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 1.16 2004/07/02 23:52:10 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].
  85 The high-order (31) bits of
  86 r(n+1) are loaded into the lower bits of the returned value, with
  87 the topmost (sign) bit set to zero.
  88 .Pp
  89 The
  90 .Fn mrand48
  91 and
  92 .Fn jrand48
  93 functions
  94 return values of type long in the range
  95 [-2**31, 2**31-1].
  96 The high-order (32) bits of
  97 r(n+1) are loaded into the returned value.
  98 .Pp
  99 The
 100 .Fn drand48 ,
 101 .Fn lrand48 ,
 102 and
 103 .Fn mrand48
 104 functions
 105 use an internal buffer to store r(n).
 106 For these functions
 107 the initial value of r(0) = 0x1234abcd330e = 20017429951246.
 108 .Pp
 109 On the other hand,
 110 .Fn erand48 ,
 111 .Fn nrand48 ,
 112 and
 113 .Fn jrand48
 114 use a user-supplied buffer to store the seed r(n),
 115 which consists of an array of 3 shorts, where the zeroth member
 116 holds the least significant bits.
 117 .Pp
 118 All functions share the same multiplicand and addend.
 119 .Pp
 120 The
 121 .Fn srand48
 122 function
 123 is used to initialize the internal buffer r(n) of
 124 .Fn drand48 ,
 125 .Fn lrand48 ,
 126 and
 127 .Fn mrand48
 128 such that the 32 bits of the seed value are copied into the upper 32 bits
 129 of r(n), with the lower 16 bits of r(n) arbitrarily being set to 0x330e.
 130 Additionally, the constant multiplicand and addend of the algorithm are
 131 reset to the default values given above.
 132 .Pp
 133 The
 134 .Fn seed48
 135 function
 136 also initializes the internal buffer r(n) of
 137 .Fn drand48 ,
 138 .Fn lrand48 ,
 139 and
 140 .Fn mrand48 ,
 141 but here all 48 bits of the seed can be specified in an array of 3 shorts,
 142 where the zeroth member specifies the lowest bits.
 143 Again,
 144 the constant multiplicand and addend of the algorithm are
 145 reset to the default values given above.
 146 The
 147 .Fn seed48
 148 function
 149 returns a pointer to an array of 3 shorts which contains the old seed.
 150 This array is statically allocated, thus its contents are lost after
 151 each new call to
 152 .Fn seed48 .
 153 .Pp
 154 Finally,
 155 .Fn lcong48
 156 allows full control over the multiplicand and addend used in
 157 .Fn drand48 ,
 158 .Fn erand48 ,
 159 .Fn lrand48 ,
 160 .Fn nrand48 ,
 161 .Fn mrand48 ,
 162 and
 163 .Fn jrand48 ,
 164 and the seed used in
 165 .Fn drand48 ,
 166 .Fn lrand48 ,
 167 and
 168 .Fn mrand48 .
 169 An array of 7 shorts is passed as argument; the first three shorts are
 170 used to initialize the seed; the second three are used to initialize the
 171 multiplicand; and the last short is used to initialize the addend.
 172 It is thus not possible to use values greater than 0xffff as the addend.
 173 .Pp
 174 Note that all three methods of seeding the random number generator
 175 always also set the multiplicand and addend for any of the six
 176 generator calls.
 177 .Pp
 178 For a more powerful random number generator, see
 179 .Xr random 3 .
 180 .Sh AUTHORS
 181 .An Martin Birgmeier
 182 .Sh SEE ALSO
 183 .Xr rand 3 ,
 184 .Xr random 3