xref: /gem5/ext/systemc/src/sysc/datatypes/fx/scfx_rep.cpp

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/*****************************************************************************

  scfx_rep.cpp -

  Original Author: Robert Graulich, Synopsys, Inc.
                   Martin Janssen,  Synopsys, Inc.

 *****************************************************************************/

/*****************************************************************************

  MODIFICATION LOG - modifiers, enter your name, affiliation, date and
  changes you are making here.

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// $Log: scfx_rep.cpp,v $
// Revision 1.4  2011/08/24 22:05:43  acg
//  Torsten Maehne: initialization changes to remove warnings.
//
// Revision 1.3  2011/08/15 16:43:24  acg
//  Torsten Maehne: changes to remove unused argument warnings.
//
// Revision 1.2  2009/02/28 00:26:20  acg
//  Andy Goodrich: bug fixes.
//
// Revision 1.2  2008/11/06 17:22:47  acg
//  Andy Goodrich: bug fixes for 2.2.1.
//
// Revision 1.1.1.1  2006/12/15 20:31:36  acg
// SystemC 2.2
//
// Revision 1.3  2006/01/13 18:53:58  acg
// Andy Goodrich: added $Log command so that CVS comments are reproduced in
// the source.
//

#include "sysc/utils/sc_machine.h"
#include "sysc/datatypes/fx/scfx_rep.h"

#include "sysc/datatypes/fx/scfx_ieee.h"
#include "sysc/datatypes/fx/scfx_pow10.h"
#include "sysc/datatypes/fx/scfx_utils.h"

#include "sysc/datatypes/bit/sc_bv_base.h"

#include <ctype.h>
#include <cstdio>
#include <stdlib.h>
#include <math.h>


namespace sc_dt
{

// ----------------------------------------------------------------------------
//  some utilities
// ----------------------------------------------------------------------------

static scfx_pow10 pow10_fx;

static const int mantissa0_size = SCFX_IEEE_DOUBLE_M_SIZE - bits_in_int;

static inline
int
n_word( int x )
{
    return ( x + bits_in_word - 1 ) / bits_in_word;
}


// ----------------------------------------------------------------------------
//  CONSTRUCTORS
// ----------------------------------------------------------------------------

scfx_rep::scfx_rep()
: m_mant( min_mant ), m_wp(), m_sign(), m_state(), m_msw(), m_lsw(),
  m_r_flag( false )
{
    set_zero();
}

scfx_rep::scfx_rep( int a )
: m_mant( min_mant ), m_wp(), m_sign(), m_state(), m_msw(), m_lsw(),
  m_r_flag( false )
{
    if( a != 0 )
    {
        m_mant.clear();
	m_wp = m_msw = m_lsw = 2;
	m_state = normal;
	if( a > 0 )
	{
	    m_mant[2] = a;
	    m_sign = 1;
	}
	else
	{
	    m_mant[2] = -a;
	    m_sign = -1;
	}
    }
    else
        set_zero();
}

scfx_rep::scfx_rep( unsigned int a )
: m_mant( min_mant ), m_wp(), m_sign(), m_state(), m_msw(), m_lsw(),
  m_r_flag( false )
{
    if( a != 0 )
    {
        m_mant.clear();
	m_wp = m_msw = m_lsw = 2;
	m_state = normal;
	m_mant[2] = a;
	m_sign = 1;
    }
    else
        set_zero();
}

scfx_rep::scfx_rep( long a )
: m_mant( min_mant ), m_wp(), m_sign(), m_state(), m_msw(), m_lsw(),
  m_r_flag( false )
{
    if( a != 0 )
    {
        m_mant.clear();
	m_state = normal;
        if ( a > 0 )
        {
	    m_sign = 1;
        }
        else
        {
            a = -a;
            m_sign = -1;
        }
#       if defined(SC_LONG_64)
            m_wp = 1;
            m_mant[1] = static_cast<word>( a );
            m_mant[2] = static_cast<word>( a >> bits_in_word );
	    find_sw();
#       else
            m_wp = 2;
            m_msw = 2;
            m_lsw = 2;
            m_mant[2] = a;
#       endif

    }
    else
        set_zero();
}

scfx_rep::scfx_rep( unsigned long a )
: m_mant( min_mant ), m_wp(), m_sign(), m_state(), m_msw(), m_lsw(),
  m_r_flag( false )
{
    if( a != 0 )
    {
        m_mant.clear();
	m_wp = m_msw = m_lsw = 2;
	m_state = normal;
#       if defined(SC_LONG_64)
	    m_wp = 1;
	    m_mant[1] = static_cast<word>( a );
	    m_mant[2] = static_cast<word>( a >> bits_in_word );
	    find_sw();
#       else
	    m_wp = 2;
	    m_msw = 2;
	    m_lsw = 2;
	    m_mant[2] = a;
#	endif
	m_sign = 1;
    }
    else
        set_zero();
}

scfx_rep::scfx_rep( double a )
: m_mant( min_mant ), m_wp( 0 ), m_sign(), m_state( normal ), m_msw( 0 ),
  m_lsw( 0 ), m_r_flag( false )
{
    m_mant.clear();

    scfx_ieee_double id( a );

    m_sign = id.negative() ? -1 : 1;

    if( id.is_nan() )
        m_state = not_a_number;
    else if( id.is_inf() )
        m_state = infinity;
    else if( id.is_subnormal() )
    {
	m_mant[0] = id.mantissa1();
	m_mant[1] = id.mantissa0();
	normalize( id.exponent() + 1 - SCFX_IEEE_DOUBLE_M_SIZE );
    }
    else if( id.is_normal() )
    {
	m_mant[0] = id.mantissa1();
	m_mant[1] = id.mantissa0() | ( 1 << mantissa0_size );
	normalize( id.exponent() - SCFX_IEEE_DOUBLE_M_SIZE );
    }
}

scfx_rep::scfx_rep( int64 a )
: m_mant( min_mant ), m_wp(), m_sign(), m_state(), m_msw(), m_lsw(),
  m_r_flag( false )
{
    if( a != 0 )
    {
        m_mant.clear();
	m_wp = 1;
	m_state = normal;
	if( a > 0 )
	{
	    m_mant[1] = static_cast<word>( a );
	    m_mant[2] = static_cast<word>( a >> bits_in_word );
	    m_sign = 1;
	}
	else
	{
	    m_mant[1] = static_cast<word>( -a );
	    m_mant[2] = static_cast<word>( (-a) >> bits_in_word );
	    m_sign = -1;
	}
	find_sw();
    }
    else
        set_zero();
}

scfx_rep::scfx_rep( uint64 a )
: m_mant( min_mant ), m_wp(), m_sign(), m_state(), m_msw(), m_lsw(),
  m_r_flag( false )
{
    if( a != 0 )
    {
        m_mant.clear();
	m_wp = 1;
	m_state = normal;
	m_mant[1] = static_cast<word>( a );
	m_mant[2] = static_cast<word>( a >> bits_in_word );
	m_sign = 1;
	find_sw();
    }
    else
        set_zero();
}

scfx_rep::scfx_rep( const sc_signed& a )
: m_mant( min_mant ), m_wp(), m_sign(), m_state(), m_msw(), m_lsw(),
  m_r_flag( false )
{
    if( a.iszero() )
	set_zero();
    else
    {
	int words = n_word( a.length() );
	if( words > size() )
	    resize_to( words );
	m_mant.clear();
	m_wp = 0;
	m_state = normal;
	if( a.sign() )
	{
	    sc_signed a2 = -a;
	    for( int i = 0; i < a2.length(); ++ i )
	    {
		if( a2[i] )
		{
		    scfx_index x = calc_indices( i );
		    m_mant[x.wi()] |= 1 << x.bi();
		}
	    }
	    m_sign = -1;
	}
	else
	{
	    for( int i = 0; i < a.length(); ++ i )
	    {
		if( a[i] )
		{
		    scfx_index x = calc_indices( i );
		    m_mant[x.wi()] |= 1 << x.bi();
		}
	    }
	    m_sign = 1;
	}
	find_sw();
    }
}

scfx_rep::scfx_rep( const sc_unsigned& a )
: m_mant( min_mant ), m_wp(), m_sign(), m_state(), m_msw(), m_lsw(),
  m_r_flag( false )
{
    if( a.iszero() )
	set_zero();
    else
    {
	int words = n_word( a.length() );
	if( words > size() )
	    resize_to( words );
	m_mant.clear();
	m_wp = 0;
	m_state = normal;
	for( int i = 0; i < a.length(); ++ i )
	{
	    if( a[i] )
	    {
		scfx_index x = calc_indices( i );
		m_mant[x.wi()] |= 1 << x.bi();
	    }
	}
	m_sign = 1;
	find_sw();
    }
}


// copy constructor

scfx_rep::scfx_rep( const scfx_rep& a )
: m_mant( a.m_mant ), m_wp( a.m_wp ), m_sign( a.m_sign ), m_state( a.m_state ),
  m_msw( a.m_msw ), m_lsw( a.m_lsw ), m_r_flag( false )
{}


// ----------------------------------------------------------------------------
//  OPERATORS : new, delete
//
//  Memory management for class scfx_rep.
// ----------------------------------------------------------------------------

union scfx_rep_node
{
    char           data[sizeof( scfx_rep )];
    scfx_rep_node* next;
};


static scfx_rep_node* list = 0;


void*
scfx_rep::operator new( std::size_t size )
{
    const int ALLOC_SIZE = 1024;

    if( size != sizeof( scfx_rep ) )
	return ::operator new( size );

    if( ! list )
    {
	list = new scfx_rep_node[ALLOC_SIZE];
	for( int i = 0; i < ALLOC_SIZE - 1; i ++ )
	    list[i].next = list + i + 1;
	list[ALLOC_SIZE - 1].next = 0;
    }

    scfx_rep* ptr = reinterpret_cast<scfx_rep*>( list->data );
    list = list->next;

    return ptr;
}


void scfx_rep::operator delete( void* ptr, std::size_t size )
{
    if( size != sizeof( scfx_rep ) )
    {
	::operator delete( ptr );
	return;
    }

    scfx_rep_node* node = static_cast<scfx_rep_node*>( ptr );
    node->next = list;
    list = node;
}


// ----------------------------------------------------------------------------
//  METHOD : from_string
//
//  Convert from character string to sc_fxrep.
// ----------------------------------------------------------------------------

#define SCFX_FAIL_IF_(cnd)                                                    \
{                                                                             \
    if( ( cnd ) )                                                             \
    {                                                                         \
        m_state = not_a_number;                                               \
	m_mant.clear(); /* to avoid Purify UMRs during assignment */          \
        return;                                                               \
    }                                                                         \
}


void
scfx_rep::from_string( const char* s, int cte_wl )
{
    SCFX_FAIL_IF_( s == 0 || *s == 0 );

    scfx_string s2;
    s2 += s;
    s2 += '\0';

    bool sign_char;
    m_sign = scfx_parse_sign( s, sign_char );

    sc_numrep numrep = scfx_parse_prefix( s );

    int base = 0;

    switch( numrep )
    {
	case SC_DEC:
	{
	    base = 10;
	    if( scfx_is_nan( s ) )
	    {   // special case: NaN
		m_state = not_a_number;
		m_mant.clear(); /* to avoid Purify UMRs during assignment */
		return;
	    }
	    if( scfx_is_inf( s ) )
	    {   // special case: Infinity
		m_state = infinity;
		m_mant.clear(); /* to avoid Purify UMRs during assignment */
		return;
	    }
	    break;
	}
	case SC_BIN:
	case SC_BIN_US:
	{
	    SCFX_FAIL_IF_( sign_char );
	    base = 2;
	    break;
	}

	case SC_BIN_SM:
	{
	    base = 2;
	    break;
	}
	case SC_OCT:
	case SC_OCT_US:
	{
	    SCFX_FAIL_IF_( sign_char );
	    base = 8;
	    break;
	}
	case SC_OCT_SM:
	{
	    base = 8;
	    break;
	}
	case SC_HEX:
	case SC_HEX_US:
	{
	    SCFX_FAIL_IF_( sign_char );
	    base = 16;
	    break;
	}
	case SC_HEX_SM:
	{
	    base = 16;
	    break;
	}
	case SC_CSD:
	{
	    SCFX_FAIL_IF_( sign_char );
	    base = 2;
	    scfx_csd2tc( s2 );
	    s = (const char*) s2 + 4;
	    numrep = SC_BIN;
	    break;
	}
        default:;
    }

    //
    // find end of mantissa and count the digits and points
    //

    const char *end = s;
    bool based_point = false;
    int int_digits = 0;
    int frac_digits = 0;

    while( *end )
    {
	if( scfx_exp_start( end ) )
	    break;

	if( *end == '.' )
	{
	    SCFX_FAIL_IF_( based_point );
	    based_point = true;
	}
	else
	{
	    SCFX_FAIL_IF_( ! scfx_is_digit( *end, numrep ) );
	    if( based_point )
		frac_digits ++;
	    else
		int_digits ++;
	}

	++ end;
    }

    SCFX_FAIL_IF_( int_digits == 0 && frac_digits == 0 );

    // [ exponent ]

    int exponent = 0;

    if( *end )
    {
	for( const char *e = end + 2; *e; ++ e )
	    SCFX_FAIL_IF_( ! scfx_is_digit( *e, SC_DEC ) );
	exponent = atoi( end + 1 );
    }

    //
    // check if the mantissa is negative
    //

    bool mant_is_neg = false;

    switch( numrep )
    {
	case SC_BIN:
	case SC_OCT:
	case SC_HEX:
	{
	    const char* p = s;
	    if( *p == '.' )
		++ p;

	    mant_is_neg = ( scfx_to_digit( *p, numrep ) >= ( base >> 1 ) );

	    break;
	}
	default:
	    ;
    }

    //
    // convert the mantissa
    //

    switch( base )
    {
        case 2:
	{
	    int bit_offset = exponent % bits_in_word;
	    int word_offset = exponent / bits_in_word;

	    int_digits += bit_offset;
	    frac_digits -= bit_offset;

	    int words = n_word( int_digits ) + n_word( frac_digits );
	    if( words > size() )
		resize_to( words );
	    m_mant.clear();

	    int j = n_word( frac_digits ) * bits_in_word + int_digits - 1;

	    for( ; s < end; s ++ )
	    {
		switch( *s )
		{
		    case '1':
		        set_bin( j );
		    case '0':
			j --;
		    case '.':
			break;
		    default:
			SCFX_FAIL_IF_( true );  // should not happen
		}
	    }

	    m_wp = n_word( frac_digits ) - word_offset;
	    break;
	}
        case 8:
	{
	    exponent *= 3;
	    int_digits *= 3;
	    frac_digits *= 3;

	    int bit_offset = exponent % bits_in_word;
	    int word_offset = exponent / bits_in_word;

	    int_digits += bit_offset;
	    frac_digits -= bit_offset;

	    int words = n_word( int_digits ) + n_word( frac_digits );
	    if( words > size() )
		resize_to( words );
	    m_mant.clear();

	    int j = n_word( frac_digits ) * bits_in_word + int_digits - 3;

	    for( ; s < end; s ++ )
	    {
		switch( *s )
		{
		    case '7': case '6': case '5': case '4':
		    case '3': case '2': case '1':
		        set_oct( j, *s - '0' );
		    case '0':
			j -= 3;
		    case '.':
			break;
		    default:
			SCFX_FAIL_IF_( true );  // should not happen
		}
	    }

	    m_wp = n_word( frac_digits ) - word_offset;
	    break;
	}
        case 10:
	{
	    word carry, temp;
	    int length = int_digits + frac_digits;
	    resize_to( sc_max( min_mant, n_word( 4 * length ) ) );

	    m_mant.clear();
	    m_msw = m_lsw = 0;

	    for( ; s < end; s ++ )
	    {
		switch( *s )
		{
		    case '9': case '8': case '7': case '6': case '5':
		    case '4': case '3': case '2': case '1': case '0':
		        multiply_by_ten();
			carry = *s - '0';
			for ( int i = 0; carry && i < m_mant.size(); i++ )
			{
			    temp = m_mant[i];
                            temp += carry;
			    carry = temp < m_mant[i];
			    m_mant[i] = temp;
			}
		    case '.':
			break;
		    default:
			SCFX_FAIL_IF_( true );  // should not happen
		}
	    }

	    m_wp = 0;
	    find_sw();

	    int denominator = frac_digits - exponent;

	    if( denominator )
	    {
		scfx_rep frac_num = pow10_fx( denominator );
		scfx_rep* temp_num =
		    div_scfx_rep( const_cast<const scfx_rep&>( *this ),
				   frac_num, cte_wl );
		*this = *temp_num;
		delete temp_num;
	    }

	    break;
	}
        case 16:
	{
	    exponent *= 4;
	    int_digits *= 4;
	    frac_digits *= 4;

	    int bit_offset = exponent % bits_in_word;
	    int word_offset = exponent / bits_in_word;

	    int_digits += bit_offset;
	    frac_digits -= bit_offset;

	    int words = n_word( int_digits ) + n_word( frac_digits );
	    if( words > size() )
		resize_to( words );
	    m_mant.clear();

	    int j = n_word( frac_digits ) * bits_in_word + int_digits - 4;

	    for( ; s < end; s ++ )
	    {
		switch( *s )
		{
		    case 'f': case 'e': case 'd': case 'c': case 'b': case 'a':
		       set_hex( j, *s - 'a' + 10 );
		       j -= 4;
		       break;
		    case 'F': case 'E': case 'D': case 'C': case 'B': case 'A':
		       set_hex( j, *s - 'A' + 10 );
		       j -= 4;
		       break;
		    case '9': case '8': case '7': case '6': case '5':
		    case '4': case '3': case '2': case '1':
		       set_hex( j, *s - '0' );
		    case '0':
		       j -= 4;
		    case '.':
		       break;
		   default:
		       SCFX_FAIL_IF_( true );  // should not happen
		}
	    }

	    m_wp = n_word( frac_digits ) - word_offset;
	    break;
	}
    }

    m_state = normal;
    find_sw();

    //
    // two's complement of mantissa if it is negative
    //

    if( mant_is_neg )
    {
	m_mant[m_msw] |=  -1 << scfx_find_msb( m_mant[m_msw] );
	for( int i = m_msw + 1; i < m_mant.size(); ++ i )
	    m_mant[i] = static_cast<word>( -1 );
	complement( m_mant, m_mant, m_mant.size() );
	inc( m_mant );
	m_sign *= -1;
	find_sw();
    }
}


#undef SCFX_FAIL_IF_


// ----------------------------------------------------------------------------
//  METHOD : to_double
//
//  Convert from scfx_rep to double.
// ----------------------------------------------------------------------------

double
scfx_rep::to_double() const
{
    scfx_ieee_double id;

    // handle special cases

    if( is_nan() )
    {
        id.set_nan();
	return id;
    }

    if( is_inf() )
    {
        id.set_inf();
	id.negative( m_sign < 0 );
	return id;
    }

    if( is_zero() )
    {
	id = 0.;
	id.negative( m_sign < 0 );
	return id;
    }

    int msb = scfx_find_msb( m_mant[m_msw] );

    int exp = (m_msw - m_wp) * bits_in_word + msb;

    if( exp > SCFX_IEEE_DOUBLE_E_MAX )
    {
	id.set_inf();
	id.negative( m_sign < 0 );
	return id;
    }

    if( exp < SCFX_IEEE_DOUBLE_E_MIN
	- static_cast<int>( SCFX_IEEE_DOUBLE_M_SIZE ) )
    {
	id = 0.;
	return id;
    }

    int shift = mantissa0_size - msb;

    unsigned int m0;
    unsigned int m1 = 0;
    unsigned int guard = 0;

    if( shift == 0 )
    {
        m0 = m_mant[m_msw] & ~( 1 << mantissa0_size );
	if( m_msw > m_lsw )
	{
	    m1 = m_mant[m_msw - 1];
	    if( m_msw - 1 > m_lsw )
	        guard = m_mant[m_msw - 2] >> ( bits_in_word - 1 );
	}
    }
    else if( shift < 0 )
    {
	m0 = ( m_mant[m_msw] >> -shift ) & ~( 1 << mantissa0_size );
	m1 = m_mant[m_msw] << ( bits_in_word + shift );
	if( m_msw > m_lsw )
	{
	    m1 |= m_mant[m_msw - 1] >> -shift;
	    guard = ( m_mant[m_msw - 1] >> ( -shift - 1 ) ) & 1;
	}
    }
    else
    {
	m0 = ( m_mant[m_msw] << shift ) & ~( 1 << mantissa0_size );
	if( m_msw > m_lsw )
	{
	    m0 |= m_mant[m_msw - 1] >> ( bits_in_word - shift );
	    m1 = m_mant[m_msw - 1] << shift;
	    if( m_msw - 1 > m_lsw )
	    {
	        m1 |= m_mant[m_msw - 2] >> ( bits_in_word - shift );
		guard = ( m_mant[m_msw - 2] >> (bits_in_word - shift - 1) )
                      & 1;
	    }
	}
    }

    if( exp < SCFX_IEEE_DOUBLE_E_MIN )
    {
	m0 |= ( 1 << mantissa0_size );

	int subnormal_shift = SCFX_IEEE_DOUBLE_E_MIN - exp;

	if( subnormal_shift < bits_in_word )
	{
	    m1 = m1 >> subnormal_shift
	       | m0 << ( bits_in_word - subnormal_shift );
	    m0 = m0 >> subnormal_shift;
	}
	else
	{
	    m1 = m0 >> ( subnormal_shift - bits_in_word );
	    m0 = 0;
	}

	guard = 0;

	exp = SCFX_IEEE_DOUBLE_E_MIN - 1;
    }

    id.mantissa0( m0 );
    id.mantissa1( m1 );
    id.exponent( exp );
    id.negative( m_sign < 0 );

    double result = id;

    if( guard != 0 )
        result += m_sign * scfx_pow2( exp - SCFX_IEEE_DOUBLE_M_SIZE );

    return result;
}


// ----------------------------------------------------------------------------
//  METHOD : to_string
//
//  Convert from scfx_rep to character string.
// ----------------------------------------------------------------------------

void
print_dec( scfx_string& s, const scfx_rep& num, int w_prefix, sc_fmt fmt )
{
    if( num.is_neg() )
	s += '-';

    if( w_prefix == 1 ) {
	scfx_print_prefix( s, SC_DEC );
    }

    if( num.is_zero() )
    {
	s += '0';
	return;
    }

    // split 'num' into its integer and fractional part

    scfx_rep int_part  = num;
    scfx_rep frac_part = num;

    int i;

    for( i = int_part.m_lsw; i <= int_part.m_msw && i < int_part.m_wp; i ++ )
	int_part.m_mant[i] = 0;
    int_part.find_sw();
    if( int_part.m_wp < int_part.m_lsw )
	int_part.resize_to( int_part.size() - int_part.m_wp, -1 );

    for( i = frac_part.m_msw;
	 i >= frac_part.m_lsw && i >= frac_part.m_wp;
	 i -- )
	frac_part.m_mant[i] = 0;
    frac_part.find_sw();
    if( frac_part.m_msw == frac_part.size() - 1 )
	frac_part.resize_to( frac_part.size() + 1, 1 );

    // print integer part

    int int_digits = 0;
    int int_zeros  = 0;

    if( ! int_part.is_zero() )
    {
	double int_wl = ( int_part.m_msw - int_part.m_wp ) * bits_in_word
	              + scfx_find_msb( int_part.m_mant[int_part.m_msw] ) + 1;
	int_digits = (int) ceil( int_wl * log10( 2. ) );

	int len = s.length();
	s.append( int_digits );

	bool zero_digits = ( frac_part.is_zero() && fmt != SC_F );

	for( i = int_digits + len - 1; i >= len; i-- )
	{
	    unsigned int remainder = int_part.divide_by_ten();
	    s[i] = static_cast<char>( '0' + remainder );

	    if( zero_digits )
	    {
		if( remainder == 0 )
		    int_zeros ++;
		else
		    zero_digits = false;
	    }
	}

	// discard trailing zeros from int_part
	s.discard( int_zeros );

	if( s[len] == '0' )
	{
	    // int_digits was overestimated by one
	    s.remove( len );
	    -- int_digits;
	}
    }

    // print fractional part

    int frac_digits = 0;
    int frac_zeros  = 0;

    if( ! frac_part.is_zero() )
    {
	s += '.';

	bool zero_digits = ( int_digits == 0 && fmt != SC_F );

	double frac_wl = ( frac_part.m_wp - frac_part.m_msw ) * bits_in_word
	               - scfx_find_msb( frac_part.m_mant[frac_part.m_msw] )
                       - 1;
	frac_zeros = (int) floor( frac_wl * log10( 2. ) );

	scfx_rep temp;
	sc_dt::multiply( temp, frac_part, pow10_fx( frac_zeros ) );
	frac_part = temp;
	if( frac_part.m_msw == frac_part.size() - 1 )
	    frac_part.resize_to( frac_part.size() + 1, 1 );

	frac_digits = frac_zeros;
	if( ! zero_digits )
	{
	    for( i = 0; i < frac_zeros; i ++ )
		s += '0';
	    frac_zeros = 0;
	}

	while( ! frac_part.is_zero() )
	{
	    frac_part.multiply_by_ten();
	    int n = frac_part.m_mant[frac_part.m_msw + 1];

	    if( zero_digits )
	    {
		if( n == 0 )
		    frac_zeros ++;
		else
		    zero_digits = false;
	    }

	    if( ! zero_digits )
		s += static_cast<char>( '0' + n );

	    frac_part.m_mant[frac_part.m_msw + 1] = 0;
	    frac_digits ++;
	}
    }

    // print exponent

    if( fmt != SC_F )
    {
        if( frac_digits == 0 )
	    scfx_print_exp( s, int_zeros );
	else if( int_digits == 0 )
	    scfx_print_exp( s, - frac_zeros );
    }
}

void
print_other( scfx_string& s, const scfx_rep& a, sc_numrep numrep, int w_prefix,
	     sc_fmt fmt, const scfx_params* params )
{
    scfx_rep b = a;

    sc_numrep numrep2 = numrep;

    bool numrep_is_sm = ( numrep == SC_BIN_SM ||
			  numrep == SC_OCT_SM ||
			  numrep == SC_HEX_SM );

    if( numrep_is_sm )
    {
	if( b.is_neg() )
	{
	    s += '-';
	    b = *neg_scfx_rep( a );
	}
	switch( numrep )
	{
	    case SC_BIN_SM:
		numrep2 = SC_BIN_US;
		break;
	    case SC_OCT_SM:
		numrep2 = SC_OCT_US;
		break;
	    case SC_HEX_SM:
		numrep2 = SC_HEX_US;
		break;
	    default:
		;
	}
    }

    if( w_prefix != 0 ) {
	scfx_print_prefix( s, numrep );
    }

    numrep = numrep2;

    int msb, lsb;

    if( params != 0 )
    {
	msb = params->iwl() - 1;
	lsb = params->iwl() - params->wl();

	if( params->enc() == SC_TC_ &&
	    ( numrep == SC_BIN_US ||
	      numrep == SC_OCT_US ||
	      numrep == SC_HEX_US ) &&
	    ! numrep_is_sm &&
	    params->wl() > 1 )
	    -- msb;
	else if( params->enc() == SC_US_ &&
	    ( numrep == SC_BIN ||
	      numrep == SC_OCT ||
	      numrep == SC_HEX ||
	      numrep == SC_CSD ) )
	    ++ msb;
    }
    else
    {
	if( b.is_zero() )
	{
	    msb = 0;
	    lsb = 0;
	}
	else
	{
	    msb = ( b.m_msw - b.m_wp ) * bits_in_word
		+ scfx_find_msb( b.m_mant[ b.m_msw ] ) + 1;
	    while( b.get_bit( msb ) == b.get_bit( msb - 1 ) )
		-- msb;

	    if( numrep == SC_BIN_US ||
		numrep == SC_OCT_US ||
		numrep == SC_HEX_US )
		-- msb;

	    lsb = ( b.m_lsw - b.m_wp ) * bits_in_word
		+ scfx_find_lsb( b.m_mant[ b.m_lsw ] );
	}
    }

    int step;

    switch( numrep )
    {
	case SC_BIN:
	case SC_BIN_US:
	case SC_CSD:
	    step = 1;
	   break;
	case SC_OCT:
	case SC_OCT_US:
	    step = 3;
	    break;
	case SC_HEX:
	case SC_HEX_US:
	    step = 4;
	    break;
	default:
	    step = 0;
    }

    msb = (int) ceil( double( msb + 1 ) / step ) * step - 1;

    lsb = (int) floor( double( lsb ) / step ) * step;

    if( msb < 0 )
    {
	s += '.';
	if( fmt == SC_F )
	{
	    int sign = ( b.is_neg() ) ? ( 1 << step ) - 1 : 0;
	    for( int i = ( msb + 1 ) / step; i < 0; i ++ )
	    {
		if( sign < 10 )
		    s += static_cast<char>( sign + '0' );
		else
		    s += static_cast<char>( sign + 'a' - 10 );
	    }
	}
    }

    int i = msb;
    while( i >= lsb )
    {
        int value = 0;
        for( int j = step - 1; j >= 0; -- j )
	{
            value += static_cast<int>( b.get_bit( i ) ) << j;
            -- i;
        }
        if( value < 10 )
            s += static_cast<char>( value + '0' );
	else
            s += static_cast<char>( value + 'a' - 10 );
	if( i == -1 )
	    s += '.';
    }

    if( lsb > 0 && fmt == SC_F )
    {
	for( int i = lsb / step; i > 0; i -- )
	    s += '0';
    }

    if( s[s.length() - 1] == '.' )
	s.discard( 1 );

    if( fmt != SC_F )
    {
	if( msb < 0 )
	    scfx_print_exp( s, ( msb + 1 ) / step );
	else if( lsb > 0 )
	    scfx_print_exp( s, lsb / step );
    }

    if( numrep == SC_CSD )
	scfx_tc2csd( s, w_prefix );
}

const char*
scfx_rep::to_string( sc_numrep numrep, int w_prefix,
		     sc_fmt fmt, const scfx_params* params ) const
{
    static scfx_string s;

    s.clear();

    if( is_nan() )
        scfx_print_nan( s );
    else if( is_inf() )
        scfx_print_inf( s, is_neg() );
    else if( is_neg() && ! is_zero() &&
	     ( numrep == SC_BIN_US ||
	       numrep == SC_OCT_US ||
	       numrep == SC_HEX_US ) )
        s += "negative";
    else if( numrep == SC_DEC || numrep == SC_NOBASE )
        sc_dt::print_dec( s, *this, w_prefix, fmt );
    else
        sc_dt::print_other( s, *this, numrep, w_prefix, fmt, params );

    return s;
}


// ----------------------------------------------------------------------------
//  ADD
//
//  add two mantissas of the same size
//  result has the same size
//  returns carry of operation
// ----------------------------------------------------------------------------

static inline
int
add_mants( int size, scfx_mant& result,
	   const scfx_mant& a, const scfx_mant& b )
{
    unsigned int carry = 0;

    int index = 0;

    do
    {
        word x = a[index];
	word y = b[index];

	y += carry;
	carry = y < carry;
	y += x;
	carry += y < x;
	result[index] = y;
    }
    while( ++ index < size );

    return ( carry ? 1 : 0 );
}


static inline
int
sub_mants( int size, scfx_mant& result,
	   const scfx_mant& a, const scfx_mant& b )
{
    unsigned carry = 0;

    int index = 0;

    do
    {
	word x = a[index];
	word y = b[index];

	y += carry;
	carry = y < carry;
	y = x - y;
	carry += y > x;
	result[index] = y;
    }
    while( ++ index < size );

    return ( carry ? 1 : 0 );
}


scfx_rep*
add_scfx_rep( const scfx_rep& lhs, const scfx_rep& rhs, int max_wl )
{
    scfx_rep& result = *new scfx_rep;

    //
    // check for special cases
    //

    if( lhs.is_nan() || rhs.is_nan()
    ||  ( lhs.is_inf() && rhs.is_inf() && lhs.m_sign != rhs.m_sign ) )
    {
	result.set_nan();
	return &result;
    }

    if( lhs.is_inf() )
    {
	result.set_inf( lhs.m_sign );
	return &result;
    }

    if( rhs.is_inf() )
    {
	result.set_inf( rhs.m_sign );
	return &result;
    }

    //
    // align operands if needed
    //

    scfx_mant_ref lhs_mant;
    scfx_mant_ref rhs_mant;

    int len_mant = lhs.size();
    int new_wp = lhs.m_wp;

    align( lhs, rhs, new_wp, len_mant, lhs_mant, rhs_mant );

    //
    // size the result mantissa
    //

    result.resize_to( len_mant );
    result.m_wp = new_wp;

    //
    // do it
    //

    if( lhs.m_sign == rhs.m_sign )
    {
	add_mants( len_mant, result.m_mant, lhs_mant, rhs_mant );
	result.m_sign = lhs.m_sign;
    }
    else
    {
	int cmp = compare_abs( lhs, rhs );

	if( cmp == 1 )
	{
	    sub_mants( len_mant, result.m_mant, lhs_mant, rhs_mant );
	    result.m_sign = lhs.m_sign;
	}
	else if ( cmp == -1 )
	{
	    sub_mants( len_mant, result.m_mant, rhs_mant, lhs_mant );
	    result.m_sign = rhs.m_sign;
	}
	else
	{
	    result.m_mant.clear();
	    result.m_sign = 1;
	}
    }

    result.find_sw();
    result.round( max_wl );

    return &result;
}


// ----------------------------------------------------------------------------
//  SUB
//
//  sub two word's of the same size
//  result has the same size
//  returns carry of operation
// ----------------------------------------------------------------------------

static inline
int
sub_with_index(       scfx_mant& a, int a_msw, int /*a_lsw*/,
		const scfx_mant& b, int b_msw, int b_lsw )
{
    unsigned carry = 0;

    int size    = b_msw - b_lsw;
    int a_index = a_msw - size;
    int b_index = b_msw - size;

    do
    {
	word x = a[a_index];
	word y = b[b_index];

	y += carry;
	carry = y < carry;
	y = x - y;
	carry += y > x;
	a[a_index] = y;

	a_index ++;
	b_index ++;
    }
    while( size -- );

    if( carry )
    {
        // special case: a[a_msw + 1 ] == 1
        a[a_msw + 1] = 0;
    }

    return ( carry ? 1 : 0 );
}


scfx_rep*
sub_scfx_rep( const scfx_rep& lhs, const scfx_rep& rhs, int max_wl )
{
    scfx_rep& result = *new scfx_rep;

    //
    // check for special cases
    //

    if( lhs.is_nan() || rhs.is_nan()
    ||  ( lhs.is_inf() && rhs.is_inf() && lhs.m_sign == rhs.m_sign ) )
    {
	result.set_nan();
	return &result;
    }

    if( lhs.is_inf() )
    {
	result.set_inf( lhs.m_sign );
	return &result;
    }

    if( rhs.is_inf() )
    {
	result.set_inf( -1 * rhs.m_sign );
	return &result;
    }

    //
    // align operands if needed
    //

    scfx_mant_ref lhs_mant;
    scfx_mant_ref rhs_mant;

    int len_mant = lhs.size();
    int new_wp = lhs.m_wp;

    align( lhs, rhs, new_wp, len_mant, lhs_mant, rhs_mant );

    //
    // size the result mantissa
    //

    result.resize_to( len_mant );
    result.m_wp = new_wp;

    //
    // do it
    //

    if( lhs.m_sign != rhs.m_sign )
    {
	add_mants( len_mant, result.m_mant, lhs_mant, rhs_mant );
	result.m_sign = lhs.m_sign;
    }
    else
    {
	int cmp = compare_abs( lhs, rhs );

	if( cmp == 1 )
	{
	    sub_mants( len_mant, result.m_mant, lhs_mant, rhs_mant );
	    result.m_sign = lhs.m_sign;
	}
	else if ( cmp == -1 )
	{
	    sub_mants( len_mant, result.m_mant, rhs_mant, lhs_mant );
	    result.m_sign = -rhs.m_sign;
	} else {
	    result.m_mant.clear();
	    result.m_sign = 1;
	}
    }

    result.find_sw();
    result.round( max_wl );

    return &result;
}


// ----------------------------------------------------------------------------
//  MUL
// ----------------------------------------------------------------------------

union word_short
{
    word l;
    struct
    {
#if defined( SC_BIG_ENDIAN )
        half_word u;
        half_word l;
#elif defined( SC_LITTLE_ENDIAN )
        half_word l;
        half_word u;
#endif
    } s;
};


#if defined( SC_BIG_ENDIAN )
static const int half_word_incr = -1;
#elif defined( SC_LITTLE_ENDIAN )
static const int half_word_incr = 1;
#endif


void
multiply( scfx_rep& result, const scfx_rep& lhs, const scfx_rep& rhs,
	  int max_wl )
{
    //
    // check for special cases
    //

    if( lhs.is_nan() || rhs.is_nan()
    ||  (lhs.is_inf() && rhs.is_zero())
    ||  (lhs.is_zero() && rhs.is_inf()) )
    {
	result.set_nan();
	return;
    }

    if( lhs.is_inf() || rhs.is_inf() )
    {
	result.set_inf( lhs.m_sign * rhs.m_sign );
	return;
    }

    if( lhs.is_zero() || rhs.is_zero() ) {
	result.set_zero( lhs.m_sign * rhs.m_sign );
	return;
    }

    //
    // do it
    //

    int len_lhs = lhs.m_msw - lhs.m_lsw + 1;
    int len_rhs = rhs.m_msw - rhs.m_lsw + 1;

    int new_size = sc_max( min_mant, len_lhs + len_rhs );
    int new_wp   = ( lhs.m_wp - lhs.m_lsw ) + ( rhs.m_wp - rhs.m_lsw );
    int new_sign = lhs.m_sign * rhs.m_sign;

    result.resize_to( new_size );
    result.m_mant.clear();
    result.m_wp    = new_wp;
    result.m_sign  = new_sign;
    result.m_state = scfx_rep::normal;

    half_word *s1 = lhs.m_mant.half_addr( lhs.m_lsw );
    half_word *s2 = rhs.m_mant.half_addr( rhs.m_lsw );

    half_word *t = result.m_mant.half_addr();

    len_lhs <<= 1;
    len_rhs <<= 1;

    int i1, i2;

    for( i1 = 0; i1 * half_word_incr < len_lhs; i1 += half_word_incr )
    {
	word_short ls;
	ls.l = 0;

	half_word v1 = s1[i1];

	for( i2  = 0; i2 * half_word_incr < len_rhs; i2 += half_word_incr )
	{
	    ls.l  += v1 * s2[i2];
	    ls.s.l = ls.s.u + ( ( t[i2] += ls.s.l ) < ls.s.l );
	    ls.s.u = 0;
	}

	t[i2] = ls.s.l;
	t += half_word_incr;
    }

    result.find_sw();
    result.round( max_wl );
}


// ----------------------------------------------------------------------------
//  DIV
// ----------------------------------------------------------------------------

scfx_rep*
div_scfx_rep( const scfx_rep& lhs, const scfx_rep& rhs, int div_wl )
{
    scfx_rep& result = *new scfx_rep;

    //
    // check for special cases
    //

    if( lhs.is_nan() || rhs.is_nan() || (lhs.is_inf() && rhs.is_inf()) ||
	(lhs.is_zero() && rhs.is_zero()) )
    {
	result.set_nan();
	return &result;
    }

    if( lhs.is_inf() || rhs.is_zero() )
    {
	result.set_inf( lhs.m_sign * rhs.m_sign );
	return &result;
    }

    if( lhs.is_zero() || rhs.is_inf() )
    {
	result.set_zero( lhs.m_sign * rhs.m_sign );
	return &result;
    }

    //
    // do it
    //

    // compute one bit more for rounding
    div_wl ++;

    result.resize_to( sc_max( n_word( div_wl ) + 1, min_mant ) );
    result.m_mant.clear();
    result.m_sign = lhs.m_sign * rhs.m_sign;

    int msb_lhs = scfx_find_msb( lhs.m_mant[lhs.m_msw] )
	        + ( lhs.m_msw - lhs.m_wp ) * bits_in_word;
    int msb_rhs = scfx_find_msb( rhs.m_mant[rhs.m_msw] )
	        + ( rhs.m_msw - rhs.m_wp ) * bits_in_word;

    int msb_res = msb_lhs - msb_rhs;
    int to_shift = -msb_res % bits_in_word;
    int result_index;

    int c = ( msb_res % bits_in_word >= 0 ) ? 1 : 0;

    result_index = (result.size() - c) * bits_in_word + msb_res % bits_in_word;
    result.m_wp   = (result.size() - c) - msb_res / bits_in_word;

    scfx_rep remainder = lhs;

    // align msb from remainder to msb from rhs
    remainder.lshift( to_shift );

    // make sure msw( remainder ) < size - 1
    if( remainder.m_msw == remainder.size() - 1 )
	remainder.resize_to( remainder.size() + 1, 1 );

    // make sure msw( remainder ) >= msw( rhs )!
    int msw_diff = rhs.m_msw - remainder.m_msw;
    if (msw_diff > 0)
	remainder.resize_to( remainder.size() + msw_diff, -1 );

    int counter;

    for( counter = div_wl; counter && ! remainder.is_zero(); counter -- )
    {
	if( compare_msw_ff( rhs, remainder ) <= 0 )
	{
	    result.set_bin( result_index );
	    sub_with_index( remainder.m_mant, remainder.m_msw, remainder.m_lsw,
			    rhs.m_mant, rhs.m_msw, rhs.m_lsw );
	}
	result_index --;
	remainder.shift_left( 1 );
        remainder.m_lsw = remainder.find_lsw();
    }

    // perform convergent rounding, if needed
    if( counter == 0 )
    {
	int index = result_index + 1 - result.m_wp * bits_in_word;

	scfx_index x = result.calc_indices( index );
	scfx_index x1 = result.calc_indices( index + 1 );

	if( result.o_bit_at( x ) && result.o_bit_at( x1 ) )
	    result.q_incr( x );

	result.m_r_flag = true;
    }

    result.find_sw();

    return &result;
}


// ----------------------------------------------------------------------------
//  destructive shift mantissa to the left
// ----------------------------------------------------------------------------

void
scfx_rep::lshift( int n )
{
    if( n == 0 )
        return;

    if( n < 0 )
    {
        rshift( -n );
	return;
    }

    if( is_normal() )
    {
        int shift_bits  = n % bits_in_word;
	int shift_words = n / bits_in_word;

	// resize if needed
	if( m_msw == size() - 1 &&
	    scfx_find_msb( m_mant[m_msw] ) >= bits_in_word - shift_bits )
	    resize_to( size() + 1, 1 );

	// do it
	m_wp -= shift_words;
	shift_left( shift_bits );
	find_sw();
    }
}


// ----------------------------------------------------------------------------
//  destructive shift mantissa to the right
// ----------------------------------------------------------------------------

void
scfx_rep::rshift( int n )
{
    if( n == 0 )
        return;

    if( n < 0 )
    {
        lshift( -n );
	return;
    }

    if( is_normal() )
    {
        int shift_bits  = n % bits_in_word;
	int shift_words = n / bits_in_word;

	// resize if needed
	if( m_lsw == 0 && scfx_find_lsb( m_mant[m_lsw] ) < shift_bits )
	    resize_to( size() + 1, -1 );

	// do it
	m_wp += shift_words;
	shift_right( shift_bits );
	find_sw();
    }
}


// ----------------------------------------------------------------------------
//  FRIEND FUNCTION : compare_abs
//
//  Compares the absolute values of two scfx_reps, excluding the special cases.
// ----------------------------------------------------------------------------

int
compare_abs( const scfx_rep& a, const scfx_rep& b )
{
    // check for zero

    word a_word = a.m_mant[a.m_msw];
    word b_word = b.m_mant[b.m_msw];

    if( a_word == 0 || b_word == 0 )
    {
	if( a_word != 0 )
	    return 1;
	if( b_word != 0 )
	    return -1;
	return 0;
    }

    // compare msw index

    int a_msw = a.m_msw - a.m_wp;
    int b_msw = b.m_msw - b.m_wp;

    if( a_msw > b_msw )
	return 1;

    if( a_msw < b_msw )
	return -1;

    // compare content

    int a_i = a.m_msw;
    int b_i = b.m_msw;

    while( a_i >= a.m_lsw && b_i >= b.m_lsw )
    {
	a_word = a.m_mant[a_i];
	b_word = b.m_mant[b_i];
	if( a_word > b_word )
	    return 1;
	if( a_word < b_word )
	    return -1;
	-- a_i;
	-- b_i;
    }

    bool a_zero = true;
    while( a_i >= a.m_lsw )
    {
	a_zero = a_zero && ( a.m_mant[a_i] == 0 );
	-- a_i;
    }

    bool b_zero = true;
    while( b_i >= b.m_lsw )
    {
	b_zero = b_zero && ( b.m_mant[b_i] == 0 );
	-- b_i;
    }

    // assertion: a_zero || b_zero == true

    if( ! a_zero && b_zero )
	return 1;

    if( a_zero && ! b_zero )
	return -1;

    return 0;
}


// ----------------------------------------------------------------------------
//  FRIEND FUNCTION : cmp_scfx_rep
//
//  Compares the values of two scfx_reps, including the special cases.
// ----------------------------------------------------------------------------

int
cmp_scfx_rep( const scfx_rep& a, const scfx_rep& b )
{
    // handle special cases

    if( a.is_nan() || b.is_nan() )
    {
#if 0
	if( a.is_nan() && b.is_nan() )
	{
	    return 0;
	}
#endif
	return 2;
    }

    if( a.is_inf() || b.is_inf() )
    {
	if( a.is_inf() )
	{
	    if( ! a.is_neg() )
	    {
		if( b.is_inf() && ! b.is_neg() )
		{
		    return 0;
		}
		else
		{
		    return 1;
		}
	    }
	    else
	    {
		if( b.is_inf() && b.is_neg() )
		{
		    return 0;
		}
		else
		{
		    return -1;
		}
	    }
	}
	if( b.is_inf() )
	{
	    if( ! b.is_neg() )
	    {
		return -1;
	    }
	    else
	    {
		return 1;
	    }
	}
    }

    if( a.is_zero() && b.is_zero() )
    {
	return 0;
    }

    // compare sign

    if( a.m_sign != b.m_sign )
    {
	return a.m_sign;
    }

    return ( a.m_sign * compare_abs( a, b ) );
}


// ----------------------------------------------------------------------------
//  PRIVATE METHOD : quantization
//
//  Performs destructive quantization.
// ----------------------------------------------------------------------------

void
scfx_rep::quantization( const scfx_params& params, bool& q_flag )
{
    scfx_index x = calc_indices( params.iwl() - params.wl() );

    if( x.wi() < 0 )
        return;

    if( x.wi() >= size() )
        resize_to( x.wi() + 1, 1 );

    bool qb = q_bit( x );
    bool qz = q_zero( x );

    q_flag = ( qb || ! qz );

    if( q_flag )
    {
        switch( params.q_mode() )
	{
            case SC_TRN:			// truncation
	    {
	        if( is_neg() )
		    q_incr( x );
		break;
	    }
            case SC_RND:			// rounding to plus infinity
	    {
	        if( ! is_neg() )
		{
		    if( qb )
			q_incr( x );
		}
		else
		{
		    if( qb && ! qz )
			q_incr( x );
		}
		break;
	    }
            case SC_TRN_ZERO:			// truncation to zero
	    {
	        break;
	    }
            case SC_RND_INF:			// rounding to infinity
	    {
	        if( qb )
		    q_incr( x );
		break;
	    }
            case SC_RND_CONV:			// convergent rounding
	    {
		if( (qb && ! qz) || (qb && qz && q_odd( x )) )
		    q_incr( x );
		break;
	    }
            case SC_RND_ZERO:			// rounding to zero
	    {
		if( qb && ! qz )
		    q_incr( x );
		break;
	    }
            case SC_RND_MIN_INF:		// rounding to minus infinity
	    {
		if( ! is_neg() )
		{
		    if( qb && ! qz )
			q_incr( x );
		}
		else
		{
		    if( qb )
			q_incr( x );
		}
		break;
	    }
            default:
	        ;
	}
	q_clear( x );

	find_sw();
    }
}


// ----------------------------------------------------------------------------
//  PRIVATE METHOD : overflow
//
//  Performs destructive overflow handling.
// ----------------------------------------------------------------------------

void
scfx_rep::overflow( const scfx_params& params, bool& o_flag )
{
    scfx_index x = calc_indices( params.iwl() - 1 );

    if( x.wi() >= size() )
        resize_to( x.wi() + 1, 1 );

    if( x.wi() < 0 )
    {
        resize_to( size() - x.wi(), -1 );
        x.wi( 0 );
    }

    bool zero_left = o_zero_left( x );
    bool bit_at = o_bit_at( x );
    bool zero_right = o_zero_right( x );

    bool under = false;
    bool over = false;

    sc_enc enc = params.enc();

    if( enc == SC_TC_ )
    {
	if( is_neg() )
	{
	    if( params.o_mode() == SC_SAT_SYM )
		under = ( ! zero_left || bit_at );
	    else
		under = (! zero_left || (zero_left && bit_at && ! zero_right));
	}
	else
	    over = ( ! zero_left || bit_at );
    }
    else
    {
	if( is_neg() )
	    under = ( ! is_zero() );
        else
	    over = ( ! zero_left );
    }

    o_flag = ( under || over );

    if( o_flag )
    {
	scfx_index x2 = calc_indices( params.iwl() - params.wl() );

	if( x2.wi() < 0 )
	{
	    resize_to( size() - x2.wi(), -1 );
	    x.wi( x.wi() - x2.wi() );
	    x2.wi( 0 );
	}

	switch( params.o_mode() )
	{
            case SC_WRAP:			// wrap-around
	    {
		int n_bits = params.n_bits();

		if( n_bits == 0 )
		{
		    // wrap-around all 'wl' bits
		    toggle_tc();
		    o_extend( x, enc );
		    toggle_tc();
		}
		else if( n_bits < params.wl() )
		{
		    scfx_index x3 = calc_indices( params.iwl() - 1 - n_bits );

		    // wrap-around least significant 'wl - n_bits' bits;
		    // saturate most significant 'n_bits' bits
		    toggle_tc();
		    o_set( x, x3, enc, under );
		    o_extend( x, enc );
		    toggle_tc();
		}
		else
		{
		    // saturate all 'wl' bits
		    if( under )
			o_set_low( x, enc );
		    else
			o_set_high( x, x2, enc );
		}
		break;
	    }
            case SC_SAT:			// saturation
	    {
		if( under )
		    o_set_low( x, enc );
		else
		    o_set_high( x, x2, enc );
		break;
	    }
            case SC_SAT_SYM:			// symmetrical saturation
	    {
		if( under )
		{
		    if( enc == SC_TC_ )
			o_set_high( x, x2, SC_TC_, -1 );
		    else
			o_set_low( x, SC_US_ );
		}
		else
		    o_set_high( x, x2, enc );
		break;
	    }
            case SC_SAT_ZERO:			// saturation to zero
	    {
		set_zero();
		break;
	    }
            case SC_WRAP_SM:			// sign magnitude wrap-around
	    {
		SC_ERROR_IF_( enc == SC_US_,
			      sc_core::SC_ID_WRAP_SM_NOT_DEFINED_ );

		int n_bits = params.n_bits();

		if( n_bits == 0 )
		{
		    scfx_index x4 = calc_indices( params.iwl() );

		    if( x4.wi() >= size() )
			resize_to( x4.wi() + 1, 1 );

		    toggle_tc();
		    if( o_bit_at( x4 ) != o_bit_at( x ) )
			o_invert( x2 );
		    o_extend( x, SC_TC_ );
		    toggle_tc();
		}
		else if( n_bits == 1 )
		{
		    toggle_tc();
		    if( is_neg() != o_bit_at( x ) )
			o_invert( x2 );
		    o_extend( x, SC_TC_ );
		    toggle_tc();
		}
		else if( n_bits < params.wl() )
		{
		    scfx_index x3 = calc_indices( params.iwl() - 1 - n_bits );
		    scfx_index x4 = calc_indices( params.iwl() - n_bits );

		    // wrap-around least significant 'wl - n_bits' bits;
		    // saturate most significant 'n_bits' bits
		    toggle_tc();
		    if( is_neg() == o_bit_at( x4 ) )
			o_invert( x2 );
		    o_set( x, x3, SC_TC_, under );
		    o_extend( x, SC_TC_ );
		    toggle_tc();
		}
		else
		{
		    if( under )
			o_set_low( x, SC_TC_ );
		    else
			o_set_high( x, x2, SC_TC_ );
		}
		break;
	    }
            default:
	        ;
	}

	find_sw();
    }
}


// ----------------------------------------------------------------------------
//  PUBLIC METHOD : cast
//
//  Performs a destructive cast operation on a scfx_rep.
// ----------------------------------------------------------------------------

void
scfx_rep::cast( const scfx_params& params, bool& q_flag, bool& o_flag )
{
    q_flag = false;
    o_flag = false;

    // check for special cases

    if( is_zero() )
    {
	if( is_neg() )
	    m_sign = 1;
	return;
    }

    // perform casting

    quantization( params, q_flag );
    overflow( params, o_flag );

    // check for special case: -0

    if( is_zero() && is_neg() )
	m_sign = 1;
}


// ----------------------------------------------------------------------------
//  make sure, the two mantissas are aligned
// ----------------------------------------------------------------------------

void
align( const scfx_rep& lhs, const scfx_rep& rhs, int& new_wp,
       int& len_mant, scfx_mant_ref& lhs_mant, scfx_mant_ref& rhs_mant )
{
    bool need_lhs = true;
    bool need_rhs = true;

    if( lhs.m_wp != rhs.m_wp || lhs.size() != rhs.size() )
    {
	int lower_bound_lhs = lhs.m_lsw - lhs.m_wp;
	int upper_bound_lhs = lhs.m_msw - lhs.m_wp;
	int lower_bound_rhs = rhs.m_lsw - rhs.m_wp;
	int upper_bound_rhs = rhs.m_msw - rhs.m_wp;

	int lower_bound = sc_min( lower_bound_lhs, lower_bound_rhs );
	int upper_bound = sc_max( upper_bound_lhs, upper_bound_rhs );

	new_wp   = -lower_bound;
	len_mant = sc_max( min_mant, upper_bound - lower_bound + 1 );

	if( new_wp != lhs.m_wp || len_mant != lhs.size() )
	{
	    lhs_mant = lhs.resize( len_mant, new_wp );
	    need_lhs = false;
	}

	if( new_wp != rhs.m_wp || len_mant != rhs.size() )
        {
	    rhs_mant = rhs.resize( len_mant, new_wp );
	    need_rhs = false;
	}
    }

    if( need_lhs )
    {
	lhs_mant = lhs.m_mant;
    }

    if( need_rhs )
    {
	rhs_mant = rhs.m_mant;
    }
}


// ----------------------------------------------------------------------------
//  compare two mantissas
// ----------------------------------------------------------------------------

int
compare_msw_ff( const scfx_rep& lhs, const scfx_rep& rhs )
{
    // special case: rhs.m_mant[rhs.m_msw + 1] == 1
    if( rhs.m_msw < rhs.size() - 1 && rhs.m_mant[rhs.m_msw + 1 ] != 0 )
    {
	return -1;
    }

    int lhs_size = lhs.m_msw - lhs.m_lsw + 1;
    int rhs_size = rhs.m_msw - rhs.m_lsw + 1;

    int size = sc_min( lhs_size, rhs_size );

    int lhs_index = lhs.m_msw;
    int rhs_index = rhs.m_msw;

    int i;

    for( i = 0;
	 i < size && lhs.m_mant[lhs_index] == rhs.m_mant[rhs_index];
	 i ++ )
    {
	lhs_index --;
	rhs_index --;
    }

    if( i == size )
    {
	if( lhs_size == rhs_size )
	{
	    return 0;
	}

	if( lhs_size < rhs_size )
	{
	    return -1;
	}
	else
	{
	    return 1;
	}
  }

  if( lhs.m_mant[lhs_index] < rhs.m_mant[rhs_index] )
  {
      return -1;
  } else {
      return 1;
  }
}


// ----------------------------------------------------------------------------
//  divide the mantissa by ten
// ----------------------------------------------------------------------------

unsigned int
scfx_rep::divide_by_ten()
{
#if defined( SC_BIG_ENDIAN )
    half_word* hw = (half_word*) &m_mant[m_msw];
#elif defined( SC_LITTLE_ENDIAN )
    half_word* hw = ( (half_word*) &m_mant[m_msw] ) + 1;
#endif

    unsigned int remainder = 0;

    word_short ls;
    ls.l = 0;

#if defined( SC_BIG_ENDIAN )
    for( int i = 0, end = ( m_msw - m_wp + 1 ) * 2; i < end; i ++ )
#elif defined( SC_LITTLE_ENDIAN )
    for( int i = 0, end = -( m_msw - m_wp + 1 ) * 2; i > end; i -- )
#endif
    {
	ls.s.u = static_cast<half_word>( remainder );
	ls.s.l = hw[i];
	remainder = ls.l % 10;
	ls.l /= 10;
	hw[i] = ls.s.l;
    }

    return remainder;
}


// ----------------------------------------------------------------------------
//  multiply the mantissa by ten
// ----------------------------------------------------------------------------

void
scfx_rep::multiply_by_ten()
{
    int size = m_mant.size() + 1;

    scfx_mant mant8( size );
    scfx_mant mant2( size );

    size --;

    mant8[size] = (m_mant[size - 1] >> (bits_in_word - 3));
    mant2[size] = (m_mant[size - 1] >> (bits_in_word - 1));

    while( -- size )
    {
	mant8[size] = ( m_mant[size] << 3 ) |
	              ( m_mant[size - 1] >> ( bits_in_word - 3 ) );
	mant2[size] = ( m_mant[size] << 1 ) |
	              ( m_mant[size - 1] >> ( bits_in_word - 1 ) );
    }

    mant8[0] = ( m_mant[0] << 3 );
    mant2[0] = ( m_mant[0] << 1 );

    add_mants( m_mant.size(), m_mant, mant8, mant2 );

#if 0
    for( int i = size() - 1; i > 0; i -- )
    {
	m_mant[i] = ( m_mant[i] << 3 ) |
                    ( m_mant[i-1] >> ( bits_in_word - 3 ) )
	          + ( m_mant[i] << 1 ) |
                    ( m_mant[i-1] >> ( bits_in_word - 1 ) );
    }
    m_mant[0] = ( m_mant[0] << 3 ) + ( m_mant[0] << 1 );
#endif
}


// ----------------------------------------------------------------------------
//  normalize
// ----------------------------------------------------------------------------

void
scfx_rep::normalize( int exponent )
{
    int shift = exponent % bits_in_word;
    if( shift < 0 )
    {
	shift += bits_in_word;
    }

    if( shift )
    {
	shift_left( shift );
    }

    find_sw();

    m_wp = (shift - exponent) / bits_in_word;
}


// ----------------------------------------------------------------------------
//  return a new mantissa that is aligned and resized
// ----------------------------------------------------------------------------

scfx_mant*
scfx_rep::resize( int new_size, int new_wp ) const
{
    scfx_mant *result = new scfx_mant( new_size );

    result->clear();

    int shift = new_wp - m_wp;

    for( int j = m_lsw; j <= m_msw; j ++ )
    {
	(*result)[j+shift] = m_mant[j];
    }

    return result;
}


// ----------------------------------------------------------------------------
//  set a single bit
// ----------------------------------------------------------------------------

void
scfx_rep::set_bin( int i )
{
    m_mant[i >> 5] |= 1 << ( i & 31 );
}


// ----------------------------------------------------------------------------
//  set three bits
// ----------------------------------------------------------------------------

void
scfx_rep::set_oct( int i, int n )
{
    if( n & 1 )
    {
	m_mant[i >> 5] |= 1 << ( i & 31 );
    }
    i ++;
    if( n & 2 )
    {
	m_mant[i >> 5] |= 1 << ( i & 31 );
    }
    i ++;
    if( n & 4 )
    {
	m_mant[i >> 5] |= 1 << ( i & 31 );
    }
}


// ----------------------------------------------------------------------------
//  set four bits
// ----------------------------------------------------------------------------

void
scfx_rep::set_hex( int i, int n )
{
    if( n & 1 )
    {
	m_mant[i >> 5] |= 1 << ( i & 31 );
    }
    i ++;
    if( n & 2 )
    {
	m_mant[i >> 5] |= 1 << ( i & 31 );
    }
    i ++;
    if( n & 4 )
    {
	m_mant[i >> 5] |= 1 << ( i & 31 );
    }
    i ++;
    if( n & 8 )
    {
	m_mant[i >> 5] |= 1 << ( i & 31 );
    }
}


// ----------------------------------------------------------------------------
//  PRIVATE METHOD : shift_left
//
//  Shifts a scfx_rep to the left by a MAXIMUM of bits_in_word - 1 bits.
// ----------------------------------------------------------------------------

void
scfx_rep::shift_left( int n )
{
    if( n != 0 )
    {
	int shift_left  = n;
	int shift_right = bits_in_word - n;

	SC_ASSERT_( !(m_mant[size()-1] >> shift_right),
		    "shift_left overflow" );

	for( int i = size() - 1; i > 0; i -- )
	{
	    m_mant[i] = ( m_mant[i] << shift_left ) |
		       ( m_mant[i-1] >> shift_right );
	}
	m_mant[0] <<= shift_left;
    }
}


// ----------------------------------------------------------------------------
//  PRIVATE METHOD : shift_right
//
//  Shifts a scfx_rep to the right by a MAXIMUM of bits_in_word - 1 bits.
// ----------------------------------------------------------------------------

void
scfx_rep::shift_right( int n )
{
    if( n != 0 )
    {
	int shift_left  = bits_in_word - n;
	int shift_right = n;

	SC_ASSERT_( !(m_mant[0] << shift_left), "shift_right overflow" );

	for( int i = 0; i < size() - 1; i ++ )
	{
	    m_mant[i] = ( m_mant[i] >> shift_right ) |
		       ( m_mant[i+1] << shift_left );
	}
	m_mant[size()-1] >>= shift_right;
    }
}


// ----------------------------------------------------------------------------
//  METHOD : get_bit
//
//  Tests a bit, in two's complement.
// ----------------------------------------------------------------------------

bool
scfx_rep::get_bit( int i ) const
{
    if( ! is_normal() )
	return false;

    scfx_index x = calc_indices( i );

    if( x.wi() >= size() )
	return is_neg();

    if( x.wi() < 0 )
	return false;

    const_cast<scfx_rep*>( this )->toggle_tc();

    bool result = ( m_mant[x.wi()] & ( 1 << x.bi() ) ) != 0;

    const_cast<scfx_rep*>( this )->toggle_tc();

    return result;
}


// ----------------------------------------------------------------------------
//  METHOD : set
//
//  Sets a bit, in two's complement, between iwl-1 and -fwl.
// ----------------------------------------------------------------------------

bool
scfx_rep::set( int i, const scfx_params& params )
{
    if( ! is_normal() )
	return false;

    scfx_index x = calc_indices( i );

    if( x.wi() >= size() )
    {
	if( is_neg() )
	    return true;
	else
	    resize_to( x.wi() + 1, 1 );
    }
    else if( x.wi() < 0 )
    {
	resize_to( size() - x.wi(), -1 );
	x.wi( 0 );
    }

    toggle_tc();

    m_mant[x.wi()] |= 1 << x.bi();

    if( i == params.iwl() - 1 )
        o_extend( x, params.enc() );  // sign extension

    toggle_tc();

    find_sw();

    return true;
}


// ----------------------------------------------------------------------------
//  METHOD : clear
//
//  Clears a bit, in two's complement, between iwl-1 and -fwl.
// ----------------------------------------------------------------------------

bool
scfx_rep::clear( int i, const scfx_params& params )
{
    if( ! is_normal() )
	return false;

    scfx_index x = calc_indices( i );

    if( x.wi() >= size() )
    {
	if( ! is_neg() )
	    return true;
	else
	    resize_to( x.wi() + 1, 1 );
    }
    else if( x.wi() < 0 )
	return true;

    toggle_tc();

    m_mant[x.wi()] &= ~( 1 << x.bi() );

    if( i == params.iwl() - 1 )
        o_extend( x, params.enc() );  // sign extension

    toggle_tc();

    find_sw();

    return true;
}


// ----------------------------------------------------------------------------
//  METHOD : get_slice
// ----------------------------------------------------------------------------

bool
scfx_rep::get_slice( int i, int j, const scfx_params&,
		     sc_bv_base& bv ) const
{
    if( is_nan() || is_inf() )
	return false;

    // get the bits

    int l = j;
    for( int k = 0; k < bv.length(); ++ k )
    {
	bv[k] = get_bit( l );

	if( i >= j )
	    ++ l;
	else
	    -- l;
    }

    return true;
}

bool
scfx_rep::set_slice( int i, int j, const scfx_params& params,
		     const sc_bv_base& bv )
{
    if( is_nan() || is_inf() )
        return false;

    // set the bits

    int l = j;
    for( int k = 0; k < bv.length(); ++ k )
    {
	if( bv[k].to_bool() )
	    set( l, params );
	else
	    clear( l, params );

	if( i >= j )
	    ++ l;
	else
	    -- l;
    }

    return true;
}


// ----------------------------------------------------------------------------
//  METHOD : print
// ----------------------------------------------------------------------------

void
scfx_rep::print( ::std::ostream& os ) const
{
    os << to_string( SC_DEC, -1, SC_E );
}


// ----------------------------------------------------------------------------
//  METHOD : dump
// ----------------------------------------------------------------------------

void
scfx_rep::dump( ::std::ostream& os ) const
{
    os << "scfx_rep" << ::std::endl;
    os << "(" << ::std::endl;

    os << "mant  =" << ::std::endl;
    for( int i = size() - 1; i >= 0; i -- )
    {
	char buf[BUFSIZ];
	std::sprintf( buf, " %d: %10u (%8x)", i, (int) m_mant[i], (int) m_mant[i] );
	os << buf << ::std::endl;
    }

    os << "wp    = " << m_wp << ::std::endl;
    os << "sign  = " << m_sign << ::std::endl;

    os << "state = ";
    switch( m_state )
    {
        case normal:
	    os << "normal";
	    break;
        case infinity:
	    os << "infinity";
	    break;
        case not_a_number:
	    os << "not_a_number";
	    break;
        default:
	    os << "unknown";
    }
    os << ::std::endl;

    os << "msw   = " << m_msw << ::std::endl;
    os << "lsw   = " << m_lsw << ::std::endl;

    os << ")" << ::std::endl;
}


// ----------------------------------------------------------------------------
//  METHOD : get_type
// ----------------------------------------------------------------------------

void
scfx_rep::get_type( int& wl, int& iwl, sc_enc& enc ) const
{
    if( is_nan() || is_inf() )
    {
        wl  = 0;
        iwl = 0;
        enc = SC_TC_;
        return;
    }

    if( is_zero() )
    {
        wl  = 1;
        iwl = 1;
        enc = SC_US_;
        return;
    }

    int msb = ( m_msw - m_wp ) * bits_in_word
            + scfx_find_msb( m_mant[ m_msw ] ) + 1;
    while( get_bit( msb ) == get_bit( msb - 1 ) )
    {
        -- msb;
    }

    int lsb = ( m_lsw - m_wp ) * bits_in_word
            + scfx_find_lsb( m_mant[ m_lsw ] );

    if( is_neg() )
    {
        wl  = msb - lsb + 1;
        iwl = msb + 1;
        enc = SC_TC_;
    }
    else
    {
        wl  = msb - lsb;
        iwl = msb;
        enc = SC_US_;
    }
}


// ----------------------------------------------------------------------------
//  PRIVATE METHOD : round
//
//  Performs convergent rounding (rounding to even) as in floating-point.
// ----------------------------------------------------------------------------

void
scfx_rep::round( int wl )
{
    // check for special cases

    if( is_nan() || is_inf() || is_zero() )
	return;

    // estimate effective wordlength and compare

    int wl_effective;

    wl_effective = ( m_msw - m_lsw + 1 ) * bits_in_word;
    if( wl_effective <= wl )
	return;

    // calculate effective wordlength and compare

    int msb = scfx_find_msb( m_mant[m_msw] );
    int lsb = scfx_find_lsb( m_mant[m_lsw] );

    wl_effective = ( m_msw * bits_in_word + msb ) -
	           ( m_lsw * bits_in_word + lsb ) + 1;
    if( wl_effective <= wl )
	return;

    // perform rounding

    int wi = m_msw - ( wl - 1 ) / bits_in_word;
    int bi =  msb - ( wl - 1 ) % bits_in_word;
    if( bi < 0 )
    {
	-- wi;
	bi += bits_in_word;
    }

    scfx_index x( wi, bi );

    if( (q_bit( x ) && ! q_zero( x )) ||
	(q_bit( x ) && q_zero( x ) && q_odd( x )) )
	q_incr( x );
    q_clear( x );

    find_sw();

    m_r_flag = true;
}

} // namespace sc_dt


// Taf!