xref: /gem5/src/systemc/dt/fx/scfx_rep.cc

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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 <cctype>
#include <cmath>
#include <cstdio>
#include <cstdlib>

#include "base/compiler.hh"
#include "systemc/ext/dt/bit/sc_bv_base.hh"
#include "systemc/ext/dt/bit/sc_lv_base.hh"
#include "systemc/ext/dt/fx/scfx_ieee.hh"
#include "systemc/ext/dt/fx/scfx_pow10.hh"
#include "systemc/ext/dt/fx/scfx_rep.hh"
#include "systemc/ext/dt/fx/scfx_utils.hh"
#include "systemc/ext/utils/endian.hh"

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 = std::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);
                    M5_FALLTHROUGH;
                  case '0':
                    j--;
                    M5_FALLTHROUGH;
                  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');
                    M5_FALLTHROUGH;
                  case '0':
                    j -= 3;
                    M5_FALLTHROUGH;
                  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');
                    M5_FALLTHROUGH;
                  case '0':
                    j -= 4;
                    M5_FALLTHROUGH;
                  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] |=  ~0U << 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_uint64
//
//  Convert from scfx_rep to uint64.
//  Truncates towards 0 _then_ wraps; infinities and NaN go to zero.
// ----------------------------------------------------------------------------

uint64
scfx_rep::to_uint64() const
{
    if (!is_normal() || is_zero()) {
        return 0;
    }

    uint64 result = 0;
    int shift = 0;
    int idx = m_wp;

    // Ignore bits off the top; they modulo out.
    // Ignore bits off the bottom; we're truncating.
    while (shift < 64 && m_msw >= idx && idx >= m_lsw) {
        result += static_cast<uint64>(m_mant[idx]) << shift;
        shift += bits_in_word;
        idx += 1;
    }

    return m_sign > 0 ? result : -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)std::ceil(int_wl * std::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)std::floor(frac_wl * std::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:
        SC_REPORT_FATAL("assertion failed", "unexpected sc_numrep");
        sc_core::sc_abort();
    }

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

    lsb = (int)std::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_BOOST_BIG_ENDIAN)
        half_word u;
        half_word l;
#elif defined(SC_BOOST_LITTLE_ENDIAN)
        half_word l;
        half_word u;
#endif
    } s;
};

#if defined(SC_BOOST_BIG_ENDIAN)
static const int half_word_incr = -1;
#elif defined(SC_BOOST_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

    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()) {
        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_WRAP_SM not defined for unsigned numbers");

                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_BOOST_BIG_ENDIAN)
    half_word *hw = (half_word *)&m_mant[m_msw];
#elif defined(SC_BOOST_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_BOOST_BIG_ENDIAN)
    for (int i = 0, end = (m_msw - m_wp + 1) * 2; i < end; i++) {
#elif defined(SC_BOOST_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);
}


// ----------------------------------------------------------------------------
//  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