12.5. Math Precision¶

12.5.1. 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

12.5.2. 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

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¶

0.1
# 0.1

0.2
# 0.2

0.3
# 0.3

0.1 + 0.2 == 0.3
# False

0.1 + 0.2
# 0.30000000000000004

0.1 + 0.1
# 0.2

0.1 + 0.1 + 0.1
# 0.30000000000000004

round(0.1+0.2, 16)
# 0.3

round(0.1+0.2, 17)
# 0.30000000000000004

round(0.1+0.2, 16)
# True

round(0.1+0.2, 17) == 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(a, b):
    """
    >>> add(1.0, 2.0)
    3.0

    >>> add(0.1, 0.2)
    0.30000000000000004

    >>> add(0.1, 0.2)   # doctest: +ELLIPSIS
    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