       Re: normal distribution random number generation

• To: mathgroup at smc.vnet.net
• Subject: [mg51217] Re: normal distribution random number generation
• From: koopman at sfu.ca (Ray Koopman)
• Date: Sat, 9 Oct 2004 04:18:30 -0400 (EDT)
• References: <ck0ccp\$o1u\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Bill Rowe <readnewsciv at earthlink.net> wrote in message
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}

```

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