar-1]&0xf) == 3) qb += p->cigar[p->n_cigar-1]>>4;
    }
    ks_resize(str, str->l + (qe - qb) + 1);
    for (i = qe-1; i >= qb; --i) str->s[str->l++] = "TGCAN"[(int)s->seq[i]];
    kputc('\t', str);
    if (s->qual) { // printf qual
      ks_resize(str, str->l + (qe - qb) + 1);
      for (i = qe-1; i >= qb; --i) str->s[str->l++] = s->qual[i];
      str->s[str->l] = 0;
    } else kputc('*', str);
  }

  // print optional tags
  if (p->n_cigar) {
    kputsn("\tNM:i:", 6, str); kputw(p->NM, str);
    kputsn("\tMD:Z:", 6, str); kputs((char*)(p->cigar + p->n_cigar), str);
  }
  if (m && m->n_cigar) { kputsn("\tMC:Z:", 6, str); add_cigar(opt, m, str, which); }
  if (p->score >= 0) { kputsn("\tAS:i:", 6, str); kputw(p->score, str); }
  if (p->sub >= 0) { kputsn("\tXS:i:", 6, str); kputw(p->sub, str); }
  if (bwa_rg_id[0]) { kputsn("\tRG:Z:", 6, str); kputs(bwa_rg_id, str); }
  if (!(p->flag & 0x100)) { // not multi-hit
    for (i = 0; i < n; ++i)
      if (i != which && !(list[i].flag&0x100)) break;
    if (i < n) { // there are other primary hits; output them
      kputsn("\tSA:Z:", 6, str);
      for (i = 0; i < n; ++i) {
	const mem_aln_t *r = &list[i];
	int k;
	if (i == which || (r->flag&0x100)) continue; // proceed if: 1) different from the current; 2) not shadowed multi hit
	kputs(bns->anns[r->rid].name, str); kputc(',', str);
	kputl(r->pos+1, str); kputc(',', str);
	kputc("+-"[r->is_rev], str); kputc(',', str);
	for (k = 0; k < r->n_cigar; ++k) {
	  kputw(r->cigar[k]>>4, str); kputc("MIDSH"[r->cigar[k]&0xf], str);
	}
	kputc(',', str); kputw(r->mapq, str);
	kputc(',', str); kputw(r->NM, str);
	kputc(';', str);
      }
    }
    if (p->alt_sc > 0)
      ksprintf(str, "\tpa:f:%.3f", (double)p->score / p->alt_sc);
  }
  if (p->XA) {
    kputsn((opt->flag&MEM_F_XB)? "\tXB:Z:" : "\tXA:Z:", 6, str);
    kputs(p->XA, str);
  }
  if (s->comment) { kputc('\t', str); kputs(s->comment, str); }
  if ((opt->flag&MEM_F_REF_HDR) && p->rid >= 0 && bns->anns[p->rid].anno != 0 && bns->anns[p->rid].anno[0] != 0) {
    int tmp;
    kputsn("\tXR:Z:", 6, str);
    tmp = str->l;
    kputs(bns->anns[p->rid].anno, str);
    for (i = tmp; i < str->l; ++i) // replace TAB in the comment to SPACE
      if (str->s[i] == '\t') str->s[i] = ' ';
  }
  kputc('\n', str);
}

/************************
 * Integrated interface *
 ************************/

int mem_approx_mapq_se(const mem_opt_t *opt, const mem_alnreg_t *a)
{
  int mapq, l, sub = a->sub? a->sub : opt->min_seed_len * opt->a;
  double identity;
  sub = a->csub > sub? a->csub : sub;
  if (sub >= a->score) return 0;
  l = a->qe - a->qb > a->re - a->rb? a->qe - a->qb : a->re - a->rb;
  identity = 1. - (double)(l * opt->a - a->score) / (opt->a + opt->b) / l;
  if (a->score == 0) {
    mapq = 0;
  } else if (opt->mapQ_coef_len > 0) {
    double tmp;
    tmp = l < opt->mapQ_coef_len? 1. : opt->mapQ_coef_fac / log(l);
    tmp *= identity * identity;
    mapq = (int)(6.02 * (a->score - sub) / opt->a * tmp * tmp + .499);
  } else {
    mapq = (int)(MEM_MAPQ_COEF * (1. - (double)sub / a->score) * log(a->seedcov) + .499);
    mapq = identity < 0.95? (int)(mapq * identity * identity + .499) : mapq;
  }
  if (a->sub_n > 0) mapq -= (int)(4.343 * log(a->sub_n+1) + .499);
  if (mapq > 60) mapq = 60;
  if (mapq < 0) mapq = 0;
  mapq = (int)(mapq * (1. - a->frac_rep) + .499);
  return mapq;
}

void mem_reorder_primary5(int T, mem_alnreg_v *a)
{
  int k, n_pri = 0, left_st = INT_MAX, left_k = -1;
  mem_alnreg_t t;
  for (k = 0; k < a->n; ++k)
    if (a->a[k].secondary < 0 && !a->a[k].is_alt && a->a[k].score >= T) ++n_pri;
  if (n_pri <= 1) return; // only one alignment
  for (k = 0; k < a->n; ++k) {
    mem_alnreg_t *p = &a->a[k];
    if (p->secondary >= 0 || p->is_alt || p->score < T) continue;
    if (p->qb < left_st) left_st = p->qb, left_k = k;
  }
  assert(a->a[0].secondary < 0);
  if (left_k == 0) return; // no need to reorder
  t = a->a[0], a->a[0] = a->a[left_k], a->a[left_k] = t;
  for (k = 1; k < a->n; ++k) { // update secondary and secondary_all
    mem_alnreg_t *p = &a->a[k];
    if (p->secondary == 0) p->secondary = left_k;
    else if (p->secondary == left_k) p->secondary = 0;
    if (p->secondary_all == 0) p->secondary_all = left_k;
    else if (p->secondary_all == left_k) p->secondary_all = 0;
  }
}

// TODO (future plan): group hits into a uint64_t[] array. This will be cleaner and more flexible
void mem_reg2sam(const mem_opt_t *opt, const bntseq_t *bns, const uint8_t *pac, bseq1_t *s, mem_alnreg_v *a, int extra_flag, const mem_aln_t *m)
{
  extern char **mem_gen_alt(const mem_opt_t *opt, const bntseq_t *bns, const uint8_t *pac, mem_alnreg_v *a, int l_query, const char *query);
  kstring_t str;
  kvec_t(mem_aln_t) aa;
  int k, l;
  char **XA = 0;

  if (!(opt->flag & MEM_F_ALL))
    XA = mem_gen_alt(opt, bns, pac, a, s->l_seq, s->seq);
  kv_init(aa);
  str.l = str.m = 0; str.s = 0;
  for (k = l = 0; k < a->n; ++k) {
    mem_alnreg_t *p = &a->a[k];
    mem_aln_t *q;
    if (p->score < opt->T) continue;
    if (p->secondary >= 0 && (p->is_alt || !(opt->flag&MEM_F_ALL))) continue;
    if (p->secondary >= 0 && p->secondary < INT_MAX && p->score < a->a[p->secondary].score * opt->drop_ratio) continue;
    q = kv_pushp(mem_aln_t, aa);
    *q = mem_reg2aln(opt, bns, pac, s->l_seq, s->seq, p);
    assert(q->rid >= 0); // this should not happen with the new code
    q->XA = XA? XA[k] : 0;
    q->flag |= extra_flag; // flag secondary
    if (p->secondary >= 0) q->sub = -1; // don't output sub-optimal score
    if (l && p->secondary < 0) // if supplementary
      q->flag |= (opt->flag&MEM_F_NO_MULTI)? 0x10000 : 0x800;
    if (!(opt->flag & MEM_F_KEEP_SUPP_MAPQ) && l && !p->is_alt && q->mapq > aa.a[0].mapq)
      q->mapq = aa.a[0].mapq; // lower mapq for supplementary mappings, unless -5 or -q is applied
    ++l;
  }
  if (aa.n == 0) { // no alignments good enough; then write an unaligned record
    mem_aln_t t;
    t = mem_reg2aln(opt, bns, pac, s->l_seq, s->seq, 0);
    t.flag |= extra_flag;
    mem_aln2sam(opt, bns, &str, s, 1, &t, 0, m);
  } else {
    for (k = 0; k < aa.n; ++k)
      mem_aln2sam(opt, bns, &str, s, aa.n, aa.a, k, m);
    for (k = 0; k < aa.n; ++k) free(aa.a[k].cigar);
    free(aa.a);
  }
  s->sam = str.s;
  if (XA) {
    for (k = 0; k < a->n; ++k) free(XA[k]);
    free(XA);
  }
}

mem_alnreg_v mem_align1_core(const mem_opt_t *opt, const lbwt_t *lbwt, const bntseq_t *bns, const uint8_t *pac, int l_seq, char *seq, void *buf)
{
  int i;
  mem_chain_v chn;
  mem_alnreg_v regs;

  for (i = 0; i < l_seq; ++i) // convert to 2-bit encoding if we have not done so
    seq[i] = seq[i] < 4? seq[i] : nst_nt4_table[(int)seq[i]];

  chn = mem_chain(opt, lbwt, bns, l_seq, (uint8_t*)seq, buf);
  chn.n = mem_chain_flt(opt, chn.n, chn.a);
  mem_flt_chained_seeds(opt, bns, pac, l_seq, (uint8_t*)seq, chn.n, chn.a);
  if (bwa_verbose >= 4) mem_print_chain(bns, &chn);

  kv_init(regs);
  for (i = 0; i < chn.n; ++i) {
    mem_chain_t *p = &chn.a[i];
    if (bwa_verbose >= 4) err_printf("* ---> Processing chain(%d) <---\n", i);
    mem_chain2aln(opt, bns, pac, l_seq, (uint8_t*)seq, p, &regs);
    free(chn.a[i].seeds);
  }
  free(chn.a);
  regs.n = mem_sort_dedup_patch(opt, bns, pac, (uint8_t*)seq, regs.n, regs.a);
  if (bwa_verbose >= 4) {
    err_printf("* %ld chains remain after removing duplicated chains\n", regs.n);
    for (i = 0; i < regs.n; ++i) {
      mem_alnreg_t *p = &regs.a[i];
      printf("** %d, [%d,%d) <=> [%ld,%ld)\n", p->score, p->qb, p->qe, (long)p->rb, (long)p->re);
    }
  }
  for (i = 0; i < regs.n; ++i) {//copy information
    mem_alnreg_t *p = &regs.a[i];
    if (p->rid >= 0 && bns->anns[p->rid].is_alt)
      p->is_alt = 1;
  }
  return regs;
}

mem_aln_t mem_reg2aln(const mem_opt_t *opt, const bntseq_t *bns, const uint8_t *pac, int l_query, const char *query_, const mem_alnreg_t *ar)
{
  mem_aln_t a;
  int i, w2, tmp, qb, qe, NM, score, is_rev, last_sc = -(1<<30), l_MD;
  int64_t pos, rb, re;
  uint8_t *query;

  memset(&a, 0, sizeof(mem_aln_t));
  if (ar == 0 || ar->rb < 0 || ar->re < 0) { // generate an unmapped record
    a.rid = -1; a.pos = -1; a.flag |= 0x4;
    return a;
  }
  qb = ar->qb, qe = ar->qe;
  rb = ar->rb, re = ar->re;
  query = malloc(l_query);
  for (i = 0; i < l_query; ++i) // convert to the nt4 encoding
    query[i] = query_[i] < 5? query_[i] : nst_nt4_table[(int)query_[i]];
  a.mapq = ar->secondary < 0? mem_approx_mapq_se(opt, ar) : 0;
  if (ar->secondary >= 0) a.flag |= 0x100; // secondary alignment
  tmp = infer_bw(qe - qb, re - rb, ar->truesc, opt->a, opt->o_del, opt->e_del);
  w2  = infer_bw(qe - qb, re - rb, ar->truesc, opt->a, opt->o_ins, opt->e_ins);
  w2 = w2 > tmp? w2 : tmp;
  if (bwa_verbose >= 4) printf("* Band width: inferred=%d, cmd_opt=%d, alnreg=%d\n", w2, opt->w, ar->w);
  if (w2 > opt->w) w2 = w2 < ar->w? w2 : ar->w;
  i = 0; a.cigar = 0;
  do {
    free(a.cigar);
    w2 = w2 < opt->w<<2? w2 : opt->w<<2;
    a.cigar = bwa_gen_cigar2(opt->mat, opt->o_del, opt->e_del, opt->o_ins, opt->e_ins, w2, bns->l_pac, pac, qe - qb, (uint8_t*)&query[qb], rb, re, &score, &a.n_cigar, &NM);
    if (bwa_verbose >= 4) printf("* Final alignment: w2=%d, global_sc=%d, local_sc=%d\n", w2, score, ar->truesc);
    if (score == last_sc || w2 == opt->w<<2) break; // it is possible that global alignment and local alignment give different scores
    last_sc = score;
    w2 <<= 1;
  } while (++i < 3 && score < ar->truesc - opt->a);
  l_MD = strlen((char*)(a.cigar + a.n_cigar)) + 1;
  a.NM = NM;
  pos = bns_depos(bns, rb < bns->l_pac? rb : re - 1, &is_rev);
  a.is_rev = is_rev;
  if (a.n_cigar > 0) { // squeeze out leading or trailing deletions
    if ((a.cigar[0]&0xf) == 2) {
      pos += a.cigar[0]>>4;
      --a.n_cigar;
      memmove(a.cigar, a.cigar + 1, a.n_cigar * 4 + l_MD);
    } else if ((a.cigar[a.n_cigar-1]&0xf) == 2) {
      --a.n_cigar;
      memmove(a.cigar + a.n_cigar, a.cigar + a.n_cigar + 1, l_MD); // MD needs to be moved accordingly
    }
  }
  if (qb != 0 || qe != l_query) { // add clipping to CIGAR
    int clip5, clip3;
    clip5 = is_rev? l_query - qe : qb;
    clip3 = is_rev? qb : l_query - qe;
    a.cigar = realloc(a.cigar, 4 * (a.n_cigar + 2) + l_MD);
    if (clip5) {
      memmove(a.cigar+1, a.cigar, a.n_cigar * 4 + l_MD); // make room for 5'-end clipping
      a.cigar[0] = clip5<<4 | 3;
      ++a.n_cigar;
    }
    if (clip3) {
      memmove(a.cigar + a.n_cigar + 1, a.cigar + a.n_cigar, l_MD); // make room for 3'-end clipping
      a.cigar[a.n_cigar++] = clip3<<4 | 3;
    }
  }
  a.rid = bns_pos2rid(bns, pos);
  assert(a.rid == ar->rid);
  a.pos = pos - bns->anns[a.rid].offset;
  a.score = ar->score; a.sub = ar->sub > ar->csub? ar->sub : ar->csub;
  a.is_alt = ar->is_alt; a.alt_sc = ar->alt_sc;
  free(query);
  return a;
}

typedef struct {
  const mem_opt_t *opt;
  const lbwt_t *lbwt;
  const bntseq_t *bns;
  const uint8_t *pac;
  const mem_pestat_t *pes;
  smem_aux_t **aux;
  bseq1_t *seqs;
  mem_alnreg_v *regs;
  int64_t n_processed;
} worker_t;

static void worker1(void *data, int i, int tid)
{
  worker_t *w = (worker_t*)data;
  if (!(w->opt->flag&MEM_F_PE)) {
    if (bwa_verbose >= 4) printf("=====> Processing read '%s' <=====\n", w->seqs[i].name);
    w->regs[i] = mem_align1_core(w->opt, w->lbwt, w->bns, w->pac, w->seqs[i].l_seq, w->seqs[i].seq, w->aux[tid]);
  } else {
    if (bwa_verbose >= 4) printf("=====> Processing read '%s'/1 <=====\n", w->seqs[i<<1|0].name);
    w->regs[i<<1|0] = mem_align1_core(w->opt, w->lbwt, w->bns, w->pac, w->seqs[i<<1|0].l_seq, w->seqs[i<<1|0].seq, w->aux[tid]);
    if (bwa_verbose >= 4) printf("=====> Processing read '%s'/2 <=====\n", w->seqs[i<<1|1].name);
    w->regs[i<<1|1] = mem_align1_core(w->opt, w->lbwt, w->bns, w->pac, w->seqs[i<<1|1].l_seq, w->seqs[i<<1|1].seq, w->aux[tid]);
  }
}

static void worker2(void *data, int i, int tid)
{
  extern int mem_sam_pe(const mem_opt_t *opt, const bntseq_t *bns, const uint8_t *pac, const mem_pestat_t pes[4], uint64_t id, bseq1_t s[2], mem_alnreg_v a[2]);
  extern void mem_reg2ovlp(const mem_opt_t *opt, const bntseq_t *bns, const uint8_t *pac, bseq1_t *s, mem_alnreg_v *a);
  worker_t *w = (worker_t*)data;
  if (!(w->opt->flag&MEM_F_PE)) {
    if (bwa_verbose >= 4) printf("=====> Finalizing read '%s' <=====\n", w->seqs[i].name);
    mem_mark_primary_se(w->opt, w->regs[i].n, w->regs[i].a, w->n_processed + i);
    if (w->opt->flag & MEM_F_PRIMARY5) mem_reorder_primary5(w->opt->T, &w->regs[i]);
    mem_reg2sam(w->opt, w->bns, w->pac, &w->seqs[i], &w->regs[i], 0, 0);
    free(w->regs[i].a);
  } else {
    if (bwa_verbose >= 4) printf("=====> Finalizing read pair '%s' <=====\n", w->seqs[i<<1|0].name);
    mem_sam_pe(w->opt, w->bns, w->pac, w->pes, (w->n_processed>>1) + i, &w->seqs[i<<1], &w->regs[i<<1]);
    free(w->regs[i<<1|0].a); free(w->regs[i<<1|1].a);
  }
}

void mem_process_seqs(const mem_opt_t *opt, const lbwt_t *lbwt, const bntseq_t *bns, const uint8_t *pac, int64_t n_processed, int n, bseq1_t *seqs, const mem_pestat_t *pes0)
{
  extern void kt_for(int n_threads, void (*func)(void*,int,int), void *data, int n);
  worker_t w;
  mem_pestat_t pes[4];
  double ctime, rtime;
  int i;

  ctime = cputime(); rtime = realtime();
  global_bns = bns;
  w.regs = malloc(n * sizeof(mem_alnreg_v));
  w.opt = opt; w.lbwt = lbwt; w.bns = bns; w.pac = pac;
  w.seqs = seqs; w.n_processed = n_processed;
  w.pes = &pes[0];
  w.aux = malloc(opt->n_threads * sizeof(smem_aux_t));
  for (i = 0; i < opt->n_threads; ++i)
    w.aux[i] = smem_aux_init();
  kt_for(opt->n_threads, worker1, &w, (opt->flag&MEM_F_PE)? n>>1 : n); // find mapping positions
  for (i = 0; i < opt->n_threads; ++i)
    smem_aux_destroy(w.aux[i]);
  free(w.aux);
  if (opt->flag&MEM_F_PE) { // infer insert sizes if not provided
    if (pes0) memcpy(pes, pes0, 4 * sizeof(mem_pestat_t)); // if pes0 != NULL, set the insert-size distribution as pes0
    else mem_pestat(opt, bns->l_pac, n, w.regs, pes); // otherwise, infer the insert size distribution from data
  }
  kt_for(opt->n_threads, worker2, &w, (opt->flag&MEM_F_PE)? n>>1 : n); // generate alignment
  free(w.regs);
  if (bwa_verbose >= 3)
    fprintf(stderr, "[M::%s] Processed %d reads in %.3f CPU sec, %.3f real sec\n", __func__, n, cputime() - ctime, realtime() - rtime);
}