# -*- coding: utf-8 -*- """ pint.pint_eval ~~~~~~~~~~~~~~ An expression evaluator to be used as a safe replacement for builtin eval. :copyright: 2016 by Pint Authors, see AUTHORS for more details. :license: BSD, see LICENSE for more details. """ from decimal import Decimal import math import operator import token as tokenlib # For controlling order of operations _OP_PRIORITY = { '**': 3, '^': 3, 'unary': 2, '*': 1, '': 1, # operator for implicit ops '/': 1, '+': 0, '-' : 0 } _BINARY_OPERATOR_MAP = { '**': operator.pow, '*': operator.mul, '': operator.mul, # operator for implicit ops '/': operator.truediv, '+': operator.add, '-': operator.sub } _UNARY_OPERATOR_MAP = { '+': lambda x: x, '-': lambda x: x * -1 } class EvalTreeNode(object): def __init__(self, left, operator=None, right=None): """ left + operator + right --> binary op left + operator --> unary op left + right --> implicit op left --> single value """ self.left = left self.operator = operator self.right = right def to_string(self): # For debugging purposes if self.right: comps = [self.left.to_string()] if self.operator: comps.append(self.operator[1]) comps.append(self.right.to_string()) elif self.operator: comps = [self.operator[1], self.left.to_string()] else: return self.left[1] return '(%s)' % ' '.join(comps) def evaluate(self, define_op, bin_op=_BINARY_OPERATOR_MAP, un_op=_UNARY_OPERATOR_MAP): """ define_op is a callable that translates tokens into objects bin_op and un_op provide functions for performing binary and unary operations """ if self.right: # binary or implicit operator op_text = self.operator[1] if self.operator else '' if op_text not in bin_op: raise Exception('missing binary operator "%s"' % op_text) left = self.left.evaluate(define_op, bin_op, un_op) return bin_op[op_text](left, self.right.evaluate(define_op, bin_op, un_op)) elif self.operator: # unary operator op_text = self.operator[1] if op_text not in un_op: raise Exception('missing unary operator "%s"' % op_text) return un_op[op_text](self.left.evaluate(define_op, bin_op, un_op)) else: # single value return define_op(self.left) def build_eval_tree(tokens, op_priority=_OP_PRIORITY, index=0, depth=0, prev_op=None, ): """ Params: Index, depth, and prev_op used recursively, so don't touch. Tokens is an iterable of tokens from an expression to be evaluated. Transform the tokens from an expression into a recursive parse tree, following order of operations. Operations can include binary ops (3 + 4), implicit ops (3 kg), or unary ops (-1). General Strategy: 1) Get left side of operator 2) If no tokens left, return final result 3) Get operator 4) Use recursion to create tree starting at token on right side of operator (start at step #1) 4.1) If recursive call encounters an operator with lower or equal priority to step #2, exit recursion 5) Combine left side, operator, and right side into a new left side 6) Go back to step #2 """ if depth == 0 and prev_op == None: # ensure tokens is list so we can access by index tokens = list(tokens) result = None while True: current_token = tokens[index] token_type = current_token[0] token_text = current_token[1] if token_type == tokenlib.OP: if token_text == ')': if prev_op is None: raise Exception('unopened parentheses in tokens: %s' % current_token) elif prev_op == '(': # close parenthetical group return result, index else: # parenthetical group ending, but we need to close sub-operations within group return result, index - 1 elif token_text == '(': # gather parenthetical group right, index = build_eval_tree(tokens, op_priority, index+1, 0, token_text) if not tokens[index][1] == ')': raise Exception('weird exit from parentheses') if result: # implicit op with a parenthetical group, i.e. "3 (kg ** 2)" result = EvalTreeNode(left=result, right=right) else: # get first token result = right elif token_text in op_priority: if result: # equal-priority operators are grouped in a left-to-right order, unless they're # exponentiation, in which case they're grouped right-to-left # this allows us to get the expected behavior for multiple exponents # (2^3^4) --> (2^(3^4)) # (2 * 3 / 4) --> ((2 * 3) / 4) if op_priority[token_text] <= op_priority.get(prev_op, -1) and token_text not in ['**', '^']: # previous operator is higher priority, so end previous binary op return result, index - 1 # get right side of binary op right, index = build_eval_tree(tokens, op_priority, index+1, depth+1, token_text) result = EvalTreeNode(left=result, operator=current_token, right=right) else: # unary operator right, index = build_eval_tree(tokens, op_priority, index+1, depth+1, 'unary') result = EvalTreeNode(left=right, operator=current_token) elif token_type == tokenlib.NUMBER or token_type == tokenlib.NAME: if result: # tokens with an implicit operation i.e. "1 kg" if op_priority[''] <= op_priority.get(prev_op, -1): # previous operator is higher priority than implicit, so end previous binary op return result, index - 1 right, index = build_eval_tree(tokens, op_priority, index, depth+1, '') result = EvalTreeNode(left=result, right=right) else: # get first token result = EvalTreeNode(left=current_token) if tokens[index][0] == tokenlib.ENDMARKER: if prev_op == '(': raise Exception('unclosed parentheses in tokens') if depth > 0 or prev_op: # have to close recursion return result, index else: # recursion all closed, so just return the final result return result if index + 1 >= len(tokens): # should hit ENDMARKER before this ever happens raise Exception('unexpected end to tokens') index += 1