📄 rand.mldoc

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<!-- rand.mldoc --><!DOCTYPE ML-DOC SYSTEM><COPYRIGHT OWNER="Bell Labs, Lucent Technologies" YEAR=1998><VERSION VERID="1.1" YEAR=1998 MONTH=5 DAY=6><TITLE>The Rand structure</TITLE><INTERFACE><HEAD>The <CD/Rand/ structure</HEAD><SEEALSO>  <STRREF TOPID/Random/</SEEALSO><PP>The <STRREF NOLINK/Rand/ structure implements a simple linear congruentialrandom number generator with a uniform distribution.It is based on the one described in Paulson's book (pp. 170-171),which is derived from the article``Random number generators: good ones are hard to find,''by Stephen K. Park and Keith W. Miller, <IT/CACM/ 31 (1988), pp. 1192-1201.It also incorporates the changes suggested by Park and Miller in <IT/CACM/ 36 (1993), pp. 105-110.The generator has period <MATH/2<SUP/31/-1/.The values returned by <CD/random/ and <CD/mkRandom/ are 31-bit wordsin the range <MATH/[<CD/randMin/,<CD/randMax/]/. In the current implementation,<CD/randMin/ is <MATH/1.0/ and <CD/randMax/ is <MATH/2<SUP/31/-2/.<STRUCTURE STRID="Rand">  <SIGBODY SIGID="RAND" FILE=RAND>    <SPEC>      <TYPE><ID>rand<TY>Word31.word    <SPEC>      <VAL>randMin<TY>rand      <VAL>randMax<TY>rand        <COMMENT>          <PROTOTY>            <PROTO/randMin/            <PROTO/randMax/          </PROTOTY>          specify the minimum and maximum values returned by <CD/random/ and <CD/mkRandom/.    <SPEC>      <VAL>random<TY>rand -> rand        <COMMENT>          <PROTOTY>          random <ARG/r/          </PROTOTY>       returns a random number in the range <MATH/[<CD/randMin/,<CD/randMax/]/       using the seed <ARG/r/. Iteratively using the value returned by        <CD/random/ as the next seed to <CD/random/ will produce a sequence        of pseudo-random numbers.    <SPEC>      <VAL>mkRandom<TY>rand -> unit -> rand        <COMMENT>          <PROTOTY>          mkRandom <ARG/r/          </PROTOTY>       returns a stateful function generating a sequence of       random numbers in the range <MATH/[<CD/randMin/,<CD/randMax/]/,       starting from the seed <ARG/r/.    <SPEC>      <VAL>norm<TY>rand -> real        <COMMENT>        <PP>          Uniformly maps the range <MATH/[<CD/randMin/,<CD/randMax/]/ to          the range <MATH/(0.0,1.0)/.           This can be used in combination with          <CD/random/ or <CD/mkRandom/ to generate normalized real-valued          random numbers.    <SPEC>      <VAL>range<TY>(int * int) -> rand -> int      <RAISES><EXNREF DOCUMENT=SML-BASIS-DOC STRID="General"/Fail/        <COMMENT>          <PROTOTY>          range (<ARG/i/, <ARG/j/)          </PROTOTY>       returns a function mapping the range <MATH/[<CD/randMin/,<CD/randMax/]/       uniformly to the range <MATH/[<ARG/i/,<ARG/j/]/.       This can be used in combination with       <CD/random/ or <CD/mkRandom/ to generate random numbers in a given       integer range.       This raises the exception <EXNREF DOCUMENT=SML-BASIS-DOC STRID="General"/Fail/       if <MATH/<ARG/j/ &LT; <ARG/i//.</STRUCTURE></INTERFACE>
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