[/
  Copyright 2011 - 2020 John Maddock.
  Copyright 2013 - 2019 Paul A. Bristow.
  Copyright 2013 Christopher Kormanyos.

  Distributed under the Boost Software License, Version 1.0.
  (See accompanying file LICENSE_1_0.txt or copy at
  http://www.boost.org/LICENSE_1_0.txt).
]

[section:overhead The Overhead in the Number Class Wrapper]

Using a simple [@../../performance/arithmetic_backend.hpp backend class] that wraps any __fundamental arithmetic type
we can measure the overhead involved in wrapping a type inside the `number` frontend, and the effect that turning
on expression templates has.  The following table compares the performance between `double` and a `double` wrapped
inside class `number`:

[table Bessel Functions (16 digit precision)
[[Type][Time]]
[[arithmetic_backend<double>][2.09301 (0.00133409s)]]
[[arithmetic_backend<double> - no expression templates][1 (0.000637403s)]]
[[double][1.07956 (0.000688113s)]]
]

As you can see whether or not there is an overhead, and how large it is depends on the actual situation,
but the overhead is in any cases small.  Expression templates generally add a greater overhead the
more complex the expression becomes due to the logic of figuring out how to best unpack and evaluate
the expression, but of course this is also the situation where you save more temporaries.  For a
"trivial" backend like this, saving temporaries has no benefit, but for larger types it becomes
a bigger win.

The following table compares arithmetic using either `long long` or `number<arithmetic_backend<long long> >`
for the [@../../performance/voronoi_performance.cpp voronoi-diagram builder test]:

[table
[[Type][Relative time]]
[[`int64_t`][[*1.0](0.0128646s)]]
[[`number<arithmetic_backend<int64_t>, et_off>`][1.005 (0.0129255s)]]
]

This test involves mainly creating a lot of temporaries and performing a small amount of arithmetic on them,
with very little difference in performance between the native and "wrapped" types.

[table:platform Platform Details
[[][Version]]
[[Compiler][GNU C++ version 10.3.0]]
[[GMP][6.2.0]]
[[MPFR][262146]]
[[Boost][107800]]
[[Run date][Sep 30 2021]]
]

[endsect]