sc_nbutils.cc

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

  sc_nbutils.cpp -- External and friend functions for both sc_signed and
                    sc_unsigned classes.

  Original Author: Ali Dasdan, Synopsys, Inc.

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

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

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

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// $Log: sc_nbutils.cpp,v $
// Revision 1.4  2011/08/24 22:05:46  acg
//  Torsten Maehne: initialization changes to remove warnings.
//
// Revision 1.3  2011/02/18 20:19:15  acg
//  Andy Goodrich: updating Copyright notice.
//
// Revision 1.2  2007/11/04 21:26:40  acg
//  Andy Goodrich: added a buffer to the allocation of the q array to address
//  an issue with references outside the array by 1 byte detected by valgrind.
//
// Revision 1.1.1.1  2006/12/15 20:20:05  acg
// SystemC 2.3
//
// 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 <cstdio>
#include <cstring>
#include <sstream>

#include "systemc/ext/dt/bit/messages.hh"
#include "systemc/ext/dt/int/messages.hh"
#include "systemc/ext/dt/int/sc_nbutils.hh"
#include "systemc/ext/utils/functions.hh"

namespace sc_dt
{

// only used within vec_from_str (non-standard, deprecated)
static inline void
is_valid_base(sc_numrep base)
{
    switch (base) {
      case SC_NOBASE: case SC_BIN:
      case SC_OCT: case SC_DEC:
      case SC_HEX:
        break;
      case SC_BIN_US: case SC_BIN_SM:
      case SC_OCT_US: case SC_OCT_SM:
      case SC_HEX_US: case SC_HEX_SM:
      case SC_CSD:
        SC_REPORT_ERROR("not implemented",
                        "is_valid_base( sc_numrep base ) : "
                        "bases SC_CSD, or ending in _US and _SM are "
                        "not supported");
        break;
      default:
        std::stringstream msg;
        msg << "is_valid_base( sc_numrep base ) : base = " << base <<
               " is not valid";
        SC_REPORT_ERROR(sc_core::SC_ID_VALUE_NOT_VALID_, msg.str().c_str());
    }
}

// ----------------------------------------------------------------------------
//  ENUM : sc_numrep
//
//  Enumeration of number representations for character string conversion.
// ----------------------------------------------------------------------------

const std::string
to_string(sc_numrep numrep)
{
    switch (numrep) {
#define CASE_ENUM2STR(Value) case Value: return #Value

      CASE_ENUM2STR(SC_DEC);

      CASE_ENUM2STR(SC_BIN);
      CASE_ENUM2STR(SC_BIN_US);
      CASE_ENUM2STR(SC_BIN_SM);

      CASE_ENUM2STR(SC_OCT);
      CASE_ENUM2STR(SC_OCT_US);
      CASE_ENUM2STR(SC_OCT_SM);

      CASE_ENUM2STR(SC_HEX);
      CASE_ENUM2STR(SC_HEX_US);
      CASE_ENUM2STR(SC_HEX_SM);

      CASE_ENUM2STR(SC_CSD);

#undef CASE_ENUM2STR

      default:
        return "unknown";
    }
}

// ----------------------------------------------------------------------------
//  SECTION: General utility functions.
// ----------------------------------------------------------------------------

// Return the number of characters to advance the source of c.  This
// function implements one move of the FSM to parse the following
// regular expressions. Error checking is done in the caller.

small_type
fsm_move(char c, small_type &b, small_type &s, small_type &state)
{
    // Possible regular expressions (REs):
    // Let N = any digit depending on the base.
    //    1. [0|1|..|9]N*
    //    2. [+|-][0|1|..|9]N*
    //    3. 0[b|B|d|D|o|O|x|X][0|1|..|F]N*
    //    4. [+|-]?0[b|B|d|D|o|O|x|X][0|1|..|F]N*
    //
    // The finite state machine (FMS) to parse these regular expressions
    // has 4 states, 0 to 3. 0 is the initial state and 3 is the final
    // state.
    //
    // Default sign = SC_POS, default base = NB_DEFAULT_BASE.

    switch (state) {
      case 0: // The initial state.
        switch (c) {
          case '0': s = SC_POS; state = 1; return 0; // RE 1 or 3
          case '+': s = SC_POS; state = 2; return 1; // RE 2
          case '-': s = SC_NEG; state = 2; return 1; // RE 2
          default:
            s = SC_POS; b = NB_DEFAULT_BASE; state = 3; return 0; // RE 1
        }
        // break; //unreachable code
      case 1: // 0...
        switch (c) {
          case 'x': case 'X': b = SC_HEX; state = 3; return 2; // RE 3 or 4
          case 'd': case 'D': b = SC_DEC; state = 3; return 2; // RE 3 or 4
          case 'o': case 'O': b = SC_OCT; state = 3; return 2; // RE 3 or 4
          case 'b': case 'B': b = SC_BIN; state = 3; return 2; // RE 3 or 4
          default: b = NB_DEFAULT_BASE; state = 3; return 0; // RE 1
        }
        // break; //unreachable code
      case 2: // +... or -...
        switch (c) {
          case '0': state = 1; return 0; // RE 2 or 4
          default: b = NB_DEFAULT_BASE; state = 3; return 0; // RE 2
        }
        // break; //unreachable code
      case 3: // The final state.
        break;
      default:
        // Any other state is not possible.
        sc_assert((0 <= state) && (state <= 3));
    } // switch
    return 0;
}


// Get base b and sign s of the number in the char string v. Return a
// pointer to the first char after the point where b and s are
// determined or where the end of v is reached. The input string v has
// to be null terminated.
const char *
get_base_and_sign(const char *v, small_type &b, small_type &s)
{
#ifdef DEBUG_SYSTEMC
    sc_assert(v != NULL);
#endif
    const small_type STATE_START = 0;
    const small_type STATE_FINISH = 3;

    // Default sign = SC_POS, default base = 10.
    s = SC_POS;
    b = NB_DEFAULT_BASE;

    small_type state = STATE_START;
    small_type nskip = 0; // Skip that many chars.
    const char *u = v;

    while (*u) {
        if (isspace(*u)) { // Skip white space.
            ++u;
        } else {
            nskip += fsm_move(*u, b, s, state);
            if (state == STATE_FINISH)
              break;
            else
              ++u;
        }
    }

    // Test to see if the above loop executed more than it should
    // have. The max number of skipped chars is equal to the length of
    // the longest format specifier, e.g., "-0x".
    sc_assert(nskip <= 3);

    v += nskip;

    // Handles empty strings or strings without any digits after the
    // base or base and sign specifier.
    if (*v == '\0') {
        static const char msg[] =
            "get_base_and_sign( const char* v, small_type&, small_type& ) : "
            "v = \"\" is not valid";
        SC_REPORT_ERROR(sc_core::SC_ID_CONVERSION_FAILED_, msg);
    }
    return v;
}

//-----------------------------------------------------------------------------
//"parse_binary_bits"
//
// This function parses the supplied string into the supplied vector as a
// right justified bit value.
//    src_p  -> character string representing the bits to be parsed.
//    dst_n  =  number of words in data_p and ctrl_p.
//    data_p -> words w/BITS_PER_DIGIT bits to receive the value's data bits.
//    ctrl_p -> words w/BITS_PER_DIGIT bits to receive the value's control
//              bits, or zero.
// Result is true if value was non-zero.
//-----------------------------------------------------------------------------
void
parse_binary_bits(const char *src_p, int dst_n,
                  sc_digit *data_p, sc_digit *ctrl_p)
{
    int bit_i; // Number of bit now processing.
    sc_digit ctrl; // Control word now assembling.
    sc_digit data; // Data word now assembling.
    int delta_n; // src_n - dst_n*BITS_PER_DIGIT.
    int src_i; // Index in src_p now accessing (left to right).
    int src_n; // Length of source that is left in bits.
    int word_i; // Bit within word now accessing (left to right).

    // MAKE SURE WE HAVE A STRING TO PARSE:
    if (src_p == 0) {
        SC_REPORT_ERROR(sc_core::SC_ID_CONVERSION_FAILED_,
                        "character string is zero");
        return;
    }
    if (*src_p == 0) {
        SC_REPORT_ERROR(sc_core::SC_ID_CONVERSION_FAILED_,
                        "character string is empty");
        return;
    }


    // INDEX INTO THE SOURCE TO A DEPTH THAT WILL ACCOMODATE OUR SIZE:
    //
    // If the source is smaller than our value initialize our value to zero.

    src_n = strlen(src_p);
    delta_n = src_n - (dst_n*BITS_PER_DIGIT);
    if (delta_n > 0) {
        src_p = &src_p[delta_n];
        src_n -= delta_n;
    } else {
        for (word_i = 0; word_i < dst_n; word_i++)
            data_p[word_i] = 0;
        if (ctrl_p)
            for (word_i = 0; word_i < dst_n; word_i++)
                ctrl_p[word_i] = 0;
    }

    // LOOP OVER THE SOURCE ASSEMBLING WORDS AND PLACING THEM IN OUR VALUE:
    //
    // We stride right to left through the source in BITS_PER_DIGIT chunks.
    // Each of those chunks is processed from left to right a bit at a time.
    // We process the high order word specially, since there are less bits.
    src_n = src_n - BITS_PER_DIGIT;
    for (word_i=0; word_i < dst_n; word_i++) {
        src_i = src_n;

        // PARTIAL LAST WORD TO ASSEMBLE:
        if (src_i < 0) {
            src_n += BITS_PER_DIGIT;
            data = 0;
            ctrl = 0;
            for (src_i = 0; src_i < src_n; src_i++) {
                ctrl = ctrl << 1;
                data = data << 1;
                switch (src_p[src_i]) {
                  case 'X':
                  case 'x': ctrl = ctrl | 1; data = data | 1; break;
                  case '1': data = data | 1; break;
                  case 'Z':
                  case 'z': ctrl = ctrl | 1; break;
                  case '0': break;
                  default:
                    {
                        std::stringstream msg;
                        msg << "character string '" << src_p <<
                               "' is not valid";
                        SC_REPORT_ERROR(sc_core::SC_ID_CONVERSION_FAILED_,
                                        msg.str().c_str());
                        return;
                    }
                    break;
                }
            }
            if (ctrl_p)
                ctrl_p[word_i] = ctrl;
            data_p[word_i] = data;
            break;
        }

        // FULL WORD TO BE ASSEMBLED:
        ctrl = 0;
        data = 0;
        for (bit_i = 0; bit_i < BITS_PER_DIGIT; bit_i++) {
            ctrl = ctrl << 1;
            data = data << 1;
            switch (src_p[src_i++]) {
              case 'X':
              case 'x': ctrl = ctrl | 1; data = data | 1; break;
              case '1': data = data | 1; break;
              case 'Z':
              case 'z': ctrl = ctrl | 1; break;
              case '0': break;
              default:
                {
                    std::stringstream msg;
                    msg << "character string '" << src_p <<
                           "' is not valid";
                    SC_REPORT_ERROR(sc_core::SC_ID_CONVERSION_FAILED_,
                                    msg.str().c_str());
                    return;
                }
                break;
            }
        }
        if (ctrl_p)
            ctrl_p[word_i] = ctrl;
        data_p[word_i] = data;
        src_n = src_n - BITS_PER_DIGIT;
    }
}


//-----------------------------------------------------------------------------
//"parse_hex_bits"
//
// This function parses the supplied string into the supplied vector as a
// right justified bit value.
//    src_p  -> character string representing the bits to be parsed.
//    dst_n  =  number of words in data_p and ctrl_p.
//    data_p -> words w/32 bits to receive the value's data bits.
//    ctrl_p -> words w/32 bits to receive the value's control bits,
//              or zero.
// Result is true if value was non-zero.
//-----------------------------------------------------------------------------
void
parse_hex_bits(const char *src_p, int dst_n,
               sc_digit *data_p, sc_digit *ctrl_p)
{
    sc_digit ctrl; // Control word now assembling.
    sc_digit data; // Data word now assembling.
    int delta_n; // src_n - dst_n*BITS_PER_DIGIT.
    int digit_i; // Number of digit now processing.
    int src_i; // Index in src_p now accessing (left to right).
    int src_n; // Length of source that is left in bits.
    int word_i; // Bit within word now accessing (left to right).

    // MAKE SURE WE HAVE A STRING TO PARSE:
    if (src_p == 0) {
        SC_REPORT_ERROR(sc_core::SC_ID_CONVERSION_FAILED_,
                        "character string is zero");
        return;
    }
    if (*src_p == 0) {
        SC_REPORT_ERROR(sc_core::SC_ID_CONVERSION_FAILED_,
                        "character string is empty");
        return;
    }

    // INDEX INTO THE SOURCE TO A DEPTH THAT WILL ACCOMODATE OUR SIZE:
    //
    // If the source is smaller than our value initialize our value to zero.
    src_n = strlen(src_p);
    delta_n = src_n - (dst_n*8);
    if (delta_n > 0) {
        src_p = &src_p[delta_n];
        src_n -= delta_n;
    } else {
        for (word_i = 0; word_i < dst_n; word_i++)
            data_p[word_i] = 0;
        if (ctrl_p)
            for (word_i = 0; word_i < dst_n; word_i++)
                ctrl_p[word_i] = 0;
    }

    // LOOP OVER THE SOURCE ASSEMBLING WORDS AND PLACING THEM IN OUR VALUE:
    //
    // We stride right to left through the source in BITS_PER_DIGIT chunks.
    // Each of those chunks is processed from left to right a bit at a time.
    // We process the high order word specially, since there are less bits.
    src_n = src_n - 8;
    for (word_i = 0; word_i < dst_n; word_i++) {
        src_i = src_n;

        // PARTIAL LAST WORD TO ASSEMBLE:
        if (src_i < 0) {
            src_n += 8;
            data = 0;
            ctrl = 0;
            for (src_i = 0; src_i < src_n; src_i++) {
                ctrl = ctrl << 4;
                data = data << 4;
                switch (src_p[src_i]) {
                  case 'X':
                  case 'x': ctrl = ctrl | 15; data = data | 15; break;
                  case 'F':
                  case 'f': data = data | 15; break;
                  case 'E':
                  case 'e': data = data | 14; break;
                  case 'D':
                  case 'd': data = data | 13; break;
                  case 'C':
                  case 'c': data = data | 12; break;
                  case 'B':
                  case 'b': data = data | 11; break;
                  case 'A':
                  case 'a': data = data | 10; break;
                  case '9': data = data |  9; break;
                  case '8': data = data |  8; break;
                  case '7': data = data |  7; break;
                  case '6': data = data |  6; break;
                  case '5': data = data |  5; break;
                  case '4': data = data |  4; break;
                  case '3': data = data |  3; break;
                  case '2': data = data |  2; break;
                  case '1': data = data |  1; break;
                  case '0': break;
                  case 'Z':
                  case 'z': ctrl = ctrl | 15; break;
                  default:
                    {
                        std::stringstream msg;
                        msg << "character string '" << src_p <<
                               "' is not valid";
                        SC_REPORT_ERROR(sc_core::SC_ID_CONVERSION_FAILED_,
                                        msg.str().c_str());
                        return;
                    }
                    break;
                }
            }
            if (ctrl_p)
                ctrl_p[word_i] = ctrl;
            data_p[word_i] = data;
            break;
        }

        // FULL WORD TO BE ASSEMBLED:
        ctrl = 0;
        data = 0;
        for (digit_i = 0; digit_i < 8; digit_i++) {
            ctrl = ctrl << 4;
            data = data << 4;
            switch (src_p[src_i++]) {
              case 'X':
              case 'x': ctrl = ctrl | 15; data = data | 15; break;
              case 'F':
              case 'f': data = data | 15; break;
              case 'E':
              case 'e': data = data | 14; break;
              case 'D':
              case 'd': data = data | 13; break;
              case 'C':
              case 'c': data = data | 12; break;
              case 'B':
              case 'b': data = data | 11; break;
              case 'A':
              case 'a': data = data | 10; break;
              case '9': data = data |  9; break;
              case '8': data = data |  8; break;
              case '7': data = data |  7; break;
              case '6': data = data |  6; break;
              case '5': data = data |  5; break;
              case '4': data = data |  4; break;
              case '3': data = data |  3; break;
              case '2': data = data |  2; break;
              case '1': data = data |  1; break;
              case '0': break;
              case 'Z':
              case 'z': ctrl = ctrl | 15; break;
              default:
                {
                    std::stringstream msg;
                    msg << "character string '" << src_p << "' is not valid";
                    SC_REPORT_ERROR(sc_core::SC_ID_CONVERSION_FAILED_,
                                    msg.str().c_str() );
                    return;
                }
                break;
            }
        }
        if (ctrl_p)
            ctrl_p[word_i] = ctrl;
        data_p[word_i] = data;
        src_n = src_n - BITS_PER_DIGIT;
    }
}


// ----------------------------------------------------------------------------
//  SECTION: Utility functions involving unsigned vectors.
// ----------------------------------------------------------------------------

// Read u from a null terminated char string v. Note that operator>>
// in sc_nbcommon.cpp is similar to this function.
small_type
vec_from_str(int unb, int und, sc_digit *u, const char *v, sc_numrep base)
{

#ifdef DEBUG_SYSTEMC
    sc_assert((unb > 0) && (und > 0) && (u != NULL));
    sc_assert(v != NULL);
#endif
    is_valid_base(base);

    small_type b, s; // base and sign.

    v = get_base_and_sign(v, b, s);

    if (base != SC_NOBASE) {
        if (b == NB_DEFAULT_BASE) {
            b = base;
        } else {
            std::stringstream msg;
            msg << "vec_from_str( int, int, sc_digit*, const char*, " <<
                   "sc_numrep base ) : base = " << base <<
                   " does not match the default base";
            SC_REPORT_ERROR(sc_core::SC_ID_CONVERSION_FAILED_,
                            msg.str().c_str());
            return 0;
        }
    }

    vec_zero(und, u);

    char c;
    for (; (c = *v); ++v) {
        if (isalnum(c)) {
            small_type val;  // Numeric value of a char.

            if (isalpha(c)) // Hex digit.
                val = toupper(c) - 'A' + 10;
            else
                val = c - '0';

            if (val >= b) {
                std::stringstream msg;
                msg << "vec_from_str( int, int, sc_digit*, const char*, " <<
                       "sc_numrep base ) : '" << *v << "' is not a valid " <<
                       "digit in base " << b;
                SC_REPORT_ERROR(sc_core::SC_ID_CONVERSION_FAILED_,
                                msg.str().c_str());
                return 0;
            }

            // digit = digit * b + val;
            vec_mul_small_on(und, u, b);

            if (val)
                vec_add_small_on(und, u, val);
        } else {
            std::stringstream msg;
            msg << "vec_from_str( int, int, sc_digit*, const char*, " <<
                   "sc_numrep base ) : '" << *v << "' is not a valid " <<
                   "digit in base " << b;
            SC_REPORT_ERROR(sc_core::SC_ID_CONVERSION_FAILED_,
                            msg.str().c_str());
            return 0;
        }
    }

    return convert_signed_SM_to_2C_to_SM(s, unb, und, u);
}


// All vec_ functions assume that the vector to hold the result,
// called w, has sufficient length to hold the result. For efficiency
// reasons, we do not test whether or not we are out of bounds.

// Compute w = u + v, where w, u, and v are vectors.
// - ulen >= vlen
// - wlen >= sc_max(ulen, vlen) + 1
void
vec_add(int ulen, const sc_digit *u, int vlen, const sc_digit *v, sc_digit *w)
{
#ifdef DEBUG_SYSTEMC
    sc_assert((ulen > 0) && (u != NULL));
    sc_assert((vlen > 0) && (v != NULL));
    sc_assert(w != NULL);
    sc_assert(ulen >= vlen);
#endif

    const sc_digit *uend = (u + ulen);
    const sc_digit *vend = (v + vlen);

    sc_digit carry = 0; // Also used as sum to save space.

    // Add along the shorter v.
    while (v < vend) {
        carry += (*u++) + (*v++);
        (*w++) = carry & DIGIT_MASK;
        carry >>= BITS_PER_DIGIT;
    }

    // Propagate the carry.
    while (carry && (u < uend)) {
        carry = (*u++) + 1;
        (*w++) = carry & DIGIT_MASK;
        carry >>= BITS_PER_DIGIT;
    }

    // Copy the rest of u to the result.
    while (u < uend)
        (*w++) = (*u++);

    // Propagate the carry if it is still 1.
    if (carry)
        (*w) = 1;
}


// Compute u += v, where u and v are vectors.
// - ulen >= vlen
void
vec_add_on(int ulen, sc_digit *ubegin, int vlen, const sc_digit *v)
{
#ifdef DEBUG_SYSTEMC
    sc_assert((ulen > 0) && (ubegin != NULL));
    sc_assert((vlen > 0) && (v != NULL));
    sc_assert(ulen >= vlen);
#endif

    sc_digit *u = ubegin;
    const sc_digit *uend = (u + ulen);
    const sc_digit *vend = (v + vlen);

    sc_digit carry = 0; // Also used as sum to save space.

    // Add along the shorter v.
    while (v < vend) {
        carry += (*u) + (*v++);
        (*u++) = carry & DIGIT_MASK;
        carry >>= BITS_PER_DIGIT;
    }

    // Propagate the carry.
    while (carry && (u < uend)) {
        carry = (*u) + 1;
        (*u++) = carry & DIGIT_MASK;
        carry >>= BITS_PER_DIGIT;
    }

#ifdef   DEBUG_SYSTEMC
    if (carry != 0) {
        SC_REPORT_WARNING(sc_core::SC_ID_WITHOUT_MESSAGE_,
                          "vec_add_on( int, sc_digit*, int, const "
                          "sc_digit* ) : "
                          "result of addition is wrapped around");
    }
#endif
}


// Compute u += v, where u and v are vectors.
// - ulen < vlen
void
vec_add_on2(int ulen, sc_digit *ubegin, int,
#ifdef DEBUG_SYSTEMC
            vlen,
#endif
            const sc_digit *v)
{
#ifdef DEBUG_SYSTEMC
    sc_assert((ulen > 0) && (ubegin != NULL));
    sc_assert((vlen > 0) && (v != NULL));
    sc_assert(ulen < vlen);
#endif

    sc_digit *u = ubegin;
    const sc_digit *uend = (u + ulen);

    sc_digit carry = 0; // Also used as sum to save space.

    // Add along the shorter u.
    while (u < uend) {
        carry += (*u) + (*v++);
        (*u++) = carry & DIGIT_MASK;
        carry >>= BITS_PER_DIGIT;
    }

#ifdef   DEBUG_SYSTEMC
    if (carry != 0) {
        SC_REPORT_WARNING(sc_core::SC_ID_WITHOUT_MESSAGE_,
                          "vec_add_on2( int, sc_digit*, int, const "
                          "sc_digit* ) : "
                          "result of addition is wrapped around");
    }
#endif
}


// Compute w = u + v, where w and u are vectors, and v is a scalar.
void
vec_add_small(int ulen, const sc_digit *u, sc_digit v, sc_digit *w)
{
#ifdef DEBUG_SYSTEMC
    sc_assert((ulen > 0) && (u != NULL));
    sc_assert(w != NULL);
#endif

    const sc_digit *uend = (u + ulen);

    // Add along the shorter v.
    sc_digit carry = (*u++) + v;
    (*w++) = carry & DIGIT_MASK;
    carry >>= BITS_PER_DIGIT;

    // Propagate the carry.
    while (carry && (u < uend)) {
        carry = (*u++) + 1;
        (*w++) = carry & DIGIT_MASK;
        carry >>= BITS_PER_DIGIT;
    }

    // Copy the rest of u to the result.
    while (u < uend)
        (*w++) = (*u++);

    // Propagate the carry if it is still 1.
    if (carry)
        (*w) = 1;
}

// Compute u += v, where u is vectors, and v is a scalar.
void
vec_add_small_on(int ulen, sc_digit *u, sc_digit v)
{
#ifdef DEBUG_SYSTEMC
    sc_assert((ulen > 0) && (u != NULL));
#endif

    int i = 0;

    while (v && (i < ulen)) {
        v += u[i];
        u[i++] = v & DIGIT_MASK;
        v >>= BITS_PER_DIGIT;
    }

#ifdef   DEBUG_SYSTEMC
    if (v != 0) {
        SC_REPORT_WARNING(sc_core::SC_ID_WITHOUT_MESSAGE_,
                          "vec_add_small_on( int, sc_digit*, unsigned "
                          "long ) : "
                          "result of addition is wrapped around");
    }
#endif
}

// Compute w = u - v, where w, u, and v are vectors.
// - ulen >= vlen
// - wlen >= sc_max(ulen, vlen)
void
vec_sub(int ulen, const sc_digit *u, int vlen, const sc_digit *v, sc_digit *w)
{
#ifdef DEBUG_SYSTEMC
    sc_assert((ulen > 0) && (u != NULL));
    sc_assert((vlen > 0) && (v != NULL));
    sc_assert(w != NULL);
    sc_assert(ulen >= vlen);
#endif

    const sc_digit *uend = (u + ulen);
    const sc_digit *vend = (v + vlen);

    sc_digit borrow = 0; // Also used as diff to save space.

    // Subtract along the shorter v.
    while (v < vend) {
        borrow = ((*u++) + DIGIT_RADIX) - (*v++) - borrow;
        (*w++) = borrow & DIGIT_MASK;
        borrow = 1 - (borrow >> BITS_PER_DIGIT);
    }

    // Propagate the borrow.
    while (borrow && (u < uend)) {
        borrow = ((*u++) + DIGIT_RADIX) - 1;
        (*w++) = borrow & DIGIT_MASK;
        borrow = 1 - (borrow >> BITS_PER_DIGIT);
    }

#ifdef DEBUG_SYSTEMC
    sc_assert(borrow == 0);
#endif

    // Copy the rest of u to the result.
    while (u < uend)
        (*w++) = (*u++);
}

// Compute u = u - v, where u and v are vectors.
// - u > v
// - ulen >= vlen
void
vec_sub_on(int ulen, sc_digit *ubegin, int vlen, const sc_digit *v)
{
#ifdef DEBUG_SYSTEMC
    sc_assert((ulen > 0) && (ubegin != NULL));
    sc_assert((vlen > 0) && (v != NULL));
    sc_assert(ulen >= vlen);
#endif

    sc_digit *u = ubegin;
    const sc_digit *uend = (u + ulen);
    const sc_digit *vend = (v + vlen);

    sc_digit borrow = 0;   // Also used as diff to save space.

    // Subtract along the shorter v.
    while (v < vend) {
        borrow = ((*u) + DIGIT_RADIX) - (*v++) - borrow;
        (*u++) = borrow & DIGIT_MASK;
        borrow = 1 - (borrow >> BITS_PER_DIGIT);
    }

    // Propagate the borrow.
    while (borrow && (u < uend)) {
        borrow = ((*u) + DIGIT_RADIX) - 1;
        (*u++) = borrow & DIGIT_MASK;
        borrow = 1 - (borrow >> BITS_PER_DIGIT);
    }

#ifdef DEBUG_SYSTEMC
    sc_assert(borrow == 0);
#endif
}

// Compute u = v - u, where u and v are vectors.
// - v > u
// - ulen <= vlen or ulen > ulen
void
vec_sub_on2(int ulen, sc_digit *ubegin, int vlen, const sc_digit *v)
{
#ifdef DEBUG_SYSTEMC
    sc_assert((ulen > 0) && (ubegin != NULL));
    sc_assert((vlen > 0) && (v != NULL));
#endif

    sc_digit *u = ubegin;
    const sc_digit *uend = (u + sc_min(ulen, vlen));

    sc_digit borrow = 0;   // Also used as diff to save space.

    // Subtract along the shorter u.
    while (u < uend) {
        borrow = ((*v++) + DIGIT_RADIX) - (*u) - borrow;
        (*u++) = borrow & DIGIT_MASK;
        borrow = 1 - (borrow >> BITS_PER_DIGIT);
    }

#ifdef DEBUG_SYSTEMC
    if (borrow != 0) {
        SC_REPORT_WARNING(sc_core::SC_ID_WITHOUT_MESSAGE_,
                          "vec_sub_on2( int, sc_digit*, int, const "
                          "sc_digit* ) : "
                          "result of subtraction is wrapped around");
    }
#endif
}

// Compute w = u - v, where w and u are vectors, and v is a scalar.
void
vec_sub_small(int ulen, const sc_digit *u, sc_digit v, sc_digit *w)
{
#ifdef DEBUG_SYSTEMC
    sc_assert(ulen > 0);
    sc_assert(u != NULL);
#endif

    const sc_digit *uend = (u + ulen);

    // Add along the shorter v.
    sc_digit borrow = ((*u++) + DIGIT_RADIX) - v;
    (*w++) = borrow & DIGIT_MASK;
    borrow = 1 - (borrow >> BITS_PER_DIGIT);

    // Propagate the borrow.
    while (borrow && (u < uend)) {
        borrow = ((*u++) + DIGIT_RADIX) - 1;
        (*w++) = borrow & DIGIT_MASK;
        borrow = 1 - (borrow >> BITS_PER_DIGIT);
    }

#ifdef   DEBUG_SYSTEMC
    sc_assert(borrow == 0);
#endif

    // Copy the rest of u to the result.
    while (u < uend)
        (*w++) = (*u++);
}


// Compute u -= v, where u is vectors, and v is a scalar.
void
vec_sub_small_on(int ulen, sc_digit *u, sc_digit v)
{
#ifdef DEBUG_SYSTEMC
    sc_assert((ulen > 0) && (u != NULL));
#endif

    for (int i = 0; i < ulen; ++i) {
      v = (u[i] + DIGIT_RADIX) - v;
      u[i] = v & DIGIT_MASK;
      v = 1 - (v >> BITS_PER_DIGIT);
    }

#ifdef DEBUG_SYSTEMC
    sc_assert(v == 0);
#endif
}

// Compute w = u * v, where w, u, and v are vectors.
void
vec_mul(int ulen, const sc_digit *u, int vlen, const sc_digit *vbegin,
        sc_digit *wbegin)
{

  /* Consider u = Ax + B and v = Cx + D where x is equal to
     HALF_DIGIT_RADIX. In other words, A is the higher half of u and
     B is the lower half of u. The interpretation for v is
     similar. Then, we have the following picture:

              u_h     u_l
     u: -------- --------
               A        B

              v_h     v_l
     v: -------- --------
               C        D

     result (d):
     carry_before:                           -------- --------
                                              carry_h  carry_l
     result_before:        -------- -------- -------- --------
                               R1_h     R1_l     R0_h     R0_l
                                             -------- --------
                                                 BD_h     BD_l
                                    -------- --------
                                        AD_h     AD_l
                                    -------- --------
                                        BC_h     BC_l
                           -------- --------
                               AC_h     AC_l
     result_after:         -------- -------- -------- --------
                              R1_h'    R1_l'    R0_h'    R0_l'

     prod_l = R0_h|R0_l + B * D  + 0|carry_l
            = R0_h|R0_l + BD_h|BD_l + 0|carry_l

     prod_h = A * D + B * C + high_half(prod_l) + carry_h
            = AD_h|AD_l + BC_h|BC_l + high_half(prod_l) + 0|carry_h

     carry = A * C + high_half(prod_h)
           = AC_h|AC_l + high_half(prod_h)

     R0_l' = low_half(prod_l)

     R0_h' = low_half(prod_h)

     R0 = high_half(prod_h)|low_half(prod_l)

     where '|' is the concatenation operation and the suffixes 0 and 1
     show the iteration number, i.e., 0 is the current iteration and 1
     is the next iteration.

     NOTE: sc_max(prod_l, prod_h, carry) <= 2 * x^2 - 1, so any
     of these numbers can be stored in a digit.

     NOTE: low_half(u) returns the lower BITS_PER_HALF_DIGIT of u,
     whereas high_half(u) returns the rest of the bits, which may
     contain more bits than BITS_PER_HALF_DIGIT.
  */

#ifdef DEBUG_SYSTEMC
    sc_assert((ulen > 0) && (u != NULL));
    sc_assert((vlen > 0) && (vbegin != NULL));
    sc_assert(wbegin != NULL);
#endif

#define prod_h carry
    const sc_digit *uend = (u + ulen);
    const sc_digit *vend = (vbegin + vlen);

    while (u < uend) {
        sc_digit u_h = (*u++); // A|B
        sc_digit u_l = low_half(u_h); // B
        u_h = high_half(u_h); // A

#ifdef DEBUG_SYSTEMC
        // The overflow bits must be zero.
        sc_assert(u_h == (u_h & HALF_DIGIT_MASK));
#endif
        sc_digit carry = 0;
        sc_digit *w = (wbegin++);
        const sc_digit *v = vbegin;

        while (v < vend) {
            sc_digit v_h = (*v++); // C|D
            sc_digit v_l = low_half(v_h); // D

            v_h = high_half(v_h); // C

#ifdef   DEBUG_SYSTEMC
            // The overflow bits must be zero.
            sc_assert(v_h == (v_h & HALF_DIGIT_MASK));
#endif

            sc_digit prod_l = (*w) + u_l * v_l + low_half(carry);
            prod_h = u_h * v_l + u_l * v_h +
                high_half(prod_l) + high_half(carry);
            (*w++) = concat(low_half(prod_h), low_half(prod_l));
            carry = u_h * v_h + high_half(prod_h);
        }
        (*w) = carry;
    }
#undef prod_h
}

// Compute w = u * v, where w and u are vectors, and v is a scalar.
// - 0 < v < HALF_DIGIT_RADIX.
void
vec_mul_small(int ulen, const sc_digit *u, sc_digit v, sc_digit *w)
{
#ifdef DEBUG_SYSTEMC
    sc_assert((ulen > 0) && (u != NULL));
    sc_assert(w != NULL);
    sc_assert((0 < v) && (v < HALF_DIGIT_RADIX));
#endif

#define prod_h carry

    const sc_digit *uend = (u + ulen);
    sc_digit carry = 0;
    while (u < uend) {
        sc_digit u_AB = (*u++);
#ifdef DEBUG_SYSTEMC
        // The overflow bits must be zero.
        sc_assert(high_half(u_AB) == high_half_masked(u_AB));
#endif
        sc_digit prod_l = v * low_half(u_AB) + low_half(carry);
        prod_h = v * high_half(u_AB) + high_half(prod_l) + high_half(carry);
        (*w++) = concat(low_half(prod_h), low_half(prod_l));
        carry = high_half(prod_h);
    }
    (*w) = carry;
#undef prod_h
}

// Compute u = u * v, where u is a vector, and v is a scalar.
// - 0 < v < HALF_DIGIT_RADIX.
void
vec_mul_small_on(int ulen, sc_digit *u, sc_digit v)
{
#ifdef DEBUG_SYSTEMC
    sc_assert((ulen > 0) && (u != NULL));
    sc_assert((0 < v) && (v < HALF_DIGIT_RADIX));
#endif

#define   prod_h carry
    sc_digit carry = 0;
    for (int i = 0; i < ulen; ++i) {
#ifdef DEBUG_SYSTEMC
        // The overflow bits must be zero.
        sc_assert(high_half(u[i]) == high_half_masked(u[i]));
#endif
        sc_digit prod_l = v * low_half(u[i]) + low_half(carry);
        prod_h = v * high_half(u[i]) + high_half(prod_l) + high_half(carry);
        u[i] = concat(low_half(prod_h), low_half(prod_l));
        carry = high_half(prod_h);
    }
#undef   prod_h

#ifdef   DEBUG_SYSTEMC
    if (carry != 0) {
        SC_REPORT_WARNING(sc_core::SC_ID_WITHOUT_MESSAGE_,
                          "vec_mul_small_on( int, sc_digit*, unsigned "
                          "long ) : "
                          "result of multiplication is wrapped around");
    }
#endif
}

// Compute w = u / v, where w, u, and v are vectors.
// - u and v are assumed to have at least two digits as uchars.
void
vec_div_large(int ulen, const sc_digit *u, int vlen, const sc_digit *v,
              sc_digit *w)
{
#ifdef DEBUG_SYSTEMC
    sc_assert((ulen > 0) && (u != NULL));
    sc_assert((vlen > 0) && (v != NULL));
    sc_assert(w != NULL);
    sc_assert(BITS_PER_DIGIT >= 3 * BITS_PER_BYTE);
#endif

    // We will compute q = x / y where x = u and y = v. The reason for
    // using x and y is that x and y are BYTE_RADIX copies of u and v,
    // respectively. The use of BYTE_RADIX radix greatly simplifies the
    // complexity of the division operation. These copies are also
    // needed even when we use DIGIT_RADIX representation.

    int xlen = BYTES_PER_DIGIT * ulen + 1;
    int ylen = BYTES_PER_DIGIT * vlen;

#ifdef SC_MAX_NBITS
    uchar x[DIV_CEIL2(SC_MAX_NBITS, BITS_PER_BYTE)];
    uchar y[DIV_CEIL2(SC_MAX_NBITS, BITS_PER_BYTE)];
    uchar q[DIV_CEIL2(SC_MAX_NBITS, BITS_PER_BYTE)];
#else
    uchar *x = new uchar[xlen];
    uchar *y = new uchar[ylen];
    // valgrind complains about us accessing too far to so leave a buffer.
    uchar *q = new uchar[(xlen - ylen) + 10];
#endif

    // q corresponds to w.

    // Set (uchar) x = (sc_digit) u.
    xlen = vec_to_char(ulen, u, xlen, x);

    // Skip all the leading zeros in x.
    while ((--xlen >= 0) && (! x[xlen]))
        continue;
    xlen++;

    // Set (uchar) y = (sc_digit) v.
    ylen = vec_to_char(vlen, v, ylen, y);

    // Skip all the leading zeros in y.
    while ((--ylen >= 0) && (! y[ylen]))
        continue;
    ylen++;

#ifdef DEBUG_SYSTEMC
    sc_assert(xlen > 1);
    sc_assert(ylen > 1);
#endif

    // At this point, all the leading zeros are eliminated from x and y.

    // Zero the last digit of x.
    x[xlen] = 0;

    // The first two digits of y.
    sc_digit y2 = (y[ylen - 1] << BITS_PER_BYTE) + y[ylen - 2];

    const sc_digit DOUBLE_BITS_PER_BYTE = 2 * BITS_PER_BYTE;

    // Find each q[k].
    for (int k = (xlen - ylen); k >= 0; --k) {
        // qk is a guess for q[k] such that q[k] = qk or qk - 1.
        sc_digit qk;

        // Find qk by just using 2 digits of y and 3 digits of x. The
        // following code assumes that sizeof(sc_digit) >= 3 BYTEs.
        int k2 = k + ylen;

        qk = ((x[k2] << DOUBLE_BITS_PER_BYTE) +
              (x[k2 - 1] << BITS_PER_BYTE) + x[k2 - 2]) / y2;

        if (qk >= BYTE_RADIX) // qk cannot be larger than the largest
            qk = BYTE_RADIX - 1; // digit in BYTE_RADIX.

        // q[k] = qk or qk - 1. The following if-statement determines which:
        if (qk) {
            uchar *xk = (x + k);  // A shortcut for x[k].

            // x = x - y * qk :
            sc_digit carry = 0;

            for (int i = 0; i < ylen; ++i) {
                carry += y[i] * qk;
                sc_digit diff = (xk[i] + BYTE_RADIX) - (carry & BYTE_MASK);
                xk[i] = (uchar)(diff & BYTE_MASK);
                carry = (carry >> BITS_PER_BYTE) +
                    (1 - (diff >> BITS_PER_BYTE));
            }

            // If carry, qk may be one too large.
            if (carry) {
                // 2's complement the last digit.
                carry = (xk[ylen] + BYTE_RADIX) - carry;
                xk[ylen] = (uchar)(carry & BYTE_MASK);
                carry = 1 - (carry >> BITS_PER_BYTE);

                if (carry) {

                  // qk was one too large, so decrement it.
                  --qk;

                  // Since qk was decreased by one, y must be added to x:
                  // x = x - y * (qk - 1) = x - y * qk + y = x_above + y.
                  carry = 0;

                  for (int i = 0; i < ylen; ++i) {
                      carry += xk[i] + y[i];
                      xk[i] = (uchar)(carry & BYTE_MASK);
                      carry >>= BITS_PER_BYTE;
                  }

                  if (carry)
                      xk[ylen] = (uchar)((xk[ylen] + 1) & BYTE_MASK);

                }  // second if carry
            }  // first if carry
        }  // if qk
        q[k] = (uchar)qk;
    }  // for k

    // Set (sc_digit) w = (uchar) q.
    vec_from_char(xlen - ylen + 1, q, ulen, w);

#ifndef SC_MAX_NBITS
    delete [] x;
    delete [] y;
    delete [] q;
#endif

}

// Compute w = u / v, where u and w are vectors, and v is a scalar.
// - 0 < v < HALF_DIGIT_RADIX. Below, we rename w to q.
void
vec_div_small(int ulen, const sc_digit *u, sc_digit v, sc_digit *q)
{
    // Given (u = u_1u_2...u_n)_b = (q = q_1q_2...q_n) * v + r, where b
    // is the base, and 0 <= r < v. Then, the algorithm is as follows:
    //
    // r = 0;
    // for (j = 1; j <= n; j++) {
    //   q_j = (r * b + u_j) / v;
    //   r = (r * b + u_j) % v;
    // }
    //
    // In our case, b = DIGIT_RADIX, and u = Ax + B and q = Cx + D where
    // x = HALF_DIGIT_RADIX. Note that r < v < x and b = x^2. Then, a
    // typical situation is as follows:
    //
    // ---- ----
    // 0    r
    //           ---- ----
    //           A    B
    //      ---- ---- ----
    //      r    A    B     = r * b + u
    //
    // Hence, C = (r|A) / v.
    //        D = (((r|A) % v)|B) / v
    //        r = (((r|A) % v)|B) % v

#ifdef DEBUG_SYSTEMC
    sc_assert((ulen > 0) && (u != NULL));
    sc_assert(q != NULL);
    sc_assert((0 < v) && (v < HALF_DIGIT_RADIX));
#endif

#define q_h r
    sc_digit r = 0;
    const sc_digit *ubegin = u;

    u += ulen;
    q += ulen;

    while (ubegin < u) {
        sc_digit u_AB = (*--u); // A|B

#ifdef DEBUG_SYSTEMC
        // The overflow bits must be zero.
        sc_assert(high_half(u_AB) == high_half_masked(u_AB));
#endif

        sc_digit num = concat(r, high_half(u_AB)); // num = r|A
        q_h = num / v; // C
        num = concat((num % v), low_half(u_AB)); // num = (((r|A) % v)|B)
        (*--q) = concat(q_h, num / v); // q = C|D
        r = num % v;
    }
#undef q_h
}

// Compute w = u % v, where w, u, and v are vectors.
// - u and v are assumed to have at least two digits as uchars.
void
vec_rem_large(int ulen, const sc_digit *u, int vlen, const sc_digit *v,
              sc_digit *w)
{
#ifdef DEBUG_SYSTEMC
    sc_assert((ulen > 0) && (u != NULL));
    sc_assert((vlen > 0) && (v != NULL));
    sc_assert(w != NULL);
    sc_assert(BITS_PER_DIGIT >= 3 * BITS_PER_BYTE);
#endif

    // This function is adapted from vec_div_large.
    int xlen = BYTES_PER_DIGIT * ulen + 1;
    int ylen = BYTES_PER_DIGIT * vlen;

#ifdef SC_MAX_NBITS
    uchar x[DIV_CEIL2(SC_MAX_NBITS, BITS_PER_BYTE)];
    uchar y[DIV_CEIL2(SC_MAX_NBITS, BITS_PER_BYTE)];
#else
    uchar *x = new uchar[xlen];
    uchar *y = new uchar[ylen];
#endif

    // r corresponds to w.

    // Set (uchar) x = (sc_digit) u.
    xlen = vec_to_char(ulen, u, xlen, x);

    // Skip all the leading zeros in x.
    while ((--xlen >= 0) && (!x[xlen]))
        continue;
    xlen++;

    // Set (uchar) y = (sc_digit) v.
    ylen = vec_to_char(vlen, v, ylen, y);

    // Skip all the leading zeros in y.
    while ((--ylen >= 0) && (!y[ylen]))
        continue;
    ylen++;

#ifdef DEBUG_SYSTEMC
    sc_assert(xlen > 1);
    sc_assert(ylen > 1);
#endif

    // At this point, all the leading zeros are eliminated from x and y.

    // Zero the last digit of x.
    x[xlen] = 0;

    // The first two digits of y.
    sc_digit y2 = (y[ylen - 1] << BITS_PER_BYTE) + y[ylen - 2];

    const sc_digit DOUBLE_BITS_PER_BYTE = 2 * BITS_PER_BYTE;

    // Find each q[k].
    for (int k = xlen - ylen; k >= 0; --k) {
        // qk is a guess for q[k] such that q[k] = qk or qk - 1.
        sc_digit qk;

        // Find qk by just using 2 digits of y and 3 digits of x. The
        // following code assumes that sizeof(sc_digit) >= 3 BYTEs.
        int k2 = k + ylen;

        qk = ((x[k2] << DOUBLE_BITS_PER_BYTE) +
            (x[k2 - 1] << BITS_PER_BYTE) + x[k2 - 2]) / y2;

        if (qk >= BYTE_RADIX) // qk cannot be larger than the largest
            qk = BYTE_RADIX - 1; // digit in BYTE_RADIX.

        // q[k] = qk or qk - 1. The following if-statement determines which.
        if (qk) {
            uchar *xk = (x + k);  // A shortcut for x[k].

            // x = x - y * qk;
            sc_digit carry = 0;

            for (int i = 0; i < ylen; ++i) {
                carry += y[i] * qk;
                sc_digit diff = (xk[i] + BYTE_RADIX) - (carry & BYTE_MASK);
                xk[i] = (uchar)(diff & BYTE_MASK);
                carry = (carry >> BITS_PER_BYTE) +
                    (1 - (diff >> BITS_PER_BYTE));
            }

            if (carry) {
                // 2's complement the last digit.
                carry = (xk[ylen] + BYTE_RADIX) - carry;
                xk[ylen] = (uchar)(carry & BYTE_MASK);
                carry = 1 - (carry >> BITS_PER_BYTE);

                if (carry) {
                  // qk was one too large, so decrement it.
                  // --qk;

                  // x = x - y * (qk - 1) = x - y * qk + y = x_above + y.
                  carry = 0;

                  for (int i = 0; i < ylen; ++i) {
                      carry += xk[i] + y[i];
                      xk[i] = (uchar)(carry & BYTE_MASK);
                      carry >>= BITS_PER_BYTE;
                  }

                  if (carry)
                      xk[ylen] = (uchar)((xk[ylen] + 1) & BYTE_MASK);
                }  // second if carry
            } // first if carry
        }  // if qk
    }  // for k

    // Set (sc_digit) w = (uchar) x for the remainder.
    vec_from_char(ylen, x, ulen, w);

#ifndef SC_MAX_NBITS
    delete [] x;
    delete [] y;
#endif

}

// Compute r = u % v, where u is a vector, and r and v are scalars.
// - 0 < v < HALF_DIGIT_RADIX.
// - The remainder r is returned.
sc_digit
vec_rem_small(int ulen, const sc_digit *u, sc_digit v)
{

#ifdef DEBUG_SYSTEMC
    sc_assert((ulen > 0) && (u != NULL));
    sc_assert((0 < v) && (v < HALF_DIGIT_RADIX));
#endif

    // This function is adapted from vec_div_small().

    sc_digit r = 0;
    const sc_digit *ubegin = u;

    u += ulen;

    while (ubegin < u) {
        sc_digit u_AB = (*--u); // A|B
#ifdef DEBUG_SYSTEMC
        // The overflow bits must be zero.
        sc_assert(high_half(u_AB) == high_half_masked(u_AB));
#endif
        // r = (((r|A) % v)|B) % v
        r = (concat(((concat(r, high_half(u_AB))) % v), low_half(u_AB))) % v;
    }

    return r;
}

// u = u / v, r = u % v.
sc_digit
vec_rem_on_small(int ulen, sc_digit *u, sc_digit v)
{
#ifdef DEBUG_SYSTEMC
    sc_assert((ulen > 0) && (u != NULL));
    sc_assert(v > 0);
#endif

#define q_h r
    sc_digit r = 0;
    const sc_digit *ubegin = u;

    u += ulen;
    while (ubegin < u) {
        sc_digit u_AB = (*--u); // A|B
#ifdef DEBUG_SYSTEMC
        // The overflow bits must be zero.
        sc_assert(high_half(u_AB) == high_half_masked(u_AB));
#endif
        sc_digit num = concat(r, high_half(u_AB)); // num = r|A
        q_h = num / v; // C
        num = concat((num % v), low_half(u_AB)); // num = (((r|A) % v)|B)
        (*u) = concat(q_h, num / v); // q = C|D
        r = num % v;
    }
#undef q_h
    return r;
}

// Set (uchar) v = (sc_digit) u. Return the new vlen.
int
vec_to_char(int ulen, const sc_digit *u, int vlen, uchar *v)
{
#ifdef DEBUG_SYSTEMC
    sc_assert((ulen > 0) && (u != NULL));
    sc_assert((vlen > 0) && (v != NULL));
#endif

    int nbits = ulen * BITS_PER_DIGIT;
    int right = 0;
    int left = right + BITS_PER_BYTE - 1;

    vlen = 0;
    while (nbits > 0) {
        int left_digit = left / BITS_PER_DIGIT;
        int right_digit = right / BITS_PER_DIGIT;
        int nsr = ((vlen << LOG2_BITS_PER_BYTE) % BITS_PER_DIGIT);
        int d = u[right_digit] >> nsr;

        if (left_digit != right_digit) {
            if (left_digit < ulen)
                d |= u[left_digit] << (BITS_PER_DIGIT - nsr);
        }

        v[vlen++] = (uchar)(d & BYTE_MASK);

        left += BITS_PER_BYTE;
        right += BITS_PER_BYTE;
        nbits -= BITS_PER_BYTE;
    }
    return vlen;
}

// Set (sc_digit) v = (uchar) u.
// - sizeof(uchar) <= sizeof(sc_digit),
void
vec_from_char(int ulen, const uchar *u, int vlen, sc_digit *v)
{
#ifdef DEBUG_SYSTEMC
    sc_assert((ulen > 0) && (u != NULL));
    sc_assert((vlen > 0) && (v != NULL));
    sc_assert(sizeof(uchar) <= sizeof(sc_digit));
#endif

    sc_digit *vend = (v + vlen);

    const int nsr = BITS_PER_DIGIT - BITS_PER_BYTE;
    const sc_digit mask = one_and_ones(nsr);

    (*v) = (sc_digit) u[ulen - 1];

    for (int i = ulen - 2; i >= 0; --i) {
        // Manual inlining of vec_shift_left().
        sc_digit *viter = v;
        sc_digit carry = 0;
        while (viter < vend) {
            sc_digit vval = (*viter);
            (*viter++) = (((vval & mask) << BITS_PER_BYTE) | carry);
            carry = vval >> nsr;
        }

        if (viter < vend)
            (*viter) = carry;

        (*v) |= (sc_digit)u[i];
    }
}

// Set u <<= nsl.
// If nsl is negative, it is ignored.
void
vec_shift_left(int ulen, sc_digit *u, int nsl)
{
#ifdef DEBUG_SYSTEMC
    sc_assert((ulen > 0) && (u != NULL));
#endif

    if (nsl <= 0)
        return;

    // Shift left whole digits if nsl is large enough.
    if (nsl >= (int) BITS_PER_DIGIT) {
        int nd;
        if (nsl % BITS_PER_DIGIT == 0) {
            nd = nsl / BITS_PER_DIGIT; // No need to use DIV_CEIL(nsl).
            nsl = 0;
        } else {
            nd = DIV_CEIL(nsl) - 1;
            nsl -= nd * BITS_PER_DIGIT;
        }

        if (nd) {
            // Shift left for nd digits.
            for (int j = ulen - 1; j >= nd; --j)
                u[j] = u[j - nd];

            vec_zero(sc_min(nd, ulen), u);
        }
        if (nsl == 0)
            return;
    }

    // Shift left if nsl < BITS_PER_DIGIT.
    sc_digit *uiter = u;
    sc_digit *uend = uiter + ulen;

    int nsr = BITS_PER_DIGIT - nsl;
    sc_digit mask = one_and_ones(nsr);

    sc_digit carry = 0;

    while (uiter < uend) {
        sc_digit uval = (*uiter);
        (*uiter++) = (((uval & mask) << nsl) | carry);
        carry = uval >> nsr;
    }

    if (uiter < uend)
        (*uiter) = carry;
}

// Set u >>= nsr.
// If nsr is negative, it is ignored.
void
vec_shift_right(int ulen, sc_digit *u, int nsr, sc_digit fill)
{
#ifdef DEBUG_SYSTEMC
    sc_assert((ulen > 0) && (u != NULL));
#endif

    // fill is usually either 0 or DIGIT_MASK; it can be any value.
    if (nsr <= 0)
        return;

    // Shift right whole digits if nsr is large enough.
    if (nsr >= (int) BITS_PER_DIGIT) {
        int nd;
        if (nsr % BITS_PER_DIGIT == 0) {
            nd = nsr / BITS_PER_DIGIT;
            nsr = 0;
        } else {
            nd = DIV_CEIL(nsr) - 1;
            nsr -= nd * BITS_PER_DIGIT;
        }

        if (nd) {
            // Shift right for nd digits.
            for (int j = 0; j < (ulen - nd); ++j)
                u[j] = u[j + nd];

            if (fill) {
                for (int j = ulen - sc_min( nd, ulen ); j < ulen; ++j)
                    u[j] = fill;
            } else {
                vec_zero(ulen - sc_min( nd, ulen ), ulen, u);
            }
        }
        if (nsr == 0)
          return;
    }

    // Shift right if nsr < BITS_PER_DIGIT.
    sc_digit *ubegin = u;
    sc_digit *uiter = (ubegin + ulen);

    int nsl = BITS_PER_DIGIT - nsr;
    sc_digit mask = one_and_ones(nsr);

    sc_digit carry = (fill & mask) << nsl;

    while (ubegin < uiter) {
        sc_digit uval = (*--uiter);
        (*uiter) = (uval >> nsr) | carry;
        carry = (uval & mask) << nsl;
    }
}


// Let u[l..r], where l and r are left and right bit positions
// respectively, be equal to its mirror image.
void
vec_reverse(int unb, int und, sc_digit *ud, int l, int r)
{
#ifdef DEBUG_SYSTEMC
    sc_assert((unb > 0) && (und > 0) && (ud != NULL));
    sc_assert((0 <= r) && (r <= l) && (l < unb));
#endif

    if (l < r) {
        std::stringstream msg;
        msg << "vec_reverse( int, int, sc_digit*, int l, int r ) : " <<
               "l = " << l << " < r = " << r << " is not valid",
        SC_REPORT_ERROR(sc_core::SC_ID_CONVERSION_FAILED_, msg.str().c_str());
        return;
    }

    // Make sure that l and r are within bounds.
    r = sc_max(r, 0);
    l = sc_min(l, unb - 1);

    // Allocate memory for processing.
#ifdef SC_MAX_NBITS
    sc_digit d[MAX_NDIGITS];
#else
    sc_digit *d = new sc_digit[und];
#endif

    // d is a copy of ud.
    vec_copy(und, d, ud);

    // Based on the value of the ith in d, find the value of the jth bit
    // in ud.
    for (int i = l, j = r; i >= r; --i, ++j) {
        if ((d[digit_ord(i)] & one_and_zeros(bit_ord(i))) != 0) // Test.
            ud[digit_ord(j)] |= one_and_zeros(bit_ord(j)); // Set.
        else
            ud[digit_ord(j)] &= ~(one_and_zeros(bit_ord(j))); // Clear.
    }

#ifndef SC_MAX_NBITS
    delete [] d;
#endif
}

#ifdef SC_MAX_NBITS
void test_bound_failed(int nb)
{
    std::stringstream msg;
    msg << "test_bound( int nb ) : "
           "nb = " << nb << " > SC_MAX_NBITS = " << SC_MAX_NBITS <<
           "  is not valid";
    SC_REPORT_ERROR(sc_core::SC_ID_OUT_OF_BOUNDS_, msg.str().c_str());
}
#endif // SC_MAX_NBITS

} // namespace sc_dt