Integers, Floats, and Math

Tip

python is dynamically-typed, so we don’t need to give the datatype when creating a variable / object. Instead the type is inferred from the object we are assigning a variable to.

Integers

To create an integer in python, we simply assign a variable:

a = 10

Since we didn’t include a decimal point, this is treated as an integer.

We can use the type function to ask python what datatype an object is holding:

type(a)

this returns int.

Integer division works differently in python than in C++:

h = 1/2
print(h, type(h))

This outputs:

0.5 <class 'float'>

As noticed previously, in python the number of bits used to store an integer will grow as needed, preventing overflow.

For example:

a = 123456789012345678901234567890
print(a.bit_length())

shows that this number requires 97-bits.

Note

Here we are seeing that python treats integers as objects of the int class, and .bit_length() is a member-function (or a method, in python naming conventions).

Floating point

Floating-point math works the same in python as in C++. The core operators are +, -, *, and /, just like in C++, and the operator precedence is the same as well.

Just like in C++, when we do an operation involving an integer and a floating point number, the result is a floating point number. E.g.,

1 + 2.0

is a float.

Floating point limits

The python equivalent of the C++ std::numeric_limits is sys.float_info:

import sys
print(sys.float_info)

** operator

Python has a power operator, **, so we can do \(x^{5/2}\) as x**2.5.

math module

The python math module provides much of the same functionality as the C++ standard library does when we include <cmath>.

We first need to import it:

import math

then we can access all its functionality using the . operator (for instance, math.cos()).

We can get the value of \(\pi\) as math.pi:

print(math.pi)

Just like in C++, the trig function expect arguments in radians, so we can find \(\cos(45^\circ)\) as:

angle = 45 * math.pi / 180
c = math.cos(angle)

we can also use math.radians to convert it for us:

c = math.cos(math.radians(45))

help

python has a help function that will provide a description of a function and the arguments that it takes. For instance, we can do:

import math
help(math.cos)

Built-in help is a core-feature of python. This works for any function / module in the python standard library, and for most functions / modules in other libraries that we will used.