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! -- François Pottier francois.pottier@inria.fr http://gallium.inria.fr/~fpottier/

[-- Attachment #1: Type: text/plain, Size: 1399 bytes --] See the Make_random functor in the janestreet Bigint library, which is built on top of zarith. (It's a functor to produce random distributions based on both Random.State.t and Base_quickcheck.Generator.t; the functor itself is not exposed.) https://github.com/janestreet/bignum/blob/master/bigint/src/bigint.ml In short, we generate 30-bit chunks of randomness until we have at least enough bits for our range. We combine those into a number. Usually, we just modulo that by the range and return it. But to preserve fairness, we first have to check if the number is in the last fraction-of-range part of the N bits, and if so retry from scratch. The odds of retry are always less than 50%, so retrying is never too bad. This is the same trick that Random.int does, but with an unbounded number of bits instead of a fixed number of bits. On Wed, Nov 27, 2019 at 4:31 PM François 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 how to program it in an efficient > and correct way. Any suggestions would be welcome. Thanks! > > -- > François Pottier > francois.pottier@inria.fr > http://gallium.inria.fr/~fpottier/ > -- Carl Eastlund [-- Attachment #2: Type: text/html, Size: 2116 bytes --] <div dir="ltr">See the Make_random functor in the janestreet Bigint library, which is built on top of zarith. (It's a functor to produce random distributions based on both Random.State.t and Base_quickcheck.Generator.t; the functor itself is not exposed.)<div><br></div><div><a href="https://github.com/janestreet/bignum/blob/master/bigint/src/bigint.ml" target="_blank">https://github.com/janestreet/bignum/blob/master/bigint/src/bigint.ml</a></div><div><br></div><div>In short, we generate 30-bit chunks of randomness until we have at least enough bits for our range. We combine those into a number. Usually, we just modulo that by the range and return it. But to preserve fairness, we first have to check if the number is in the last fraction-of-range part of the N bits, and if so retry from scratch. The odds of retry are always less than 50%, so retrying is never too bad.</div><div><br></div><div>This is the same trick that Random.int does, but with an unbounded number of bits instead of a fixed number of bits.</div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Wed, Nov 27, 2019 at 4:31 PM François Pottier <<a href="mailto:francois.pottier@inria.fr" target="_blank">francois.pottier@inria.fr</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><br> Hello,<br> <br> I am using zarith and would like to pick a random integer<br> comprised between 0 and some bound. I would like a function<br> Z.random of type Z.t -> Z.t, but this function seems to be<br> missing, and I am not sure how to program it in an efficient<br> and correct way. Any suggestions would be welcome. Thanks!<br> <br> -- <br> François Pottier<br> <a href="mailto:francois.pottier@inria.fr" target="_blank">francois.pottier@inria.fr</a><br> <a href="http://gallium.inria.fr/~fpottier/" rel="noreferrer" target="_blank">http://gallium.inria.fr/~fpottier/</a><br> </blockquote></div><br clear="all"><div><br></div>-- <br><div dir="ltr"><div dir="ltr"><div>Carl Eastlund<br></div></div></div>

On 27/11/2019 22:51, Carl Eastlund wrote: > See the Make_random functor in the janestreet Bigint library, Thanks Carl, this is really helpful! -- François Pottier francois.pottier@inria.fr http://gallium.inria.fr/~fpottier/

[-- Attachment #1: Type: text/plain, Size: 1060 bytes --] On Wednesday, November 27, 2019 22:31 CET, François 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 how to program it in an efficient and correct way. Any suggestions would be welcome. Thanks! I tend to believe that the following idea might be good, but please check with real probability experts. I definitely am not one (but one of my 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 random number and on the next iteration the R would be that P But check with an expert, I am not one -- Basile [-- Attachment #2: Type: text/html, Size: 1325 bytes --] <html><br />On Wednesday, November 27, 2019 22:31 CET, François Pottier <francois.pottier@inria.fr> wrote:<br /> <blockquote type="cite" cite="a025b23b-a84d-164f-7fb9-06a5ee083753@inria.fr"><br />Hello,<br /><br />I am using zarith and would like to pick a random integer<br />comprised between 0 and some bound. I would like a function<br />Z.random of type Z.t -> Z.t, but this function seems to be<br />missing, and I am not sure how to program it in an efficient<br />and correct way. Any suggestions would be welcome. Thanks!<br /><br /> </blockquote><br />I tend to believe that the following idea might be good, but please check with real probability experts. I definitely am not one (but one of my best colleagues is one).<br /><br />Let B be the bound.<br /><br />You take a random number modulus 2*B. Let R be that number<br /><br />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<br /><br /><br />You memoize the previously given random number N<br /><br />On that ring, you go R steps forward and obtain P. That is your new random number and on the next iteration the R would be that P<br /><br />But check with an expert, I am not one<br /><br />--<br /><br />Basile<br /> </html>

[-- Attachment #1: Type: text/plain, Size: 1269 bytes --] On Thursday, November 28, 2019 10:27 CET, basile@starynkevitch.net <basile@starynkevitch.net> wrote: Sorry for the important typo. Corrected below On Wednesday, November 27, 2019 22:31 CET, François 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 how to program it in an efficient and correct way. Any suggestions would be welcome. Thanks! I tend to believe that the following idea might be good, but please check with real probability experts. I definitely am not one (but one of my 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 random 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 [-- Attachment #2: Type: text/html, Size: 1593 bytes --] <html><br />On Thursday, November 28, 2019 10:27 CET, basile@starynkevitch.net <basile@starynkevitch.net> wrote:<br /><br /><br />Sorry for the important typo. Corrected below<br /><br />On Wednesday, November 27, 2019 22:31 CET, François Pottier <francois.pottier@inria.fr> wrote:<br /> <blockquote type="cite" cite="a025b23b-a84d-164f-7fb9-06a5ee083753@inria.fr"><br />Hello,<br /><br />I am using zarith and would like to pick a random integer<br />comprised between 0 and some bound. I would like a function<br />Z.random of type Z.t -> Z.t, but this function seems to be<br />missing, and I am not sure how to program it in an efficient<br />and correct way. Any suggestions would be welcome. Thanks!<br /><br /> </blockquote><br />I tend to believe that the following idea might be good, but please check with real probability experts. I definitely am not one (but one of my best colleagues is one).<br /><br />Let B be the bound.<br /><br />You take a random number modulus 2*B. Let R be that number<br /><br />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<br /><br /><br />You memoize the previously given random number N<br /><br />On that ring, you go R steps forward and obtain P. That is your new random number and on the next iteration the <strong>N</strong> would be that P<br /><br />But check with an expert, I am not one<br /><br />--<br /><br />Basile Starynkevitch http://starynkevitch.net/Basile<br /> <br /><br /><br /> </html>