gen/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.
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   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 jrand48 ,
  22 .Nm lcong48 ,
  23 .Nm lrand48 ,
  24 .Nm mrand48 ,
  25 .Nm nrand48 ,
  26 .Nm seed48 ,
  27 .Nm srand48
  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 .Fo drand48
  35 .Fa void
  36 .Fc
  37 .Ft double
  38 .Fo erand48
  39 .Fa "unsigned short xsubi[3]"
  40 .Fc
  41 .Ft long
  42 .Fo jrand48
  43 .Fa "unsigned short xsubi[3]"
  44 .Fc
  45 .Ft void
  46 .Fo lcong48
  47 .Fa "unsigned short param[7]"
  48 .Fc
  49 .Ft long
  50 .Fo lrand48
  51 .Fa void
  52 .Fc
  53 .Ft long
  54 .Fo mrand48
  55 .Fa void
  56 .Fc
  57 .Ft long
  58 .Fo nrand48
  59 .Fa "unsigned short xsubi[3]"
  60 .Fc
  61 .Ft "unsigned short *"
  62 .Fo seed48
  63 .Fa "unsigned short seed16v[3]"
  64 .Fc
  65 .Ft void
  66 .Fo srand48
  67 .Fa "long seedval"
  68 .Fc
  69 .Sh DESCRIPTION
  70 The
  71 .Fn rand48
  72 family of functions generates pseudo-random numbers, using a linear
  73 congruential algorithm working on integers 48 bits in size.
  74 The
  75 particular formula employed is
  76 r(n+1) = (a * r(n) + c) mod m.
  77 The default value for the multiplicand `a' is 0xfdeece66d (25214903917).
  78 The default value for the the addend `c' is 0xb (11).
  79 The modulo is always fixed at m = 2 ** 48.
  80 r(n) is called the seed of the random number generator.
  81 .Pp
  82 For the six generator routines described next, the first
  83 computational step is to perform a single iteration of the algorithm.
  84 .Pp
  85 The
  86 .Fn drand48
  87 and
  88 .Fn erand48
  89 functions
  90 return values of type double.
  91 The full 48 bits of r(n+1) are
  92 loaded into the mantissa of the returned value, with the exponent set
  93 such that the values produced lie in the interval [0.0, 1.0).
  94 .Pp
  95 The
  96 .Fn lrand48
  97 and
  98 .Fn nrand48
  99 functions
 100 return values of type long in the range
 101 [0, 2**31-1].
 102 The high-order (31) bits of
 103 r(n+1) are loaded into the lower bits of the returned value, with
 104 the topmost (sign) bit set to zero.
 105 .Pp
 106 The
 107 .Fn mrand48
 108 and
 109 .Fn jrand48
 110 functions
 111 return values of type long in the range
 112 [-2**31, 2**31-1].
 113 The high-order (32) bits of
 114 r(n+1) are loaded into the returned value.
 115 .Pp
 116 The
 117 .Fn drand48 ,
 118 .Fn lrand48 ,
 119 and
 120 .Fn mrand48
 121 functions
 122 use an internal buffer to store r(n).
 123 For these functions
 124 the initial value of r(0) = 0x1234abcd330e = 20017429951246.
 125 .Pp
 126 On the other hand,
 127 .Fn erand48 ,
 128 .Fn nrand48 ,
 129 and
 130 .Fn jrand48
 131 use a user-supplied buffer to store the seed r(n),
 132 which consists of an array of 3 shorts, where the zeroth member
 133 holds the least significant bits.
 134 .Pp
 135 All functions share the same multiplicand and addend.
 136 .Pp
 137 The
 138 .Fn srand48
 139 function
 140 is used to initialize the internal buffer r(n) of
 141 .Fn drand48 ,
 142 .Fn lrand48 ,
 143 and
 144 .Fn mrand48 ,
 145 such that the 32 bits of the seed value are copied into the upper 32 bits
 146 of r(n), with the lower 16 bits of r(n) arbitrarily being set to 0x330e.
 147 Additionally, the constant multiplicand and addend of the algorithm are
 148 reset to the default values given above.
 149 .Pp
 150 The
 151 .Fn seed48
 152 function
 153 also initializes the internal buffer r(n) of
 154 .Fn drand48 ,
 155 .Fn lrand48 ,
 156 and
 157 .Fn mrand48 ,
 158 but here all 48 bits of the seed can be specified in an array of 3 shorts,
 159 where the zeroth member specifies the lowest bits.
 160 Again,
 161 the constant multiplicand and addend of the algorithm are
 162 reset to the default values given above.
 163 The
 164 .Fn seed48
 165 function
 166 returns a pointer to an array of 3 shorts which contains the old seed.
 167 This array is statically allocated; thus, its contents are lost after
 168 each new call to
 169 .Fn seed48 .
 170 .Pp
 171 Finally,
 172 .Fn lcong48
 173 allows full control over the multiplicand and addend used in
 174 .Fn drand48 ,
 175 .Fn erand48 ,
 176 .Fn lrand48 ,
 177 .Fn nrand48 ,
 178 .Fn mrand48 ,
 179 and
 180 .Fn jrand48 ,
 181 and the seed used in
 182 .Fn drand48 ,
 183 .Fn lrand48 ,
 184 and
 185 .Fn mrand48 .
 186 An array of 7 shorts is passed as argument; the first three shorts are
 187 used to initialize the seed; the second three are used to initialize the
 188 multiplicand; and the last short is used to initialize the addend.
 189 It is thus not possible to use values greater than 0xffff as the addend.
 190 .Pp
 191 Note that all three methods of seeding the random number generator
 192 always also set the multiplicand and addend for any of the six
 193 generator calls.
 194 .Pp
 195 For a more powerful random number generator, see
 196 .Xr random 3 .
 197 .Sh AUTHORS
 198 .An Martin Birgmeier
 199 .Sh SEE ALSO
 200 .Xr rand 3 ,
 201 .Xr random 3