12.5. Math Precision¶

12.5.1. Minimal and Maximal Values¶

Listing 12.13. Maximal and minimal float values¶

import sys

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

12.5.2. Infinity¶

Listing 12.14. Infinity representation¶

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

1e309                   # inf
-1e309                  # -inf

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

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

12.5.3. Not-a-Number¶

float('nan')
# nan

float('-nan')
# nan

12.5.4. 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

12.5.5. Floating Numbers Precision¶

Solution: Store values as int, do operation and then divide. For example instead of 1.99 USD, store price as 199 US cents
Solution: Use Decimal type

Listing 12.15. Problem¶

0.1 + 0.2
# 0.30000000000000004

0.1 + 0.2 == 0.3
# False

12.5.6. IEEE 754 standard¶

Figure 12.3. What is float as defined by IEEE 754 standard¶

Figure 12.4. Points chart¶

Figure 12.5. How computer store float? As defined by IEEE 754 standard¶

Figure 12.6. How to read/write float from/to memory?¶

Figure 12.7. Normalized Line¶

12.5.7. Floats in Doctest¶

def add_numbers(a, b):
    """
    >>> add_numbers(2.5, 1.2)
    3.7

    >>> add_numbers(0.1, 0.2)
    0.30000000000000004

    >>> add_numbers(0.1, 0.2)   # doctest: +ELLIPSIS
    0.1 + 0.2 == 0.3000...
    """
    return a + b

12.5.8. 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