Issue 0471: Complex math functions cacosh and ctanh

This issue has been automatically converted from the original issue lists and some formatting may not have been preserved.

Authors: WG14, Fred Tydeman
Date: 2014-10-28
Reference document: N1886
Submitted against: C11 / C17
Status: Fixed
Fixed in: C17
Converted from: n2396.htm

Summary

Complex math functions (cacosh (G.6.2.1) and ctanh(G.6.2.6)) are incorrectly specified.

  1. cacosh( 0.0 + I*NaN ) should be NaN + I*pi/2 (not NaN + I*NaN).

Reasons: Mathematically, cacosh(0.0+I*y) = asinh(y) + I*pi/2. Also, C requires cacos(0+I*NaN) to be pi/2+I*NAN, which along with the mathematically identity cacosh(z) = +/-I * cacos(z), means cacosh(0.0 + I*NaN) is NaN + I*pi/2.

  1. ctanh(+0.0+I*NaN) should be 0.0 + I*NaN (not NaN+I*NaN)
  2. ctanh(+0.0+I*INF) should be 0.0 + I*NaN w/ invalid (not NaN+I*NaN w/ invalid)

Reason for above two: Since ctanh(x+I*y) = (sinh(2x) + I*sin(2y)) / (cosh(2x) + cos(2y)), for any rational number y, cos(2y) cannot be exactly -1, so no 0/(1+(-1)),so no 0/0, so no NaN for the real component of the result

Suggested Technical Corrigendum

Add to G.6.2.1 cacosh before 4th bullet: cacosh(0.0+I*NaN) returns NaN + I*pi/2

Add to G.6.2.1 cacosh 4th bullet: "non-zero" so it reads: cacosh(x + iNaN) returns NaN + i*NaN and optionally raises the “invalid” floating-point exception, for finite non-zero x.

Add to G.6.2.6 ctanh before 3rd bullet: ctanh(0.0+I*INF) returns 0.0+I*NAN and raises the “invalid” floating-point exception.

Add to G.6.2.6 ctanh 3rd bullet: "non-zero" so it reads: ctanh(x + I*INF) returns NaN + i*NaN and raises the “invalid” floating-point exception, for finite non-zero x.

Add to G.6.2.6 ctanh before 4th bullet: ctanh(0.0+I*NaN) returns 0.0+I*NAN

Add to G.6.2.6 ctanh 4th bullet: "non-zero" so it reads: ctanh(x + I*NAN) returns NaN + i*NaN and optionally raises the “invalid” floating-point exception, for finite non-zero x.

Comment from WG14 on 2017-11-03:

Oct 2014 meeting

Committee Discussion

This DR is derived from N1867. The committee agrees with the Suggested Technical Corrigendum.

Oct 2017 meeting

Committee Discussion

In light of the paper N2173 the committee agrees to amend the PTC to specify that

cacosh(0.0+iNaN) returns NaN ± iπ/2

Proposed Technical Corrigendum

Add new paragraph to G.6.2.1 cacosh before 4th bullet:

cacosh(0.0+iNaN) returns NaN ± iπ/2

Change G.6.2.1 cacosh 4th bullet from:

cacosh(x + iNaN) returns NaN + iNaN and optionally raises the “invalid” floating-point exception, for finite x.

to

cacosh(x + iNaN) returns NaN + iNaN and optionally raises the “invalid” floating-point exception, for finite non-zero x.

Add new paragraph to G.6.2.6 ctanh before 3rd bullet:

ctanh(0.0+i∞) returns 0.0+iNAN and raises the “invalid” floating-point exception.

Change G.6.2.6 ctanh 3rd bullet clause from:

ctanh(x + i∞) returns NaN + iNaN and raises the “invalid” floating-point exception, for finite x.

to

ctanh(x + i∞) returns NaN + iNaN and raises the “invalid” floating-point exception, for finite non-zero x.

Add new paragraph to G.6.2.6 ctanh before 4th bullet:

ctanh(0.0+iNaN) returns 0.0+iNAN

Change G.6.2.6 ctanh 4th bullet from:

ctanh(x + iNAN) returns NaN + iNaN and optionally raises the “invalid” floating-point exception, for finite x.

to

ctanh(x + iNAN) returns NaN + iNaN and optionally raises the “invalid” floating-point exception, for finite non-zero x.