Path: ...!weretis.net!feeder6.news.weretis.net!i2pn.org!i2pn2.org!.POSTED!not-for-mail
From: mitchalsup@aol.com (MitchAlsup1)
Newsgroups: comp.lang.c,comp.arch
Subject: Re: Radians Or =?UTF-8?B?RGVncmVlcz8=?=
Date: Mon, 18 Mar 2024 22:19:19 +0000
Organization: Rocksolid Light
Message-ID: <9a5b9a6a445bd41ff75a93b589982970@www.novabbs.org>
References: <ur5trn$3d64t$1@dont-email.me> <ur5v05$3ccut$1@dont-email.me> <20240222015920.00000260@yahoo.com> <ur69j9$3ftgj$3@dont-email.me> <ur86eg$1aip$1@dont-email.me> <ur88e4$1rr1$5@dont-email.me> <ur8a2p$2446$1@dont-email.me> <ur8ctk$2vbd$2@dont-email.me> <20240222233838.0000572f@yahoo.com> <3b2e86cdb0ee8785b4405ab10871c5ca@www.novabbs.org> <ur8nud$4n1r$1@dont-email.me> <936a852388e7e4414cb7e529da7095ea@www.novabbs.org> <ur9qtp$fnm9$1@dont-email.me> <20240314112655.000011f8@yahoo.com> <jwv1q87l5ou.fsf-monnier+comp.arch@gnu.org>
MIME-Version: 1.0
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Info: i2pn2.org;
	logging-data="2450516"; mail-complaints-to="usenet@i2pn2.org";
	posting-account="PGd4t4cXnWwgUWG9VtTiCsm47oOWbHLcTr4rYoM0Edo";
User-Agent: Rocksolid Light
X-Rslight-Posting-User: ac58ceb75ea22753186dae54d967fed894c3dce8
X-Rslight-Site: $2y$10$SDhewOpTzRidS/IKEccjX.KJp3SZSjGaulWnSOka8OqDLhtAK96oO
X-Spam-Checker-Version: SpamAssassin 4.0.0
Bytes: 3221
Lines: 42

Stefan Monnier wrote:

>>> There are groups who have shown that exactly rounded trancendental
>>> functions are in fact achievable with maybe 3X reduced performance.

> That much?  I had the impression it was significantly cheaper.

The J. M. Muller book indicates about 2× to 2.5×

>> At which cost in tables sizes?

Making transcendental faster is always a tradeoff between table size
and speed. SIN() COS() can use 10-term polynomials when the reduced 
argument is -¼pi..+¼pi, on the other hand, when the reduced argument
is ±0.008 a 3 term polynomial is just as accurate but you need 128×3
tables.

> My impression was that it wasn't costly in that respect, but since my
> recollection seems to be off on the performance, maybe it's off here
> as well.

ITANIC did rather well, here, because it had 2 FMAC units and could use
both for the polynomials.

>> The critical point here is definition of what considered exact. If
>> 'exact' is measured only on y side of y=foo(x), disregarding
>> possible imprecision on the x side then you are very likely to end up
>> with results that are slower to calculate, but not at all more useful
>> from point of view of engineer or physicist. Exactly like Payne-Hanek
>> or Mitch's equivalent of Payne-Hanek.

> I don't know what are/were the motivations for the people working on
> exact transcendentals, but they have applications unrelated to the fact
> that they're "better": the main benefit (from this here PL guy) is that
> it gives them a reliable, reproducible semantics.
> Bit-for-bit reproducibility makes several things much easier.

Consider moving an application which uses libm from machine to machine.
When libm is correctly rounded, there is no issue at all; not so other-
wise.


>         Stefan