Evaluate math equations from unsafe user input in Python
Question: I have a website where the user enters math equations (expressions) and then
those equations are evaluated against data (constants) provided by the
website. The math operations needed include symbols, arithmetic operations,
`min()`, `max()` and some other basic functions. A sample equation could be:

    
    
    max(a * b + 100, a / b - 200)
    

One could simply `eval()` this using Python, but as we all know this leads
compromising the site. What would be the safe approach of doing math equation
evaluation?

  * What math equation parsing and evaluation engines there are for Python

  * If one chooses to use Python itself to evaluate the expression are there any Python sandboxes which would limit the Python, so that only user supplier operators and functions are available. Full-fledged Python, like defining functions, should be totally disabled. Subprocesses are ok (see [PyPy sandbox](http://pypy.readthedocs.org/en/latest/sandbox.html)). Specially, for loops and other holes for exploiting memory and CPU usage should be closed.

  * Any other approaches e.g. by using a command line binary (bc)?


Answer: There is a relatively easy of doing this in Python without third party
packages.

  * Using `compile()` to prepare a single-line Python expression to be bytecode for `eval()`

  * Not running the bytecode through `eval()`, but instead run it in your custom opcode loop and only implement opcodes which you really need. E.g. no built-ins, no attribute access, so the sandbox cannot escaped.

However there are some gotchas, like preparing for CPU exhaustion and memory
exhaustion, which are not specific to this method and are issue on other
approaches too.

[Here is a full blog post about the
topic](http://opensourcehacker.com/2014/10/29/safe-evaluation-of-math-
expressions-in-pure-python/). [Here is a related
gist](https://gist.github.com/miohtama/34a83d870a14aa7e580d). Below is
shortened sample code.

    
    
    """"
    
        The orignal author: Alexer / #python.fi
    
    """
    
    import opcode
    import dis
    import sys
    import multiprocessing
    import time
    
    # Python 3 required
    assert sys.version_info[0] == 3, "No country for old snakes"
    
    
    class UnknownSymbol(Exception):
        """ There was a function or constant in the expression we don't support. """
    
    
    class BadValue(Exception):
        """ The user tried to input dangerously big value. """
    
        MAX_ALLOWED_VALUE = 2**63
    
    
    class BadCompilingInput(Exception):
        """ The user tried to input something which might cause compiler to slow down. """
    
    
    def disassemble(co):
        """ Loop through Python bytecode and match instructions  with our internal opcodes.
    
        :param co: Python code object
        """
        code = co.co_code
        n = len(code)
        i = 0
        extended_arg = 0
        result = []
        while i < n:
            op = code[i]
    
            curi = i
            i = i+1
            if op >= dis.HAVE_ARGUMENT:
                # Python 2
                # oparg = ord(code[i]) + ord(code[i+1])*256 + extended_arg
                oparg = code[i] + code[i+1] * 256 + extended_arg
                extended_arg = 0
                i = i+2
                if op == dis.EXTENDED_ARG:
                    # Python 2
                    #extended_arg = oparg*65536L
                    extended_arg = oparg*65536
            else:
                oparg = None
    
            # print(opcode.opname[op])
    
            opv = globals()[opcode.opname[op].replace('+', '_')](co, curi, i, op, oparg)
    
            result.append(opv)
    
        return result
    
    # For the opcodes see dis.py
    # (Copy-paste)
    # https://docs.python.org/2/library/dis.html
    
    class Opcode:
        """ Base class for out internal opcodes. """
        args = 0
        pops = 0
        pushes = 0
        def __init__(self, co, i, nexti, op, oparg):
            self.co = co
            self.i = i
            self.nexti = nexti
            self.op = op
            self.oparg = oparg
    
        def get_pops(self):
            return self.pops
    
        def get_pushes(self):
            return self.pushes
    
        def touch_value(self, stack, frame):
            assert self.pushes == 0
            for i in range(self.pops):
                stack.pop()
    
    
    class OpcodeArg(Opcode):
        args = 1
    
    
    class OpcodeConst(OpcodeArg):
        def get_arg(self):
            return self.co.co_consts[self.oparg]
    
    
    class OpcodeName(OpcodeArg):
        def get_arg(self):
            return self.co.co_names[self.oparg]
    
    
    class POP_TOP(Opcode):
        """Removes the top-of-stack (TOS) item."""
        pops = 1
        def touch_value(self, stack, frame):
            stack.pop()
    
    
    class DUP_TOP(Opcode):
        """Duplicates the reference on top of the stack."""
        # XXX: +-1
        pops = 1
        pushes = 2
        def touch_value(self, stack, frame):
            stack[-1:] = 2 * stack[-1:]
    
    
    class ROT_TWO(Opcode):
        """Swaps the two top-most stack items."""
        pops = 2
        pushes = 2
        def touch_value(self, stack, frame):
            stack[-2:] = stack[-2:][::-1]
    
    
    class ROT_THREE(Opcode):
        """Lifts second and third stack item one position up, moves top down to position three."""
        pops = 3
        pushes = 3
        direct = True
        def touch_value(self, stack, frame):
            v3, v2, v1 = stack[-3:]
            stack[-3:] = [v1, v3, v2]
    
    
    class ROT_FOUR(Opcode):
        """Lifts second, third and forth stack item one position up, moves top down to position four."""
        pops = 4
        pushes = 4
        direct = True
        def touch_value(self, stack, frame):
            v4, v3, v2, v1 = stack[-3:]
            stack[-3:] = [v1, v4, v3, v2]
    
    
    class UNARY(Opcode):
        """Unary Operations take the top of the stack, apply the operation, and push the result back on the stack."""
        pops = 1
        pushes = 1
    
    
    class UNARY_POSITIVE(UNARY):
        """Implements TOS = +TOS."""
        def touch_value(self, stack, frame):
            stack[-1] = +stack[-1]
    
    
    class UNARY_NEGATIVE(UNARY):
        """Implements TOS = -TOS."""
        def touch_value(self, stack, frame):
            stack[-1] = -stack[-1]
    
    
    class BINARY(Opcode):
        """Binary operations remove the top of the stack (TOS) and the second top-most stack item (TOS1) from the stack. They perform the operation, and put the result back on the stack."""
        pops = 2
        pushes = 1
    
    
    class BINARY_POWER(BINARY):
        """Implements TOS = TOS1 ** TOS."""
        def touch_value(self, stack, frame):
            TOS1, TOS = stack[-2:]
            print(TOS1, TOS)
            if abs(TOS1) > BadValue.MAX_ALLOWED_VALUE or abs(TOS) > BadValue.MAX_ALLOWED_VALUE:
                raise BadValue("The value for exponent was too big")
    
            stack[-2:] = [TOS1 ** TOS]
    
    
    class BINARY_MULTIPLY(BINARY):
        """Implements TOS = TOS1 * TOS."""
        def touch_value(self, stack, frame):
            TOS1, TOS = stack[-2:]
            stack[-2:] = [TOS1 * TOS]
    
    
    class BINARY_DIVIDE(BINARY):
        """Implements TOS = TOS1 / TOS when from __future__ import division is not in effect."""
        def touch_value(self, stack, frame):
            TOS1, TOS = stack[-2:]
            stack[-2:] = [TOS1 / TOS]
    
    
    class BINARY_MODULO(BINARY):
        """Implements TOS = TOS1 % TOS."""
        def touch_value(self, stack, frame):
            TOS1, TOS = stack[-2:]
            stack[-2:] = [TOS1 % TOS]
    
    
    class BINARY_ADD(BINARY):
        """Implements TOS = TOS1 + TOS."""
        def touch_value(self, stack, frame):
            TOS1, TOS = stack[-2:]
            stack[-2:] = [TOS1 + TOS]
    
    
    class BINARY_SUBTRACT(BINARY):
        """Implements TOS = TOS1 - TOS."""
        def touch_value(self, stack, frame):
            TOS1, TOS = stack[-2:]
            stack[-2:] = [TOS1 - TOS]
    
    
    class BINARY_FLOOR_DIVIDE(BINARY):
        """Implements TOS = TOS1 // TOS."""
        def touch_value(self, stack, frame):
            TOS1, TOS = stack[-2:]
            stack[-2:] = [TOS1 // TOS]
    
    
    class BINARY_TRUE_DIVIDE(BINARY):
        """Implements TOS = TOS1 / TOS when from __future__ import division is in effect."""
        def touch_value(self, stack, frame):
            TOS1, TOS = stack[-2:]
            stack[-2:] = [TOS1 / TOS]
    
    
    class BINARY_LSHIFT(BINARY):
        """Implements TOS = TOS1 << TOS."""
        def touch_value(self, stack, frame):
            TOS1, TOS = stack[-2:]
            stack[-2:] = [TOS1 << TOS]
    
    
    class BINARY_RSHIFT(BINARY):
        """Implements TOS = TOS1 >> TOS."""
        def touch_value(self, stack, frame):
            TOS1, TOS = stack[-2:]
            stack[-2:] = [TOS1 >> TOS]
    
    
    class BINARY_AND(BINARY):
        """Implements TOS = TOS1 & TOS."""
        def touch_value(self, stack, frame):
            TOS1, TOS = stack[-2:]
            stack[-2:] = [TOS1 & TOS]
    
    
    class BINARY_XOR(BINARY):
        """Implements TOS = TOS1 ^ TOS."""
        def touch_value(self, stack, frame):
            TOS1, TOS = stack[-2:]
            stack[-2:] = [TOS1 ^ TOS]
    
    
    class BINARY_OR(BINARY):
        """Implements TOS = TOS1 | TOS."""
        def touch_value(self, stack, frame):
            TOS1, TOS = stack[-2:]
            stack[-2:] = [TOS1 | TOS]
    
    
    class RETURN_VALUE(Opcode):
        """Returns with TOS to the caller of the function."""
        pops = 1
        final = True
        def touch_value(self, stack, frame):
            value = stack.pop()
            return value
    
    
    class LOAD_CONST(OpcodeConst):
        """Pushes co_consts[consti] onto the stack.""" # consti
        pushes = 1
        def touch_value(self, stack, frame):
            # XXX moo: Validate type
            value = self.get_arg()
            assert isinstance(value, (int, float))
            stack.append(value)
    
    
    class LOAD_NAME(OpcodeName):
        """Pushes the value associated with co_names[namei] onto the stack.""" # namei
        pushes = 1
        def touch_value(self, stack, frame):
            # XXX moo: Get name from dict of valid variables/functions
            name = self.get_arg()
            if name not in frame:
                raise UnknownSymbol("Does not know symbol {}".format(name))
            stack.append(frame[name])
    
    
    class CALL_FUNCTION(OpcodeArg):
        """Calls a function. The low byte of argc indicates the number of positional parameters, the high byte the number of keyword parameters. On the stack, the opcode finds the keyword parameters first. For each keyword argument, the value is on top of the key. Below the keyword parameters, the positional parameters are on the stack, with the right-most parameter on top. Below the parameters, the function object to call is on the stack. Pops all function arguments, and the function itself off the stack, and pushes the return value.""" # argc
        pops = None
        pushes = 1
    
        def get_pops(self):
            args = self.oparg & 0xff
            kwargs = (self.oparg >> 8) & 0xff
            return 1 + args + 2 * kwargs
    
        def touch_value(self, stack, frame):
            argc = self.oparg & 0xff
            kwargc = (self.oparg >> 8) & 0xff
            assert kwargc == 0
            if argc > 0:
                args = stack[-argc:]
                stack[:] = stack[:-argc]
            else:
                args = []
            func = stack.pop()
    
            assert func in frame.values(), "Uh-oh somebody injected bad function. This does not happen."
    
            result = func(*args)
            stack.append(result)
    
    
    def check_for_pow(expr):
        """ Python evaluates power operator during the compile time if its on constants.
    
        You can do CPU / memory burning attack with ``2**999999999999999999999**9999999999999``.
        We mainly care about memory now, as we catch timeoutting in any case.
    
        We just disable pow and do not care about it.
        """
        if "**" in expr:
            raise BadCompilingInput("Power operation is not allowed")
    
    
    def _safe_eval(expr, functions_and_constants={}, check_compiling_input=True):
        """ Evaluate a Pythonic math expression and return the output as a string.
    
        The expr is limited to 1024 characters / 1024 operations
        to prevent CPU burning or memory stealing.
    
        :param functions_and_constants: Supplied "built-in" data for evaluation
        """
    
        # Some safety checks
        assert len(expr) < 1024
    
        # Check for potential bad compiler input
        if check_compiling_input:
            check_for_pow(expr)
    
        # Compile Python source code to Python code for eval()
        code = compile(expr, '', 'eval')
    
        # Dissect bytecode back to Python opcodes
        ops = disassemble(code)
        assert len(ops) < 1024
    
        stack = []
        for op in ops:
            value = op.touch_value(stack, functions_and_constants)
    
        return value
    

