.. _cbenchmarksumtyperst:

=====================================================
Measures a vector sum with different accumulator type
=====================================================


.. only:: html

    **Links:** :download:`notebook <cbenchmark_sum_type.ipynb>`, :downloadlink:`html <cbenchmark_sum_type2html.html>`, :download:`PDF <cbenchmark_sum_type.pdf>`, :download:`python <cbenchmark_sum_type.py>`, :downloadlink:`slides <cbenchmark_sum_type.slides.html>`, :githublink:`GitHub|_doc/notebooks/cbenchmark_sum_type.ipynb|*`


This notebook compares how fast is the sum if the accumulator used to
store the sum is of a different type than the summed elements.

.. code:: ipython3

    from jyquickhelper import add_notebook_menu
    add_notebook_menu()






.. contents::
    :local:





.. code:: ipython3

    %matplotlib inline

`numpy <http://www.numpy.org/>`__ is multithreaded. For an accurate
comparison, this needs to be disabled. This can be done as follows or by
setting environment variable ``MKL_NUM_THREADS=1``.

.. code:: ipython3

    try:
        import mkl
        mkl.set_num_threads(1)
    except ModuleNotFoundError as e:
        print('mkl not found', e)
        import os
        os.environ['MKL_NUM_THREADS']='1'

First comparison
----------------

We compare the two following implementation.

.. code:: ipython3

    # float scenario_Float(const float *p1, size_t size)
    # {
    #     float sum = 0;
    #     const float * end1 = p1 + size;
    #     for(; p1 != end1; ++p1)
    #         sum += *p1;
    #     return sum;
    # }
    # 
    # float scenario_Double(const float *p1, size_t size)
    # {
    #     double sum = 0;
    #     const float * end1 = p1 + size;
    #     for(; p1 != end1; ++p1)
    #         sum += *p1;
    #     return (float)sum;
    # }

The third line is also repeated 10 times to avoid the loop being too
significant.

.. code:: ipython3

    from cpyquickhelper.numbers.cbenchmark_sum_type import measure_scenario_Double, measure_scenario_Float

.. code:: ipython3

    import pandas
    import numpy
    
    def test_benchmark(label, values, repeat=100, number=100):
        funcs = [(k, v) for k, v in globals().copy().items() if k.startswith("measure_scenario")]
        rows = []
        for k, v in funcs:
            exe = v(values, repeat, number)
            d = exe.todict()
            d['doc'] = " ".join(v.__doc__.split('ExecutionStat')[1].strip().split(' ')[-3:]).strip('.')
            d['label'] = label
            d['name'] = k.replace("measure_", "")
            rows.append(d)        
        df = pandas.DataFrame(rows)
        return df
    
    test_benchmark("sorted", numpy.random.rand(10).astype(numpy.float32))






.. raw:: html

    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
            vertical-align: top;
        }

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>average</th>
          <th>deviation</th>
          <th>doc</th>
          <th>label</th>
          <th>max_exec</th>
          <th>min_exec</th>
          <th>name</th>
          <th>number</th>
          <th>repeat</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>7.664200e-09</td>
          <td>7.683250e-08</td>
          <td>a double accumulator</td>
          <td>sorted</td>
          <td>7.910000e-07</td>
          <td>3.950000e-07</td>
          <td>scenario_Double</td>
          <td>100.0</td>
          <td>100.0</td>
        </tr>
        <tr>
          <th>1</th>
          <td>5.096300e-09</td>
          <td>5.378331e-08</td>
          <td>a float accumulator</td>
          <td>sorted</td>
          <td>7.910000e-07</td>
          <td>3.950000e-07</td>
          <td>scenario_Float</td>
          <td>100.0</td>
          <td>100.0</td>
        </tr>
      </tbody>
    </table>
    </div>



Times are not very conclusive on such small lists.

.. code:: ipython3

    values = numpy.random.rand(100000).astype(numpy.float32)
    
    df = test_benchmark("sorted", values)
    df






.. raw:: html

    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
            vertical-align: top;
        }

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>average</th>
          <th>deviation</th>
          <th>doc</th>
          <th>label</th>
          <th>max_exec</th>
          <th>min_exec</th>
          <th>name</th>
          <th>number</th>
          <th>repeat</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>0.000140</td>
          <td>0.00143</td>
          <td>a double accumulator</td>
          <td>sorted</td>
          <td>0.042079</td>
          <td>0.013098</td>
          <td>scenario_Double</td>
          <td>100.0</td>
          <td>100.0</td>
        </tr>
        <tr>
          <th>1</th>
          <td>0.000141</td>
          <td>0.00143</td>
          <td>a float accumulator</td>
          <td>sorted</td>
          <td>0.037468</td>
          <td>0.013094</td>
          <td>scenario_Float</td>
          <td>100.0</td>
          <td>100.0</td>
        </tr>
      </tbody>
    </table>
    </div>



.. code:: ipython3

    df = pandas.concat([df])
    dfg = df[["doc", "label", "average"]].pivot("doc", "label", "average")

.. code:: ipython3

    ax = dfg.plot.bar(rot=30)
    labels = [l.get_text() for l in ax.get_xticklabels()]
    ax.set_xticklabels(labels, ha='right')
    ax.set_title("Comparison of all implementations");



.. image:: cbenchmark_sum_type_13_0.png


For different sizes
-------------------

.. code:: ipython3

    dfs = []
    
    for i in range(2, 7):
        n = 10 ** i
        values = numpy.random.rand(n).astype(numpy.float32)
        df = test_benchmark("sorted", values, repeat=20)
        df["size"] = float(n)
        dfs.append(df)
        
    df = pandas.concat(dfs)
    df.head()






.. raw:: html

    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
            vertical-align: top;
        }

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>average</th>
          <th>deviation</th>
          <th>doc</th>
          <th>label</th>
          <th>max_exec</th>
          <th>min_exec</th>
          <th>name</th>
          <th>number</th>
          <th>repeat</th>
          <th>size</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>1.418275e-07</td>
          <td>0.000001</td>
          <td>a double accumulator</td>
          <td>sorted</td>
          <td>0.000026</td>
          <td>0.000013</td>
          <td>scenario_Double</td>
          <td>100.0</td>
          <td>20.0</td>
          <td>100.0</td>
        </tr>
        <tr>
          <th>1</th>
          <td>1.590125e-07</td>
          <td>0.000002</td>
          <td>a float accumulator</td>
          <td>sorted</td>
          <td>0.000043</td>
          <td>0.000012</td>
          <td>scenario_Float</td>
          <td>100.0</td>
          <td>20.0</td>
          <td>100.0</td>
        </tr>
        <tr>
          <th>0</th>
          <td>1.380739e-06</td>
          <td>0.000014</td>
          <td>a double accumulator</td>
          <td>sorted</td>
          <td>0.000190</td>
          <td>0.000127</td>
          <td>scenario_Double</td>
          <td>100.0</td>
          <td>20.0</td>
          <td>1000.0</td>
        </tr>
        <tr>
          <th>1</th>
          <td>1.292245e-06</td>
          <td>0.000013</td>
          <td>a float accumulator</td>
          <td>sorted</td>
          <td>0.000161</td>
          <td>0.000124</td>
          <td>scenario_Float</td>
          <td>100.0</td>
          <td>20.0</td>
          <td>1000.0</td>
        </tr>
        <tr>
          <th>0</th>
          <td>1.415682e-05</td>
          <td>0.000142</td>
          <td>a double accumulator</td>
          <td>sorted</td>
          <td>0.001969</td>
          <td>0.001293</td>
          <td>scenario_Double</td>
          <td>100.0</td>
          <td>20.0</td>
          <td>10000.0</td>
        </tr>
      </tbody>
    </table>
    </div>



.. code:: ipython3

    piv = df.pivot("size", "doc", "average")
    cols = piv.columns
    piv = piv.reset_index(drop=False)
    piv["ratio"] = piv["a double accumulator"] / piv["a float accumulator"]
    piv






.. raw:: html

    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
            vertical-align: top;
        }

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th>doc</th>
          <th>size</th>
          <th>a double accumulator</th>
          <th>a float accumulator</th>
          <th>ratio</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>100.0</td>
          <td>1.418275e-07</td>
          <td>1.590125e-07</td>
          <td>0.891927</td>
        </tr>
        <tr>
          <th>1</th>
          <td>1000.0</td>
          <td>1.380739e-06</td>
          <td>1.292245e-06</td>
          <td>1.068480</td>
        </tr>
        <tr>
          <th>2</th>
          <td>10000.0</td>
          <td>1.415682e-05</td>
          <td>1.347988e-05</td>
          <td>1.050218</td>
        </tr>
        <tr>
          <th>3</th>
          <td>100000.0</td>
          <td>1.558953e-04</td>
          <td>1.326750e-04</td>
          <td>1.175017</td>
        </tr>
        <tr>
          <th>4</th>
          <td>1000000.0</td>
          <td>1.391328e-03</td>
          <td>1.367595e-03</td>
          <td>1.017354</td>
        </tr>
      </tbody>
    </table>
    </div>



.. code:: ipython3

    ax = piv.plot(x='size', y=cols, logy=True, logx=True)
    ax.set_title("Compares float and double accumulator for a sum.");



.. image:: cbenchmark_sum_type_17_0.png


There is almost no difference.