\" $NetBSD: rand48.3,v 1.14 2021/02/16 14:44:25 riastradh Exp $
\"
\" Copyright (c) 1993 Martin Birgmeier
\" All rights reserved.
\"
\" You may redistribute unmodified or modified versions of this source
\" code provided that the above copyright notice and this and the
\" following conditions are retained.
\"
\" This software is provided ``as is'', and comes with no warranties
\" of any kind. I shall in no event be liable for anything that happens
\" to anyone/anything when using this software.
\"
Dd February 22, 2020
Dt RAND48 3
Os
Sh NAME
Nm drand48 ,
Nm erand48 ,
Nm lrand48 ,
Nm nrand48 ,
Nm mrand48 ,
Nm jrand48 ,
Nm srand48 ,
Nm seed48 ,
Nm lcong48
Nd pseudo-random number generators and initialization routines
Sh LIBRARY
Lb libc
Sh SYNOPSIS
In stdlib.h
Ft double
Fn drand48 void
Ft double
Fn erand48 "unsigned short xseed[3]"
Ft long
Fn lrand48 void
Ft long
Fn nrand48 "unsigned short xseed[3]"
Ft long
Fn mrand48 void
Ft long
Fn jrand48 "unsigned short xseed[3]"
Ft void
Fn srand48 "long seed"
Ft "unsigned short *"
Fn seed48 "unsigned short xseed[3]"
Ft void
Fn lcong48 "unsigned short p[7]"
Sh DESCRIPTION
The
Fn rand48
family of functions generates pseudo-random numbers using a linear
congruential algorithm working on integers 48 bits in size.
The particular formula employed is
r(n+1) = (a * r(n) + c) mod m
where the default values are
for the multiplicand a = 0x5deece66d = 25214903917 and
the addend c = 0xb = 11.
The modulus is always fixed at m = 2 ** 48.
r(n) is called the seed of the random number generator.
Pp
For all the six generator routines described next, the first
computational step is to perform a single iteration of the algorithm.
Pp
Fn drand48
and
Fn erand48
return values of type double.
The full 48 bits of r(n+1) are loaded into the significand of the
returned value, with the exponent set such that the values produced
lie in the interval [0.0, 1.0).
Pp
Fn lrand48
and
Fn nrand48
return values of type long in the range [0, 2**31-1].
The high-order (31) bits of r(n+1) are loaded into the lower bits
of the returned value, with the topmost (sign) bit set to zero.
Pp
Fn mrand48
and
Fn jrand48
return values of type long in the range [-2**31, 2**31-1].
The high-order (32) bits of r(n+1) are loaded into the returned value.
Pp
Fn drand48 ,
Fn lrand48 ,
and
Fn mrand48
use an internal buffer to store r(n).
For these functions
the initial value of r(0) = 0x1234abcd330e = 20017429951246.
Pp
On the other hand,
Fn erand48 ,
Fn nrand48 ,
and
Fn jrand48
use a user-supplied buffer to store the seed r(n), which consists
of an array of 3 unsigned shorts, where the zeroth member holds the least
significant bits.
Pp
All functions share the same multiplicand and addend.
Pp
Fn srand48
is used to initialize the internal buffer r(n) of
Fn drand48 ,
Fn lrand48 ,
and
Fn mrand48
such that the 32 bits of the seed value are copied into the upper 32 bits
of r(n), with the lower 16 bits of r(n) arbitrarily being set to 0x330e.
Additionally, the constant multiplicand and addend of the algorithm are
reset to the default values given above.
Pp
Fn seed48
also initializes the internal buffer r(n) of
Fn drand48 ,
Fn lrand48 ,
and
Fn mrand48 ,
but here all 48 bits of the seed can be specified in an array of 3 unsigned shorts,
where the zeroth member specifies the lowest bits.
Again, the constant multiplicand and addend of the algorithm are
reset to the default values given above.
Fn seed48
returns a pointer to an array of 3 unsigned shorts which contains the old seed.
This array is statically allocated, thus its contents are lost after
each new call to
Fn seed48 .
Pp
Finally,
Fn lcong48
allows full control over the multiplicand and addend used in
Fn drand48 ,
Fn erand48 ,
Fn lrand48 ,
Fn nrand48 ,
Fn mrand48 ,
and
Fn jrand48 ,
and the seed used in
Fn drand48 ,
Fn lrand48 ,
and
Fn mrand48 .
An array of 7 unsigned shorts is passed as parameter; the first three shorts are
used to initialize the seed; the second three are used to initialize the
multiplicand; and the last short is used to initialize the addend.
It is thus not possible to use values greater than 0xffff as the addend.
Pp
Note that all three methods of seeding the random number generator
always also set the multiplicand and addend for any of the six
generator calls.
Pp
For a more powerful random number generator, see
Xr random 3 .
Sh SEE ALSO
Xr rand 3 ,
Xr random 3
Sh AUTHORS
Martin Birgmeier
