.. index:: floating-point
 
.. _floating-point:
 
.. Created floating-point.rst: Wed 14 Dec 2022 03:14:24 AEDT 
.. Full Path: /home/tp/mecrisp-unofficial-doc/floating-point.rst 
.. Author Copyright 2022 by t.j.porter <techman001@protonmail.com> 
.. Made by /home/tp/projects/scripts/makerst.sh -->/usr/local/bin/makerst 
.. license: MIT, please see COPYING 
 
Floating Point
==============

.. image:: pics/floating-point.jpg

Peter Schmidt
-------------
https://www.spyr.ch/twiki/bin/view/MecrispCube/FloatingPointUnit

A very interesting article by Peter Schmidt, author of :ref:`Mecrisp-Cube<mecrisp-cube>` where he uses the FPU of the STM32F407 and does various comparisons with Fixed Point (s31.32) and benchmarks the time involved.

   (excerpt from Peters article)
   
   **Floating-Point Unit**

   The STM32 ARM Cortex M4F MPUs (e.g. STM32WB, STM32F4, STM32L4) have a single precision floating-point unit. The STM32H7 MPUs have a double precision FPU (not supported yet).

   Also from STM AN4044

   Floating-point calculations require a lot of resources, as for any operation between two numbers. For example, we need to:
   ::

    Align the two numbers (have them with the same exponent)
    Perform the operation
    Round out the result
    Code the result 

   On an FPU-less processor, all these operations are done by software through the C compiler library (or Forth Words) and are not visible to the programmer; but the performances are very low. On a processor having an FPU, all of the operations are entirely done by hardware in a single cycle, for most of the instructions. The C (or Forth) compiler does not use its own floating-point library but directly generates FPU native instructions.

   When implementing a mathematical algorithm on a microprocessor having an FPU, the programmer does not have to choose between performance and development time. The FPU brings reliability allowing to use directly any generated code through a high level tool, such as MATLAB or Scilab, with the highest level of performance.

   Any integer with absolute value less than 2^24 can be exactly represented in the single-precision format, and any integer with absolute value less than 2^53 can be exactly represented in the double-precision format.

   ...

   **Conclusion**

   As long as you do only elementary arithmetic, fixed- and floating-point have comparable execution time (but division and multiplication is a magnitude slower). But for more elaborate calculation (trigonomteric, exponential functions) the execution time is for fixed-point at least two magnitudes slower.

   If time is not an issue in either development or execution, you can easily do without the FPU. 

.. seealso:: :ref:`Fixed Point<fixed.point>`