oct-cmplx.h

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/*

Copyright (C) 1995-2017 John W. Eaton
Copyright (C) 2009 VZLU Prague, a.s.

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
<http://www.gnu.org/licenses/>.

*/

#if ! defined (octave_oct_cmplx_h)
#define octave_oct_cmplx_h 1

#include "octave-config.h"

#include <complex>

typedef std::complex<double> Complex;
typedef std::complex<float> FloatComplex;

// For complex-complex and complex-real comparisons, we use the following
// ordering: compare absolute values first; if they match, compare phase angles.
// This is partially inconsistent with M*b, which compares complex numbers only
// by their real parts; OTOH, it uses the same definition for max/min and sort.
// The abs/arg comparison is definitely more useful (the other one is emulated
// rather trivially), so let's be consistent and use that all over.

// The standard C library function arg() returns [-pi,pi], which creates a
// non-unique representation for numbers along the negative real axis branch
// cut.  Change this to principal value (-pi,pi] by mapping -pi to pi.

#define DEF_COMPLEXR_COMP(OP, OPS)                                      \
  template <typename T>                                                 \
  inline bool operator OP (const std::complex<T>& a, const std::complex<T>& b) \
  {                                                                     \
    OCTAVE_FLOAT_TRUNCATE const T ax = std::abs (a);                    \
    OCTAVE_FLOAT_TRUNCATE const T bx = std::abs (b);                    \
    if (ax == bx)                                                       \
      {                                                                 \
        OCTAVE_FLOAT_TRUNCATE const T ay = std::arg (a);                \
        OCTAVE_FLOAT_TRUNCATE const T by = std::arg (b);                \
        if (ay == static_cast<T> (-M_PI))                               \
          {                                                             \
            if (by != static_cast<T> (-M_PI))                           \
              return static_cast<T> (M_PI) OP by;                       \
          }                                                             \
        else if (by == static_cast<T> (-M_PI))                          \
          {                                                             \
            return ay OP static_cast<T> (M_PI);                         \
          }                                                             \
        return ay OP by;                                                \
      }                                                                 \
    else                                                                \
      return ax OPS bx;                                                 \
  }                                                                     \
  template <typename T>                                                 \
  inline bool operator OP (const std::complex<T>& a, T b)               \
  {                                                                     \
    OCTAVE_FLOAT_TRUNCATE const T ax = std::abs (a);                    \
    OCTAVE_FLOAT_TRUNCATE const T bx = std::abs (b);                    \
    if (ax == bx)                                                       \
      {                                                                 \
        OCTAVE_FLOAT_TRUNCATE const T ay = std::arg (a);                \
        if (ay == static_cast<T> (-M_PI))                               \
          return static_cast<T> (M_PI) OP 0;                            \
        return ay OP 0;                                                 \
      }                                                                 \
    else                                                                \
      return ax OPS bx;                                                 \
  }                                                                     \
  template <typename T>                                                 \
  inline bool operator OP (T a, const std::complex<T>& b)               \
  {                                                                     \
    OCTAVE_FLOAT_TRUNCATE const T ax = std::abs (a);                    \
    OCTAVE_FLOAT_TRUNCATE const T bx = std::abs (b);                    \
    if (ax == bx)                                                       \
      {                                                                 \
        OCTAVE_FLOAT_TRUNCATE const T by = std::arg (b);                \
        if (by == static_cast<T> (-M_PI))                               \
          return 0 OP static_cast<T> (M_PI);                            \
        return 0 OP by;                                                 \
      }                                                                 \
    else                                                                \
      return ax OPS bx;                                                 \
  }

DEF_COMPLEXR_COMP (>, >)
DEF_COMPLEXR_COMP (<, <)
DEF_COMPLEXR_COMP (<=, <)
DEF_COMPLEXR_COMP (>=, >)

#endif