16.5. Math Precision¶

16.5.1. 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

16.5.2. 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

16.5.3. Not-a-Number¶

float('nan')
# nan

float('-nan')
# nan

16.5.4. 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

16.5.5. 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

16.5.6. IEEE 754 standard¶

../../_images/float-anatomy.png — Figure 16.3. What is `float` as defined by IEEE 754 standard¶

../../_images/float-expression.png — Figure 16.4. Points chart¶

../../_images/float-mantissa-1.png — Figure 16.5. How computer store `float`? As defined by IEEE 754 standard¶

../../_images/float-mantissa-2.png — Figure 16.6. How to read/write `float` from/to memory?¶

../../_images/float-normalized.png — Figure 16.7. Normalized Line¶

16.5.7. 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

16.5.8. 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