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# -*- 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
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