[cfp-interest 3862] Re: [SC22WG14.35726] N3731 Range bounds for math functions

[Jim Thomas]

The forwarded message below from Joseph Myers points out that the range bounds issue addressed by CFP’s N3731 does cover the same issue for complex functions. Here is possible rewording to address the issue for cacos (7.3.5.1). Similar rewording is needed for casin, catan, cacosh, casinh and catanh.

+++++

Change to 7.3.5.1:

FROM:

Description
2 The cacos functions compute the complex arc cosine of z, with branch cuts outside the interval [−1, +1] along the real axis.

Returns
3 The cacos functions return the complex arc cosine value, in the range of a strip mathematically unbounded along the imaginary axis and in the interval [0, pi] along the real axis.

TO:

Description
2 The cacos functions compute the branch of the complex arc sine of z whose range is the strip unbounded along the imaginary axis and in the interval [0, pi] along the real axis, with branch cuts outside the interval [-1, +1] along the real axis.

Returns
3 The cacos functions return the complex arc cosine of z.

4 NOTE The cacos functions, and similarly the casin, catan, cacosh, casinh and catanh functions, can return a value outside the specified branch for the computed mathematical function. Because the branch has boundary points with a coordinate that is not representable as a floating-point number, even correct rounding can yield values outside the branch boundary, depending on the return type and rounding direction.

+++++

- Jim Thomas

> On Apr 7, 2026, at 8:26 AM, Jim Thomas <jaswthomas at sbcglobal.net> wrote:
> 
> This regards action item
> 
>>     Jim: Add agenda item to fix range bounds problem for complex fcns (as done for real functions in N3731).
> 
> 
> Following is background for the discussion.
> 
> - Jim Thomas
> 
>> Begin forwarded message:
>> 
>> From: RAJAN BHAKTA <rbhakta at us.ibm.com>
>> Subject: [SC22WG14.35726] N3731 Range bounds for math functions
>> Date: March 5, 2026 at 3:19:10 PM PST
>> To: Joseph Myers <josmyers at redhat.com>, "sc22wg14 at open-std.org" <sc22wg14 at open-std.org>
>> 
>> Thanks for the review!
>> 
>> CFP will look at making similar changes for cacos, casin, catan, cacosh, casinh, catanh in a future paper.
>> 
>> Regards,
>> 
>> CFP
>>  
>> From: owner-sc22wg14 at open-std.org <owner-sc22wg14 at open-std.org> on behalf of Joseph Myers <josmyers at redhat.com>
>> Date: Monday, October 20, 2025 at 6:58 PM
>> To: sc22wg14 at open-std.org <sc22wg14 at open-std.org>
>> Subject: [EXTERNAL] [SC22WG14.34179] N3731 Range bounds for math functions
>> 
>> A comment on the N3731 proposal to reword specifications about the range
>> of values for mathematical functions where correct rounding might produce
>> a result outside a given interval:
>> 
>> There's similar wording "in the interval" for various <complex.h>
>> functions, where I'd also expect that it should not be required that the
>> rounded result actually lies inside that interval and so the wording
>> should probably have similar changes: cacos, casin, catan, cacosh, casinh,
>> catanh.
>> 
>> --
>> Joseph S. Myers
>> josmyers at redhat.com
>> 
> 
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