.\" 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.
.\"
.\"	$OpenBSD: rand48.3,v 1.21 2019/12/20 19:16:40 tb Exp $
.\"
.Dd $Mdocdate: December 20 2019 $
.Dt DRAND48 3
.Os
.Sh NAME
.Nm drand48 ,
.Nm erand48 ,
.Nm lrand48 ,
.Nm nrand48 ,
.Nm mrand48 ,
.Nm jrand48 ,
.Nm srand48 ,
.Nm srand48_deterministic ,
.Nm seed48 ,
.Nm seed48_deterministic ,
.Nm lcong48 ,
.Nm lcong48_deterministic
.Nd pseudo-random number generators and initialization routines
.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 void
.Fn srand48_deterministic "long seed"
.Ft "unsigned short *"
.Fn seed48 "unsigned short xseed[3]"
.Ft "unsigned short *"
.Fn seed48_deterministic "unsigned short xseed[3]"
.Ft void
.Fn lcong48 "unsigned short p[7]"
.Ft void
.Fn lcong48_deterministic "unsigned short p[7]"
.Sh DESCRIPTION
.Bf -symbolic
Standards insist that this interface return deterministic results.
Unsafe usage is very common, so
.Ox
changed the subsystem to return non-deterministic results by default.
.Ef
.Pp
To satisfy portable code,
.Fn srand48 ,
.Fn seed48 ,
or
.Fn lcong48
should be called to initialize the subsystem.
In
.Ox
the
seeding parameters are ignored, and strong random number results will be
provided from
.Xr arc4random 3 .
In other systems, the
parameters prime a simplistic deterministic algorithm.
.Pp
If the standardized behavior is required then
.Fn srand48_deterministic ,
.Fn seed48_deterministic ,
and
.Fn lcong48_deterministic
can be substituted for
.Fn srand48 ,
.Fn seed48 ,
and
.Fn lcong48 .
That will cause subsequent
calls to
.Fn drand48 ,
.Fn lrand48 ,
and
.Fn jrand48
to return results using the deterministic 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
In the deterministic mode, the
.Fn rand48
family of functions generates 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 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 ,
.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_deterministic
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_deterministic
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_deterministic
returns a pointer to an array of 3 shorts which contains the old seed.
This array is statically allocated, so its contents are lost after
each new call to
.Fn seed48_deterministic .
.Pp
Finally,
.Fn lcong48_deterministic
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.
.Sh SEE ALSO
.Xr arc4random 3 ,
.Xr rand 3 ,
.Xr random 3
.Sh STANDARDS
The
.Fn drand48 ,
.Fn erand48 ,
.Fn jrand48 ,
.Fn lrand48 ,
.Fn mrand48 ,
and
.Fn nrand48 ,
functions conform to
.St -p1003.1-2008 .
.Pp
The
.Fn seed48 ,
.Fn srand48 ,
and
.Fn lcong48
function do not conform to
.St -ansiC ,
intentionally.
.Pp
The
.Fn seed48_deterministic ,
.Fn srand48_deterministic ,
and
.Fn lcong48_deterministic
functions are
.Ox
extensions.
.Sh AUTHORS
.An Martin Birgmeier