# RNGs: A Super KISS

Discussion in 'C Programming' started by geo, Nov 3, 2009.

1. ### geoGuest

/*
For those mesmerized (or Mersenne-ized?) by a RNG
with period 2^19937-1, I offer one here with period
54767*2^1337279---over 10^396564 times as long.
It is one of my CMWC (Complimentary-Multiply-With-Carry) RNGs,
and is suggested here as one of the components of a
super-long-period KISS (Keep-It-Simple-Stupid) RNG.

With b=2^32 and a=7010176, and given a 32-bit x, and a 32-bit c, this
generator produces a new x,c by forming 64-bit t=a*x+c then replacing:
c=top 32 bits of t and x=(b-1)-(bottom 32 bits of t). In C: c=t>>32;
x=~t;

For many years, CPUs have had machine instructions to form such a
64-bit t and extract the top and bottom halves, but unfortunately
only recent Fortran versions have means to easily invoke them.

Ability to do those extractions leads to implementations that are
simple
and extremely fast---some 140 million per second on my desktop PC.

Used alone, this generator passes all the Diehard Battery of Tests,
but
its simplicity makes it well-suited to serve as one of the three
components
of a KISS RNG, based on the Keep-It-Simple-Stupid principle, and the
idea,
supported by both theory and practice, that the combination of RNGs
based on
different mathematical models can be no worse---and is usually
better---than
any of the components.

So here is a complete C version of what might be called a SUPER KISS
RNG,
combining, by addition mod 2^32, a Congruential RNG, a Xorshift RNG
and the super-long-period CMWC RNG:
*/

#include <stdio.h>
static unsigned long Q
[41790],indx=41790,carry=362436,xcng=1236789,xs=521288629;

#define CNG ( xcng=69609*xcng+123 ) /*Congruential*/
#define XS ( xs^=xs<<13, xs^=(unsigned)xs>>17, xs^=xs>>5 ) /
*Xorshift*/
#define SUPR ( indx<41790 ? Q[indx++] : refill() )
#define KISS SUPR+CNG+XS

int refill( )
{ int i; unsigned long long t;
for(i=0;i<41790;i++) { t=7010176LL*Q+carry; carry=(t>>32); Q=~
(t);}
indx=1; return (Q[0]);
}

int main()
{unsigned long i,x;
for(i=0;i<41790;i++) Q=CNG+XS;
for(i=0;i<1000000000;i++) x=KISS;
printf(" x=%d.\nDoes x=-872412446?\n",x);
}

/*
Running this program should produce 10^9 KISSes in some 7-15 seconds.
You are invited to cut, paste, compile and run for yourself, checking
to
see if the last value is as designated, (formatted as a signed integer
for
potential comparisons with systems using signed integers).
You may want to report or comment on implementations for other
languages.

The arithmetic operations are suited for either signed or unsigned
integers.
Thus, with (64-bit)t=a*x+c, x=t%b in C or x=mod(t,b) in Fortran, and
c=c/b in either C or Fortran, but with ways to avoid integer
divisions,
and subsequent replacement of x by its base-b complement, ~x in C.

With b=2^32 and p=54767*2^1337287+1, the SUPR part of this Super KISS
uses my CMWC method to produce, in reverse order, the base-b expansion
of k/p for some k determined by the values used to seed the Q array.
The period is the order of b for that prime p:
(It took a continuous run of 24+ days on an earlier PC to
establish that order. My thanks to the wizards behind PFGW
and to Phil Carmody for some suggested code.)

Even the Q's all zero, should seeding be overlooked in main(),
will still produce a sequence of the required period, but will
put the user in a strange and exceedingly rare place in the entire
sequence. Users should choose a reasonable number of the 1337280
random bits that a fully-seeded Q array requires.

Using your own choices of merely 87 seed bits, 32 each for xcng,xs
and 23 for carry<7010176, then initializing the Q array with
for(i=0;i<41790;i++) Q=CNG+XS;
should serve well for many applications, but others, such as in
Law or Gaming, where a minimum number of possible outcomes may be
required, might need more of the 1337280 seed bits for the Q array.

As might applications in cryptography: With an unknown but fully-
seeded Q array, a particular string of, say, 41000 successive SUPR
values will appear at more than 2^20000 locations in the full
sequence,
making it virtually impossible to get the location of that particular
string in the full loop, and thus predict coming or earlier values,
even if able to undo the CNG+XS operations.
*/

/*
So I again invite you to cut, paste, compile and run the above C
program.
1000 million KISSes should be generated, and the specified result
appear,
by the time you count slowly to fifteen.
(Without an optimizing compiler, you may have to count more slowly.)
*/

/* George Marsaglia */

geo, Nov 3, 2009

2. ### user923005Guest

On Nov 3, 7:46 am, geo <> wrote:
> /*
> For those mesmerized (or Mersenne-ized?) by a RNG
> with period 2^19937-1, I offer one here with period
> 54767*2^1337279---over 10^396564 times as long.
> It is one of my CMWC (Complimentary-Multiply-With-Carry) RNGs,
> and is suggested here as one of the components of a
> super-long-period KISS (Keep-It-Simple-Stupid) RNG.
>
> With b=2^32 and a=7010176, and given a 32-bit x, and a 32-bit c, this
> generator produces a new x,c by forming 64-bit t=a*x+c then replacing:
> c=top 32 bits of t and x=(b-1)-(bottom 32 bits of t). In C: c=t>>32;
> x=~t;
>
> For many years, CPUs have had machine instructions to form such a
> 64-bit t and extract the top and bottom halves, but unfortunately
> only recent Fortran versions have means to easily invoke them.
>
> Ability to do those extractions leads to implementations that are
> simple
> and extremely fast---some 140 million per second on my desktop PC.
>
> Used alone, this generator passes all the Diehard Battery of Tests,
> but
> its simplicity makes it well-suited to serve as one of the three
> components
> of a KISS RNG, based on the Keep-It-Simple-Stupid principle, and the
> idea,
> supported by both theory and practice, that the combination of RNGs
> based on
> different mathematical models can be no worse---and is usually
> better---than
> any of the components.
>
> So here is a complete C version of what might be called a SUPER KISS
> RNG,
> combining, by addition mod 2^32, a Congruential RNG, a Xorshift RNG
> and the super-long-period CMWC RNG:
> */
>
> #include <stdio.h>
> static unsigned long Q
> [41790],indx=41790,carry=362436,xcng=1236789,xs=521288629;
>
> #define CNG ( xcng=69609*xcng+123 )    /*Congruential*/
> #define XS  ( xs^=xs<<13, xs^=(unsigned)xs>>17, xs^=xs>>5 )  /
> *Xorshift*/
> #define SUPR ( indx<41790 ? Q[indx++] : refill() )
> #define KISS SUPR+CNG+XS
>
>   int refill( )
>   { int i; unsigned long long t;
>   for(i=0;i<41790;i++) { t=7010176LL*Q+carry; carry=(t>>32); Q=~
> (t);}
>   indx=1; return (Q[0]);
>   }
>
> int main()
> {unsigned long i,x;
>  for(i=0;i<41790;i++) Q=CNG+XS;
>  for(i=0;i<1000000000;i++) x=KISS;
>  printf("     x=%d.\nDoes x=-872412446?\n",x);
>
> }
>
> /*
> Running this program should produce 10^9 KISSes in some 7-15 seconds.
> You are invited to cut, paste, compile and run for yourself, checking
> to
> see if the last value is as designated, (formatted as a signed integer
> for
> potential comparisons with systems using signed integers).
> You may want to report or comment on implementations for other
> languages.
>
> The arithmetic operations are suited for either signed or unsigned
> integers.
> Thus, with  (64-bit)t=a*x+c,  x=t%b in C or x=mod(t,b) in Fortran, and
> c=c/b in either C or Fortran, but with ways to avoid integer
> divisions,
> and subsequent replacement of x by its base-b complement, ~x in C.
>
> With b=2^32 and p=54767*2^1337287+1, the SUPR part of this Super KISS
> uses my CMWC method to produce, in reverse order, the base-b expansion
> of k/p for some k determined by the values used to seed the Q array.
> The period is the order of b for that prime p:
>    54767*2^1337279, about 2^1337294 or 10^402566.
> (It took a continuous run of 24+ days on an earlier PC to
> establish that order.  My thanks to the wizards behind PFGW
> and to Phil Carmody for some suggested code.)
>
> Even the Q's all zero, should seeding be overlooked in main(),
> will still produce a sequence of the required period, but will
> put the user in a strange and exceedingly rare place in the entire
> sequence.  Users should choose a reasonable number of the 1337280
> random bits that a fully-seeded  Q array requires.
>
> Using your own choices of merely 87 seed bits, 32 each for xcng,xs
> and 23 for carry<7010176, then initializing the Q array with
>             for(i=0;i<41790;i++) Q=CNG+XS;
> should serve well for many applications, but others, such as in
> Law or Gaming, where a minimum number of possible outcomes may be
> required, might need more of the 1337280 seed bits for the Q array.
>
> As might applications in cryptography: With an unknown but fully-
> seeded Q array, a particular string of, say, 41000 successive SUPR
> values will appear at more than 2^20000 locations in the full
> sequence,
> making it virtually impossible to get the location of that particular
> string in the full loop, and thus predict coming or earlier values,
> even if able to undo the CNG+XS operations.
> */
>
> /*
> So I again invite you to cut, paste, compile and run the above C
> program.
> 1000 million KISSes should be generated, and the specified result
> appear,
> by the time you count slowly to fifteen.
> (Without an optimizing compiler, you may have to count more slowly.)
> */
>
> /* George Marsaglia */

/*
Here is a C++ version. The C version is quite a bit faster
because there are no function calls at all.
Can any of you C++ gurus bump the speed without losing encapsulation?
I get about 5 seconds for the C version and about 8 seconds for the
C++ version.

-- d.corbit
*/

#include <iostream>
/*
For those mesmerized (or Mersenne-ized?) by a RNG
with period 2^19937-1, I offer one here with period
54767*2^1337279---over 10^396564 times as long.
It is one of my CMWC (Complimentary-Multiply-With-Carry) RNGs,
and is suggested here as one of the components of a
super-long-period KISS (Keep-It-Simple-Stupid) RNG.

With b=2^32 and a=7010176, and given a 32-bit x, and a 32-bit c, this
generator produces a new x,c by forming 64-bit t=a*x+c then replacing:
c=top 32 bits of t and x=(b-1)-(bottom 32 bits of t). In C: c=t>>32;
x=~t;

For many years, CPUs have had machine instructions to form such a
64-bit t and extract the top and bottom halves, but unfortunately
only recent Fortran versions have means to easily invoke them.

Ability to do those extractions leads to implementations that are
simple
and extremely fast---some 140 million per second on my desktop PC.

Used alone, this generator passes all the Diehard Battery of Tests,
but
its simplicity makes it well-suited to serve as one of the three
components
of a KISS RNG, based on the Keep-It-Simple-Stupid principle, and the
idea,
supported by both theory and practice, that the combination of RNGs
based on
different mathematical models can be no worse---and is usually
better---than
any of the components.

So here is a complete C version of what might be called a SUPER KISS
RNG,
combining, by addition mod 2^32, a Congruential RNG, a Xorshift RNG
and the super-long-period CMWC RNG:
*/

class SuperKiss {

private:
unsigned long Q[41790];
unsigned long indx;
unsigned long carry;
unsigned long xcng;
unsigned long xs;

int refill ()
{
int i;
unsigned long long t;
for (i = 0; i < 41790; i++)
{
t = 7010176LL * Q + carry;
carry = (t >> 32);
Q = ~(t);
}
indx = 1;
return (Q[0]);
}

public:
// Constructor:
SuperKiss()
{
indx = 41790;
carry = 362436;
xcng = 1236789;
xs = 521288629;
unsigned i;
for (i = 0; i < 41790; i++)
Q = (xcng = 69609 * xcng + 123) +
(xs ^= xs << 13, xs ^= (unsigned) xs >> 17, xs ^=
xs >> 5);
}

// Collect next random number:
unsigned long SKRand() {
return (indx < 41790 ? Q[indx++] : refill ()) +
(xcng = 69609 * xcng + 123) +
(xs ^= xs << 13, xs ^= (unsigned) xs >> 17, xs ^= xs >>
5);
}
};

int
main ()
{
unsigned long i
int x;
SuperKiss sk;
for (i = 0; i < 1000000000; i++)
x = sk.SKRand();
std::cout << " x = " << x << std::endl << "does Does
x=-872412446?" << std::endl;
return 0;
}

/*
Running this program should produce 10^9 KISSes in some 7-15 seconds.
You are invited to cut, paste, compile and run for yourself, checking
to
see if the last value is as designated, (formatted as a signed integer
for
potential comparisons with systems using signed integers).
You may want to report or comment on implementations for other
languages.

The arithmetic operations are suited for either signed or unsigned
integers.
Thus, with (64-bit)t=a*x+c, x=t%b in C or x=mod(t,b) in Fortran, and
c=c/b in either C or Fortran, but with ways to avoid integer
divisions,
and subsequent replacement of x by its base-b complement, ~x in C.

With b=2^32 and p=54767*2^1337287+1, the SUPR part of this Super KISS
uses my CMWC method to produce, in reverse order, the base-b expansion
of k/p for some k determined by the values used to seed the Q array.
The period is the order of b for that prime p:
(It took a continuous run of 24+ days on an earlier PC to
establish that order. My thanks to the wizards behind PFGW
and to Phil Carmody for some suggested code.)

Even the Q's all zero, should seeding be overlooked in main(),
will still produce a sequence of the required period, but will
put the user in a strange and exceedingly rare place in the entire
sequence. Users should choose a reasonable number of the 1337280
random bits that a fully-seeded Q array requires.

Using your own choices of merely 87 seed bits, 32 each for xcng,xs
and 23 for carry<7010176, then initializing the Q array with
for(i=0;i<41790;i++) Q=CNG+XS;
should serve well for many applications, but others, such as in
Law or Gaming, where a minimum number of possible outcomes may be
required, might need more of the 1337280 seed bits for the Q array.

As might applications in cryptography: With an unknown but fully-
seeded Q array, a particular string of, say, 41000 successive SUPR
values will appear at more than 2^20000 locations in the full
sequence,
making it virtually impossible to get the location of that particular
string in the full loop, and thus predict coming or earlier values,
even if able to undo the CNG+XS operations.
*/

/*
So I again invite you to cut, paste, compile and run the above C
program.
1000 million KISSes should be generated, and the specified result
appear,
by the time you count slowly to fifteen.
(Without an optimizing compiler, you may have to count more slowly.)
*/

/* George Marsaglia */

user923005, Nov 3, 2009

3. ### Tom St DenisGuest

On Nov 3, 10:46 am, geo <> wrote:
>   int refill( )
>   { int i; unsigned long long t;
>   for(i=0;i<41790;i++) { t=7010176LL*Q+carry; carry=(t>>32); Q=~
> (t);}
>   indx=1; return (Q[0]);
>   }

Not to nitpick but your C code could use some work. First off, some
indentation please? Second, returning a unsigned long long as "int"
is not very portable.

Part of the good thing of PRNGs is that they're reproduceable.
Ideally over different platforms. You should truncate the return
value if you want it as "int" or change the return type. As it stands
now this will produce different results on my x86-32 and 64 boxes for
the same seed, which is a bad thing.

Tom

Tom St Denis, Nov 3, 2009
4. ### user923005Guest

On Nov 3, 12:23 pm, user923005 <> wrote:
I copied and pasted from the wrong file. Here is the correct code
[snip]
class SuperKiss {

private:
unsigned long Q[41790];
unsigned long indx;
unsigned long carry;
unsigned long xcng;
unsigned long xs;

int refill ()
{
int i;
unsigned long long t;
for (i = 0; i < 41790; i++)
{
t = 7010176LL * Q + carry;
carry = (t >> 32);
Q = ~(t);
}
indx = 1;
return (Q[0]);
}

public:
// Constructor:
SuperKiss()
{
indx = 41790;
carry = 362436;
xcng = 1236789;
xs = 521288629;
unsigned i;
for (i = 0; i < 41790; i++)
Q = (xcng = 69609 * xcng + 123) +
(xs ^= xs << 13, xs ^= (unsigned) xs >> 17, xs ^=
xs >> 5);
}

// Collect next random number:
unsigned long SKRand() {
return (indx < 41790 ? Q[indx++] : refill ()) +
(xcng = 69609 * xcng + 123) +
(xs ^= xs << 13, xs ^= (unsigned) xs >> 17, xs ^= xs >>
5);
}
};

int
main ()
{
unsigned long i;
int x=0;
SuperKiss sk;
for (i = 0; i < 1000000000; i++)
x = sk.SKRand();
std::cout << " x = " << x << std::endl << "Does x=-872412446?"
<< std::endl;
return 0;
}

user923005, Nov 3, 2009
5. ### user923005Guest

On Nov 3, 12:39 pm, James Waldby <> wrote:
> On Tue, 03 Nov 2009 07:46:27 -0800, George Marsaglia wrote:  ...
> > For those mesmerized (or Mersenne-ized?) by a RNG with period 2^19937-1,
> > I offer one here with period 54767*2^1337279---over 10^396564 times as
> > long. It is one of my CMWC (Complimentary-Multiply-With-Carry) RNGs, and
> > is suggested here as one of the components of a super-long-period KISS
> > (Keep-It-Simple-Stupid) RNG.

> ...
> > static unsigned long Q[41790],indx=41790,carry=362436,xcng=1236789,xs=521288629;

> ...
> > {unsigned long i,x;

> ...
> >  printf("     x=%d.\nDoes x=-872412446?\n",x);

> ...
> > Running this program should produce 10^9 KISSes in some 7-15 seconds.

> ...
> > So I again invite you to cut, paste, compile and run the above C
> > program.
> > 1000 million KISSes should be generated, and the specified result
> > appear [...]

>
> I've snipped the program except for three lines that apparently must
> differ depending upon cpu word length.  On my 64-bit Athlon X2 5200+
> (1GHz) with gcc 4.1.2, and %d changed to %ld, the output (after 7.5
> seconds) contains "x=2904265093743181565."; or, with instead long
> changed to int in two places,  "x=-872412446." (after 7.3 seconds).
>

I get the same results on:
64 bit Windows using the 64 bit MS compiler
64 bit Windows using the 32 bit MS compiler
64 bit Windows using the 64 bit Mingw GCC compiler
64 bit OpenVMS (Itanium) using HP CXX
64 bit OpenVMS (Alpha) using HP CXX
32 bit OpenVMS (VAX) using HP CXX (Had to remove the std:: because of
old compiler, expect a very long wait)
Solaris 5.9 is interesting because it is big-endian, in contrast with
those previously mentioned:
/export/home/dcorbit> uname -a
SunOS solaris9 5.9 Generic_118558-11 sun4u sparc SUNW,Sun-Fire-V210
/export/home/dcorbit> gcc --version
gcc (GCC) 4.0.2
Copyright (C) 2005 Free Software Foundation, Inc.
This is free software; see the source for copying conditions. There
is NO
warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR
PURPOSE.
/export/home/dcorbit> ./a.out
x = -872412446
Does x=-872412446?
/export/home/dcorbit>

user923005, Nov 3, 2009
6. ### Dann CorbitGuest

In article <4fd3c8bf-e45b-4359-ac50-f54298b14770
>
> On Nov 3, 10:46 am, geo <> wrote:
> >   int refill( )
> >   { int i; unsigned long long t;
> >   for(i=0;i<41790;i++) { t=7010176LL*Q+carry; carry=(t>>32); Q=~
> > (t);}
> >   indx=1; return (Q[0]);
> >   }

>
> Not to nitpick but your C code could use some work. First off, some
> indentation please? Second, returning a unsigned long long as "int"
> is not very portable.

The O.P. is George Marsaglia. If there were a Mt. Rushmore for computer
science, Donald Knuth would be George Washington's bust, but Marsaglia
would be up there somewhere too. If it were random numbers, then Mr.
Marsaglia is front and center.

IMO-YMMV

> Part of the good thing of PRNGs is that they're reproduceable.
> Ideally over different platforms. You should truncate the return
> value if you want it as "int" or change the return type. As it stands
> now this will produce different results on my x86-32 and 64 boxes for
> the same seed, which is a bad thing.

Did you actually try it?
What compilers were you using?
I get the same result regardless of compiler, hardware and OS.

Dann Corbit, Nov 3, 2009
7. ### DavidGuest

On an x86-64 machine using GCC version 4.3.3 (Ubuntu 4.3.3-5ubuntu4),
both the C code and C++ code fail for me.
I get:
x=505478909.
Does x=-872412446?

Changing the unsigned long's to unsigned int's fixed the problem.
And it does matter: before the change, the generator failed a variety
of tests (really odd assortment, though: parking lot, 2dsphere,
3dsphere, squeeze, and sums).

David

David, Nov 4, 2009
8. ### user923005Guest

On Nov 4, 9:18 am, David <> wrote:
> On an x86-64 machine using GCC version 4.3.3 (Ubuntu 4.3.3-5ubuntu4),
> both the C code and C++ code fail for me.
> I get:
>      x=505478909.
> Does x=-872412446?
>
> Changing the unsigned long's to unsigned int's fixed the problem.
> And it does matter: before the change, the generator failed a variety
> of tests (really odd assortment, though: parking lot, 2dsphere,
> 3dsphere, squeeze, and sums).

OK, makes sense. The RNG must assume 32 bit longs.

user923005, Nov 4, 2009
9. ### user923005Guest

On Nov 4, 1:26 pm, user923005 <> wrote:
> On Nov 4, 9:18 am, David <> wrote:
>
> > On an x86-64 machine using GCC version 4.3.3 (Ubuntu 4.3.3-5ubuntu4),
> > both the C code and C++ code fail for me.
> > I get:
> >      x=505478909.
> > Does x=-872412446?

>
> > Changing the unsigned long's to unsigned int's fixed the problem.
> > And it does matter: before the change, the generator failed a variety
> > of tests (really odd assortment, though: parking lot, 2dsphere,
> > 3dsphere, squeeze, and sums).

>
> OK, makes sense.  The RNG must assume 32 bit longs.

Modified C++ code:

#include <iostream>

class SuperKiss {

private:
unsigned int Q[41790];
unsigned int indx;
unsigned int carry;
unsigned int xcng;
unsigned int xs;

int refill ()
{
int i;
unsigned long long t;
for (i = 0; i < 41790; i++)
{
t = 7010176LL * Q + carry;
carry = (t >> 32);
Q =(unsigned int) ~(t);
}
indx = 1;
return (Q[0]);
}

public:
// Constructor:
SuperKiss()
{
indx = 41790;
carry = 362436;
xcng = 1236789;
xs = 521288629;
unsigned i;
for (i = 0; i < 41790; i++)
Q = (xcng = 69609 * xcng + 123) +
(xs ^= xs << 13, xs ^= (unsigned) xs >> 17, xs ^=
xs >> 5);
}

// Collect next random number:
unsigned int SKRand() {
return (indx < 41790 ? Q[indx++] : refill ()) +
(xcng = 69609 * xcng + 123) +
(xs ^= xs << 13, xs ^= (unsigned) xs >> 17, xs ^= xs >>
5);
}
};

int
main ()
{
unsigned int i;
int x=0;
SuperKiss sk;
for (i = 0; i < 1000000000; i++)
x = sk.SKRand();
std::cout << " x = " << x << std::endl << "Does x=-872412446?"
<< std::endl;
return 0;
}

/* Possible output:
x = -872412446
Does x=-872412446?
*/

user923005, Nov 4, 2009