108 lines
3.2 KiB
Markdown
108 lines
3.2 KiB
Markdown
---
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title: Python Floating Point Numbers
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---
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Some general information about floating point numbers and how they work in Python, can be found <a href='https://docs.python.org/3/tutorial/floatingpoint.html' target='_blank' rel='nofollow'>here</a>.
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Nearly all implementations of Python follow the IEEE 754 specification: Standard for Binary Floating-Point Arithmetic. More information found on the <a href='http://grouper.ieee.org/groups/754/' target='_blank' rel='nofollow'>IEEE site</a>.
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Float objects can be created using using <a href='https://docs.python.org/3/reference/lexical_analysis.html#floating-point-literals' target='_blank' rel='nofollow'>floating point literals</a>:
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>>> 3.14
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3.14
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>>> 314\. # Trailing zero(s) not required.
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314.0
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>>> .314 # Leading zero(s) not required.
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0.314
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>>> 3e0
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3.0
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>>> 3E0 # 'e' or 'E' can be used.
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3.0
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>>> 3e1 # Positive value after e moves the decimal to the right.
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30.0
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>>> 3e-1 # Negative value after e moves the decimal to the left.
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0.3
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>>> 3.14e+2 # '+' not required but can be used for exponent part.
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314.0
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Numeric literals do not contain a sign, however creating negative float objects is possible by prefixing with a unary `-` (minus) operator with no space before the literal
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>>> -3.141592653589793
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-3.141592653589793
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>>> type(-3.141592653589793)
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<class 'float'>
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Likewise, positive float objects can be prefixed with a unary `+ (`plus) operator with no space before the literal. Usually `+` is omitted:
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>>> +3.141592653589793
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3.141592653589793
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Note that leading and trailing zero(s) are valid for floating point literals
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>>> 0.0
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0.0
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>>> 00.00
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0.0
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>>> 00100.00100
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100.001
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>>> 001e0010 # Same as 1e10
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10000000000.0
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The <a href='https://docs.python.org/3/library/functions.html#float' target='_blank' rel='nofollow'>`float` constructor</a> is another way to create `float` objects.
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Creating `float` objects with floating point literals is preferred when possible:
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>>> a = 3.14 # Prefer floating point literal when possible.
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>>> type(a)
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<class 'float'>
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>>> b = int(3.14) # Works but unnecessary.
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>>> type(b)
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<class 'float'>
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However, the float constructor allows for creating float objects from other number types:
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>>> a = 4
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>>> type(a)
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<class 'int'>
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>>> print(a)
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4
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>>> b = float(4)
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>>> type(b)
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<class 'float'>
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>>> print(b)
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4.0
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>>> float(400000000000000000000000000000000)
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4e+32
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>>> float(.00000000000000000000000000000004)
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4e-32
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>>> float(True)
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1.0
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>>> float(False)
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0.0
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The `float` constructor will also make `float` objects from strings that represent number literals:
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>>> float('1')
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1.0
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>>> float('.1')
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0.1
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>>> float('3.')
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3.0
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>>> float('1e-3')
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0.001
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>>> float('3.14')
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3.14
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>>> float('-.15e-2')
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-0.0015
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The `float` constructor can also be used to make numeric representation of `NaN` (Not a Number), negative `infinity` and `infinity` (note strings for these are case insensitive):
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>>> float('nan')
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nan
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>>> float('inf')
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inf
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>>> float('-inf')
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-inf
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>>> float('infinity')
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inf
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>>> float('-infinity')
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-inf |