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Re: [Patch,Fortran] PR 33197 Add NORM2 and PARITY

From: Toon Moene <toon at moene dot org>
To: Tobias Schlüter <tobias dot schlueter at physik dot uni-muenchen dot de>
Cc: Tobias Burnus <burnus at net-b dot de>, gcc patches f <gcc-patches at gcc dot gnu dot org>, gfortran <fortran at gcc dot gnu dot org>
Date: Thu, 26 Aug 2010 20:07:18 +0200
Subject: Re: [Patch,Fortran] PR 33197 Add NORM2 and PARITY
References: <4C766E7C.7000408@net-b.de> <4C76A1B7.3010707@physik.uni-muenchen.de>

Tobias Schlüter wrote:

On 2010-08-26 15:39, Tobias Burnus wrote:

For norm2 (L2 norm), one essentially does:
tmp = max(array) ! = L_infinity norm
norm2 = tmp * sqrt( (array/tmp)**2)
to avoid an overflow.

Just a random idea: the maximum precision that such a single pass algorithm can achieve is probably obtained by using and modifying the binary exponent instead of multiplying with a scale factor as this renders the scale transformations exact.

That's what people told me to do for quick complex divide in the '90s - however, at that time there were multiple supported floating point formats, so it was not *that* simple.

If IEEE-754 format is the only one supported now, that might be doable.

Cheers,

--
Toon Moene - e-mail: toon@moene.org - phone: +31 346 214290
Saturnushof 14, 3738 XG  Maartensdijk, The Netherlands
At home: http://moene.org/~toon/; weather: http://moene.org/~hirlam/
Progress of GNU Fortran: http://gcc.gnu.org/gcc-4.5/changes.html#Fortran

References:
- [Patch,Fortran] PR 33197 Add NORM2 and PARITY
  - From: Tobias Burnus
- Re: [Patch,Fortran] PR 33197 Add NORM2 and PARITY
  - From: Tobias Schlüter

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