python: benchmark math / numpy / buffer protocol things.

Lots of optimization opportunities here. In particular, the conversion
of Vector3 to np.array is *crazy slow*, turns out to be caused mainly by
the overhead of exception throwing in pybind11. In case of Matrix3 to
np.array conversion there's no such overhead because the buffer protocol
takes care of that.

Another thing is that pybind11 buffer protocol interface has a
relatively large overhead compared to e.g. python's own array.array. I
blame the unneded allocations.

src/python/magnum/test/benchmark_math.py

@@ -0,0 +1,105 @@
+#!/usr/bin/env python3
+
+#
+#   This file is part of Magnum.
+#
+#   Copyright © 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019
+#             Vladimír Vondruš <mosra@centrum.cz>
+#
+#   Permission is hereby granted, free of charge, to any person obtaining a
+#   copy of this software and associated documentation files (the "Software"),
+#   to deal in the Software without restriction, including without limitation
+#   the rights to use, copy, modify, merge, publish, distribute, sublicense,
+#   and/or sell copies of the Software, and to permit persons to whom the
+#   Software is furnished to do so, subject to the following conditions:
+#
+#   The above copyright notice and this permission notice shall be included
+#   in all copies or substantial portions of the Software.
+#
+#   THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+#   IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+#   FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+#   THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+#   LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+#   FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
+#   DEALINGS IN THE SOFTWARE.
+#
+
+# Avoid this being run implicitly during unit tests
+if __name__ != '__main__': exit()
+
+import timeit
+
+import array
+from magnum import *
+import numpy as np
+
+repeats = 100000
+
+def timethat(expr: str, *, setup:str = 'pass', title=None):
+    if not title:
+        if setup != 'pass': title = f'{setup}; {expr}'
+        else: title = expr
+
+    print('{:67} {:8.5f} µs'.format(title, timeit.timeit(expr, number=repeats, globals=globals(), setup=setup)*1000000.0/repeats))
+
+def timethat_exception(expr: str):
+    return timethat(f"""
+try:
+    {expr}
+except:
+    pass
+""", title=f'{expr} # throws')
+
+print("  plain list expressions:\n")
+
+timethat('[]')
+timethat('list([])')
+timethat('[1.0, 2.0, 3.0]')
+timethat('list([1.0, 2.0, 3.0])')
+
+print("\n  Vector3 from/to list:\n")
+
+timethat('Vector3()')
+timethat('Vector3(1.0, 2.0, 3.0)')
+timethat('Vector3([1.0, 2.0, 3.0])')
+timethat('list(Vector3(1.0, 2.0, 3.0))')
+timethat('a = Vector3(1.0, 2.0, 3.0); [a.x, a.y, a.z]')
+
+print("\n  constructing builtin array:\n")
+
+timethat('array.array("f", [])')
+timethat('array.array("f", [1.0, 2.0, 3.0])')
+timethat('memoryview(a)', setup='a = array.array("f", [1.0, 2.0, 3.0])')
+#timethat('memoryview(a)', setup='a = Vector3(1.0, 2.0, 3.0)')
+
+print("\n  constructing np.array:\n")
+
+timethat('np.array([])')
+timethat('np.array([1.0, 2.0, 3.0])')
+timethat('np.array(a)', setup='a = array.array("f", [1.0, 2.0, 3.0])')
+timethat('np.array(a)', setup='a = Vector3(1.0, 2.0, 3.0)')
+
+print("\n  Matrix3 from/to list, equivalent np.array operations:\n")
+
+timethat('Matrix3()')
+timethat('Matrix3.from_diagonal(Vector3(1.0, 2.0, 3.0))')
+timethat('Matrix3.from_diagonal([1.0, 2.0, 3.0])')
+timethat('list(Matrix3.from_diagonal(Vector3(1.0, 2.0, 3.0)))')
+timethat('np.diagflat([1.0, 2.0, 3.0])')
+timethat('np.array(Matrix3.from_diagonal(Vector3(1.0, 2.0, 3.0)))')
+
+print("\n  exception throwing:\n")
+
+timethat('Vector3()[0] # doesn\'t throw')
+timethat_exception('Vector3()[3]')
+timethat_exception('raise IndexError()')
+
+print("\n  basic operations:\n")
+
+timethat('a + a', setup='a = Vector4d(1.0, 2.0, 3.0, 4.0)')
+timethat('a + a', setup='a = np.array([1.0, 2.0, 3.0, 4.0])')
+timethat('a.dot()', setup='a = Vector4d(1.0, 2.0, 3.0, 4.0)')
+timethat('np.dot(a, a)', setup='a = np.array([1.0, 2.0, 3.0, 4.0])')
+timethat('a@a', setup='a = Matrix4d.from_diagonal([1.0, 2.0, 3.0, 4.0])')
+timethat('a@a', setup='a = np.diagflat([1.0, 2.0, 3.0, 4.0])')