bwamem_pair.c

#include <stdlib.h>
#include <string.h>
#include <stdio.h>
#include <math.h>
#include "kstring.h"
#include "bwamem.h"
#include "kvec.h"
#include "utils.h"
#include "ksw.h"

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


#define MIN_RATIO     0.8
#define MIN_DIR_CNT   10
#define MIN_DIR_RATIO 0.05
#define OUTLIER_BOUND 2.0
#define MAPPING_BOUND 3.0
#define MAX_STDDEV    4.0

static inline int mem_infer_dir(int64_t l_pac, int64_t b1, int64_t b2, int64_t *dist)
{
	int64_t p2;
	int r1 = (b1 >= l_pac), r2 = (b2 >= l_pac);
	p2 = r1 == r2? b2 : (l_pac<<1) - 1 - b2; // p2 is the coordinate of read 2 on the read 1 strand
	*dist = p2 > b1? p2 - b1 : b1 - p2;
	return (r1 == r2? 0 : 1) ^ (p2 > b1? 0 : 3);
}

static int cal_sub(const mem_opt_t *opt, mem_alnreg_v *r)
{
	int j;
	for (j = 1; j < r->n; ++j) { // choose unique alignment
		int b_max = r->a[j].qb > r->a[0].qb? r->a[j].qb : r->a[0].qb;
		int e_min = r->a[j].qe < r->a[0].qe? r->a[j].qe : r->a[0].qe;
		if (e_min > b_max) { // have overlap
			int min_l = r->a[j].qe - r->a[j].qb < r->a[0].qe - r->a[0].qb? r->a[j].qe - r->a[j].qb : r->a[0].qe - r->a[0].qb;
			if (e_min - b_max >= min_l * opt->mask_level) break; // significant overlap
		}
	}
	return j < r->n? r->a[j].score : opt->min_seed_len * opt->a;
}

void mem_pestat(const mem_opt_t *opt, int64_t l_pac, int n, const mem_alnreg_v *regs, mem_pestat_t pes[4])
{
	int i, d, max;
	uint64_v isize[4];
	memset(pes, 0, 4 * sizeof(mem_pestat_t));
	memset(isize, 0, sizeof(kvec_t(int)) * 4);
	for (i = 0; i < n>>1; ++i) {
		int dir;
		int64_t is;
		mem_alnreg_v *r[2];
		r[0] = (mem_alnreg_v*)&regs[i<<1|0];
		r[1] = (mem_alnreg_v*)&regs[i<<1|1];
		if (r[0]->n == 0 || r[1]->n == 0) continue;
		if (cal_sub(opt, r[0]) > MIN_RATIO * r[0]->a[0].score) continue;
		if (cal_sub(opt, r[1]) > MIN_RATIO * r[1]->a[0].score) continue;
		if (r[0]->a[0].rid != r[1]->a[0].rid) continue; // not on the same chr
		dir = mem_infer_dir(l_pac, r[0]->a[0].rb, r[1]->a[0].rb, &is);
		if (is && is <= opt->max_ins) kv_push(uint64_t, isize[dir], is);
	}
	if (bwa_verbose >= 3) fprintf(stderr, "[M::%s] # candidate unique pairs for (FF, FR, RF, RR): (%ld, %ld, %ld, %ld)\n", __func__, isize[0].n, isize[1].n, isize[2].n, isize[3].n);
	for (d = 0; d < 4; ++d) { // TODO: this block is nearly identical to the one in bwtsw2_pair.c. It would be better to merge these two.
		mem_pestat_t *r = &pes[d];
		uint64_v *q = &isize[d];
		int p25, p50, p75, x;
		if (q->n < MIN_DIR_CNT) {
			fprintf(stderr, "[M::%s] skip orientation %c%c as there are not enough pairs\n", __func__, "FR"[d>>1&1], "FR"[d&1]);
			r->failed = 1;
			free(q->a);
			continue;
		} else fprintf(stderr, "[M::%s] analyzing insert size distribution for orientation %c%c...\n", __func__, "FR"[d>>1&1], "FR"[d&1]);
		ks_introsort_64(q->n, q->a);
		p25 = q->a[(int)(.25 * q->n + .499)];
		p50 = q->a[(int)(.50 * q->n + .499)];
		p75 = q->a[(int)(.75 * q->n + .499)];
		r->low  = (int)(p25 - OUTLIER_BOUND * (p75 - p25) + .499);
		if (r->low < 1) r->low = 1;
		r->high = (int)(p75 + OUTLIER_BOUND * (p75 - p25) + .499);
		fprintf(stderr, "[M::%s] (25, 50, 75) percentile: (%d, %d, %d)\n", __func__, p25, p50, p75);
		fprintf(stderr, "[M::%s] low and high boundaries for computing mean and std.dev: (%d, %d)\n", __func__, r->low, r->high);
		for (i = x = 0, r->avg = 0; i < q->n; ++i)
			if (q->a[i] >= r->low && q->a[i] <= r->high)
				r->avg += q->a[i], ++x;
		r->avg /= x;
		for (i = 0, r->std = 0; i < q->n; ++i)
			if (q->a[i] >= r->low && q->a[i] <= r->high)
				r->std += (q->a[i] - r->avg) * (q->a[i] - r->avg);
		r->std = sqrt(r->std / x);
		fprintf(stderr, "[M::%s] mean and std.dev: (%.2f, %.2f)\n", __func__, r->avg, r->std);
		r->low  = (int)(p25 - MAPPING_BOUND * (p75 - p25) + .499);
		r->high = (int)(p75 + MAPPING_BOUND * (p75 - p25) + .499);
		if (r->low  > r->avg - MAX_STDDEV * r->std) r->low  = (int)(r->avg - MAX_STDDEV * r->std + .499);
		if (r->high < r->avg + MAX_STDDEV * r->std) r->high = (int)(r->avg + MAX_STDDEV * r->std + .499);
		if (r->low < 1) r->low = 1;
		fprintf(stderr, "[M::%s] low and high boundaries for proper pairs: (%d, %d)\n", __func__, r->low, r->high);
		free(q->a);
	}
	for (d = 0, max = 0; d < 4; ++d)
		max = max > isize[d].n? max : isize[d].n;
	for (d = 0; d < 4; ++d)
		if (pes[d].failed == 0 && isize[d].n < max * MIN_DIR_RATIO) {
			pes[d].failed = 1;
			fprintf(stderr, "[M::%s] skip orientation %c%c\n", __func__, "FR"[d>>1&1], "FR"[d&1]);
		}
}

int mem_matesw(const mem_opt_t *opt, const bntseq_t *bns, const uint8_t *pac, const mem_pestat_t pes[4], const mem_alnreg_t *a, int l_ms, const uint8_t *ms, mem_alnreg_v *ma)
{
	extern 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);
	int64_t l_pac = bns->l_pac;
	int i, r, skip[4], n = 0, rid;
	for (r = 0; r < 4; ++r)
		skip[r] = pes[r].failed? 1 : 0;
	for (i = 0; i < ma->n; ++i) { // check which orinentation has been found
		int64_t dist;
		r = mem_infer_dir(l_pac, a->rb, ma->a[i].rb, &dist);
		if (dist >= pes[r].low && dist <= pes[r].high)
			skip[r] = 1;
	}
	if (skip[0] + skip[1] + skip[2] + skip[3] == 4) return 0; // consistent pair exist; no need to perform SW
	for (r = 0; r < 4; ++r) {
		int is_rev, is_larger;
		uint8_t *seq, *rev = 0, *ref = 0;
		int64_t rb, re;
		if (skip[r]) continue;
		is_rev = (r>>1 != (r&1)); // whether to reverse complement the mate
		is_larger = !(r>>1); // whether the mate has larger coordinate
		if (is_rev) {
			rev = malloc(l_ms); // this is the reverse complement of $ms
			for (i = 0; i < l_ms; ++i) rev[l_ms - 1 - i] = ms[i] < 4? 3 - ms[i] : 4;
			seq = rev;
		} else seq = (uint8_t*)ms;
		if (!is_rev) {
			rb = is_larger? a->rb + pes[r].low : a->rb - pes[r].high;
			re = (is_larger? a->rb + pes[r].high: a->rb - pes[r].low) + l_ms; // if on the same strand, end position should be larger to make room for the seq length
		} else {
			rb = (is_larger? a->rb + pes[r].low : a->rb - pes[r].high) - l_ms; // similarly on opposite strands
			re = is_larger? a->rb + pes[r].high: a->rb - pes[r].low;
		}
		if (rb < 0) rb = 0;
		if (re > l_pac<<1) re = l_pac<<1;
		if (rb < re) ref = bns_fetch_seq(bns, pac, &rb, (rb+re)>>1, &re, &rid);
		if (a->rid == rid && re - rb >= opt->min_seed_len) { // no funny things happening
			kswr_t aln;
			mem_alnreg_t b;
			int tmp, xtra = KSW_XSUBO | KSW_XSTART | (l_ms * opt->a < 250? KSW_XBYTE : 0) | (opt->min_seed_len * opt->a);
			aln = ksw_align2(l_ms, seq, re - rb, ref, 5, opt->mat, opt->o_del, opt->e_del, opt->o_ins, opt->e_ins, xtra, 0);
			memset(&b, 0, sizeof(mem_alnreg_t));
			if (aln.score >= opt->min_seed_len && aln.qb >= 0) { // something goes wrong if aln.qb < 0
				b.rid = a->rid;
				b.is_alt = a->is_alt;
				b.qb = is_rev? l_ms - (aln.qe + 1) : aln.qb;                                                                                                                                                                              
				b.qe = is_rev? l_ms - aln.qb : aln.qe + 1; 
				b.rb = is_rev? (l_pac<<1) - (rb + aln.te + 1) : rb + aln.tb;
				b.re = is_rev? (l_pac<<1) - (rb + aln.tb) : rb + aln.te + 1;
				b.score = aln.score;
				b.csub = aln.score2;
				b.secondary = -1;
				b.seedcov = (b.re - b.rb < b.qe - b.qb? b.re - b.rb : b.qe - b.qb) >> 1;
//				printf("*** %d, [%lld,%lld], %d:%d, (%lld,%lld), (%lld,%lld) == (%lld,%lld)\n", aln.score, rb, re, is_rev, is_larger, a->rb, a->re, ma->a[0].rb, ma->a[0].re, b.rb, b.re);
				kv_push(mem_alnreg_t, *ma, b); // make room for a new element
				// move b s.t. ma is sorted
				for (i = 0; i < ma->n - 1; ++i) // find the insertion point
					if (ma->a[i].score < b.score) break;
				tmp = i;
				for (i = ma->n - 1; i > tmp; --i) ma->a[i] = ma->a[i-1];
				ma->a[i] = b;
			}
			++n;
		}
		if (n) ma->n = mem_sort_dedup_patch(opt, 0, 0, 0, ma->n, ma->a);
		if (rev) free(rev);
		free(ref);
	}
	return n;
}

int mem_pair(const mem_opt_t *opt, const bntseq_t *bns, const uint8_t *pac, const mem_pestat_t pes[4], bseq1_t s[2], mem_alnreg_v a[2], int id, int *sub, int *n_sub, int z[2], int n_pri[2])
{
	pair64_v v, u;
	int r, i, k, y[4], ret; // y[] keeps the last hit
	int64_t l_pac = bns->l_pac;
	kv_init(v); kv_init(u);
	for (r = 0; r < 2; ++r) { // loop through read number
		for (i = 0; i < n_pri[r]; ++i) {
			pair64_t key;
			mem_alnreg_t *e = &a[r].a[i];
			key.x = e->rb < l_pac? e->rb : (l_pac<<1) - 1 - e->rb; // forward position
			key.x = (uint64_t)e->rid<<32 | (key.x - bns->anns[e->rid].offset);
			key.y = (uint64_t)e->score << 32 | i << 2 | (e->rb >= l_pac)<<1 | r;
			kv_push(pair64_t, v, key);
		}
	}
	ks_introsort_128(v.n, v.a);
	y[0] = y[1] = y[2] = y[3] = -1;
	//for (i = 0; i < v.n; ++i) printf("[%d]\t%d\t%c%ld\n", i, (int)(v.a[i].y&1)+1, "+-"[v.a[i].y>>1&1], (long)v.a[i].x);
	for (i = 0; i < v.n; ++i) {
		for (r = 0; r < 2; ++r) { // loop through direction
			int dir = r<<1 | (v.a[i].y>>1&1), which;
			if (pes[dir].failed) continue; // invalid orientation
			which = r<<1 | ((v.a[i].y&1)^1);
			if (y[which] < 0) continue; // no previous hits
			for (k = y[which]; k >= 0; --k) { // TODO: this is a O(n^2) solution in the worst case; remember to check if this loop takes a lot of time (I doubt)
				int64_t dist;
				int q;
				double ns;
				pair64_t *p;
				if ((v.a[k].y&3) != which) continue;
				dist = (int64_t)v.a[i].x - v.a[k].x;
				//printf("%d: %lld\n", k, dist);
				if (dist > pes[dir].high) break;
				if (dist < pes[dir].low)  continue;
				ns = (dist - pes[dir].avg) / pes[dir].std;
				q = (int)((v.a[i].y>>32) + (v.a[k].y>>32) + .721 * log(2. * erfc(fabs(ns) * M_SQRT1_2)) * opt->a + .499); // .721 = 1/log(4)
				if (q < 0) q = 0;
				p = kv_pushp(pair64_t, u);
				p->y = (uint64_t)k<<32 | i;
				p->x = (uint64_t)q<<32 | (hash_64(p->y ^ id<<8) & 0xffffffffU);
				//printf("[%lld,%lld]\t%d\tdist=%ld\n", v.a[k].x, v.a[i].x, q, (long)dist);
			}
		}
		y[v.a[i].y&3] = i;
	}
	if (u.n) { // found at least one proper pair
		int tmp = opt->a + opt->b;
		tmp = 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;
		ks_introsort_128(u.n, u.a);
		i = u.a[u.n-1].y >> 32; k = u.a[u.n-1].y << 32 >> 32;
		z[v.a[i].y&1] = v.a[i].y<<32>>34; // index of the best pair
		z[v.a[k].y&1] = v.a[k].y<<32>>34;
		ret = u.a[u.n-1].x >> 32;
		*sub = u.n > 1? u.a[u.n-2].x>>32 : 0;
		for (i = (long)u.n - 2, *n_sub = 0; i >= 0; --i)
			if (*sub - (int)(u.a[i].x>>32) <= tmp) ++*n_sub;
	} else ret = 0, *sub = 0, *n_sub = 0;
	free(u.a); free(v.a);
	return ret;
}

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);
void mem_reorder_primary5(int T, mem_alnreg_v *a);

#define raw_mapq(diff, a) ((int)(6.02 * (diff) / (a) + .499))

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 int mem_mark_primary_se(const mem_opt_t *opt, int n, mem_alnreg_t *a, int64_t id);
	extern int mem_approx_mapq_se(const mem_opt_t *opt, const mem_alnreg_t *a);
	extern 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, const mem_alnreg_v *a, int l_query, const char *query);

	int n = 0, i, j, z[2], o, subo, n_sub, extra_flag = 1, n_pri[2], n_aa[2];
	kstring_t str;
	mem_aln_t h[2], g[2], aa[2][2];

	str.l = str.m = 0; str.s = 0;
	memset(h, 0, sizeof(mem_aln_t) * 2);
	memset(g, 0, sizeof(mem_aln_t) * 2);
	n_aa[0] = n_aa[1] = 0;
	if (!(opt->flag & MEM_F_NO_RESCUE)) { // then perform SW for the best alignment
		mem_alnreg_v b[2];
		kv_init(b[0]); kv_init(b[1]);
		for (i = 0; i < 2; ++i)
			for (j = 0; j < a[i].n; ++j)
				if (a[i].a[j].score >= a[i].a[0].score  - opt->pen_unpaired)
					kv_push(mem_alnreg_t, b[i], a[i].a[j]);
		for (i = 0; i < 2; ++i)
			for (j = 0; j < b[i].n && j < opt->max_matesw; ++j)
				n += mem_matesw(opt, bns, pac, pes, &b[i].a[j], s[!i].l_seq, (uint8_t*)s[!i].seq, &a[!i]);
		free(b[0].a); free(b[1].a);
	}
	n_pri[0] = mem_mark_primary_se(opt, a[0].n, a[0].a, id<<1|0);
	n_pri[1] = mem_mark_primary_se(opt, a[1].n, a[1].a, id<<1|1);
	if (opt->flag & MEM_F_PRIMARY5) {
		mem_reorder_primary5(opt->T, &a[0]);
		mem_reorder_primary5(opt->T, &a[1]);
	}
	if (opt->flag&MEM_F_NOPAIRING) goto no_pairing;
	// pairing single-end hits
	if (n_pri[0] && n_pri[1] && (o = mem_pair(opt, bns, pac, pes, s, a, id, &subo, &n_sub, z, n_pri)) > 0) {
		int is_multi[2], q_pe, score_un, q_se[2];
		char **XA[2];
		// check if an end has multiple hits even after mate-SW
		for (i = 0; i < 2; ++i) {
			for (j = 1; j < n_pri[i]; ++j)
				if (a[i].a[j].secondary < 0 && a[i].a[j].score >= opt->T) break;
			is_multi[i] = j < n_pri[i]? 1 : 0;
		}
		if (is_multi[0] || is_multi[1]) goto no_pairing; // TODO: in rare cases, the true hit may be long but with low score
		// compute mapQ for the best SE hit
		score_un = a[0].a[0].score + a[1].a[0].score - opt->pen_unpaired;
		//q_pe = o && subo < o? (int)(MEM_MAPQ_COEF * (1. - (double)subo / o) * log(a[0].a[z[0]].seedcov + a[1].a[z[1]].seedcov) + .499) : 0;
		subo = subo > score_un? subo : score_un;
		q_pe = raw_mapq(o - subo, opt->a);
		if (n_sub > 0) q_pe -= (int)(4.343 * log(n_sub+1) + .499);
		if (q_pe < 0) q_pe = 0;
		if (q_pe > 60) q_pe = 60;
		q_pe = (int)(q_pe * (1. - .5 * (a[0].a[0].frac_rep + a[1].a[0].frac_rep)) + .499);
		// the following assumes no split hits
		if (o > score_un) { // paired alignment is preferred
			mem_alnreg_t *c[2];
			c[0] = &a[0].a[z[0]]; c[1] = &a[1].a[z[1]];
			for (i = 0; i < 2; ++i) {
				if (c[i]->secondary >= 0)
					c[i]->sub = a[i].a[c[i]->secondary].score, c[i]->secondary = -2;
				q_se[i] = mem_approx_mapq_se(opt, c[i]);
			}
			q_se[0] = q_se[0] > q_pe? q_se[0] : q_pe < q_se[0] + 40? q_pe : q_se[0] + 40;
			q_se[1] = q_se[1] > q_pe? q_se[1] : q_pe < q_se[1] + 40? q_pe : q_se[1] + 40;
			extra_flag |= 2;
			// cap at the tandem repeat score
			q_se[0] = q_se[0] < raw_mapq(c[0]->score - c[0]->csub, opt->a)? q_se[0] : raw_mapq(c[0]->score - c[0]->csub, opt->a);
			q_se[1] = q_se[1] < raw_mapq(c[1]->score - c[1]->csub, opt->a)? q_se[1] : raw_mapq(c[1]->score - c[1]->csub, opt->a);
		} else { // the unpaired alignment is preferred
			z[0] = z[1] = 0;
			q_se[0] = mem_approx_mapq_se(opt, &a[0].a[0]);
			q_se[1] = mem_approx_mapq_se(opt, &a[1].a[0]);
		}
		for (i = 0; i < 2; ++i) {
			int k = a[i].a[z[i]].secondary_all;
			if (k >= 0 && k < n_pri[i]) { // switch secondary and primary if both of them are non-ALT
				assert(a[i].a[k].secondary_all < 0);
				for (j = 0; j < a[i].n; ++j)
					if (a[i].a[j].secondary_all == k || j == k)
						a[i].a[j].secondary_all = z[i];
				a[i].a[z[i]].secondary_all = -1;
			}
		}
		if (!(opt->flag & MEM_F_ALL)) {
			for (i = 0; i < 2; ++i)
				XA[i] = mem_gen_alt(opt, bns, pac, &a[i], s[i].l_seq, s[i].seq);
		} else XA[0] = XA[1] = 0;
		// write SAM
		for (i = 0; i < 2; ++i) {
			h[i] = mem_reg2aln(opt, bns, pac, s[i].l_seq, s[i].seq, &a[i].a[z[i]]);
			h[i].mapq = q_se[i];
			h[i].flag |= 0x40<<i | extra_flag;
			h[i].XA = XA[i]? XA[i][z[i]] : 0;
			aa[i][n_aa[i]++] = h[i];
			if (n_pri[i] < a[i].n) { // the read has ALT hits
				mem_alnreg_t *p = &a[i].a[n_pri[i]];
				if (p->score < opt->T || p->secondary >= 0 || !p->is_alt) continue;
				g[i] = mem_reg2aln(opt, bns, pac, s[i].l_seq, s[i].seq, p);
				g[i].flag |= 0x800 | 0x40<<i | extra_flag;
				g[i].XA = XA[i]? XA[i][n_pri[i]] : 0;
				aa[i][n_aa[i]++] = g[i];
			}
		}
		for (i = 0; i < n_aa[0]; ++i)
			mem_aln2sam(opt, bns, &str, &s[0], n_aa[0], aa[0], i, &h[1]); // write read1 hits
		s[0].sam = strdup(str.s); str.l = 0;
		for (i = 0; i < n_aa[1]; ++i)
			mem_aln2sam(opt, bns, &str, &s[1], n_aa[1], aa[1], i, &h[0]); // write read2 hits
		s[1].sam = str.s;
		if (strcmp(s[0].name, s[1].name) != 0) err_fatal(__func__, "paired reads have different names: \"%s\", \"%s\"\n", s[0].name, s[1].name);
		// free
		for (i = 0; i < 2; ++i) {
			free(h[i].cigar); free(g[i].cigar);
			if (XA[i] == 0) continue;
			for (j = 0; j < a[i].n; ++j) free(XA[i][j]);
			free(XA[i]);
		}
	} else goto no_pairing;
	return n;

no_pairing:
	for (i = 0; i < 2; ++i) {
		int which = -1;
		if (a[i].n) {
			if (a[i].a[0].score >= opt->T) which = 0;
			else if (n_pri[i] < a[i].n && a[i].a[n_pri[i]].score >= opt->T)
				which = n_pri[i];
		}
		if (which >= 0) h[i] = mem_reg2aln(opt, bns, pac, s[i].l_seq, s[i].seq, &a[i].a[which]);
		else h[i] = mem_reg2aln(opt, bns, pac, s[i].l_seq, s[i].seq, 0);
	}
	if (!(opt->flag & MEM_F_NOPAIRING) && h[0].rid == h[1].rid && h[0].rid >= 0) { // if the top hits from the two ends constitute a proper pair, flag it.
		int64_t dist;
		int d;
		d = mem_infer_dir(bns->l_pac, a[0].a[0].rb, a[1].a[0].rb, &dist);
		if (!pes[d].failed && dist >= pes[d].low && dist <= pes[d].high) extra_flag |= 2;
	}
	mem_reg2sam(opt, bns, pac, &s[0], &a[0], 0x41|extra_flag, &h[1]);
	mem_reg2sam(opt, bns, pac, &s[1], &a[1], 0x81|extra_flag, &h[0]);
	if (strcmp(s[0].name, s[1].name) != 0) err_fatal(__func__, "paired reads have different names: \"%s\", \"%s\"\n", s[0].name, s[1].name);
	free(h[0].cigar); free(h[1].cigar);
	return n;
}

int mem_sam_pe_results(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], 
    mem_aln_t aa[2][2], int n_aa[2])
{
	extern int mem_mark_primary_se(const mem_opt_t *opt, int n, mem_alnreg_t *a, int64_t id);
	extern int mem_approx_mapq_se(const mem_opt_t *opt, const mem_alnreg_t *a);
	extern void mem_reg2result(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, mem_aln_t alignments[2], int* n_aa);
	extern char **mem_gen_alt(const mem_opt_t *opt, const bntseq_t *bns, const uint8_t *pac, const mem_alnreg_v *a, int l_query, const char *query);

	int n = 0, i, j, z[2], o, subo, n_sub, extra_flag = 1, n_pri[2];// n_aa[2];
	kstring_t str;
	mem_aln_t h[2], g[2];//, aa[2][2];

	str.l = str.m = 0; str.s = 0;
	memset(h, 0, sizeof(mem_aln_t) * 2);
	memset(g, 0, sizeof(mem_aln_t) * 2);
	n_aa[0] = n_aa[1] = 0;
	if (!(opt->flag & MEM_F_NO_RESCUE)) { // then perform SW for the best alignment
		mem_alnreg_v b[2];
		kv_init(b[0]); kv_init(b[1]);
		for (i = 0; i < 2; ++i)
			for (j = 0; j < a[i].n; ++j)
				if (a[i].a[j].score >= a[i].a[0].score  - opt->pen_unpaired)
					kv_push(mem_alnreg_t, b[i], a[i].a[j]);
		for (i = 0; i < 2; ++i)
			for (j = 0; j < b[i].n && j < opt->max_matesw; ++j)
				n += mem_matesw(opt, bns, pac, pes, &b[i].a[j], s[!i].l_seq, (uint8_t*)s[!i].seq, &a[!i]);
		free(b[0].a); free(b[1].a);
	}
	n_pri[0] = mem_mark_primary_se(opt, a[0].n, a[0].a, id<<1|0);
	n_pri[1] = mem_mark_primary_se(opt, a[1].n, a[1].a, id<<1|1);
	if (opt->flag & MEM_F_PRIMARY5) {
		mem_reorder_primary5(opt->T, &a[0]);
		mem_reorder_primary5(opt->T, &a[1]);
	}
	if (opt->flag&MEM_F_NOPAIRING) goto no_pairing;
	// pairing single-end hits
	if (n_pri[0] && n_pri[1] && (o = mem_pair(opt, bns, pac, pes, s, a, id, &subo, &n_sub, z, n_pri)) > 0) {
		int is_multi[2], q_pe, score_un, q_se[2];
		char **XA[2];
		// check if an end has multiple hits even after mate-SW
		for (i = 0; i < 2; ++i) {
			for (j = 1; j < n_pri[i]; ++j)
				if (a[i].a[j].secondary < 0 && a[i].a[j].score >= opt->T) break;
			is_multi[i] = j < n_pri[i]? 1 : 0;
		}
		if (is_multi[0] || is_multi[1]) goto no_pairing; // TODO: in rare cases, the true hit may be long but with low score
		// compute mapQ for the best SE hit
		score_un = a[0].a[0].score + a[1].a[0].score - opt->pen_unpaired;
		//q_pe = o && subo < o? (int)(MEM_MAPQ_COEF * (1. - (double)subo / o) * log(a[0].a[z[0]].seedcov + a[1].a[z[1]].seedcov) + .499) : 0;
		subo = subo > score_un? subo : score_un;
		q_pe = raw_mapq(o - subo, opt->a);
		if (n_sub > 0) q_pe -= (int)(4.343 * log(n_sub+1) + .499);
		if (q_pe < 0) q_pe = 0;
		if (q_pe > 60) q_pe = 60;
		q_pe = (int)(q_pe * (1. - .5 * (a[0].a[0].frac_rep + a[1].a[0].frac_rep)) + .499);
		// the following assumes no split hits
		if (o > score_un) { // paired alignment is preferred
			mem_alnreg_t *c[2];
			c[0] = &a[0].a[z[0]]; c[1] = &a[1].a[z[1]];
			for (i = 0; i < 2; ++i) {
				if (c[i]->secondary >= 0)
					c[i]->sub = a[i].a[c[i]->secondary].score, c[i]->secondary = -2;
				q_se[i] = mem_approx_mapq_se(opt, c[i]);
			}
			q_se[0] = q_se[0] > q_pe? q_se[0] : q_pe < q_se[0] + 40? q_pe : q_se[0] + 40;
			q_se[1] = q_se[1] > q_pe? q_se[1] : q_pe < q_se[1] + 40? q_pe : q_se[1] + 40;
			extra_flag |= 2;
			// cap at the tandem repeat score
			q_se[0] = q_se[0] < raw_mapq(c[0]->score - c[0]->csub, opt->a)? q_se[0] : raw_mapq(c[0]->score - c[0]->csub, opt->a);
			q_se[1] = q_se[1] < raw_mapq(c[1]->score - c[1]->csub, opt->a)? q_se[1] : raw_mapq(c[1]->score - c[1]->csub, opt->a);
		} else { // the unpaired alignment is preferred
			z[0] = z[1] = 0;
			q_se[0] = mem_approx_mapq_se(opt, &a[0].a[0]);
			q_se[1] = mem_approx_mapq_se(opt, &a[1].a[0]);
		}
		for (i = 0; i < 2; ++i) {
			int k = a[i].a[z[i]].secondary_all;
			if (k >= 0 && k < n_pri[i]) { // switch secondary and primary if both of them are non-ALT
				assert(a[i].a[k].secondary_all < 0);
				for (j = 0; j < a[i].n; ++j)
					if (a[i].a[j].secondary_all == k || j == k)
						a[i].a[j].secondary_all = z[i];
				a[i].a[z[i]].secondary_all = -1;
			}
		}
		if (!(opt->flag & MEM_F_ALL)) {
			for (i = 0; i < 2; ++i)
				XA[i] = mem_gen_alt(opt, bns, pac, &a[i], s[i].l_seq, s[i].seq);
		} else XA[0] = XA[1] = 0;
		// write SAM
		for (i = 0; i < 2; ++i) {
			h[i] = mem_reg2aln(opt, bns, pac, s[i].l_seq, s[i].seq, &a[i].a[z[i]]);
			h[i].mapq = q_se[i];
			h[i].flag |= 0x40<<i | extra_flag;
			h[i].XA = XA[i]? XA[i][z[i]] : 0;
			aa[i][n_aa[i]++] = h[i];
			if (n_pri[i] < a[i].n) { // the read has ALT hits
				mem_alnreg_t *p = &a[i].a[n_pri[i]];
				if (p->score < opt->T || p->secondary >= 0 || !p->is_alt) continue;
				g[i] = mem_reg2aln(opt, bns, pac, s[i].l_seq, s[i].seq, p);
				g[i].flag |= 0x800 | 0x40<<i | extra_flag;
				g[i].XA = XA[i]? XA[i][n_pri[i]] : 0;
				aa[i][n_aa[i]++] = g[i];
			}
		}
		/*for (i = 0; i < n_aa[0]; ++i)
			mem_aln2sam(opt, bns, &str, &s[0], n_aa[0], aa[0], i, &h[1]); // write read1 hits
		s[0].sam = strdup(str.s); str.l = 0;
		for (i = 0; i < n_aa[1]; ++i)
			mem_aln2sam(opt, bns, &str, &s[1], n_aa[1], aa[1], i, &h[0]); // write read2 hits
		s[1].sam = str.s;
		if (strcmp(s[0].name, s[1].name) != 0) err_fatal(__func__, "paired reads have different names: \"%s\", \"%s\"\n", s[0].name, s[1].name);*/
		// free
		for (i = 0; i < 2; ++i) {
			//free(h[i].cigar); free(g[i].cigar);
			if (XA[i] == 0) continue;
			for (j = 0; j < a[i].n; ++j) free(XA[i][j]);
			free(XA[i]);
		}
	} else goto no_pairing;
	return n;

no_pairing:
  //printf("got to no pairing\n");
	for (i = 0; i < 2; ++i) {
		int which = -1;
		if (a[i].n) {
			if (a[i].a[0].score >= opt->T) which = 0;
			else if (n_pri[i] < a[i].n && a[i].a[n_pri[i]].score >= opt->T)
				which = n_pri[i];
		}
		if (which >= 0) h[i] = mem_reg2aln(opt, bns, pac, s[i].l_seq, s[i].seq, &a[i].a[which]);
		else h[i] = mem_reg2aln(opt, bns, pac, s[i].l_seq, s[i].seq, 0);
	}
	if (!(opt->flag & MEM_F_NOPAIRING) && h[0].rid == h[1].rid && h[0].rid >= 0) { // if the top hits from the two ends constitute a proper pair, flag it.
		int64_t dist;
		int d;
		d = mem_infer_dir(bns->l_pac, a[0].a[0].rb, a[1].a[0].rb, &dist);
		if (!pes[d].failed && dist >= pes[d].low && dist <= pes[d].high) extra_flag |= 2;
	}
	mem_reg2result(opt, bns, pac, &s[0], &a[0], 0x41|extra_flag, &h[1], aa[0], &n_aa[0]);
	mem_reg2result(opt, bns, pac, &s[1], &a[1], 0x81|extra_flag, &h[0], aa[1], &n_aa[1]);
	if (strcmp(s[0].name, s[1].name) != 0) err_fatal(__func__, "paired reads have different names: \"%s\", \"%s\"\n", s[0].name, s[1].name);
	//free(h[0].cigar); free(h[1].cigar);
	return n;
}