15.2. Math Precision

15.2.1. Minimal and Maximal Values

Maximal and minimal float values:

import sys

sys.float_info.min      # 2.2250738585072014e-308
sys.float_info.max      # 1.7976931348623157e+308

15.2.2. Infinity

Infinity representation:

1e308                   # 1e+308
-1e308                  # -1e+308

1e309                   # inf
-1e309                  # -inf

float('inf')            # inf
float('-inf')           # -inf

float('Infinity')       # inf
float('-Infinity')      # -inf

15.2.3. Not-a-Number

float('nan')
# nan

float('-nan')
# nan

15.2.4. NaN vs Inf

float('inf') + float('inf')     # inf
float('inf') + float('-inf')    # nan
float('-inf') + float('inf')    # nan
float('-inf') + float('-inf')   # -inf

float('inf') - float('inf')     # nan
float('inf') - float('-inf')    # inf
float('-inf') - float('inf')    # -inf
float('-inf') - float('-inf')   # nan

float('inf') * float('inf')     # inf
float('inf') * float('-inf')    # -inf
float('-inf') * float('inf')    # -inf
float('-inf') * float('-inf')   # inf

float('inf') / float('inf')     # nan
float('inf') / float('-inf')    # nan
float('-inf') / float('inf')    # nan
float('-inf') / float('-inf')   # nan

15.2.5. Floating Numbers Precision

>>> 0.1
0.1
>>>
>>> 0.2
0.2
>>>
>>> 0.3
0.3
>>>
>>> 0.1 + 0.2 == 0.3
False

>>> round(0.1+0.2, 16) == 0.3
True
>>>
>>> round(0.1+0.2, 17) == 0.3
False

>>> 0.1 + 0.2
0.30000000000000004

15.2.6. IEEE 754 standard

>>> a = 1.234
>>> b = 1234 * 10e-4
>>>
>>> a == b
True

>>> 1234 * 10e-4
1.234

>>> 1.234 == 1234 * 10e-4
True

Figure 15.2. What is float as defined by IEEE 754 standard

Figure 15.3. Points chart

Figure 15.4. How computer store float? As defined by IEEE 754 standard

Figure 15.5. How to read/write float from/to memory?

Figure 15.6. Normalized Line

15.2.7. Floats in Doctest

>>> def add(a, b):
...     """
...     >>> add(1.0, 2.0)
...     3.0
...
...     >>> add(0.1, 0.2)
...     0.30000000000000004
...
...     >>> add(0.1, 0.2)   
...     0.3000...
...     """
...     return a + b

15.2.8. Decimal Type

from decimal import Decimal


a = Decimal('0.1')
b = Decimal('0.2')

a + b
# Decimal('0.3')

from decimal import Decimal


a = Decimal('0.3')

float(a)
# 0.3

15.2.9. Solutions

• Round values to 4 decimal places (generally acceptable)

• Store values as int, do operation and then divide. For example instead of 1.99 USD, store price as 199 US cents

• Use Decimal type

• Decimal type is much slower

Problem:

>>> candy = 0.10      # price in dollars
>>> cookie = 0.20     # price in dollars
>>>
>>> result = candy + cookie
>>> print(result)
0.30000000000000004

Round values to 4 decimal places (generally acceptable):

>>> candy = 0.10      # price in dollars
>>> cookie = 0.20     # price in dollars
>>>
>>> result = round(candy + cookie, 4)
>>> print(result)
0.3

Store values as int, do operation and then divide:

>>> CENT = 1
>>> DOLLAR = 100 * CENT
>>>
>>> candy = 10*CENT
>>> cookie = 20*CENT
>>>
>>> result = (candy + cookie) / DOLLAR
>>> print(result)
0.3

Use Decimal type:

>>> from decimal import Decimal
>>>
>>>
>>> candy = Decimal('0.10')     # price in dollars
>>> cookie = Decimal('0.20')    # price in dollars
>>>
>>> result = candy + cookie
>>> print(result)
0.30