185 lines
4.4 KiB
Groff
185 lines
4.4 KiB
Groff
.\" Copyright (c) 1993 Martin Birgmeier
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.\" All rights reserved.
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.\"
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.\" You may redistribute unmodified or modified versions of this source
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.\" code provided that the above copyright notice and this and the
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.\" following conditions are retained.
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.\"
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.\" This software is provided ``as is'', and comes with no warranties
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.\" of any kind. I shall in no event be liable for anything that happens
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.\" to anyone/anything when using this software.
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.\"
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.\" @(#)rand48.3 V1.0 MB 8 Oct 1993
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.\" $FreeBSD$
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.\"
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.Dd February 2, 2010
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.Dt RAND48 3
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.Os
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.Sh NAME
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.Nm drand48 ,
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.Nm erand48 ,
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.Nm lrand48 ,
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.Nm nrand48 ,
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.Nm mrand48 ,
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.Nm jrand48 ,
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.Nm srand48 ,
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.Nm seed48 ,
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.Nm lcong48
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.Nd pseudo random number generators and initialization routines
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.Sh LIBRARY
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.Lb libc
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.Sh SYNOPSIS
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.In stdlib.h
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.Ft double
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.Fn drand48 void
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.Ft double
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.Fn erand48 "unsigned short xseed[3]"
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.Ft long
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.Fn lrand48 void
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.Ft long
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.Fn nrand48 "unsigned short xseed[3]"
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.Ft long
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.Fn mrand48 void
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.Ft long
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.Fn jrand48 "unsigned short xseed[3]"
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.Ft void
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.Fn srand48 "long seed"
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.Ft "unsigned short *"
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.Fn seed48 "unsigned short xseed[3]"
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.Ft void
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.Fn lcong48 "unsigned short p[7]"
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.Sh DESCRIPTION
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The
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.Fn rand48
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family of functions generates pseudo-random numbers using a linear
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congruential algorithm working on integers 48 bits in size.
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The
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particular formula employed is
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r(n+1) = (a * r(n) + c) mod m
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where the default values are
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for the multiplicand a = 0x5deece66d = 25214903917 and
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the addend c = 0xb = 11.
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The modulo is always fixed at m = 2 ** 48.
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r(n) is called the seed of the random number generator.
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.Pp
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For all the six generator routines described next, the first
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computational step is to perform a single iteration of the algorithm.
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.Pp
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The
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.Fn drand48
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and
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.Fn erand48
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functions
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return values of type double.
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The full 48 bits of r(n+1) are
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loaded into the mantissa of the returned value, with the exponent set
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such that the values produced lie in the interval [0.0, 1.0).
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.Pp
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The
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.Fn lrand48
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and
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.Fn nrand48
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functions
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return values of type long in the range
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[0, 2**31-1].
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The high-order (31) bits of
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r(n+1) are loaded into the lower bits of the returned value, with
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the topmost (sign) bit set to zero.
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.Pp
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The
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.Fn mrand48
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and
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.Fn jrand48
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functions
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return values of type long in the range
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[-2**31, 2**31-1].
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The high-order (32) bits of
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r(n+1) are loaded into the returned value.
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.Pp
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The
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.Fn drand48 ,
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.Fn lrand48 ,
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and
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.Fn mrand48
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functions
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use an internal buffer to store r(n).
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For these functions
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the initial value of r(0) = 0x1234abcd330e = 20017429951246.
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.Pp
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On the other hand,
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.Fn erand48 ,
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.Fn nrand48 ,
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and
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.Fn jrand48
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use a user-supplied buffer to store the seed r(n),
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which consists of an array of 3 shorts, where the zeroth member
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holds the least significant bits.
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.Pp
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All functions share the same multiplicand and addend.
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.Pp
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The
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.Fn srand48
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function
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is used to initialize the internal buffer r(n) of
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.Fn drand48 ,
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.Fn lrand48 ,
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and
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.Fn mrand48
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such that the 32 bits of the seed value are copied into the upper 32 bits
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of r(n), with the lower 16 bits of r(n) arbitrarily being set to 0x330e.
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Additionally, the constant multiplicand and addend of the algorithm are
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reset to the default values given above.
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.Pp
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The
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.Fn seed48
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function
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also initializes the internal buffer r(n) of
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.Fn drand48 ,
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.Fn lrand48 ,
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and
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.Fn mrand48 ,
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but here all 48 bits of the seed can be specified in an array of 3 shorts,
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where the zeroth member specifies the lowest bits.
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Again,
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the constant multiplicand and addend of the algorithm are
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reset to the default values given above.
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The
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.Fn seed48
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function
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returns a pointer to an array of 3 shorts which contains the old seed.
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This array is statically allocated, thus its contents are lost after
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each new call to
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.Fn seed48 .
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.Pp
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Finally,
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.Fn lcong48
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allows full control over the multiplicand and addend used in
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.Fn drand48 ,
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.Fn erand48 ,
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.Fn lrand48 ,
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.Fn nrand48 ,
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.Fn mrand48 ,
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and
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.Fn jrand48 ,
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and the seed used in
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.Fn drand48 ,
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.Fn lrand48 ,
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and
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.Fn mrand48 .
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An array of 7 shorts is passed as argument; the first three shorts are
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used to initialize the seed; the second three are used to initialize the
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multiplicand; and the last short is used to initialize the addend.
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It is thus not possible to use values greater than 0xffff as the addend.
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.Pp
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Note that all three methods of seeding the random number generator
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always also set the multiplicand and addend for any of the six
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generator calls.
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.Pp
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For a more powerful random number generator, see
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.Xr random 3 .
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.Sh SEE ALSO
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.Xr rand 3 ,
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.Xr random 3
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.Sh AUTHORS
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.An Martin Birgmeier
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