.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/vm/foundations/plot_03_hardware_stack.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_vm_foundations_plot_03_hardware_stack.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_vm_foundations_plot_03_hardware_stack.py:


Stack hardware: a bounded stack (Burroughs B5000, Barton 1961)
==============================================================

Robert Barton designed the Burroughs B5000 around a hardware stack: programs
compiled from Algol were sequences of stack operations, with no general
registers to allocate. A real stack has finite size, so the machine must
know how deep a computation goes. The EVM limits its stack to 1024 words
for the same reason.

What to look for
----------------

The same sum needs very different stack depths depending on its shape:
``((1 + 2) + 3) + ...`` never holds more than two values, while
``1 + (2 + (3 + ...))`` holds every operand at once. With a small stack
limit, the right-nested form overflows.

The history behind this experiment: :doc:`/history/vm_breakthroughs`.
See :doc:`/exercises/vm` for a worked solution to the exercise.

.. GENERATED FROM PYTHON SOURCE LINES 24-26

Two shapes of the same sum
--------------------------

.. GENERATED FROM PYTHON SOURCE LINES 26-43

.. code-block:: Python

    import matplotlib.pyplot as plt

    import blockchainkit as bk
    from blockchainkit.vm.visualizers import plot_stack_height

    n = 12
    left = "(" * (n - 2) + "1 + 2" + "".join(f") + {k}" for k in range(3, n + 1))
    right = "".join(f"{k} + (" for k in range(1, n)) + str(n) + ")" * (n - 1)
    traces = {}
    for name, expression in (("left-nested", left), ("right-nested", right)):
        result = bk.vm.execute(bk.vm.compile_expression(expression), trace=True)
        assert result.stack == (n * (n + 1) // 2,)
        traces[name] = result.trace
    peaks = {name: max(len(step.stack) for step in trace) for name, trace in traces.items()}
    print(peaks)
    assert peaks == {"left-nested": 2, "right-nested": n}





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    {'left-nested': 2, 'right-nested': 12}




.. GENERATED FROM PYTHON SOURCE LINES 44-46

A hardware limit
----------------

.. GENERATED FROM PYTHON SOURCE LINES 46-59

.. code-block:: Python

    try:
        bk.vm.execute(bk.vm.compile_expression(right), stack_limit=8)
    except bk.vm.VMError as error:
        print("right-nested with 8 slots:", error)
    assert bk.vm.execute(bk.vm.compile_expression(left), stack_limit=8).stack == (78,)

    fig, ax = plt.subplots(figsize=(7, 4))
    for name, trace in traces.items():
        plot_stack_height(trace, label=name, ax=ax)
    ax.axhline(8, color="black", linestyle="--")
    ax.set_title("Same sum, different stack needs")
    fig.tight_layout()




.. image-sg:: /api/gallery/vm/foundations/images/sphx_glr_plot_03_hardware_stack_001.png
   :alt: Same sum, different stack needs
   :srcset: /api/gallery/vm/foundations/images/sphx_glr_plot_03_hardware_stack_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    right-nested with 8 slots: stack limit exceeded




.. GENERATED FROM PYTHON SOURCE LINES 60-64

Exercise
--------
For a balanced tree of additions over 2**k numbers, what is the peak stack
height? (This is the Ershov or Strahler number of the expression tree.)


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.107 seconds)


.. _sphx_glr_download_api_gallery_vm_foundations_plot_03_hardware_stack.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../../lite/lab/index.html?path=api/gallery/vm/foundations/plot_03_hardware_stack.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_03_hardware_stack.ipynb <plot_03_hardware_stack.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_03_hardware_stack.py <plot_03_hardware_stack.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_03_hardware_stack.zip <plot_03_hardware_stack.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_