sc_signed.cc

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  Licensed to Accellera Systems Initiative Inc. (Accellera) under one or
  more contributor license agreements.  See the NOTICE file distributed
  with this work for additional information regarding copyright ownership.
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/*****************************************************************************
 
  sc_signed.cpp -- Arbitrary precision signed arithmetic.
 
                   This file includes the definitions of sc_signed_bitref,
                   sc_signed_subref, and sc_signed classes. The first two
                   classes are proxy classes to reference one bit and a range
                   of bits of a sc_signed number, respectively. This file also
                   includes sc_nbcommon.cpp and sc_nbfriends.cpp, which
                   contain the definitions shared by sc_unsigned.
 
  Original Author: Ali Dasdan, Synopsys, Inc.
 
 *****************************************************************************/
 
/*****************************************************************************
 
  MODIFICATION LOG - modifiers, enter your name, affiliation, date and
  changes you are making here.
 
      Name, Affiliation, Date:
  Description of Modification:
 
 *****************************************************************************/
 
 
// $Log: sc_signed.cpp,v $
// Revision 1.6  2011/02/18 20:19:15  acg
//  Andy Goodrich: updating Copyright notice.
//
// Revision 1.5  2008/12/10 20:38:45  acg
//  Andy Goodrich: fixed conversion of double values to the digits vector.
//  The bits above the radix were not being masked off.
//
// Revision 1.4  2008/06/19 17:47:56  acg
//  Andy Goodrich: fixes for bugs. See 2.2.1 RELEASENOTES.
//
// Revision 1.3  2008/04/29 21:20:41  acg
//  Andy Goodrich: added mask to first word transferred when processing
//  a negative sc_signed value in sc_signed::concat_get_data().
//
// Revision 1.2  2007/11/04 21:27:00  acg
//  Andy Goodrich: changes to make sure the proper value is returned from
//  concat_get_data().
//
// Revision 1.1.1.1  2006/12/15 20:20:05  acg
// SystemC 2.3
//
// Revision 1.5  2006/10/23 19:32:47  acg
//  Andy Goodrich: further fix for incorrect value being returned from
//  concat_get_data. This one is in the non-aligned value code.
//
// Revision 1.3  2006/01/13 18:49:32  acg
// Added $Log command so that CVS check in comments are reproduced in the
// source.
//
 
#include <cctype>
#include <cmath>
#include <sstream>
 
#include "systemc/ext/dt/bit/sc_bv_base.hh"
#include "systemc/ext/dt/bit/sc_lv_base.hh"
#include "systemc/ext/dt/fx/sc_fix.hh"
#include "systemc/ext/dt/fx/scfx_other_defs.hh"
#include "systemc/ext/dt/int/messages.hh"
#include "systemc/ext/dt/int/sc_int_base.hh"
#include "systemc/ext/dt/int/sc_signed.hh"
#include "systemc/ext/dt/int/sc_uint_base.hh"
#include "systemc/ext/dt/int/sc_unsigned.hh"
#include "systemc/ext/dt/misc/sc_concatref.hh"
 
// explicit template instantiations
namespace sc_core
{
 
template class sc_vpool<sc_dt::sc_signed_bitref>;
template class sc_vpool<sc_dt::sc_signed_subref>;
 
} // namespace sc_core
 
namespace sc_dt
{
 
// Pool of temporary instances:
 
sc_core::sc_vpool<sc_signed_bitref> sc_signed_bitref::m_pool(9);
sc_core::sc_vpool<sc_signed_subref> sc_signed_subref::m_pool(9);
 
void
sc_signed::invalid_init(const char *type_name, int nb) const
{
    std::stringstream msg;
    msg << "sc_signed("<< type_name << ") : nb = " << nb << " is not valid";
    SC_REPORT_ERROR(sc_core::SC_ID_INIT_FAILED_, msg.str().c_str());
}
 
// ----------------------------------------------------------------------------
// SECTION: Public members - Invalid selections.
// ----------------------------------------------------------------------------
 
void
sc_signed::invalid_index(int i) const
{
    std::stringstream msg;
    msg << "sc_bigint bit selection: index = " << i << " violates "
           "0 <= index <= " << (nbits - 1);
    SC_REPORT_ERROR(sc_core::SC_ID_OUT_OF_BOUNDS_, msg.str().c_str());
    sc_core::sc_abort(); // can't recover from here
}
 
void
sc_signed::invalid_range(int l, int r) const
{
    std::stringstream msg;
    msg << "sc_bigint part selection: left = " <<
           l << ", right = " << r << " \n"
           "  violates either (" << (nbits-1) << " >= left >= 0) or "
           "(" << (nbits-1) << " >= right >= 0)";
    SC_REPORT_ERROR(sc_core::SC_ID_OUT_OF_BOUNDS_, msg.str().c_str());
    sc_core::sc_abort(); // can't recover from here
}
 
 
// ----------------------------------------------------------------------------
 
// ----------------------------------------------------------------------------
//  SECTION: Public members.
// ----------------------------------------------------------------------------
 
// Most public members are included from sc_nbcommon.inc. However, some
// concatenation support appears here to optimize between the signed and
// unsigned cases.
 
// Insert this object's value at the specified place in a vector of biguint
// style values.
 
bool
sc_signed::concat_get_ctrl(sc_digit *dst_p, int low_i) const
{
    int dst_i; // Index to next word to set in dst_p.
    int end_i; // Index of high order word to set.
    int left_shift; // Amount to shift value left.
    sc_digit mask; // Mask for partial word sets.
 
    // CALCULATE METRICS FOR DATA MOVEMENT:
    dst_i = low_i / BITS_PER_DIGIT;
    end_i = (low_i + nbits - 1) / BITS_PER_DIGIT;
    left_shift = low_i % BITS_PER_DIGIT;
 
    // ALL DATA TO BE MOVED IS IN A SINGLE WORD:
    mask = ~(~0U << left_shift);
    dst_p[dst_i] = (dst_p[dst_i] & ~mask);
    dst_i++;
 
    for (; dst_i <= end_i; dst_i++)
        dst_p[dst_i] = 0;
 
    return false;
}
 
bool
sc_signed::concat_get_data(sc_digit *dst_p, int low_i) const
{
    sc_digit carry; // Carry bit for complements.
    int dst_i; // Index to next word to set in dst_p.
    int end_i; // Index of high order word to set.
    int high_i; // Index w/in word of high order bit.
    int left_shift; // Amount to shift value left.
    sc_digit left_word; // High word component for set.
    sc_digit mask; // Mask for partial word sets.
    bool result; // True if inserted non-zero data.
    int right_shift; // Amount to shift value right.
    sc_digit right_word; // Low word component for set.
    int src_i; // Index to next word to get from digit.
 
    // CALCULATE METRICS FOR DATA MOVEMENT:
    dst_i = low_i / BITS_PER_DIGIT;
    high_i = low_i + nbits - 1;
    end_i = high_i / BITS_PER_DIGIT;
    left_shift = low_i % BITS_PER_DIGIT;
 
    switch (sgn) {
      // POSITIVE SOURCE VALUE:
      case SC_POS:
        result = true;
 
        // ALL DATA TO BE MOVED IS IN A SINGLE WORD:
        if (dst_i == end_i) {
            mask = ~(~0U << left_shift);
            dst_p[dst_i] = ((dst_p[dst_i] & mask) |
                (digit[0] << left_shift)) & DIGIT_MASK;
 
        // DATA IS IN MORE THAN ONE WORD, BUT IS WORD ALIGNED:
        } else if (left_shift == 0) {
            for (src_i = 0; dst_i < end_i; dst_i++, src_i++) {
                dst_p[dst_i] = digit[src_i];
            }
            high_i = high_i % BITS_PER_DIGIT;
            mask = ~(~1U << high_i) & DIGIT_MASK;
            dst_p[dst_i] = digit[src_i] & mask;
 
        // DATA IS IN MORE THAN ONE WORD, AND NOT WORD ALIGNED:
        } else {
            high_i = high_i % BITS_PER_DIGIT;
            right_shift = BITS_PER_DIGIT - left_shift;
            mask = ~(~0U << left_shift);
            right_word = digit[0];
            dst_p[dst_i] = (dst_p[dst_i] & mask) |
                ((right_word << left_shift) & DIGIT_MASK);
            for (src_i = 1, dst_i++; dst_i < end_i; dst_i++, src_i++) {
                left_word = digit[src_i];
                dst_p[dst_i] = ((left_word << left_shift)&DIGIT_MASK) |
                    (right_word >> right_shift);
                right_word = left_word;
            }
            left_word = (src_i < ndigits) ? digit[src_i] : 0;
            mask = ~(~1U << high_i) & DIGIT_MASK;
            dst_p[dst_i] = ((left_word << left_shift) |
                (right_word >> right_shift)) & mask;
        }
        break;
 
      // SOURCE VALUE IS NEGATIVE:
      case SC_NEG:
        // ALL DATA TO BE MOVED IS IN A SINGLE WORD:
        result = true;
        if (dst_i == end_i) {
            mask = ~(~0U << nbits);
            right_word = ((digit[0] ^ DIGIT_MASK) + 1) & mask;
            mask = ~(~0U << left_shift);
            dst_p[dst_i] = ((dst_p[dst_i] & mask) |
                (right_word << left_shift)) & DIGIT_MASK;
 
        // DATA IS IN MORE THAN ONE WORD, BUT IS WORD ALIGNED:
        } else if (left_shift == 0) {
            carry = 1;
            for (src_i = 0; dst_i < end_i; dst_i++, src_i++) {
                right_word = (digit[src_i] ^ DIGIT_MASK) + carry;
                dst_p[dst_i] = right_word &  DIGIT_MASK;
                carry = right_word >> BITS_PER_DIGIT;
            }
            high_i = high_i % BITS_PER_DIGIT;
            mask = (~(~1U << high_i)) & DIGIT_MASK;
            right_word = (src_i < ndigits) ?
                (digit[src_i] ^ DIGIT_MASK) + carry : DIGIT_MASK + carry;
            dst_p[dst_i] = right_word & mask;
 
        // DATA IS IN MORE THAN ONE WORD, AND NOT WORD ALIGNED:
        } else {
            high_i = high_i % BITS_PER_DIGIT;
            right_shift = BITS_PER_DIGIT - left_shift;
            mask = ~(~0U << left_shift);
            carry = 1;
            right_word = (digit[0] ^ DIGIT_MASK) + carry;
            dst_p[dst_i] = (dst_p[dst_i] & mask) |
                ((right_word << left_shift) & DIGIT_MASK);
            carry = right_word >> BITS_PER_DIGIT;
            right_word &= DIGIT_MASK;
            for (src_i = 1, dst_i++; dst_i < end_i; dst_i++, src_i++) {
                left_word = (digit[src_i] ^ DIGIT_MASK) + carry;
                dst_p[dst_i] = ((left_word << left_shift)&DIGIT_MASK) |
                    (right_word >> right_shift);
                carry = left_word >> BITS_PER_DIGIT;
                right_word = left_word & DIGIT_MASK;
            }
            left_word = (src_i < ndigits) ?
                (digit[src_i] ^ DIGIT_MASK) + carry : carry;
            mask = ~(~1U << high_i) & DIGIT_MASK;
            dst_p[dst_i] = ((left_word << left_shift) |
                (right_word >> right_shift)) & mask;
        }
        break;
 
      // VALUE IS ZERO:
      default:
        result = false;
        // ALL DATA TO BE MOVED IS IN A SINGLE WORD:
        if (dst_i == end_i) {
            mask = ~(~0U << nbits) << left_shift;
            dst_p[dst_i] = dst_p[dst_i] & ~mask;
 
        // DATA IS IN MORE THAN ONE WORD, BUT IS WORD ALIGNED:
        } else if (left_shift == 0) {
            for (src_i = 0; dst_i < end_i; dst_i++, src_i++) {
                dst_p[dst_i] = 0;
            }
            dst_p[dst_i] = 0;
 
        // DATA IS IN MORE THAN ONE WORD, AND NOT WORD ALIGNED:
        } else {
            mask = ~(~0U << left_shift);
            dst_p[dst_i] = (dst_p[dst_i] & mask);
            for (dst_i++; dst_i <= end_i; dst_i++) {
                dst_p[dst_i] = 0;
            }
        }
        break;
    }
    return result;
}
 
// Return this object instance's bits as a uint64 without sign extension.
 
uint64
sc_signed::concat_get_uint64() const
{
    uint64        result;
    switch (sgn) {
      case SC_POS:
        result = 0;
        if (ndigits > 2)
            result = digit[2];
        if (ndigits > 1)
            result = (result << BITS_PER_DIGIT) | digit[1];
        result = (result << BITS_PER_DIGIT) | digit[0];
        break;
      case SC_NEG:
        result = 0;
        if (ndigits > 2)
            result = digit[2];
        if (ndigits > 1)
            result = (result << BITS_PER_DIGIT) | digit[1];
        result = (result << BITS_PER_DIGIT) | digit[0];
        result = -result;
        if (nbits < 64) {
            uint64 mask = ~0;
            result = result & ~(mask << nbits);
        }
        break;
      default:
        result = 0;
        break;
    }
    return result;
}
 
// #### OPTIMIZE
void
sc_signed::concat_set(int64 src, int low_i)
{
    *this = (low_i < 64) ? src >> low_i : src >> 63;
}
 
void
sc_signed::concat_set(const sc_signed &src, int low_i)
{
    if (low_i < src.length())
        *this = src >> low_i;
    else
        *this = (src<0) ? (int_type)-1 : 0;
}
 
void
sc_signed::concat_set(const sc_unsigned &src, int low_i)
{
    if (low_i < src.length())
        *this = src >> low_i;
    else
        *this = 0;
}
 
void
sc_signed::concat_set(uint64 src, int low_i)
{
    *this = (low_i < 64) ? src >> low_i : 0;
}
 
// ----------------------------------------------------------------------------
//  SECTION: Public members - Reduction methods.
// ----------------------------------------------------------------------------
 
bool
sc_signed::and_reduce() const
{
    sc_digit current; // Current digit examining.
    int i; // Index of digit examining.
 
    if (sgn == SC_NEG) {
        current = (1 << BITS_PER_DIGIT);
        for (i = 0; i < ndigits-1; i++) {
            current = (current >> BITS_PER_DIGIT) + (digit[i]^DIGIT_MASK);
            if ((current & DIGIT_MASK) != DIGIT_MASK) return false;
        }
        current = (current >> BITS_PER_DIGIT) + (digit[i]^DIGIT_MASK);
        if ((current & ~(~0U << (nbits % BITS_PER_DIGIT))) ==
             static_cast<sc_digit>(~(~0U << (nbits % BITS_PER_DIGIT)))) {
            return true;
        }
    }
    return false;
}
 
bool
sc_signed::or_reduce() const
{
    return sgn == SC_ZERO ? false : true;
}
 
bool
sc_signed::xor_reduce() const
{
    int i; // Digit examining.
    int odd; // Flag for odd number of digits.
 
    odd = 0;
    for (i = 0; i < nbits; i++)
        if (test(i))
            odd = ~odd;
    return odd ? true : false;
}
 
 
 
// ----------------------------------------------------------------------------
//  SECTION: Public members - Assignment operators.
// ----------------------------------------------------------------------------
 
// assignment operators
 
const sc_signed &
sc_signed::operator = (const char *a)
{
    if (a == 0) {
        SC_REPORT_ERROR(sc_core::SC_ID_CONVERSION_FAILED_,
                        "character string is zero");
    } else if (*a == 0) {
        SC_REPORT_ERROR(sc_core::SC_ID_CONVERSION_FAILED_,
                        "character string is empty");
    } else try {
        int len = length();
        sc_fix aa(a, len, len, SC_TRN, SC_WRAP, 0, SC_ON);
        return this->operator = (aa);
    } catch(const sc_core::sc_report &) {
        std::stringstream msg;
        msg << "character string '" << a << "' is not valid";
        SC_REPORT_ERROR(sc_core::SC_ID_CONVERSION_FAILED_, msg.str().c_str());
    }
    return *this;
}
 
const sc_signed &
sc_signed::operator=(int64 v)
{
    sgn = get_sign(v);
    // v >= 0 now.
    if (sgn == SC_ZERO) {
        vec_zero(ndigits, digit);
    } else {
        from_uint(ndigits, digit, (uint64)v);
        if (nbits <= (int)BITS_PER_INT64)
            convert_SM_to_2C_to_SM();
    }
    return *this;
}
 
const sc_signed &
sc_signed::operator=(uint64 v)
{
    sgn = get_sign(v);
    if (sgn == SC_ZERO) {
        vec_zero(ndigits, digit);
    } else {
        from_uint(ndigits, digit, v);
        if (nbits <= (int)BITS_PER_INT64)
            convert_SM_to_2C_to_SM();
    }
    return *this;
}
 
const sc_signed &
sc_signed::operator=(long v)
{
    sgn = get_sign(v);
    // v >= 0 now.
    if (sgn == SC_ZERO) {
        vec_zero(ndigits, digit);
    } else {
        from_uint(ndigits, digit, (unsigned long)v);
        if (nbits <= (int)BITS_PER_LONG)
            convert_SM_to_2C_to_SM();
    }
    return *this;
}
 
const sc_signed &
sc_signed::operator=(unsigned long v)
{
    sgn = get_sign(v);
    if (sgn == SC_ZERO) {
        vec_zero(ndigits, digit);
    } else {
        from_uint(ndigits, digit, v);
        if (nbits <= (int)BITS_PER_LONG)
            convert_SM_to_2C_to_SM();
    }
    return *this;
}
 
const sc_signed &
sc_signed::operator=(double v)
{
    is_bad_double(v);
    if (v < 0) {
        v = -v;
        sgn = SC_NEG;
    } else {
      sgn = SC_POS;
    }
 
    int i = 0;
    while (std::floor(v) && (i < ndigits)) {
        digit[i++] = ((sc_digit)std::floor(remainder(v, DIGIT_RADIX))) &
                                           DIGIT_MASK;
        v /= DIGIT_RADIX;
    }
    vec_zero(i, ndigits, digit);
    convert_SM_to_2C_to_SM();
    return *this;
}
 
 
// ----------------------------------------------------------------------------
 
const sc_signed &
sc_signed::operator = (const sc_bv_base &v)
{
    int minlen = sc_min(nbits, v.length());
    int i = 0;
    for (; i < minlen; ++i) {
        safe_set(i, v.get_bit(i), digit);
    }
    for (; i < nbits; ++i) {
        safe_set(i, 0, digit); // zero-extend
    }
    convert_2C_to_SM();
    return *this;
}
 
const sc_signed &
sc_signed::operator = (const sc_lv_base &v)
{
    int minlen = sc_min(nbits, v.length());
    int i = 0;
    for (; i < minlen; ++i) {
        safe_set(i, sc_logic(v.get_bit(i)).to_bool(), digit);
    }
    for (; i < nbits; ++i) {
        safe_set(i, 0, digit);  // zero-extend
    }
    convert_2C_to_SM();
    return *this;
}
 
 
// explicit conversion to character string
const std::string
sc_signed::to_string(sc_numrep numrep) const
{
    int len = length();
    sc_fix aa(*this, len, len, SC_TRN, SC_WRAP, 0, SC_ON);
    return aa.to_string(numrep);
}
 
const std::string
sc_signed::to_string(sc_numrep numrep, bool w_prefix) const
{
    int len = length();
    sc_fix aa(*this, len, len, SC_TRN, SC_WRAP, 0, SC_ON);
    return aa.to_string(numrep, w_prefix);
}
 
 
// ----------------------------------------------------------------------------
//  SECTION: Interfacing with sc_int_base
// ----------------------------------------------------------------------------
 
const sc_signed &
sc_signed::operator = (const sc_int_base &v)
{
    return operator = ((int64)v);
}
 
 
sc_signed
operator + (const sc_unsigned &u, const sc_int_base &v)
{
    return operator + (u, static_cast<int64>(v));
}
 
sc_signed
operator + (const sc_int_base &u, const sc_unsigned &v)
{
    return operator + (static_cast<int64>(u), v);
}
 
sc_signed
operator + (const sc_signed &u, const sc_int_base &v)
{
    return operator + (u, (int64)v);
}
 
sc_signed
operator + (const sc_int_base &u, const sc_signed &v)
{
    return operator + ((int64)u, v);
}
 
const sc_signed &
sc_signed::operator += (const sc_int_base &v)
{
    return operator += ((int64)v);
}
 
 
sc_signed
operator - (const sc_unsigned &u, const sc_int_base &v)
{
    return operator - (u, (int64)v);
}
 
sc_signed
operator - (const sc_int_base &u, const sc_unsigned &v)
{
    return operator - ((int64)u, v);
}
 
sc_signed
operator - (const sc_signed &u, const sc_int_base &v)
{
    return operator - (u, (int64)v);
}
 
sc_signed
operator - (const sc_int_base &u, const sc_signed &v)
{
    return operator - ((int64)u, v);
}
 
const sc_signed &
sc_signed::operator -= (const sc_int_base &v)
{
    return operator -= ((int64)v);
}
 
 
sc_signed
operator * (const sc_unsigned &u, const sc_int_base &v)
{
    return operator * (u, static_cast<int64>(v));
}
 
sc_signed
operator * (const sc_int_base &u, const sc_unsigned &v)
{
    return operator * (static_cast<int64>(u), v);
}
 
sc_signed
operator * (const sc_signed &u, const sc_int_base &v)
{
    return operator * (u, (int64)v);
}
 
sc_signed
operator * (const sc_int_base &u, const sc_signed &v)
{
    return operator * ((int64)u, v);
}
 
const sc_signed &
sc_signed::operator *= (const sc_int_base &v)
{
    return operator *= ((int64)v);
}
 
 
sc_signed
operator / (const sc_unsigned &u, const sc_int_base &v)
{
    return operator / (u, static_cast<int64>(v));
}
 
sc_signed
operator / (const sc_int_base &u, const sc_unsigned &v)
{
    return operator / (static_cast<int64>(u), v);
}
 
sc_signed
operator / (const sc_signed &u, const sc_int_base &v)
{
    return operator / (u, (int64)v);
}
 
sc_signed
operator / (const sc_int_base &u, const sc_signed &v)
{
    return operator / ((int64)u, v);
}
 
const sc_signed &
sc_signed::operator /= (const sc_int_base &v)
{
    return operator /= ((int64)v);
}
 
 
sc_signed
operator % (const sc_unsigned &u, const sc_int_base &v)
{
    return operator % (u, static_cast<int64>(v));
}
 
sc_signed
operator % (const sc_int_base &u, const sc_unsigned &v)
{
    return operator % (static_cast<int64>(u), v);
}
 
sc_signed
operator % (const sc_signed &u, const sc_int_base &v)
{
    return operator % (u, (int64)v);
}
 
sc_signed
operator % (const sc_int_base &u, const sc_signed &v)
{
    return operator % ((int64)u, v);
}
 
const sc_signed &
sc_signed::operator %= (const sc_int_base &v)
{
    return operator %= ((int64)v);
}
 
 
sc_signed
operator & (const sc_unsigned &u, const sc_int_base &v)
{
    return operator & (u, static_cast<int64>(v));
}
 
sc_signed
operator & (const sc_int_base &u, const sc_unsigned &v)
{
    return operator & (static_cast<int64>(u), v);
}
 
sc_signed
operator & (const sc_signed &u, const sc_int_base &v)
{
    return operator & (u, (int64)v);
}
 
sc_signed
operator & (const sc_int_base &u, const sc_signed &v)
{
    return operator & ((int64)u, v);
}
 
const sc_signed &
sc_signed::operator &= (const sc_int_base &v)
{
    return operator &= ((int64)v);
}
 
 
sc_signed
operator | (const sc_unsigned &u, const sc_int_base &v)
{
    return operator | (u, static_cast<int64>(v));
}
 
sc_signed
operator | (const sc_int_base &u, const sc_unsigned &v)
{
    return operator | (static_cast<int64>(u), v);
}
 
sc_signed
operator | (const sc_signed& u, const sc_int_base &v)
{
    return operator|(u, (int64)v);
}
 
sc_signed
operator | (const sc_int_base &u, const sc_signed &v)
{
    return operator | ((int64)u, v);
}
 
const sc_signed &
sc_signed::operator |= (const sc_int_base &v)
{
    return operator |= ((int64)v);
}
 
 
sc_signed
operator ^ (const sc_unsigned &u, const sc_int_base &v)
{
    return operator ^ (u, static_cast<int64>(v));
}
 
sc_signed
operator ^ (const sc_int_base &u, const sc_unsigned &v)
{
    return operator ^ (static_cast<int64>(u), v);
}
 
sc_signed
operator ^ (const sc_signed &u, const sc_int_base &v)
{
    return operator ^ (u, (int64)v);
}
 
sc_signed
operator ^ (const sc_int_base &u, const sc_signed &v)
{
    return operator ^ ((int64)u, v);
}
 
const sc_signed &
sc_signed::operator ^= (const sc_int_base &v)
{
    return operator ^= ((int64)v);
}
 
 
sc_signed
operator << (const sc_signed &u, const sc_int_base &v)
{
    return operator << (u, (int64)v);
}
 
const sc_signed &
sc_signed::operator <<= (const sc_int_base &v)
{
    return operator <<= ((int64)v);
}
 
 
sc_signed
operator >> (const sc_signed &u, const sc_int_base &v)
{
    return operator >> (u, (int64)v);
}
 
const sc_signed &
sc_signed::operator >>= (const sc_int_base &v)
{
    return operator >>= ((int64)v);
}
 
 
bool
operator == (const sc_signed &u, const sc_int_base &v)
{
    return operator == (u, (int64)v);
}
 
bool
operator == (const sc_int_base &u, const sc_signed &v)
{
    return operator == ((int64)u, v);
}
 
 
bool
operator != (const sc_signed &u, const sc_int_base &v)
{
    return operator != (u, (int64)v);
}
 
bool
operator != (const sc_int_base &u, const sc_signed &v)
{
    return operator != ((int64)u, v);
}
 
 
bool
operator < (const sc_signed &u, const sc_int_base &v)
{
    return operator < (u, (int64)v);
}
 
bool
operator  <  (const sc_int_base &u, const sc_signed &v)
{
    return operator < ((int64)u, v);
}
 
 
bool
operator  <=  (const sc_signed &u, const sc_int_base &v)
{
    return operator <= (u, (int64)v);
}
 
bool
operator  <=  (const sc_int_base &u, const sc_signed &v)
{
    return operator <= ((int64)u, v);
}
 
 
bool
operator  >  (const sc_signed &u, const sc_int_base &v)
{
    return operator > (u, (int64)v);
}
 
bool
operator  >  (const sc_int_base &u, const sc_signed &v)
{
    return operator > ((int64)u, v);
}
 
 
bool
operator  >=  (const sc_signed &u, const sc_int_base &v)
{
    return operator >= (u, (int64)v);
}
 
bool
operator  >=  (const sc_int_base &u, const sc_signed &v)
{
    return operator >= ((int64)u, v);
}
 
 
// ----------------------------------------------------------------------------
//  SECTION: Interfacing with sc_uint_base
// ----------------------------------------------------------------------------
 
const sc_signed &
sc_signed::operator = (const sc_uint_base &v)
{
    return operator = ((uint64)v);
}
 
 
sc_signed
operator + (const sc_signed &u, const sc_uint_base &v)
{
    return operator + (u, (uint64)v);
}
 
sc_signed
operator + (const sc_uint_base &u, const sc_signed &v)
{
    return operator + ((uint64)u, v);
}
 
const sc_signed &
sc_signed::operator += (const sc_uint_base &v)
{
    return operator += ((uint64)v);
}
 
 
sc_signed
operator - (const sc_unsigned &u, const sc_uint_base &v)
{
    return operator - (u, (uint64)v);
}
 
sc_signed
operator - (const sc_uint_base &u, const sc_unsigned &v)
{
    return operator - ((uint64)u, v);
}
 
sc_signed
operator - (const sc_signed &u, const sc_uint_base &v)
{
    return operator - (u, (uint64)v);
}
 
sc_signed
operator - (const sc_uint_base &u, const sc_signed &v)
{
    return operator - ((uint64)u, v);
}
 
const sc_signed &
sc_signed::operator -= (const sc_uint_base &v)
{
    return operator -= ((uint64)v);
}
 
 
sc_signed
operator * (const sc_signed &u, const sc_uint_base &v)
{
    return operator * (u, (uint64)v);
}
 
sc_signed
operator * (const sc_uint_base &u, const sc_signed &v)
{
    return operator * ((uint64)u, v);
}
 
const sc_signed &
sc_signed::operator *= (const sc_uint_base &v)
{
    return operator *= ((uint64)v);
}
 
 
sc_signed
operator / (const sc_signed &u, const sc_uint_base &v)
{
    return operator / (u, (uint64)v);
}
 
sc_signed
operator / (const sc_uint_base &u, const sc_signed &v)
{
    return operator / ((uint64)u, v);
}
 
const sc_signed &
sc_signed::operator /= (const sc_uint_base &v)
{
    return operator /= ((uint64)v);
}
 
 
sc_signed
operator % (const sc_signed &u, const sc_uint_base &v)
{
    return operator % (u, (uint64)v);
}
 
sc_signed
operator % (const sc_uint_base &u, const sc_signed &v)
{
    return operator % ((uint64)u, v);
}
 
const sc_signed&
sc_signed::operator %= (const sc_uint_base &v)
{
    return operator %= ((uint64)v);
}
 
 
sc_signed
operator & (const sc_signed &u, const sc_uint_base &v)
{
    return operator & (u, (uint64)v);
}
 
sc_signed
operator & (const sc_uint_base &u, const sc_signed &v)
{
    return operator & ((uint64)u, v);
}
 
const sc_signed &
sc_signed::operator &= (const sc_uint_base &v)
{
    return operator &= ((uint64)v);
}
 
 
sc_signed
operator | (const sc_signed &u, const sc_uint_base &v)
{
    return operator | (u, (uint64)v);
}
 
sc_signed
operator | (const sc_uint_base &u, const sc_signed &v)
{
    return operator | ((uint64)u, v);
}
 
const sc_signed &
sc_signed::operator |= (const sc_uint_base &v)
{
    return operator |= ((uint64)v);
}
 
 
sc_signed
operator ^ (const sc_signed &u, const sc_uint_base &v)
{
    return operator ^ (u, (uint64)v);
}
 
sc_signed
operator ^ (const sc_uint_base &u, const sc_signed &v)
{
    return operator ^ ((uint64)u, v);
}
 
const sc_signed &
sc_signed::operator ^= (const sc_uint_base &v)
{
    return operator ^= ((uint64)v);
}
 
 
sc_signed
operator << (const sc_signed &u, const sc_uint_base &v)
{
    return operator << (u, (uint64)v);
}
 
const sc_signed &
sc_signed::operator <<= (const sc_uint_base &v)
{
    return operator <<= ((uint64)v);
}
 
 
sc_signed
operator >> (const sc_signed& u, const sc_uint_base& v)
{
    return operator >> (u, (uint64)v);
}
 
const sc_signed &
sc_signed::operator >>= (const sc_uint_base& v)
{
    return operator >>= ((uint64)v);
}
 
 
bool
operator == (const sc_signed &u, const sc_uint_base &v)
{
    return operator == (u, (uint64)v);
}
 
bool
operator == (const sc_uint_base &u, const sc_signed &v)
{
    return operator == ((uint64)u, v);
}
 
 
bool
operator != (const sc_signed &u, const sc_uint_base &v)
{
    return operator != (u, (uint64)v);
}
 
bool
operator != (const sc_uint_base &u, const sc_signed &v)
{
    return operator != ((uint64)u, v);
}
 
 
bool
operator < (const sc_signed &u, const sc_uint_base &v)
{
    return operator < (u, (uint64)v);
}
 
bool
operator < (const sc_uint_base &u, const sc_signed &v)
{
    return operator < ((uint64)u, v);
}
 
 
bool
operator <= (const sc_signed &u, const sc_uint_base &v)
{
    return operator <= (u, (uint64)v);
}
 
bool
operator <= (const sc_uint_base &u, const sc_signed &v)
{
    return operator <= ((uint64)u, v);
}
 
 
bool
operator > (const sc_signed &u, const sc_uint_base &v)
{
    return operator > (u, (uint64)v);
}
 
bool
operator > (const sc_uint_base &u, const sc_signed &v)
{
    return operator > ((uint64)u, v);
}
 
 
bool
operator >= (const sc_signed &u, const sc_uint_base &v)
{
    return operator >= (u, (uint64)v);
}
 
bool
operator >= (const sc_uint_base &u, const sc_signed &v)
{
    return operator >= ((uint64)u, v);
}
 
 
// ----------------------------------------------------------------------------
//  SECTION: Input and output operators
// ----------------------------------------------------------------------------
 
// Operators in this section are included from sc_nbcommon.cpp.
 
 
// ----------------------------------------------------------------------------
//  SECTION: Operator macros.
// ----------------------------------------------------------------------------
 
#define CONVERT_LONG(u) \
small_type u ## s = get_sign(u); \
sc_digit u ## d[DIGITS_PER_ULONG]; \
from_uint(DIGITS_PER_ULONG, u ## d, (unsigned long) u);
 
#define CONVERT_LONG_2(u) \
sc_digit u ## d[DIGITS_PER_ULONG]; \
from_uint(DIGITS_PER_ULONG, u ## d, (unsigned long) u);
 
#define CONVERT_INT(u) \
small_type u ## s = get_sign(u); \
sc_digit u ## d[DIGITS_PER_UINT]; \
from_uint(DIGITS_PER_UINT, u ## d, (unsigned int) u);
 
#define CONVERT_INT_2(u) \
sc_digit u ## d[DIGITS_PER_UINT]; \
from_uint(DIGITS_PER_UINT, u ## d, (unsigned int) u);
 
#define CONVERT_INT64(u) \
small_type u ## s = get_sign(u); \
sc_digit u ## d[DIGITS_PER_UINT64]; \
from_uint(DIGITS_PER_UINT64, u ## d, (uint64) u);
 
#define CONVERT_INT64_2(u) \
sc_digit u ## d[DIGITS_PER_UINT64]; \
from_uint(DIGITS_PER_UINT64, u ## d, (uint64) u);
 
 
// ----------------------------------------------------------------------------
//  SECTION: PLUS operators: +, +=, ++
// ----------------------------------------------------------------------------
 
// Cases to consider when computing u + v:
// 1. 0 + v = v
// 2. u + 0 = u
// 3. if sgn(u) == sgn(v)
//    3.1 u + v = +(u + v) = sgn(u) * (u + v)
//    3.2 (-u) + (-v) = -(u + v) = sgn(u) * (u + v)
// 4. if sgn(u) != sgn(v)
//    4.1 u + (-v) = u - v = sgn(u) * (u - v)
//    4.2 (-u) + v = -(u - v) ==> sgn(u) * (u - v)
//
// Specialization of above cases for computing ++u or u++:
// 1. 0 + 1 = 1
// 3. u + 1 = u + 1 = sgn(u) * (u + 1)
// 4. (-u) + 1 = -(u - 1) = sgn(u) * (u - 1)
 
sc_signed
operator + (const sc_unsigned &u, const sc_signed &v)
{
    if (u.sgn == SC_ZERO) // case 1
        return sc_signed(v);
 
    if (v.sgn == SC_ZERO) // case 2
        return sc_signed(u);
 
    // cases 3 and 4
    return add_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator + (const sc_signed &u, const sc_unsigned &v)
{
    if (u.sgn == SC_ZERO) // case 1
        return sc_signed(v);
 
    if (v.sgn == SC_ZERO) // case 2
        return sc_signed(u);
 
    // cases 3 and 4
    return add_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator + (const sc_signed &u, const sc_signed &v)
{
    if (u.sgn == SC_ZERO) // case 1
        return sc_signed(v);
 
    if (v.sgn == SC_ZERO) // case 2
        return sc_signed(u);
 
    // cases 3 and 4
    return add_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator + (const sc_signed &u, int64 v)
{
    if (v == 0) // case 2
        return sc_signed(u);
 
    CONVERT_INT64(v);
 
    if (u.sgn == SC_ZERO) // case 1
        return sc_signed(vs, BITS_PER_UINT64, DIGITS_PER_UINT64, vd, false);
 
    // cases 3 and 4
    return add_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             vs, BITS_PER_UINT64, DIGITS_PER_UINT64, vd);
}
 
 
sc_signed
operator + (int64 u, const sc_signed &v)
{
    if (u == 0) // case 1
        return sc_signed(v);
 
    CONVERT_INT64(u);
 
    if (v.sgn == SC_ZERO) // case 2
        return sc_signed(us, BITS_PER_UINT64, DIGITS_PER_UINT64, ud, false);
 
    // cases 3 and 4
    return add_signed_friend(us, BITS_PER_UINT64, DIGITS_PER_UINT64, ud,
                             v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator + (const sc_unsigned &u, int64 v)
{
    if (v == 0) // case 2
        return sc_signed(u);
 
    CONVERT_INT64(v);
 
    if (u.sgn == SC_ZERO) // case 1
        return sc_signed(vs, BITS_PER_UINT64, DIGITS_PER_UINT64, vd, false);
 
    // cases 3 and 4
    return add_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             vs, BITS_PER_UINT64, DIGITS_PER_UINT64, vd);
}
 
 
sc_signed
operator + (int64 u, const sc_unsigned &v)
{
    if (u == 0) // case 1
        return sc_signed(v);
 
    CONVERT_INT64(u);
 
    if (v.sgn == SC_ZERO) // case 2
        return sc_signed(us, BITS_PER_UINT64, DIGITS_PER_UINT64, ud, false);
 
    // cases 3 and 4
    return add_signed_friend(us, BITS_PER_UINT64, DIGITS_PER_UINT64, ud,
                             v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator + (const sc_signed &u, uint64 v)
{
    if (v == 0) // case 2
        return sc_signed(u);
 
    CONVERT_INT64(v);
 
    if (u.sgn == SC_ZERO) // case 1
        return sc_signed(vs, BITS_PER_UINT64, DIGITS_PER_UINT64, vd, false);
 
    // cases 3 and 4
    return add_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             vs, BITS_PER_UINT64, DIGITS_PER_UINT64, vd);
}
 
 
sc_signed
operator + (uint64 u, const sc_signed &v)
{
    if (u == 0) // case 1
        return sc_signed(v);
 
    CONVERT_INT64(u);
 
    if (v.sgn == SC_ZERO) // case 2
        return sc_signed(us, BITS_PER_UINT64, DIGITS_PER_UINT64, ud, false);
 
    // cases 3 and 4
    return add_signed_friend(us, BITS_PER_UINT64, DIGITS_PER_UINT64, ud,
                             v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator + (const sc_signed &u, long v)
{
    if (v == 0) // case 2
        return sc_signed(u);
 
    CONVERT_LONG(v);
 
    if (u.sgn == SC_ZERO) // case 1
        return sc_signed(vs, BITS_PER_ULONG, DIGITS_PER_ULONG, vd, false);
 
    // cases 3 and 4
    return add_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             vs, BITS_PER_ULONG, DIGITS_PER_ULONG, vd);
}
 
 
sc_signed
operator + (long u, const sc_signed &v)
{
    if (u == 0) // case 1
        return sc_signed(v);
 
    CONVERT_LONG(u);
 
    if (v.sgn == SC_ZERO) // case 2
        return sc_signed(us, BITS_PER_ULONG, DIGITS_PER_ULONG, ud, false);
 
    // cases 3 and 4
    return add_signed_friend(us, BITS_PER_ULONG, DIGITS_PER_ULONG, ud,
                             v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator + (const sc_unsigned &u, long v)
{
    if (v == 0) // case 2
        return sc_signed(u);
 
    CONVERT_LONG(v);
 
    if (u.sgn == SC_ZERO) // case 1
        return sc_signed(vs, BITS_PER_ULONG, DIGITS_PER_ULONG, vd, false);
 
    // cases 3 and 4
    return add_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             vs, BITS_PER_ULONG, DIGITS_PER_ULONG, vd);
}
 
 
sc_signed
operator + (long u, const sc_unsigned &v)
{
    if (u == 0) // case 1
        return sc_signed(v);
 
    CONVERT_LONG(u);
 
    if (v.sgn == SC_ZERO) // case 2
        return sc_signed(us, BITS_PER_ULONG, DIGITS_PER_ULONG, ud, false);
 
    // cases 3 and 4
    return add_signed_friend(us, BITS_PER_ULONG, DIGITS_PER_ULONG, ud,
                             v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator + (const sc_signed &u, unsigned long v)
{
    if (v == 0) // case 2
        return sc_signed(u);
 
    CONVERT_LONG(v);
 
    if (u.sgn == SC_ZERO) // case 1
        return sc_signed(vs, BITS_PER_ULONG, DIGITS_PER_ULONG, vd, false);
 
    // cases 3 and 4
    return add_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             vs, BITS_PER_ULONG, DIGITS_PER_ULONG, vd);
}
 
 
sc_signed
operator + (unsigned long u, const sc_signed &v)
{
    if (u == 0) // case 1
        return sc_signed(v);
 
    CONVERT_LONG(u);
 
    if (v.sgn == SC_ZERO)  // case 2
        return sc_signed(us, BITS_PER_ULONG, DIGITS_PER_ULONG, ud, false);
 
    // cases 3 and 4
    return add_signed_friend(us, BITS_PER_ULONG, DIGITS_PER_ULONG, ud,
                             v.sgn, v.nbits, v.ndigits, v.digit);
}
 
// The rest of the operators in this section are included from
// sc_nbcommon.cpp.
 
// ----------------------------------------------------------------------------
//  SECTION: MINUS operators: -, -=, --
// ----------------------------------------------------------------------------
 
// Cases to consider when computing u + v:
// 1. u - 0 = u
// 2. 0 - v = -v
// 3. if sgn(u) != sgn(v)
//    3.1 u - (-v) = u + v = sgn(u) * (u + v)
//    3.2 (-u) - v = -(u + v) ==> sgn(u) * (u + v)
// 4. if sgn(u) == sgn(v)
//    4.1 u - v = +(u - v) = sgn(u) * (u - v)
//    4.2 (-u) - (-v) = -(u - v) = sgn(u) * (u - v)
//
// Specialization of above cases for computing --u or u--:
// 1. 0 - 1 = -1
// 3. (-u) - 1 = -(u + 1) = sgn(u) * (u + 1)
// 4. u - 1 = u - 1 = sgn(u) * (u - 1)
 
sc_signed
operator - (const sc_unsigned &u, const sc_unsigned &v)
{
    if (v.sgn == SC_ZERO)  // case 1
        return sc_signed(u);
 
    if (u.sgn == SC_ZERO) // case 2
        return sc_signed(v, -v.sgn);
 
    // cases 3 and 4
    return add_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             -v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator - (const sc_unsigned &u, const sc_signed &v)
{
    if (v.sgn == SC_ZERO) // case 1
        return sc_signed(u);
 
    if (u.sgn == SC_ZERO) // case 2
        return sc_signed(v, -v.sgn);
 
    // cases 3 and 4
    return add_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             -v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator - (const sc_signed &u, const sc_unsigned &v)
{
    if (v.sgn == SC_ZERO) // case 1
        return sc_signed(u);
 
    if (u.sgn == SC_ZERO) // case 2
        return sc_signed(v, -v.sgn);
 
    // cases 3 and 4
    return add_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             -v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator - (const sc_signed &u, const sc_signed &v)
{
    if (v.sgn == SC_ZERO)  // case 1
        return sc_signed(u);
 
    if (u.sgn == SC_ZERO) // case 2
        return sc_signed(v, -v.sgn);
 
    // cases 3 and 4
    return add_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             -v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator - (const sc_signed &u, int64 v)
{
    if (v == 0) // case 1
        return sc_signed(u);
 
    CONVERT_INT64(v);
 
    if (u.sgn == SC_ZERO) // case 2
        return sc_signed(-vs, BITS_PER_UINT64, DIGITS_PER_UINT64, vd, false);
 
    // cases 3 and 4
    return add_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             -vs, BITS_PER_UINT64, DIGITS_PER_UINT64, vd);
}
 
 
sc_signed
operator - (int64 u, const sc_signed &v)
{
    if (u == 0) // case 1
        return sc_signed(v, -v.sgn);
 
    CONVERT_INT64(u);
 
    if (v.sgn == SC_ZERO) // case 2
        return sc_signed(us, BITS_PER_UINT64, DIGITS_PER_UINT64, ud, false);
 
    // cases 3 and 4
    return add_signed_friend(us, BITS_PER_UINT64, DIGITS_PER_UINT64, ud,
                             -v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator - (const sc_unsigned &u, int64 v)
{
    if (v == 0) // case 1
        return sc_signed(u);
 
    CONVERT_INT64(v);
 
    if (u.sgn == SC_ZERO) // case 2
        return sc_signed(-vs, BITS_PER_UINT64, DIGITS_PER_UINT64, vd, false);
 
    // cases 3 and 4
    return add_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             -vs, BITS_PER_UINT64, DIGITS_PER_UINT64, vd);
}
 
 
sc_signed
operator - (int64 u, const sc_unsigned &v)
{
    if (u == 0) // case 1
        return sc_signed(v, -v.sgn);
 
    CONVERT_INT64(u);
 
    if (v.sgn == SC_ZERO) // case 2
        return sc_signed(us, BITS_PER_UINT64, DIGITS_PER_UINT64, ud, false);
 
    // cases 3 and 4
    return add_signed_friend(us, BITS_PER_UINT64, DIGITS_PER_UINT64, ud,
                             -v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator - (const sc_signed &u, uint64 v)
{
    if (v == 0) // case 1
        return sc_signed(u);
 
    CONVERT_INT64(v);
 
    if (u.sgn == SC_ZERO) // case 2
        return sc_signed(-vs, BITS_PER_UINT64, DIGITS_PER_UINT64, vd, false);
 
    // cases 3 and 4
 
    return add_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             -vs, BITS_PER_UINT64, DIGITS_PER_UINT64, vd);
}
 
 
sc_signed
operator - (uint64 u, const sc_signed &v)
{
    if (u == 0) // case 1
        return sc_signed(v, -v.sgn);
 
    CONVERT_INT64(u);
 
    if (v.sgn == SC_ZERO) // case 2
        return sc_signed(us, BITS_PER_UINT64, DIGITS_PER_UINT64, ud, false);
 
    // cases 3 and 4
    return add_signed_friend(us, BITS_PER_UINT64, DIGITS_PER_UINT64, ud,
                             -v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator - (const sc_unsigned &u, uint64 v)
{
    if (v == 0) // case 1
        return sc_signed(u);
 
    CONVERT_INT64(v);
 
    if (u.sgn == SC_ZERO) // case 2
        return sc_signed(-vs, BITS_PER_UINT64, DIGITS_PER_UINT64, vd, false);
 
    // cases 3 and 4
    return add_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             -vs, BITS_PER_UINT64, DIGITS_PER_UINT64, vd);
}
 
 
sc_signed
operator - (uint64 u, const sc_unsigned &v)
{
    if (u == 0) // case 1
        return sc_signed(v, -v.sgn);
 
    CONVERT_INT64(u);
 
    if (v.sgn == SC_ZERO) // case 2
        return sc_signed(us, BITS_PER_UINT64, DIGITS_PER_UINT64, ud, false);
 
    // cases 3 and 4
    return add_signed_friend(us, BITS_PER_UINT64, DIGITS_PER_UINT64, ud,
                             -v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator - (const sc_signed &u, long v)
{
    if (v == 0) // case 1
        return sc_signed(u);
 
    CONVERT_LONG(v);
 
    if (u.sgn == SC_ZERO) // case 2
        return sc_signed(-vs, BITS_PER_ULONG, DIGITS_PER_ULONG, vd, false);
 
    // cases 3 and 4
    return add_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             -vs, BITS_PER_ULONG, DIGITS_PER_ULONG, vd);
}
 
 
sc_signed
operator - (long u, const sc_signed &v)
{
    if (u == 0) // case 1
        return sc_signed(v, -v.sgn);
 
    CONVERT_LONG(u);
 
    if (v.sgn == SC_ZERO) // case 2
        return sc_signed(us, BITS_PER_ULONG, DIGITS_PER_ULONG, ud, false);
 
    // cases 3 and 4
    return add_signed_friend(us, BITS_PER_ULONG, DIGITS_PER_ULONG, ud,
                             -v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator - (const sc_unsigned &u, long v)
{
    if (v == 0) // case 1
        return sc_signed(u);
 
    CONVERT_LONG(v);
 
    if (u.sgn == SC_ZERO) // case 2
        return sc_signed(-vs, BITS_PER_ULONG, DIGITS_PER_ULONG, vd, false);
 
    // cases 3 and 4
    return add_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             -vs, BITS_PER_ULONG, DIGITS_PER_ULONG, vd);
}
 
 
sc_signed
operator - (long u, const sc_unsigned &v)
{
    if (u == 0) // case 1
        return sc_signed(v, -v.sgn);
 
    CONVERT_LONG(u);
 
    if (v.sgn == SC_ZERO) // case 2
        return sc_signed(us, BITS_PER_ULONG, DIGITS_PER_ULONG, ud, false);
 
    // cases 3 and 4
    return add_signed_friend(us, BITS_PER_ULONG, DIGITS_PER_ULONG, ud,
                             -v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator - (const sc_signed &u, unsigned long v)
{
    if (v == 0) // case 1
        return sc_signed(u);
 
    CONVERT_LONG(v);
 
    if (u.sgn == SC_ZERO) // case 2
        return sc_signed(-vs, BITS_PER_ULONG, DIGITS_PER_ULONG, vd, false);
 
    // cases 3 and 4
    return add_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             -vs, BITS_PER_ULONG, DIGITS_PER_ULONG, vd);
}
 
 
sc_signed
operator - (unsigned long u, const sc_signed &v)
{
    if (u == 0) // case 1
        return sc_signed(v, -v.sgn);
 
    CONVERT_LONG(u);
 
    if (v.sgn == SC_ZERO) // case 2
        return sc_signed(us, BITS_PER_ULONG, DIGITS_PER_ULONG, ud, false);
 
    // cases 3 and 4
    return add_signed_friend(us, BITS_PER_ULONG, DIGITS_PER_ULONG, ud,
                             -v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator - (const sc_unsigned &u, unsigned long v)
{
    if (v == 0) // case 1
        return sc_signed(u);
 
    CONVERT_LONG(v);
 
    if (u.sgn == SC_ZERO) // case 2
        return sc_signed(-vs, BITS_PER_ULONG, DIGITS_PER_ULONG, vd, false);
 
    // cases 3 and 4
    return add_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             -vs, BITS_PER_ULONG, DIGITS_PER_ULONG, vd);
}
 
 
sc_signed
operator - (unsigned long u, const sc_unsigned &v)
{
    if (u == 0) // case 1
        return sc_signed(v, -v.sgn);
 
    CONVERT_LONG(u);
 
    if (v.sgn == SC_ZERO) // case 2
        return sc_signed(us, BITS_PER_ULONG, DIGITS_PER_ULONG, ud, false);
 
    // cases 3 and 4
    return add_signed_friend(us, BITS_PER_ULONG, DIGITS_PER_ULONG, ud,
                             -v.sgn, v.nbits, v.ndigits, v.digit);
}
 
// The rest of the operators in this section are included from
// sc_nbcommon.cpp.
 
 
// ----------------------------------------------------------------------------
//  SECTION: MULTIPLICATION operators: *, *=
// ----------------------------------------------------------------------------
 
// Cases to consider when computing u * v:
// 1. u * 0 = 0 * v = 0
// 2. 1 * v = v and -1 * v = -v
// 3. u * 1 = u and u * -1 = -u
// 4. u * v = u * v
 
sc_signed
operator * (const sc_unsigned &u, const sc_signed &v)
{
    small_type s = mul_signs(u.sgn, v.sgn);
 
    if (s == SC_ZERO) // case 1
        return sc_signed();
 
    // cases 2-4
    return mul_signed_friend(s, u.nbits, u.ndigits, u.digit,
                             v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator * (const sc_signed &u, const sc_unsigned &v)
{
    small_type s = mul_signs(u.sgn, v.sgn);
 
    if (s == SC_ZERO) // case 1
        return sc_signed();
 
    // cases 2-4
    return mul_signed_friend(s, u.nbits, u.ndigits, u.digit,
                             v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator * (const sc_signed &u, const sc_signed &v)
{
    small_type s = mul_signs(u.sgn, v.sgn);
 
    if (s == SC_ZERO) // case 1
        return sc_signed();
 
    // cases 2-4
    return mul_signed_friend(s, u.nbits, u.ndigits, u.digit,
                             v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator * (const sc_signed &u, int64 v)
{
    small_type s = mul_signs(u.sgn, get_sign(v));
 
    if (s == SC_ZERO) // case 1
        return sc_signed();
 
    CONVERT_INT64_2(v);
 
    // cases 2-4
    return mul_signed_friend(s, u.nbits, u.ndigits, u.digit,
                             BITS_PER_UINT64, DIGITS_PER_UINT64, vd);
}
 
 
sc_signed
operator * (int64 u, const sc_signed &v)
{
    small_type s = mul_signs(v.sgn, get_sign(u));
 
    if (s == SC_ZERO) // case 1
        return sc_signed();
 
    CONVERT_INT64_2(u);
 
    // cases 2-4
    return mul_signed_friend(s, BITS_PER_UINT64, DIGITS_PER_UINT64, ud,
                             v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator * (const sc_unsigned &u, int64 v)
{
    small_type s = mul_signs(u.sgn, get_sign(v));
 
    if (s == SC_ZERO) // case 1
        return sc_signed();
 
    CONVERT_INT64_2(v);
 
    // cases 2-4
    return mul_signed_friend(s, u.nbits, u.ndigits, u.digit,
                             BITS_PER_UINT64, DIGITS_PER_UINT64, vd);
}
 
 
sc_signed
operator * (int64 u, const sc_unsigned &v)
{
    small_type s = mul_signs(v.sgn, get_sign(u));
 
    if (s == SC_ZERO) // case 1
        return sc_signed();
 
    CONVERT_INT64_2(u);
 
    // cases 2-4
    return mul_signed_friend(s, BITS_PER_UINT64, DIGITS_PER_UINT64, ud,
                             v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator * (const sc_signed &u, uint64 v)
{
    small_type s = mul_signs(u.sgn, get_sign(v));
 
    if (s == SC_ZERO) // case 1
        return sc_signed();
 
    CONVERT_INT64_2(v);
 
    // cases 2-4
    return mul_signed_friend(s, u.nbits, u.ndigits, u.digit,
                             BITS_PER_UINT64, DIGITS_PER_UINT64, vd);
}
 
 
sc_signed
operator * (uint64 u, const sc_signed &v)
{
    small_type s = mul_signs(v.sgn, get_sign(u));
 
    if (s == SC_ZERO) // case 1
        return sc_signed();
 
    CONVERT_INT64_2(u);
 
    // cases 2-4
    return mul_signed_friend(s, BITS_PER_UINT64, DIGITS_PER_UINT64, ud,
                             v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator * (const sc_signed &u, long v)
{
    small_type s = mul_signs(u.sgn, get_sign(v));
 
    if (s == SC_ZERO) // case 1
        return sc_signed();
 
    CONVERT_LONG_2(v);
 
    // cases 2-4
    return mul_signed_friend(s, u.nbits, u.ndigits, u.digit,
                             BITS_PER_ULONG, DIGITS_PER_ULONG, vd);
}
 
 
sc_signed
operator * (long u, const sc_signed &v)
{
    small_type s = mul_signs(v.sgn, get_sign(u));
 
    if (s == SC_ZERO) // case 1
        return sc_signed();
 
    CONVERT_LONG_2(u);
 
    // cases 2-4
    return mul_signed_friend(s, BITS_PER_ULONG, DIGITS_PER_ULONG, ud,
                             v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator * (const sc_unsigned &u, long v)
{
    small_type s = mul_signs(u.sgn, get_sign(v));
 
    if (s == SC_ZERO) // case 1
        return sc_signed();
 
    CONVERT_LONG_2(v);
 
    // cases 2-4
    return mul_signed_friend(s, u.nbits, u.ndigits, u.digit,
                             BITS_PER_ULONG, DIGITS_PER_ULONG, vd);
}
 
 
sc_signed
operator * (long u, const sc_unsigned &v)
{
    small_type s = mul_signs(v.sgn, get_sign(u));
 
    if (s == SC_ZERO) // case 1
        return sc_signed();
 
    CONVERT_LONG_2(u);
 
    // cases 2-4
    return mul_signed_friend(s, BITS_PER_ULONG, DIGITS_PER_ULONG, ud,
                             v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator * (const sc_signed &u, unsigned long v)
{
    small_type s = mul_signs(u.sgn, get_sign(v));
 
    if (s == SC_ZERO) // case 1
        return sc_signed();
 
    CONVERT_LONG_2(v);
 
    // else cases 2-4
    return mul_signed_friend(s, u.nbits, u.ndigits, u.digit,
                             BITS_PER_ULONG, DIGITS_PER_ULONG, vd);
}
 
sc_signed
operator * (unsigned long u, const sc_signed &v)
{
    small_type s = mul_signs(v.sgn, get_sign(u));
 
    if (s == SC_ZERO) // case 1
        return sc_signed();
 
    CONVERT_LONG_2(u);
 
    // cases 2-4
    return mul_signed_friend(s, BITS_PER_ULONG, DIGITS_PER_ULONG, ud,
                             v.nbits, v.ndigits, v.digit);
}
 
// The rest of the operators in this section are included from
// sc_nbcommon.cpp.
 
 
// ----------------------------------------------------------------------------
//  SECTION: DIVISION operators: /, /=
// ----------------------------------------------------------------------------
 
// Cases to consider when finding the quotient q = floor(u/v):
// Note that u = q * v + r for r < q.
// 1. 0 / 0 or u / 0 => error
// 2. 0 / v => 0 = 0 * v + 0
// 3. u / v & &u = v => u = 1 * u + 0  - u or v can be 1 or -1
// 4. u / v & &u < v => u = 0 * v + u  - u can be 1 or -1
// 5. u / v & &u > v => u = q * v + r  - v can be 1 or -1
 
sc_signed
operator / (const sc_unsigned &u, const sc_signed &v)
{
    small_type s = mul_signs(u.sgn, v.sgn);
 
    if (s == SC_ZERO) {
        div_by_zero(v.sgn); // case 1
        return sc_signed(); // case 2
    }
 
    // other cases
    return div_signed_friend(s, u.nbits, u.ndigits, u.digit,
                             v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator / (const sc_signed &u, const sc_unsigned &v)
{
    small_type s = mul_signs(u.sgn, v.sgn);
 
    if (s == SC_ZERO) {
        div_by_zero(v.sgn); // case 1
        return sc_signed(); // case 2
    }
 
    // other cases
    return div_signed_friend(s, u.nbits, u.ndigits, u.digit,
                             v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator / (const sc_signed &u, const sc_signed &v)
{
    small_type s = mul_signs(u.sgn, v.sgn);
 
    if (s == SC_ZERO) {
        div_by_zero(v.sgn); // case 1
        return sc_signed(); // case 2
    }
 
    // other cases
    return div_signed_friend(s, u.nbits, u.ndigits, u.digit,
                             v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator / (const sc_signed &u, int64 v)
{
    small_type s = mul_signs(u.sgn, get_sign(v));
 
    if (s == SC_ZERO) {
        div_by_zero(v); // case 1
        return sc_signed(); // case 2
    }
 
    CONVERT_INT64_2(v);
 
    // other cases
    return div_signed_friend(s, u.nbits, u.ndigits, u.digit,
                             BITS_PER_UINT64, DIGITS_PER_UINT64, vd);
}
 
 
sc_signed
operator / (int64 u, const sc_signed &v)
{
    small_type s = mul_signs(v.sgn, get_sign(u));
 
    if (s == SC_ZERO) {
        div_by_zero(v.sgn); // case 1
        return sc_signed(); // case 2
    }
 
    CONVERT_INT64_2(u);
 
    // other cases
    return div_signed_friend(s, BITS_PER_UINT64, DIGITS_PER_UINT64, ud,
                             v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator / (const sc_unsigned &u, int64 v)
{
    small_type s = mul_signs(u.sgn, get_sign(v));
 
    if (s == SC_ZERO) {
        div_by_zero(v); // case 1
        return sc_signed(); // case 2
    }
 
    CONVERT_INT64_2(v);
 
    // other cases
    return div_signed_friend(s, u.nbits, u.ndigits, u.digit,
                             BITS_PER_UINT64, DIGITS_PER_UINT64, vd);
}
 
 
sc_signed
operator / (int64 u, const sc_unsigned &v)
{
    small_type s = mul_signs(v.sgn, get_sign(u));
 
    if (s == SC_ZERO) {
        div_by_zero(v.sgn); // case 1
        return sc_signed(); // case 2
    }
 
    CONVERT_INT64_2(u);
 
    // other cases
    return div_signed_friend(s, BITS_PER_UINT64, DIGITS_PER_UINT64, ud,
                             v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator / (const sc_signed &u, uint64 v)
{
    small_type s = mul_signs(u.sgn, get_sign(v));
 
    if (s == SC_ZERO) {
        div_by_zero(v); // case 1
        return sc_signed(); // case 2
    }
 
    CONVERT_INT64_2(v);
 
    // other cases
    return div_signed_friend(s, u.nbits, u.ndigits, u.digit,
                             BITS_PER_UINT64, DIGITS_PER_UINT64, vd);
}
 
 
sc_signed
operator / (uint64 u, const sc_signed &v)
{
    small_type s = mul_signs(v.sgn, get_sign(u));
 
    if (s == SC_ZERO) {
        div_by_zero(v.sgn); // case 1
        return sc_signed(); // case 2
 
    }
 
    CONVERT_INT64_2(u);
 
    // other cases
    return div_signed_friend(s, BITS_PER_UINT64, DIGITS_PER_UINT64, ud,
                             v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator / (const sc_signed &u, long v)
{
    small_type s = mul_signs(u.sgn, get_sign(v));
 
    if (s == SC_ZERO) {
        div_by_zero(v); // case 1
        return sc_signed(); // case 2
    }
 
    CONVERT_LONG_2(v);
 
    // other cases
    return div_signed_friend(s, u.nbits, u.ndigits, u.digit,
                             BITS_PER_ULONG, DIGITS_PER_ULONG, vd);
}
 
 
sc_signed
operator / (long u, const sc_signed &v)
{
    small_type s = mul_signs(v.sgn, get_sign(u));
 
    if (s == SC_ZERO) {
        div_by_zero(v.sgn); // case 1
        return sc_signed(); // case 2
    }
 
    CONVERT_LONG_2(u);
 
    // other cases
    return div_signed_friend(s, BITS_PER_ULONG, DIGITS_PER_ULONG, ud,
                             v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator / (const sc_unsigned &u, long v)
{
    small_type s = mul_signs(u.sgn, get_sign(v));
 
    if (s == SC_ZERO) {
        div_by_zero(v); // case 1
        return sc_signed(); // case 2
    }
 
    CONVERT_LONG_2(v);
 
    // other cases
    return div_signed_friend(s, u.nbits, u.ndigits, u.digit,
                             BITS_PER_ULONG, DIGITS_PER_ULONG, vd);
}
 
 
sc_signed
operator / (long u, const sc_unsigned &v)
{
    small_type s = mul_signs(v.sgn, get_sign(u));
 
    if (s == SC_ZERO) {
        div_by_zero(v.sgn); // case 1
        return sc_signed(); // case 2
    }
 
    CONVERT_LONG_2(u);
 
    // other cases
    return div_signed_friend(s, BITS_PER_ULONG, DIGITS_PER_ULONG, ud,
                             v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator / (const sc_signed &u, unsigned long v)
{
    small_type s = mul_signs(u.sgn, get_sign(v));
 
    if (s == SC_ZERO) {
        div_by_zero(v); // case 1
        return sc_signed(); // case 2
    }
 
    CONVERT_LONG_2(v);
 
    // other cases
    return div_signed_friend(s, u.nbits, u.ndigits, u.digit,
                             BITS_PER_ULONG, DIGITS_PER_ULONG, vd);
}
 
 
sc_signed
operator / (unsigned long u, const sc_signed &v)
{
    small_type s = mul_signs(v.sgn, get_sign(u));
 
    if (s == SC_ZERO) {
        div_by_zero(v.sgn); // case 1
        return sc_signed(); // case 2
 
    }
 
    CONVERT_LONG_2(u);
 
    // other cases
    return div_signed_friend(s, BITS_PER_ULONG, DIGITS_PER_ULONG, ud,
                             v.nbits, v.ndigits, v.digit);
}
 
// The rest of the operators in this section are included from
// sc_nbcommon.cpp.
 
 
// ----------------------------------------------------------------------------
//  SECTION: MOD operators: %, %=.
// ----------------------------------------------------------------------------
 
// Cases to consider when finding the remainder r = u % v:
// Note that u = q * v + r for r < q.
// 1. 0 % 0 or u % 0 => error
// 2. 0 % v => 0 = 0 * v + 0
// 3. u % v & &u = v => u = 1 * u + 0  - u or v can be 1 or -1
// 4. u % v & &u < v => u = 0 * v + u  - u can be 1 or -1
// 5. u % v & &u > v => u = q * v + r  - v can be 1 or -1
 
sc_signed
operator % (const sc_unsigned &u, const sc_signed &v)
{
    if ((u.sgn == SC_ZERO) || (v.sgn == SC_ZERO)) {
        div_by_zero(v.sgn); // case 1
        return sc_signed(); // case 2
    }
 
    // other cases
    return mod_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator % (const sc_signed &u, const sc_unsigned &v)
{
    if ((u.sgn == SC_ZERO) || (v.sgn == SC_ZERO)) {
        div_by_zero(v.sgn); // case 1
        return sc_signed(); // case 2
    }
 
    // other cases
    return mod_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator % (const sc_signed &u, const sc_signed &v)
{
    if ((u.sgn == SC_ZERO) || (v.sgn == SC_ZERO)) {
        div_by_zero(v.sgn); // case 1
        return sc_signed(); // case 2
    }
 
    // other cases
    return mod_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator % (const sc_signed &u, int64 v)
{
    small_type vs = get_sign(v);
 
    if ((u.sgn == SC_ZERO) || (vs == SC_ZERO)) {
        div_by_zero(v); // case 1
        return sc_signed(); // case 2
    }
 
    CONVERT_INT64_2(v);
 
    // other cases
    return mod_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             BITS_PER_UINT64, DIGITS_PER_UINT64, vd);
}
 
 
sc_signed
operator % (int64 u, const sc_signed &v)
{
    small_type us = get_sign(u);
 
    if ((us == SC_ZERO) || (v.sgn == SC_ZERO)) {
        div_by_zero(v.sgn); // case 1
        return sc_signed(); // case 2
    }
 
    CONVERT_INT64_2(u);
 
    // other cases
    return mod_signed_friend(us, BITS_PER_UINT64, DIGITS_PER_UINT64, ud,
                             v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator % (const sc_unsigned &u, int64 v)
{
    small_type vs = get_sign(v);
 
    if ((u.sgn == SC_ZERO) || (vs == SC_ZERO)) {
        div_by_zero(v); // case 1
        return sc_signed(); // case 2
    }
 
    CONVERT_INT64_2(v);
 
    // other cases
    return mod_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             BITS_PER_UINT64, DIGITS_PER_UINT64, vd);
}
 
 
sc_signed
operator % (int64 u, const sc_unsigned &v)
{
    small_type us = get_sign(u);
 
    if ((us == SC_ZERO) || (v.sgn == SC_ZERO)) {
        div_by_zero(v.sgn); // case 1
        return sc_signed(); // case 2
    }
 
    CONVERT_INT64_2(u);
 
    // other cases
    return mod_signed_friend(us, BITS_PER_UINT64, DIGITS_PER_UINT64, ud,
                             v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator % (const sc_signed &u, uint64 v)
{
    if ((u.sgn == SC_ZERO) || (v == 0)) {
        div_by_zero(v); // case 1
        return sc_signed(); // case 2
    }
 
    CONVERT_INT64_2(v);
 
    // other cases
    return mod_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             BITS_PER_UINT64, DIGITS_PER_UINT64, vd);
}
 
 
sc_signed
operator % (uint64 u, const sc_signed &v)
{
    if ((u == 0) || (v.sgn == SC_ZERO)) {
        div_by_zero(v.sgn); // case 1
        return sc_signed(); // case 2
    }
 
    CONVERT_INT64(u);
 
    // other cases
    return mod_signed_friend(us, BITS_PER_UINT64, DIGITS_PER_UINT64, ud,
                             v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator % (const sc_signed &u, long v)
{
    small_type vs = get_sign(v);
 
    if ((u.sgn == SC_ZERO) || (vs == SC_ZERO)) {
        div_by_zero(v); // case 1
        return sc_signed(); // case 2
    }
 
    CONVERT_LONG_2(v);
 
    // other cases
    return mod_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             BITS_PER_ULONG, DIGITS_PER_ULONG, vd);
}
 
 
sc_signed
operator % (long u, const sc_signed &v)
{
    small_type us = get_sign(u);
 
    if ((us == SC_ZERO) || (v.sgn == SC_ZERO)) {
        div_by_zero(v.sgn); // case 1
        return sc_signed(); // case 2
    }
 
    CONVERT_LONG_2(u);
 
    // other cases
    return mod_signed_friend(us, BITS_PER_ULONG, DIGITS_PER_ULONG, ud,
                             v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator % (const sc_unsigned &u, long v)
{
 
  small_type vs = get_sign(v);
 
  if ((u.sgn == SC_ZERO) || (vs == SC_ZERO)) {
    div_by_zero(v); // case 1
    return sc_signed(); // case 2
  }
 
  CONVERT_LONG_2(v);
 
  // other cases
  return mod_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                           BITS_PER_ULONG, DIGITS_PER_ULONG, vd);
}
 
 
sc_signed
operator % (long u, const sc_unsigned &v)
{
    small_type us = get_sign(u);
 
    if ((us == SC_ZERO) || (v.sgn == SC_ZERO)) {
        div_by_zero(v.sgn); // case 1
        return sc_signed(); // case 2
    }
 
    CONVERT_LONG_2(u);
 
    // other cases
    return mod_signed_friend(us, BITS_PER_ULONG, DIGITS_PER_ULONG, ud,
                             v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator % (const sc_signed &u, unsigned long v)
{
    if ((u.sgn == SC_ZERO) || (v == 0)) {
        div_by_zero(v); // case 1
        return sc_signed(); // case 2
    }
 
    CONVERT_LONG_2(v);
 
    // other cases
    return mod_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             BITS_PER_ULONG, DIGITS_PER_ULONG, vd);
}
 
 
sc_signed
operator % (unsigned long u, const sc_signed &v)
{
    if ((u == 0) || (v.sgn == SC_ZERO)) {
        div_by_zero(v.sgn); // case 1
        return sc_signed(); // case 2
    }
 
    CONVERT_LONG(u);
 
    // other cases
    return mod_signed_friend(us, BITS_PER_ULONG, DIGITS_PER_ULONG, ud,
                             v.nbits, v.ndigits, v.digit);
}
 
// The rest of the operators in this section are included from
// sc_nbcommon.cpp.
 
 
// ----------------------------------------------------------------------------
//  SECTION: Bitwise AND operators: &, &=
// ----------------------------------------------------------------------------
 
// Cases to consider when computing u  &v:
// 1. u & 0 = 0  &v = 0
// 2. u  &v => sgn = +
// 3. (-u) & (-v) => sgn = -
// 4. u & (-v) => sgn = +
// 5. (-u)  &v => sgn = +
 
sc_signed
operator & (const sc_unsigned &u, const sc_signed &v)
{
    if ((u.sgn == SC_ZERO) || (v.sgn == SC_ZERO)) // case 1
        return sc_signed();
 
    // other cases
    return and_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator & (const sc_signed &u, const sc_unsigned &v)
{
    if ((u.sgn == SC_ZERO) || (v.sgn == SC_ZERO)) // case 1
        return sc_signed();
 
    // other cases
    return and_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator & (const sc_signed &u, const sc_signed &v)
{
    if ((u.sgn == SC_ZERO) || (v.sgn == SC_ZERO)) // case 1
        return sc_signed();
 
    // other cases
    return and_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator & (const sc_signed &u, int64 v)
{
    if ((u.sgn == SC_ZERO) || (v == 0)) // case 1
        return sc_signed();
 
    CONVERT_INT64(v);
 
    // other cases
    return and_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             vs, BITS_PER_UINT64, DIGITS_PER_UINT64, vd);
}
 
 
sc_signed
operator & (int64 u, const sc_signed &v)
{
    if ((u == 0) || (v.sgn == SC_ZERO)) // case 1
        return sc_signed();
 
    CONVERT_INT64(u);
 
    // other cases
    return and_signed_friend(us, BITS_PER_UINT64, DIGITS_PER_UINT64, ud,
                             v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator & (const sc_unsigned &u, int64 v)
{
    if ((u.sgn == SC_ZERO) || (v == 0)) // case 1
        return sc_signed();
 
    CONVERT_INT64(v);
 
    // other cases
    return and_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             vs, BITS_PER_UINT64, DIGITS_PER_UINT64, vd);
}
 
 
sc_signed
operator & (int64 u, const sc_unsigned &v)
{
    if ((u == 0) || (v.sgn == SC_ZERO)) // case 1
        return sc_signed();
 
    CONVERT_INT64(u);
 
    // other cases
    return and_signed_friend(us, BITS_PER_UINT64, DIGITS_PER_UINT64, ud,
                             v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator & (const sc_signed &u, uint64 v)
{
    if ((u.sgn == SC_ZERO) || (v == 0)) // case 1
        return sc_signed();
 
    CONVERT_INT64(v);
 
    // other cases
    return and_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             vs, BITS_PER_UINT64, DIGITS_PER_UINT64, vd);
}
 
 
sc_signed
operator & (uint64 u, const sc_signed &v)
{
    if ((u == 0) || (v.sgn == SC_ZERO)) // case 1
        return sc_signed();
 
    CONVERT_INT64(u);
 
    // other cases
    return and_signed_friend(us, BITS_PER_UINT64, DIGITS_PER_UINT64, ud,
                             v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator & (const sc_signed &u, long v)
{
    if ((u.sgn == SC_ZERO) || (v == 0)) // case 1
        return sc_signed();
 
    CONVERT_LONG(v);
 
    // other cases
    return and_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             vs, BITS_PER_ULONG, DIGITS_PER_ULONG, vd);
}
 
 
sc_signed
operator & (long u, const sc_signed &v)
{
    if ((u == 0) || (v.sgn == SC_ZERO)) // case 1
        return sc_signed();
 
    CONVERT_LONG(u);
 
    // other cases
    return and_signed_friend(us, BITS_PER_ULONG, DIGITS_PER_ULONG, ud,
                             v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator & (const sc_unsigned &u, long v)
{
    if ((u.sgn == SC_ZERO) || (v == 0)) // case 1
        return sc_signed();
 
    CONVERT_LONG(v);
 
    // other cases
    return and_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             vs, BITS_PER_ULONG, DIGITS_PER_ULONG, vd);
}
 
 
sc_signed
operator & (long u, const sc_unsigned &v)
{
    if ((u == 0) || (v.sgn == SC_ZERO)) // case 1
        return sc_signed();
 
    CONVERT_LONG(u);
 
    // other cases
    return and_signed_friend(us, BITS_PER_ULONG, DIGITS_PER_ULONG, ud,
                             v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator & (const sc_signed &u, unsigned long v)
{
    if ((u.sgn == SC_ZERO) || (v == 0)) // case 1
        return sc_signed();
 
    CONVERT_LONG(v);
 
    // other cases
    return and_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             vs, BITS_PER_ULONG, DIGITS_PER_ULONG, vd);
}
 
 
sc_signed
operator & (unsigned long u, const sc_signed &v)
{
    if ((u == 0) || (v.sgn == SC_ZERO)) // case 1
        return sc_signed();
 
    CONVERT_LONG(u);
 
    // other cases
    return and_signed_friend(us, BITS_PER_ULONG, DIGITS_PER_ULONG, ud,
                             v.sgn, v.nbits, v.ndigits, v.digit);
}
 
// The rest of the operators in this section are included from
// sc_nbcommon.cpp.
 
 
// ----------------------------------------------------------------------------
//  SECTION: Bitwise OR operators: |, |=
// ----------------------------------------------------------------------------
 
// Cases to consider when computing u | v:
// 1. u | 0 = u
// 2. 0 | v = v
// 3. u | v => sgn = +
// 4. (-u) | (-v) => sgn = -
// 5. u | (-v) => sgn = -
// 6. (-u) | v => sgn = -
 
sc_signed
operator | (const sc_unsigned &u, const sc_signed &v)
{
    if (v.sgn == SC_ZERO) // case 1
        return sc_signed(u);
 
    if (u.sgn == SC_ZERO) // case 2
        return sc_signed(v);
 
    // other cases
    return or_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                            v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator | (const sc_signed &u, const sc_unsigned &v)
{
    if (v.sgn == SC_ZERO) // case 1
        return sc_signed(u);
 
    if (u.sgn == SC_ZERO) // case 2
        return sc_signed(v);
 
    // other cases
    return or_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                            v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator | (const sc_signed &u, const sc_signed &v)
{
    if (v.sgn == SC_ZERO) // case 1
        return sc_signed(u);
 
    if (u.sgn == SC_ZERO) // case 2
        return sc_signed(v);
 
    // other cases
    return or_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                            v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator | (const sc_signed &u, int64 v)
{
    if (v == 0) // case 1
        return sc_signed(u);
 
    CONVERT_INT64(v);
 
    if (u.sgn == SC_ZERO) // case 2
        return sc_signed(vs, BITS_PER_UINT64, DIGITS_PER_UINT64, vd, false);
 
    // other cases
    return or_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                            vs, BITS_PER_UINT64, DIGITS_PER_UINT64, vd);
}
 
 
sc_signed
operator | (int64 u, const sc_signed &v)
{
    if (u == 0)
        return sc_signed(v);
 
    CONVERT_INT64(u);
 
    if (v.sgn == SC_ZERO)
        return sc_signed(us, BITS_PER_UINT64, DIGITS_PER_UINT64, ud, false);
 
    // other cases
    return or_signed_friend(us, BITS_PER_UINT64, DIGITS_PER_UINT64, ud,
                            v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator | (const sc_unsigned &u, int64 v)
{
    if (v == 0) // case 1
        return sc_signed(u);
 
    CONVERT_INT64(v);
 
    if (u.sgn == SC_ZERO) // case 2
        return sc_signed(vs, BITS_PER_UINT64, DIGITS_PER_UINT64, vd, false);
 
    // other cases
    return or_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                            vs, BITS_PER_UINT64, DIGITS_PER_UINT64, vd);
}
 
 
sc_signed
operator | (int64 u, const sc_unsigned &v)
{
    if (u == 0)
        return sc_signed(v);
 
    CONVERT_INT64(u);
 
    if (v.sgn == SC_ZERO)
        return sc_signed(us, BITS_PER_UINT64, DIGITS_PER_UINT64, ud, false);
 
    // other cases
    return or_signed_friend(us, BITS_PER_UINT64, DIGITS_PER_UINT64, ud,
                            v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator | (const sc_signed &u, uint64 v)
{
    if (v == 0) // case 1
        return sc_signed(u);
 
    CONVERT_INT64(v);
 
    if (u.sgn == SC_ZERO) // case 2
        return sc_signed(vs, BITS_PER_UINT64, DIGITS_PER_UINT64, vd, false);
 
    // other cases
    return or_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                            vs, BITS_PER_UINT64, DIGITS_PER_UINT64, vd);
}
 
 
sc_signed
operator | (uint64 u, const sc_signed &v)
{
    if (u == 0)
        return sc_signed(v);
 
    CONVERT_INT64(u);
 
    if (v.sgn == SC_ZERO)
        return sc_signed(us, BITS_PER_UINT64, DIGITS_PER_UINT64, ud, false);
 
    // other cases
    return or_signed_friend(us, BITS_PER_UINT64, DIGITS_PER_UINT64, ud,
                            v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator | (const sc_signed &u, long v)
{
    if (v == 0) // case 1
        return sc_signed(u);
 
    CONVERT_LONG(v);
 
    if (u.sgn == SC_ZERO) // case 2
        return sc_signed(vs, BITS_PER_ULONG, DIGITS_PER_ULONG, vd, false);
 
    // other cases
    return or_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                            vs, BITS_PER_ULONG, DIGITS_PER_ULONG, vd);
}
 
 
sc_signed
operator | (long u, const sc_signed &v)
{
    if (u == 0)
        return sc_signed(v);
 
    CONVERT_LONG(u);
 
    if (v.sgn == SC_ZERO)
        return sc_signed(us, BITS_PER_ULONG, DIGITS_PER_ULONG, ud, false);
 
    // other cases
    return or_signed_friend(us, BITS_PER_ULONG, DIGITS_PER_ULONG, ud,
                            v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator | (const sc_unsigned &u, long v)
{
    if (v == 0) // case 1
        return sc_signed(u);
 
    CONVERT_LONG(v);
 
    if (u.sgn == SC_ZERO) // case 2
        return sc_signed(vs, BITS_PER_ULONG, DIGITS_PER_ULONG, vd, false);
 
    // other cases
    return or_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                            vs, BITS_PER_ULONG, DIGITS_PER_ULONG, vd);
}
 
 
sc_signed
operator | (long u, const sc_unsigned &v)
{
    if (u == 0)
        return sc_signed(v);
 
    CONVERT_LONG(u);
 
    if (v.sgn == SC_ZERO)
        return sc_signed(us, BITS_PER_ULONG, DIGITS_PER_ULONG, ud, false);
 
    // other cases
    return or_signed_friend(us, BITS_PER_ULONG, DIGITS_PER_ULONG, ud,
                            v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator | (const sc_signed &u, unsigned long v)
{
    if (v == 0) // case 1
        return sc_signed(u);
 
    CONVERT_LONG(v);
 
    if (u.sgn == SC_ZERO) // case 2
        return sc_signed(vs, BITS_PER_ULONG, DIGITS_PER_ULONG, vd, false);
 
    // other cases
    return or_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                            vs, BITS_PER_ULONG, DIGITS_PER_ULONG, vd);
}
 
 
sc_signed
operator | (unsigned long u, const sc_signed &v)
{
    if (u == 0)
        return sc_signed(v);
 
    CONVERT_LONG(u);
 
    if (v.sgn == SC_ZERO)
        return sc_signed(us, BITS_PER_ULONG, DIGITS_PER_ULONG, ud, false);
 
    // other cases
    return or_signed_friend(us, BITS_PER_ULONG, DIGITS_PER_ULONG, ud,
                            v.sgn, v.nbits, v.ndigits, v.digit);
}
 
// The rest of the operators in this section are included from
// sc_nbcommon.cpp.
 
 
// ----------------------------------------------------------------------------
//  SECTION: Bitwise XOR operators: ^, ^=
// ----------------------------------------------------------------------------
 
// Cases to consider when computing u ^ v:
// Note that  u ^ v = (~u  &v) | (u & ~v).
// 1. u ^ 0 = u
// 2. 0 ^ v = v
// 3. u ^ v => sgn = +
// 4. (-u) ^ (-v) => sgn = -
// 5. u ^ (-v) => sgn = -
// 6. (-u) ^ v => sgn = +
 
sc_signed
operator ^ (const sc_unsigned &u, const sc_signed &v)
{
 
  if (v.sgn == SC_ZERO) // case 1
    return sc_signed(u);
 
  if (u.sgn == SC_ZERO) // case 2
    return sc_signed(v);
 
  // other cases
  return xor_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                           v.sgn, v.nbits, v.ndigits, v.digit);
 
}
 
 
sc_signed
operator ^ (const sc_signed &u, const sc_unsigned &v)
{
    if (v.sgn == SC_ZERO) // case 1
        return sc_signed(u);
 
    if (u.sgn == SC_ZERO) // case 2
        return sc_signed(v);
 
    // other cases
    return xor_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator ^ (const sc_signed &u, const sc_signed &v)
{
    if (v.sgn == SC_ZERO) // case 1
        return sc_signed(u);
 
    if (u.sgn == SC_ZERO) // case 2
        return sc_signed(v);
 
    // other cases
    return xor_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator ^ (const sc_signed &u, int64 v)
{
    if (v == 0) // case 1
        return sc_signed(u);
 
    CONVERT_INT64(v);
 
    if (u.sgn == SC_ZERO) // case 2
        return sc_signed(vs, BITS_PER_UINT64, DIGITS_PER_UINT64, vd, false);
 
    // other cases
    return xor_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             vs, BITS_PER_UINT64, DIGITS_PER_UINT64, vd);
}
 
 
sc_signed
operator ^ (int64 u, const sc_signed &v)
{
    if (u == 0)
        return sc_signed(v);
 
    CONVERT_INT64(u);
 
    if (v.sgn == SC_ZERO)
        return sc_signed(us, BITS_PER_UINT64, DIGITS_PER_UINT64, ud, false);
 
    // other cases
    return xor_signed_friend(us, BITS_PER_UINT64, DIGITS_PER_UINT64, ud,
                             v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator ^ (const sc_unsigned &u, int64 v)
{
    if (v == 0) // case 1
        return sc_signed(u);
 
    CONVERT_INT64(v);
 
    if (u.sgn == SC_ZERO) // case 2
        return sc_signed(vs, BITS_PER_UINT64, DIGITS_PER_UINT64, vd, false);
 
    // other cases
    return xor_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             vs, BITS_PER_UINT64, DIGITS_PER_UINT64, vd);
}
 
 
sc_signed
operator ^ (int64 u, const sc_unsigned &v)
{
    if (u == 0)
        return sc_signed(v);
 
    CONVERT_INT64(u);
 
    if (v.sgn == SC_ZERO)
        return sc_signed(us, BITS_PER_UINT64, DIGITS_PER_UINT64, ud, false);
 
    // other cases
    return xor_signed_friend(us, BITS_PER_UINT64, DIGITS_PER_UINT64, ud,
                             v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator ^ (const sc_signed &u, uint64 v)
{
    if (v == 0) // case 1
        return sc_signed(u);
 
    CONVERT_INT64(v);
 
    if (u.sgn == SC_ZERO) // case 2
        return sc_signed(vs, BITS_PER_UINT64, DIGITS_PER_UINT64, vd, false);
 
    // other cases
    return xor_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             vs, BITS_PER_UINT64, DIGITS_PER_UINT64, vd);
}
 
sc_signed
operator ^ (uint64 u, const sc_signed &v)
{
    if (u == 0)
        return sc_signed(v);
 
    CONVERT_INT64(u);
 
    if (v.sgn == SC_ZERO)
        return sc_signed(us, BITS_PER_UINT64, DIGITS_PER_UINT64, ud, false);
 
    // other cases
    return xor_signed_friend(us, BITS_PER_UINT64, DIGITS_PER_UINT64, ud,
                             v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator ^ (const sc_signed &u, long v)
{
    if (v == 0) // case 1
        return sc_signed(u);
 
    CONVERT_LONG(v);
 
    if (u.sgn == SC_ZERO) // case 2
        return sc_signed(vs, BITS_PER_ULONG, DIGITS_PER_ULONG, vd, false);
 
    // other cases
    return xor_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             vs, BITS_PER_ULONG, DIGITS_PER_ULONG, vd);
}
 
 
sc_signed
operator ^ (long u, const sc_signed &v)
{
    if (u == 0)
        return sc_signed(v);
 
    CONVERT_LONG(u);
 
    if (v.sgn == SC_ZERO)
        return sc_signed(us, BITS_PER_ULONG, DIGITS_PER_ULONG, ud, false);
 
    // other cases
    return xor_signed_friend(us, BITS_PER_ULONG, DIGITS_PER_ULONG, ud,
                             v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator ^ (const sc_unsigned &u, long v)
{
    if (v == 0) // case 1
        return sc_signed(u);
 
    CONVERT_LONG(v);
 
    if (u.sgn == SC_ZERO) // case 2
        return sc_signed(vs, BITS_PER_ULONG, DIGITS_PER_ULONG, vd, false);
 
    // other cases
    return xor_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             vs, BITS_PER_ULONG, DIGITS_PER_ULONG, vd);
}
 
 
sc_signed
operator ^ (long u, const sc_unsigned &v)
{
    if (u == 0)
        return sc_signed(v);
 
    CONVERT_LONG(u);
 
    if (v.sgn == SC_ZERO)
        return sc_signed(us, BITS_PER_ULONG, DIGITS_PER_ULONG, ud, false);
 
    // other cases
    return xor_signed_friend(us, BITS_PER_ULONG, DIGITS_PER_ULONG, ud,
                             v.sgn, v.nbits, v.ndigits, v.digit);
}
 
 
sc_signed
operator ^ (const sc_signed &u, unsigned long v)
{
    if (v == 0) // case 1
        return sc_signed(u);
 
    CONVERT_LONG(v);
 
    if (u.sgn == SC_ZERO) // case 2
        return sc_signed(vs, BITS_PER_ULONG, DIGITS_PER_ULONG, vd, false);
 
    // other cases
    return xor_signed_friend(u.sgn, u.nbits, u.ndigits, u.digit,
                             vs, BITS_PER_ULONG, DIGITS_PER_ULONG, vd);
}
 
sc_signed
operator ^ (unsigned long u, const sc_signed &v)
{
    if (u == 0)
        return sc_signed(v);
 
    CONVERT_LONG(u);
 
    if (v.sgn == SC_ZERO)
        return sc_signed(us, BITS_PER_ULONG, DIGITS_PER_ULONG, ud, false);
 
    // other cases
    return xor_signed_friend(us, BITS_PER_ULONG, DIGITS_PER_ULONG, ud,
                             v.sgn, v.nbits, v.ndigits, v.digit);
}
 
// The rest of the operators in this section are included from
// sc_nbcommon.cpp.
 
 
// ----------------------------------------------------------------------------
//  SECTION: Bitwise NOT operator: ~
// ----------------------------------------------------------------------------
 
// Operators in this section are included from sc_nbcommon.cpp.
 
 
// ----------------------------------------------------------------------------
//  SECTION: LEFT SHIFT operators: <<, <<=
// ----------------------------------------------------------------------------
 
sc_signed
operator << (const sc_signed &u, const sc_unsigned &v)
{
    if (v.sgn == SC_ZERO)
        return sc_signed(u);
 
    return operator << (u, v.to_ulong());
}
 
// The rest of the operators in this section are included from
// sc_nbcommon.cpp.
 
 
// ----------------------------------------------------------------------------
//  SECTION: RIGHT SHIFT operators: >>, >>=
// ----------------------------------------------------------------------------
 
sc_signed
operator >> (const sc_signed &u, const sc_unsigned &v)
{
    if (v.sgn == SC_ZERO)
        return sc_signed(u);
 
    return operator >> (u, v.to_ulong());
}
 
// The rest of the operators in this section are included from
// sc_nbcommon.cpp.
 
 
// ----------------------------------------------------------------------------
//  SECTION: Unary arithmetic operators.
// ----------------------------------------------------------------------------
 
sc_signed
operator + (const sc_signed &u)
{
    return sc_signed(u);
}
 
sc_signed
operator - (const sc_signed &u)
{
    return sc_signed(u, -u.sgn);
}
 
sc_signed
operator - (const sc_unsigned &u)
{
    return sc_signed(u, -u.sgn);
}
 
 
// ----------------------------------------------------------------------------
//    SECTION: EQUAL operator: ==
// ----------------------------------------------------------------------------
 
bool
operator == (const sc_signed &u, const sc_signed &v)
{
    if (u.sgn != v.sgn)
        return false;
 
    if (&u == &v)
        return true;
 
    if (vec_skip_and_cmp(u.ndigits, u.digit, v.ndigits, v.digit) != 0)
        return false;
 
    return true;
}
 
 
bool
operator == (const sc_signed &u, int64 v)
{
    CONVERT_INT64(v);
 
    if (u.sgn != vs)
        return false;
 
    if (vec_skip_and_cmp(u.ndigits, u.digit, DIGITS_PER_INT64, vd) != 0)
        return false;
 
    return true;
}
 
 
bool
operator == (int64 u, const sc_signed &v)
{
    CONVERT_INT64(u);
 
    if (us != v.sgn)
        return false;
 
    if (vec_skip_and_cmp(DIGITS_PER_INT64, ud, v.ndigits, v.digit) != 0)
        return false;
 
    return true;
}
 
 
bool
operator == (const sc_signed &u, uint64 v)
{
    CONVERT_INT64(v);
 
    if (u.sgn != vs)
        return false;
 
    if (vec_skip_and_cmp(u.ndigits, u.digit, DIGITS_PER_INT64, vd) != 0)
        return false;
 
    return true;
}
 
 
bool
operator == (uint64 u, const sc_signed &v)
{
    CONVERT_INT64(u);
 
    if (us != v.sgn)
        return false;
 
    if (vec_skip_and_cmp(DIGITS_PER_INT64, ud, v.ndigits, v.digit) != 0)
        return false;
 
    return true;
}
 
 
bool
operator == (const sc_signed &u, long v)
{
    CONVERT_LONG(v);
 
    if (u.sgn != vs)
        return false;
 
    if (vec_skip_and_cmp(u.ndigits, u.digit, DIGITS_PER_LONG, vd) != 0)
        return false;
 
    return true;
}
 
 
bool
operator == (long u, const sc_signed &v)
{
    CONVERT_LONG(u);
 
    if (us != v.sgn)
        return false;
 
    if (vec_skip_and_cmp(DIGITS_PER_LONG, ud, v.ndigits, v.digit) != 0)
        return false;
 
    return true;
}
 
 
bool
operator == (const sc_signed &u, unsigned long v)
{
    CONVERT_LONG(v);
 
    if (u.sgn != vs)
        return false;
 
    if (vec_skip_and_cmp(u.ndigits, u.digit, DIGITS_PER_LONG, vd) != 0)
        return false;
 
    return true;
}
 
 
bool
operator == (unsigned long u, const sc_signed &v)
{
    CONVERT_LONG(u);
 
    if (us != v.sgn)
        return false;
 
    if (vec_skip_and_cmp(DIGITS_PER_LONG, ud, v.ndigits, v.digit) != 0)
        return false;
 
    return true;
}
 
 
// ----------------------------------------------------------------------------
//    SECTION: NOT_EQUAL operator: !=
// ----------------------------------------------------------------------------
 
// Operators in this section are included from sc_nbcommon.cpp.
 
 
// ----------------------------------------------------------------------------
//    SECTION: LESS THAN operator: <
// ----------------------------------------------------------------------------
 
bool
operator < (const sc_signed &u, const sc_signed &v)
{
    if (u.sgn < v.sgn)
        return true;
 
    if (u.sgn > v.sgn)
        return false;
 
    // u.sgn == v.sgn
 
    if (&u == &v)
        return false;
 
    if (u.sgn == SC_POS) {
        if (vec_skip_and_cmp(u.ndigits, u.digit, v.ndigits, v.digit) < 0)
            return true;
    } else if (u.sgn == SC_NEG) {
        if (vec_skip_and_cmp(u.ndigits, u.digit, v.ndigits, v.digit) > 0)
            return true;
    }
 
    return false;
}
 
 
bool
operator < (const sc_signed &u, int64 v)
{
    CONVERT_INT64(v);
 
    if (u.sgn < vs)
        return true;
 
    if (u.sgn > vs)
        return false;
 
    // u.sgn == vs
 
    if (vs == SC_POS) {
        if (vec_skip_and_cmp(u.ndigits, u.digit, DIGITS_PER_INT64, vd) < 0)
            return true;
    } else if (vs == SC_NEG) {
        if (vec_skip_and_cmp(u.ndigits, u.digit, DIGITS_PER_INT64, vd) > 0)
            return true;
    }
 
    return false;
}
 
 
bool
operator < (int64 u, const sc_signed &v)
{
    CONVERT_INT64(u);
 
    if (us < v.sgn)
        return true;
 
    if (us > v.sgn)
        return false;
 
    // us == v.sgn
 
    if (us == SC_POS) {
        if (vec_skip_and_cmp(DIGITS_PER_INT64, ud, v.ndigits, v.digit) < 0)
            return true;
    } else if (us == SC_NEG) {
        if (vec_skip_and_cmp(DIGITS_PER_INT64, ud, v.ndigits, v.digit) > 0)
            return true;
    }
 
    return false;
}
 
 
bool
operator < (const sc_signed &u, uint64 v)
{
    CONVERT_INT64(v);
 
    if (u.sgn < vs)
        return true;
 
    if (u.sgn > vs)
        return false;
 
    // u.sgn == vs
 
    if (vs == SC_POS) {
        if (vec_skip_and_cmp(u.ndigits, u.digit, DIGITS_PER_INT64, vd) < 0)
            return true;
    }
 
    return false;
}
 
 
bool
operator < (uint64 u, const sc_signed &v)
{
    CONVERT_INT64(u);
 
    if (us < v.sgn)
        return true;
 
    if (us > v.sgn)
        return false;
 
    // us == v.sgn
 
    if (us == SC_POS) {
        if (vec_skip_and_cmp(DIGITS_PER_INT64, ud, v.ndigits, v.digit) < 0)
            return true;
    }
 
    return false;
}
 
 
bool
operator < (const sc_signed &u, long v)
{
    CONVERT_LONG(v);
 
    if (u.sgn < vs)
        return true;
 
    if (u.sgn > vs)
        return false;
 
    // u.sgn == vs
 
    if (vs == SC_POS) {
        if (vec_skip_and_cmp(u.ndigits, u.digit, DIGITS_PER_LONG, vd) < 0)
            return true;
 
    } else if (vs == SC_NEG) {
        if (vec_skip_and_cmp(u.ndigits, u.digit, DIGITS_PER_LONG, vd) > 0)
            return true;
    }
 
    return false;
}
 
 
bool
operator < (long u, const sc_signed &v)
{
    CONVERT_LONG(u);
 
    if (us < v.sgn)
        return true;
 
    if (us > v.sgn)
        return false;
 
    // us == v.sgn
 
    if (us == SC_POS) {
        if (vec_skip_and_cmp(DIGITS_PER_LONG, ud, v.ndigits, v.digit) < 0)
            return true;
    } else if (us == SC_NEG) {
        if (vec_skip_and_cmp(DIGITS_PER_LONG, ud, v.ndigits, v.digit) > 0)
            return true;
    }
 
    return false;
}
 
 
bool
operator < (const sc_signed &u, unsigned long v)
{
    CONVERT_LONG(v);
 
    if (u.sgn < vs)
        return true;
 
    if (u.sgn > vs)
        return false;
 
    // u.sgn == vs
 
    if (vs == SC_POS) {
        if (vec_skip_and_cmp(u.ndigits, u.digit, DIGITS_PER_LONG, vd) < 0)
            return true;
    }
 
    return false;
}
 
 
bool
operator < (unsigned long u, const sc_signed &v)
{
    CONVERT_LONG(u);
 
    if (us < v.sgn)
        return true;
 
    if (us > v.sgn)
        return false;
 
    // us == v.sgn
 
    if (us == SC_POS) {
        if (vec_skip_and_cmp(DIGITS_PER_LONG, ud, v.ndigits, v.digit) < 0)
            return true;
    }
 
    return false;
}
 
 
// ---------------------------------------------------------------------------
//    SECTION: LESS THAN or EQUAL operator: <=
// ---------------------------------------------------------------------------
 
// Operators in this section are included from sc_nbcommon.cpp.
 
 
// ---------------------------------------------------------------------------
//    SECTION: GREATER THAN operator: >
// ---------------------------------------------------------------------------
 
// Operators in this section are included from sc_nbcommon.cpp.
 
 
// ---------------------------------------------------------------------------
//    SECTION: GREATER THAN or EQUAL operator: >=
// ---------------------------------------------------------------------------
 
// Operators in this section are included from sc_nbcommon.cpp.
 
 
// ---------------------------------------------------------------------------
//    SECTION: Public members - Other utils.
// ---------------------------------------------------------------------------
 
bool
sc_signed::iszero() const
{
    if (sgn == SC_ZERO)
        return true;
    else if (sgn != SC_NOSIGN)
        return false;
    else
        return check_for_zero(ndigits, digit);
}
 
 
bool
sc_signed::sign() const
{
    if (sgn == SC_NEG)
        return 1;
    else if (sgn != SC_NOSIGN)
        return 0;
    else
        return ((digit[ndigits - 1] & one_and_zeros(bit_ord(nbits - 1))) != 0);
}
 
// The rest of the utils in this section are included from sc_nbcommon.cpp.
 
 
// ----------------------------------------------------------------------------
//    SECTION: Private members.
// ----------------------------------------------------------------------------
 
// The private members in this section are included from sc_nbcommon.cpp.
 
#define CLASS_TYPE sc_signed
#define CLASS_TYPE_STR "sc_signed"
 
#define ADD_HELPER add_signed_friend
#define SUB_HELPER sub_signed_friend
#define MUL_HELPER mul_signed_friend
#define DIV_HELPER div_signed_friend
#define MOD_HELPER mod_signed_friend
#define AND_HELPER and_signed_friend
#define OR_HELPER or_signed_friend
#define XOR_HELPER xor_signed_friend
 
#include "sc_nbfriends.inc"
 
#undef SC_UNSIGNED
#define SC_SIGNED
#define IF_SC_SIGNED 1 // 1 = sc_signed
#define CLASS_TYPE_SUBREF sc_signed_subref_r
#define OTHER_CLASS_TYPE sc_unsigned
#define OTHER_CLASS_TYPE_SUBREF sc_unsigned_subref_r
 
#define MUL_ON_HELPER mul_on_help_signed
#define DIV_ON_HELPER div_on_help_signed
#define MOD_ON_HELPER mod_on_help_signed
 
#include "sc_nbcommon.inc"
 
#undef MOD_ON_HELPER
#undef DIV_ON_HELPER
#undef MUL_ON_HELPER
 
#undef OTHER_CLASS_TYPE_SUBREF
#undef OTHER_CLASS_TYPE
#undef CLASS_TYPE_SUBREF
#undef IF_SC_SIGNED
#undef SC_SIGNED
 
#undef XOR_HELPER
#undef OR_HELPER
#undef AND_HELPER
#undef MOD_HELPER
#undef DIV_HELPER
#undef MUL_HELPER
#undef SUB_HELPER
#undef ADD_HELPER
 
#undef CLASS_TYPE
#undef CLASS_TYPE_STR
 
#include "sc_signed_bitref.inc"
#include "sc_signed_subref.inc"
 
#undef CONVERT_LONG
#undef CONVERT_LONG_2
#undef CONVERT_INT64
#undef CONVERT_INT64_2
 
} // namespace sc_dt