From mboxrd@z Thu Jan  1 00:00:00 1970
X-Spam-Checker-Version: SpamAssassin 3.4.6 (2021-04-09) on
	ip-172-31-74-118.ec2.internal
X-Spam-Level: 
X-Spam-Status: No, score=-2.9 required=3.0 tests=BAYES_00,NICE_REPLY_A
	autolearn=ham autolearn_force=no version=3.4.6
Path: eternal-september.org!reader02.eternal-september.org!news.swapon.de!fu-berlin.de!uni-berlin.de!individual.net!not-for-mail
From: Niklas Holsti <niklas.holsti@tidorum.invalid>
Newsgroups: comp.lang.ada
Subject: Re: Ada.Numerics.Big_Numbers.Big_Integer has a limit of 300 digits?
Date: Thu, 23 Dec 2021 14:18:34 +0200
Organization: Tidorum Ltd
Message-ID: <j2j7osFnt0vU1@mid.individual.net>
References: <afc2e263-66d3-4047-aecd-22932484a9a6n@googlegroups.com>
 <spvlm8$qv4$1@gioia.aioe.org>
 <304dcae2-8b20-43ff-8769-32fa06d4dc10n@googlegroups.com>
 <j2h6nrFc4ppU1@mid.individual.net>
 <41879a68-95cf-41e7-a582-4358a39f9d47n@googlegroups.com>
 <j2hb7eFd05oU1@mid.individual.net>
 <1880ebf1-a27a-4ae1-958b-cfb1e1fe50f2n@googlegroups.com>
Mime-Version: 1.0
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Transfer-Encoding: 7bit
X-Trace: individual.net 5O0CP7p+5fMfohUYXt4qhA8Kp7gkvtgQdsbX1LhqlymhCh78XX
Cancel-Lock: sha1:KV5k/hFfqe/KBs8sasoAl4pR3ho=
User-Agent: Mozilla/5.0 (Macintosh; Intel Mac OS X 10.14; rv:78.0)
 Gecko/20100101 Thunderbird/78.14.0
In-Reply-To: <1880ebf1-a27a-4ae1-958b-cfb1e1fe50f2n@googlegroups.com>
Content-Language: en-US
Xref: reader02.eternal-september.org comp.lang.ada:63255
List-Id: <comp.lang.ada>

On 2021-12-23 13:41, AdaMagica wrote:
> Niklas Holsti schrieb am Mittwoch, 22. Dezember 2021 um 20:05:21 UTC+1:
>> However, the
>> Big_Integers package does not directly support computations "mod"
> 
> It does A.5.6(18/5).


Yes, there is a "mod" operator for Big_Integer. My point was that there 
are no Big_Integer operations, such as multiplication, that are 
intrinsically modular in the same way as the operations for modular 
types are. So the only way to perform a modular multiplication of 
Big_Integers is to first multiply the numbers in the usual way, 
producing a possibly very large product, and then apply "mod" to reduce 
that product.

In my imperfect understanding, intrinsically modular big-number 
computations can be much more efficient than such post-computation 
applications of "mod", at least if the modulus is not itself a big number.