oct-inttypes.cc

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////////////////////////////////////////////////////////////////////////
//
// Copyright (C) 2004-2022 The Octave Project Developers
//
// See the file COPYRIGHT.md in the top-level directory of this
// distribution or <https://octave.org/copyright/>.
//
// This file is part of Octave.
//
// Octave is free software: you can redistribute it and/or modify it
// under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// Octave is distributed in the hope that it will be useful, but
// WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with Octave; see the file COPYING.  If not, see
// <https://www.gnu.org/licenses/>.
//
////////////////////////////////////////////////////////////////////////
 
#if defined (HAVE_CONFIG_H)
#  include "config.h"
#endif
 
#include "fpucw-wrappers.h"
#include "lo-error.h"
#include "oct-inttypes.h"
 
template <typename T>
const octave_int<T> octave_int<T>::s_zero (static_cast<T> (0));
 
template <typename T>
const octave_int<T> octave_int<T>::s_one (static_cast<T> (1));
 
// Define type names.
 
#define DEFINE_OCTAVE_INT_TYPENAME(TYPE, TYPENAME)              \
  template <>                                                   \
  OCTAVE_API const char *                                       \
  octave_int<TYPE>::type_name (void) { return TYPENAME; }
 
DEFINE_OCTAVE_INT_TYPENAME (int8_t, "int8")
DEFINE_OCTAVE_INT_TYPENAME (int16_t, "int16")
DEFINE_OCTAVE_INT_TYPENAME (int32_t, "int32")
DEFINE_OCTAVE_INT_TYPENAME (int64_t, "int64")
DEFINE_OCTAVE_INT_TYPENAME (uint8_t, "uint8")
DEFINE_OCTAVE_INT_TYPENAME (uint16_t, "uint16")
DEFINE_OCTAVE_INT_TYPENAME (uint32_t, "uint32")
DEFINE_OCTAVE_INT_TYPENAME (uint64_t, "uint64")
 
template <class T>
template <class S>
T
octave_int_base<T>::convert_real (const S& value)
{
  // Compute proper thresholds.
  static const S thmin = compute_threshold (static_cast<S> (min_val ()),
                                            min_val ());
  static const S thmax = compute_threshold (static_cast<S> (max_val ()),
                                            max_val ());
  if (octave::math::isnan (value))
    return static_cast<T> (0);
  else if (value < thmin)
    return min_val ();
  else if (value > thmax)
    return max_val ();
  else
    {
      S rvalue = octave::math::round (value);
      return static_cast<T> (rvalue);
    }
}
 
#define INSTANTIATE_CONVERT_REAL_1(T, S)        \
  template                                      \
  OCTAVE_API                                    \
  T                                             \
  octave_int_base<T>::convert_real (const S&)
 
#define INSTANTIATE_CONVERT_REAL(S)             \
  INSTANTIATE_CONVERT_REAL_1 (int8_t, S);       \
  INSTANTIATE_CONVERT_REAL_1 (uint8_t, S);      \
  INSTANTIATE_CONVERT_REAL_1 (int16_t, S);      \
  INSTANTIATE_CONVERT_REAL_1 (uint16_t, S);     \
  INSTANTIATE_CONVERT_REAL_1 (int32_t, S);      \
  INSTANTIATE_CONVERT_REAL_1 (uint32_t, S);     \
  INSTANTIATE_CONVERT_REAL_1 (int64_t, S);      \
  INSTANTIATE_CONVERT_REAL_1 (uint64_t, S)
 
INSTANTIATE_CONVERT_REAL (double);
INSTANTIATE_CONVERT_REAL (float);
#if defined (OCTAVE_INT_USE_LONG_DOUBLE)
INSTANTIATE_CONVERT_REAL (long double);
#endif
 
#if defined (OCTAVE_INT_USE_LONG_DOUBLE)
 
#  if defined (OCTAVE_ENSURE_LONG_DOUBLE_OPERATIONS_ARE_NOT_TRUNCATED)
 
#    define DEFINE_OCTAVE_LONG_DOUBLE_CMP_OP_TEMPLATES(T)       \
  template <typename xop>                                       \
  bool                                                          \
  octave_int_cmp_op::external_mop (double x, T y)               \
  {                                                             \
    unsigned int oldcw = octave_begin_long_double_rounding ();  \
                                                                \
    bool retval = xop::op (static_cast<long double> (x),        \
                           static_cast<long double> (y));       \
                                                                \
    octave_end_long_double_rounding (oldcw);                    \
                                                                \
    return retval;                                              \
  }                                                             \
                                                                \
  template <typename xop>                                       \
  bool                                                          \
  octave_int_cmp_op::external_mop (T x, double y)               \
  {                                                             \
    unsigned int oldcw = octave_begin_long_double_rounding ();  \
                                                                \
    bool retval = xop::op (static_cast<long double> (x),        \
                           static_cast<long double> (y));       \
                                                                \
    octave_end_long_double_rounding (oldcw);                    \
                                                                \
    return retval;                                              \
  }
 
DEFINE_OCTAVE_LONG_DOUBLE_CMP_OP_TEMPLATES (int64_t)
DEFINE_OCTAVE_LONG_DOUBLE_CMP_OP_TEMPLATES (uint64_t)
 
#    define INSTANTIATE_LONG_DOUBLE_LONG_DOUBLE_CMP_OP(OP, T)           \
  template OCTAVE_API bool                                              \
  octave_int_cmp_op::external_mop<octave_int_cmp_op::OP> (double, T);   \
                                                                        \
  template OCTAVE_API bool                                              \
  octave_int_cmp_op::external_mop<octave_int_cmp_op::OP> (T, double)
 
#    define INSTANTIATE_LONG_DOUBLE_LONG_DOUBLE_CMP_OPS(T)      \
  INSTANTIATE_LONG_DOUBLE_LONG_DOUBLE_CMP_OP (lt, T);           \
  INSTANTIATE_LONG_DOUBLE_LONG_DOUBLE_CMP_OP (le, T);           \
  INSTANTIATE_LONG_DOUBLE_LONG_DOUBLE_CMP_OP (gt, T);           \
  INSTANTIATE_LONG_DOUBLE_LONG_DOUBLE_CMP_OP (ge, T);           \
  INSTANTIATE_LONG_DOUBLE_LONG_DOUBLE_CMP_OP (eq, T);           \
  INSTANTIATE_LONG_DOUBLE_LONG_DOUBLE_CMP_OP (ne, T)
 
INSTANTIATE_LONG_DOUBLE_LONG_DOUBLE_CMP_OPS (int64_t);
INSTANTIATE_LONG_DOUBLE_LONG_DOUBLE_CMP_OPS (uint64_t);
 
uint64_t
octave_external_uint64_uint64_mul (uint64_t x, uint64_t y)
{
  unsigned int oldcw = octave_begin_long_double_rounding ();
 
  uint64_t retval = octave_int_arith_base<uint64_t, false>::mul_internal (x, y);
 
  octave_end_long_double_rounding (oldcw);
 
  return retval;
}
 
int64_t
octave_external_int64_int64_mul (int64_t x, int64_t y)
{
  unsigned int oldcw = octave_begin_long_double_rounding ();
 
  int64_t retval = octave_int_arith_base<int64_t, true>::mul_internal (x, y);
 
  octave_end_long_double_rounding (oldcw);
 
  return retval;
}
 
// Note that if we return long double it is apparently possible for
// truncation to happen at the point of storing the result in retval,
// which can happen after we end long double rounding.  Attempt to avoid
// that problem by storing the full precision temporary value in the
// integer value before we end the long double rounding mode.
// Similarly, the conversion from the 64-bit integer type to long double
// must also occur in long double rounding mode.
 
#    define DEFINE_OCTAVE_LONG_DOUBLE_OP(T, OP, NAME)           \
  T                                                             \
  external_double_ ## T ## _ ## NAME (double x, T y)            \
  {                                                             \
    unsigned int oldcw = octave_begin_long_double_rounding ();  \
                                                                \
    T retval = T (x OP static_cast<long double> (y.value ()));  \
                                                                \
    octave_end_long_double_rounding (oldcw);                    \
                                                                \
    return retval;                                              \
  }                                                             \
                                                                \
  T                                                             \
  external_ ## T ## _double_ ## NAME (T x, double y)            \
  {                                                             \
    unsigned int oldcw = octave_begin_long_double_rounding ();  \
                                                                \
    T retval = T (static_cast<long double> (x.value ()) OP y);  \
                                                                \
    octave_end_long_double_rounding (oldcw);                    \
                                                                \
    return retval;                                              \
  }
 
#    define DEFINE_OCTAVE_LONG_DOUBLE_OPS(T)    \
  DEFINE_OCTAVE_LONG_DOUBLE_OP (T, +, add);     \
  DEFINE_OCTAVE_LONG_DOUBLE_OP (T, -, sub);     \
  DEFINE_OCTAVE_LONG_DOUBLE_OP (T, *, mul);     \
  DEFINE_OCTAVE_LONG_DOUBLE_OP (T, /, div)
 
DEFINE_OCTAVE_LONG_DOUBLE_OPS (octave_int64);
DEFINE_OCTAVE_LONG_DOUBLE_OPS (octave_uint64);
 
#  endif
 
#else
 
// Define comparison operators
 
template <typename xop>
bool
octave_int_cmp_op::emulate_mop (uint64_t x, double y)
{
  // The following cast changes the value to 2^64 (which is outside the range
  // of `uint64_t`).  Take care to handle this correctly (e.g., don't cast back
  // to `uint64_t`)!
  static const double xxup
    = static_cast<double> (std::numeric_limits<uint64_t>::max ());
  // This converts to the nearest double.  Unless there's an equality, the
  // result is clear.
  double xx = x;
  if (xx != y)
    return xop::op (xx, y);
  else
    {
      // If equality occurred we compare as integers.
      if (xx == xxup)
        return xop::gtval;
      else
        return xop::op (x, static_cast<uint64_t> (xx));
    }
}
 
template <typename xop>
bool
octave_int_cmp_op::emulate_mop (int64_t x, double y)
{
  // The following cast changes the value to 2^63 (which is outside the range
  // of `int64_t`).  Take care to handle this correctly (e.g., don't cast back
  // to `int64_t`)!  The same applies to the lower limit on systems using one's
  // complement.
  static const double xxup
    = static_cast<double> (std::numeric_limits<int64_t>::max ());
  static const double xxlo
    = static_cast<double> (std::numeric_limits<int64_t>::min ());
  // This converts to the nearest double.  Unless there's an equality, the
  // result is clear.
  double xx = x;
  if (xx != y)
    return xop::op (xx, y);
  else
    {
      // If equality occurred we compare as integers.
      if (xx == xxup)
        return xop::gtval;
      else if (xx == xxlo)
        return xop::ltval;
      else
        return xop::op (x, static_cast<int64_t> (xx));
    }
 
}
 
// We define double-int operations by reverting the operator
 
// A trait class reverting the operator
template <typename xop>
class rev_op
{
public:
  typedef xop op;
};
 
#define DEFINE_REVERTED_OPERATOR(OP1, OP2)      \
  template <>                                   \
  class rev_op<octave_int_cmp_op::OP1>          \
  {                                             \
  public:                                       \
    typedef octave_int_cmp_op::OP2 op;          \
  }
 
DEFINE_REVERTED_OPERATOR (lt, gt);
DEFINE_REVERTED_OPERATOR (gt, lt);
DEFINE_REVERTED_OPERATOR (le, ge);
DEFINE_REVERTED_OPERATOR (ge, le);
 
template <typename xop>
bool
octave_int_cmp_op::emulate_mop (double x, uint64_t y)
{
  typedef typename rev_op<xop>::op rop;
  return mop<rop> (y, x);
}
 
template <typename xop>
bool
octave_int_cmp_op::emulate_mop (double x, int64_t y)
{
  typedef typename rev_op<xop>::op rop;
  return mop<rop> (y, x);
}
 
// Define handlers for (u)int64 multiplication.
 
template <>
uint64_t
octave_int_arith_base<uint64_t, false>::mul_internal (uint64_t x, uint64_t y)
{
  // Get upper words
  uint64_t ux = x >> 32;
  uint64_t uy = y >> 32;
  uint64_t res;
  if (ux)
    {
      if (uy)
        goto overflow;
      else
        {
          uint64_t ly = static_cast<uint32_t> (y);
          uint64_t uxly = ux*ly;
          if (uxly >> 32)
            goto overflow;
          uxly <<= 32;  // never overflows
          uint64_t lx = static_cast<uint32_t> (x);
          uint64_t lxly = lx*ly;
          res = add (uxly, lxly);
        }
    }
  else if (uy)
    {
      uint64_t lx = static_cast<uint32_t> (x);
      uint64_t uylx = uy*lx;
      if (uylx >> 32)
        goto overflow;
      uylx <<= 32;  // never overflows
      uint64_t ly = static_cast<uint32_t> (y);
      uint64_t lylx = ly*lx;
      res = add (uylx, lylx);
    }
  else
    {
      uint64_t lx = static_cast<uint32_t> (x);
      uint64_t ly = static_cast<uint32_t> (y);
      res = lx*ly;
    }
 
  return res;
 
overflow:
  return max_val ();
}
 
template <>
int64_t
octave_int_arith_base<int64_t, true>::mul_internal (int64_t x, int64_t y)
{
  // The signed case is far worse.  The problem is that even if neither
  // integer fits into signed 32-bit range, the result may still be OK.
  // Uh oh.
 
  // Essentially, what we do is compute sign, multiply absolute values
  // (as above) and impose the sign.
 
  uint64_t usx = octave_int_abs (x);
  uint64_t usy = octave_int_abs (y);
  bool positive = (x < 0) == (y < 0);
 
  // Get upper words
  uint64_t ux = usx >> 32;
  uint64_t uy = usy >> 32;
  uint64_t res;
  if (ux)
    {
      if (uy)
        goto overflow;
      else
        {
          uint64_t ly = static_cast<uint32_t> (usy);
          uint64_t uxly = ux*ly;
          if (uxly >> 32)
            goto overflow;
          uxly <<= 32;  // never overflows
          uint64_t lx = static_cast<uint32_t> (usx);
          uint64_t lxly = lx*ly;
          res = uxly + lxly;
          if (res < uxly)
            goto overflow;
        }
    }
  else if (uy)
    {
      uint64_t lx = static_cast<uint32_t> (usx);
      uint64_t uylx = uy*lx;
      if (uylx >> 32)
        goto overflow;
      uylx <<= 32;  // never overflows
      uint64_t ly = static_cast<uint32_t> (usy);
      uint64_t lylx = ly*lx;
      res = uylx + lylx;
      if (res < uylx)
        goto overflow;
    }
  else
    {
      uint64_t lx = static_cast<uint32_t> (usx);
      uint64_t ly = static_cast<uint32_t> (usy);
      res = lx*ly;
    }
 
  if (positive)
    {
      if (res > static_cast<uint64_t> (max_val ()))
        return max_val ();
      else
        return static_cast<int64_t> (res);
    }
  else
    {
      if (res > static_cast<uint64_t> (min_val ()))
        return min_val ();
      else
        return -static_cast<int64_t> (res);
    }
 
overflow:
  return positive ? max_val () : min_val ();
 
}
 
template <>
OCTAVE_API octave_uint64
operator + (const octave_uint64& x, const double& y)
{
  return (y < 0) ? x - octave_uint64 (-y) : x + octave_uint64 (y);
}
 
template <>
OCTAVE_API octave_uint64
operator + (const double& x, const octave_uint64& y)
{
  return y + x;
}
 
template <>
OCTAVE_API octave_int64
operator + (const octave_int64& x, const double& y)
{
  // The following cast changes the value to 2^63 (which is outside the range
  // of `int64_t`).
  if (fabs (y) < static_cast<double> (octave_int64::max ()))
    return x + octave_int64 (y);
  else
    {
      // If the number is within the int64 range (the most common case,
      // probably), the above will work as expected.  If not, it's more
      // complicated - as long as y is within _twice_ the signed range, the
      // result may still be an integer.  An instance of such an operation is
      // 3*2^62 + (1+intmin ('int64')) that should yield int64 (2^62) + 1.
      // So what we do is to try to convert y/2 and add it twice.  Note that
      // if y/2 overflows, the result must overflow as well, and that y/2
      // cannot be a fractional number.
      octave_int64 y2 (y / 2);
      return (x + y2) + y2;
    }
}
 
template <>
OCTAVE_API octave_int64
operator + (const double& x, const octave_int64& y)
{
  return y + x;
}
 
template <>
OCTAVE_API octave_uint64
operator - (const octave_uint64& x, const double& y)
{
  return x + (-y);
}
 
template <>
OCTAVE_API octave_uint64
operator - (const double& x, const octave_uint64& y)
{
  // The following cast changes the value to 2^64 (which is outside the range
  // of `uint64_t`).
  if (x < static_cast<double> (octave_uint64::max ()))
    return octave_uint64 (x) - y;
  else
    {
      // Again a trick to get the corner cases right.  Things like
      // 3^2^63 - intmax ('uint64') should produce the correct result, i.e.
      // int64 (2^63) + 1.
      const double p2_64 = std::pow (2.0, 64);
      if (y.bool_value ())
        {
          const uint64_t p2_64my = (~y.value ()) + 1; // Equals 2^64 - y
          return octave_uint64 (x - p2_64) + octave_uint64 (p2_64my);
        }
      else
        return octave_uint64 (p2_64);
    }
}
 
template <>
OCTAVE_API octave_int64
operator - (const octave_int64& x, const double& y)
{
  return x + (-y);
}
 
template <>
OCTAVE_API octave_int64
operator - (const double& x, const octave_int64& y)
{
  static const bool twosc = (std::numeric_limits<int64_t>::min ()
                             < -std::numeric_limits<int64_t>::max ());
  // In case of symmetric integers (not two's complement), this will probably
  // be eliminated at compile time.
  if (twosc && y.value () == std::numeric_limits<int64_t>::min ())
    return octave_int64 (x + std::pow (2.0, 63));
  else
    return x + (-y);
}
 
// NOTE:
// Emulated mixed multiplications are tricky due to possible precision loss.
// Here, after sorting out common cases for speed, we follow the strategy
// of converting the double number into the form sign * 64-bit integer *
// 2^exponent, multiply the 64-bit integers to get a 128-bit number, split that
// number into 32-bit words and form 4 double-valued summands (none of which
// loses precision), then convert these into integers and sum them.  Though it
// is not immediately obvious, this should work even w.r.t. rounding (none of
// the summands lose precision).
 
// Multiplies two unsigned 64-bit ints to get a 128-bit number represented
// as four 32-bit words.
static void
umul128 (uint64_t x, uint64_t y, uint32_t w[4])
{
  uint64_t lx = static_cast<uint32_t> (x);
  uint64_t ux = x >> 32;
  uint64_t ly = static_cast<uint32_t> (y);
  uint64_t uy = y >> 32;
  uint64_t a = lx * ly;
  w[0] = a; a >>= 32;
  uint64_t uxly = ux*ly;
  uint64_t uylx = uy*lx;
  a += static_cast<uint32_t> (uxly); uxly >>= 32;
  a += static_cast<uint32_t> (uylx); uylx >>= 32;
  w[1] = a; a >>= 32;
  uint64_t uxuy = ux * uy;
  a += uxly; a += uylx; a += uxuy;
  w[2] = a; a >>= 32;
  w[3] = a;
}
 
// Splits a double into bool sign, unsigned 64-bit mantissa and int exponent
static void
dblesplit (double x, bool& sign, uint64_t& mtis, int& exp)
{
  sign = x < 0; x = fabs (x);
  x = octave::math::frexp (x, &exp);
  exp -= 52;
  mtis = static_cast<uint64_t> (ldexp (x, 52));
}
 
// Gets a double number from a
// 32-bit unsigned integer mantissa, exponent, and sign.
static double
dbleget (bool sign, uint32_t mtis, int exp)
{
  double x = ldexp (static_cast<double> (mtis), exp);
  return sign ? -x : x;
}
 
template <>
OCTAVE_API octave_uint64
operator * (const octave_uint64& x, const double& y)
{
  // The following cast changes the value to 2^64 (which is outside the range
  // of `uint64_t`).
  if (y >= 0 && y < static_cast<double> (octave_uint64::max ())
      && y == octave::math::fix (y))
    return x * octave_uint64 (static_cast<uint64_t> (y));
  else if (y == 0.5)
    return x / octave_uint64 (static_cast<uint64_t> (2));
  else if (y < 0 || octave::math::isnan (y) || octave::math::isinf (y))
    return octave_uint64 (x.value () * y);
  else
    {
      bool sign;
      uint64_t my;
      int e;
      dblesplit (y, sign, my, e);
      uint32_t w[4];
      umul128 (x.value (), my, w);
      octave_uint64 res = octave_uint64::s_zero;
      for (short i = 0; i < 4; i++)
        {
          res += octave_uint64 (dbleget (sign, w[i], e));
          e += 32;
        }
      return res;
    }
}
 
template <>
OCTAVE_API octave_uint64
operator * (const double& x, const octave_uint64& y)
{
  return y * x;
}
 
template <>
OCTAVE_API octave_int64
operator * (const octave_int64& x, const double& y)
{
  // The following cast changes the value to 2^63 (which is outside the range
  // of `int64_t`).
  if (fabs (y) < static_cast<double> (octave_int64::max ())
      && y == octave::math::fix (y))
    return x * octave_int64 (static_cast<int64_t> (y));
  else if (fabs (y) == 0.5)
    return x / octave_int64 (static_cast<uint64_t> (4*y));
  else if (octave::math::isnan (y) || octave::math::isinf (y))
    return octave_int64 (x.value () * y);
  else
    {
      bool sign;
      uint64_t my;
      int e;
      dblesplit (y, sign, my, e);
      uint32_t w[4];
      sign = (sign != (x.value () < 0));
      umul128 (octave_int_abs (x.value ()), my, w);
      octave_int64 res = octave_int64::s_zero;
      for (short i = 0; i < 4; i++)
        {
          res += octave_int64 (dbleget (sign, w[i], e));
          e += 32;
        }
      return res;
    }
}
 
template <>
OCTAVE_API octave_int64
operator * (const double& x, const octave_int64& y)
{
  return y * x;
}
 
template <>
OCTAVE_API octave_uint64
operator / (const double& x, const octave_uint64& y)
{
  return octave_uint64 (x / static_cast<double> (y));
}
 
template <>
OCTAVE_API octave_int64
operator / (const double& x, const octave_int64& y)
{
  return octave_int64 (x / static_cast<double> (y));
}
 
template <>
OCTAVE_API octave_uint64
operator / (const octave_uint64& x, const double& y)
{
  // The following cast changes the value to 2^64 (which is outside the range
  // of `uint64_t`).
  if (y >= 0 && y < static_cast<double> (octave_uint64::max ())
      && y == octave::math::fix (y))
    return x / octave_uint64 (y);
  else
    return x * (1.0/y);
}
 
template <>
OCTAVE_API octave_int64
operator / (const octave_int64& x, const double& y)
{
  // The following cast changes the value to 2^63 (which is outside the range
  // of `int64_t`).
  if (fabs (y) < static_cast<double> (octave_int64::max ())
      && y == octave::math::fix (y))
    return x / octave_int64 (y);
  else
    return x * (1.0/y);
}
 
#define INSTANTIATE_INT64_DOUBLE_CMP_OP0(OP, T1, T2)                    \
  template OCTAVE_API bool                                              \
  octave_int_cmp_op::emulate_mop<octave_int_cmp_op::OP> (T1 x, T2 y)
 
#define INSTANTIATE_INT64_DOUBLE_CMP_OP(OP)                     \
  INSTANTIATE_INT64_DOUBLE_CMP_OP0 (OP, double, int64_t);       \
  INSTANTIATE_INT64_DOUBLE_CMP_OP0 (OP, double, uint64_t);      \
  INSTANTIATE_INT64_DOUBLE_CMP_OP0 (OP, int64_t, double);       \
  INSTANTIATE_INT64_DOUBLE_CMP_OP0 (OP, uint64_t, double)
 
INSTANTIATE_INT64_DOUBLE_CMP_OP (lt);
INSTANTIATE_INT64_DOUBLE_CMP_OP (le);
INSTANTIATE_INT64_DOUBLE_CMP_OP (gt);
INSTANTIATE_INT64_DOUBLE_CMP_OP (ge);
INSTANTIATE_INT64_DOUBLE_CMP_OP (eq);
INSTANTIATE_INT64_DOUBLE_CMP_OP (ne);
 
#endif
 
template <typename T>
octave_int<T>
pow (const octave_int<T>& a, const octave_int<T>& b)
{
  octave_int<T> retval;
 
  const octave_int<T> zero = octave_int<T>::s_zero;
  const octave_int<T> one = octave_int<T>::s_one;
 
  if (b == zero || a == one)
    retval = one;
  else if (b < zero)
    {
      if (a == -one)
        retval = (b.value () % 2) ? a : one;
      else
        retval = zero;
    }
  else
    {
      octave_int<T> a_val = a;
      T b_val = b; // no need to do saturation on b
 
      retval = a;
 
      b_val -= 1;
 
      while (b_val != 0)
        {
          if (b_val & 1)
            retval = retval * a_val;
 
          b_val = b_val >> 1;
 
          if (b_val)
            a_val = a_val * a_val;
        }
    }
 
  return retval;
}
 
template <typename T>
octave_int<T>
pow (const double& a, const octave_int<T>& b)
{ return octave_int<T> (std::pow (a, b.double_value ())); }
 
template <typename T>
octave_int<T>
pow (const octave_int<T>& a, const double& b)
{
  return ((b >= 0 && b < std::numeric_limits<T>::digits
           && b == octave::math::fix (b))
          ? pow (a, octave_int<T> (static_cast<T> (b)))
          : octave_int<T> (std::pow (a.double_value (), b)));
}
 
template <typename T>
octave_int<T>
pow (const float& a, const octave_int<T>& b)
{ return octave_int<T> (std::pow (a, b.float_value ())); }
 
template <typename T>
octave_int<T>
pow (const octave_int<T>& a, const float& b)
{
  return ((b >= 0 && b < std::numeric_limits<T>::digits
           && b == octave::math::fix (b))
          ? pow (a, octave_int<T> (static_cast<T> (b)))
          : octave_int<T> (std::pow (a.double_value (),
                                     static_cast<double> (b))));
}
 
// FIXME: Do we really need a differently named single-precision function
//        integer power function here instead of an overloaded one?
template <typename T>
octave_int<T>
powf (const float& a, const octave_int<T>& b)
{ return octave_int<T> (pow (a, b.float_value ())); }
 
template <typename T>
octave_int<T>
powf (const octave_int<T>& a, const float& b)
{
  return ((b >= 0 && b < std::numeric_limits<T>::digits
           && b == octave::math::fix (b))
          ? pow (a, octave_int<T> (static_cast<T> (b)))
          : octave_int<T> (std::pow (a.double_value (),
                                     static_cast<double> (b))));
}
 
#define INSTANTIATE_INTTYPE(T)                                          \
  template class octave_int<T>;                                         \
                                                                        \
  template OCTAVE_API octave_int<T>                                     \
  pow (const octave_int<T>&, const octave_int<T>&);                     \
                                                                        \
  template OCTAVE_API octave_int<T>                                     \
  pow (const double&, const octave_int<T>&);                            \
                                                                        \
  template OCTAVE_API octave_int<T>                                     \
  pow (const octave_int<T>&, const double&);                            \
                                                                        \
  template OCTAVE_API octave_int<T>                                     \
  pow (const float&, const octave_int<T>&);                             \
                                                                        \
  template OCTAVE_API octave_int<T>                                     \
  pow (const octave_int<T>&, const float&);                             \
                                                                        \
  template OCTAVE_API octave_int<T>                                     \
  powf (const float&, const octave_int<T>&);                            \
                                                                        \
  template OCTAVE_API octave_int<T>                                     \
  powf (const octave_int<T>&, const float&);                            \
                                                                        \
  template OCTAVE_API octave_int<T>                                     \
  bitshift (const octave_int<T>&, int, const octave_int<T>&);
 
INSTANTIATE_INTTYPE (int8_t);
INSTANTIATE_INTTYPE (int16_t);
INSTANTIATE_INTTYPE (int32_t);
INSTANTIATE_INTTYPE (int64_t);
 
INSTANTIATE_INTTYPE (uint8_t);
INSTANTIATE_INTTYPE (uint16_t);
INSTANTIATE_INTTYPE (uint32_t);
INSTANTIATE_INTTYPE (uint64_t);
 
/*
 
%!assert (intmax ("int64") / intmin ("int64"), int64 (-1))
%!assert (intmin ("int64") / int64 (-1), intmax ("int64"))
%!assert (int64 (2^63), intmax ("int64"))
%!assert (uint64 (2^64), intmax ("uint64"))
%!test
%! a = 1.9*2^61; b = uint64 (a); b++; assert (b > a);
%!test
%! a = -1.9*2^61; b = int64 (a); b++; assert (b > a);
%!test
%! a = int64 (-2^60) + 2; assert (1.25*a == (5*a)/4);
%!test
%! a = uint64 (2^61) + 2; assert (1.25*a == (5*a)/4);
%!assert (int32 (2^31+0.5), intmax ("int32"))
%!assert (int32 (-2^31-0.5), intmin ("int32"))
%!assert ((int64 (2^62)+1)^1, int64 (2^62)+1)
%!assert ((int64 (2^30)+1)^2, int64 (2^60+2^31) + 1)
 
%!assert <54382> (uint8 (char (128)), uint8 (128))
%!assert <54382> (uint8 (char (255)), uint8 (255))
%!assert <54382> (int8 (char (128)), int8 (128))
%!assert <54382> (int8 (char (255)), int8 (255))
 
%!assert <54382> (uint16 (char (128)), uint16 (128))
%!assert <54382> (uint16 (char (255)), uint16 (255))
%!assert <54382> (int16 (char (128)), int16 (128))
%!assert <54382> (int16 (char (255)), int16 (255))
 
%!assert <54382> (uint32 (char (128)), uint32 (128))
%!assert <54382> (uint32 (char (255)), uint32 (255))
%!assert <54382> (int32 (char (128)), int32 (128))
%!assert <54382> (int32 (char (255)), int32 (255))
 
%!assert <54382> (uint64 (char (128)), uint64 (128))
%!assert <54382> (uint64 (char (255)), uint64 (255))
%!assert <54382> (int64 (char (128)), int64 (128))
%!assert <54382> (int64 (char (255)), int64 (255))
*/