       Re: Re: normal distribution random number generation

• To: mathgroup at smc.vnet.net
• Subject: [mg51256] Re: [mg51217] Re: normal distribution random number generation
• From: DrBob <drbob at bigfoot.com>
• Date: Sun, 10 Oct 2004 01:57:41 -0400 (EDT)
• References: <ck0ccp\$o1u\$1@smc.vnet.net> <200410090818.EAA09618@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```I'm trying to combine that idea with Andrzej Kozlowski's recent fix for Random, and here's what I came up with:

Unprotect[Random];
With[{m1 = 1/(2.^30 - 1.), m2 = 2^30 - 2},
randomSubstitutionFunction =
Compile[{}, ((Random[Integer, m2] + .5)*m1 + Random[Integer, m2])*m1];
Random[] := randomSubstitutionFunction[]
]
Random[Real, {a_Real, b_Real}] := a + Random[]*(b - a)
Random[Real, b_Real] := Random[Real, {0, b}]
Random[Real] := Random[Real, {0, 1}]
Random[Complex, {a_Complex | a_Real | a_Integer, b_Complex | b_Real | \
b_Integer}] := a + Random[]*Re[(b - a)] + Random[]*Im[(b - a)]*I
Random[Complex] := Random[Complex, {0, 1 + I}]
Protect[Random];

I wanted NOT to use a Global (randomSubstitutionFunction) for the Compiled function, but I haven't stumbled on a way to manage it.

Bobby

On Sat, 9 Oct 2004 04:18:30 -0400 (EDT), Ray Koopman <koopman at sfu.ca> wrote:

> news:<ck0ccp\$o1u\$1 at smc.vnet.net>...
>> [...]
>> you will have modified Random to use the Wolfram rule 30 cellular
>> automaton and avoid the subtract with borrow algorithm. The main
>> consequence of this is Random will now be considerably slower.
>> [...]
>
> If time is an issue, you might want to consider generating integers
> on 0...2^n-2 instead of 0...2^n-1. It's always much faster. And if
> you're willing to spend a little of the time you've saved, you can
> add a half and avoid ever having to worry about getting a zero.
>
> In:= ToString[TableForm[Table[With[{m1 = 2^n - 1, m2 = 2^n - 2},
>         {n, First[Timing[Do[Random[Integer,m1],{1*^6}]]]/.Second->1.,
>             First[Timing[Do[Random[Integer,m2],{1*^6}]]]/.Second->1.}],
>         {n,2,30}],TableSpacing->{0,2}]]
>
> Out= 2   1.96  1.42
>         3   2.12  1.5
>         4   2.38  1.61
>         5   2.66  1.73
>         6   2.91  1.86
>         7   3.16  2.
>         8   3.41  2.1
>         9   3.68  2.19
>         10  3.92  2.35
>         11  4.21  2.56
>         12  4.5   2.68
>         13  4.79  2.82
>         14  5.07  3.02
>         15  5.34  3.08
>         16  5.56  3.26
>         17  5.84  3.38
>         18  6.09  3.53
>         19  6.33  3.64
>         20  6.57  3.77
>         21  6.84  3.87
>         22  7.1   4.03
>         23  7.33  4.2
>         24  7.63  4.25
>         25  7.89  4.37
>         26  8.15  4.56
>         27  8.4   4.61
>         28  8.56  4.79
>         29  8.95  4.95
>         30  9.16  5.07
>
> In:= ran1 = With[{m = 2.^-30, m1 = 2^30 - 1},
>         Compile[{},(Random[Integer,m1]*m + Random[Integer,m1])*m]];
>
> In:= ran2 = With[{m1 = 1/(2.^30 - 1.), m2 = 2^30 - 2},
>         Compile[{},(Random[Integer,m2]*m1 + Random[Integer,m2])*m1]];
>
> In:= ran2h = With[{m1 = 1/(2.^30 - 1.), m2 = 2^30 - 2},
>         Compile[{},((Random[Integer,m2]+.5)*m1+Random[Integer,m2])*m1]];
>
> In:= First/@{Timing@Do[ran1[],{1*^5}],Timing@Do[ran2[],{1*^5}],
>                                          Timing@Do[ran2h[],{1*^5}]}
> Out= {2.03 Second, 1.05 Second, 1.08 Second}
>
>
>
>

--
DrBob at bigfoot.com
www.eclecticdreams.net

```

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