The decimal module implements fixed and floating point arithmetic using the model familiar to most people, rather than the IEEE floating point version implemented by most computer hardware and familiar to programmers. A Decimal instance can represent any number exactly, round up or down, and apply a limit to the number of significant digits.

Decimal



In [2]:

    
import decimal
fmt = '{0:<25}{1:<25}'
print(fmt.format('Input', 'Output'))
print(fmt.format('-'*25, '-'*25))
#Integer
print(fmt.format(5, decimal.Decimal(5)))
#String
print(fmt.format('3.14', decimal.Decimal('3.14')))
#Float
f = 0.1
print(fmt.format(repr(f), decimal.Decimal(str(f))))
print('{:0.23g}{:<25}'.format(f, str(decimal.Decimal.from_float(f))[:25]))









    



Input                    Output                   
--------------------------------------------------
5                        5                        
3.14                     3.14                     
0.1                      0.1                      
0.100000000000000005551120.10000000000000000555111

Decimals can also be created from tuples containing a sign flag



In [3]:

    
import decimal

# Tuple
t = (1, (1, 1), -2)
print('Input  :', t)
print('Decimal:', decimal.Decimal(t))









    



Input  : (1, (1, 1), -2)
Decimal: -0.11

Formatting



In [4]:

    
import decimal

d = decimal.Decimal(1.1)
print('Precision:')
print('{:.1}'.format(d))
print('{:.2}'.format(d))
print('{:.3}'.format(d))
print('{:.18}'.format(d))

print('\nWidth and precision combined:')
print('{:5.1f} {:5.1g}'.format(d, d))
print('{:5.2f} {:5.2g}'.format(d, d))
print('{:5.2f} {:5.2g}'.format(d, d))

print('\nZero padding:')
print('{:05.1}'.format(d))
print('{:05.2}'.format(d))
print('{:05.3}'.format(d))









    



Precision:
1
1.1
1.10
1.10000000000000009

Width and precision combined:
  1.1     1
 1.10   1.1
 1.10   1.1

Zero padding:
00001
001.1
01.10

Arithmetic



In [5]:

    
import decimal

a = decimal.Decimal('5.1')
b = decimal.Decimal('3.14')
c = 4
d = 3.14

print('a     =', repr(a))
print('b     =', repr(b))
print('c     =', repr(c))
print('d     =', repr(d))
print()

print('a + b =', a + b)
print('a - b =', a - b)
print('a * b =', a * b)
print('a / b =', a / b)
print()

print('a + c =', a + c)
print('a - c =', a - c)
print('a * c =', a * c)
print('a / c =', a / c)
print()

print('a + d =', end=' ')
try:
    print(a + d)
except TypeError as e:
    print(e)









    



a     = Decimal('5.1')
b     = Decimal('3.14')
c     = 4
d     = 3.14

a + b = 8.24
a - b = 1.96
a * b = 16.014
a / b = 1.624203821656050955414012739

a + c = 9.1
a - c = 1.1
a * c = 20.4
a / c = 1.275

a + d = unsupported operand type(s) for +: 'decimal.Decimal' and 'float'

Special Value



In [6]:

    
import decimal

for value in ['Infinity', 'NaN', '0']:
    print(decimal.Decimal(value), decimal.Decimal('-' + value))
print()

# Math with infinity
print('Infinity + 1:', (decimal.Decimal('Infinity') + 1))
print('-Infinity + 1:', (decimal.Decimal('-Infinity') + 1))

# Print comparing NaN
print(decimal.Decimal('NaN') == decimal.Decimal('Infinity'))
print(decimal.Decimal('NaN') != decimal.Decimal(1))









    



Infinity -Infinity
NaN -NaN
0 -0

Infinity + 1: Infinity
-Infinity + 1: -Infinity
False
True

Context



In [7]:

    
import decimal

context = decimal.getcontext()

print('Emax     =', context.Emax)
print('Emin     =', context.Emin)
print('capitals =', context.capitals)
print('prec     =', context.prec)
print('rounding =', context.rounding)
print('flags    =')
for f, v in context.flags.items():
    print('  {}: {}'.format(f, v))
print('traps    =')
for t, v in context.traps.items():
    print('  {}: {}'.format(t, v))









    



Emax     = 999999
Emin     = -999999
capitals = 1
prec     = 28
rounding = ROUND_HALF_EVEN
flags    =
  <class 'decimal.InvalidOperation'>: False
  <class 'decimal.FloatOperation'>: True
  <class 'decimal.DivisionByZero'>: False
  <class 'decimal.Overflow'>: False
  <class 'decimal.Underflow'>: False
  <class 'decimal.Subnormal'>: False
  <class 'decimal.Inexact'>: True
  <class 'decimal.Rounded'>: True
  <class 'decimal.Clamped'>: False
traps    =
  <class 'decimal.InvalidOperation'>: True
  <class 'decimal.FloatOperation'>: False
  <class 'decimal.DivisionByZero'>: True
  <class 'decimal.Overflow'>: True
  <class 'decimal.Underflow'>: False
  <class 'decimal.Subnormal'>: False
  <class 'decimal.Inexact'>: False
  <class 'decimal.Rounded'>: False
  <class 'decimal.Clamped'>: False

Precision



In [8]:

    
import decimal

d = decimal.Decimal('0.123456')

for i in range(1, 5):
    decimal.getcontext().prec = i
    print(i, ':', d, d * 1)









    



1 : 0.123456 0.1
2 : 0.123456 0.12
3 : 0.123456 0.123
4 : 0.123456 0.1235

Local Context



In [9]:

    
import decimal

with decimal.localcontext() as c:
    c.prec = 2
    print('Local precision:', c.prec)
    print('3.14 / 3 =', (decimal.Decimal('3.14') / 3))

print()
print('Default precision:', decimal.getcontext().prec)
print('3.14 / 3 =', (decimal.Decimal('3.14') / 3))









    



Local precision: 2
3.14 / 3 = 1.0

Default precision: 4
3.14 / 3 = 1.047



In [10]:

    
import decimal

# Set up a context with limited precision
c = decimal.getcontext().copy()
c.prec = 3

# Create our constant
pi = c.create_decimal('3.1415')

# The constant value is rounded off
print('PI    :', pi)

# The result of using the constant uses the global context
print('RESULT:', decimal.Decimal('2.01') * pi)









    



PI    : 3.14
RESULT: 6.311



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