[seqfan] Re: PARI/GP's random function, A260083

[israel at math.ubc.ca]

I get the same numbers as Hugo, on GP/PARI CALCULATOR Version 2.7.4 
(released).

Cheers,
Robert


On Sep 18 2016, Hugo Pfoertner wrote:

>Seqfans,
>
> Felix Fröhlich's http://oeis.org/A260083 claims to be the numbers 
> produced by PARI's random function when called without argument (i.e. 
> using the default argument 2^31). Nothing is said about initialization, 
> also not in the PARI documentation at 
> http://pari.math.u-bordeaux.fr/dochtml/html/Conversions_and_similar_elementary_functions_or_commands.html
>
>When I try to reproduce the sequence by calling PARI/GP, I get
>GP/PARI CALCULATOR Version 2.5.3 (released)
>
>? for(n=1,10,print(random))
>1546275796
>879788114
>1745191708
>771966234
>1247963869
>1611845387
>1529973242
>2093650929
>1860635684
>1497261229
>...
>
>which differs from A260083: 326511477, 1362174608, 903267448, 656347688,
>1853455872, ...
>
>My results are compliant with the initialization by seed=1 of the internal
>function given in PARI's current source code in function random.c
>
>void pari_init_rand(void) { init_xor4096i(1); }
>
>I get the same result by running Richard Brent's source code from the link
>http://wwwmaths.anu.edu.au/~brent/ftp/random/xorgens305.tar.gz provided at
>http://maths-people.anu.edu.au/~brent/random.html
>
>With an initialization by the seed 1, the function UINT xor4096i(UINT
>seed)  provided by R. Brent yields the 64-bit number sequence in the first
>column, and the PARI random numbers by a right shift of 33.
>
>const int seed0=1;
>
>int main() {
>  UINT i, x, xp, seed=seed0;
>  x = xor4096i(seed);
>  printf("First random number  %llu %lu %llu\n",x, x>>33, seed);
>  for (i=0; i<20; i++) { x=xor4096i(0); xp = x>>33; printf ("%llu %lu\n",x,
>xp); }
>
>First random number
>13282407956253574712 1546275796 1
>7557322358563246340 879788114
>14991082624209354397 1745191708
>6631139461101160670 771966234
>10719928016004921607 1247963869
>13845646450878251009 1611845387
>13142370077570254774 1529973242
>17984324540840297179 2093650929
>15982738825684268908 1860635684
>12861376030615125811 1497261229
>9837491998535547791 1145234796
>10009796384580774444 1165293667
>10598342506117936052 1233809453
>6743270311476307786 785019983
>2169871353760194456 252606271
>959683757796537189 111721893
>4063307077606482163 473031201
>8614063320694916486 1002808953
>5278298332222909972 614474799
>4049421542817092888 471414712
>562706585515371056 65507668
>
>I tried all possible 32-bit seeds, but failed to produce the first term of
>A260083, 326511477.
>
>Can someone please try to run a recent version of PARI to check my and
>Felix's results?
>
>Hugo Pfoertner
>
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>
>