"""
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 __future__ import annotations
import operator
import token as tokenlib
import tokenize
from collections.abc import Iterable
from io import BytesIO
from tokenize import TokenInfo
from typing import Any, Callable, Generator, Generic, Iterator, TypeVar
from .compat import HAS_UNCERTAINTIES, ufloat
from .errors import DefinitionSyntaxError
S = TypeVar("S")
if HAS_UNCERTAINTIES:
_ufloat = ufloat # type: ignore
else:
def _ufloat(*args: Any, **kwargs: Any):
raise TypeError(
"Please install the uncertainties package to be able to parse quantities with uncertainty."
)
def _power(left: Any, right: Any) -> Any:
from . import Quantity
from .compat import is_duck_array
if (
isinstance(left, Quantity)
and is_duck_array(left.magnitude)
and left.dtype.kind not in "cf"
and right < 0
):
left = left.astype(float)
return operator.pow(left, right)
UnaryOpT = Callable[
[
Any,
],
Any,
]
BinaryOpT = Callable[[Any, Any], Any]
_UNARY_OPERATOR_MAP: dict[str, UnaryOpT] = {"+": lambda x: x, "-": lambda x: x * -1}
_BINARY_OPERATOR_MAP: dict[str, BinaryOpT] = {
"+/-": _ufloat,
"**": _power,
"*": operator.mul,
"": operator.mul, # operator for implicit ops
"/": operator.truediv,
"+": operator.add,
"-": operator.sub,
"%": operator.mod,
"//": operator.floordiv,
}
# For controlling order of operations
_OP_PRIORITY = {
"+/-": 4,
"**": 3,
"^": 3,
"unary": 2,
"*": 1,
"": 1, # operator for implicit ops
"//": 1,
"/": 1,
"%": 1,
"+": 0,
"-": 0,
}
[docs]
class IteratorLookAhead(Generic[S]):
"""An iterator with lookahead buffer.
Adapted: https://stackoverflow.com/a/1517965/1291237
"""
def __init__(self, iter: Iterator[S]):
self.iter = iter
self.buffer: list[S] = []
def __iter__(self):
return self
def __next__(self) -> S:
if self.buffer:
return self.buffer.pop(0)
else:
return self.iter.__next__()
[docs]
def lookahead(self, n: int) -> S:
"""Return an item n entries ahead in the iteration."""
while n >= len(self.buffer):
try:
self.buffer.append(self.iter.__next__())
except StopIteration:
raise ValueError("Cannot look ahead, out of range")
return self.buffer[n]
[docs]
def plain_tokenizer(input_string: str) -> Generator[TokenInfo, None, None]:
"""Standard python tokenizer"""
for tokinfo in tokenize.tokenize(BytesIO(input_string.encode("utf-8")).readline):
if tokinfo.type != tokenlib.ENCODING:
yield tokinfo
[docs]
def uncertainty_tokenizer(input_string: str) -> Generator[TokenInfo, None, None]:
"""Tokenizer capable of parsing uncertainties as v+/-u and v±u"""
def _number_or_nan(token: TokenInfo) -> bool:
if token.type == tokenlib.NUMBER or (
token.type == tokenlib.NAME and token.string == "nan"
):
return True
return False
def _get_possible_e(
toklist: IteratorLookAhead[TokenInfo], e_index: int
) -> TokenInfo | None:
possible_e_token = toklist.lookahead(e_index)
if (
possible_e_token.string[0] == "e"
and len(possible_e_token.string) > 1
and possible_e_token.string[1].isdigit()
):
end = possible_e_token.end
possible_e = tokenize.TokenInfo(
type=tokenlib.STRING,
string=possible_e_token.string,
start=possible_e_token.start,
end=end,
line=possible_e_token.line,
)
elif (
possible_e_token.string[0] in ["e", "E"]
and toklist.lookahead(e_index + 1).string in ["+", "-"]
and toklist.lookahead(e_index + 2).type == tokenlib.NUMBER
):
# Special case: Python allows a leading zero for exponents (i.e., 042) but not for numbers
if (
toklist.lookahead(e_index + 2).string == "0"
and toklist.lookahead(e_index + 3).type == tokenlib.NUMBER
):
exp_number = toklist.lookahead(e_index + 3).string
end = toklist.lookahead(e_index + 3).end
else:
exp_number = toklist.lookahead(e_index + 2).string
end = toklist.lookahead(e_index + 2).end
possible_e = tokenize.TokenInfo(
type=tokenlib.STRING,
string=f"e{toklist.lookahead(e_index + 1).string}{exp_number}",
start=possible_e_token.start,
end=end,
line=possible_e_token.line,
)
else:
possible_e = None
return possible_e
def _apply_e_notation(mantissa: TokenInfo, exponent: TokenInfo) -> TokenInfo:
if mantissa.string == "nan":
return mantissa
if float(mantissa.string) == 0.0:
return mantissa
return tokenize.TokenInfo(
type=tokenlib.NUMBER,
string=f"{mantissa.string}{exponent.string}",
start=mantissa.start,
end=exponent.end,
line=exponent.line,
)
def _finalize_e(
nominal_value: TokenInfo,
std_dev: TokenInfo,
toklist: IteratorLookAhead[TokenInfo],
possible_e: TokenInfo,
) -> tuple[TokenInfo, TokenInfo]:
nominal_value = _apply_e_notation(nominal_value, possible_e)
std_dev = _apply_e_notation(std_dev, possible_e)
next(toklist) # consume 'e' and positive exponent value
if possible_e.string[1] in ["+", "-"]:
next(toklist) # consume "+" or "-" in exponent
exp_number = next(toklist) # consume exponent value
if (
exp_number.string == "0"
and toklist.lookahead(0).type == tokenlib.NUMBER
):
exp_number = next(toklist)
assert exp_number.end == end
# We've already applied the number, we're just consuming all the tokens
return nominal_value, std_dev
# when tokenize encounters whitespace followed by an unknown character,
# (such as ±) it proceeds to mark every character of the whitespace as ERRORTOKEN,
# in addition to marking the unknown character as ERRORTOKEN. Rather than
# wading through all that vomit, just eliminate the problem
# in the input by rewriting ± as +/-.
input_string = input_string.replace("±", "+/-")
toklist = IteratorLookAhead(plain_tokenizer(input_string))
for tokinfo in toklist:
assert tokinfo is not None
line = tokinfo.line
start = tokinfo.start
if (
tokinfo.string == "+"
and toklist.lookahead(0).string == "/"
and toklist.lookahead(1).string == "-"
):
plus_minus_op = tokenize.TokenInfo(
type=tokenlib.OP,
string="+/-",
start=start,
end=toklist.lookahead(1).end,
line=line,
)
for _ in range(-1, 1):
next(toklist)
yield plus_minus_op
elif (
tokinfo.string == "("
and ((seen_minus := 1 if toklist.lookahead(0).string == "-" else 0) or True)
and _number_or_nan(toklist.lookahead(seen_minus))
and toklist.lookahead(seen_minus + 1).string == "+"
and toklist.lookahead(seen_minus + 2).string == "/"
and toklist.lookahead(seen_minus + 3).string == "-"
and _number_or_nan(toklist.lookahead(seen_minus + 4))
and toklist.lookahead(seen_minus + 5).string == ")"
):
# ( NUM_OR_NAN +/- NUM_OR_NAN ) POSSIBLE_E_NOTATION
possible_e = _get_possible_e(toklist, seen_minus + 6)
if possible_e:
end = possible_e.end
else:
end = toklist.lookahead(seen_minus + 5).end
if seen_minus:
minus_op = next(toklist)
yield minus_op
nominal_value = next(toklist)
tokinfo = next(toklist) # consume '+'
next(toklist) # consume '/'
plus_minus_op = tokenize.TokenInfo(
type=tokenlib.OP,
string="+/-",
start=tokinfo.start,
end=next(toklist).end, # consume '-'
line=line,
)
std_dev = next(toklist)
next(toklist) # consume final ')'
if possible_e:
nominal_value, std_dev = _finalize_e(
nominal_value, std_dev, toklist, possible_e
)
yield nominal_value
yield plus_minus_op
yield std_dev
elif (
tokinfo.type == tokenlib.NUMBER
and toklist.lookahead(0).string == "("
and toklist.lookahead(1).type == tokenlib.NUMBER
and toklist.lookahead(2).string == ")"
):
# NUM_OR_NAN ( NUM_OR_NAN ) POSSIBLE_E_NOTATION
possible_e = _get_possible_e(toklist, 3)
if possible_e:
end = possible_e.end
else:
end = toklist.lookahead(2).end
nominal_value = tokinfo
tokinfo = next(toklist) # consume '('
plus_minus_op = tokenize.TokenInfo(
type=tokenlib.OP,
string="+/-",
start=tokinfo.start,
end=tokinfo.end, # this is funky because there's no "+/-" in nominal(std_dev) notation
line=line,
)
std_dev = next(toklist)
if "." not in std_dev.string:
std_dev = tokenize.TokenInfo(
type=std_dev.type,
string="0." + std_dev.string,
start=std_dev.start,
end=std_dev.end,
line=line,
)
next(toklist) # consume final ')'
if possible_e:
nominal_value, std_dev = _finalize_e(
nominal_value, std_dev, toklist, possible_e
)
yield nominal_value
yield plus_minus_op
yield std_dev
else:
yield tokinfo
if HAS_UNCERTAINTIES:
tokenizer = uncertainty_tokenizer
else:
tokenizer = plain_tokenizer
[docs]
class EvalTreeNode:
"""Single node within an evaluation tree
left + operator + right --> binary op
left + operator --> unary op
left + right --> implicit op
left --> single value
"""
def __init__(
self,
left: EvalTreeNode | TokenInfo,
operator: TokenInfo | None = None,
right: EvalTreeNode | None = None,
):
self.left = left
self.operator = operator
self.right = right
def to_string(self) -> str:
# For debugging purposes
if self.right:
assert isinstance(self.left, EvalTreeNode), "self.left not EvalTreeNode (1)"
comps = [self.left.to_string()]
if self.operator:
comps.append(self.operator.string)
comps.append(self.right.to_string())
elif self.operator:
assert isinstance(self.left, EvalTreeNode), "self.left not EvalTreeNode (2)"
comps = [self.operator.string, self.left.to_string()]
else:
assert isinstance(self.left, TokenInfo), "self.left not TokenInfo (1)"
return self.left.string
return "(%s)" % " ".join(comps)
[docs]
def evaluate(
self,
define_op: UnaryOpT,
bin_op: dict[str, BinaryOpT] | None = None,
un_op: dict[str, UnaryOpT] | None = None,
):
"""Evaluate node.
Parameters
----------
define_op : callable
Translates tokens into objects.
bin_op : dict or None, optional
(Default value = _BINARY_OPERATOR_MAP)
un_op : dict or None, optional
(Default value = _UNARY_OPERATOR_MAP)
Returns
-------
"""
bin_op = bin_op or _BINARY_OPERATOR_MAP
un_op = un_op or _UNARY_OPERATOR_MAP
if self.right:
assert isinstance(self.left, EvalTreeNode), "self.left not EvalTreeNode (3)"
# binary or implicit operator
op_text = self.operator.string if self.operator else ""
if op_text not in bin_op:
raise DefinitionSyntaxError(f"missing binary operator '{op_text}'")
return bin_op[op_text](
self.left.evaluate(define_op, bin_op, un_op),
self.right.evaluate(define_op, bin_op, un_op),
)
elif self.operator:
assert isinstance(self.left, EvalTreeNode), "self.left not EvalTreeNode (4)"
# unary operator
op_text = self.operator.string
if op_text not in un_op:
raise DefinitionSyntaxError(f"missing unary operator '{op_text}'")
return un_op[op_text](self.left.evaluate(define_op, bin_op, un_op))
# single value
return define_op(self.left)
def _build_eval_tree(
tokens: list[TokenInfo],
op_priority: dict[str, int],
index: int = 0,
depth: int = 0,
prev_op: str = "<none>",
) -> tuple[EvalTreeNode, int]:
"""Build an evaluation tree from a set of tokens.
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
Raises
------
DefinitionSyntaxError
If there is a syntax error.
"""
result = None
while True:
current_token = tokens[index]
token_type = current_token.type
token_text = current_token.string
if token_type == tokenlib.OP:
if token_text == ")":
if prev_op == "<none>":
raise DefinitionSyntaxError(
f"unopened parentheses in tokens: {current_token}"
)
elif prev_op == "(":
# close parenthetical group
assert result is not None
return result, index
else:
# parenthetical group ending, but we need to close sub-operations within group
assert result is not None
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 DefinitionSyntaxError("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 in (tokenlib.NUMBER, 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 DefinitionSyntaxError("unclosed parentheses in tokens")
if depth > 0 or prev_op:
# have to close recursion
assert result is not None
return result, index
else:
# recursion all closed, so just return the final result
assert result is not None
return result, -1
if index + 1 >= len(tokens):
# should hit ENDMARKER before this ever happens
raise DefinitionSyntaxError("unexpected end to tokens")
index += 1
[docs]
def build_eval_tree(
tokens: Iterable[TokenInfo],
op_priority: dict[str, int] | None = None,
) -> EvalTreeNode:
"""Build an evaluation tree from a set of tokens.
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
Raises
------
DefinitionSyntaxError
If there is a syntax error.
"""
if op_priority is None:
op_priority = _OP_PRIORITY
if not isinstance(tokens, list):
# ensure tokens is list so we can access by index
tokens = list(tokens)
result, _ = _build_eval_tree(tokens, op_priority, 0, 0)
return result
