From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: Received: from mail2-relais-roc.national.inria.fr (mail2-relais-roc.national.inria.fr [192.134.164.83]) by c5ff346549e7 (Postfix) with ESMTP id 6ADC45D5 for ; Thu, 28 Nov 2019 09:30:23 +0000 (UTC) X-IronPort-AV: E=Sophos;i="5.69,253,1571695200"; d="scan'208,217";a="413921513" Received: from sympa.inria.fr ([193.51.193.213]) by mail2-relais-roc.national.inria.fr with ESMTP; 28 Nov 2019 10:30:21 +0100 Received: by sympa.inria.fr (Postfix, from userid 20132) id 47F897F38A; Thu, 28 Nov 2019 10:30:21 +0100 (CET) Received: from mail3-relais-sop.national.inria.fr (mail3-relais-sop.national.inria.fr [192.134.164.104]) by sympa.inria.fr (Postfix) with ESMTPS id ED1A47F332 for ; Thu, 28 Nov 2019 10:30:15 +0100 (CET) Authentication-Results: mail3-smtp-sop.national.inria.fr; spf=None smtp.pra=basile@starynkevitch.net; spf=Pass smtp.mailfrom=basile@starynkevitch.net; spf=None smtp.helo=postmaster@relay11.mail.gandi.net IronPort-PHdr: =?us-ascii?q?9a23=3AxSaCvxQUj/uk00iWpVhHXFtygdpsv+yvbD5Q0YIu?= =?us-ascii?q?jvd0So/mwa6zYB2N2/xhgRfzUJnB7Loc0qyK6vumADJfqs7Y+Fk5M7V0Hycfjs?= =?us-ascii?q?sXmwFySOWkMmbcaMDQUiohAc5ZX0Vk9XzoeWJcGcL5ekGA6ibqtW1aFRrwLxd6?= =?us-ascii?q?KfroEYDOkcu3y/qy+5rOaAlUmTaxe7x/IAi4oAnLq8UbgIlvJqktxhfUv3BFZ/?= =?us-ascii?q?lYyWR0KFyJgh3y/N2w/Jlt8yRRv/Iu6ctNWrjkcqo7ULJVEi0oP3g668P3uxbD?= =?us-ascii?q?SxCP5mYHXWUNjhVIGQnF4wrkUZr3ryD3q/By2CiePc3xULA0RTGv5LplRRP0lC?= =?us-ascii?q?sKMSMy/XrJgcJskq1UvBOhpwR+w4HKZoGVKOF+db7Zcd8DWGZNQtpdWylHD4ih?= =?us-ascii?q?bYUAEvABMP5EoIb/p1UAowWwCgavCu3yxDBFnWX50bEg3uk7DQ3Lxg4tEtQTu3?= =?us-ascii?q?rUttX1M6ISXPiuw6bS1jXDbvdW1inm5YjTbhAuu+uMXLJ2ccrS10YvCQLFjkmM?= =?us-ascii?q?pozlJT+V0PoCs3SG5OdnTu2gkXUnqwB1ojex3coskZXJiZgPylHE8yV5w5g6Jc?= =?us-ascii?q?O5SE5nfdGkEIFctyeEOItqW84vRXxjtig9yr0Do5G7fS4KxYw8xx7DcfOHaYiJ?= =?us-ascii?q?4hTgVOmPPzd4hW5ld66/hxqo90iv1PH8W8+p21hJtipIisfAum0P2hDJ6MWLVu?= =?us-ascii?q?Fx8lqj1DuMzQzf9O9JLV0ymKHGMZAu2KQwmYAWsUnbHi/5hkH2jKiOe0U+5Oeo?= =?us-ascii?q?7/7oY7X7qpOBLYN0jxvxMqUqmsClDuQ3KA4OUHWa+eim0r3s41H5TK1Ljv0wjK?= =?us-ascii?q?bZrIjXKdoGqqO7GQNY0Jov5wyiAzqk09kUh2cLIVxYdB6fiojmIVDOIPT2Dfel?= =?us-ascii?q?hFSslS9myOvcMb36A5XNKmbMnaz6fbZh8UFc0goyzdZc551KFLEBIe7zVVPxtN?= =?us-ascii?q?DCCB82LRC0z/79CNphzoMeRX6PAqiBPazOq1CI4+YvL/CIZI8Uozb9N+Mo5+Xu?= =?us-ascii?q?jH88gV8SZ7Ol3ZoRaHCiH/RpOV+VYXT2gt0ZC2cFohI+TPD2iF2FSTNTaW6yX6?= =?us-ascii?q?Ug5jEnCYKpE53DS5usgbyA2Se0BYdWaXpcBlCNF3fobYSEVO0WZCKcOM8y2gAD?= =?us-ascii?q?AJa7Qomu0hC1gzf916ZmI/CcriMCvJTo09luofXUiQ0z+CZcDsKH0mjLQXsizU?= =?us-ascii?q?0SQDpj1qlkoEhw4kyf2LJphf9VC91P7PMPVAomfcrWxvd7D93aQR7IZMaPS1u4?= =?us-ascii?q?Q8mtAXc3Q85nkIxGWFp0B9j31kOL5CGtGbJA0uXTXMVpoJKZ5GD4IoNG81iD1K?= =?us-ascii?q?QliAN6ENFCMWS33/c58gHSA8jGmkOVluCseLhOhHecplfG9nKHuQRjaCA1VKzE?= =?us-ascii?q?WX4FYU6P/Ibi+krYXrmtBKomLgBBj8iPNvkTM4G7vRB9XP7mfe/mTSepgW7pVE?= =?us-ascii?q?ST2rqWfYzpdnscwC7dTk4Jj1JL8A=3D=3D?= X-IronPort-Anti-Spam-Filtered: true X-IronPort-Anti-Spam-Result: =?us-ascii?q?A0DPAQAdk99dh+eyRtllHgELHIUACiwpM?= =?us-ascii?q?iqEK5BuhSGKIIwRCQEDAQwfEAEBhEACTAEIgS4cBwEENBMCEAEBBAEBAQIBAgM?= =?us-ascii?q?EARMBAQEIDQkIKYU+DIIpEikBgm4DAyMERA4bBD4CWQYTgyIBgnuyNn8ziSIjg?= =?us-ascii?q?Q+BNoUbhDaCRRo+AYFBgTsJgmA+glmFAIJeBI0zkXWOInAHgjGGOWSOYoI0c4Z?= =?us-ascii?q?4j3WVfoEGhQ2JUEWCX4FpgXp7CjuCbAlHERSLBogyhXtAAzCRRwEB?= X-IPAS-Result: =?us-ascii?q?A0DPAQAdk99dh+eyRtllHgELHIUACiwpMiqEK5BuhSGKIIw?= =?us-ascii?q?RCQEDAQwfEAEBhEACTAEIgS4cBwEENBMCEAEBBAEBAQIBAgMEARMBAQEIDQkIK?= =?us-ascii?q?YU+DIIpEikBgm4DAyMERA4bBD4CWQYTgyIBgnuyNn8ziSIjgQ+BNoUbhDaCRRo?= =?us-ascii?q?+AYFBgTsJgmA+glmFAIJeBI0zkXWOInAHgjGGOWSOYoI0c4Z4j3WVfoEGhQ2JU?= =?us-ascii?q?EWCX4FpgXp7CjuCbAlHERSLBogyhXtAAzCRRwEB?= X-IronPort-AV: E=Sophos;i="5.69,253,1571695200"; d="scan'208,217";a="328328963" X-MGA-submission: =?us-ascii?q?MDHrpPc/yo52IcVDmDPAsy5fiJCW2vFVFXiMKm?= =?us-ascii?q?Zaf1skuL7S2S7dxaMDBm/Hv3Npx4/Yiof6xAKeecduXarXt8n+m0RXjN?= =?us-ascii?q?S66FO4IJ2qrl79dWaQVNI8wFQOl4tuAZ254o47iXTyrF8QI0SwqhriYD?= =?us-ascii?q?USUYHT3iTFpVXb2at2bbDywA=3D=3D?= Received: from relay11.mail.gandi.net ([217.70.178.231]) by mail3-smtp-sop.national.inria.fr with ESMTP/TLS/DHE-RSA-AES256-GCM-SHA384; 28 Nov 2019 10:30:14 +0100 Received: from sogo10.sd4.0x35.net (sogo10.sd4.0x35.net [10.200.201.60]) (Authenticated sender: basile@starynkevitch.net) by relay11.mail.gandi.net (Postfix) with ESMTPA id 9F20F10001B; Thu, 28 Nov 2019 09:30:10 +0000 (UTC) Content-Type: multipart/alternative; boundary="----=_=-_OpenGroupware_org_NGMime-8117-1574933410.309710-52------" In-Reply-To: <5cef-5ddf9300-35-4e2fd700@138599352> From: =?utf-8?q?basile=40starynkevitch=2Enet?= X-Forward: 127.0.0.1 Date: Thu, 28 Nov 2019 10:30:10 +0100 Cc: caml-list@inria.fr To: =?utf-8?q?Fran=C3=A7ois_Pottier?= MIME-Version: 1.0 Message-ID: <1fb5-5ddf9380-79-5558b880@243503475> User-Agent: SOGoMail 4.0.8 Subject: Re: [Caml-list] zarith: how to pick a random integer? Reply-To: =?utf-8?q?basile=40starynkevitch=2Enet?= X-Loop: caml-list@inria.fr X-Sequence: 17890 Errors-to: caml-list-owner@inria.fr Precedence: list Precedence: bulk Sender: caml-list-request@inria.fr X-no-archive: yes List-Id: List-Archive: List-Help: List-Owner: List-Post: List-Subscribe: List-Unsubscribe: ------=_=-_OpenGroupware_org_NGMime-8117-1574933410.309710-52------ Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: quoted-printable Content-Length: 1267 On Thursday, November 28, 2019 10:27 CET, basile@starynkevitch.net wrote: Sorry for the important typo. Corrected below On Wednesday, November 27, 2019 22:31 CET, Fran=C3=A7ois Pottier wrote: =C2=A0 Hello, I am using zarith and would like to pick a random integer comprised between 0 and some bound. I would like a function Z.random of type Z.t -> Z.t, but this function seems to be missing, and I am not sure how to program it in an efficient and correct way. Any suggestions would be welcome. Thanks! =C2=A0 I tend to believe that the following idea might be good, but please che= ck with real probability experts. I definitely am not one (but one of m= y best colleagues is one). Let B be the bound. You take a random number modulus 2*B. Let R be that number You modelize the [0;B[ interval as a ring of numbers. For example if B = is 5 : 0 -> 1 -> 2 -> 3 -> 4 -> 0 -> 1 -> .... ad infinitium You memoize the previously given random number N On that ring, you go R steps forward and obtain P. That is your new ran= dom number and on the next iteration the N would be that P But check with an expert, I am not one -- Basile Starynkevitch http://starynkevitch.net/Basile =C2=A0 =C2=A0 ------=_=-_OpenGroupware_org_NGMime-8117-1574933410.309710-52------ Content-Type: text/html; charset=utf-8 Content-Transfer-Encoding: quoted-printable Content-Length: 1665
On Thursday, November 28, 2019 10:27 CET, basile@starynkevi= tch.net <basile@starynkevitch.net> wrote:


Sorry = for the important typo. Corrected below

On Wednesday, Novemb= er 27, 2019 22:31 CET, Fran=C3=A7ois Pottier <francois.pottier@inria= .fr> wrote:
 

Hello,

I am using = zarith and would like to pick a random integer
comprised between 0= and some bound. I would like a function
Z.random of type Z.t ->= ; Z.t, but this function seems to be
missing, and I am not sure ho= w to program it in an efficient
and correct way. Any suggestions w= ould be welcome. Thanks!

 

I tend to = believe that the following idea might be good, but please check with re= al probability experts. I definitely am not one (but one of my best col= leagues is one).

Let B be the bound.

You take a r= andom number modulus 2*B. Let R be that number

You modelize = the [0;B[ interval as a ring of numbers. For example if B is 5 : 0 ->= ; 1 -> 2 -> 3 -> 4 -> 0 -> 1 -> .... ad infinitium

You memoize the previously given random number N
On that ring, you go R steps forward and obtain P. That is your new= random number and on the next iteration the N would b= e that P

But check with an expert, I am not one

-= -

Basile Starynkevitch http://starynkevitch.net/Basile
=  


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