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Release calc version 2.11.5t3

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Landon Curt Noll
2001-04-14 16:10:29 -07:00
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help/rand
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@@ -1,5 +1,5 @@
NAME
rand - additive 55 shuffle pseudo-random number generator
rand - subtractive 100 shuffle pseudo-random number generator
SYNOPSIS
rand([[min, ] max])
@@ -11,7 +11,7 @@ TYPES
return integer
DESCRIPTION
Generate a pseudo-random number using an additive 55 shuffle generator.
Generate a pseudo-random number using an subtractive 100 shuffle generator.
We return a pseudo-random number over the half closed interval [min,max).
By default, min is 0 and max is 2^64.
@@ -38,36 +38,40 @@ DESCRIPTION
when seeded with the same seed.
The rand generator has two distinct parts, the additive 55 method
and the shuffle method. The additive 55 method is described in:
The rand generator has two distinct parts, the subtractive 100 method
and the shuffle method. The subtractive 100 method is described in:
"The Art of Computer Programming - Seminumerical Algorithms"
by Knuth, Vol 2, 2nd edition (1981), Section 3.2.2, page 27,
Algorithm A.
"The Art of Computer Programming - Seminumerical Algorithms",
Vol 2, 3rd edition (1998), Section 3.6, page 186, formula (2).
The period and other properties of the additive 55 method
The "use only the first 100 our of every 1009" is described in
Knuth's "The Art of Computer Programming - Seminumerical Algorithms",
Vol 2, 3rd edition (1998), Section 3.6, page 188".
The period and other properties of the subtractive 100 method
make it very useful to 'seed' other generators.
The shuffle method is feed values by the additive 55 method.
The shuffle method is feed values by the subtractive 100 method.
The shuffle method is described in:
"The Art of Computer Programming - Seminumerical Algorithms"
by Knuth, Vol 2, 2nd edition (1981), Section 3.2.2, page 32,
Algorithm B.
"The Art of Computer Programming - Seminumerical Algorithms",
Vol 2, 3rd edition (1998), Section 3.2.2, page 34, Algorithm B.
The rand generator has a good period, and is fast. It is reasonable as
generators go, though there are better ones available. The shuffle
method has a very good period, and is fast. It is fairly good as
generators go, particularly when it is feed reasonably random
numbers. Because of this, we use feed values from the additive 55
numbers. Because of this, we use feed values from the subtractive 100
method into the shuffle method.
The rand generator uses two internal tables:
additive table - 55 entries of 64 bits used by the additive 55 method
additive table - 100 entries of 64 bits used by the subtractive
100 method
shuffle table - 256 entries of 64 bits used by the shuffle method
feed by the additive 55 method from the additive table
feed by the subtractive 100 method from the
subtractive table
The goals of this generator are:
@@ -95,21 +99,21 @@ DESCRIPTION
a standard against which other generators may be measured.
The Rand book of numbers was groups into groups of 20 digits. The
first 55 groups < 2^64 were used to initialize the default additive
first 100 groups < 2^64 were used to initialize the default additive
table. The size of 20 digits was used because 2^64 is 20 digits
long. The restriction of < 2^64 was used to prevent modulus biasing.
The shuffle table size is longer than the 100 entries recommended
by Knuth. We use a power of 2 shuffle table length so that the
shuffle process can select a table entry from a new additive 55
shuffle process can select a table entry from a new subtractive 100
value by extracting its low order bits. The value 256 is convenient
in that it is the size of a byte which allows for easy extraction.
We use the upper byte of the additive 55 value to select the
We use the upper byte of the subtractive 100 value to select the
shuffle table entry because it allows all of 64 bits to play a part
in the entry selection. If we were to select a lower 8 bits in the
64 bit value, carries that propagate above our 8 bits would not
impact the additive 55 generator output.
impact the subtractive 100 generator output.
It is 'nice' when a seed of "n" produces a 'significantly different'
sequence than a seed of "n+1". Generators, by convention, assign
@@ -161,7 +165,7 @@ DESCRIPTION
The values 'a' and 'c for randreseed64 are taken from the Rand book
of numbers. Because m=2^64 is 20 decimal digits long, we will
search the Rand book of numbers 20 at a time. We will skip any of
the 55 values that were used to initialize the additive 55
the 100 values that were used to initialize the subtractive 100
generators. The values obtained from the Rand book are:
a = 6316878969928993981
@@ -190,36 +194,40 @@ DESCRIPTION
The truly paranoid might suggest that my claims in the MAGIC NUMBERS
section are a lie intended to entrap people. Well they are not, but
you need not take my (Landon Curt Noll) word for it.
if you that paranoid why would you use a non-cryprographically strong
pseudo-random number generator in the first place? You would be
better off using the random() builtin function.
The random numbers from the Rand book of random numbers can be
The two constants that were picked from the Rand Book of Random Numbers
The random numbers from the Rand Book of Random Numbers can be
verified by anyone who obtains the book. As these numbers were
created before I (Landon Curt Noll) was born (you can look up my
birth record if you want), I claim to have no possible influence on
their generation.
created before I (Landon Curt Noll) was born (you can look up
my birth record if you want), I claim to have no possible influence
on their generation.
There is a very slight chance that the electronic copy of the
Rand book that I was given access to differs from the printed text.
I am willing to provide access to this electronic copy should
anyone wants to compare it to the printed text.
Rand Book of Random Numbers that I was given access to differs
from the printed text. I am willing to provide access to this
electronic copy should anyone wants to compare it to the printed text.
When using the a55 generator, one may select your own 55 additive
When using the s100 generator, one may select your own 100 subtractive
values by calling:
srand(mat55)
srand(mat100)
and avoid using my magic numbers. Of course, you must pick good
additive 55 values yourself!
and avoid using my magic numbers. The randreseed64 process is NOT
applied to the matrix values. Of course, you must pick good subtractive
100 values yourself!
EXAMPLE
> print srand(0), rand(), rand(), rand()
RAND state 14384206130809570460 10173010522823332484 5713611208311484212
RAND state 2298441576805697181 3498508396312845423 5031615567549397476
> print rand(123), rand(123), rand(123), rand(123), rand(123), rand(123)
17 104 74 47 48 46
106 59 99 99 25 88
> print rand(2,12), rand(2^50,3^50), rand(0,2), rand(-400000, 120000)
11 170570393286648531699560 1 -96605
2 658186291252503497642116 1 -324097
LIMITS
min < max
@@ -248,8 +256,8 @@ SEE ALSO
## received a copy with calc; if not, write to Free Software Foundation, Inc.
## 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA.
##
## @(#) $Revision: 29.2 $
## @(#) $Id: rand,v 29.2 2000/06/07 14:02:33 chongo Exp $
## @(#) $Revision: 29.3 $
## @(#) $Id: rand,v 29.3 2001/04/14 22:46:33 chongo Exp $
## @(#) $Source: /usr/local/src/cmd/calc/help/RCS/rand,v $
##
## Under source code control: 1996/01/01 02:16:09