Are they natural APIs?

Float and exact matching

Well our intuition of number is the one from math. Computer numbers are not the same. I know this is a trivia, but I see all the time developers ignoring this:

Since computer IEEE754 is only exact an precise for sums of power of 1/2, thus exact matching is made this way:

>>> good_enough=10e-5
>>> wanted = 0.01
>>> .1 * .1
>>> 0.010000000000000002
>>> abs( ( .1*.1 ) - wanted ) < good_enough
True

Okay nice. This is our first example.

Complex or the class 2D Point

So, in stdlib documentation for named tuple we propose writing a useless class: the 2D point.

While in python we a base type that having all the needed feature: the complex type.

Given you call x the real part, and y the imaginary part, then you have a 2D point.

Let’s restate the obvious::

>>> a=complex(1,2)

This is both a point declaration and a vector whose origin is complex(0,0).

Now, let’s shrink the vector by an homothetia a 100 scale::

>>> a=.1*(.1*a)
>>> a
(0.010000000000000002+0.020000000000000004j)
>>> wanted=.01+.02j
>>> tolerable_margin=10e-5
>>> abs(wanted-a)<tolerable_margin
True

It works!

By the way, what is abs?

Norm of a vector

What does abs in python?:

Return the absolute value of a number. The argument may be a plain or long integer or a floating point number. If the argument is a complex number, its magnitude is returned.

Well it is basically the distance from the origin 0.

So basically the preivous python code is

is the distance between a and wanted comprised in a 10e-5 radius.

And what does a - wanted means?

So with the datetime example we now understand minus (__sub__) is in fact an addition of the reversed value of wanted to a.

wanted and a are de facto vectors. Thus, addition is put simply a translation.

What is a multiplication?

A multiplication is an homothetia from a vector.

Summarizing up

For the following types:

• complex;
• floats;
• datetime we have a natural API.

That is based on:

• by combining two vectors, we always a vector;
• interval are vectors;
• abs transforms a vector into a scalar called norm or distance.

Thus ::

>>> abs( a-b ) < margin
## is the same as
>>> a == b ± margin

And since computer makes mistakes in some cases (by rounding) it is therefore the closest answer we have to the mathematical truth called equality.

Next question is does it works for everything?