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From: jonathan <johnscpg@googlemail.com>
Newsgroups: comp.lang.ada
Subject: Re: Is there an Ada compiler whose
 Ada.Numerics.Generic_Elementary_Functions.Log(Base=>10,
	X=>variable) is efficient?
Date: Mon, 15 Feb 2010 16:09:36 -0800 (PST)
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Date: 2010-02-15T16:09:36-08:00
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I said:

>The remaining puzzle
> is the smallish difference between the gnat Log and the gcc Log. I
> will (also) leave this to the experts. =A0When I looked at this in
> the past it has always been because gnat did the calculation to 18
> significant figures (even if you use type
> Real is digits 15), gcc to 15.

Well, I can't resist .. its easy to demonstrate (on Intel cpu's).
Let's do a benchmark of 10_000_000 base e Log's with 15 digits
and then 18 digits.  Must compile without -gnatn or -gnatN
so that it doesn't optimize away the constant in the inner loop.
I just used -O3. (Couldn't find anything faster.)

with ada.numerics.generic_elementary_functions;
with text_io; use text_io;

procedure log_bench_2 is

  type Real is digits 15;
--type Real is digits 18;

  package Math is
     new ada.numerics.generic_elementary_functions(Real);
  use Math;
  x, y : Real :=3D 0.5;

begin

  for i in 1 .. 10_000_000 loop
    x :=3D Log (y);
  end loop;
  Put (Real'Image (x));

end log_bench_2;

Using 15 digits I get:

-6.93147180559945E-01
real    0m0.209s
user    0m0.208s
sys     0m0.000s

Using 18 digits I get:

-6.93147180559945309E-01
real    0m0.208s
user    0m0.208s
sys     0m0.000s

So 18 digits are calculated just as fast as 15.

Jonathan