#!/usr/bin/env python3
# -*- coding: utf-8 -*-
# =============================================================================
# copied from https://raw.githubusercontent.com/PythonCHB/close_pep/master/is_close.py
# =============================================================================
"""
Test implementation for an isclose() function, for possible inclusion in
the Python standard library -- PEP0485

This version has multiple methods in it for experimentation and testing.

The ``final'' version can be found in isclose.py

This implementation is the result of much discussion on the python-ideas list
in January, 2015:

   https://mail.python.org/pipermail/python-ideas/2015-January/030947.html

   https://mail.python.org/pipermail/python-ideas/2015-January/031124.html

   https://mail.python.org/pipermail/python-ideas/2015-January/031313.html

Copyright: Christopher H. Barker
License: Apache License 2.0 http://opensource.org/licenses/apache2.0.php

"""
__all__ = (
    'isclose'       , ## close using relative and absolute distances 
    )

import cmath


def isclose(a,
            b,
            rel_tol=1e-9,
            abs_tol=0.0,
            method='weak'):
    """
    returns True if a is close in value to b. False otherwise

    :param a: one of the values to be tested

    :param b: the other value to be tested

    :param rel_tol=1e-8: The relative tolerance -- the amount of error
                         allowed, relative to the magnitude of the input
                         values.

    :param abs_tol=0.0: The minimum absolute tolerance level -- useful for
                        comparisons to zero.

    :param method: The method to use. options are:
                  "asymmetric" : the b value is used for scaling the tolerance
                  "strong" : The tolerance is scaled by the smaller of
                             the two values
                  "weak" : The tolerance is scaled by the larger of
                           the two values
                  "average" : The tolerance is scaled by the average of
                              the two values.

    NOTES:

    -inf, inf and NaN behave similar to the IEEE 754 standard. That
    -is, NaN is not close to anything, even itself. inf and -inf are
    -only close to themselves.

    Complex values are compared based on their absolute value.

    The function can be used with Decimal types, if the tolerance(s) are
    specified as Decimals::

      isclose(a, b, rel_tol=Decimal('1e-9'))

    See PEP-0485 for a detailed description

    """
    if method not in ("asymmetric", "strong", "weak", "average"):
        raise ValueError('method must be one of: "asymmetric",'
                         ' "strong", "weak", "average"')

    if rel_tol < 0.0 or abs_tol < 0.0:
        raise ValueError('error tolerances must be non-negative')

    if a == b:  # short-circuit exact equality
        return True
    # use cmath so it will work with complex or float
    if cmath.isinf(a) or cmath.isinf(b):
        # This includes the case of two infinities of opposite sign, or
        # one infinity and one finite number. Two infinities of opposite sign
        # would otherwise have an infinite relative tolerance.
        return False
    diff = abs(b - a)
    if method == "asymmetric":
        return (diff <= abs(rel_tol * b)) or (diff <= abs_tol)
    elif method == "strong":
        return (((diff <= abs(rel_tol * b)) and
                 (diff <= abs(rel_tol * a))) or
                (diff <= abs_tol))
    elif method == "weak":
        return (((diff <= abs(rel_tol * b)) or
                 (diff <= abs(rel_tol * a))) or
                (diff <= abs_tol))
    elif method == "average":
        return ((diff <= abs(rel_tol * (a + b) / 2) or
                (diff <= abs_tol)))
    else:
        raise ValueError('method must be one of:'
                         ' "asymmetric", "strong", "weak", "average"')

    
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## The END
# =============================================================================
