mirror of https://github.com/python/cpython
311 lines
8.6 KiB
Python
Executable File
311 lines
8.6 KiB
Python
Executable File
'''\
|
|
This module implements rational numbers.
|
|
|
|
The entry point of this module is the function
|
|
rat(numerator, denominator)
|
|
If either numerator or denominator is of an integral or rational type,
|
|
the result is a rational number, else, the result is the simplest of
|
|
the types float and complex which can hold numerator/denominator.
|
|
If denominator is omitted, it defaults to 1.
|
|
Rational numbers can be used in calculations with any other numeric
|
|
type. The result of the calculation will be rational if possible.
|
|
|
|
There is also a test function with calling sequence
|
|
test()
|
|
The documentation string of the test function contains the expected
|
|
output.
|
|
'''
|
|
|
|
# Contributed by Sjoerd Mullender
|
|
|
|
from types import *
|
|
|
|
def gcd(a, b):
|
|
'''Calculate the Greatest Common Divisor.'''
|
|
while b:
|
|
a, b = b, a%b
|
|
return a
|
|
|
|
def rat(num, den = 1):
|
|
# must check complex before float
|
|
if isinstance(num, complex) or isinstance(den, complex):
|
|
# numerator or denominator is complex: return a complex
|
|
return complex(num) / complex(den)
|
|
if isinstance(num, float) or isinstance(den, float):
|
|
# numerator or denominator is float: return a float
|
|
return float(num) / float(den)
|
|
# otherwise return a rational
|
|
return Rat(num, den)
|
|
|
|
class Rat:
|
|
'''This class implements rational numbers.'''
|
|
|
|
def __init__(self, num, den = 1):
|
|
if den == 0:
|
|
raise ZeroDivisionError, 'rat(x, 0)'
|
|
|
|
# normalize
|
|
|
|
# must check complex before float
|
|
if (isinstance(num, complex) or
|
|
isinstance(den, complex)):
|
|
# numerator or denominator is complex:
|
|
# normalized form has denominator == 1+0j
|
|
self.__num = complex(num) / complex(den)
|
|
self.__den = complex(1)
|
|
return
|
|
if isinstance(num, float) or isinstance(den, float):
|
|
# numerator or denominator is float:
|
|
# normalized form has denominator == 1.0
|
|
self.__num = float(num) / float(den)
|
|
self.__den = 1.0
|
|
return
|
|
if (isinstance(num, self.__class__) or
|
|
isinstance(den, self.__class__)):
|
|
# numerator or denominator is rational
|
|
new = num / den
|
|
if not isinstance(new, self.__class__):
|
|
self.__num = new
|
|
if isinstance(new, complex):
|
|
self.__den = complex(1)
|
|
else:
|
|
self.__den = 1.0
|
|
else:
|
|
self.__num = new.__num
|
|
self.__den = new.__den
|
|
else:
|
|
# make sure numerator and denominator don't
|
|
# have common factors
|
|
# this also makes sure that denominator > 0
|
|
g = gcd(num, den)
|
|
self.__num = num / g
|
|
self.__den = den / g
|
|
# try making numerator and denominator of IntType if they fit
|
|
try:
|
|
numi = int(self.__num)
|
|
deni = int(self.__den)
|
|
except (OverflowError, TypeError):
|
|
pass
|
|
else:
|
|
if self.__num == numi and self.__den == deni:
|
|
self.__num = numi
|
|
self.__den = deni
|
|
|
|
def __repr__(self):
|
|
return 'Rat(%s,%s)' % (self.__num, self.__den)
|
|
|
|
def __str__(self):
|
|
if self.__den == 1:
|
|
return str(self.__num)
|
|
else:
|
|
return '(%s/%s)' % (str(self.__num), str(self.__den))
|
|
|
|
# a + b
|
|
def __add__(a, b):
|
|
try:
|
|
return rat(a.__num * b.__den + b.__num * a.__den,
|
|
a.__den * b.__den)
|
|
except OverflowError:
|
|
return rat(long(a.__num) * long(b.__den) +
|
|
long(b.__num) * long(a.__den),
|
|
long(a.__den) * long(b.__den))
|
|
|
|
def __radd__(b, a):
|
|
return Rat(a) + b
|
|
|
|
# a - b
|
|
def __sub__(a, b):
|
|
try:
|
|
return rat(a.__num * b.__den - b.__num * a.__den,
|
|
a.__den * b.__den)
|
|
except OverflowError:
|
|
return rat(long(a.__num) * long(b.__den) -
|
|
long(b.__num) * long(a.__den),
|
|
long(a.__den) * long(b.__den))
|
|
|
|
def __rsub__(b, a):
|
|
return Rat(a) - b
|
|
|
|
# a * b
|
|
def __mul__(a, b):
|
|
try:
|
|
return rat(a.__num * b.__num, a.__den * b.__den)
|
|
except OverflowError:
|
|
return rat(long(a.__num) * long(b.__num),
|
|
long(a.__den) * long(b.__den))
|
|
|
|
def __rmul__(b, a):
|
|
return Rat(a) * b
|
|
|
|
# a / b
|
|
def __div__(a, b):
|
|
try:
|
|
return rat(a.__num * b.__den, a.__den * b.__num)
|
|
except OverflowError:
|
|
return rat(long(a.__num) * long(b.__den),
|
|
long(a.__den) * long(b.__num))
|
|
|
|
def __rdiv__(b, a):
|
|
return Rat(a) / b
|
|
|
|
# a % b
|
|
def __mod__(a, b):
|
|
div = a / b
|
|
try:
|
|
div = int(div)
|
|
except OverflowError:
|
|
div = long(div)
|
|
return a - b * div
|
|
|
|
def __rmod__(b, a):
|
|
return Rat(a) % b
|
|
|
|
# a ** b
|
|
def __pow__(a, b):
|
|
if b.__den != 1:
|
|
if isinstance(a.__num, complex):
|
|
a = complex(a)
|
|
else:
|
|
a = float(a)
|
|
if isinstance(b.__num, complex):
|
|
b = complex(b)
|
|
else:
|
|
b = float(b)
|
|
return a ** b
|
|
try:
|
|
return rat(a.__num ** b.__num, a.__den ** b.__num)
|
|
except OverflowError:
|
|
return rat(long(a.__num) ** b.__num,
|
|
long(a.__den) ** b.__num)
|
|
|
|
def __rpow__(b, a):
|
|
return Rat(a) ** b
|
|
|
|
# -a
|
|
def __neg__(a):
|
|
try:
|
|
return rat(-a.__num, a.__den)
|
|
except OverflowError:
|
|
# a.__num == sys.maxint
|
|
return rat(-long(a.__num), a.__den)
|
|
|
|
# abs(a)
|
|
def __abs__(a):
|
|
return rat(abs(a.__num), a.__den)
|
|
|
|
# int(a)
|
|
def __int__(a):
|
|
return int(a.__num / a.__den)
|
|
|
|
# long(a)
|
|
def __long__(a):
|
|
return long(a.__num) / long(a.__den)
|
|
|
|
# float(a)
|
|
def __float__(a):
|
|
return float(a.__num) / float(a.__den)
|
|
|
|
# complex(a)
|
|
def __complex__(a):
|
|
return complex(a.__num) / complex(a.__den)
|
|
|
|
# cmp(a,b)
|
|
def __cmp__(a, b):
|
|
diff = Rat(a - b)
|
|
if diff.__num < 0:
|
|
return -1
|
|
elif diff.__num > 0:
|
|
return 1
|
|
else:
|
|
return 0
|
|
|
|
def __rcmp__(b, a):
|
|
return cmp(Rat(a), b)
|
|
|
|
# a != 0
|
|
def __bool__(a):
|
|
return a.__num != 0
|
|
|
|
# coercion
|
|
def __coerce__(a, b):
|
|
return a, Rat(b)
|
|
|
|
def test():
|
|
'''\
|
|
Test function for rat module.
|
|
|
|
The expected output is (module some differences in floating
|
|
precission):
|
|
-1
|
|
-1
|
|
0 0L 0.1 (0.1+0j)
|
|
[Rat(1,2), Rat(-3,10), Rat(1,25), Rat(1,4)]
|
|
[Rat(-3,10), Rat(1,25), Rat(1,4), Rat(1,2)]
|
|
0
|
|
(11/10)
|
|
(11/10)
|
|
1.1
|
|
OK
|
|
2 1.5 (3/2) (1.5+1.5j) (15707963/5000000)
|
|
2 2 2.0 (2+0j)
|
|
|
|
4 0 4 1 4 0
|
|
3.5 0.5 3.0 1.33333333333 2.82842712475 1
|
|
(7/2) (1/2) 3 (4/3) 2.82842712475 1
|
|
(3.5+1.5j) (0.5-1.5j) (3+3j) (0.666666666667-0.666666666667j) (1.43248815986+2.43884761145j) 1
|
|
1.5 1 1.5 (1.5+0j)
|
|
|
|
3.5 -0.5 3.0 0.75 2.25 -1
|
|
3.0 0.0 2.25 1.0 1.83711730709 0
|
|
3.0 0.0 2.25 1.0 1.83711730709 1
|
|
(3+1.5j) -1.5j (2.25+2.25j) (0.5-0.5j) (1.50768393746+1.04970907623j) -1
|
|
(3/2) 1 1.5 (1.5+0j)
|
|
|
|
(7/2) (-1/2) 3 (3/4) (9/4) -1
|
|
3.0 0.0 2.25 1.0 1.83711730709 -1
|
|
3 0 (9/4) 1 1.83711730709 0
|
|
(3+1.5j) -1.5j (2.25+2.25j) (0.5-0.5j) (1.50768393746+1.04970907623j) -1
|
|
(1.5+1.5j) (1.5+1.5j)
|
|
|
|
(3.5+1.5j) (-0.5+1.5j) (3+3j) (0.75+0.75j) 4.5j -1
|
|
(3+1.5j) 1.5j (2.25+2.25j) (1+1j) (1.18235814075+2.85446505899j) 1
|
|
(3+1.5j) 1.5j (2.25+2.25j) (1+1j) (1.18235814075+2.85446505899j) 1
|
|
(3+3j) 0j 4.5j (1+0j) (-0.638110484918+0.705394566962j) 0
|
|
'''
|
|
print rat(-1L, 1)
|
|
print rat(1, -1)
|
|
a = rat(1, 10)
|
|
print int(a), long(a), float(a), complex(a)
|
|
b = rat(2, 5)
|
|
l = [a+b, a-b, a*b, a/b]
|
|
print l
|
|
l.sort()
|
|
print l
|
|
print rat(0, 1)
|
|
print a+1
|
|
print a+1L
|
|
print a+1.0
|
|
try:
|
|
print rat(1, 0)
|
|
raise SystemError, 'should have been ZeroDivisionError'
|
|
except ZeroDivisionError:
|
|
print 'OK'
|
|
print rat(2), rat(1.5), rat(3, 2), rat(1.5+1.5j), rat(31415926,10000000)
|
|
list = [2, 1.5, rat(3,2), 1.5+1.5j]
|
|
for i in list:
|
|
print i,
|
|
if not isinstance(i, complex):
|
|
print int(i), float(i),
|
|
print complex(i)
|
|
print
|
|
for j in list:
|
|
print i + j, i - j, i * j, i / j, i ** j,
|
|
if not (isinstance(i, complex) or
|
|
isinstance(j, complex)):
|
|
print cmp(i, j)
|
|
print
|
|
|
|
|
|
if __name__ == '__main__':
|
|
test()
|