Module lange.abs.progression

#  Copyright (c) 2021. Davi Pereira dos Santos
#  This file is part of the lange project.
#  Please respect the license - more about this in the section (*) below.
#
#  lange 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.
#
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#  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 lange.  If not, see <http://www.gnu.org/licenses/>.
#
#  (*) Removing authorship by any means, e.g. by distribution of derived
#  works or verbatim, obfuscated, compiled or rewritten versions of any
#  part of this work is a crime and is unethical regarding the effort and
#  time spent here.
#  Relevant employers or funding agencies will be notified accordingly.

import decimal as dec
import math

from lange.tricks import detect_precision


# TODO implement (lazy) reverse: ap[. . .].r
# TODO implement lazy direct access to item/slice (use math formulas to know value without iterating)


class Progression:
    _l = None

    def __init__(self, op, null, prod_f, div_f, pow_f, bins_f, args, maxdigits=28):
        self.__str__ = self.__repr__
        self.args = args
        self.maxdigits = maxdigits
        self.prod_f, self.div_f, self.pow_f = prod_f, div_f, pow_f
        self.op = op
        self.decctx = dec.Context()
        null = self.decctx.create_decimal(null)
        if Ellipsis in args:
            if not (3 <= len(args) <= 4) or args[2] is not Ellipsis:
                raise Exception("Among 3 or 4 arguments, '...' should be the third.")

            # Detect level of precision and enforce it for the rest of this object life.
            end = 0 if len(args) == 3 else args[-1]
            self.precision = max(
                detect_precision(args[0], maxdigits),
                detect_precision(args[1], maxdigits),
                detect_precision(end, maxdigits),
            )
            self.decctx.prec = self.precision

            # Protect all provided numbers from floating point inequality issues (e.g. 0.8 - 0.6 != 0.2).
            self.start = self.decctx.create_decimal(args[0])
            self.second = self.decctx.create_decimal(args[1])
            self.end = self.decctx.create_decimal(math.inf if len(args) == 3 else args[-1])

            # Derived attributes.
            self.step = div_f(self.second, self.start)
            self.cast = int if all(isinstance(v, int) for v in args[:2]) and int(self.step) == self.step else float
            bins = bins_f(self.start, self.end, self.step).to_integral_exact(rounding=dec.ROUND_FLOOR)
            self.n = bins + self.decctx.create_decimal(1)

            def g():
                s, i = self.start, 0
                while i < self.n:
                    yield self.cast(s)
                    s = prod_f(s, self.step)
                    i += 1

            self.gen = g
        elif len(args) == 0:
            self.start, self.step, self.end = None, None, None
            self.n = 0
            self.gen = lambda: iter(())
            self.cast = lambda x: x
        elif 1 <= len(args) <= 2:
            self.start = self.decctx.create_decimal(args[0])
            self.step = null if len(args) == 1 else self.div_f(self.decctx.create_decimal(args[1]), self.start)
            self.end = self.decctx.create_decimal(args[-1])
            self.n = len(args)
            self.gen = lambda: iter(args)
            self.cast = int if all(isinstance(v, int) for v in args) and int(self.step) == self.step else float
        else:
            self.start, self.step, self.end = None, None, None
            self.n = len(args)
            self.gen = lambda: iter(args)
            self.cast = int if all(isinstance(v, int) for v in args) else float

    @property
    def l(self):
        """Return progression evaluated as a list.

        Usage:
            >>> from lange import ap
            >>> len(ap[1, 2, ..., 5])
            5
            >>> ap[1, 2, ..., 5].l
            [1, 2, 3, 4, 5]
        """
        if self._l is None:
            self._l = list(self)
        return self._l

    def __iter__(self):
        return self.gen()

    def __getitem__(self, item):
        if isinstance(item, slice):
            if self.start is None:
                return self.__class__(*list(self)[item])
            item_start = item.start or self.decctx.create_decimal(0)
            item_step = item.step or self.decctx.create_decimal(1)
            start = self.decctx.create_decimal(self[item_start])
            step = self.div_f(self.decctx.create_decimal(self[item_start + item_step]), start)
            second = self.prod_f(start, step)
            end = self.prod_f(start, self.pow_f(step, (item.stop - item_start - 1) // item_step))
            args = start, second, ..., end
            return self.__class__(*args)  # REMINDER: calling child class.

        if self.start is None:
            return self.__class__(list(self)[item]) if self.n > 0 else self.__class__()

        if not (0 <= item < self.n):
            raise Exception(f"Index {item} outside valid range [0; {self.n}[.")
        return self.cast(self.prod_f(self.start, self.pow_f(self.step, item)))

    def __len__(self):
        return int(self.n)

    def __repr__(self):
        if self.n < 4 or None in [self.end, self.start, self.step]:
            return f"[{' '.join(map(str, self))}]"
        try:
            end = self.cast(self.end)
        except OverflowError:
            end = "∞"
        return f"[{self.cast(self.start)} {self.cast(self.prod_f(self.start, self.step))} .{self.op}. {end}]"

    def __invert__(self):
        return list(self)