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[patch,libgfortran] Fix binary128 ERFC_SCALED

From: FX <fxcoudert at gmail dot com>
To: gfortran <fortran at gcc dot gnu dot org>
Cc: gcc-patches at gcc dot gnu dot org
Date: Sun, 17 Nov 2013 11:29:50 +0100
Subject: [patch,libgfortran] Fix binary128 ERFC_SCALED
Authentication-results: sourceware.org; auth=none

This patch fixes libgfortran’s binary128 [aka real(kind=16)] variant of ERFC_SCALED. The original code, which I had lifted from netlib, gives only 18 significant decimal digits, which is not enough for binary128 (33 decimal digits).

I thus implemented a new variant for binary128. For arguments < 12, it simply calls erfcq() then multiplies by expq(x*x). For larger arguments, it uses a power expansion in 1/x. The new implementation provides answers within to 2 ulp of the correct value.

Regtested on x86_64-apple-darwin13, comes with a testcase. OK to commit?
FX

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Follow-Ups:
- Re: [patch,libgfortran] Fix binary128 ERFC_SCALED
  - From: Steve Kargl

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