bwape.c

//#include <unistd.h>
#include <math.h>
#include <stdlib.h>
#include <time.h>
#include <stdio.h>
#include <string.h>
#include "bwtaln.h"
#include "kvec.h"
#include "bntseq.h"
#include "utils.h"
#include "stdaln.h"
#include "bwase.h"

#include <float.h>
#include "glibc_win64_flat/_math_.h"
#include "glibc_win64_flat/getopt.h"
#include "glibc_win64_flat/stdlib.h"
#define erfc __erfc

typedef struct {
    int n;
    bwtint_t *a;
} poslist_t;

typedef struct {
    double avg, std, ap_prior;
    bwtint_t low, high, high_bayesian;
} isize_info_t;

typedef struct {
    uint64_t x, y;
} b128_t;

#define b128_lt(a, b) ((a).x < (b).x)
#define b128_eq(a, b) ((a).x == (b).x && (a).y == (b).y)
#define b128_hash(a) ((uint32_t)(a).x)

#include "khash.h"
KHASH_INIT(b128, b128_t, poslist_t, 1, b128_hash, b128_eq)

#include "ksort.h"
KSORT_INIT(b128, b128_t, b128_lt)
KSORT_INIT_GENERIC(uint64_t)

typedef struct {
    kvec_t(b128_t) arr;
    kvec_t(b128_t) pos[2];
    kvec_t(bwt_aln1_t) aln[2];
} pe_data_t;

#define MIN_HASH_WIDTH 1000

extern int g_log_n[256]; // in bwase.c
static kh_b128_t *g_hash;

void bwa_aln2seq_core(int n_aln, const bwt_aln1_t *aln, bwa_seq_t *s, int set_main, int n_multi);
void bwa_aln2seq(int n_aln, const bwt_aln1_t *aln, bwa_seq_t *s);
int bwa_approx_mapQ(const bwa_seq_t *p, int mm);
void bwa_print_sam1(const bntseq_t *bns, bwa_seq_t *p, const bwa_seq_t *mate, int mode, int max_top2);
bntseq_t *bwa_open_nt(const char *prefix);
void bwa_print_sam_SQ(const bntseq_t *bns);
void bwa_print_sam_PG();

pe_opt_t *bwa_init_pe_opt()
{
    pe_opt_t *po;
    po = (pe_opt_t*)calloc(1, sizeof(pe_opt_t));
    po->max_isize = 500;
    po->force_isize = 0;
    po->max_occ = 100000;
    po->n_multi = 3;
    po->N_multi = 10;
    po->type = BWA_PET_STD;
    po->is_sw = 1;
    po->ap_prior = 1e-5;
    return po;
}

static __inline uint64_t hash_64(uint64_t key)
{
    key += ~(key << 32);
    key ^= (key >> 22);
    key += ~(key << 13);
    key ^= (key >> 8);
    key += (key << 3);
    key ^= (key >> 15);
    key += ~(key << 27);
    key ^= (key >> 31);
    return key;
}
/*
static double ierfc(double x) // inverse erfc(); iphi(x) = M_SQRT2 *ierfc(2 * x);
{
    const double a = 0.140012;
    double b, c;
    b = log(x * (2 - x));
    c = 2./M_PI/a + b / 2.;
    return sqrt(sqrt(c * c - b / a) - c);
}
*/

// for normal distribution, this is about 3std
#define OUTLIER_BOUND 2.0

static int infer_isize(int n_seqs, bwa_seq_t *seqs[2], isize_info_t *ii, double ap_prior, int64_t L)
{
    uint64_t x, *isizes, n_ap = 0;
    int n, i, tot, p25, p75, p50, max_len = 1, tmp;
    double skewness = 0.0, kurtosis = 0.0, y;

    ii->avg = ii->std = -1.0;
    ii->low = ii->high = ii->high_bayesian = 0;
    isizes = (uint64_t*)calloc(n_seqs, 8);
    for (i = 0, tot = 0; i != n_seqs; ++i) {
        bwa_seq_t *p[2];
        p[0] = seqs[0] + i; p[1] = seqs[1] + i;
        if (p[0]->mapQ >= 20 && p[1]->mapQ >= 20) {
            x = (p[0]->pos < p[1]->pos)? p[1]->pos + p[1]->len - p[0]->pos : p[0]->pos + p[0]->len - p[1]->pos;
            if (x < 100000) isizes[tot++] = x;
        }
        if (p[0]->len > max_len) max_len = p[0]->len;
        if (p[1]->len > max_len) max_len = p[1]->len;
    }
    if (tot < 20) {
        fprintf(stderr, "[infer_isize] fail to infer insert size: too few good pairs\n");
        free(isizes);
        return -1;
    }
    ks_introsort(uint64_t, tot, isizes);
    p25 = isizes[(int)(tot*0.25 + 0.5)];
    p50 = isizes[(int)(tot*0.50 + 0.5)];
    p75 = isizes[(int)(tot*0.75 + 0.5)];
    tmp  = (int)(p25 - OUTLIER_BOUND * (p75 - p25) + .499);
    ii->low = tmp > max_len? tmp : max_len; // ii->low is unsigned
    ii->high = (int)(p75 + OUTLIER_BOUND * (p75 - p25) + .499);
    for (i = 0, x = n = 0; i < tot; ++i)
        if (isizes[i] >= ii->low && isizes[i] <= ii->high)
            ++n, x += isizes[i];
    ii->avg = (double)x / n;
    for (i = 0; i < tot; ++i) {
        if (isizes[i] >= ii->low && isizes[i] <= ii->high) {
            double tmp = (isizes[i] - ii->avg) * (isizes[i] - ii->avg);
            ii->std += tmp;
            skewness += tmp * (isizes[i] - ii->avg);
            kurtosis += tmp * tmp;
        }
    }
    kurtosis = kurtosis/n / (ii->std / n * ii->std / n) - 3;
    ii->std = sqrt(ii->std / n); // it would be better as n-1, but n is usually very large
    skewness = skewness / n / (ii->std * ii->std * ii->std);
    for (y = 1.0; y < 10.0; y += 0.01)
        if (.5 * erfc(y / M_SQRT2) < ap_prior / L * (y * ii->std + ii->avg)) break;
    ii->high_bayesian = (bwtint_t)(y * ii->std + ii->avg + .499);
    for (i = 0; i < tot; ++i)
        if (isizes[i] > ii->high_bayesian) ++n_ap;
    ii->ap_prior = .01 * (n_ap + .01) / tot;
    if (ii->ap_prior < ap_prior) ii->ap_prior = ap_prior;
    free(isizes);
    fprintf(stderr, "[infer_isize] (25, 50, 75) percentile: (%d, %d, %d)\n", p25, p50, p75);
    if (_isnan(ii->std) || p75 > 100000) {
        ii->low = ii->high = ii->high_bayesian = 0; ii->avg = ii->std = -1.0;
        fprintf(stderr, "[infer_isize] fail to infer insert size: weird pairing\n");
        return -1;
    }
    for (y = 1.0; y < 10.0; y += 0.01)
        if (.5 * erfc(y / M_SQRT2) < ap_prior / L * (y * ii->std + ii->avg)) break;
    ii->high_bayesian = (bwtint_t)(y * ii->std + ii->avg + .499);
    fprintf(stderr, "[infer_isize] low and high boundaries: %ld and %ld for estimating avg and std\n", (long)ii->low, (long)ii->high);
    fprintf(stderr, "[infer_isize] inferred external isize from %d pairs: %.3lf +/- %.3lf\n", n, ii->avg, ii->std);
    fprintf(stderr, "[infer_isize] skewness: %.3lf; kurtosis: %.3lf; ap_prior: %.2e\n", skewness, kurtosis, ii->ap_prior);
    fprintf(stderr, "[infer_isize] inferred maximum insert size: %ld (%.2lf sigma)\n", (long)ii->high_bayesian, y);
    return 0;
}

static int pairing(bwa_seq_t *p[2], pe_data_t *d, const pe_opt_t *opt, int s_mm, const isize_info_t *ii)
{
    int i, j, o_n, subo_n, cnt_chg = 0, low_bound = ii->low, max_len;
    uint64_t o_score, subo_score;
    b128_t last_pos[2][2], o_pos[2];
    max_len = p[0]->full_len;
    if (max_len < p[1]->full_len) max_len = p[1]->full_len;
    if (low_bound < max_len) low_bound = max_len;

    // here v>=u. When ii is set, we check insert size with ii; otherwise with opt->max_isize
#define __pairing_aux(u,v) do { \
        bwtint_t l = (v).x + p[(v).y&1]->len - ((u).x); \
        if ((u).x != (uint64_t)-1 && (v).x > (u).x && l >= max_len \
            && ((ii->high && l <= ii->high_bayesian) || (ii->high == 0 && l <= opt->max_isize))) \
        { \
            uint64_t s = d->aln[(v).y&1].a[(v).y>>2].score + d->aln[(u).y&1].a[(u).y>>2].score; \
            s *= 10; \
            if (ii->high) s += (int)(-4.343 * log(.5 * erfc(M_SQRT1_2 * fabs(l - ii->avg) / ii->std)) + .499); \
            s = s<<32 | (uint32_t)hash_64((u).x<<32 | (v).x); \
            if (s>>32 == o_score>>32) ++o_n; \
            else if (s>>32 < o_score>>32) { subo_n += o_n; o_n = 1; } \
            else ++subo_n; \
            if (s < o_score) subo_score = o_score, o_score = s, o_pos[(u).y&1] = (u), o_pos[(v).y&1] = (v); \
            else if (s < subo_score) subo_score = s; \
        } \
    } while (0)

#define __pairing_aux2(q, w) do { \
        const bwt_aln1_t *r = d->aln[(w).y&1].a + ((w).y>>2); \
        (q)->extra_flag |= SAM_FPP; \
        if ((q)->pos != (w).x || (q)->strand != ((w).y>>1&1)) { \
            (q)->n_mm = r->n_mm; (q)->n_gapo = r->n_gapo; (q)->n_gape = r->n_gape; (q)->strand = (w).y>>1&1; \
            (q)->score = r->score; \
            (q)->pos = (w).x; \
            if ((q)->mapQ > 0) ++cnt_chg; \
        } \
    } while (0)

    o_score = subo_score = (uint64_t)-1;
    o_n = subo_n = 0;
    ks_introsort(b128, d->arr.n, d->arr.a);
    for (j = 0; j < 2; ++j) last_pos[j][0].x = last_pos[j][0].y = last_pos[j][1].x = last_pos[j][1].y = (uint64_t)-1;
    if (opt->type == BWA_PET_STD) {
        for (i = 0; i < d->arr.n; ++i) {
            b128_t x = d->arr.a[i];
            int strand = x.y>>1&1;
            if (strand == 1) { // reverse strand, then check
                int y = 1 - (x.y&1);
                __pairing_aux(last_pos[y][1], x);
                __pairing_aux(last_pos[y][0], x);
            } else { // forward strand, then push
                last_pos[x.y&1][0] = last_pos[x.y&1][1];
                last_pos[x.y&1][1] = x;
            }
        }
    } else if (opt->type == BWA_PET_SOLID) {
        for (i = 0; i < d->arr.n; ++i) {
            b128_t x = d->arr.a[i];
            int strand = x.y>>1&1;
            if ((strand^x.y)&1) { // push
                int y = 1 - (x.y&1);
                __pairing_aux(last_pos[y][1], x);
                __pairing_aux(last_pos[y][0], x);
            } else { // check
                last_pos[x.y&1][0] = last_pos[x.y&1][1];
                last_pos[x.y&1][1] = x;
            }
        }
    } else {
        fprintf(stderr, "[paring] not implemented yet!\n");
        exit(1);
    }
    // set pairing
    //fprintf(stderr, "[%ld, %d, %d, %d]\n", d->arr.n, (int)(o_score>>32), (int)(subo_score>>32), o_n);
    if (o_score != (uint64_t)-1) {
        int mapQ_p = 0; // this is the maximum mapping quality when one end is moved
        //fprintf(stderr, "%d, %d\n", o_n, subo_n);
        if (o_n == 1) {
            if (subo_score == (uint64_t)-1) mapQ_p = 29; // no sub-optimal pair
            else if ((subo_score>>32) - (o_score>>32) > s_mm * 10) mapQ_p = 23; // poor sub-optimal pair
            else {
                int n = subo_n > 255? 255 : subo_n;
                mapQ_p = ((subo_score>>32) - (o_score>>32)) / 2 - g_log_n[n];
                if (mapQ_p < 0) mapQ_p = 0;
            }
        }
        if ((p[0]->pos == o_pos[0].x && p[0]->strand == (o_pos[0].y>>1&1)) && (p[1]->pos == o_pos[1].x && p[1]->strand == (o_pos[1].y>>1&1))) { // both ends not moved
            if (p[0]->mapQ > 0 && p[1]->mapQ > 0) {
                int mapQ = p[0]->mapQ + p[1]->mapQ;
                if (mapQ > 60) mapQ = 60;
                p[0]->mapQ = p[1]->mapQ = mapQ;
            } else {
                if (p[0]->mapQ == 0) p[0]->mapQ = (mapQ_p + 7 < p[1]->mapQ)? mapQ_p + 7 : p[1]->mapQ;
                if (p[1]->mapQ == 0) p[1]->mapQ = (mapQ_p + 7 < p[0]->mapQ)? mapQ_p + 7 : p[0]->mapQ;
            }
        } else if (p[0]->pos == o_pos[0].x && p[0]->strand == (o_pos[0].y>>1&1)) { // [1] moved
            p[1]->seQ = 0; p[1]->mapQ = p[0]->mapQ;
            if (p[1]->mapQ > mapQ_p) p[1]->mapQ = mapQ_p;
        } else if (p[1]->pos == o_pos[1].x && p[1]->strand == (o_pos[1].y>>1&1)) { // [0] moved
            p[0]->seQ = 0; p[0]->mapQ = p[1]->mapQ;
            if (p[0]->mapQ > mapQ_p) p[0]->mapQ = mapQ_p;
        } else { // both ends moved
            p[0]->seQ = p[1]->seQ = 0;
            mapQ_p -= 20;
            if (mapQ_p < 0) mapQ_p = 0;
            p[0]->mapQ = p[1]->mapQ = mapQ_p;
        }
        __pairing_aux2(p[0], o_pos[0]);
        __pairing_aux2(p[1], o_pos[1]);
    }
    return cnt_chg;
}

typedef struct {
    kvec_t(bwt_aln1_t) aln;
} aln_buf_t;

int bwa_cal_pac_pos_pe(const bntseq_t *bns, const char *prefix, bwt_t *const _bwt, int n_seqs, bwa_seq_t *seqs[2], FILE *fp_sa[2], isize_info_t *ii,
                       const pe_opt_t *opt, const gap_opt_t *gopt, const isize_info_t *last_ii)
{
    int i, j, cnt_chg = 0;
    char str[1024];
    bwt_t *bwt;
    pe_data_t *d;
    aln_buf_t *buf[2];

    d = (pe_data_t*)calloc(1, sizeof(pe_data_t));
    buf[0] = (aln_buf_t*)calloc(n_seqs, sizeof(aln_buf_t));
    buf[1] = (aln_buf_t*)calloc(n_seqs, sizeof(aln_buf_t));

    if (_bwt == 0) { // load forward SA
        strcpy(str, prefix); strcat(str, ".bwt");  bwt = bwt_restore_bwt(str);
        strcpy(str, prefix); strcat(str, ".sa"); bwt_restore_sa(str, bwt);
    } else bwt = _bwt;

    // SE
    for (i = 0; i != n_seqs; ++i) {
        bwa_seq_t *p[2];
        for (j = 0; j < 2; ++j) {
            int n_aln;
            p[j] = seqs[j] + i;
            p[j]->n_multi = 0;
            p[j]->extra_flag |= SAM_FPD | (j == 0? SAM_FR1 : SAM_FR2);
            fread(&n_aln, 4, 1, fp_sa[j]);
            if (n_aln > kv_max(d->aln[j]))
                kv_resize(bwt_aln1_t, d->aln[j], n_aln);
            d->aln[j].n = n_aln;
            fread(d->aln[j].a, sizeof(bwt_aln1_t), n_aln, fp_sa[j]);
            kv_copy(bwt_aln1_t, buf[j][i].aln, d->aln[j]); // backup d->aln[j]
            // generate SE alignment and mapping quality
            bwa_aln2seq(n_aln, d->aln[j].a, p[j]);
            if (p[j]->type == BWA_TYPE_UNIQUE || p[j]->type == BWA_TYPE_REPEAT) {
                int strand;
                int max_diff = gopt->fnr > 0.0? bwa_cal_maxdiff(p[j]->len, BWA_AVG_ERR, gopt->fnr) : gopt->max_diff;
                p[j]->seQ = p[j]->mapQ = bwa_approx_mapQ(p[j], max_diff);
                p[j]->pos = bwa_sa2pos(bns, bwt, p[j]->sa, p[j]->len, &strand);
                p[j]->strand = strand;
            }
        }
    }

    // infer isize
    infer_isize(n_seqs, seqs, ii, opt->ap_prior, bwt->seq_len/2);
    if (ii->avg < 0.0 && last_ii->avg > 0.0) *ii = *last_ii;
    if (opt->force_isize) {
        fprintf(stderr, "[%s] discard insert size estimate as user's request.\n", __FUNCTION__);
        ii->low = ii->high = 0; ii->avg = ii->std = -1.0;
    }

    // PE
    for (i = 0; i != n_seqs; ++i) {
        bwa_seq_t *p[2];
        for (j = 0; j < 2; ++j) {
            p[j] = seqs[j] + i;
            kv_copy(bwt_aln1_t, d->aln[j], buf[j][i].aln);
        }
        if ((p[0]->type == BWA_TYPE_UNIQUE || p[0]->type == BWA_TYPE_REPEAT)
            && (p[1]->type == BWA_TYPE_UNIQUE || p[1]->type == BWA_TYPE_REPEAT))
        { // only when both ends mapped
            khint_t iter;
            b128_t x;
            int j, k;
            long long n_occ[2];
            for (j = 0; j < 2; ++j) {
                n_occ[j] = 0;
                for (k = 0; k < d->aln[j].n; ++k)
                    n_occ[j] += d->aln[j].a[k].l - d->aln[j].a[k].k + 1;
            }
            if (n_occ[0] > opt->max_occ || n_occ[1] > opt->max_occ) continue;
            d->arr.n = 0;
            for (j = 0; j < 2; ++j) {
                for (k = 0; k < d->aln[j].n; ++k) {
                    bwt_aln1_t *r = d->aln[j].a + k;
                    bwtint_t l;
                    if (0 && r->l - r->k + 1 >= MIN_HASH_WIDTH) { // then check hash table
                        b128_t key;
                        int ret;
                        key.x = r->k; key.y = r->l;
                        iter = kh_put(b128, g_hash, key, &ret);
                        if (ret) { // not in the hash table; ret must equal 1 as we never remove elements
                            poslist_t *z = &kh_val(g_hash, iter);
                            z->n = r->l - r->k + 1;
                            z->a = (bwtint_t*)malloc(sizeof(bwtint_t) * z->n);
                            for (l = r->k; l <= r->l; ++l) {
                                int strand;
                                z->a[l - r->k] = bwa_sa2pos(bns, bwt, l, p[j]->len, &strand)<<1;
                                z->a[l - r->k] |= strand;
                            }
                        }
                        for (l = 0; l < kh_val(g_hash, iter).n; ++l) {
                            x.x = kh_val(g_hash, iter).a[l]>>1;
                            x.y = k<<2 | (kh_val(g_hash, iter).a[l]&1)<<1 | j;
                            kv_push(b128_t, d->arr, x);
                        }
                    } else { // then calculate on the fly
                        for (l = r->k; l <= r->l; ++l) {
                            int strand;
                            x.x = bwa_sa2pos(bns, bwt, l, p[j]->len, &strand);
                            x.y = k<<2 | strand<<1 | j;
                            kv_push(b128_t, d->arr, x);
                        }
                    }
                }
            }
            cnt_chg += pairing(p, d, opt, gopt->s_mm, ii);
        }

        if (opt->N_multi || opt->n_multi) {
            for (j = 0; j < 2; ++j) {
                if (p[j]->type != BWA_TYPE_NO_MATCH) {
                    int k, n_multi;
                    if (!(p[j]->extra_flag&SAM_FPP) && p[1-j]->type != BWA_TYPE_NO_MATCH) {
                        bwa_aln2seq_core(d->aln[j].n, d->aln[j].a, p[j], 0, p[j]->c1+p[j]->c2-1 > opt->N_multi? opt->n_multi : opt->N_multi);
                    } else bwa_aln2seq_core(d->aln[j].n, d->aln[j].a, p[j], 0, opt->n_multi);
                    for (k = 0, n_multi = 0; k < p[j]->n_multi; ++k) {
                        int strand;
                        bwt_multi1_t *q = p[j]->multi + k;
                        q->pos = bwa_sa2pos(bns, bwt, q->pos, p[j]->len, &strand);
                        q->strand = strand;
                        if (q->pos != p[j]->pos)
                            p[j]->multi[n_multi++] = *q;
                    }
                    p[j]->n_multi = n_multi;
                }
            }
        }
    }

    // free
    for (i = 0; i < n_seqs; ++i) {
        kv_destroy(buf[0][i].aln);
        kv_destroy(buf[1][i].aln);
    }
    free(buf[0]); free(buf[1]);
    if (_bwt == 0) bwt_destroy(bwt);
    kv_destroy(d->arr);
    kv_destroy(d->pos[0]); kv_destroy(d->pos[1]);
    kv_destroy(d->aln[0]); kv_destroy(d->aln[1]);
    free(d);
    return cnt_chg;
}

#define SW_MIN_MATCH_LEN 20
#define SW_MIN_MAPQ 17

// cnt = n_mm<<16 | n_gapo<<8 | n_gape
bwa_cigar_t *bwa_sw_core(bwtint_t l_pac, const ubyte_t *pacseq, int len, const ubyte_t *seq, int64_t *beg, int reglen,
                      int *n_cigar, uint32_t *_cnt)
{
    bwa_cigar_t *cigar = 0;
    ubyte_t *ref_seq;
    bwtint_t k, x, y, l;
    int path_len, ret, subo;
    AlnParam ap = aln_param_bwa;
    path_t *path, *p;

    // check whether there are too many N's
    if (reglen < SW_MIN_MATCH_LEN || (int64_t)l_pac - *beg < len) return 0;
    for (k = 0, x = 0; k < len; ++k)
        if (seq[k] >= 4) ++x;
    if ((float)x/len >= 0.25 || len - x < SW_MIN_MATCH_LEN) return 0;

    // get reference subsequence
    ref_seq = (ubyte_t*)calloc(reglen, 1);
    for (k = *beg, l = 0; l < reglen && k < l_pac; ++k)
        ref_seq[l++] = pacseq[k>>2] >> ((~k&3)<<1) & 3;
    path = (path_t*)calloc(l+len, sizeof(path_t));

    // do alignment
    ret = aln_local_core(ref_seq, l, (ubyte_t*)seq, len, &ap, path, &path_len, 1, &subo);
    if (ret < 0 || subo == ret) { // no hit or tandem hits
        free(path); free(cigar); free(ref_seq); *n_cigar = 0;
        return 0;
    }
    cigar = bwa_aln_path2cigar(path, path_len, n_cigar);

    // check whether the alignment is good enough
    for (k = 0, x = y = 0; k < *n_cigar; ++k) {
        bwa_cigar_t c = cigar[k];
        if (__cigar_op(c) == FROM_M) x += __cigar_len(c), y += __cigar_len(c);
        else if (__cigar_op(c) == FROM_D) x += __cigar_len(c);
        else y += __cigar_len(c);
    }
    if (x < SW_MIN_MATCH_LEN || y < SW_MIN_MATCH_LEN) { // not good enough
        free(path); free(cigar); free(ref_seq);
        *n_cigar = 0;
        return 0;
    }

    { // update cigar and coordinate;
        int start, end;
        p = path + path_len - 1;
        *beg += (p->i? p->i : 1) - 1;
        start = (p->j? p->j : 1) - 1;
        end = path->j;
        cigar = (bwa_cigar_t*)realloc(cigar, sizeof(bwa_cigar_t) * (*n_cigar + 2));
        if (start) {
            memmove(cigar + 1, cigar, sizeof(bwa_cigar_t) * (*n_cigar));
            cigar[0] = __cigar_create(3, start);
            ++(*n_cigar);
        }
        if (end < len) {
            /*cigar[*n_cigar] = 3<<14 | (len - end);*/
            cigar[*n_cigar] = __cigar_create(3, (len - end));
            ++(*n_cigar);
        }
    }

    { // set *cnt
        int n_mm, n_gapo, n_gape;
        n_mm = n_gapo = n_gape = 0;
        p = path + path_len - 1;
        x = p->i? p->i - 1 : 0; y = p->j? p->j - 1 : 0;
        for (k = 0; k < *n_cigar; ++k) {
            bwa_cigar_t c = cigar[k];
            if (__cigar_op(c) == FROM_M) {
                for (l = 0; l < (__cigar_len(c)); ++l)
                    if (ref_seq[x+l] < 4 && seq[y+l] < 4 && ref_seq[x+l] != seq[y+l]) ++n_mm;
                x += __cigar_len(c), y += __cigar_len(c);
            } else if (__cigar_op(c) == FROM_D) {
                x += __cigar_len(c), ++n_gapo, n_gape += (__cigar_len(c)) - 1;
            } else if (__cigar_op(c) == FROM_I) {
                y += __cigar_len(c), ++n_gapo, n_gape += (__cigar_len(c)) - 1;
            }
        }
        *_cnt = (uint32_t)n_mm<<16 | n_gapo<<8 | n_gape;
    }
    
    free(ref_seq); free(path);
    return cigar;
}

ubyte_t *bwa_paired_sw(const bntseq_t *bns, const ubyte_t *_pacseq, int n_seqs, bwa_seq_t *seqs[2], const pe_opt_t *popt, const isize_info_t *ii)
{
    ubyte_t *pacseq;
    int i;
    uint64_t n_tot[2], n_mapped[2];

    // load reference sequence
    if (_pacseq == 0) {
        pacseq = (ubyte_t*)calloc(bns->l_pac/4+1, 1);
        rewind(bns->fp_pac);
        fread(pacseq, 1, bns->l_pac/4+1, bns->fp_pac);
    } else pacseq = (ubyte_t*)_pacseq;
    if (!popt->is_sw || ii->avg < 0.0) return pacseq;

    // perform mate alignment
    n_tot[0] = n_tot[1] = n_mapped[0] = n_mapped[1] = 0;
    for (i = 0; i != n_seqs; ++i) {
        bwa_seq_t *p[2];
        p[0] = seqs[0] + i; p[1] = seqs[1] + i;
        if ((p[0]->mapQ >= SW_MIN_MAPQ || p[1]->mapQ >= SW_MIN_MAPQ) && (p[0]->extra_flag&SAM_FPP) == 0) { // unpaired and one read has high mapQ
            int k, n_cigar[2], is_singleton, mapQ = 0, mq_adjust[2];
            int64_t beg[2], end[2];
            bwa_cigar_t *cigar[2];
            uint32_t cnt[2];

            /* In the following, _pref points to the reference read
             * which must be aligned; _pmate points to its mate which is
             * considered to be modified. */

#define __set_rght_coor(_a, _b, _pref, _pmate) do {						\
                (_a) = (int64_t)_pref->pos + ii->avg - 3 * ii->std - _pmate->len * 1.5; \
                (_b) = (_a) + 6 * ii->std + 2 * _pmate->len;			\
                if ((_a) < (int64_t)_pref->pos + _pref->len) (_a) = _pref->pos + _pref->len; \
                if ((_b) > bns->l_pac) (_b) = bns->l_pac;				\
            } while (0)

#define __set_left_coor(_a, _b, _pref, _pmate) do {						\
                (_a) = (int64_t)_pref->pos + _pref->len - ii->avg - 3 * ii->std - _pmate->len * 0.5; \
                (_b) = (_a) + 6 * ii->std + 2 * _pmate->len;			\
                if ((_a) < 0) (_a) = 0;									\
                if ((_b) > _pref->pos) (_b) = _pref->pos;				\
            } while (0)
            
#define __set_fixed(_pref, _pmate, _beg, _cnt) do {						\
                _pmate->type = BWA_TYPE_MATESW;							\
                _pmate->pos = _beg;										\
                _pmate->seQ = _pref->seQ;								\
                _pmate->strand = (popt->type == BWA_PET_STD)? 1 - _pref->strand : _pref->strand; \
                _pmate->n_mm = _cnt>>16; _pmate->n_gapo = _cnt>>8&0xff; _pmate->n_gape = _cnt&0xff; \
                _pmate->extra_flag |= SAM_FPP;							\
                _pref->extra_flag |= SAM_FPP;							\
            } while (0)

            mq_adjust[0] = mq_adjust[1] = 255; // not effective
            is_singleton = (p[0]->type == BWA_TYPE_NO_MATCH || p[1]->type == BWA_TYPE_NO_MATCH)? 1 : 0;

            ++n_tot[is_singleton];
            cigar[0] = cigar[1] = 0;
            n_cigar[0] = n_cigar[1] = 0;
            if (popt->type != BWA_PET_STD && popt->type != BWA_PET_SOLID) continue; // other types of pairing is not considered
            for (k = 0; k < 2; ++k) { // p[1-k] is the reference read and p[k] is the read considered to be modified
                ubyte_t *seq;
                if (p[1-k]->type == BWA_TYPE_NO_MATCH) continue; // if p[1-k] is unmapped, skip
                if (popt->type == BWA_PET_STD) {
                    if (p[1-k]->strand == 0) { // then the mate is on the reverse strand and has larger coordinate
                        __set_rght_coor(beg[k], end[k], p[1-k], p[k]);
                        seq = p[k]->rseq;
                    } else { // then the mate is on forward stand and has smaller coordinate
                        __set_left_coor(beg[k], end[k], p[1-k], p[k]);
                        seq = p[k]->seq;
                        seq_reverse(p[k]->len, seq, 0); // because ->seq is reversed; this will reversed back shortly
                    }
                } else { // BWA_PET_SOLID
                    if (p[1-k]->strand == 0) { // R3-F3 pairing
                        if (k == 0) __set_left_coor(beg[k], end[k], p[1-k], p[k]); // p[k] is R3
                        else __set_rght_coor(beg[k], end[k], p[1-k], p[k]); // p[k] is F3
                        seq = p[k]->rseq;
                        seq_reverse(p[k]->len, seq, 0); // because ->seq is reversed
                    } else { // F3-R3 pairing
                        if (k == 0) __set_rght_coor(beg[k], end[k], p[1-k], p[k]); // p[k] is R3
                        else __set_left_coor(beg[k], end[k], p[1-k], p[k]); // p[k] is F3
                        seq = p[k]->seq;
                    }
                }
                // perform SW alignment
                cigar[k] = bwa_sw_core(bns->l_pac, pacseq, p[k]->len, seq, &beg[k], end[k] - beg[k], &n_cigar[k], &cnt[k]);
                if (cigar[k] && p[k]->type != BWA_TYPE_NO_MATCH) { // re-evaluate cigar[k]
                    int s_old, clip = 0, s_new;
                    if (__cigar_op(cigar[k][0]) == 3) clip += __cigar_len(cigar[k][0]);
                    if (__cigar_op(cigar[k][n_cigar[k]-1]) == 3) clip += __cigar_len(cigar[k][n_cigar[k]-1]);
                    s_old = (int)((p[k]->n_mm * 9 + p[k]->n_gapo * 13 + p[k]->n_gape * 2) / 3. * 8. + .499);
                    s_new = (int)(((cnt[k]>>16) * 9 + (cnt[k]>>8&0xff) * 13 + (cnt[k]&0xff) * 2 + clip * 3) / 3. * 8. + .499);
                    s_old += -4.343 * log(ii->ap_prior / bns->l_pac);
                    s_new += (int)(-4.343 * log(.5 * erfc(M_SQRT1_2 * 1.5) + .499)); // assume the mapped isize is 1.5\sigma
                    if (s_old < s_new) { // reject SW alignment
                        mq_adjust[k] = s_new - s_old;
                        free(cigar[k]); cigar[k] = 0; n_cigar[k] = 0;
                    } else mq_adjust[k] = s_old - s_new;
                }
                // now revserse sequence back such that p[*]->seq looks untouched
                if (popt->type == BWA_PET_STD) {
                    if (p[1-k]->strand == 1) seq_reverse(p[k]->len, seq, 0);
                } else {
                    if (p[1-k]->strand == 0) seq_reverse(p[k]->len, seq, 0);
                }
            }
            k = -1; // no read to be changed
            if (cigar[0] && cigar[1]) {
                k = p[0]->mapQ < p[1]->mapQ? 0 : 1; // p[k] to be fixed
                mapQ = abs(p[1]->mapQ - p[0]->mapQ);
            } else if (cigar[0]) k = 0, mapQ = p[1]->mapQ;
            else if (cigar[1]) k = 1, mapQ = p[0]->mapQ;
            if (k >= 0 && p[k]->pos != beg[k]) {
                ++n_mapped[is_singleton];
                { // recalculate mapping quality
                    int tmp = (int)p[1-k]->mapQ - p[k]->mapQ/2 - 8;
                    if (tmp <= 0) tmp = 1;
                    if (mapQ > tmp) mapQ = tmp;
                    p[k]->mapQ = p[1-k]->mapQ = mapQ;
                    p[k]->seQ = p[1-k]->seQ = p[1-k]->seQ < mapQ? p[1-k]->seQ : mapQ;
                    if (p[k]->mapQ > mq_adjust[k]) p[k]->mapQ = mq_adjust[k];
                    if (p[k]->seQ > mq_adjust[k]) p[k]->seQ = mq_adjust[k];
                }
                // update CIGAR
                free(p[k]->cigar); p[k]->cigar = cigar[k]; cigar[k] = 0;
                p[k]->n_cigar = n_cigar[k];
                // update the rest of information
                __set_fixed(p[1-k], p[k], beg[k], cnt[k]);
            }
            free(cigar[0]); free(cigar[1]);
        }
    }
    fprintf(stderr, "[bwa_paired_sw] %lld out of %lld Q%d singletons are mated.\n",
            (long long)n_mapped[1], (long long)n_tot[1], SW_MIN_MAPQ);
    fprintf(stderr, "[bwa_paired_sw] %lld out of %lld Q%d discordant pairs are fixed.\n",
            (long long)n_mapped[0], (long long)n_tot[0], SW_MIN_MAPQ);
    return pacseq;
}

void bwa_sai2sam_pe_core(const char *prefix, char *const fn_sa[2], char *const fn_fa[2], pe_opt_t *popt)
{
    extern bwa_seqio_t *bwa_open_reads(int mode, const char *fn_fa);
    int i, j, n_seqs, tot_seqs = 0;
    bwa_seq_t *seqs[2];
    bwa_seqio_t *ks[2];
    clock_t t;
    bntseq_t *bns, *ntbns = 0;
    FILE *fp_sa[2];
    gap_opt_t opt, opt0;
    khint_t iter;
    isize_info_t last_ii; // this is for the last batch of reads
    char str[1024];
    bwt_t *bwt;
    uint8_t *pac;

    // initialization
    bwase_initialize(); // initialize g_log_n[] in bwase.c
    pac = 0; bwt = 0;
    for (i = 1; i != 256; ++i) g_log_n[i] = (int)(4.343 * log(i) + 0.5);
    bns = bns_restore(prefix);
    srand48(bns->seed);
    fp_sa[0] = xopen(fn_sa[0], "rb");
    fp_sa[1] = xopen(fn_sa[1], "rb");
    g_hash = kh_init(b128);
    last_ii.avg = -1.0;

    fread(&opt, sizeof(gap_opt_t), 1, fp_sa[0]);
    ks[0] = bwa_open_reads(opt.mode, fn_fa[0]);
    opt0 = opt;
    fread(&opt, sizeof(gap_opt_t), 1, fp_sa[1]); // overwritten!
    ks[1] = bwa_open_reads(opt.mode, fn_fa[1]);
    if (!(opt.mode & BWA_MODE_COMPREAD)) {
        popt->type = BWA_PET_SOLID;
        ntbns = bwa_open_nt(prefix);
    } else { // for Illumina alignment only
        if (popt->is_preload) {
            strcpy(str, prefix); strcat(str, ".bwt");  bwt = bwt_restore_bwt(str);
            strcpy(str, prefix); strcat(str, ".sa"); bwt_restore_sa(str, bwt);
            pac = (ubyte_t*)calloc(bns->l_pac/4+1, 1);
            rewind(bns->fp_pac);
            fread(pac, 1, bns->l_pac/4+1, bns->fp_pac);
        }
    }

    // core loop
    bwa_print_sam_SQ(bns);
    bwa_print_sam_PG();
    while ((seqs[0] = bwa_read_seq(ks[0], 0x40000, &n_seqs, opt0.mode, opt0.trim_qual)) != 0) {
        int cnt_chg;
        isize_info_t ii;
        ubyte_t *pacseq;

        seqs[1] = bwa_read_seq(ks[1], 0x40000, &n_seqs, opt.mode, opt.trim_qual);
        tot_seqs += n_seqs;
        t = clock();

        fprintf(stderr, "[bwa_sai2sam_pe_core] convert to sequence coordinate... \n");
        cnt_chg = bwa_cal_pac_pos_pe(bns, prefix, bwt, n_seqs, seqs, fp_sa, &ii, popt, &opt, &last_ii);
        fprintf(stderr, "[bwa_sai2sam_pe_core] time elapses: %.2f sec\n", (float)(clock() - t) / CLOCKS_PER_SEC); t = clock();
        fprintf(stderr, "[bwa_sai2sam_pe_core] changing coordinates of %d alignments.\n", cnt_chg);

        fprintf(stderr, "[bwa_sai2sam_pe_core] align unmapped mate...\n");
        pacseq = bwa_paired_sw(bns, pac, n_seqs, seqs, popt, &ii);
        fprintf(stderr, "[bwa_sai2sam_pe_core] time elapses: %.2f sec\n", (float)(clock() - t) / CLOCKS_PER_SEC); t = clock();

        fprintf(stderr, "[bwa_sai2sam_pe_core] refine gapped alignments... ");
        for (j = 0; j < 2; ++j)
            bwa_refine_gapped(bns, n_seqs, seqs[j], pacseq, ntbns);
        fprintf(stderr, "%.2f sec\n", (float)(clock() - t) / CLOCKS_PER_SEC); t = clock();
        if (pac == 0) free(pacseq);

        fprintf(stderr, "[bwa_sai2sam_pe_core] print alignments... ");
        for (i = 0; i < n_seqs; ++i) {
            bwa_seq_t *p[2];
            p[0] = seqs[0] + i; p[1] = seqs[1] + i;
            if (p[0]->bc[0] || p[1]->bc[0]) {
                strcat(p[0]->bc, p[1]->bc);
                strcpy(p[1]->bc, p[0]->bc);
            }
            bwa_print_sam1(bns, p[0], p[1], opt.mode, opt.max_top2);
            bwa_print_sam1(bns, p[1], p[0], opt.mode, opt.max_top2);
        }
        fprintf(stderr, "%.2f sec\n", (float)(clock() - t) / CLOCKS_PER_SEC); t = clock();

        for (j = 0; j < 2; ++j)
            bwa_free_read_seq(n_seqs, seqs[j]);
        fprintf(stderr, "[bwa_sai2sam_pe_core] %d sequences have been processed.\n", tot_seqs);
        last_ii = ii;
    }

    // destroy
    bns_destroy(bns);
    if (ntbns) bns_destroy(ntbns);
    for (i = 0; i < 2; ++i) {
        bwa_seq_close(ks[i]);
        fclose(fp_sa[i]);
    }
    for (iter = kh_begin(g_hash); iter != kh_end(g_hash); ++iter)
        if (kh_exist(g_hash, iter)) free(kh_val(g_hash, iter).a);
    kh_destroy(b128, g_hash);
    if (pac) {
        free(pac); bwt_destroy(bwt);
    }
}

int bwa_sai2sam_pe(int argc, char *argv[])
{
    extern char *bwa_rg_line, *bwa_rg_id;
    extern int bwa_set_rg(const char *s);
    int c;
    pe_opt_t *popt;
    popt = bwa_init_pe_opt();
    while ((c = getopt(argc, argv, "a:o:sPn:N:c:f:Ar:")) >= 0) {
        switch (c) {
        case 'r':
            if (bwa_set_rg(optarg) < 0) {
                fprintf(stderr, "[%s] malformated @RG line\n", __FUNCTION__);
                return 1;
            }
            break;
        case 'a': popt->max_isize = atoi(optarg); break;
        case 'o': popt->max_occ = atoi(optarg); break;
        case 's': popt->is_sw = 0; break;
        case 'P': popt->is_preload = 1; break;
        case 'n': popt->n_multi = atoi(optarg); break;
        case 'N': popt->N_multi = atoi(optarg); break;
        case 'c': popt->ap_prior = atof(optarg); break;
        case 'f': xreopen(optarg, "w", stdout); break;
        case 'A': popt->force_isize = 1; break;
        default: return 1;
        }
    }

    if (optind + 5 > argc) {
        fprintf(stderr, "\n");
        fprintf(stderr, "Usage:   bwa sampe [options] <prefix> <in1.sai> <in2.sai> <in1.fq> <in2.fq>\n\n");
        fprintf(stderr, "Options: -a INT   maximum insert size [%d]\n", popt->max_isize);
        fprintf(stderr, "         -o INT   maximum occurrences for one end [%d]\n", popt->max_occ);
        fprintf(stderr, "         -n INT   maximum hits to output for paired reads [%d]\n", popt->n_multi);
        fprintf(stderr, "         -N INT   maximum hits to output for discordant pairs [%d]\n", popt->N_multi);
        fprintf(stderr, "         -c FLOAT prior of chimeric rate (lower bound) [%.1le]\n", popt->ap_prior);
        fprintf(stderr, "         -f FILE  sam file to output results to [stdout]\n");
        fprintf(stderr, "         -r STR   read group header line such as `@RG\\tID:foo\\tSM:bar' [null]\n");
        fprintf(stderr, "         -P       preload index into memory (for base-space reads only)\n");
        fprintf(stderr, "         -s       disable Smith-Waterman for the unmapped mate\n");
        fprintf(stderr, "         -A       disable insert size estimate (force -s)\n\n");
        fprintf(stderr, "Notes: 1. For SOLiD reads, <in1.fq> corresponds R3 reads and <in2.fq> to F3.\n");
        fprintf(stderr, "       2. For reads shorter than 30bp, applying a smaller -o is recommended to\n");
        fprintf(stderr, "          to get a sensible speed at the cost of pairing accuracy.\n");
        fprintf(stderr, "\n");
        return 1;
    }
    bwa_sai2sam_pe_core(argv[optind], argv + optind + 1, argv + optind+3, popt);
    free(bwa_rg_line); free(bwa_rg_id);
    free(popt);
    return 0;
}