from builtins import range

"""
Provides the NumericOutputChecker implementing doctest's OutputChecker.

It provides a set of extra flags NUMERIC6, NUMERIC9, ... for doctests
allowing numbers in an example to differ by an epsilon = 1e-6, 1e-9, ...

See init_precisions(...) for the precisions we support.

See documentation of NumericExample for more.
"""

class NumericExample:
    """
    The actual result (3.141592653589793) differs from the given result,
    but the difference is less than 1e-6, so it still passes::

        >>> 1.5707963267948966 * 2 # doctest: +NUMERIC6
        3.14159285

    The text pieces between the numbers are also compared, performing
    white-space normalization::

        >>> ['a', 4.5, 6.9] # doctest: +NUMERIC6
        ['a', 4.5,       6.9000000001]

    Intervals in the notation emitted by sage are allows::

        >>> print("4.5?e-1") # doctest: +NUMERIC6
        4.50000000001?e-1

    """

import doctest, re, decimal

# Generate flags NUMERIC6, ...

# Store as pairs (precision, FLAG)
NUMERIC_LIST = []
# Store in dict precision : FLAG
NUMERIC_DICT = {}
# All or'ed together
ALL_NUMERIC  = 0

def init_precisions(precisions):
    """
    Register flags for given precisions with doctest module.

    Unfortunately, doctest doesn't seem to support a more generic mechanism
    such as "# doctest: +NUMERIC: 6" to specify the precision and we need to
    unroll each precision we want to its own flag.
    """

    global NUMERIC_LIST
    global NUMERIC_DICT
    global ALL_NUMERIC

    for precision in precisions:
        # Check key such that clients having demand for different
        # precisions could register them.
        if precision not in NUMERIC_DICT:
            flag = doctest.register_optionflag('NUMERIC%d' % precision)
            NUMERIC_LIST.append((precision, flag))
            NUMERIC_DICT[precision] = flag
            ALL_NUMERIC |= flag

# The precisions NUMERIC0, ... we support are hard-coded here:
init_precisions(range(0,33,3))

def get_precision(optionflags):
    """
    Get precision from optionflags
    """
    for precision, flag in NUMERIC_LIST:
        if optionflags & flag:
            return precision

# Regular expressions matching numbers and intervals such as
# 23, 2.3, 3.5e-4, 3.4 E-5, 3.4?, 5.6?e-3

mantissa_pat = r'([0-9]+(?:\.[0-9]+)?)'
# Intervals can be 3.4? or 3.4?e-2, account for the "?"
interval_pat = r'(\?)?'
# Pari prints 3.4E-3 as "3.4 E-3", account for the space
exponent_pat = r'(?:\ ?([eE][+-]?[0-9]+))?'

# 4.5?e-3 would split into groups ('4.5?e-3', '4.5', '?", 'e-3').
number_re = re.compile('(' + mantissa_pat + interval_pat + exponent_pat + ')')
number_group_count  = 4
number_split_stride = number_group_count + 1

# Use whitespace normalization for text pieces
NUMERIC_DEFAULT_OPTIONFLAGS = doctest.NORMALIZE_WHITESPACE

# Given the above groups, e.g., ('4.5?e-3', '4.5', '?", 'e-3'), return
# decimal.Decimal("4.5E-3")
def to_decimal(groups):
    number, mantissa, interval, exponent = groups
    if exponent:
        n = mantissa + exponent
    else:
        n = mantissa
    return decimal.Decimal(n)

class NumericOutputChecker(doctest.OutputChecker):
    """
    Implements doctest's OutputChecker, see documentation of
    NumericExample for examples.

    >>> N = NumericOutputChecker()

    >>> a   = "[3.499e-8, 4.5?e-8]"
    >>> b   = "[3.499e-8,   4.5?e-8]"

    >>> N.check_output(a, b, NUMERIC_DICT[12])
    True

    >>> b   = "[3.499999e-8,   3.2?e-8]"
    >>> N.check_output(a, b, NUMERIC_DICT[6])
    True
    >>> N.check_output(a, b, NUMERIC_DICT[9])
    False
    >>> N.formatted_compare_numeric(a, b, NUMERIC_DICT[9])
    'Numbers differed by 1.3E-8\\n\\nExpected     : 3.499e-8\\nGot          : 3.499999e-8\\nDifference          : 9.99E-12\\n\\nExpected     : 4.5?e-8\\nGot          : 3.2?e-8\\nDifference (FAILURE): 1.3E-8\\n'
    >>> N.compare_numeric(a, b, NUMERIC_DICT[12])
    ('NUMERIC', ([('3.499e-8', '3.499999e-8', True, Decimal('9.99E-12')), ('4.5?e-8', '3.2?e-8', True, Decimal('1.3E-8'))], Decimal('1.3E-8')))

    >>> b   = "[3.4999e-8,  4.5e-8]"
    >>> N.formatted_compare_numeric(a, b, NUMERIC_DICT[6])
    'Expected interval, but got 4.5e-8.'

    >>> b   = "[3.4999?e-8, 4.5e-8]"
    >>> N.formatted_compare_numeric(a, b, NUMERIC_DICT[6])
    'Expected number, but got 3.4999?e-8.'

    >>> b  = "a = [3.4999e-8,  4.5?e-8]"
    >>> N.formatted_compare_numeric(a, b, NUMERIC_DICT[6])
    'Text between numbers differs'

    >>> b  = "[3.4999e-8,  4.5?e-8, 5.63]"
    >>> N.formatted_compare_numeric(a, b, NUMERIC_DICT[6])
    'Expected 2 numbers but got 3 numbers.'

    >>> a   = "[4.5,       6.7e1,       2e+3]"
    >>> b   = "[4.5000001, 67.00000001, 2.0000000000000000001e+3]"
    >>> N.compare_numeric(a, b, NUMERIC_DICT[6])
    ('OK', None)
    >>> N.compare_numeric(a, b, NUMERIC_DICT[12])    
    ('NUMERIC', ([('4.5', '4.5000001', True, Decimal('1E-7')), ('6.7e1', '67.00000001', True, Decimal('1E-8')), ('2e+3', '2.0000000000000000001e+3', False, Decimal('1E-16'))], Decimal('1E-7')))

    Account for pari adding a space before the E::

    >>> a   = "4.5e-9"
    >>> b   = "4.5 E-9"
    >>> N.compare_numeric(a, b, NUMERIC_DICT[12])
    ('OK', None)

    """
    
    def compare_numeric(self, want, got, optionflags):
        """
        Compares want and got by scanning for numbers. The numbers are
        compared using an epsilon extracted from optionflags. The text
        pieces between the numbers are compared falling back to the
        default implementation of OutputChecker.

        Returns a pair (status, data) where status is 'OK' if the
        comparison passed or indicates how it failed with data containing
        information that can be used to format the text explaining the
        differences.
        """

        # "[4.5e-9]" yields ('[', '4.5e-9', '4.5', None, 'e-9', ']')
        split_want = re.split(number_re, want)
        split_got  = re.split(number_re, got)

        # Check same number of numbers
        if len(split_want) != len(split_got):
            return ('COUNT',
                    (len(split_want) // number_split_stride,
                     len(split_got)  // number_split_stride))

        # Compare text pieces between numbers
        flags = optionflags | NUMERIC_DEFAULT_OPTIONFLAGS

        for i in range(0, len(split_want), number_split_stride):
            if not doctest.OutputChecker.check_output(
                    self, split_want[i], split_got[i], flags):
                return ('TEXT', None)
        
        epsilon = decimal.Decimal(0.1) ** get_precision(optionflags)

        rows = []
        max_diff = 0

        for i in range(1, len(split_want), number_split_stride):
            # Number how it literally appears
            number_want = split_want[i]
            number_got  = split_got [i]

            # Check whether both intervals or numbers
            is_interval_want = bool(split_want[i + 2])
            is_interval_got  = bool(split_got [i + 2])
            if is_interval_want != is_interval_got:
                return ('TYPE', (is_interval_want, number_got))
            
            # Number (or crushed interval) as decimal.Decimal
            decimal_want = to_decimal(split_want[i : i + number_group_count])
            decimal_got  = to_decimal(split_got [i : i + number_group_count])

            # Compute diff
            diff = abs(decimal_want - decimal_got)
            failed = (diff > epsilon)

            max_diff = max(max_diff, diff)

            # Record data
            rows.append((number_want, number_got, failed, diff))

        if max_diff > epsilon:
            # Larger than epsilon: failed
            return ('NUMERIC', (rows, max_diff))

        # Ok
        return ('OK', None)

    def format_compare_numeric_result(self, status, data):
        """
        Formats a nice text from the result of compare_numeric.
        """

        if status == 'COUNT':
            return 'Expected %d numbers but got %d numbers.' % data
        elif status == 'TEXT':
            return 'Text between numbers differs'
        elif status == 'TYPE':
            is_interval_want, number_got = data
            if is_interval_want:
                k = 'interval'
            else:
                k = 'number'
            return 'Expected %s, but got %s.' % (k, number_got)
        elif status == 'NUMERIC':
            rows, max_diff = data
            result = 'Numbers differed by %s\n' % max_diff
            for number_want, number_got, failed, diff in rows:
                if result:
                    result += '\n'
                result += 'Expected     : %s\n' % number_want
                result += 'Got          : %s\n' % number_got
                if failed:
                    result += 'Difference (FAILURE): %s\n' % diff
                else:
                    result += 'Difference          : %s\n' % diff
            return result
        else:
            raise Exception('Internal error in OutputChecker.')

    def formatted_compare_numeric(self, want, got, optionflags):
        """
        Performs comparison of compare_numeric and returns formatted
        text.

        Only supposed to be used if comparison failed.
        """

        status, data = self.compare_numeric(want, got, optionflags)
        
        return self.format_compare_numeric_result(status, data)

    def check_output(self, want, got, optionflags):
        """
        Implementation of OutputChecker method.
        """

        if want == got:
            # Early bail
            return True

        if optionflags & ALL_NUMERIC:
            # Use our method if any NUMERIC flag set
            status, data = self.compare_numeric(want, got, optionflags)
            return status == 'OK'
        else:
            # Otherwise fallback to base implementation.
            return doctest.OutputChecker.check_output(
                self, want, got, optionflags)

    def output_difference(self, example, got, optionflags):
        """
        Implementation of OutputChecker method.
        """
        if (not optionflags & ALL_NUMERIC) or example.exc_msg:
            # Fallback to base implementation if no NUMERIC flag
            # set or there was an exception.
            return doctest.OutputChecker.output_difference(
                self, example, got, optionflags)
        else:
            # Result of base implementation
            flags = optionflags | NUMERIC_DEFAULT_OPTIONFLAGS
            base_result = doctest.OutputChecker.output_difference(
                self, example, got, flags)
            
            # Our compare result
            compare_result = self.formatted_compare_numeric(
                example.want, got, optionflags)

            # Concatenate together
            return base_result + '\nReason for failure: ' + compare_result + '\n'

def run_doctests(verbose = False):
    failed, attempted = 0, 0

    finder = doctest.DocTestFinder()
    
    # Use the default docTest.OutputChecker to test our NumericOutputChecker
    runner = doctest.DocTestRunner(verbose = verbose)
    for test in finder.find(NumericOutputChecker):
        runner.run(test)
    result = runner.summarize()
    failed += result.failed
    attempted += result.attempted

    # Test our NumericOutputChecker in action!
    runner = doctest.DocTestRunner(checker = NumericOutputChecker(), verbose = verbose)
    for test in finder.find(NumericExample):
        runner.run(test)
        result = runner.summarize()
        failed += result.failed
        attempted += result.attempted

    return doctest.TestResults(failed, attempted)

run_doctests.__name__ = 'NumericOutputChecker'
