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
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  11 .\"
  12 .\"     @(#)rand48.3 V1.0 MB 8 Oct 1993
  13 .\" $FreeBSD: src/lib/libc/gen/rand48.3,v 1.13 2001/10/01 16:08:51 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 .Fn drand48
  69 and
  70 .Fn erand48
  71 return values of type double.
  72 The full 48 bits of r(n+1) are
  73 loaded into the mantissa of the returned value, with the exponent set
  74 such that the values produced lie in the interval [0.0, 1.0).
  75 .Pp
  76 .Fn lrand48
  77 and
  78 .Fn nrand48
  79 return values of type long in the range
  80 [0, 2**31-1]. The high-order (31) bits of
  81 r(n+1) are loaded into the lower bits of the returned value, with
  82 the topmost (sign) bit set to zero.
  83 .Pp
  84 .Fn mrand48
  85 and
  86 .Fn jrand48
  87 return values of type long in the range
  88 [-2**31, 2**31-1]. The high-order (32) bits of
  89 r(n+1) are loaded into the returned value.
  90 .Pp
  91 .Fn drand48 ,
  92 .Fn lrand48 ,
  93 and
  94 .Fn mrand48
  95 use an internal buffer to store r(n). For these functions
  96 the initial value of r(0) = 0x1234abcd330e = 20017429951246.
  97 .Pp
  98 On the other hand,
  99 .Fn erand48 ,
 100 .Fn nrand48 ,
 101 and
 102 .Fn jrand48
 103 use a user-supplied buffer to store the seed r(n),
 104 which consists of an array of 3 shorts, where the zeroth member
 105 holds the least significant bits.
 106 .Pp
 107 All functions share the same multiplicand and addend.
 108 .Pp
 109 .Fn srand48
 110 is used to initialize the internal buffer r(n) of
 111 .Fn drand48 ,
 112 .Fn lrand48 ,
 113 and
 114 .Fn mrand48
 115 such that the 32 bits of the seed value are copied into the upper 32 bits
 116 of r(n), with the lower 16 bits of r(n) arbitrarily being set to 0x330e.
 117 Additionally, the constant multiplicand and addend of the algorithm are
 118 reset to the default values given above.
 119 .Pp
 120 .Fn seed48
 121 also initializes the internal buffer r(n) of
 122 .Fn drand48 ,
 123 .Fn lrand48 ,
 124 and
 125 .Fn mrand48 ,
 126 but here all 48 bits of the seed can be specified in an array of 3 shorts,
 127 where the zeroth member specifies the lowest bits.
 128 Again,
 129 the constant multiplicand and addend of the algorithm are
 130 reset to the default values given above.
 131 .Fn seed48
 132 returns a pointer to an array of 3 shorts which contains the old seed.
 133 This array is statically allocated, thus its contents are lost after
 134 each new call to
 135 .Fn seed48 .
 136 .Pp
 137 Finally,
 138 .Fn lcong48
 139 allows full control over the multiplicand and addend used in
 140 .Fn drand48 ,
 141 .Fn erand48 ,
 142 .Fn lrand48 ,
 143 .Fn nrand48 ,
 144 .Fn mrand48 ,
 145 and
 146 .Fn jrand48 ,
 147 and the seed used in
 148 .Fn drand48 ,
 149 .Fn lrand48 ,
 150 and
 151 .Fn mrand48 .
 152 An array of 7 shorts is passed as parameter; the first three shorts are
 153 used to initialize the seed; the second three are used to initialize the
 154 multiplicand; and the last short is used to initialize the addend.
 155 It is thus not possible to use values greater than 0xffff as the addend.
 156 .Pp
 157 Note that all three methods of seeding the random number generator
 158 always also set the multiplicand and addend for any of the six
 159 generator calls.
 160 .Pp
 161 For a more powerful random number generator, see
 162 .Xr random 3 .
 163 .Sh AUTHORS
 164 .An Martin Birgmeier
 165 .Sh SEE ALSO
 166 .Xr rand 3 ,
 167 .Xr random 3