cpython/Demo/classes/Rat.py

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'''\
This module implements rational numbers.
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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.
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There is also a test function with calling sequence
test()
The documentation string of the test function contains the expected
output.
'''
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# Contributed by Sjoerd Mullender
from types import *
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def gcd(a, b):
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'''Calculate the Greatest Common Divisor.'''
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while b:
a, b = b, a%b
return a
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def rat(num, den = 1):
# must check complex before float
if type(num) is ComplexType or type(den) is ComplexType:
# numerator or denominator is complex: return a complex
return complex(num) / complex(den)
if type(num) is FloatType or type(den) is FloatType:
# numerator or denominator is float: return a float
return float(num) / float(den)
# otherwise return a rational
return Rat(num, den)
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class Rat:
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'''This class implements rational numbers.'''
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def __init__(self, num, den = 1):
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if den == 0:
raise ZeroDivisionError, 'rat(x, 0)'
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# normalize
# must check complex before float
if type(num) is ComplexType or type(den) is ComplexType:
# numerator or denominator is complex:
# normalized form has denominator == 1+0j
self.__num = complex(num) / complex(den)
self.__den = complex(1)
return
if type(num) is FloatType or type(den) is FloatType:
# numerator or denominator is float:
# normalized form has denominator == 1.0
self.__num = float(num) / float(den)
self.__den = 1.0
return
if (type(num) is InstanceType and
num.__class__ is self.__class__) or \
(type(den) is InstanceType and
den.__class__ is self.__class__):
# numerator or denominator is rational
new = num / den
if type(new) is not InstanceType or \
new.__class__ is not self.__class__:
self.__num = new
if type(new) is ComplexType:
self.__den = complex(1)
else:
self.__den = 1.0
else:
self.__num = new.__num
self.__den = new.__den
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else:
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# make sure numerator and denominator don't
# have common factors
# this also makes sure that denominator > 0
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g = gcd(num, den)
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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
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def __repr__(self):
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return 'Rat(%s,%s)' % (self.__num, self.__den)
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def __str__(self):
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if self.__den == 1:
return str(self.__num)
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else:
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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
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# 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 type(a.__num) is ComplexType:
a = complex(a)
else:
a = float(a)
if type(b.__num) is ComplexType:
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)
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def __cmp__(a, b):
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diff = a - b
if diff.__num < 0:
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return -1
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elif diff.__num > 0:
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return 1
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else:
return 0
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def __rcmp__(b, a):
return cmp(Rat(a), b)
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# a != 0
def __nonzero__(a):
return a.__num != 0
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# coercion
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def __coerce__(a, b):
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return a, Rat(b)
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def test():
'''\
Test function for rat module.
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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)
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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)
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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)
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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)
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(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)
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l = [a+b, a-b, a*b, a/b]
print l
l.sort()
print l
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print rat(0, 1)
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print a+1
print a+1L
print a+1.0
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try:
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print rat(1, 0)
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raise SystemError, 'should have been ZeroDivisionError'
except ZeroDivisionError:
print 'OK'
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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 type(i) is not ComplexType:
print int(i), float(i),
print complex(i)
print
for j in list:
print i + j, i - j, i * j, i / j, i ** j, cmp(i, j)
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if __name__ == '__main__':
test()