.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/vm/foundations/plot_05_structured_programming.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_05_structured_programming.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_05_structured_programming.py:


Structured programming: sequence, selection, iteration (Böhm and Jacopini 1966)
===============================================================================

Böhm and Jacopini proved that any flowchart can be rewritten using only
three constructs: doing things in sequence, choosing between two branches,
and repeating while a condition holds. On a stack machine those are simply
straight-line code, a conditional jump (``JZ``) and a backward jump
(``JMP``). The assembler lets us write them with labels instead of
addresses.

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

The loop computes ``1 + 2 + ... + n`` and agrees with Gauss's formula. The
backward jump is what makes iteration possible, and also what makes the
running time depend on the input: the gas used grows linearly with n.

The history behind this experiment: :doc:`/history/vm_breakthroughs`.

.. GENERATED FROM PYTHON SOURCE LINES 23-25

A loop written with labels
--------------------------

.. GENERATED FROM PYTHON SOURCE LINES 25-67

.. code-block:: Python

    import matplotlib.pyplot as plt

    import blockchainkit as bk

    source = """
    # Sum 1 + 2 + ... + n, with n in slot 0 and the sum in slot 1.
    loop:                # iteration: test, body, jump back
        LOAD 0
        JZ done          # selection: leave when n reaches 0
        LOAD 1
        LOAD 0
        ADD
        STORE 1          # sequence: sum = sum + n
        LOAD 0
        PUSH 1
        SUB
        STORE 0          # n = n - 1
        JMP loop
    done:
        STOP
    """
    program = bk.vm.assemble(source)
    for address, instruction in enumerate(program):
        print(address, instruction)

    sizes = [0, 1, 5, 10, 20, 40, 80]
    gas = []
    for n in sizes:
        result = bk.vm.execute(program, storage={0: n})
        assert result.storage.get(1, 0) == n * (n + 1) // 2
        gas.append(result.gas_used)
    print(gas)
    assert all(
        b - a == (sizes[i + 1] - sizes[i]) * 11
        for i, (a, b) in enumerate(zip(gas, gas[1:], strict=False))
    )

    fig, ax = plt.subplots(figsize=(6, 4))
    ax.plot(sizes, gas, "o-")
    ax.set(xlabel="n", ylabel="gas used", title="11 instructions per iteration")
    fig.tight_layout()




.. image-sg:: /api/gallery/vm/foundations/images/sphx_glr_plot_05_structured_programming_001.png
   :alt: 11 instructions per iteration
   :srcset: /api/gallery/vm/foundations/images/sphx_glr_plot_05_structured_programming_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    0 ('LOAD', 0)
    1 ('JZ', 11)
    2 ('LOAD', 1)
    3 ('LOAD', 0)
    4 ('ADD', None)
    5 ('STORE', 1)
    6 ('LOAD', 0)
    7 ('PUSH', 1)
    8 ('SUB', None)
    9 ('STORE', 0)
    10 ('JMP', 0)
    11 ('STOP', None)
    [3, 14, 58, 113, 223, 443, 883]




.. GENERATED FROM PYTHON SOURCE LINES 68-73

Exercise
--------
Add a selection inside the body so that only even numbers are added.
(The machine has no MOD: compute ``n - 2 * (n / 2)``.) Which of the three
constructs did you use, and where?


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

   **Total running time of the script:** (0 minutes 0.094 seconds)


.. _sphx_glr_download_api_gallery_vm_foundations_plot_05_structured_programming.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_05_structured_programming.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_05_structured_programming.ipynb <plot_05_structured_programming.ipynb>`

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

      :download:`Download Python source code: plot_05_structured_programming.py <plot_05_structured_programming.py>`

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

      :download:`Download zipped: plot_05_structured_programming.zip <plot_05_structured_programming.zip>`


.. only:: html

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

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