166 lines
5.1 KiB
Python
166 lines
5.1 KiB
Python
"""Tiny arithmetic expression evaluator with proper precedence.
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Supports: + - * / // % **, unary +/-, parentheses, variables (dict),
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functions (sin, cos, sqrt, abs, max, min), and error reporting with
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position. No eval/exec — pure recursive descent.
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"""
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import math
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import re
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class EvalError(Exception):
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def __init__(self, msg, pos=None):
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super().__init__(msg)
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self.pos = pos
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_TOKEN_RE = re.compile(r"""
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\s*(?:
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(?P<num>\d+(?:\.\d+)?(?:[eE][+-]?\d+)?)
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| (?P<ident>[A-Za-z_][A-Za-z0-9_]*)
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| (?P<op>\*\*|//|[+\-*/%(),])
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)
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""", re.VERBOSE)
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def tokenize(s):
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toks = []
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i = 0
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n = len(s)
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while i < n:
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m = _TOKEN_RE.match(s, i)
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if not m:
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raise EvalError(f"unexpected char {s[i:i+5]!r}", i)
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i = m.end()
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if m.group('num') is not None:
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toks.append(('num', float(m.group('num')), m.start()))
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elif m.group('ident') is not None:
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toks.append(('ident', m.group('ident'), m.start()))
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else:
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toks.append(('op', m.group('op'), m.start()))
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toks.append(('eof', None, n))
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return toks
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FUNCS = {
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'sin': lambda a: math.sin(a),
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'cos': lambda a: math.cos(a),
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'sqrt': lambda a: math.sqrt(a),
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'abs': lambda a: abs(a),
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'max': lambda *a: max(a),
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'min': lambda *a: min(a),
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'round': lambda a: round(a),
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'pow': lambda a, b: a ** b,
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}
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class Parser:
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def __init__(self, toks, env=None):
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self.toks = toks
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self.pos = 0
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self.env = env or {}
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def peek(self):
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return self.toks[self.pos]
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def advance(self):
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t = self.toks[self.pos]
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self.pos += 1
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return t
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def expect(self, kind, val=None):
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t = self.peek()
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if t[0] != kind or (val is not None and t[1] != val):
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raise EvalError(f"expected {kind} {val!r} got {t[0]} {t[1]!r}", t[2])
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return self.advance()
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# expr := term (('+'|'-') term)*
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def parse_expr(self):
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v = self.parse_term()
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while self.peek()[0] == 'op' and self.peek()[1] in ('+', '-'):
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op = self.advance()[1]
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r = self.parse_term()
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v = v + r if op == '+' else v - r
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return v
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def parse_term(self):
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v = self.parse_factor()
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while self.peek()[0] == 'op' and self.peek()[1] in ('*', '/', '//', '%'):
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op = self.advance()[1]
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r = self.parse_factor()
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if op == '*':
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v = v * r
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elif op == '/':
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if r == 0:
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raise EvalError("division by zero", self.peek()[2])
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v = v / r
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elif op == '//':
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if r == 0:
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raise EvalError("division by zero", self.peek()[2])
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v = v // r
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elif op == '%':
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if r == 0:
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raise EvalError("modulo by zero", self.peek()[2])
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v = v % r
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return v
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def parse_factor(self):
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# right-assoc **
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base = self.parse_unary()
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if self.peek()[0] == 'op' and self.peek()[1] == '**':
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self.advance()
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exp = self.parse_factor()
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return base ** exp
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return base
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def parse_unary(self):
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if self.peek()[0] == 'op' and self.peek()[1] in ('+', '-'):
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op = self.advance()[1]
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# operand is a full power expression so that -2**2 == -(2**2)
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v = self.parse_factor()
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return -v if op == '-' else v
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return self.parse_primary()
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def parse_primary(self):
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t = self.peek()
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if t[0] == 'num':
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self.advance()
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return t[1]
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if t[0] == 'op' and t[1] == '(':
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self.advance()
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v = self.parse_expr()
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self.expect('op', ')')
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return v
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if t[0] == 'ident':
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name = t[1]
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self.advance()
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if self.peek()[0] == 'op' and self.peek()[1] == '(':
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self.advance()
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args = []
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if not (self.peek()[0] == 'op' and self.peek()[1] == ')'):
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args.append(self.parse_expr())
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while self.peek()[0] == 'op' and self.peek()[1] == ',':
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self.advance()
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args.append(self.parse_expr())
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self.expect('op', ')')
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if name not in FUNCS:
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raise EvalError(f"unknown function {name}", t[2])
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try:
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return FUNCS[name](*args)
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except Exception as e:
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raise EvalError(f"function {name}: {e}", t[2])
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# variable
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if name not in self.env:
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raise EvalError(f"unknown variable {name}", t[2])
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return self.env[name]
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raise EvalError(f"unexpected token {t[0]} {t[1]!r}", t[2])
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def evaluate(s, env=None):
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toks = tokenize(s)
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p = Parser(toks, env)
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v = p.parse_expr()
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if p.peek()[0] != 'eof':
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raise EvalError("trailing tokens", p.peek()[2])
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return v
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if __name__ == '__main__':
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import sys
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env = {'x': 3, 'pi': math.pi}
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expr = ' '.join(sys.argv[1:]) or '2 + 3*4'
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print(evaluate(expr, env))
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