To: J3                                                     J3/18-236r2
From:    Anton Shterenlikht & Malcolm Cohen
Subject: ACOSH result value error/typo
Date: 2018-October-18


1. Introduction

As (a) the ACOSH function was in Fortran 2008, and
   (b) the next revision is currently in FDIS ballot so too late to
       change, unless that ballot fails,
this has become a Defect Report (aka Interpretation Request).


2. Interpretation Request

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NUMBER: F18/0001
TITLE: ACOSH principal value specification is wrong
KEYWORDS: ACOSH
DEFECT TYPE: Erratum
STATUS: J3 consideration in progress

QUESTION:

Clause 16.9.5 ACOSH( X ) p5 Result Value has:
    "If the result is complex the imaginary part is expressed in
     radians and lies in the range 0 <= AIMAG (ACOSH (X)) <= {pi}".

There is general agreement that the principal value of ACOSH should
have the real part non-negative which means the imaginary part must
range from -pi to +pi.

Is this a mistake in the definition of ACOSH?

ANSWER:

Yes, this is a mistake.  Edits are included to correct this error.
This will be an incompatibility with Fortran 2008.

EDITS to 18-007r1:

[26:17+] 4.3.3 Fortran 2008 compatibility, p10+, insert new para
         "Fortran 2008 required ACOSH of a complex value to have the
          imaginary part non-negative and had no requirement on
          the real part.  This document requires ACOSH of a complex
          value to have a non-negative real part and has no such
          requirement on the imaginary part."

[340:34-35] 16.9.5 ACOSH, p5 Result Value,
            after "is complex"
            insert "the real part is non-negative and",
            change "range 0" to "range $-\pi$".
Making the whole p5 read
    "Result Value. The result has a value equal to a processor-
     dependent approximation to the inverse hyperbolic cosine
     function of X. If the result is complex the real part is non-
     negative, and the imaginary part is expressed in radians and
     lies in the range $-\pi$ <= AIMAG (ACOSH (X)) <= $\pi$."

SUBMITTED BY: Anton Shterenlikht

HISTORY: 18-236   m217  Submitted
         18-236r1 m217  Put into interp format, revised edits.

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