gen/FreeBSD/rand48.3

   1 .\" Copyright (c) 1993 Martin Birgmeier
   2 .\" All rights reserved.
   3 .\"
   4 .\" You may redistribute unmodified or modified versions of this source
   5 .\" code provided that the above copyright notice and this and the
   6 .\" following conditions are retained.
   7 .\"
   8 .\" This software is provided ``as is'', and comes with no warranties
   9 .\" of any kind. I shall in no event be liable for anything that happens
  10 .\" to anyone/anything when using this software.
  11 .\"
  12 .\"     @(#)rand48.3 V1.0 MB 8 Oct 1993
  13 .\" $FreeBSD: src/lib/libc/gen/rand48.3,v 1.15 2002/12/19 09:40:21 ru Exp $
  14 .\"
  15 .Dd October 8, 1993
  16 .Dt RAND48 3
  17 .Os
  18 .Sh NAME
  19 .Nm drand48 ,
  20 .Nm erand48 ,
  21 .Nm lrand48 ,
  22 .Nm nrand48 ,
  23 .Nm mrand48 ,
  24 .Nm jrand48 ,
  25 .Nm srand48 ,
  26 .Nm seed48 ,
  27 .Nm lcong48
  28 .Nd pseudo random number generators and initialization routines
  29 .Sh LIBRARY
  30 .Lb libc
  31 .Sh SYNOPSIS
  32 .In stdlib.h
  33 .Ft double
  34 .Fn drand48 void
  35 .Ft double
  36 .Fn erand48 "unsigned short xseed[3]"
  37 .Ft long
  38 .Fn lrand48 void
  39 .Ft long
  40 .Fn nrand48 "unsigned short xseed[3]"
  41 .Ft long
  42 .Fn mrand48 void
  43 .Ft long
  44 .Fn jrand48 "unsigned short xseed[3]"
  45 .Ft void
  46 .Fn srand48 "long seed"
  47 .Ft "unsigned short *"
  48 .Fn seed48 "unsigned short xseed[3]"
  49 .Ft void
  50 .Fn lcong48 "unsigned short p[7]"
  51 .Sh DESCRIPTION
  52 The
  53 .Fn rand48
  54 family of functions generates pseudo-random numbers using a linear
  55 congruential algorithm working on integers 48 bits in size.
  56 The
  57 particular formula employed is
  58 r(n+1) = (a * r(n) + c) mod m
  59 where the default values are
  60 for the multiplicand a = 0xfdeece66d = 25214903917 and
  61 the addend c = 0xb = 11.
  62 The modulo is always fixed at m = 2 ** 48.
  63 r(n) is called the seed of the random number generator.
  64 .Pp
  65 For all the six generator routines described next, the first
  66 computational step is to perform a single iteration of the algorithm.
  67 .Pp
  68 The
  69 .Fn drand48
  70 and
  71 .Fn erand48
  72 functions
  73 return values of type double.
  74 The full 48 bits of r(n+1) are
  75 loaded into the mantissa of the returned value, with the exponent set
  76 such that the values produced lie in the interval [0.0, 1.0).
  77 .Pp
  78 The
  79 .Fn lrand48
  80 and
  81 .Fn nrand48
  82 functions
  83 return values of type long in the range
  84 [0, 2**31-1]. The high-order (31) bits of
  85 r(n+1) are loaded into the lower bits of the returned value, with
  86 the topmost (sign) bit set to zero.
  87 .Pp
  88 The
  89 .Fn mrand48
  90 and
  91 .Fn jrand48
  92 functions
  93 return values of type long in the range
  94 [-2**31, 2**31-1]. The high-order (32) bits of
  95 r(n+1) are loaded into the returned value.
  96 .Pp
  97 The
  98 .Fn drand48 ,
  99 .Fn lrand48 ,
 100 and
 101 .Fn mrand48
 102 functions
 103 use an internal buffer to store r(n). For these functions
 104 the initial value of r(0) = 0x1234abcd330e = 20017429951246.
 105 .Pp
 106 On the other hand,
 107 .Fn erand48 ,
 108 .Fn nrand48 ,
 109 and
 110 .Fn jrand48
 111 use a user-supplied buffer to store the seed r(n),
 112 which consists of an array of 3 shorts, where the zeroth member
 113 holds the least significant bits.
 114 .Pp
 115 All functions share the same multiplicand and addend.
 116 .Pp
 117 The
 118 .Fn srand48
 119 function
 120 is used to initialize the internal buffer r(n) of
 121 .Fn drand48 ,
 122 .Fn lrand48 ,
 123 and
 124 .Fn mrand48
 125 such that the 32 bits of the seed value are copied into the upper 32 bits
 126 of r(n), with the lower 16 bits of r(n) arbitrarily being set to 0x330e.
 127 Additionally, the constant multiplicand and addend of the algorithm are
 128 reset to the default values given above.
 129 .Pp
 130 The
 131 .Fn seed48
 132 function
 133 also initializes the internal buffer r(n) of
 134 .Fn drand48 ,
 135 .Fn lrand48 ,
 136 and
 137 .Fn mrand48 ,
 138 but here all 48 bits of the seed can be specified in an array of 3 shorts,
 139 where the zeroth member specifies the lowest bits.
 140 Again,
 141 the constant multiplicand and addend of the algorithm are
 142 reset to the default values given above.
 143 The
 144 .Fn seed48
 145 function
 146 returns a pointer to an array of 3 shorts which contains the old seed.
 147 This array is statically allocated, thus its contents are lost after
 148 each new call to
 149 .Fn seed48 .
 150 .Pp
 151 Finally,
 152 .Fn lcong48
 153 allows full control over the multiplicand and addend used in
 154 .Fn drand48 ,
 155 .Fn erand48 ,
 156 .Fn lrand48 ,
 157 .Fn nrand48 ,
 158 .Fn mrand48 ,
 159 and
 160 .Fn jrand48 ,
 161 and the seed used in
 162 .Fn drand48 ,
 163 .Fn lrand48 ,
 164 and
 165 .Fn mrand48 .
 166 An array of 7 shorts is passed as argument; the first three shorts are
 167 used to initialize the seed; the second three are used to initialize the
 168 multiplicand; and the last short is used to initialize the addend.
 169 It is thus not possible to use values greater than 0xffff as the addend.
 170 .Pp
 171 Note that all three methods of seeding the random number generator
 172 always also set the multiplicand and addend for any of the six
 173 generator calls.
 174 .Pp
 175 For a more powerful random number generator, see
 176 .Xr random 3 .
 177 .Sh AUTHORS
 178 .An Martin Birgmeier
 179 .Sh SEE ALSO
 180 .Xr rand 3 ,
 181 .Xr random 3