text: .\" 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: src/lib/libc/gen/rand48.3,v 1.17 2005/01/20 09:17:02 ru Exp $
  .\"
  .Dd October 8, 1993
  .Dt RAND48 3
  .Os
  .Sh NAME
  .Nm drand48 ,
  .Nm erand48 ,
  .Nm jrand48 ,
  .Nm lcong48 ,
  .Nm lrand48 ,
  .Nm mrand48 ,
  .Nm nrand48 ,
  .Nm seed48 ,
  .Nm srand48
  .Nd pseudo random number generators and initialization routines
  .Sh LIBRARY
  .Lb libc
  .Sh SYNOPSIS
  .In stdlib.h
  .Ft double
  .Fo drand48
  .Fa void
  .Fc
  .Ft double
  .Fo erand48
  .Fa "unsigned short xsubi[3]"
  .Fc
  .Ft long
  .Fo jrand48
  .Fa "unsigned short xsubi[3]"
  .Fc
  .Ft void
  .Fo lcong48
  .Fa "unsigned short param[7]"
  .Fc
  .Ft long
  .Fo lrand48
  .Fa void
  .Fc
  .Ft long
  .Fo mrand48
  .Fa void
  .Fc
  .Ft long
  .Fo nrand48
  .Fa "unsigned short xsubi[3]"
  .Fc
  .Ft "unsigned short *"
  .Fo seed48
  .Fa "unsigned short seed16v[3]"
  .Fc
  .Ft void
  .Fo srand48
  .Fa "long seedval"
  .Fc
  .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.
  The default value for the multiplicand `a' is 0x5deece66d (25214903917).
  The default value for the the addend `c' is 0xb (11).
  The modulo is always fixed at m = 2 ** 48.
  r(n) is called the seed of the random number generator.
  .Pp
  For the six generator routines described next, the first
  computational step is to perform a single iteration of the algorithm.
  .Pp
  The
  .Fn drand48
  and
  .Fn erand48
  functions
  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
  The
  .Fn lrand48
  and
  .Fn nrand48
  functions
  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
  The
  .Fn mrand48
  and
  .Fn jrand48
  functions
  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
  The
  .Fn drand48 ,
  .Fn lrand48 ,
  and
  .Fn mrand48
  functions
  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
  The
  .Fn srand48
  function
  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
  The
  .Fn seed48
  function
  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.
  The
  .Fn seed48
  function
  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 argument; 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
  .An Martin Birgmeier
  