GNAT for AVR - Mathematical Functions

GNAT for AVR - Mathematical Functions

[ada.newcomer]

Hello.

I'm programming an ATmega328P with the GNAT compiler for AVR.

I need to use the Sqrt, Arctan and Atan2 functions. But maybe in the future I will need to use some more.

I don't have access to the regular Ada.Numerics package.

By now, I wrote the Sqrt using the Newton's method and Arctan using Taylor series.

I would like to know if there is a better way to use/implement mathematical functions (maybe import them from C?).

I really appreciate any help.

Re: GNAT for AVR - Mathematical Functions

[Dmitry A. Kazakov]

On 2018-09-17 04:22, ada.newcomer@gmail.com wrote:

> By now, I wrote the Sqrt using the Newton's method and Arctan using Taylor series.

Chebyshev's polynomials for arctan?

-- 
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de

Re: GNAT for AVR - Mathematical Functions

[Aurele Vitali]

I don't know anything about the ATmega328P, but if it uses a builtin floating point processor, you can use Ada inline floating point assembler.  Its not hard to do. Here is a simple example of the square root function: 

  with System.Machine_Code; use System.Machine_Code; 
  EOL : constant String := ASCII.LF & ASCII.HT;

  function Sqrt( x : in Long_Float ) return Long_Float is 
    Result : Long_Float := 0.0; 
  begin 
    Asm( ( "fldl  %1" & EOL &                 -- Load x in St(0) 
           "fsqrt   " & EOL &                 -- Take the Sqrt of St(0) 
           "fstpl %0" ),                      -- Store result and pop St(0) 
         Outputs => ( Long_Float'Asm_Output("=m", Result ) ), 
         Inputs  => ( Long_Float'Asm_Input ( "m",      x ) ) ); 
    return Result; 
  end Sqrt; 

You can do the same thing for trig functions...  Just cut and past and see if this example works. 

Cheers 

Re: GNAT for AVR - Mathematical Functions

[Simon Wright]

ada.newcomer@gmail.com writes:

> I'm programming an ATmega328P with the GNAT compiler for AVR.
>
> I need to use the Sqrt, Arctan and Atan2 functions. But maybe in the
> future I will need to use some more.
>
> I don't have access to the regular Ada.Numerics package.
>
> By now, I wrote the Sqrt using the Newton's method and Arctan using
> Taylor series.
>
> I would like to know if there is a better way to use/implement
> mathematical functions (maybe import them from C?).
>
> I really appreciate any help.

For what it's worth, the FSF GCC arm-eabi compiler/runtime that I built
imports the basic maths functions from the C library. This may be
because I built the C library (newlib) first?

The GNAT CE arm-eabi compiler goes to basics with very deep-looking
code; possibly because it's "the Ada Cert Math specific version" (from
s-libsin.ads), i.e. one with which AdaCore will support customers with
certification requirements.

Re: GNAT for AVR - Mathematical Functions

[Bill Findlay]

On 17 Sep 2018, ada.newcomer@gmail.com wrote
(in article<ed6bc2e2-a2e1-4a0b-b253-8142d47518c9@googlegroups.com>):

> Hello.
>
> I'm programming an ATmega328P with the GNAT compiler for AVR.
>
> I need to use the Sqrt, Arctan and Atan2 functions. But maybe in the future I
> will need to use some more.
>
> I don't have access to the regular Ada.Numerics package.
>
> By now, I wrote the Sqrt using the Newton's method and Arctan using Taylor
> series.
>
> I would like to know if there is a better way to use/implement mathematical
> functions (maybe import them from C?).
>
> I really appreciate any help.

Since you have sqrt, see:<http://www.findlayw.plus.com/KDF9/#ATN>

-- 
Bill Findlay

Re: GNAT for AVR - Mathematical Functions

[Aurele Vitali]

I don't know anything about the ATmega328P, but if it uses a builtin floating point processor, you can use Ada inline floating point assembler.  Its not hard to do. Here is a simple example of the square root function:

  with System.Machine_Code; use System.Machine_Code;

  function Sqrt( x : in Long_Float ) return Long_Float is
    Result : Long_Float := 0.0;
  begin
    Asm( ( "fldl  %1" & EOL &                 -- Load x in St(0)
           "fsqrt   " & EOL &                 -- Take the Sqrt of St(0)
           "fstpl %0" ),                      -- Store result and pop St(0)
         Outputs => ( Long_Float'Asm_Output("=m", Result ) ),
         Inputs  => ( Long_Float'Asm_Input ( "m",      x ) ) );
    return Result;
  end Sqrt;

You can do the same thing for trig functions...  Just cut and past and see if this example works. 

Cheers

Re: GNAT for AVR - Mathematical Functions

[rakusu_klein]

It is always be bottleneck — doing math on slow integer 8-bit CPU with tiny amount of memory and instructions only for addition and subtraction, — because it produce a huge pieces of slow machine code. So all math there are doing in integers by a table calculations, adds and shifts. Therefore in future it's better to go away from AVR for you with math, I think.
Btw, there is a quite old C-runtime library for AVR at http://savannah.nongnu.org/projects/avr-libc/ — it might be helpful for you, especially its handwritten libm. It can also be useful to look at CORDIC algorithm, frex http://www.dcs.gla.ac.uk/~jhw/cordic/index.html

Re: GNAT for AVR - Mathematical Functions

[R R]

On Monday, September 17, 2018 at 4:22:47 AM UTC+2, Ada Newcomer wrote:
> Hello.
> 
> I'm programming an ATmega328P with the GNAT compiler for AVR.
> 
> I need to use the Sqrt, Arctan and Atan2 functions. But maybe in the future I will need to use some more.
> 
> I don't have access to the regular Ada.Numerics package.
> 
> By now, I wrote the Sqrt using the Newton's method and Arctan using Taylor series.
> 
> I would like to know if there is a better way to use/implement mathematical functions (maybe import them from C?).
> 
> I really appreciate any help.

The old AVR-ADA project never supported floting point math. The AVR 8bit processors are not made for that, even though you can use float and double in Arduino. The AVR compiler by Adacore from around 2011 did support floating point variables as far as I remember, I am not sure about the math functions.

regards
    Rolf