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# fourFn.py
#
# Demonstration of the pyparsing module, implementing a simple 4-function expression parser,
# with support for scientific notation, and symbols for e and pi.
# Extended to add exponentiation and simple built-in functions.
# Extended test cases, simplified pushFirst method.
# Removed unnecessary expr.suppress() call (thanks Nathaniel Peterson!), and added Group
# Changed fnumber to use a Regex, which is now the preferred method
#
# Copyright 2003-2009 by Paul McGuire
#
from pyparsing import Literal,CaselessLiteral,Word,Group,Optional,\
ZeroOrMore,Forward,nums,alphas,alphanums,Regex,ParseException,\
CaselessKeyword, Suppress
import math
import operator
exprStack = []
def pushFirst( strg, loc, toks ):
exprStack.append( toks[0] )
def pushUMinus( strg, loc, toks ):
for t in toks:
if t == '-':
exprStack.append( 'unary -' )
#~ exprStack.append( '-1' )
#~ exprStack.append( '*' )
else:
break
bnf = None
def BNF():
"""
expop :: '^'
multop :: '*' | '/'
addop :: '+' | '-'
integer :: ['+' | '-'] '0'..'9'+
atom :: PI | E | real | fn '(' expr ')' | '(' expr ')'
factor :: atom [ expop factor ]*
term :: factor [ multop factor ]*
expr :: term [ addop term ]*
"""
global bnf
if not bnf:
point = Literal( "." )
# use CaselessKeyword for e and pi, to avoid accidentally matching
# functions that start with 'e' or 'pi' (such as 'exp'); Keyword
# and CaselessKeyword only match whole words
e = CaselessKeyword( "E" )
pi = CaselessKeyword( "PI" )
#~ fnumber = Combine( Word( "+-"+nums, nums ) +
#~ Optional( point + Optional( Word( nums ) ) ) +
#~ Optional( e + Word( "+-"+nums, nums ) ) )
fnumber = Regex(r"[+-]?\d+(?:\.\d*)?(?:[eE][+-]?\d+)?")
ident = Word(alphas, alphanums+"_$")
plus, minus, mult, div = map(Literal, "+-*/")
lpar, rpar = map(Suppress, "()")
addop = plus | minus
multop = mult | div
expop = Literal( "^" )
expr = Forward()
atom = ((0,None)*minus + ( pi | e | fnumber | ident + lpar + expr + rpar | ident ).setParseAction( pushFirst ) |
Group( lpar + expr + rpar )).setParseAction(pushUMinus)
# by defining exponentiation as "atom [ ^ factor ]..." instead of "atom [ ^ atom ]...", we get right-to-left exponents, instead of left-to-righ
# that is, 2^3^2 = 2^(3^2), not (2^3)^2.
factor = Forward()
factor << atom + ZeroOrMore( ( expop + factor ).setParseAction( pushFirst ) )
term = factor + ZeroOrMore( ( multop + factor ).setParseAction( pushFirst ) )
expr << term + ZeroOrMore( ( addop + term ).setParseAction( pushFirst ) )
bnf = expr
return bnf
# map operator symbols to corresponding arithmetic operations
epsilon = 1e-12
opn = { "+" : operator.add,
"-" : operator.sub,
"*" : operator.mul,
"/" : operator.truediv,
"^" : operator.pow }
fn = { "sin" : math.sin,
"cos" : math.cos,
"tan" : math.tan,
"exp" : math.exp,
"abs" : abs,
"trunc" : lambda a: int(a),
"round" : round,
"sgn" : lambda a: (a > epsilon) - (a < -epsilon) }
def evaluateStack( s ):
op = s.pop()
if op == 'unary -':
return -evaluateStack( s )
if op in "+-*/^":
op2 = evaluateStack( s )
op1 = evaluateStack( s )
return opn[op]( op1, op2 )
elif op == "PI":
return math.pi # 3.1415926535
elif op == "E":
return math.e # 2.718281828
elif op in fn:
return fn[op]( evaluateStack( s ) )
elif op[0].isalpha():
raise Exception("invalid identifier '%s'" % op)
else:
return float( op )
if __name__ == "__main__":
def test( s, expVal ):
global exprStack
exprStack[:] = []
try:
results = BNF().parseString( s, parseAll=True )
val = evaluateStack( exprStack[:] )
except ParseException as e:
print(s, "failed parse:", str(pe))
except Exception as e:
print(s, "failed eval:", str(e))
else:
if val == expVal:
print(s, "=", val, results, "=>", exprStack)
else:
print(s+"!!!", val, "!=", expVal, results, "=>", exprStack)
test( "9", 9 )
test( "-9", -9 )
test( "--9", 9 )
test( "-E", -math.e )
test( "9 + 3 + 6", 9 + 3 + 6 )
test( "9 + 3 / 11", 9 + 3.0 / 11 )
test( "(9 + 3)", (9 + 3) )
test( "(9+3) / 11", (9+3.0) / 11 )
test( "9 - 12 - 6", 9 - 12 - 6 )
test( "9 - (12 - 6)", 9 - (12 - 6) )
test( "2*3.14159", 2*3.14159 )
test( "3.1415926535*3.1415926535 / 10", 3.1415926535*3.1415926535 / 10 )
test( "PI * PI / 10", math.pi * math.pi / 10 )
test( "PI*PI/10", math.pi*math.pi/10 )
test( "PI^2", math.pi**2 )
test( "round(PI^2)", round(math.pi**2) )
test( "6.02E23 * 8.048", 6.02E23 * 8.048 )
test( "e / 3", math.e / 3 )
test( "sin(PI/2)", math.sin(math.pi/2) )
test( "trunc(E)", int(math.e) )
test( "trunc(-E)", int(-math.e) )
test( "round(E)", round(math.e) )
test( "round(-E)", round(-math.e) )
test( "E^PI", math.e**math.pi )
test( "exp(0)", 1 )
test( "exp(1)", math.e )
test( "2^3^2", 2**3**2 )
test( "2^3+2", 2**3+2 )
test( "2^3+5", 2**3+5 )
test( "2^9", 2**9 )
test( "sgn(-2)", -1 )
test( "sgn(0)", 0 )
test( "foo(0.1)", None )
test( "sgn(0.1)", 1 )
"""
Test output:
>pythonw -u fourFn.py
9 = 9.0 ['9'] => ['9']
9 + 3 + 6 = 18.0 ['9', '+', '3', '+', '6'] => ['9', '3', '+', '6', '+']
9 + 3 / 11 = 9.27272727273 ['9', '+', '3', '/', '11'] => ['9', '3', '11', '/', '+']
(9 + 3) = 12.0 [] => ['9', '3', '+']
(9+3) / 11 = 1.09090909091 ['/', '11'] => ['9', '3', '+', '11', '/']
9 - 12 - 6 = -9.0 ['9', '-', '12', '-', '6'] => ['9', '12', '-', '6', '-']
9 - (12 - 6) = 3.0 ['9', '-'] => ['9', '12', '6', '-', '-']
2*3.14159 = 6.28318 ['2', '*', '3.14159'] => ['2', '3.14159', '*']
3.1415926535*3.1415926535 / 10 = 0.986960440053 ['3.1415926535', '*', '3.1415926535', '/', '10'] => ['3.1415926535', '3.1415926535', '*', '10', '/']
PI * PI / 10 = 0.986960440109 ['PI', '*', 'PI', '/', '10'] => ['PI', 'PI', '*', '10', '/']
PI*PI/10 = 0.986960440109 ['PI', '*', 'PI', '/', '10'] => ['PI', 'PI', '*', '10', '/']
PI^2 = 9.86960440109 ['PI', '^', '2'] => ['PI', '2', '^']
6.02E23 * 8.048 = 4.844896e+024 ['6.02E23', '*', '8.048'] => ['6.02E23', '8.048', '*']
e / 3 = 0.90609394282 ['E', '/', '3'] => ['E', '3', '/']
sin(PI/2) = 1.0 ['sin', 'PI', '/', '2'] => ['PI', '2', '/', 'sin']
trunc(E) = 2 ['trunc', 'E'] => ['E', 'trunc']
E^PI = 23.1406926328 ['E', '^', 'PI'] => ['E', 'PI', '^']
2^3^2 = 512.0 ['2', '^', '3', '^', '2'] => ['2', '3', '2', '^', '^']
2^3+2 = 10.0 ['2', '^', '3', '+', '2'] => ['2', '3', '^', '2', '+']
2^9 = 512.0 ['2', '^', '9'] => ['2', '9', '^']
sgn(-2) = -1 ['sgn', '-2'] => ['-2', 'sgn']
sgn(0) = 0 ['sgn', '0'] => ['0', 'sgn']
sgn(0.1) = 1 ['sgn', '0.1'] => ['0.1', 'sgn']
>Exit code: 0
"""