#! /usr/bin/env python
# -*- coding: utf-8 -*-
# Author: AxiaCore S.A.S. http://axiacore.com
#
# Based on js-expression-eval, by Matthew Crumley (email@matthewcrumley.com, http://silentmatt.com/)
# https://github.com/silentmatt/js-expression-eval
#
# Ported to Python and modified by Vera Mazhuga (ctrl-alt-delete@live.com, http://vero4ka.info/)
#
# You are free to use and modify this code in anyway you find useful. Please leave this comment in the code
# to acknowledge its original source. If you feel like it, I enjoy hearing about projects that use my code,
# but don't feel like you have to let me know or ask permission.
import math
import random
import re
[docs]
class Token():
def __init__(self, type_, index_, prio_, number_):
self.type_ = type_
self.index_ = index_ or 0
self.prio_ = prio_ or 0
self.number_ = number_ if number_ != None else 0
[docs]
def toString(self):
if self.type_ == TNUMBER:
return self.number_
if self.type_ == TOP1 or self.type_ == TOP2 or self.type_ == TVAR:
return self.index_
elif self.type_ == TFUNCALL:
return 'CALL'
else:
return 'Invalid Token'
[docs]
class Expression():
def __init__(self, tokens, ops1, ops2, functions):
self.tokens = tokens
self.ops1 = ops1
self.ops2 = ops2
self.functions = functions
[docs]
def simplify(self, values):
values = values or {}
nstack = []
newexpression = []
L = len(self.tokens)
for i in range(0, L):
item = self.tokens[i]
type_ = item.type_
if type_ == TNUMBER:
nstack.append(item)
elif type_ == TVAR and item.index_ in values:
item = Token(TNUMBER, 0, 0, values[item.index_])
nstack.append(item)
elif type_ == TOP2 and len(nstack) > 1:
n2 = nstack.pop()
n1 = nstack.pop()
f = self.ops2[item.index_]
item = Token(TNUMBER, 0, 0, f(n1.number_, n2.number_))
nstack.append(item)
elif type_ == TOP1 and nstack:
n1 = nstack.pop()
f = self.ops1[item.index_]
item = Token(TNUMBER, 0, 0, f(n1.number_))
nstack.append(item)
else:
while len(nstack) > 0:
newexpression.append(nstack.pop(0))
newexpression.append(item)
while nstack:
newexpression.append(nstack.pop(0))
return Expression(newexpression, self.ops1, self.ops2, self.functions)
[docs]
def substitute(self, variable, expr):
if not isinstance(expr, Expression):
expr = Parser().parse(str(expr))
newexpression = []
L = len(self.tokens)
for i in range(0, L):
item = self.tokens[i]
type_ = item.type_
if type_ == TVAR and item.index_ == variable:
for j in range(0, len(expr.tokens)):
expritem = expr.tokens[j]
replitem = Token(
expritem.type_,
expritem.index_,
expritem.prio_,
expritem.number_,
)
newexpression.append(replitem)
else:
newexpression.append(item)
ret = Expression(newexpression, self.ops1, self.ops2, self.functions)
return ret
[docs]
def evaluate(self, values):
values = values or {}
nstack = []
L = len(self.tokens)
for item in self.tokens:
type_ = item.type_
if type_ == TNUMBER:
nstack.append(item.number_)
elif type_ == TOP2:
n2 = nstack.pop()
n1 = nstack.pop()
f = self.ops2[item.index_]
nstack.append(f(n1, n2))
elif type_ == TVAR:
if item.index_ in values:
nstack.append(values[item.index_])
elif item.index_ in self.functions:
nstack.append(self.functions[item.index_])
else:
raise Exception('undefined variable: ' + item.index_)
elif type_ == TOP1:
n1 = nstack.pop()
f = self.ops1[item.index_]
nstack.append(f(n1))
elif type_ == TFUNCALL:
n1 = nstack.pop()
f = nstack.pop()
if callable(f):
if type(n1) is list:
nstack.append(f(*n1))
else:
nstack.append(f(n1))
else:
raise Exception(f + ' is not a function')
else:
raise Exception('invalid Expression')
if len(nstack) > 1:
raise Exception('invalid Expression (parity)')
return nstack[0]
[docs]
def toString(self, toJS=False):
nstack = []
L = len(self.tokens)
for i in range(0, L):
item = self.tokens[i]
type_ = item.type_
if type_ == TNUMBER:
if type(item.number_) == str:
nstack.append("'"+item.number_+"'")
else:
nstack.append( item.number_)
elif type_ == TOP2:
n2 = nstack.pop()
n1 = nstack.pop()
f = item.index_
if toJS and f == '^':
nstack.append('math.pow(' + n1 + ',' + n2 + ')')
else:
frm='({n1}{f}{n2})'
if f == ',':
frm = '{n1}{f}{n2}'
nstack.append(frm.format(
n1=n1,
n2=n2,
f=f,
))
elif type_ == TVAR:
nstack.append(item.index_)
elif type_ == TOP1:
n1 = nstack.pop()
f = item.index_
if f == '-':
nstack.append('(' + f + str(n1) + ')')
else:
nstack.append(f + '(' + str(n1) + ')')
elif type_ == TFUNCALL:
n1 = nstack.pop()
f = nstack.pop()
nstack.append(f + '(' + n1 + ')')
else:
raise Exception('invalid Expression')
if len(nstack) > 1:
raise Exception('invalid Expression (parity)')
return nstack[0]
def __str__(self):
return self.toString()
[docs]
def symbols(self):
vars = []
for i in range(0, len(self.tokens)):
item = self.tokens[i]
if item.type_ == TVAR and not item.index_ in vars:
vars.append(item.index_)
return vars
[docs]
def variables(self):
return [
sym for sym in self.symbols()
if sym not in self.functions]
[docs]
class Parser:
[docs]
def add(self, a, b):
return a + b
[docs]
def norm(self, a, b):
return math.sqrt(a * a + b * b)
[docs]
def Froude(self, a, b, c):
return math.sqrt(a * a + b * b) / math.sqrt(9.81 * c)
[docs]
def sto(self, a, b):
return dict(a = b)
[docs]
def sub(self, a, b):
return a - b
[docs]
def mul(self, a, b):
return a * b
[docs]
def div(self, a, b):
return a / b
[docs]
def pow(self, a, b):
return a ** b
[docs]
def mod(self, a, b):
return a % b
[docs]
def concat(self, a, b,*args):
result=u'{0}{1}'.format(a, b)
for arg in args:
result=u'{0}{1}'.format(result, arg)
return result
[docs]
def equal (self, a, b ):
return a == b
[docs]
def notEqual (self, a, b ):
return a != b
[docs]
def greaterThan (self, a, b ):
return a > b
[docs]
def lessThan (self, a, b ):
return a < b
[docs]
def greaterThanEqual (self, a, b ):
return a >= b
[docs]
def lessThanEqual (self, a, b ):
return a <= b
[docs]
def andOperator (self, a, b ):
return ( a and b )
[docs]
def orOperator (self, a, b ):
return ( a or b )
[docs]
def xorOperator (self, a, b ):
return ( a ^ b )
[docs]
def inOperator(self, a, b):
return a in b
[docs]
def notOperator(self, a):
return not a
[docs]
def neg(self, a):
return -a
[docs]
def random(self, a):
return random.random() * (a or 1)
[docs]
def fac(self, a): # a!
return math.factorial(a)
[docs]
def pyt(self, a, b):
return math.sqrt(a * a + b * b)
[docs]
def sind(self, a):
return math.sin(math.radians(a))
[docs]
def cosd(self, a):
return math.cos(math.radians(a))
[docs]
def tand(self, a):
return math.tan(math.radians(a))
[docs]
def asind(self, a):
return math.degrees(math.asin(a))
[docs]
def acosd(self, a):
return math.degrees(math.acos(a))
[docs]
def atand(self, a):
return math.degrees(math.atan(a))
[docs]
def roll(self, a, b):
rolls = []
roll = 0
final = 0
for c in range(1, a):
roll = random.randint(1, b)
rolls.append(roll)
return rolls
[docs]
def ifFunction(self,a,b,c):
return b if a else c
[docs]
def append(self, a, b):
if type(a) != list:
return [a, b]
a.append(b)
return a
def __init__(self, string_literal_quotes = ("'", "\"")):
self.string_literal_quotes = string_literal_quotes
self.success = False
self.errormsg = ''
self.expression = ''
self.pos = 0
self.tokennumber = 0
self.tokenprio = 0
self.tokenindex = 0
self.tmpprio = 0
self.ops1 = {
'sin': math.sin,
'cos': math.cos,
'tan': math.tan,
'asin': math.asin,
'acos': math.acos,
'atan': math.atan,
'sind': self.sind,
'cosd': self.cosd,
'tand': self.tand,
'asind': self.asind,
'acosd': self.acosd,
'atand': self.atand,
'sqrt': math.sqrt,
'abs': abs,
'ceil': math.ceil,
'floor': math.floor,
'round': round,
'-': self.neg,
'not': self.notOperator,
'exp': math.exp,
}
self.ops2 = {
'+': self.add,
'-': self.sub,
'*': self.mul,
'/': self.div,
'%': self.mod,
'^': self.pow,
'**': self.pow,
',': self.append,
'||': self.concat,
"==": self.equal,
"!=": self.notEqual,
">": self.greaterThan,
"<": self.lessThan,
">=": self.greaterThanEqual,
"<=": self.lessThanEqual,
"and": self.andOperator,
"or": self.orOperator,
"xor": self.xorOperator,
"in": self.inOperator,
"D": self.roll,
}
self.functions = {
'random': self.random,
'fac': self.fac,
'log': math.log,
'min': min,
'max': max,
'pyt': self.pyt,
'pow': math.pow,
'atan2': math.atan2,
'concat':self.concat,
'if': self.ifFunction,
'norm': self.norm,
'Froude': self.Froude,
'sto': self.sto,
}
self.consts = {
'E': math.e,
'PI': math.pi,
'pi': math.pi,
'g':9.81
}
self.values = {
'sin': math.sin,
'cos': math.cos,
'tan': math.tan,
'asin': math.asin,
'acos': math.acos,
'atan': math.atan,
'sqrt': math.sqrt,
'log': math.log,
'abs': abs,
'ceil': math.ceil,
'floor': math.floor,
'round': round,
'random': self.random,
'fac': self.fac,
'exp': math.exp,
'min': min,
'max': max,
'pyt': self.pyt,
'pow': math.pow,
'atan2': math.atan2,
'E': math.e,
'PI': math.pi,
'g': 9.81,
'pi':math.pi
}
[docs]
def parse(self, expr) -> Expression:
self.errormsg = ''
self.success = True
operstack = []
tokenstack = []
self.tmpprio = 0
expected = self.PRIMARY | self.LPAREN | self.FUNCTION | self.SIGN
noperators = 0
self.expression = expr
self.pos = 0
while self.pos < len(self.expression):
if self.isOperator():
if self.isSign() and expected & self.SIGN:
if self.isNegativeSign():
self.tokenprio = 5
self.tokenindex = '-'
noperators += 1
self.addfunc(tokenstack, operstack, TOP1)
expected = \
self.PRIMARY | self.LPAREN | self.FUNCTION | self.SIGN
elif self.isLogicalNot() and expected & self.SIGN:
self.tokenprio = 2
self.tokenindex = 'not'
noperators += 1
self.addfunc(tokenstack, operstack, TOP1)
expected = \
self.PRIMARY | self.LPAREN | self.FUNCTION | self.SIGN
elif self.isComment():
pass
else:
if expected and self.OPERATOR == 0:
self.error_parsing(self.pos, 'unexpected operator')
noperators += 2
self.addfunc(tokenstack, operstack, TOP2)
expected = \
self.PRIMARY | self.LPAREN | self.FUNCTION | self.SIGN
elif self.isNumber():
if expected and self.PRIMARY == 0:
self.error_parsing(self.pos, 'unexpected number')
token = Token(TNUMBER, 0, 0, self.tokennumber)
tokenstack.append(token)
expected = self.OPERATOR | self.RPAREN | self.COMMA
elif self.isString():
if (expected & self.PRIMARY) == 0:
self.error_parsing(self.pos, 'unexpected string')
token = Token(TNUMBER, 0, 0, self.tokennumber)
tokenstack.append(token)
expected = self.OPERATOR | self.RPAREN | self.COMMA
elif self.isLeftParenth():
if (expected & self.LPAREN) == 0:
self.error_parsing(self.pos, 'unexpected \"(\"')
if expected & self.CALL:
noperators += 2
self.tokenprio = -2
self.tokenindex = -1
self.addfunc(tokenstack, operstack, TFUNCALL)
expected = \
self.PRIMARY | self.LPAREN | self.FUNCTION | \
self.SIGN | self.NULLARY_CALL
elif self.isRightParenth():
if expected & self.NULLARY_CALL:
token = Token(TNUMBER, 0, 0, [])
tokenstack.append(token)
elif (expected & self.RPAREN) == 0:
self.error_parsing(self.pos, 'unexpected \")\"')
expected = \
self.OPERATOR | self.RPAREN | self.COMMA | \
self.LPAREN | self.CALL
elif self.isComma():
if (expected & self.COMMA) == 0:
self.error_parsing(self.pos, 'unexpected \",\"')
self.addfunc(tokenstack, operstack, TOP2)
noperators += 2
expected = \
self.PRIMARY | self.LPAREN | self.FUNCTION | self.SIGN
elif self.isConst():
if (expected & self.PRIMARY) == 0:
self.error_parsing(self.pos, 'unexpected constant')
consttoken = Token(TNUMBER, 0, 0, self.tokennumber)
tokenstack.append(consttoken)
expected = self.OPERATOR | self.RPAREN | self.COMMA
elif self.isOp2():
if (expected & self.FUNCTION) == 0:
self.error_parsing(self.pos, 'unexpected function')
self.addfunc(tokenstack, operstack, TOP2)
noperators += 2
expected = self.LPAREN
elif self.isOp1():
if (expected & self.FUNCTION) == 0:
self.error_parsing(self.pos, 'unexpected function')
self.addfunc(tokenstack, operstack, TOP1)
noperators += 1
expected = self.LPAREN
elif self.isVar():
if (expected & self.PRIMARY) == 0:
self.error_parsing(self.pos, 'unexpected variable')
vartoken = Token(TVAR, self.tokenindex, 0, 0)
tokenstack.append(vartoken)
expected = \
self.OPERATOR | self.RPAREN | \
self.COMMA | self.LPAREN | self.CALL
elif self.isWhite():
pass
else:
if self.errormsg == '':
self.error_parsing(self.pos, 'unknown character')
else:
self.error_parsing(self.pos, self.errormsg)
if self.tmpprio < 0 or self.tmpprio >= 10:
self.error_parsing(self.pos, 'unmatched \"()\"')
while len(operstack) > 0:
tmp = operstack.pop()
tokenstack.append(tmp)
if (noperators + 1) != len(tokenstack):
self.error_parsing(self.pos, 'parity')
return Expression(tokenstack, self.ops1, self.ops2, self.functions)
[docs]
def evaluate(self, expr, variables):
return self.parse(expr).evaluate(variables)
[docs]
def error_parsing(self, column, msg):
self.success = False
self.errormsg = 'parse error [column ' + str(column) + ']: ' + msg + ', expression: ' + self.expression
raise Exception(self.errormsg)
[docs]
def addfunc(self, tokenstack, operstack, type_):
operator = Token(
type_,
self.tokenindex,
self.tokenprio + self.tmpprio,
0,
)
while len(operstack) > 0:
if operator.prio_ <= operstack[len(operstack) - 1].prio_:
tokenstack.append(operstack.pop())
else:
break
operstack.append(operator)
[docs]
def isNumber(self):
r = False
if self.expression[self.pos] == 'E':
return False
# number in scientific notation
pattern = r'([-+]?([0-9]*\.?[0-9]*)[eE][-+]?[0-9]+).*'
match = re.match(pattern, self.expression[self.pos: ])
if match:
self.pos += len(match.group(1))
self.tokennumber = float(match.group(1))
return True
hex_pattern = r'(0x[0-9a-fA-F]+)'
match = re.match(hex_pattern, self.expression[self.pos: ])
if match:
self.pos += len(match.group(1))
self.tokennumber = int(match.group(1), base=16)
return True
# number in decimal
str = ''
while self.pos < len(self.expression):
code = self.expression[self.pos]
if (code >= '0' and code <= '9') or code == '.':
if (len(str) == 0 and code == '.' ):
str = '0'
str += code
self.pos += 1
try:
self.tokennumber = int(str)
except ValueError:
self.tokennumber = float(str)
r = True
else:
break
return r
[docs]
def unescape(self, v, pos):
buffer = []
escaping = False
for i in range(0, len(v)):
c = v[i]
if escaping:
if c == "'":
buffer.append("'")
break
elif c == '\\':
buffer.append('\\')
break
elif c == '/':
buffer.append('/')
break
elif c == 'b':
buffer.append('\b')
break
elif c == 'f':
buffer.append('\f')
break
elif c == 'n':
buffer.append('\n')
break
elif c == 'r':
buffer.append('\r')
break
elif c == 't':
buffer.append('\t')
break
elif c == 'u':
# interpret the following 4 characters
# as the hex of the unicode code point
codePoint = int(v[i + 1, i + 5], 16)
buffer.append(chr(codePoint))
i += 4
break
else:
raise self.error_parsing(
pos + i,
'Illegal escape sequence: \'\\' + c + '\'',
)
escaping = False
else:
if c == '\\':
escaping = True
else:
buffer.append(c)
return ''.join(buffer)
[docs]
def isString(self):
r = False
str = ''
startpos = self.pos
if self.pos < len(self.expression) and self.expression[self.pos] in self.string_literal_quotes:
quote_type = self.expression[self.pos]
self.pos += 1
while self.pos < len(self.expression):
code = self.expression[self.pos]
if code != quote_type or (str != '' and str[-1] == '\\'):
str += self.expression[self.pos]
self.pos += 1
else:
self.pos += 1
self.tokennumber = self.unescape(str, startpos)
r = True
break
return r
[docs]
def isConst(self):
for i in self.consts:
L = len(i)
str = self.expression[self.pos:self.pos+L]
if i == str:
if len(self.expression) <= self.pos + L:
self.tokennumber = self.consts[i]
self.pos += L
return True
if not self.expression[self.pos + L].isalnum() and self.expression[self.pos + L] != "_":
self.tokennumber = self.consts[i]
self.pos += L
return True
return False
[docs]
def isOperator(self):
ops = (
('**', 8, '**'),
('^', 8, '^'),
('%', 6, '%'),
('/', 6, '/'),
(u'\u2219', 5, '*'), # bullet operator
(u'\u2022', 5, '*'), # black small circle
('*', 5, '*'),
('+', 4, '+'),
('-', 4, '-'),
('||', 3, '||'),
('==', 3, '=='),
('!=', 3, '!='),
('<=', 3, '<='),
('>=', 3, '>='),
('<', 3, '<'),
('>', 3, '>'),
('in ', 3, 'in'),
('not ', 2, 'not'),
('and ', 1, 'and'),
('xor ', 0, 'xor'),
('or ', 0, 'or'),
)
for token, priority, index in ops:
if self.expression.startswith(token, self.pos):
self.tokenprio = priority
self.tokenindex = index
self.pos += len(token)
return True
return False
[docs]
def isSign(self):
code = self.expression[self.pos - 1]
return (code == '+') or (code == '-')
[docs]
def isPositiveSign(self):
code = self.expression[self.pos - 1]
return code == '+'
[docs]
def isNegativeSign(self):
code = self.expression[self.pos - 1]
return code == '-'
[docs]
def isLogicalNot(self):
code = self.expression[self.pos - 4: self.pos]
return code == 'not '
[docs]
def isLeftParenth(self):
code = self.expression[self.pos]
if code == '(':
self.pos += 1
self.tmpprio += 10
return True
return False
[docs]
def isRightParenth(self):
code = self.expression[self.pos]
if code == ')':
self.pos += 1
self.tmpprio -= 10
return True
return False
[docs]
def isComma(self):
code = self.expression[self.pos]
if code==',':
self.pos+=1
self.tokenprio=-1
self.tokenindex=","
return True
return False
[docs]
def isWhite(self):
code = self.expression[self.pos]
if code.isspace():
self.pos += 1
return True
return False
[docs]
def isOp1(self):
str = ''
for i in range(self.pos, len(self.expression)):
c = self.expression[i]
if c.upper() == c.lower():
if i == self.pos or (c != '_' and (c < '0' or c > '9')):
break
str += c
if len(str) > 0 and str in self.ops1:
self.tokenindex = str
self.tokenprio = 9
self.pos += len(str)
return True
return False
[docs]
def isOp2(self):
str = ''
for i in range(self.pos, len(self.expression)):
c = self.expression[i]
if c.upper() == c.lower():
if i == self.pos or (c != '_' and (c < '0' or c > '9')):
break
str += c
if len(str) > 0 and (str in self.ops2):
self.tokenindex = str
self.tokenprio = 9
self.pos += len(str)
return True
return False
[docs]
def isVar(self):
str = ''
inQuotes = False
for i in range(self.pos, len(self.expression)):
c = self.expression[i]
if c.lower() == c.upper():
if ((i == self.pos and c != '"') or (not (c in '_."') and (c < '0' or c > '9'))) and not inQuotes :
break
if c == '"':
inQuotes = not inQuotes
str += c
if str:
self.tokenindex = str
self.tokenprio = 6
self.pos += len(str)
return True
return False