/* HMath: C++ high precision math routines
   Copyright (C) 2004 Ariya Hidayat <ariya.hidayat@gmail.com>
   2007 Helder Correia <helder.pereira.correia@gmail.com>

   This program is free software; you can redistribute it and/or
   modify it under the terms of the GNU General Public License
   as published by the Free Software Foundation; either version 2
   of the License, or (at your option) any later version.

   This program is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   GNU General Public License for more details.

   You should have received a copy of the GNU General Public License
   along with this program; see the file COPYING.  If not, write to
   the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
   Boston, MA 02110-1301, USA.
*/

#include "hmath.h"
#include "number.h"

#include <ctype.h>
#include <stdlib.h>
#include <string.h>
#include <stdio.h>

#include <sstream>
#include <iostream>

// internal number of decimal digits
#define HMATH_MAX_PREC 150

// digits used for number comparison
// (not all are used, to work around propagated error problem)
#define HMATH_COMPARE_PREC 70

// maximum shown digits if prec is negative
#define HMATH_MAX_SHOWN 10

// from number.c, need to be freed somehow
extern bc_num _zero_;
extern bc_num _one_;
extern bc_num _two_;

class HNumberPrivate
{
public:
    bc_num num;
    bool nan;
    char format;
};

void out_of_memory(void){
    return;
}

void rt_warn(char * ,...){
    return;
}

void rt_error(char * ,...){
    return;
}

static bc_num h_create( int len = 1, int scale = 0 )
{
    bc_num temp;
    temp = (bc_num) malloc( sizeof(bc_struct) );
    temp->n_sign = PLUS;
    temp->n_len = len;
    temp->n_scale = scale;
    temp->n_refs = 1;
    temp->n_ptr = (char*) malloc( len+scale+1 );
    temp->n_value = temp->n_ptr;
    temp->n_next = 0;
    memset (temp->n_ptr, 0, len+scale+1);
    return temp;
}

static void h_destroy( bc_num n )
{
    free( n->n_ptr );
    free( n );
}

// reclaim and free one bc_num from the freelist
// workaround for number.c, because it doesn't really free a number
// but instead put it in the pool of unused numbers
// this function will take it back from that pool and set it really free
static void h_grabfree()
{
    bc_num t = bc_new_num( 1, 0 );
    h_destroy( t );
}

// make an exact (explicit) copy
static bc_num h_copy( bc_num n )
{
    int len = n->n_len;
    int scale = n->n_scale;
    bc_num result = h_create( len, scale );
    memcpy( result->n_ptr, n->n_value, len+scale+1 );
    result->n_sign = n->n_sign;
    result->n_value = result->n_ptr;
    h_grabfree();
    return result;
}

// same as copy, but readjust decimal digits
static bc_num h_rescale( bc_num n, int sc )
{
    int len = n->n_len;
    int scale = MIN( sc, n->n_scale );
    bc_num result = h_create( len, scale );
    memcpy( result->n_ptr, n->n_value, len+scale+1 );
    result->n_sign = n->n_sign;
    result->n_value = result->n_ptr;
    h_grabfree();
    return result;
}

// add two numbers, return newly allocated number
static bc_num h_add( bc_num n1, bc_num n2 )
{
    bc_num r = h_create();
    bc_add( n1, n2, &r, 1 );
    h_grabfree();
    return r;
}

// multiply two numbers, return newly allocated number
static bc_num h_mul( bc_num n1, bc_num n2 )
{
    bc_num r = h_create();
    bc_multiply( n1, n2, &r, HMATH_MAX_PREC );
    h_grabfree();
    return r;
}

enum Base {Decimal, Hexadec, Octal, Binary};

static bool isValidDigit(const char c, const Base b)
{
    switch (b)
    {
    case Hexadec:
        return ((c >= '0' && c <= '9') || (c >= 'A' && c < 'G') || (c >= 'a' && c < 'g'));
    case Octal:
        return (c >= '0' && c < '8');
    case Binary:
        return ( c == '0' || c == '1' );
    case Decimal:
    default:
        break;
    }
    return (c >= '0' && c <= '9');
}

// convert simple string to number
static bc_num h_str2num( const char* str, int scale = HMATH_MAX_PREC )
{
    int digits, strscale;
    const char *ptr;
    char *nptr;
    bool zero_int;

    /* Check for valid number and count digits. */
    ptr = str;
    digits = 0;
    strscale = 0;
    zero_int = false;
    Base base = Decimal;
    if (*ptr == '+' || *ptr == '-') ptr++;  /* Sign */
    if ( *ptr == '0' ) //leadeing 0, could be hexadec etc.
    {
        ptr++;
        if (*ptr == 'x') { base = Hexadec; ptr++; }
        else if (*ptr == 'o') { base = Octal; ptr++; }
        else if (*ptr == 'b') { base = Binary; ptr++; }
        else if (*ptr == 'd') ptr++;
    }
    while (*ptr == '0') ptr++;			/* Skip leading zeros. */
    while (isValidDigit((int)*ptr, base)) ptr++, digits++;	/* digits, maybe non decimal base */
    if (*ptr == '.') { if (base == Decimal) ptr++; else return h_create(); } /* decimal point */
    while (isdigit((int)*ptr)) ptr++, strscale++;	/* digits, must be decimal, we had a period ; */
    if ((*ptr != '\0') || (digits+strscale == 0))
        return h_create();

    bc_num num;

    switch (base)
    {
    case Hexadec:
    {
        int chr;
        bc_num _16 = h_create(); bc_int2num( &_16, 16 );
        bc_num factor = h_create(); bc_int2num( &factor, 1 );
        bc_num tmp1, tmp2;
        num = h_create(); bc_int2num( &num, 0 );
        for (;digits > 0; --digits) // n = n+f*x;
        {
            --ptr;
            chr = CH_HEX(*ptr);
            if (chr) // skip increment if digit is '0'
            {
                tmp1 = h_create();
                bc_int2num( &tmp1, chr ); // x
                tmp2 = h_mul( factor, tmp1 ); // f*x
                h_destroy( tmp1 );
                tmp1 = h_add( num, tmp2 ); // n+f*x;
                h_destroy( num ); h_destroy( tmp2 );
                num = h_copy( tmp1 ); // n = n+f*x;
                h_destroy( tmp1 );
            }
            tmp1 = h_mul( factor, _16 ); // f*16
            h_destroy( factor );
            factor = h_copy( tmp1 ); // f = f*16;
            h_destroy( tmp1 );
        }
        if (*str == '-') num->n_sign = MINUS; else num->n_sign = PLUS;
        break;
    }
    case Octal:
    {
        int chr;
        bc_num _8 = h_create(); bc_int2num( &_8, 8 );
        bc_num factor = h_create(); bc_int2num( &factor, 1 );
        bc_num tmp1, tmp2;
        num = h_create(); bc_int2num( &num, 0 );
        for (;digits > 0; --digits) // n = n+f*x;
        {
            --ptr;
            chr = CH_VAL(*ptr);
            if (chr) // skip increment if digit is '0'
            {
                tmp1 = h_create();
                bc_int2num( &tmp1, chr ); // x
                tmp2 = h_mul( factor, tmp1 ); // f*x
                h_destroy( tmp1 );
                tmp1 = h_add( num, tmp2 ); // n+f*x;
                h_destroy( num ); h_destroy( tmp2 );
                num = h_copy( tmp1 ); // n = n+f*x;
                h_destroy( tmp1 );
            }
            tmp1 = h_mul( factor, _8 ); // f*8
            h_destroy( factor );
            factor = h_copy( tmp1 ); // f = f*8;
            h_destroy( tmp1 );
        }
        if (*str == '-') num->n_sign = MINUS; else num->n_sign = PLUS;
        break;
    }
    case Binary:
    {
        bc_num _2 = h_create(); bc_int2num( &_2, 2 );
        bc_num factor = h_create(); bc_int2num( &factor, 1 );
        bc_num tmp;
        num = h_create(); bc_int2num( &num, 0 );
        for (;digits > 0; --digits) // n = n+f;
        {
            --ptr;
            if (CH_VAL(*ptr)) // only increment if bit is set
            {
                tmp = h_add( num, factor ); // n+f;
                h_destroy( num ); num = h_copy( tmp ); // n = n+f;
                h_destroy( tmp );
            }
            tmp = h_mul( factor, _2 ); // f*2
            factor = h_copy( tmp ); // f = f*2;
            h_destroy( tmp );
        }
        if (*str == '-') num->n_sign = MINUS; else num->n_sign = PLUS;
        break;
    }
    case Decimal:
    default:
    {
        /* Adjust numbers and allocate storage and initialize fields. */
        strscale = MIN(strscale, scale);
        if (digits == 0)
        {
            zero_int = true;
            digits = 1;
        }

        num = h_create( digits, strscale );

        ptr = str;
        if (*ptr == '-')
        {
            num->n_sign = MINUS;
            ptr++;
        }
        else
        {
            num->n_sign = PLUS;
            if (*ptr == '+') ptr++;
        }
        while (*ptr == '0') ptr++;
        nptr = num->n_value;
        if (zero_int)
        {
            *nptr++ = 0;
            digits = 0;
        }
        for (;digits > 0; digits--)
            *nptr++ = (char)CH_VAL(*ptr++);


        if (strscale > 0)
        {
            ptr++;
            for (;strscale > 0; strscale--)
                *nptr++ = (char)CH_VAL(*ptr++);
        }
    }
    }
    return num;
}


// subtract two numbers, return newly allocated number
static bc_num h_sub( bc_num n1, bc_num n2 )
{
    bc_num r = h_create();
    bc_sub( n1, n2, &r, 1 );
    h_grabfree();
    return r;
}

// divide two numbers, return newly allocated number
static bc_num h_div( bc_num n1, bc_num n2 )
{
    bc_num r = h_create();
    bc_divide( n1, n2, &r, HMATH_MAX_PREC );
    h_grabfree();
    return r;
}

// find 10 raise to num
// e.g.: when num is 5, it results 100000
static bc_num h_raise10( int n )
{
    // calculate proper factor
    int len = abs(n)+2;
    char* sf = new char[len+1];
    sf[len] = '\0';
    if( n >= 0 )
    {
        sf[0] = '1';
        sf[len-1] = '\0';
        sf[len-2] = '\0';
        for( int i = 0; i < n; i++ )
            sf[i+1] = '0';
    }
    else
    {
        sf[0] = '0'; sf[1] = '.';
        for( int i = 0; i < -n; i++ )
            sf[i+2] = '0';
        sf[len-1] = '1';
    }

    bc_num factor = h_str2num( sf, abs(n) );
    delete[] sf;

    return factor;
}

// round up to certain decimal digits
static bc_num h_round( bc_num n, int prec )
{
    // no need to round?
    if( prec >= n->n_scale )
        return h_copy( n );

    // example: rounding "3.14159" to 4 decimal digits means
    //   adding 0.5e-4 to 3.14159, it becomes 3.14164
    //   taking only 4 decimal digits, so it's now 3.1416
    if( prec < 0 ) prec = 0;
    bc_num x = h_raise10( -prec-1 );
    bc_num y = 0;
    bc_int2num( &y, 5 );
    bc_num z = h_mul( x, y );
    z->n_sign = n->n_sign;
    bc_num r = h_add( n, z );
    h_destroy( x );
    h_destroy( y );
    h_destroy( z );

    // only digits we are interested in
    bc_num v = h_rescale( r, prec );
    h_destroy( r );

    return v;
}

// trunc up to certain decimal digits
static bc_num h_trunc( bc_num n, int prec )
{
    // no need to truncate?
    if( prec >= n->n_scale )
        return h_copy( n );

    if( prec < 0 )
        prec = 0;

    // only digits we are interested in
    bc_num v = h_rescale( n, prec );

    return v;
}

// remove trailing zeros
static void h_trimzeros( bc_num num )
{
    while( ( num->n_scale > 0 ) && ( num->n_len+num->n_scale > 0 ) )
        if( num->n_value[num->n_len+num->n_scale-1] == 0 )
            num->n_scale--;
        else break;
}

static void h_init()
{
    static bool h_initialized = false;
    if( !h_initialized )
    {
        h_initialized = true;
        bc_init_numbers();
    }
}


HNumber::HNumber(): d(0)
{
    h_init();
    d = new HNumberPrivate;
    d->nan = false;
    d->format = 0;
    d->num = h_create();
}

HNumber::HNumber( const HNumber& hn ): d(0)
{
    h_init();
    d = new HNumberPrivate;
    d->nan = false;
    d->num = h_create();
    operator=( hn );
}

HNumber::HNumber( int i ): d(0)
{
    h_init();
    d = new HNumberPrivate;
    d->nan = false;
    d->num = h_create();
    d->format = 0;
    bc_int2num( &d->num, i );
}

HNumber::HNumber( const char* str ): d(0)
{
    h_init();
    d = new HNumberPrivate;
    d->nan = false;
    d->num = h_create();
    d->format = 0;

    if( str )
        if( strlen(str) == 3 )
            if( tolower(str[0])=='n' )
                if( tolower(str[1])=='a' )
                    if( tolower(str[2])=='n' )
                        d->nan = true;

    if( str && !d->nan )
    {
        char* s = new char[ strlen(str)+1 ];
        strcpy( s, str );

        bool isHex = false, isDecimal = true;
        char* p = s;
        for( ;; p++ )
        {
            if (*p == 'x' && *(p-1) == '0')
            {
                isHex = true;
                isDecimal = false;
                continue;
            }
            if ((*p == 'b' || *p == 'o') && *(p-1) == '0')
            {
                isDecimal = false;
                continue;
            }
            if( *p != '+' )
                if( *p != '-' )
                    if( *p != '.' )
                        if( !isdigit(*p) )
                            if(!(isHex && *p >= 'a' && *p < 'g'))
                                break;
        }

        int expd = 0;
        if (isDecimal)
        {
            if( ( *p == 'e' ) || ( *p == 'E' ) )
            {
                *p = '\0';
                expd = atoi( p+1 );
            }
        }

        h_destroy( d->num );
        d->num = h_str2num( s );
        delete [] s;
        if (isDecimal)
        {
            if( expd >= HMATH_MAX_PREC ) // too large
            {
                d->nan = true;
            }
            else
                if( expd <= -HMATH_MAX_PREC ) // too small
                {
                    d->nan = true;
                }
                else
                    if( expd != 0 )
                    {
                        bc_num factor = h_raise10( expd );
                        bc_num nn = h_copy( d->num );
                        h_destroy( d->num );
                        d->num = h_mul( nn, factor );
                        h_destroy( nn );
                        h_destroy( factor );
                    }
        }
        h_trimzeros( d->num );
    }

}

HNumber::~HNumber()
{
    h_destroy( d->num );
    delete d;
}

bool HNumber::isNan() const
{
    return d->nan;
}

bool HNumber::isZero() const
{
    return !d->nan && ( bc_is_zero( d->num )!=0 );
}

bool HNumber::isPositive() const
{
    return !d->nan && !isNegative() && !isZero();
}

bool HNumber::isNegative() const
{
    return !d->nan && ( bc_is_neg( d->num )!=0 );
}

bool HNumber::isInteger() const
{
    return *this == HMath::integer( *this );
}

char HNumber::format() const
{
    return d->format;
}

void HNumber::setFormat(char c) const
{
    d->format = d->nan?0:c;
}

HNumber HNumber::nan()
{
    HNumber n;
    n.d->nan = true;
    return n;
}

int HNumber::toInt()
{
    char* str = HMath::formatFixed( *this );
    std::string s( str );
    delete[] str;
    std::istringstream iss( s );
    int i;
    iss >> i;

    return i;
}

HNumber& HNumber::operator=( const HNumber& hn )
{
    d->nan = hn.d->nan;
    h_destroy( d->num );
    d->num = h_copy( hn.d->num );
    d->format = hn.format();
    return *this;
}

HNumber HNumber::operator+( const HNumber& num ) const
{
    if( isNan() ) return HNumber( *this );
    if( num.isNan() ) return HNumber( num );

    HNumber result;
    h_destroy( result.d->num );
    result.d->num = h_add( d->num, num.d->num );

    return result;
}

HNumber& HNumber::operator+=( const HNumber& num )
{
    HNumber n = HNumber(*this) + num;
    operator=( n );
    return *this;
}

HNumber HNumber::operator-( const HNumber& num ) const
{
    if( isNan() ) return HNumber( *this );
    if( num.isNan() ) return HNumber( num );

    HNumber result;
    h_destroy( result.d->num );
    result.d->num = h_sub( d->num, num.d->num );

    return result;
}

HNumber& HNumber::operator-=( const HNumber& num )
{
    HNumber n = HNumber(*this) - num;
    operator=( n );
    return *this;
}

HNumber HNumber::operator*( const HNumber& num ) const
{
    if( isNan() ) return HNumber( *this );
    if( num.isNan() ) return HNumber( num );

    HNumber result;
    h_destroy( result.d->num );
    result.d->num = h_mul( d->num, num.d->num );
    return result;
}

HNumber& HNumber::operator*=( const HNumber& num )
{
    HNumber n = HNumber(*this) * num;
    operator=( n );
    return *this;
}

HNumber HNumber::operator/( const HNumber& num ) const
{
    if( isNan() ) return HNumber( *this );
    if( num.isNan() ) return HNumber( num );
    if( num == 0 ) return HNumber::nan();

    HNumber result;
    h_destroy( result.d->num );
    result.d->num = h_div( d->num, num.d->num );
    return result;
}

HNumber& HNumber::operator/=( const HNumber& num )
{
    HNumber n = HNumber(*this) / num;
    operator=( n );
    return *this;
}

HNumber HNumber::operator%( const HNumber& num ) const
{
    if( isNan() ) return HNumber( *this );
    if( num.isNan() ) return HNumber( num );

    HNumber result;
    bc_modulo (d->num, num.d->num, &result.d->num, 0);
    return result;
}

bool HNumber::operator>( const HNumber& n ) const
{
    return HMath::compare( *this, n ) > 0;
}

bool HNumber::operator<( const HNumber& n ) const
{
    return HMath::compare( *this, n ) < 0;
}

bool HNumber::operator>=( const HNumber& n ) const
{
    return HMath::compare( *this, n ) >= 0;
}

bool HNumber::operator<=( const HNumber& n ) const
{
    return HMath::compare( *this, n ) <= 0;
}

bool HNumber::operator==( const HNumber& n ) const
{
    return HMath::compare( *this, n ) == 0;
}

bool HNumber::operator!=( const HNumber& n ) const
{
    return HMath::compare( *this, n ) != 0;
}

// format number in engineering notation
char* HMath::formatEngineering( const HNumber& hn, int prec )
{
    if( hn.isNan() )
    {
        char* str = (char*)malloc( 4 );
        str[0] = 'N';
        str[1] = 'a';
        str[2] = 'N';
        str[3] = '\0';
        return str;
    }

    int    nIntDigs  = hn.d->num->n_len;
    int    nFracDigs = hn.d->num->n_scale;
    char * digs      = hn.d->num->n_value;
    int    tenExp;

    // find the exponent and the factor
    int tzeros = 0;
    for( int c=0; c<hn.d->num->n_len+hn.d->num->n_scale; c++, tzeros++ )
        if( hn.d->num->n_value[c]!= 0 ) break;
    int expd = hn.d->num->n_len - tzeros - 1;

    if ( hn >= 1 || hn <= -1 )
    {
        // point must be shifted to the left, if needed

        if ( nIntDigs % 3 == 0 )
        {
            // 3n digits to the left
            if ( hn > 999 || hn < -999 )
                // n > 1
                tenExp = nIntDigs - 3;
            else
                // n = 1
                tenExp = 0;
        }
        else
            // non-3n digits to the left
            tenExp = nIntDigs - nIntDigs % 3;
    }
    else
    {
        // point must be shifted to the right
        // find first non-zero digit to the right of the point
        int startDigIdx = nIntDigs;
        int endDigIdx   = nIntDigs + nFracDigs - 1;
        int idx;
        for ( idx = startDigIdx; idx <= endDigIdx; idx++ )
            if ( digs[idx] != 0 )
                break;
        // calculate exponent to shift right
        while ( idx % 3 != 0 )
            idx++;
        tenExp = -idx;
    }

    // scale the number by a new factor
    HNumber nn = hn * HMath::raise( 10, -tenExp );

    // too close to zero?
    if( hn.isZero() || ( expd <= -HMATH_COMPARE_PREC ) )
    {
        nn = HNumber( 0 );
        tenExp = 0;
    }

    // build result expression string with E notation
    char* str = formatFixed( nn, prec );
    std::string resString = std::string( str ) + "e";
    free( str );
    std::stringstream ss;
    ss << tenExp;
    resString += ss.str();
    char * result = (char *) malloc( resString.size() + 1 );
    strcpy( result, resString.c_str() );

    return result;
}

// format number with fixed number of decimal digits
char* HMath::formatFixed( const HNumber& hn, int prec )
{
    if( hn.isNan() )
    {
        char* str = (char*)malloc( 4 );
        str[0] = 'N';
        str[1] = 'a';
        str[2] = 'N';
        str[3] = '\0';
        return str;
    }

    bc_num n = h_copy( hn.d->num );
    h_trimzeros( n );

    int oprec = prec;
    if( prec < 0 )
    {
        prec = HMATH_MAX_SHOWN;
        if( n->n_scale < HMATH_MAX_SHOWN )
            prec = n->n_scale;
    }

    // yes, this is necessary!
    bc_num m = h_round( n, prec );
    h_trimzeros( m );
    h_destroy( n );
    n = m;
    if( oprec < 0 )
    {
        prec = HMATH_MAX_SHOWN;
        if( n->n_scale < HMATH_MAX_SHOWN )
            prec = n->n_scale;
    }

    // how many to allocate?
    int len = n->n_len + prec;
    if( n->n_sign != PLUS ) len++;
    if( prec > 0 ) len++;

    char* str = (char*)malloc( len+1 );
    char* p = str;

    // the sign and the integer part
    // but avoid printing "-0"
    if( n->n_sign != PLUS )
        if( !bc_is_zero( n ) ) *p++ = '-';
    for( int c=0; c<n->n_len; c++ )
        *p++ = (char)BCD_CHAR( n->n_value[c] );

    // the fraction part
    if( prec > 0 )
    {
        *p++ = '.';
        int k = (prec < n->n_scale) ? prec : n->n_scale;
        for( int d=0; d<k; d++ )
            *p++ = (char)BCD_CHAR( n->n_value[n->n_len+d] );
        for( int r=n->n_scale; r<prec; r++ )
            *p++ = '0';
    }

    *p = '\0';
    h_destroy( n );

    return str;
}

// format number in scientific notation
char* HMath::formatScientific( const HNumber& hn, int prec )
{
    if( hn.isNan() )
    {
        char* str = (char*)malloc( 4 );
        str[0] = 'N';
        str[1] = 'a';
        str[2] = 'N';
        str[3] = '\0';
        return str;
    }

    // find the exponent and the factor
    int tzeros = 0;
    for( int c=0; c<hn.d->num->n_len+hn.d->num->n_scale; c++, tzeros++ )
        if( hn.d->num->n_value[c]!= 0 ) break;
    int expd = hn.d->num->n_len - tzeros - 1;

    // extra digits needed for the exponent part
    int expn = 0;
    for( int e = ::abs(expd); e > 0; e/=10 ) expn++;
    if( expd <= 0 ) expn++;

    // scale the number by a new factor
    HNumber nn = hn * HMath::raise( 10, -expd );

    // too close to zero?
    if( hn.isZero() || ( expd <= -HMATH_COMPARE_PREC ) )
    {
        nn = HNumber(0);
        expd = 0;
        expn = 1;
    }

    char* str = formatFixed( nn, prec );
    char* result = (char*) malloc( strlen(str)+expn+2 );
    strcpy( result, str );
    free( str );

    // the exponential part
    char* p = result + strlen(result);
    *p++ = 'e'; p[expn] = '\0';
    if( expd < 0 ) *p = '-';
    for( int k=expn; k>0; k-- )
    {
        int digit = expd % 10;
        p[k-1] = (char)('0' + ::abs( digit ));
        expd = expd / 10;
        if( expd == 0 ) break;
    }

    return result;
}

char* HMath::formatGeneral( const HNumber& hn, int prec )
{
    if( hn.isNan() )
    {
        char* str = (char*)malloc( 4 );
        str[0] = 'N';
        str[1] = 'a';
        str[2] = 'N';
        str[3] = '\0';
        return str;
    }

    // find the exponent and the factor
    int tzeros = 0;
    for( int c=0; c<hn.d->num->n_len+hn.d->num->n_scale; c++, tzeros++ )
        if( hn.d->num->n_value[c]!= 0 ) break;
    int expd = hn.d->num->n_len - tzeros - 1;

    char* str;
    if( expd > 5 )
        str = formatScientific( hn, prec );
    else if( ( expd < -4 ) && (expd>-HMATH_COMPARE_PREC ) )
        str = formatScientific( hn, prec );
    else if ( (expd < 0) && (prec>0) && (expd < -prec) )
        str = formatScientific( hn, prec );
    else
        str = formatFixed( hn, prec );

    return str;
}

char* HMath::formatHexadec( const HNumber& hn )
{
    char* str;
    if( hn.isNan() || !hn.isInteger())
    {
        str = (char*)malloc( 4 );
        str[0] = 'N';
        str[1] = 'a';
        str[2] = 'N';
        str[3] = '\0';
        return str;
    }

    int digits = 1; HNumber _16(16);
    bool negative = (hn < 0);
    HNumber tmp = negative ? HNumber(0)-hn : hn;
    while (integer(tmp/=_16) > 0) ++digits; // how many digits
    str = (char*)malloc( digits+3+negative );
    char* ptr = &str[digits+2+negative]; *ptr = '\0';
    HNumber val;
    int i;
    tmp = negative ? HNumber(0)-hn : hn;
    HNumber f;
    HNumber f_old(1);
    while (digits--)
    {
        f = f_old*_16;
        val = tmp % (f); tmp -= val;
        val /= f_old; f_old = f; i = bc_num2long( val.d->num);
        *--ptr = (i < 10) ? '0'+i : 'A'+i-10;
    }
    *--ptr = 'x'; *--ptr = '0'; if (negative) *--ptr = '-';

    return str;
}

char* HMath::formatOctal( const HNumber& hn )
{
    char* str;
    if( hn.isNan() || !hn.isInteger())
    {
        str = (char*)malloc( 4 );
        str[0] = 'N';
        str[1] = 'a';
        str[2] = 'N';
        str[3] = '\0';
        return str;
    }

    int digits = 1; HNumber _8(8);
    bool negative = (hn < 0);
    HNumber tmp = negative ? HNumber(0)-hn : hn;
    while (integer(tmp/=_8) > 0) ++digits; // how many digits
    str = (char*)malloc( digits+3+negative );
    char* ptr = &str[digits+2+negative]; *ptr = '\0';
    HNumber val;
    tmp = negative ? HNumber(0)-hn : hn;
    HNumber f;
    HNumber f_old(1);
    while (digits--)
    {
        f = f_old*_8;
        val = tmp % (f); tmp -= val;
        val /= f_old; f_old = f;
        *--ptr = '0'+bc_num2long( val.d->num);
    }
    *--ptr = 'o'; *--ptr = '0'; if (negative) *--ptr = '-';

    return str;
}

char* HMath::formatBinary( const HNumber& hn )
{
    char* str;
    if( hn.isNan() || !hn.isInteger())
    {
        str = (char*)malloc( 4 );
        str[0] = 'N';
        str[1] = 'a';
        str[2] = 'N';
        str[3] = '\0';
        return str;
    }

    int digits = 1; HNumber _2(2);
    bool negative = (hn < 0);
    HNumber tmp = negative ? HNumber(0)-hn : hn;
    while (integer(tmp/=_2) > 0) ++digits; // how many digits
    str = (char*)malloc( digits+3+negative );
    char* ptr = &str[digits+2+negative]; *ptr = '\0';
    HNumber val;
    HNumber _0(0);
    tmp = negative ? _0-hn : hn;
    HNumber f;
    HNumber f_old(1);
    while (digits--)
    {
        f = f_old*_2;
        val = tmp % (f); tmp -= val;
        val /= f_old; f_old = f;
        *--ptr = (val == _0) ?'0':'1';
    }
    *--ptr = 'b'; *--ptr = '0'; if (negative) *--ptr = '-';

    return str;
}

char* HMath::format( const HNumber& hn, char format, int prec )
{
    if( hn.isNan() )
    {
        char* str = (char*)malloc( 4 );
        str[0] = 'N';
        str[1] = 'a';
        str[2] = 'N';
        str[3] = '\0';
        return str;
    }

    if     ( format=='g' ) return formatGeneral    ( hn, prec );
    else if( format=='f' ) return formatFixed      ( hn, prec );
    else if( format=='n' ) return formatEngineering( hn, prec );
    else if( format=='e' ) return formatScientific ( hn, prec );
    else if( format=='h' ) return formatHexadec    ( hn       );
    else if( format=='o' ) return formatOctal      ( hn       );
    else if( format=='b' ) return formatBinary     ( hn       );

    // fallback to 'g'
    return formatGeneral( hn, prec );
}

HNumber HMath::phi()
{
    return HNumber("1.61803398874989484820458683436563811772030917980576"
                   "28621354486227052604628189024497072072041893911374"
                   "84754088075386891752126633862223536931793180060766"
                   "72635443338908659593958290563832266131992829026788"
                   "06752087668925017116962070322210432162695486262963"
                   "13614438149758701220340805887954454749246185695364"
                   "86444924104432077134494704956584678850987433944221"
                   "25448770664780915884607499887124007652170575179788"
                   "34166256249407589069704000281210427621771117778053"
                   "15317141011704666599146697987317613560067087480710"
                   "13179523689427521948435305678300228785699782977834"
                   "78458782289110976250030269615617002504643382437764"
                   "86102838312683303724292675263116533924731671112115"
                   "88186385133162038400522216579128667529465490681131"
                   "71599343235973494985090409476213222981017261070596"
                   "11645629909816290555208524790352406020172799747175"
                   "34277759277862561943208275051312181562855122248093"
                   "94712341451702237358057727861600868838295230459264"
                   "78780178899219902707769038953219681986151437803149"
                   "97411069260886742962267575605231727775203536139362");
}

HNumber HMath::pi()
{
    return HNumber("3.14159265358979323846264338327950288419716939937510"
                   "58209749445923078164062862089986280348253421170679"
                   "82148086513282306647093844609550582231725359408128"
                   "48111745028410270193852110555964462294895493038196"
                   "44288109756659334461284756482337867831652712019091"
                   "45648566923460348610454326648213393607260249141273"
                   "72458700660631558817488152092096282925409171536436"
                   "78925903600113305305488204665213841469519415116094"
                   "33057270365759591953092186117381932611793105118548"
                   "07446237996274956735188575272489122793818301194912"
                   "98336733624406566430860213949463952247371907021798"
                   "60943702770539217176293176752384674818467669405132"
                   "00056812714526356082778577134275778960917363717872"
                   "14684409012249534301465495853710507922796892589235"
                   "42019956112129021960864034418159813629774771309960"
                   "51870721134999999837297804995105973173281609631859"
                   "50244594553469083026425223082533446850352619311881"
                   "71010003137838752886587533208381420617177669147303"
                   "59825349042875546873115956286388235378759375195778"
                   "1857780532171226806613001927876611195909216420198" );
}

HNumber HMath::add( const HNumber& n1, const HNumber& n2 )
{
    HNumber result = n1 + n2;
    return result;
}

HNumber HMath::sub( const HNumber& n1, const HNumber& n2 )
{
    HNumber result = n1 - n2;
    return result;
}

HNumber HMath::mul( const HNumber& n1, const HNumber& n2 )
{
    HNumber result = n1 * n2;
    return result;
}

HNumber HMath::div( const HNumber& n1, const HNumber& n2 )
{
    HNumber result = n1 / n2;
    return result;
}

int HMath::compare( const HNumber& n1, const HNumber& n2 )
{
    if( n1.isNan() && n2.isNan() ) return 0;

    HNumber delta = sub( n1, n2 );
    delta = HMath::round( delta, HMATH_COMPARE_PREC );
    if( delta.isZero() ) return 0;
    else if( delta.isNegative() ) return -1;
    return  1;
}

HNumber HMath::max( const HNumber& n1, const HNumber& n2 )
{
    if ( n1.isNan() || n2.isNan() )
        return HNumber::nan();

    if ( n1 >= n2 )
        return n1;
    else
        return n2;
}

HNumber HMath::min( const HNumber& n1, const HNumber& n2 )
{
    if ( n1.isNan() || n2.isNan() )
        return HNumber::nan();

    if ( n1 <= n2 )
        return n1;
    else
        return n2;
}

HNumber HMath::abs( const HNumber& n )
{
    HNumber r( n );
    r.d->num->n_sign = PLUS;
    return r;
}

HNumber HMath::negate( const HNumber& n )
{
    if( n.isNan() || n.isZero() )
        return HNumber( n );

    HNumber result( n );
    result.d->num->n_sign = ( n.d->num->n_sign == PLUS ) ? MINUS : PLUS;
    return result;
}

HNumber HMath::round( const HNumber& n, int prec )
{
    if( n.isNan() )
        return HNumber::nan();

    HNumber result;
    h_destroy( result.d->num );
    result.d->num = h_round( n.d->num, prec );
    return result;
}

HNumber HMath::trunc( const HNumber& n, int prec )
{
    if( n.isNan() )
        return HNumber::nan();

    HNumber result;
    h_destroy( result.d->num );
    result.d->num = h_trunc( n.d->num, prec );
    return result;
}

HNumber HMath::integer( const HNumber& n )
{
    if( n.isNan() )
        return HNumber::nan();

    if( n.isZero() )
        return HNumber( 0 );

    HNumber result;
    h_destroy( result.d->num );
    result.d->num = h_rescale( n.d->num, 0 );
    return result;
}

HNumber HMath::frac( const HNumber& n )
{
    if( n.isNan() )
        return HNumber::nan();

    return n - integer(n);
}

HNumber HMath::floor( const HNumber& n )
{
    if( n.isNan() )
        return HNumber::nan();

    if( n.isInteger() )
        return n;
    else if( n.isPositive() )
        return n - frac(n);
    else
        return n - HNumber(1) - frac(n);
}

HNumber HMath::ceil( const HNumber& n )
{
    if( n.isNan() )
        return HNumber::nan();

    if( n.isInteger() )
        return n;
    else if( n.isPositive() )
        return n + HNumber(1) - frac(n);
    else
        return n - frac(n);
}

HNumber HMath::gcd( const HNumber& n1, const HNumber& n2 )
{
    if( n1.isNan() || n2.isNan() )
        return HNumber::nan();

    HNumber a = abs( n1 );
    HNumber b = abs( n2 );

    if ( a == 0 )
        return b;
    if ( b == 0 )
        return a;

    // run Euclidean algorithm
    while ( true )
    {
        a = a % b;

        if ( a == 0 )
            return b;

        b = b % a;

        if ( b == 0 )
            return a;
    }
}

HNumber HMath::sqrt( const HNumber& n )
{
    if( n.isNan() )
        return HNumber::nan();

    if( n.isZero() )
        return n;

    if( n.isNegative() )
        return HNumber::nan();

    // useful constant
    HNumber half("0.5");

    // Use Netwon-Raphson algorithm
    HNumber r( 1 );
    for( int i = 0; i < HMATH_MAX_PREC; i++ )
    {
        HNumber q = n / r;
        if( r == q ) break;
        HNumber s = r + q;
        r = s * half;
    }

    return r;
}

HNumber HMath::cbrt( const HNumber& n )
{
    if( n.isNan() )
        return HNumber::nan();

    if( n.isZero() )
        return n;

    // useful constants
    HNumber three     = HNumber("3");
    HNumber twoThirds = HNumber("2") / three;

    // iterations to approximate result
    // X[i+1] = (2/3)X[i] + n / (3 * X[i]^2))
    // initial guess = sqrt( n )
    // r = X[i], q = X[i+1], a = n
    HNumber a = n.isNegative() ? n * HNumber("-1") : n;
    HNumber r = sqrt( a );
    for( int i = 0; i < HMATH_MAX_PREC; i++ )
    {
        HNumber q = (twoThirds * r) + (a / (three * r * r));
        if( r == q )
            break;
        r = q;
    }

    if( n.isNegative())
        return r * HNumber("-1");
    else
        return r;
}

HNumber HMath::raise( const HNumber& n1, int n )
{
    if( n1.isNan() ) return n1;

    // http://en.wikipedia.org/wiki/Exponentiation#Powers_of_zero
    if( n1.isZero() )
    {
        if( n < 0 )
            return HNumber::nan();
        if( n > 0 )
            return HNumber(0);

        // debatable, see http://en.wikipedia.org/wiki/Empty_product#0_raised_to_the_0th_power
        // vs http://mathworld.wolfram.com/Power.html
        if( n == 0 )
            return HNumber(1);
    }

    if( n1 == HNumber(1) ) return n1;
    if( n == 0 ) return HNumber(1);
    if( n == 1 ) return n1;

    if(n > 0)
    {
        // squaring algorithm to find exponentiation
        // see http://en.wikipedia.org/wiki/Exponentiation_by_squaring
        HNumber result = HNumber(1);
        HNumber x = n1;
        while(n > 0)
        {
            if(n & 1)
            {
                result = result * x;
                n--;
            }
            x = x * x;
            n = n >> 1;
        }
        return result;
    }

    HNumber result = n1;
    for( ; n < 1; n++ )
        result /= n1;

    return result;
}

HNumber HMath::raise( const HNumber& n1, const HNumber& n2  )
{
    if( n1.isNan() ) return HNumber::nan();
    if( n2.isNan() ) return HNumber::nan();

    // see previous function
    if( n1.isZero() )
    {
        if( n2.isNegative() )
            return HNumber::nan();
        if( n2.isPositive() )
            return HNumber(0);
        if( n2.isZero() )
            return HNumber(1);
    }

    if( n1 == HNumber(1) ) return n1;
    if( n2.isZero() ) return HNumber(1);
    if( n2 == HNumber(1) ) return n1;

    HNumber result;

    // n1 is negative, n2 must be integer
    if( n1.isNegative() )
    {
        if( HMath::integer(n2) != n2)
            result = HNumber::nan();
        else
        {
            // use integer raise function
            HNumber nn = n2;
            result = raise( n1, atoi( HMath::formatFixed(nn, 0) ) );
        }
    }
    else
    {
        // n2 integer? use the integer raise version
        if( HMath::integer(n2) == n2)
        {
            // use integer raise function
            HNumber nn = n2;
            result = raise( n1, atoi( HMath::formatFixed(nn, 0) ) );
        }
        else
        {
            // x^y = exp( y*ln(x) )
            result = n2 * HMath::ln(n1);
            result = HMath::exp( result );
        }
    }

    return result;
}

HNumber HMath::exp( const HNumber& x )
{
    if( x.isNan() )
        return HNumber::nan();

    bool negative = x.isNegative();
    HNumber xs = HMath::abs( x );

    // adjust so that x is less than 1
    // use the fact that e^x = (e^(x/2))^2
    HNumber one(1);
    HNumber half("0.5");
    unsigned factor = 0;
    while( xs > one )
    {
        factor ++;
        xs = xs * half;
    }

    // Taylor expansion: e^x = 1 + x + x^2/2! + x^3/3! + ...
    HNumber num = xs;
    HNumber den = 1;
    HNumber sum = xs + 1;

    // now loop to sum the series
    for( int i = 2; i < HMATH_MAX_PREC; i++ )
    {
        num *= xs;
        den *= HNumber(i);
        if( num.isZero() ) break;
        HNumber s = HMath::div( num, den );
        if( s.isZero() ) break;
        sum += s;
    }

    HNumber result = sum;
    if( factor > 0 )
        while( factor > 0 )
        {
            factor--;
            result *= result;
        }

    if( negative )
        result = HMath::div( HNumber(1), result );

    return result;
};

HNumber HMath::ln( const HNumber& x )
{
    if ( x.isNan() || x <= 0 )
        return HNumber::nan();

    // short circuit
    if( x == HNumber(10) )
        return HNumber("2.30258509299404568401799145468436420760110148862877"
                       "29760333279009675726102948650438303813865953227795"
                       "49054520440916779445247118780973037711833599749301"
                       "72118016928228381938415404059160910960135436620869" );

    // useful constants
    HNumber two(2);
    HNumber one(1);
    HNumber half("0.5");

    // adjust so that x is between 0.5 and 2.0
    // use the fact that ln(x^2) = 2*ln(x)
    HNumber xs( x );
    unsigned factor = 2;
    while( xs >= two )
    {
        factor *= 2;
        xs = HMath::sqrt( xs );
    }
    while( xs <= half )
    {
        factor *= 2;
        xs = HMath::sqrt( xs );
    }

    // Taylor expansion: ln(x) = 2(a+a^3/3+a^5/5+...)
    // where a=(x-1)/(x+1)
    HNumber p = xs - 1;
    HNumber q = xs + 1;
    HNumber a = p / q;
    HNumber as = a*a;
    HNumber t = a;
    HNumber sum = a;

    // loop for the series (limited to avoid nasty cases)
    for( int i = 3; i < HMATH_MAX_PREC; i+= 2 )
    {
        t *= as;
        if( t.isZero() ) break;
        HNumber s = HMath::div( t, HNumber(i) );
        if( s.isZero() ) break;
        sum += s;
    }

    HNumber result = sum * HNumber( factor );
    return result;
}

HNumber HMath::log( const HNumber& x )
{
    if ( x.isNan() || x <= 0 )
        return HNumber::nan();

    return HMath::ln( x ) / HMath::ln(10);
}

HNumber HMath::lg( const HNumber& x )
{
    if ( x.isNan() || x <= 0 )
        return HNumber::nan();

    return HMath::ln( x ) / HMath::ln(2);
}

// ensure angle is within 0 to 2*pi
// useful for sin, cos
static HNumber simplifyAngle( const HNumber& x )
{
    if( x.isNan() )
        return HNumber::nan();

#if 1
    // using simple method
    HNumber pi2 = HMath::pi() * 2;
    HNumber nn = x / pi2;
    HNumber xs = x - HMath::integer(nn)*pi2;
    if( xs.isNegative() ) xs += pi2;

    return xs;
#else
    // using argument reduction method
    // see http://www.derekroconnor.net/Software/Ng--ArgReduction.pdf
    HNumber factor = HNumber(2) / HMath::pi();
    HNumber y = x * factor;
    HNumber f = HMath::frac(y);
    HNumber r = f * HMath::pi()/HNumber(2);

    // find int(y) mod 4
    HNumber n = HMath::integer( y );
    HNumber m = n - HNumber(4)*HMath::integer( n / HNumber(4) );
    HNumber halfpi = HMath::pi() / HNumber(2);
    if(m == HNumber(1))
        r += halfpi;
    if(m == HNumber(2))
        r += HMath::pi();
    if(m == HNumber(3))
        r += halfpi + HMath::pi();

    return r;
#endif
}

HNumber HMath::sin( const HNumber& x )
{
    if( x.isNan() )
        return HNumber::nan();

    // adjust to small angle for speedup
    HNumber xs = simplifyAngle( x );

    // limits shortcut
    if ( x == 0 || x == HMath::pi() || x == HMath::pi() * 2 )
        return HNumber( 0 );
    else if( x == HMath::pi() / 2 )
        return HNumber( 1 );
    else if( x == HMath::pi() * 3 / 2 )
        return HNumber( -1 );

    // Taylor expansion: sin(x) = x - x^3/3! + x^5/5! - x^7/7! ...
    HNumber xsq = xs*xs;
    HNumber num = xs;
    HNumber den = 1;
    HNumber sum = xs;

    // loop for the series (limited to avoid nasty cases)
    for( int i = 3; i < HMATH_MAX_PREC; i+=2 )
    {
        num *= xsq;
        if( num.isZero() ) break;
        den *= HNumber(i-1);
        den *= HNumber(i);
        den = HMath::negate( den );
        HNumber s = HMath::div( num, den );
        if( s.isZero() ) break;
        sum += s;
    }

    return sum;
}

HNumber HMath::cos( const HNumber& x )
{
    if( x.isNan() )
        return HNumber::nan();

    // adjust to small angle for speedup
    HNumber xs = simplifyAngle( x );

    // limits shortcut
    if ( x == 0 || x == HMath::pi() * 2 )
        return HNumber( 1 );
    else if( x == HMath::pi() / 2 || x == HMath::pi() * 3 / 2 )
        return HNumber( 0 );
    else if( x == HMath::pi() )
        return HNumber( -1 );

    // Taylor expansion: cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! ...
    HNumber xsq = xs*xs;
    HNumber num = 1;
    HNumber den = 1;
    HNumber sum = 1;

    // loop for the series (limited to avoid nasty cases)
    for( int i = 2; i < HMATH_MAX_PREC; i+=2 )
    {
        num *= xsq;
        if( num.isZero() ) break;
        den *= HNumber(i-1);
        den *= HNumber(i);
        den = HMath::negate( den );
        HNumber s = num / den;
        if( s.isZero() ) break;
        sum += s;
    }

    return sum;
}

HNumber HMath::tan( const HNumber& x )
{
    return HMath::sin(x) / HMath::cos(x);
}

HNumber HMath::cot( const HNumber& x )
{
    return HMath::cos(x) / HMath::sin(x);
}

HNumber HMath::sec( const HNumber& x )
{
    return HNumber(1) / HMath::cos(x);
}

HNumber HMath::csc( const HNumber& x )
{
    return HNumber(1) / HMath::sin(x);
}

HNumber HMath::atan( const HNumber& x )
{
    if( x.isNan() )
        return HNumber::nan();

    // useful constants
    HNumber one("1.0");
    HNumber c( "0.2" );

    // short circuit
    if( x == c )
        return HNumber("0.19739555984988075837004976519479029344758510378785"
                       "21015176889402410339699782437857326978280372880441"
                       "12628118073691360104456479886794239355747565495216"
                       "30327005221074700156450155600612861855266332573187" );

    if( x == one )
        // essentially equals to HMath::pi()/4;
        return HNumber("0.78539816339744830961566084581987572104929234984377"
                       "64552437361480769541015715522496570087063355292669"
                       "95537021628320576661773461152387645557931339852032"
                       "12027936257102567548463027638991115573723873259549" );

    bool negative = x.isNegative();
    HNumber xs = HMath::abs( x );

    // adjust so that x is less than c (we choose c = 0.2)
    // use the fact that atan(x) = atan(c) + atan((x-c)/(1+xc))
    HNumber factor(0);
    HNumber base(0);
    while( xs > c )
    {
        base = HMath::atan( c );
        factor += one;
        HNumber p = xs - c;
        HNumber q = xs * c;
        xs = p / (q+one);
    }

    // Taylor series: atan(x) = x - x^3/3 + x^5/5 - x^7/7 + ...
    HNumber num = xs;
    HNumber xsq = xs*xs;
    HNumber den = 1;
    HNumber sum = xs;

    // loop for the series (limited to avoid nasty cases)
    for( int i = 3; i < HMATH_MAX_PREC; i+=2 )
    {
        num *= xsq;
        if( num.isZero() ) break;
        den = HNumber(i);
        int n = (i-1)/2;
        if( n&1 ) den = HNumber(-i);
        HNumber s = HMath::div( num, den );
        if( s.isZero() ) break;
        sum += s;
    }

    HNumber result = factor*base + sum;
    if( negative ) result = HMath::negate( result );
    return result;
};

HNumber HMath::asin( const HNumber & x )
{
    if ( x.isNan() || x < -1 || x > 1 )
        return HNumber::nan();

    // shortcuts
    if ( x == -1  )
        return HMath::pi() / 2 * (-1);
    if ( x == 0 )
        return HNumber( 0 );
    if ( x == 1 )
        return HMath::pi() / 2;

    // asin( x ) = atan( x / sqrt( 1 - x * x ) );
    HNumber d = HMath::sqrt( HNumber( 1 ) - x * x );
    if ( d == 0 )
    {
        HNumber result = HMath::pi() / 2;
        if ( x < 0 )
            result *= -1;
        return result;
    }

    return HMath::atan( x / d );
};

HNumber HMath::acos( const HNumber & x )
{
    if ( x.isNan() || x < -1 || x > 1 )
        return HNumber::nan();

    // shortcuts
    if ( x == -1 )
        return HMath::pi();
    if ( x == 0 )
        return HMath::pi()/2;
    if ( x == 1 )
        return 0;

    // acos( x ) = atan(  sqrt( 1 - x * x ) / x );
    HNumber n = HMath::sqrt( HNumber( 1 ) - x * x );
    return HMath::atan( n / x );
};

HNumber HMath::sinh( const HNumber& x )
{
    if( x.isNan() )
        return HNumber::nan();

    // sinh(x) = 0.5*(e^x - e^(-x) )
    HNumber result = HMath::exp(x) - HMath::exp( HMath::negate(x) );
    result = result / 2;

    return result;
}

HNumber HMath::cosh( const HNumber& x )
{
    if( x.isNan() )
        return HNumber::nan();

    // cosh(x) = 0.5*(e^x - e^(-x) )
    HNumber result = HMath::exp(x) + HMath::exp( HMath::negate(x) );
    result = result / 2;

    return result;
}

HNumber HMath::tanh( const HNumber& x )
{
    if( x.isNan() )
        return HNumber::nan();

    // tanh(h) = sinh(x)/cosh(x)
    HNumber c = HMath::cosh( x );
    if( c.isZero() )
        return HNumber::nan();

    HNumber s = HMath::sinh( x );
    HNumber result = s / c;

    return result;
}

HNumber HMath::sign( const HNumber& x )
{
    if( x.isNan() )
        return HNumber::nan();

    HNumber result( 0 );
    if (x == result)
        return result;
    if (x < result)
        result = HNumber(-1);
    else
        result = HNumber(1);

    return result;
}

HNumber HMath::nCr( const HNumber & n,
                    const HNumber & r )
{
    if ( n.isNan() || n < 0 ||
         r.isNan() || r < 0 ||
         r > n )
        return HNumber::nan();

    // shortcuts
    HNumber one = HNumber( 1 );
    if ( r == HNumber( 0 ) || r == n )
        return one;
    if ( r == one )
        return n;

    if ( r > n/2 )
        return factorial( n, r+1 ) / factorial( n-r, 1 );
    else
        return factorial( n, n-r+1  ) / factorial( r, 1 );
}

HNumber HMath::nPr( const HNumber & n,
                    const HNumber & r )
{
    if ( n.isNan() || n < 0 ||
         r.isNan() || r < 0 ||
         r > n )
        return HNumber::nan();

    // shortcuts
    HNumber one = HNumber( 1 );
    if ( r == HNumber( 0 ) )
        return one;
    if ( r == one )
        return n;
    if ( r == n )
        return factorial( n );

    return factorial( n, n-r+1 );
}

HNumber HMath::factorial( const HNumber& x, const HNumber& base )
{
    if( x.isNan()
        || x    < HNumber(0) || !x.isInteger()
        || base < HNumber(1) || !base.isInteger()
        || (x < base && x != HNumber(0))  )
        return HNumber::nan();

    if( x == HNumber(0) || x == HNumber(1) )
        return HNumber(1);

    if( x == base )
        return x;

    HNumber one(1);
    HNumber result = one;
    HNumber n = base - one;
    do
    {
        n = n + one;
        result = result * n;
    }
    while (n < x);

    return result;
}

HNumber HMath::binomialPmf( const HNumber & k,
                            const HNumber & n,
                            const HNumber & p )
{
    if ( k.isNan() || ! k.isInteger() || k < 0 || k > n
         || n.isNan() || ! n.isInteger() || n < 0
         || p.isNan() || p < 0 || p > 1 )
        return HNumber::nan();

    return HMath::nCr( n, k ) * HMath::raise( p, k ) *
        HMath::raise( HNumber(1)-p, n-k );
}

HNumber HMath::binomialCdf( const HNumber & k,
                            const HNumber & n,
                            const HNumber & p )
{
    if ( k.isNan() || ! k.isInteger() || k < 0 || k > n
         || n.isNan() || ! n.isInteger() || n < 0
         || p.isNan() || p < 0 || p > 1 )
        return HNumber::nan();

    HNumber result( 0 );
    for ( HNumber i( 0 ); i <= k; i += 1 )
        result += HMath::nCr( n, i ) * HMath::raise( p, i )
            * HMath::raise( HNumber(1)-p, n-i );
    return result;
}

HNumber HMath::binomialMean( const HNumber & n,
                             const HNumber & p )
{
    if ( n.isNan() || ! n.isInteger() || n < 0
         || p.isNan() || p < 0 || p > 1 )
        return HNumber::nan();

    return n * p;
}

HNumber HMath::binomialVariance( const HNumber & n,
                                 const HNumber & p )
{
    if ( n.isNan() || ! n.isInteger() || n < 0
         || p.isNan() || p < 0 || p > 1 )
        return HNumber::nan();

    return n * p * ( HNumber(1) - p );
}

HNumber HMath::hypergeometricPmf( const HNumber & k,
                                  const HNumber & N,
                                  const HNumber & M,
                                  const HNumber & n )
{
    if ( k.isNan() || ! k.isInteger() || k < max( 0, M+n-N ) || k > min( M, n )
         || N.isNan() || ! N.isInteger() || N < 0
         || M.isNan() || ! M.isInteger() || M < 0 || M > N
         || n.isNan() || ! n.isInteger() || n < 0 || n > N )
        return HNumber::nan();

    return HMath::nCr( M, k ) * HMath::nCr( N-M, n-k ) / HMath::nCr( N, n );
}

HNumber HMath::hypergeometricCdf( const HNumber & k,
                                  const HNumber & N,
                                  const HNumber & M,
                                  const HNumber & n )
{
    if ( k.isNan() || ! k.isInteger() || k < max( 0, M+n-N ) || k > min( M, n )
         || N.isNan() || ! N.isInteger() || N < 0
         || M.isNan() || ! M.isInteger() || M < 0 || M > N
         || n.isNan() || ! n.isInteger() || n < 0 || n > N )
        return HNumber::nan();

    HNumber result( 0 );
    for ( HNumber i( 0 ); i <= k; i += 1 )
        result += HMath::nCr( M, i ) * HMath::nCr( N-M, n-i ) / HMath::nCr( N, n );
    return result;
}

HNumber HMath::hypergeometricMean( const HNumber & N,
                                   const HNumber & M,
                                   const HNumber & n )
{
    if ( N.isNan() || ! N.isInteger() || N < 0
         || M.isNan() || ! M.isInteger() || M < 0 || M > N
         || n.isNan() || ! n.isInteger() || n < 0 || n > N )
        return HNumber::nan();

    return n * M / N;
}

HNumber HMath::hypergeometricVariance( const HNumber & N,
                                       const HNumber & M,
                                       const HNumber & n )
{
    if ( N.isNan() || ! N.isInteger() || N < 0
         || M.isNan() || ! M.isInteger() || M < 0 || M > N
         || n.isNan() || ! n.isInteger() || n < 0 || n > N )
        return HNumber::nan();

    return (n * (M/N) * (HNumber(1) - M/N) * (N-n)) / (N - HNumber(1));
}

HNumber HMath::poissonPmf( const HNumber & k,
                           const HNumber & l )
{
    if ( k.isNan() || ! k.isInteger() || k < 0
         || l.isNan() || l < 0 )
        return HNumber::nan();

    return exp( l*(-1) ) * raise( l, k ) / factorial( k );
}

HNumber HMath::poissonCdf( const HNumber & k,
                           const HNumber & l )
{
    if ( k.isNan() || ! k.isInteger() || k < 0
         || l.isNan() || l < 0 )
        return HNumber::nan();

    HNumber result( 0 );
    for ( HNumber i( 0 ); i <= k; i += 1 )
        result += exp( l*(-1) ) * raise( l, i ) / factorial( i );

    return result;
}

HNumber HMath::poissonMean( const HNumber & l )
{
    if ( l.isNan() || l < 0 )
        return HNumber::nan();

    return l;
}

HNumber HMath::poissonVariance( const HNumber & l )
{
    if ( l.isNan() || l < 0 )
        return HNumber::nan();

    return l;
}

void HMath::finalize()
{
    bc_free_num( &_zero_ );
    bc_free_num( &_one_ );
    bc_free_num( &_two_ );
    free( _one_ );
    free( _zero_ );
    free( _two_ );
    h_grabfree();
    h_grabfree();
    h_grabfree();
    h_grabfree();
}

std::ostream& operator<<( std::ostream& s, const HNumber& n )
{
    char* str = HMath::formatFixed( n );
    s << str;
    delete[] str;
    return s;
}