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Oct 13, 2020
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Improve recipe readability #22685

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294a18c
Move the conceptual equivalent to the end
rhettinger Oct 13, 2020
b770747
Separate the see also sections. Other minor edits.
rhettinger Oct 13, 2020
136e7bb
Tighten-up the final paragraph wording
rhettinger Oct 13, 2020
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Tweak wording of the final paragraph.
rhettinger Oct 13, 2020
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68 changes: 37 additions & 31 deletions Doc/library/random.rst
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Original file line number Diff line number Diff line change
Expand Up @@ -253,6 +253,8 @@ Functions for sequences
order so that the sample is reproducible.


.. _real-valued-distributions:

Real-valued distributions
-------------------------

Expand Down Expand Up @@ -516,26 +518,42 @@ Simulation of arrival times and service deliveries for a multiserver queue::
print(f'Mean wait: {mean(waits):.1f} Max wait: {max(waits):.1f}')
print('Quartiles:', [round(q, 1) for q in quantiles(waits)])

.. seealso::

`Statistics for Hackers <https://www.youtube.com/watch?v=Iq9DzN6mvYA>`_
a video tutorial by
`Jake Vanderplas <https://us.pycon.org/2016/speaker/profile/295/>`_
on statistical analysis using just a few fundamental concepts
including simulation, sampling, shuffling, and cross-validation.

`Economics Simulation
<http://nbviewer.jupyter.org/url/norvig.com/ipython/Economics.ipynb>`_
a simulation of a marketplace by
`Peter Norvig <http://norvig.com/bio.html>`_ that shows effective
use of many of the tools and distributions provided by this module
(gauss, uniform, sample, betavariate, choice, triangular, and randrange).

`A Concrete Introduction to Probability (using Python)
<http://nbviewer.jupyter.org/url/norvig.com/ipython/Probability.ipynb>`_
a tutorial by `Peter Norvig <http://norvig.com/bio.html>`_ covering
the basics of probability theory, how to write simulations, and
how to perform data analysis using Python.


Recipes
-------

The default :func:`.random` returns multiples of 2⁻⁵³ in the range
*0.0 ≤ x < 1.0*. All such numbers are evenly spaced and exactly
*0.0 ≤ x < 1.0*. All such numbers are evenly spaced and are exactly
representable as Python floats. However, many floats in that interval
are not possible selections. For example, ``0.05954861408025609``
isn't an integer multiple of 2⁻⁵³.

The following recipe takes a different approach. All floats in the
interval are possible selections. Conceptually it works by choosing
from evenly spaced multiples of 2⁻¹⁰⁷⁴ and then rounding down to the
nearest representable float.

For efficiency, the actual mechanics involve calling
:func:`~math.ldexp` to construct a representable float. The mantissa
comes from a uniform distribution of integers in the range *2⁵² ≤
mantissa < 2⁵³*. The exponent comes from a geometric distribution
where exponents smaller than *-53* occur half as often as the next
larger exponent.
interval are possible selections. The mantissa comes from a uniform
distribution of integers in the range *2⁵² ≤ mantissa < 2⁵³*. The
exponent comes from a geometric distribution where exponents smaller
than *-53* occur half as often as the next larger exponent.

::

Expand All @@ -553,35 +571,23 @@ larger exponent.
exponent += x.bit_length() - 32
return ldexp(mantissa, exponent)

All of the real valued distributions will use the new method::
All :ref:`real valued distributions <real-valued-distributions>`
in the class will use the new method::

>>> fr = FullRandom()
>>> fr.random()
0.05954861408025609
>>> fr.expovariate(0.25)
8.87925541791544

The recipe is conceptually equivalent to an algorithm that chooses from
all the multiples of 2⁻¹⁰⁷⁴ in the range *0.0 ≤ x < 1.0*. All such
numbers are evenly spaced, but most have to be rounded down to the
nearest representable Python float. (The value 2⁻¹⁰⁷⁴ is the smallest
positive unnormalized float and is equal to ``math.ulp(0.0)``.)

.. seealso::

`Statistics for Hackers <https://www.youtube.com/watch?v=Iq9DzN6mvYA>`_
a video tutorial by
`Jake Vanderplas <https://us.pycon.org/2016/speaker/profile/295/>`_
on statistical analysis using just a few fundamental concepts
including simulation, sampling, shuffling, and cross-validation.

`Economics Simulation
<http://nbviewer.jupyter.org/url/norvig.com/ipython/Economics.ipynb>`_
a simulation of a marketplace by
`Peter Norvig <http://norvig.com/bio.html>`_ that shows effective
use of many of the tools and distributions provided by this module
(gauss, uniform, sample, betavariate, choice, triangular, and randrange).

`A Concrete Introduction to Probability (using Python)
<http://nbviewer.jupyter.org/url/norvig.com/ipython/Probability.ipynb>`_
a tutorial by `Peter Norvig <http://norvig.com/bio.html>`_ covering
the basics of probability theory, how to write simulations, and
how to perform data analysis using Python.
.. seealso::

`Generating Pseudo-random Floating-Point Values
<https://allendowney.com/research/rand/downey07randfloat.pdf>`_ a
Expand Down