Math functions in Ada

Math functions in Ada

[William Frye]

Is a there a source of freeware Ada routines for simple math functions?
I am particularly interested in a routine  to calculate x**y where x and y are floating point numbers.  I am working with gnat on a Win95 platform.

Re: Math functions in Ada

[David C. Hoos, Sr.]

How about the package Ada.Numerics.Generic_Elementary_Functions, or one of
its instantiations for long or short float types -- all provided with your
gnat distribution?
David C. Hoos, Sr.
http://www.ada95.com
http://www.dbhwww.com

William Frye <wfrye@mnsinc.com> wrote in article
<5ka4nc$man@news1.mnsinc.com>...
> 
> Is a there a source of freeware Ada routines for simple math functions?
> I am particularly interested in a routine  to calculate x**y where x and
y are floating point numbers.  I am working with gnat on a Win95 platform.
> 

Re: Math functions in Ada

[Doug Smith]

In article <01bc5648$49652250$d08871a5@zeus>, "David C. Hoos, Sr." <david.c.hoos.sr@ada95.com> wrote:

> How about the package Ada.Numerics.Generic_Elementary_Functions, or one of
> its instantiations for long or short float types -- all provided with your
> gnat distribution?
> David C. Hoos, Sr.
> http://www.ada95.com
> http://www.dbhwww.com
> 
> William Frye <wfrye@mnsinc.com> wrote in article
> <5ka4nc$man@news1.mnsinc.com>...
> > 
> > Is a there a source of freeware Ada routines for simple math functions?
> > I am particularly interested in a routine  to calculate x**y where x and
> y are floating point numbers.  I am working with gnat on a Win95 platform.
> > 

If you haven't used generics before (or even if you have), it may not be
obvious that the functions are already available. Visit
 <http://sw-eng.falls-church.va.us/cgi-bin/webada/surfada?file=/opt/gnu/adainclude/a-nuelfu.ads#L20>
which is the predefined package Ada.Numerics.Elementary_Functions. However,
to see the list of functions (including "**") follow the link to the
generic as suggested above. The whole list of predefined packages can
be surfed at:
 <http://sw-eng.falls-church.va.us/cgi-bin/webada/file?template=predefined.html>

Doug
<mailto:dsmith@clark.net>

Re: Math functions in Ada

[Keith Thompson]

In <01bc5648$49652250$d08871a5@zeus> "David C. Hoos, Sr." <david.c.hoos.sr@ada95.com> writes:
> How about the package Ada.Numerics.Generic_Elementary_Functions, or one of
> its instantiations for long or short float types -- all provided with your
> gnat distribution?

Note also that Ada.Numerics.Generic_Elementary_Functions is included
with any Ada 95 compiler, not just GNAT.

I know the original poster asked specifically about freeware and
said that he's using GNAT.  I just want to make sure others are aware
that Ada.Numerics.Generic_Elementary_Functions is predefined and not
GNAT-specific.

-- 
Keith Thompson (The_Other_Keith) kst@sd.aonix.com <http://www.aonix.com> <*>
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Re: Math functions in Ada

[Jacob S. Rosenberg.]

wfrye@mnsinc.com (William Frye) wrote:


>Is a there a source of freeware Ada routines for simple math functions?
>I am particularly interested in a routine  to calculate x**y where x and y
>are floating point numbers.  I am working with gnat on a Win95 platform.

Hi William,

First of all, x**y equals exp(y * log(x)).  So, all you need are the
log (logarithm) and exp (exponential) functions.  It should be failrly
easy to write such a function as log and exp are generally provided.
Indeed, the whole thing would be:

return exp(y * log(x));

I strongly recommend that the input values and the functions used are
of type long_float and not float in order to provide greater range and
accuracy.  The function itself could return a float.  In that case,
you can do a conversion to float before the return statement.

Regards,

Jacob Rosenberg

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Re: Math functions in Ada

[Robert Dewar]

Jacob says

<<First of all, x**y equals exp(y * log(x)).  So, all you need are the
log (logarithm) and exp (exponential) functions.  It should be failrly
easy to write such a function as log and exp are generally provided.
Indeed, the whole thing would be:>>


AARGH! This is a *horrible* equivalence to use in any program, since the
error bounds are simply awful. In other words, even with a perfectly
accurate exp and log, the result of computing x**y can be way off (hundreds
of ULP's) 

True, as Jacob suggests, if you can use a higher precisoin intermediate
type, then this formula is OK, and indeed one of the classic illustrations
of the utility of IEEE extended precision is precisely this one (i.e. if
you have accurate extended precision long and exp, as on the x86, then
you can compute long_form x**y accurately. For a detailed analysis of 
this case, see chapter 5 of my book on Microprocessors.

Re: Math functions in Ada

[John G. Volan]

> wfrye@mnsinc.com (William Frye) wrote:
> 
> >Is a there a source of freeware Ada routines for simple math functions?
> >I am particularly interested in a routine  to calculate x**y where x and y
> >are floating point numbers.  I am working with gnat on a Win95 platform.

Of course there is such a source! In fact, you already have it! (See
below...)

Jacob S. Rosenberg. wrote:
> 
> Hi William,
> 
> First of all, x**y equals exp(y * log(x)).  So, all you need are the
> log (logarithm) and exp (exponential) functions.  It should be failrly
> easy to write such a function as log and exp are generally provided.
> Indeed, the whole thing would be:
> 
> return exp(y * log(x));
> 
> I strongly recommend that the input values and the functions used are
> of type long_float and not float in order to provide greater range and
> accuracy.  The function itself could return a float.  In that case,
> you can do a conversion to float before the return statement.

Why in heaven's name would you want to re-invent the wheel, when "**" is
already provided in the standard library?  See ARM A.5.1 Elementary
Functions:

  generic
    type Float_Type is digits <>;
  package Ada.Numerics.Generic_Elementary_Functions is
     ...
     function "**" (Left, Right : Float_Type'Base)
       return Float_Type'Base;
     ...

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