Trixy7/trixy_core/utils/math_eval.py

# -*- coding: utf-8 -*-
"""
Mathematischer Ausdruck-Evaluator (Recursive Descent Parser).

Wertet Ausdruecke der Form (:expression) aus.
Unterstuetzt: +, -, *, /, %, ^ (Potenz), &, |, xor, ~, not, and, or, nand, nor.
Klammern fuer Gruppierung. Hex-Literale (0xFF). Float/Int.

Praezedenz (niedrig → hoch):
    nor → nand → | / or → xor → & / and → + - → * / % → ^ → unaer (- ~ not)

Portiert von PrrintText_cpp/format.cpp (matheval Namespace).
"""

from __future__ import annotations

import math
from enum import Enum, auto
from typing import Any


class _TokenType(Enum):
    NUMBER = auto()
    PLUS = auto()
    MINUS = auto()
    STAR = auto()
    SLASH = auto()
    PERCENT = auto()
    CARET = auto()       # ^
    AMP = auto()         # &
    PIPE = auto()        # |
    TILDE = auto()       # ~
    LPAREN = auto()
    RPAREN = auto()
    KW_AND = auto()
    KW_OR = auto()
    KW_XOR = auto()
    KW_NOT = auto()
    KW_NAND = auto()
    KW_NOR = auto()
    END = auto()
    ERROR = auto()


class _Token:
    __slots__ = ("type", "value")

    def __init__(self, tt: _TokenType, value: float = 0.0) -> None:
        self.type = tt
        self.value = value


def _tokenize(expr: str) -> list[_Token]:
    """Tokenisiert einen mathematischen Ausdruck."""
    tokens: list[_Token] = []
    i = 0
    n = len(expr)

    while i < n:
        ch = expr[i]

        # Whitespace ueberspringen
        if ch in " \t\r\n":
            i += 1
            continue

        # Zahlen (int, float, hex, scientific)
        if ch.isdigit() or (ch == "." and i + 1 < n and expr[i + 1].isdigit()):
            start = i

            # Hex: 0x...
            if ch == "0" and i + 1 < n and expr[i + 1] in "xX":
                i += 2
                while i < n and (expr[i].isdigit() or expr[i] in "abcdefABCDEF"):
                    i += 1
                tokens.append(_Token(_TokenType.NUMBER, float(int(expr[start:i], 16))))
                continue

            # Dezimal / Float
            while i < n and expr[i].isdigit():
                i += 1
            if i < n and expr[i] == ".":
                i += 1
                while i < n and expr[i].isdigit():
                    i += 1

            # Scientific Notation: 1e6, 2.5e-3
            if i < n and expr[i] in "eE":
                i += 1
                if i < n and expr[i] in "+-":
                    i += 1
                while i < n and expr[i].isdigit():
                    i += 1

            tokens.append(_Token(_TokenType.NUMBER, float(expr[start:i])))
            continue

        # Operatoren
        if ch == "+":
            tokens.append(_Token(_TokenType.PLUS))
            i += 1
        elif ch == "-":
            tokens.append(_Token(_TokenType.MINUS))
            i += 1
        elif ch == "*":
            tokens.append(_Token(_TokenType.STAR))
            i += 1
        elif ch == "/":
            tokens.append(_Token(_TokenType.SLASH))
            i += 1
        elif ch == "%":
            tokens.append(_Token(_TokenType.PERCENT))
            i += 1
        elif ch == "^":
            tokens.append(_Token(_TokenType.CARET))
            i += 1
        elif ch == "&":
            tokens.append(_Token(_TokenType.AMP))
            i += 1
        elif ch == "|":
            tokens.append(_Token(_TokenType.PIPE))
            i += 1
        elif ch == "~":
            tokens.append(_Token(_TokenType.TILDE))
            i += 1
        elif ch == "(":
            tokens.append(_Token(_TokenType.LPAREN))
            i += 1
        elif ch == ")":
            tokens.append(_Token(_TokenType.RPAREN))
            i += 1
        elif ch.isalpha():
            # Keywords: and, or, xor, not, nand, nor
            start = i
            while i < n and expr[i].isalpha():
                i += 1
            word = expr[start:i].lower()
            kw_map = {
                "and": _TokenType.KW_AND,
                "or": _TokenType.KW_OR,
                "xor": _TokenType.KW_XOR,
                "not": _TokenType.KW_NOT,
                "nand": _TokenType.KW_NAND,
                "nor": _TokenType.KW_NOR,
            }
            if word in kw_map:
                tokens.append(_Token(kw_map[word]))
            else:
                # Unbekanntes Wort — Fehler
                tokens.append(_Token(_TokenType.ERROR))
        else:
            tokens.append(_Token(_TokenType.ERROR))
            i += 1

    tokens.append(_Token(_TokenType.END))
    return tokens


def _to_int(d: float) -> int:
    """Konvertiert float zu int fuer bitweise Operationen."""
    return round(d)


class _Parser:
    """Recursive-Descent-Parser fuer mathematische Ausdruecke."""

    def __init__(self, tokens: list[_Token]) -> None:
        self._tokens = tokens
        self._pos = 0
        self.error = False

    def _peek(self) -> _Token:
        return self._tokens[self._pos]

    def _advance(self) -> _Token:
        tok = self._tokens[self._pos]
        self._pos += 1
        return tok

    def _expect(self, tt: _TokenType) -> bool:
        if self._peek().type == tt:
            self._advance()
            return True
        self.error = True
        return False

    def parse(self) -> float:
        """Parst den kompletten Ausdruck."""
        result = self._parse_nor()
        if self._peek().type != _TokenType.END:
            self.error = True
        return result

    # Praezedenz 1: NOR
    def _parse_nor(self) -> float:
        left = self._parse_nand()
        while self._peek().type == _TokenType.KW_NOR:
            self._advance()
            right = self._parse_nand()
            left = float(~(_to_int(left) | _to_int(right)))
        return left

    # Praezedenz 2: NAND
    def _parse_nand(self) -> float:
        left = self._parse_or()
        while self._peek().type == _TokenType.KW_NAND:
            self._advance()
            right = self._parse_or()
            left = float(~(_to_int(left) & _to_int(right)))
        return left

    # Praezedenz 3: OR / |
    def _parse_or(self) -> float:
        left = self._parse_xor()
        while self._peek().type in (_TokenType.PIPE, _TokenType.KW_OR):
            self._advance()
            right = self._parse_xor()
            left = float(_to_int(left) | _to_int(right))
        return left

    # Praezedenz 4: XOR
    def _parse_xor(self) -> float:
        left = self._parse_and()
        while self._peek().type == _TokenType.KW_XOR:
            self._advance()
            right = self._parse_and()
            left = float(_to_int(left) ^ _to_int(right))
        return left

    # Praezedenz 5: AND / &
    def _parse_and(self) -> float:
        left = self._parse_add()
        while self._peek().type in (_TokenType.AMP, _TokenType.KW_AND):
            self._advance()
            right = self._parse_add()
            left = float(_to_int(left) & _to_int(right))
        return left

    # Praezedenz 6: + -
    def _parse_add(self) -> float:
        left = self._parse_mul()
        while self._peek().type in (_TokenType.PLUS, _TokenType.MINUS):
            op = self._advance().type
            right = self._parse_mul()
            if op == _TokenType.PLUS:
                left += right
            else:
                left -= right
        return left

    # Praezedenz 7: * / %
    def _parse_mul(self) -> float:
        left = self._parse_pow()
        while self._peek().type in (_TokenType.STAR, _TokenType.SLASH, _TokenType.PERCENT):
            op = self._advance().type
            right = self._parse_pow()
            if op == _TokenType.STAR:
                left *= right
            elif op == _TokenType.SLASH:
                if right == 0:
                    self.error = True
                    return 0.0
                left /= right
            else:
                if right == 0:
                    self.error = True
                    return 0.0
                left = float(_to_int(left) % _to_int(right))
        return left

    # Praezedenz 8: ^ (rechtsassoziativ)
    def _parse_pow(self) -> float:
        base = self._parse_unary()
        if self._peek().type == _TokenType.CARET:
            self._advance()
            exp = self._parse_pow()  # Rechtsassoziativ: Rekursion
            return math.pow(base, exp)
        return base

    # Praezedenz 9: unaer (- ~ not)
    def _parse_unary(self) -> float:
        if self._peek().type == _TokenType.MINUS:
            self._advance()
            return -self._parse_unary()
        if self._peek().type in (_TokenType.TILDE, _TokenType.KW_NOT):
            self._advance()
            return float(~_to_int(self._parse_unary()))
        return self._parse_primary()

    # Primaer: Zahl oder geklammert
    def _parse_primary(self) -> float:
        tok = self._peek()
        if tok.type == _TokenType.NUMBER:
            self._advance()
            return tok.value
        if tok.type == _TokenType.LPAREN:
            self._advance()
            val = self._parse_nor()
            self._expect(_TokenType.RPAREN)
            return val
        self.error = True
        self._advance()
        return 0.0


def _format_result(value: float) -> str:
    """Formatiert das Ergebnis: Ganzzahlen ohne Dezimalpunkt."""
    if value == int(value) and abs(value) < 1e15:
        return str(int(value))
    # Bis zu 10 signifikante Stellen, trailing Zeros entfernen
    s = f"{value:.10g}"
    return s


def eval_math(expr: str) -> str | None:
    """
    Wertet einen mathematischen Ausdruck aus.

    Args:
        expr: Der Ausdruck (ohne die (:...) Klammern).

    Returns:
        Das Ergebnis als String oder None bei Fehler.
    """
    tokens = _tokenize(expr.strip())
    parser = _Parser(tokens)
    result = parser.parse()
    if parser.error:
        return None
    return _format_result(result)