freebsd/lib/libc/gen/rand48.3

\" 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.
.\"
.\"     @(#)rand48.3 V1.0 MB 8 Oct 1993
.\" $FreeBSD$
.\"
.Dd October 8, 1993
.Dt RAND48 3
.Os FreeBSD
.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 SYNOPSIS
.Fd #include <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 = 0xfdeece66d = 25214903917 and
the addend c = 0xb = 11. The modulo 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 mantissa 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 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 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 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 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 AUTHORS
.An Martin Birgmeier
.Sh SEE ALSO
.Xr rand 3 ,
.Xr random 3