def _reduceAst(self):
if len(self.stack) < 4:
return False
last = self.stack[-1]
last1 = self.stack[-2]
last2 = self.stack[-3]
last3 = self.stack[-4]
if last3.precedence == 0xf and last2.hasAst(
) and last1.operator == ')':
func = BUILTIN_FUNCTIONS.get(last3.operator)
# take into account sign before brace...
if func != None:
ast2 = last2.getAst()
if last3.operator == "root":
if type(ast2) != tuple or len(ast2) != 2:
raise ParseException(
"root must have exaclty two positional arguments.",
self.formula, self.position)
# root operator
if last3.value < 0.0:
last2.ast = ast.AstNegation(
ast.AstRoot(ast2[1], ast2[0]))
else:
last2.ast = ast.AstRoot(ast2[1], ast2[0])
else:
if type(ast2) == tuple:
raise ParseException(
"builtin function must not have more than one positional argument.",
self.formula, self.position)
# builtin function
if last3.value < 0.0:
last2.ast = ast.AstNegation(
ast.AstFunctionCall(last3.operator, ast2))
else:
last2.ast = ast.AstFunctionCall(last3.operator, ast2)
else:
# open brace with negation
if last3.value < 0.0:
last2.ast = ast.AstNegation(last2.getAst())
# x( <number> ) yyy -> x( <number> yyy
self.stack.pop(-2)
# x( <number> yyy -> <number> yyy
self.stack.pop(-3)
if (log.isEnabledFor(logging.DEBUG)):
log.debug("_reduceAst(parentheses): stack is now %s" %
self.stack)
return True
# <number> <op1> <number> <op2>
if last3.hasAst() and last1.hasAst():
# <op1> has a lower precedence than pending <op2>, do nothing
if last2.precedence < last.precedence:
return False
# exponentiation is right-associative.
if last.precedence == 3 and last2.precedence == 3:
return False
if last2.operator == ',':
ast3 = last3.getAst()
if type(ast3) == tuple:
last3.ast = ast3 + (last1.getAst(), )
else:
last3.ast = (ast3, last1.getAst())
elif last2.operator == '+' or last2.operator == '-' or last2.operator == '*' or last2.operator == '/' or last2.operator == '^':
last3.ast = ast.AstBinaryOperator(last3.getAst(),
last2.operator,
last1.getAst())
else:
return False
# <number> <op1> <number> <op2> -> <number> <op2> ->
self.stack.pop(-2)
self.stack.pop(-2)
if (log.isEnabledFor(logging.DEBUG)):
log.debug("_reduceAst(binary): stack is now %s" % self.stack)
return True
return False
def _reduce(self):
if len(self.stack) < 4:
return False
last = self.stack[-1]
last1 = self.stack[-2]
last2 = self.stack[-3]
last3 = self.stack[-4]
if last3.precedence == 0xf and last2.isNumber(
) and last1.operator == ')':
func = BUILTIN_FUNCTIONS.get(last3.operator)
# take into account sign before brace...
if func != None:
# builtin function
if type(last2.value) == tuple:
# multi-arg functions.
last2.value = last3.value * func(*last2.value)
else:
last2.value = last3.value * func(last2.value)
else:
# opening brace
last2.value *= last3.value
# x( <number> ) yyy -> x( <number> yyy
self.stack.pop(-2)
# x( <number> yyy -> <number> yyy
self.stack.pop(-3)
if (log.isEnabledFor(logging.DEBUG)):
log.debug("_reduce(parentheses): stack is now %s" % self.stack)
return True
# <number> <op1> <number> <op2>
if last3.isNumber() and last1.isNumber():
# <op1> has a lower precedence than pending <op2>, do nothing
if last2.precedence < last.precedence:
return False
# exponentiation is right-associative.
if last.precedence == 3 and last2.precedence == 3:
return False
if last2.operator == ',':
if type(last3.value) == tuple:
last3.value += (last1.value, )
else:
last3.value = (last3.value, last1.value)
elif last2.operator == '+':
last3.value += last1.value
elif last2.operator == '-':
last3.value -= last1.value
elif last2.operator == '*':
last3.value *= last1.value
elif last2.operator == '/':
last3.value /= last1.value
elif last2.operator == '^':
last3.value = math.pow(last3.value, last1.value)
else:
return False
# <number> <op1> <number> <op2> -> <number> <op2> ->
self.stack.pop(-2)
self.stack.pop(-2)
if (log.isEnabledFor(logging.DEBUG)):
log.debug("_reduce(binary): stack is now %s" % self.stack)
return True
return False
def _pushToken(self):
c = self._skipWhite()
if c == None:
self.stack.append(Token.newEOS())
if (log.isEnabledFor(logging.DEBUG)):
log.debug("_pushToken(EOS): stack is now %s" % self.stack)
return False
token = None
sign = 1.0
if c == "(":
token = Token.newOpeningParentheses(sign)
c = self._advance()
elif c == ")":
token = Token.newClosingParentheses()
c = self._advance()
elif c == ",":
token = Token.newOperator(c, 0)
c = self._advance()
elif c == "^":
token = Token.newOperator(c, 3)
c = self._advance()
elif c == "/" or c == "*":
token = Token.newOperator(c, 2)
c = self._advance()
elif c == "+":
token = Token.newOperator(c, 1)
c = self._advance()
elif c == "-":
# check, whether this is a sign after an operator or at the start of an expression.
if (len(self.stack) <= 0 or self.stack[-1].precedence > 0):
c = self._advance()
if c != None:
c = self._skipWhite()
if c == None:
raise ParseException(
"Unexpected end of formula after minus sign.",
self.formula, self.position)
sign = -1.0
if c == '-':
raise ParseException(
"Formula contains superfluous minus signs.",
self.formula, self.position)
if c == '(':
token = Token.newOpeningParentheses(sign)
c = self._advance()
else:
# binary minus operator.
token = Token.newOperator(c, 1)
c = self._advance()
if token == None:
# check for identifier
if c in string.ascii_letters or c in GREEK_LETTERS or c == "_":
spos = self.position
c = self._advance()
# valid variable names are _asdf123 ___3 _asd2_3d
while (c != None
and (c in string.ascii_letters or c in GREEK_LETTERS
or c == '_' or c in string.digits)):
c = self._advance()
variable = self.formula[spos:self.position]
# FIXME check for builtin function
func = BUILTIN_FUNCTIONS.get(variable)
if func == None:
if self.variables == None:
# AST parsing
token = Token.newVariable(variable, sign)
else:
# classical, immediate evaluation
value = self.variables.get(variable)
if value == None:
raise ParseException(
"Formula contains unknown variable [%s]." %
variable, self.formula, self.position)
token = Token.newNumber(value * sign)
else:
c = self._skipWhite()
if c != "(":
raise ParseException(
"Formula does not contain an openeing paraentheses after builin function [%s]."
% variable, self.formula, self.position)
c = self._advance()
token = Token.newBuiltin(variable, sign)
elif c in string.digits or c == ".":
spos = self.position
ndigits = 0
# number befor the decimal point
while (c != None and c in string.digits):
c = self._advance()
ndigits += 1
# decimal point present?
if (self.position < len(self.formula) and c == '.'):
c = self._advance()
# digits after the decimal point
while (c != None and c in string.digits):
c = self._advance()
ndigits += 1
# no digits so far
if ndigits == 0:
raise ParseException("Formula contains a plain dot.",
self.formula, self.position)
# check for exponent
if c == 'E' or c == 'e':
edigits = 0
# check for sign of exponent
c = self._advance()
if c == '+' or c == '-':
c = self._advance()
# digits after the decimal point
while (c != None and c in string.digits):
c = self._advance()
edigits += 1
if edigits == 0:
raise ParseException(
"Formula contains number with no digist after exponent.",
self.formula, self.position)
numberString = self.formula[spos:self.position]
token = Token.newNumber(float(numberString) * sign)
else:
raise ParseException(
"Formula contains unexpected character [%s]." % c,
self.formula, self.position)
self.stack.append(token)
if (log.isEnabledFor(logging.DEBUG)):
log.debug("_pushToken: stack is now %s" % self.stack)
return True
def _reduceAst(self):
if len(self.stack)<4:
return False
last = self.stack[-1];
last1 = self.stack[-2];
last2 = self.stack[-3];
last3 = self.stack[-4];
if last3.precedence == 0xf and last2.hasAst() and last1.operator == ')':
func = BUILTIN_FUNCTIONS.get(last3.operator)
# take into account sign before brace...
if func != None:
ast2 = last2.getAst()
if last3.operator == "root":
if type(ast2) != tuple or len(ast2) != 2:
raise ParseException("root must have exaclty two positional arguments.",self.formula,self.position);
# root operator
if last3.value < 0.0 :
last2.ast = ast.AstNegation(ast.AstRoot(ast2[1],ast2[0]))
else:
last2.ast = ast.AstRoot(ast2[1],ast2[0])
else:
if type(ast2) == tuple:
raise ParseException("builtin function must not have more than one positional argument.",self.formula,self.position);
# builtin function
if last3.value < 0.0 :
last2.ast = ast.AstNegation(ast.AstFunctionCall(last3.operator,ast2))
else:
last2.ast = ast.AstFunctionCall(last3.operator,ast2)
else:
# open brace with negation
if last3.value < 0.0 :
last2.ast = ast.AstNegation(last2.getAst())
# x( <number> ) yyy -> x( <number> yyy
self.stack.pop(-2)
# x( <number> yyy -> <number> yyy
self.stack.pop(-3)
if (log.isEnabledFor(logging.DEBUG)):
log.debug("_reduceAst(parentheses): stack is now %s"%self.stack)
return True
# <number> <op1> <number> <op2>
if last3.hasAst() and last1.hasAst() :
# <op1> has a lower precedence than pending <op2>, do nothing
if last2.precedence < last.precedence:
return False
# exponentiation is right-associative.
if last.precedence == 3 and last2.precedence == 3:
return False
if last2.operator == ',':
ast3 = last3.getAst()
if type(ast3) == tuple:
last3.ast = ast3 + (last1.getAst(),)
else:
last3.ast = (ast3,last1.getAst())
elif last2.operator == '+' or last2.operator == '-' or last2.operator == '*' or last2.operator == '/'or last2.operator == '^':
last3.ast = ast.AstBinaryOperator(last3.getAst(),last2.operator,last1.getAst());
else:
return False
# <number> <op1> <number> <op2> -> <number> <op2> ->
self.stack.pop(-2)
self.stack.pop(-2)
if (log.isEnabledFor(logging.DEBUG)):
log.debug("_reduceAst(binary): stack is now %s"%self.stack)
return True
return False
def _reduce(self):
if len(self.stack)<4:
return False
last = self.stack[-1];
last1 = self.stack[-2];
last2 = self.stack[-3];
last3 = self.stack[-4];
if last3.precedence == 0xf and last2.isNumber() and last1.operator == ')':
func = BUILTIN_FUNCTIONS.get(last3.operator)
# take into account sign before brace...
if func != None:
# builtin function
if type(last2.value) == tuple:
# multi-arg functions.
last2.value = last3.value * func(*last2.value)
else:
last2.value = last3.value * func(last2.value)
else:
# opening brace
last2.value *= last3.value;
# x( <number> ) yyy -> x( <number> yyy
self.stack.pop(-2)
# x( <number> yyy -> <number> yyy
self.stack.pop(-3)
if (log.isEnabledFor(logging.DEBUG)):
log.debug("_reduce(parentheses): stack is now %s"%self.stack)
return True
# <number> <op1> <number> <op2>
if last3.isNumber() and last1.isNumber() :
# <op1> has a lower precedence than pending <op2>, do nothing
if last2.precedence < last.precedence:
return False
# exponentiation is right-associative.
if last.precedence == 3 and last2.precedence == 3:
return False
if last2.operator == ',':
if type(last3.value) == tuple:
last3.value += (last1.value,)
else:
last3.value = (last3.value,last1.value)
elif last2.operator == '+':
last3.value += last1.value
elif last2.operator == '-':
last3.value -= last1.value
elif last2.operator == '*':
last3.value *= last1.value;
elif last2.operator == '/':
last3.value /= last1.value;
elif last2.operator == '^':
last3.value = math.pow(last3.value,last1.value);
else:
return False
# <number> <op1> <number> <op2> -> <number> <op2> ->
self.stack.pop(-2)
self.stack.pop(-2)
if (log.isEnabledFor(logging.DEBUG)):
log.debug("_reduce(binary): stack is now %s"%self.stack)
return True
return False
def _pushToken(self):
c = self._skipWhite()
if c == None:
self.stack.append(Token.newEOS())
if (log.isEnabledFor(logging.DEBUG)):
log.debug("_pushToken(EOS): stack is now %s"%self.stack)
return False
token = None
sign = 1.0
if c == "(":
token = Token.newOpeningParentheses(sign)
c = self._advance()
elif c == ")":
token = Token.newClosingParentheses()
c = self._advance()
elif c == ",":
token = Token.newOperator(c,0)
c = self._advance()
elif c == "^":
token = Token.newOperator(c,3)
c = self._advance()
elif c == "/" or c == "*":
token = Token.newOperator(c,2)
c = self._advance()
elif c == "+":
token = Token.newOperator(c,1)
c = self._advance()
elif c == "-":
# check, whether this is a sign after an operator or at the start of an expression.
if (len(self.stack) <= 0 or
self.stack[-1].precedence > 0):
c = self._advance()
if c != None:
c = self._skipWhite()
if c == None:
raise ParseException("Unexpected end of formula after minus sign.",self.formula,self.position)
sign = -1.0;
if c=='-':
raise ParseException("Formula contains superfluous minus signs.",self.formula,self.position)
if c=='(':
token = Token.newOpeningParentheses(sign);
c = self._advance()
else:
# binary minus operator.
token = Token.newOperator(c,1)
c = self._advance()
if token == None:
# check for identifier
if c in string.ascii_letters or c in GREEK_LETTERS or c == "_":
spos = self.position
c = self._advance()
# valid variable names are _asdf123 ___3 _asd2_3d
while (c != None and
(c in string.ascii_letters or
c in GREEK_LETTERS or
c == '_' or c in string.digits)):
c = self._advance()
variable = self.formula[spos:self.position]
# FIXME check for builtin function
func = BUILTIN_FUNCTIONS.get(variable)
if func == None:
if self.variables == None:
# AST parsing
token = Token.newVariable(variable,sign)
else:
# classical, immediate evaluation
value = self.variables.get(variable)
if value == None:
raise ParseException("Formula contains unknown variable [%s]."%variable,self.formula,self.position)
token = Token.newNumber(value*sign)
else:
c = self._skipWhite()
if c != "(":
raise ParseException("Formula does not contain an openeing paraentheses after builin function [%s]."%variable,self.formula,self.position)
c = self._advance()
token = Token.newBuiltin(variable,sign)
elif c in string.digits or c == ".":
spos = self.position
ndigits = 0
# number befor the decimal point
while (c != None and
c in string.digits):
c = self._advance()
ndigits += 1
# decimal point present?
if (self.position < len(self.formula) and
c == '.'):
c = self._advance()
# digits after the decimal point
while (c != None and
c in string.digits):
c = self._advance()
ndigits += 1
# no digits so far
if ndigits == 0:
raise ParseException("Formula contains a plain dot.",self.formula,self.position)
# check for exponent
if c == 'E' or c == 'e':
edigits = 0
# check for sign of exponent
c = self._advance()
if c == '+' or c == '-':
c = self._advance()
# digits after the decimal point
while (c != None and
c in string.digits):
c = self._advance()
edigits += 1
if edigits == 0:
raise ParseException("Formula contains number with no digist after exponent.",self.formula,self.position)
numberString = self.formula[spos:self.position]
token = Token.newNumber(float(numberString)*sign)
else:
raise ParseException("Formula contains unexpected character [%s]."%c,self.formula,self.position)
self.stack.append(token)
if (log.isEnabledFor(logging.DEBUG)):
log.debug("_pushToken: stack is now %s"%self.stack)
return True