.. _sphx_glr_api_gallery_numerical_analysis_floating_point:

Floating-point arithmetic
-------------------------

Rounding error in floating-point computation, and algorithms that
compensate for it.


.. raw:: html

  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Adding n floating-point numbers one at a time can accumulate error proportional to n. William Kahan&#x27;s 1965 algorithm carries the rounding error of each addition forward in a correction term, so the error stays at a few units in the last place however many terms are added. This script sums 0.1 repeatedly and compares the naive loop, Kahan&#x27;s algorithm, and NumPy&#x27;s pairwise summation against the exactly rounded result from math.fsum.">

.. only:: html

  .. image:: /api/gallery/numerical_analysis/floating_point/images/thumb/sphx_glr_plot_01_kahan_summation_thumb.png
    :alt:

  :doc:`/api/gallery/numerical_analysis/floating_point/plot_01_kahan_summation`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Kahan's compensated summation</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /api/gallery/numerical_analysis/floating_point/plot_01_kahan_summation