// utility functions
//
#include "Utility.h"
#include "Sum.h"
#include "Product.h"

#define PHRED_MAX 50000.0 // max Phred seems to be about 43015 (?), could be an underflow bug...

using namespace std;

short qualityChar2ShortInt(char c) {
    return static_cast<short>(c) - 33;
}

long double qualityChar2LongDouble(char c) {
    return static_cast<long double>(c) - 33;
}

long double lnqualityChar2ShortInt(char c) {
    return log(static_cast<short>(c) - 33);
}

char qualityInt2Char(short i) {
    return static_cast<char>(i + 33);
}

long double ln2log10(long double prob) {
    return M_LOG10E * prob;
}

long double log102ln(long double prob) {
    return M_LN10 * prob;
}

long double phred2ln(int qual) {
    return M_LN10 * qual * -.1;
}

long double ln2phred(long double prob) {
    return -10 * M_LOG10E * prob;
}

long double phred2float(int qual) {
    return pow(10, qual * -.1);
}

long double float2phred(long double prob) {
    if (prob == 1)
        return PHRED_MAX;  // guards against "-0"
    long double p = -10 * (long double) log10(prob);
    if (p < 0 || p > PHRED_MAX) // int overflow guard
        return PHRED_MAX;
    else
        return p;
}

long double big2phred(const BigFloat& prob) {
    return -10 * (long double) (ttmath::Log(prob, (BigFloat)10)).ToDouble();
}

long double nan2zero(long double x) {
    if (x != x) {
        return 0;
    } else {
        return x;
    }
}

long double powln(long double m, int n) {
    return m * n;
}

// the probability that we have a completely true vector of qualities
long double jointQuality(const std::vector<short>& quals) {
    std::vector<long double> probs;
    for (int i = 0; i<quals.size(); ++i) {
        probs.push_back(phred2float(quals[i]));
    }
    // product of probability we don't have a true event for each element
    long double prod = 1 - probs.front();
    for (int i = 1; i<probs.size(); ++i) {
        prod *= 1 - probs.at(i);
    }
    // and then invert it again to get probability of an event
    return 1 - prod;
}

long double jointQuality(const std::string& qualstr) {

    long double jq = 1;
    // product of probability we don't have a true event for each element
    for (string::const_iterator q = qualstr.begin(); q != qualstr.end(); ++q) {
        jq *= 1 - phred2float(qualityChar2ShortInt(*q));
    }

    // and then invert it again to get probability of an event
    return 1 - jq;

}

std::vector<short> qualities(const std::string& qualstr) {

    std::vector<short> quals;
    for (int i=0; i<qualstr.size(); i++)
        quals.push_back(qualityChar2ShortInt(qualstr.at(i)));

    return quals;

}

long double sumQuality(const std::string& qualstr) {
    long double qual = 0;
    for (string::const_iterator q = qualstr.begin(); q != qualstr.end(); ++q)
        qual += qualityChar2LongDouble(*q);
    return qual;
}

long double minQuality(const std::string& qualstr) {
    long double qual = 0;
    for (string::const_iterator q = qualstr.begin(); q != qualstr.end(); ++q) {
        long double nq = qualityChar2LongDouble(*q);
        if (qual == 0) {
            qual = nq;
        } else if (nq < qual) {
            qual = nq;
        }
    }
    return qual;
}

short minQuality(const std::vector<short>& qualities) {
    short m = 0;
    for (vector<short>::const_iterator q = qualities.begin(); q != qualities.end(); ++q) {
        if (*q < m) m = *q;
    }
    return m;
}

// crudely averages quality scores in phred space
long double averageQuality(const std::string& qualstr) {
    long double qual = 0; //(long double) *max_element(quals.begin(), quals.end());
    for (string::const_iterator q = qualstr.begin(); q != qualstr.end(); ++q)
        qual += qualityChar2LongDouble(*q);
    return qual / qualstr.size();
}

long double averageQuality(const vector<short>& qualities) {
    long double qual = 0;
    for (vector<short>::const_iterator q = qualities.begin(); q != qualities.end(); ++q) {
        qual += *q;
    }
    return qual / qualities.size();
}

bool stringInVector(string item, vector<string> items) {
    for (vector<string>::iterator i = items.begin(); i != items.end(); ++i) {
        if (item == *i) {
            return true;
        }
    }
    return false;
}

bool allATGC(string& s) {
    for (string::iterator c = s.begin(); c != s.end(); ++c) {
        char b = *c;
        if (b != 'A' && b != 'T' && b != 'G' && b != 'C') {
            return false;
        }
    }
    return true;
}

int upper(int c) {
    return toupper((unsigned char) c);
}

string uppercase(string s) {
    transform(s.begin(), s.end(), s.begin(), upper);
    return s;
}

string strip(string const& str, char const* separators) {
    string::size_type const first = str.find_first_not_of(separators);
    return (first == string::npos) ? string()
        : str.substr(first, str.find_last_not_of(separators) - first + 1);
}


int binomialCoefficient(int n, int k) {
    int i = 1;
    int result = n - k + i++;
    while (i <= k) {
        result *= (n - k + i) / i;
        ++i;
    }
    return result;
}

// k successes in n trials with prob of success p
long double binomialProb(int k, int n, long double p) {
    return factorial(n) / (factorial(k) * factorial(n - k)) * pow(p, k) * pow(1 - p, n - k);
}

long double impl_binomialProbln(int k, int n, long double p) {
    return factorialln(n) - (factorialln(k) + factorialln(n - k)) + powln(log(p), k) + powln(log(1 - p), n - k);
}

long double binomialCoefficientLn(int k, int n) {
    return factorialln(n) - (factorialln(k) + factorialln(n - k));
}

BinomialCache binomialCache;

long double binomialProbln(int k, int n, long double p) {
    return binomialCache.binomialProbln(k, n, p);
}

/*
long double probability(int k, int n, long double p) {
    int n = n - k;
    int m = k;
    long double q = 1 - p;
    long double temp = lgammal(m + n + 1.0);
    temp -= lgammal(n + 1.0) + lgammal(m + 1.0);
    temp += m*log(p) + n*log(q);
    return temp;
}
*/

long double poissonpln(int observed, int expected) {
    return ((log(expected) * observed) - expected) - factorialln(observed);
}

long double poissonp(int observed, int expected) {
    return (double) pow((double) expected, (double) observed) * (double) pow(M_E, (double) -expected) / factorial(observed);
}


// given the expected number of events is the max of a and b
// what is the probability that we might observe less than the observed?
long double poissonPvalLn(int a, int b) {

    int expected, observed;
    if (a > b) {
        expected = a; observed = b;
    } else {
        expected = b; observed = a;
    }

    vector<long double> probs;
    for (int i = 0; i < observed; ++i) {
        probs.push_back(poissonpln(i, expected));
    }

    return logsumexp_probs(probs);

}


long double gammaln(
    long double x
    ) {

    long double cofactors[] = { 76.18009173, 
                                -86.50532033,
                                24.01409822,
                                -1.231739516,
                                0.120858003E-2,
                                -0.536382E-5 };    

    long double x1 = x - 1.0;
    long double tmp = x1 + 5.5;
    tmp -= (x1 + 0.5) * log(tmp);
    long double ser = 1.0;
    for (int j=0; j<=5; j++) {
        x1 += 1.0;
        ser += cofactors[j]/x1;
    }
    long double y =  (-1.0 * tmp + log(2.50662827465 * ser));

    return y;
}

long double factorial(
    int n
    ) {
    if (n < 0) {
        return (long double)0.0;
    }
    else if (n == 0) {
        return (long double)1.0;
    }
    else {
        return exp(gammaln(n + 1.0));
    }
}

FactorialCache factorialCache;

/*
long double factorialln(int n) {
    return factorialCache.factorialln(n);
}
*/

long double impl_factorialln(
    int n
    ) {
    if (n < 0) {
        return (long double)-1.0;
    }
    else if (n == 0) {
        return (long double)0.0;
    }
    else {
        return gammaln(n + 1.0);
    }
}

long double cofactor(
    int n, 
    int i
    ) {
    if ((n < 0) || (i < 0) || (n < i)) {
        return (long double)0.0;
    }
    else if (n == i) {
        return (long double)1.0;
    }
    else {
        return exp(gammaln(n + 1.0) - gammaln(i + 1.0) - gammaln(n-i + 1.0));
    }
}

long double cofactorln(
    int n, 
    int i
    ) {
    if ((n < 0) || (i < 0) || (n < i)) {
        return (long double)-1.0;
    }
    else if (n == i) {
        return (long double)0.0;
    }
    else {
        return gammaln(n + 1.0) - gammaln(i + 1.0) - gammaln(n-i + 1.0);
    }
}

// prevent underflows by returning exp(LDBL_MIN_EXP) if exponentiation will produce an underflow
long double safe_exp(long double ln) {
    if (ln < LDBL_MIN_EXP) {  // -16381
        return LDBL_MIN;      // 3.3621e-4932
    } else {
        return exp(ln);
    }
}

BigFloat big_exp(long double ln) {
    BigFloat x, result;
    x.FromDouble(ln);
    result = ttmath::Exp(x);
    return result;
}

// 'safe' log summation for probabilities
long double logsumexp_probs(const vector<long double>& lnv) {
    vector<long double>::const_iterator i = lnv.begin();
    long double maxN = *i;
    ++i;
    for (; i != lnv.end(); ++i) {
        if (*i > maxN)
            maxN = *i;
    }
    BigFloat sum = 0;
    for (vector<long double>::const_iterator i = lnv.begin(); i != lnv.end(); ++i) {
        sum += big_exp(*i - maxN);
    }
    BigFloat maxNb; maxNb.FromDouble(maxN);
    BigFloat bigResult = maxNb + ttmath::Ln(sum);
    long double result;
    return bigResult.ToDouble();
}

// unsafe, kept for potential future use
long double logsumexp(const vector<long double>& lnv) {
    long double maxAbs, minN, maxN, c;
    vector<long double>::const_iterator i = lnv.begin();
    long double n = *i;
    maxAbs = n; maxN = n; minN = n;
    ++i;
    for (; i != lnv.end(); ++i) {
        n = *i;
        if (n > maxN)
            maxN = n;
        if (fabs(n) > maxAbs)
            maxAbs = fabs(n);
        if (n < minN)
            minN = n;
    }
    if (maxAbs > maxN) {
        c = minN;
    } else {
        c = maxN;
    }
    long double sum = 0;
    for (vector<long double>::const_iterator i = lnv.begin(); i != lnv.end(); ++i) {
        sum += exp(*i - c);
    }
    return c + log(sum);
}

long double betaln(const vector<long double>& alphas) {
    vector<long double> gammalnAlphas;
    gammalnAlphas.resize(alphas.size());
    transform(alphas.begin(), alphas.end(), gammalnAlphas.begin(), gammaln);
    return sum(gammalnAlphas) - gammaln(sum(alphas));
}

long double beta(const vector<long double>& alphas) {
    return exp(betaln(alphas));
}

long double hoeffding(double successes, double trials, double prob) {
    return 0.5 * exp(-2 * pow(trials * prob - successes, 2) / trials);
}

long double hoeffdingln(double successes, double trials, double prob) {
    return log(0.5) + (-2 * pow(trials * prob - successes, 2) / trials);
}

// the sum of the harmonic series 1, n
long double harmonicSum(int n) {
    long double r = 0;
    long double i = 1;
    while (i <= n) {
        r += 1 / i;
        ++i;
    }
    return r;
}

bool isTransition(string& ref, string& alt) {
    if (((ref == "A" && alt == "G") || (ref == "G" && alt == "A")) ||
        ((ref == "C" && alt == "T") || (ref == "T" && alt == "C"))) {
        return true;
    } else {
        return false;
    }
}

// Levenshtein Distance Algorithm: C++ Implementation
// by Anders Sewerin Johansen
// http://www.merriampark.com/ldcpp.htm

int levenshteinDistance(const std::string source, const std::string target) {

    // Step 1

    const int n = source.length();
    const int m = target.length();
    if (n == 0) {
        return m;
    }
    if (m == 0) {
        return n;
    }

    // Good form to declare a TYPEDEF

    typedef std::vector< std::vector<int> > Tmatrix; 

    Tmatrix matrix(n+1);

    // Size the vectors in the 2.nd dimension. Unfortunately C++ doesn't
    // allow for allocation on declaration of 2.nd dimension of vec of vec

    for (int i = 0; i <= n; i++) {
        matrix[i].resize(m+1);
    }

    // Step 2

    for (int i = 0; i <= n; i++) {
        matrix[i][0]=i;
    }

    for (int j = 0; j <= m; j++) {
        matrix[0][j]=j;
    }

    // Step 3

    for (int i = 1; i <= n; i++) {

        const char s_i = source[i-1];

        // Step 4

        for (int j = 1; j <= m; j++) {

            const char t_j = target[j-1];

            // Step 5

            int cost;
            if (s_i == t_j) {
                cost = 0;
            }
            else {
                cost = 1;
            }

            // Step 6

            const int above = matrix[i-1][j];
            const int left = matrix[i][j-1];
            const int diag = matrix[i-1][j-1];
            int cell = min( above + 1, min(left + 1, diag + cost));

            // Step 6A: Cover transposition, in addition to deletion,
            // insertion and substitution. This step is taken from:
            // Berghel, Hal ; Roach, David : "An Extension of Ukkonen's 
            // Enhanced Dynamic Programming ASM Algorithm"
            // (http://www.acm.org/~hlb/publications/asm/asm.html)

            if (i>2 && j>2) {
                int trans=matrix[i-2][j-2]+1;
                if (source[i-2]!=t_j) trans++;
                if (s_i!=target[j-2]) trans++;
                if (cell>trans) cell=trans;
            }

            matrix[i][j]=cell;
        }
    }

    // Step 7

    return matrix[n][m];
}

// current date string in YYYYMMDD format
string dateStr(void) {

    time_t rawtime;
    struct tm* timeinfo;
    char buffer[80];

    time(&rawtime);
    timeinfo = localtime(&rawtime);

    strftime(buffer, 80, "%Y%m%d", timeinfo);

    return string(buffer);

}

long double string2float(const string& s) {
    long double r;
    convert(s, r);
    return r;
}

long double log10string2ln(const string& s) {
    long double r;
    convert(s, r);
    return log102ln(r);
}

long double safedivide(long double a, long double b) {
    if (b == 0) {
        if (a == 0) {
            return 1;
        } else {
            return 0;
        }
    } else {
        return a / b;
    }
}

string mergeCigar(const string& c1, const string& c2) {
    vector<pair<int, string> > cigar1 = splitCigar(c1);
    vector<pair<int, string> > cigar2 = splitCigar(c2);
    // check if the middle elements are the same
    if (cigar1.back().second == cigar2.front().second) {
        cigar1.back().first += cigar2.front().first;
        cigar2.erase(cigar2.begin());
    }
    for (vector<pair<int, string> >::iterator c = cigar2.begin(); c != cigar2.end(); ++c) {
        cigar1.push_back(*c);
    }
    return joinCigar(cigar1);
}

vector<pair<int, string> > splitCigar(const string& cigarStr) {
    vector<pair<int, string> > cigar;
    string number;
    string type;
    // strings go [Number][Type] ...
    for (string::const_iterator s = cigarStr.begin(); s != cigarStr.end(); ++s) {
        char c = *s;
        if (isdigit(c)) {
            if (type.empty()) {
                number += c;
            } else {
                // signal for next token, push back the last pair, clean up
                cigar.push_back(make_pair(atoi(number.c_str()), type));
                number.clear();
                type.clear();
                number += c;
            }
        } else {
            type += c;
        }
    }
    if (!number.empty() && !type.empty()) {
        cigar.push_back(make_pair(atoi(number.c_str()), type));
    }
    return cigar;
}

list<pair<int, string> > splitCigarList(const string& cigarStr) {
    list<pair<int, string> > cigar;
    string number;
    string type;
    // strings go [Number][Type] ...
    for (string::const_iterator s = cigarStr.begin(); s != cigarStr.end(); ++s) {
        char c = *s;
        if (isdigit(c)) {
            if (type.empty()) {
                number += c;
            } else {
                // signal for next token, push back the last pair, clean up
                cigar.push_back(make_pair(atoi(number.c_str()), type));
                number.clear();
                type.clear();
                number += c;
            }
        } else {
            type += c;
        }
    }
    if (!number.empty() && !type.empty()) {
        cigar.push_back(make_pair(atoi(number.c_str()), type));
    }
    return cigar;
}

string joinCigar(const vector<pair<int, string> >& cigar) {
    string cigarStr;
    for (vector<pair<int, string> >::const_iterator c = cigar.begin(); c != cigar.end(); ++c) {
        if (c->first) {
            cigarStr += convert(c->first) + c->second;
        }
    }
    return cigarStr;
}

string joinCigarList(const list<pair<int, string> >& cigar) {
    string cigarStr;
    for (list<pair<int, string> >::const_iterator c = cigar.begin(); c != cigar.end(); ++c) {
        cigarStr += convert(c->first) + c->second;
    }
    return cigarStr;
}

bool isEmptyCigarElement(const pair<int, string>& elem) {
    return elem.first == 0;
}


// string * overload
// from http://stackoverflow.com/a/5145880
std::string operator*(std::string const &s, size_t n)
{
    std::string r;  // empty string
    r.reserve(n * s.size());
    for (size_t i=0; i<n; i++)
        r += s;
    return r;
}

// normalize vector sum to 1
void normalizeSumToOne(vector<long double>& v) {
    long double sum = 0;
    for (vector<long double>::iterator i = v.begin(); i != v.end(); ++i) {
        sum += *i;
    }
    for (vector<long double>::iterator i = v.begin(); i != v.end(); ++i) {
        *i /= sum;
    }
}

// splits the file on '\n', adds the resulting values to v
void addLinesFromFile(vector<string>& v, const string& f) {
    ifstream ifs;
    ifs.open(f.c_str(), ifstream::in);
    if (!ifs.is_open()) {
        cerr << "could not open " << f << endl;
        exit(1);
    }
    string line;
    while (std::getline(ifs, line)) {
        v.push_back(line);
    }
}


double lf[] = {
0.000000000000000,
0.000000000000000,
0.693147180559945,
1.791759469228055,
3.178053830347946,
4.787491742782046,
6.579251212010101,
8.525161361065415,
10.604602902745251,
12.801827480081469,
15.104412573075516,
17.502307845873887,
19.987214495661885,
22.552163853123421,
25.191221182738683,
27.899271383840894,
30.671860106080675,
33.505073450136891,
36.395445208033053,
39.339884187199495,
42.335616460753485,
45.380138898476908,
48.471181351835227,
51.606675567764377,
54.784729398112319,
58.003605222980518,
61.261701761002001,
64.557538627006323,
67.889743137181526,
71.257038967168000,
74.658236348830158,
78.092223553315307,
81.557959456115029,
85.054467017581516,
88.580827542197682,
92.136175603687079,
95.719694542143202,
99.330612454787428,
102.968198614513810,
106.631760260643446,
110.320639714757391,
114.034211781461693,
117.771881399745055,
121.533081515438639,
125.317271149356884,
129.123933639127245,
132.952575035616292,
136.802722637326355,
140.673923648234251,
144.565743946344895,
148.477766951773020,
152.409592584497346,
156.360836303078798,
160.331128216630930,
164.320112263195170,
168.327445448427653,
172.352797139162817,
176.395848406997374,
180.456291417543781,
184.533828861449507,
188.628173423671598,
192.739047287844897,
196.866181672889979,
201.009316399281573,
205.168199482641199,
209.342586752536818,
213.532241494563266,
217.736934113954248,
221.956441819130362,
226.190548323727569,
230.439043565776927,
234.701723442818263,
238.978389561834348,
243.268849002982734,
247.572914096186906,
251.890402209723192,
256.221135550009478,
260.564940971863223,
264.921649798552778,
269.291097651019811,
273.673124285693689,
278.067573440366118,
282.474292687630395,
286.893133295426992,
291.323950094270288,
295.766601350760595,
300.220948647014097,
304.686856765668722,
309.164193580146900,
313.652829949878992,
318.152639620209300,
322.663499126726208,
327.185287703775202,
331.717887196928473,
336.261181979198454,
340.815058870798964,
345.379407062266864,
349.954118040770254,
354.539085519440789,
359.134205369575341,
363.739375555563470,
368.354496072404686,
372.979468885689016,
377.614197873918670,
382.258588773060012,
386.912549123217559,
391.575988217329609,
396.248817051791491,
400.930948278915764,
405.622296161144902,
410.322776526937275,
415.032306728249580,
419.750805599544776,
424.478193418257092,
429.214391866651567,
433.959323995014870,
438.712914186121168,
443.475088120918940,
448.245772745384613,
453.024896238496126,
457.812387981278107,
462.608178526874894,
467.412199571608085,
472.224383926980522,
477.044665492585580,
481.872979229887903,
486.709261136839359,
491.553448223298005,
496.405478487217579,
501.265290891579241,
506.132825342034835,
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1051287.708973656874150,
};

double factorialln(int n)
{

    if (n < 0)
    {
        std::stringstream os;
        os << "Invalid input argument (" << n 
           << "); may not be negative";
        throw std::invalid_argument( os.str() );
        
    }
    else if (n > 100000-1)
    {
        const double PI = 3.141592653589793;
        double x = n + 1;
        return (x - 0.5)*log(x) - x + 0.5*log(2*PI) + 1.0/(12.0*x);
    }
    else
    {
        return lf[n];
    }
}

double entropy(const string& st) {
    vector<char> stvec(st.begin(), st.end());
    set<char> alphabet(stvec.begin(), stvec.end());
    vector<double> freqs;
    for (set<char>::iterator c = alphabet.begin(); c != alphabet.end(); ++c) {
        int ctr = 0;
        for (vector<char>::iterator s = stvec.begin(); s != stvec.end(); ++s) {
            if (*s == *c) {
                ++ctr;
            }
        }
        freqs.push_back((double)ctr / (double)stvec.size());
    }
    double ent = 0;
    double ln2 = log(2);
    for (vector<double>::iterator f = freqs.begin(); f != freqs.end(); ++f) {
        ent += *f * log(*f)/ln2;
    }
    ent = -ent;
    return ent;
}