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The linear congruential generator is a very simple example of a random number generator.

All linear congruential generators use this formula:

$r_{n+1}=a\times r_{n}+c{\pmod {m}}$

Where:

$r_{0}$ is a seed.
$r_{1}$ , $r_{2}$ , $r_{3}$ , ..., are the random numbers.
$a$ , $c$ , $m$ are constants.

If one chooses the values of $a$ , $c$ and $m$ with care, then the generator produces a uniform distribution of integers from $0$ to $m-1$ .

LCG numbers have poor quality. $r_{n}$ and $r_{n+1}$ are not independent, as true random numbers would be. Anyone who knows $r_{n}$ can predict $r_{n+1}$ , therefore LCG is not cryptographically secure. The LCG is still good enough for simple tasks like Miller-Rabin primality test, or FreeCell deals. Among the benefits of the LCG, one can easily reproduce a sequence of numbers, from the same $r_{0}$ . One can also reproduce such sequence with a different programming language, because the formula is so simple.

The task is to replicate two historic random number generators. One is the rand() function from BSD libc, and the other is the rand() function from the Microsoft C Runtime (MSCVRT.DLL). Each replica must yield the same sequence of integers as the original generator, when starting from the same seed.

In these formulas, the seed becomes $state_{0}$ . The random sequence is $rand_{1}$ , $rand_{2}$ and so on.

BSD formula

$state_{n+1}=1103515245\times state_{n}+12345{\pmod {2^{31}}}$
$rand_{n}=state_{n}$
$rand_{n}$ is in range 0 to 2147483647.

Microsoft formula

$state_{n+1}=214013\times state_{n}+2531011{\pmod {2^{31}}}$
$rand_{n}=state_{n}\div 2^{16}$
$rand_{n}$ is in range 0 to 32767.

The BSD formula was so awful that FreeBSD switched to a different formula.

More info is at Random number generator (included)#C.

360 Assembly

<lang 360asm>* Linear congruential generator 07/03/2017 LINCONG CSECT

        USING  LINCONG,R12
        LR     R12,R15            set base register

BEGIN SR R5,R5 bsdseed=0

        SR     R7,R7              msseed=0
        LA     R8,1               i=1
        L      R9,=F'10'          number of loop

LOOP M R4,=F'1103515245' bsdseed*=1103515245

        A      R5,=F'12345'       bsdseed+=12345
        LR     R3,R5              bsdrand=bsdseed
        LTR    R5,R5              if bsdseed<0
        BP     CONT               then
        L      R3,COMP2             -2**31 
        SR     R3,R5                -bsdseed 
        LPR    R3,R3                bsdrand=abs(-2**31-bsdseed)

CONT M R6,=F'214013' msseed*=214013

        A      R7,=F'2531011'     msseed+=2531011
        XR     R6,R6
        D      R6,TWO16           /2**16
        XDECO  R8,XDEC            i
        MVC    PG(4),XDEC+8
        XDECO  R3,XDEC            bsdrand
        MVC    PG+4(12),XDEC
        XDECO  R7,XDEC            msseed
        MVC    PG+16(7),XDEC+5
        XPRNT  PG,L'PG            print buffer
        LA     R8,1(R8)           i=i+1
        BCT    R9,LOOP            loop

RETURN XR R15,R15 set return code

        BR     R14                return to caller
        DS     0F                 alignment

TWO16 DC XL4'00010000' 2**16 COMP2 DC XL4'80000000' -2**31 PG DC CL80' ' XDEC DS CL12

        YREGS  
        END    LINCONG</lang>

Output:

   1       12345     38
   2  1406932606    162
   3   654583775    567
   4  1449466924   1890
   5   229283573   6210
   6  1109335178  20317
   7  1051550459    849
   8  1293799192   2811
   9   794471793   9218
  10   551188310  30140

Ada

We first specify a generic package LCG:

<lang Ada>generic

  type Base_Type is mod <>;
  Multiplyer, Adder: Base_Type;
  Output_Divisor: Base_Type := 1;

package LCG is

  procedure Initialize(Seed: Base_Type);
  function Random return Base_Type;
  -- changes the state and outputs the result

end LCG;</lang>

Then we provide a generic implementation:

<lang Ada>package body LCG is

  State: Base_Type := Base_Type'First;

  procedure Initialize(Seed: Base_Type) is
  begin
     State := Seed;
  end Initialize;

  function Random return Base_Type is
  begin
     State := State * Multiplyer + Adder;
     return State / Output_Divisor;
  end Random;

end LCG;</lang>

Next, we define the MS- and BSD-instantiations of the generic package:

<lang Ada>with Ada.Text_IO, LCG;

procedure Run_LCGs is

  type M31 is mod 2**31;

  package BSD_Rand is new LCG(Base_Type => M31, Multiplyer => 1103515245,
                              Adder => 12345);

  package MS_Rand  is new LCG(Base_Type => M31, Multiplyer => 214013,
                              Adder => 2531011, Output_Divisor => 2**16);

begin

  for I in 1 .. 10 loop
     Ada.Text_IO.Put_Line(M31'Image(BSD_Rand.Random));
  end loop;
  for I in 1 .. 10 loop
      Ada.Text_IO.Put_Line(M31'Image(MS_Rand.Random));
  end loop;

end Run_LCGs;</lang>

Finally, we run the program, which generates the following output (note that the first ten lines are from the BSD generator, the next ten from the MS generator):

ALGOL 68

<lang algol68> BEGIN COMMENT

  Algol 68 Genie checks for integer overflow whereas the reference
  language leaves the result undefined so for portability we need to
  see how wide a variable must be to hold the maximum possible value
  before range reduction. This occurs in the BSD RNG when
  rseed=2147483647 and is therefore 2147483647 * 1103515245 + 12345 =
  2369780942852710860, which itself is 19 decimal digits.  Use
  evironmental queries to determine the width needed.

COMMENT

  MODE RANDINT = UNION (INT, LONG INT, LONG LONG INT);
  RANDINT rseed := (int width > 18 | 0 |:

long int width > 18 | LONG 0 | LONG LONG 0);

  PROC srand = (INT x) VOID :
  (rseed | (INT): rseed := x,
   (LONG INT): rseed := LENG x | rseed := LENG LENG x);
  PROC bsd rand = INT :
  BEGIN
     CASE rseed IN
     (INT ri):
     BEGIN

INT a = 1103515245, c = 12345, m1 = 2^16, m2 = 2^15; COMMENT

  That curious declaration is because 2^31 might overflow during
  compilation but the MODE declaration for RANDINT guarantees that it
  will not overflow at run-time.  We assume that an INT is at least
  32 bits wide, otherwise a similar workaround would be needed for
  the declaration of a.

COMMENT INT result = (ri * a + c) MOD (m1 * m2); rseed := result; result

     END,
     (LONG INT rli):
     BEGIN

LONG INT a = LONG 1103515245, c = LONG 12345, m = LONG 2^31; LONG INT result = (rli * a + c) MOD m; rseed := result; SHORTEN result

     END,
     (LONG LONG INT rlli) :
     BEGIN

LONG LONG INT a = LONG LONG 1103515245, c = LONG LONG 12345, m = LONG LONG 2^31; LONG LONG INT result = (rlli * a + c) MOD m; rseed := result; SHORTEN SHORTEN result

     END
     ESAC
  END;
  PROC ms rand = INT :
  BEGIN
     CASE rseed IN
     (INT ri):
     BEGIN

INT a = 214013, c = 2531011, m1 = 2^15, m2 = 2^16; INT result = (ri * a + c) MOD (m1 * m2); rseed := result; result % m2

     END,
     (LONG INT rli):
     BEGIN

LONG INT a = LONG 214013, c = LONG 2531011, m = LONG 2^31, m2 = LONG 2^16; LONG INT result = (rli * a + c) MOD m; rseed := result; SHORTEN (result % m2)

     END,
     (LONG LONG INT rlli) :
     BEGIN

LONG LONG INT a = LONG LONG 214013, c = LONG LONG 2531011, m = LONG LONG 2^31, m2 = LONG LONG 2^16; LONG LONG INT result = (rlli * a + c) MOD m; rseed := result; SHORTEN SHORTEN (result % m2)

     END
     ESAC
  END;
  srand (0);
  TO 10 DO printf (($g(0)l$, bsd rand)) OD;
  print (newline);
  srand (0);
  TO 10 DO printf (($g(0)l$, ms rand)) OD;
  srand (0)

END </lang>

Output:

AutoHotkey

<lang AutoHotkey>a := 0, b:= [0] Loop, 10 BSD .= "`t" (a := BSD(a)) "`n" , b := MS(b[1]) , MS .= "`t" (b[2]) "`n"

MsgBox, % "BSD:`n" BSD "`nMS:`n" MS

BSD(Seed) { return, Mod(1103515245 * Seed + 12345, 2147483648) }

MS(Seed) { Seed := Mod(214013 * Seed + 2531011, 2147483648) return, [Seed, Seed // 65536] }</lang> Output:

Batch

<lang batch> @echo off & setlocal enabledelayedexpansion

echo BSD Rand set /a a=0,cnt=1

b

set /a "a=1103515245 *a+12345,a&=0x7fffffff, cnt+=1" call:prettyprint !cnt! !a! if !cnt! leq 10 goto :b

echo. echo Microsoft Rand set /a a=0,cnt=1

c

set /a "a=214013 *a+2531011,a&=0x7fffffff, b=a>>16,cnt+=1" call:prettyprint !cnt! !b! if !cnt! lss 10 goto :c pause goto:eof

prettyprint

set p1= %1 set p2= %2 echo %p1:~-2% %p2:~-10% goto:eof

</lang> Output:

BSD Rand
 2       12345
 3  1406932606
 4   654583775
 5  1449466924
 6   229283573
 7  1109335178
 8  1051550459
 9  1293799192
10   794471793
11   551188310

Microsoft Rand
 2          38
 3        7719
 4       21238
 5        2437
 6        8855
 7       11797
 8        8365
 9       32285
10       10450

BBC BASIC

Works with: BBC BASIC for Windows

<lang bbcbasic> @% = &D0D

     PRINT "MS generator:"
     dummy% = FNrandMS(0)
     FOR i% = 1 TO 10
       PRINT FNrandMS(-1)
     NEXT
     PRINT '"BSD generator:"
     dummy% = FNrandBSD(0)
     FOR i% = 1 TO 10
       PRINT FNrandBSD(-1)
     NEXT
     END
     
     DEF FNrandMS(seed%)
     PRIVATE state%
     IF seed% >= 0 THEN
       state% = seed%
     ELSE
       state% = FNmuladd(state%, 214013, 2531011)
     ENDIF
     = state% >> 16
     
     DEF FNrandBSD(seed%)
     PRIVATE state%
     IF seed% >= 0 THEN
       state% = seed%
     ELSE
       state% = FNmuladd(state%, 1103515245, 12345)
     ENDIF
     = state%
     
     DEF FNmuladd(A%,B%,C%) : PRIVATE M% : LOCAL P% : IF M% = 0 DIM P% 8
     IF P% THEN [OPT 0 : .M% mul ebx : add eax,ecx : btr eax,31 : ret :]
     = USR M%</lang>

Output:

MS generator:
           38
         7719
        21238
         2437
         8855
        11797
         8365
        32285
        10450
        30612

BSD generator:
        12345
   1406932606
    654583775
   1449466924
    229283573
   1109335178
   1051550459
   1293799192
    794471793
    551188310

bc

Translation of: dc

Works with: GNU bc

Works with: OpenBSD bc

As with dc, bc has no bitwise operators. <lang bc>/* BSD rand */

define rand() { randseed = (randseed * 1103515245 + 12345) % 2147483648 return randseed }

randseed = 1 rand(); rand(); rand(); print "\n"

/* Microsoft rand */

define rand() { randseed = (randseed * 214013 + 2531011) % 2147483648 return randseed / 65536 }

randseed = 1 rand(); rand(); rand(); print "\n"</lang>

Befunge

This required a bit of trickery to handle signed overflow and negative division in a portable way. It still won't work on all implementations, though. In particular Javascript-based interpreters can't handle the BSD formula because of the way Javascript numbers lose their least significant digits when they become too large.

<lang befunge>>025*>\::0\`288*::*:****+.55+,"iQ"5982156*:v v $$_^#!\-1:\%***:*::*882 ++*"yf"3***+***+*< >025*>\:488**:*/:0\`6"~7"+:*+01-2/-*+."O?+"55v @ $$_^#!\-1:\%***:*::*882 ++***" 4C"*+2**,+<</lang>

Output:

Bracmat

<lang bracmat>( 2^31:?RANDMAX & 2^-16:?rshift & (randBSD=mod$(!seed*1103515245+12345.!RANDMAX):?seed) & ( randMS

 =   div
   $ ((mod$(!seed*214013+2531011.!RANDMAX):?seed)*!rshift.1)
 )

& out$\nBSD & 0:?seed & 0:?i & whl'(1+!i:~>10:?i&out$!randBSD) & out$\nMicrosoft & 0:?seed & 0:?i & whl'(1+!i:~>10:?i&out$!randMS) )</lang>

Output:

C

In a pretended lib style, this code produces a rand() function depends on compiler macro: gcc -DMS_RAND uses MS style, otherwise it's BSD rand by default. <lang C>#include <stdio.h>

/* always assuming int is at least 32 bits */ int rand(); int rseed = 0;

inline void srand(int x) { rseed = x; }

ifndef MS_RAND
define RAND_MAX ((1U << 31) - 1)

inline int rand() { return rseed = (rseed * 1103515245 + 12345) & RAND_MAX; }

else /* MS rand */

define RAND_MAX_32 ((1U << 31) - 1)
define RAND_MAX ((1U << 15) - 1)

inline int rand() { return (rseed = (rseed * 214013 + 2531011) & RAND_MAX_32) >> 16; }

endif/* MS_RAND */

int main() { int i; printf("rand max is %d\n", RAND_MAX);

for (i = 0; i < 100; i++) printf("%d\n", rand());

return 0; }</lang>

C#

Works with: C# version 6+

<lang Csharp>using System; using System.Collections.Generic; using System.Linq; using static System.Console;

namespace LinearCongruentialGenerator {

   static class LinearCongruentialGenerator
   {
       static int _seed = (int)DateTime.Now.Ticks; // from bad random gens might as well have bad seed!
       static int _bsdCurrent = _seed;
       static int _msvcrtCurrent = _seed;

       static int Next(int seed, int a, int b) => (a * seed + b) & int.MaxValue;

       static int BsdRand() => _bsdCurrent = Next(_bsdCurrent, 1103515245, 12345);

       static int MscvrtRand() => _msvcrtCurrent = Next (_msvcrtCurrent << 16,214013,2531011) >> 16;

       static void PrintRandom(int count, bool isBsd)
       {
           var name = isBsd ? "BSD" : "MS";
           WriteLine($"{name} next {count} Random");
           var gen = isBsd ? (Func<int>)(BsdRand) : MscvrtRand;
           foreach (var r in Enumerable.Repeat(gen, count))
               WriteLine(r.Invoke());
       }

       static void Main(string[] args)
       {
           PrintRandom(10, true);
           PrintRandom(10, false);
           Read();
       }
   }

}</lang> Produces:

BSD next 10 Random
1587930915
19022880
1025044953
1143293854
1642451583
1110934092
773706389
1830436778
1527715739
2072016696
MS next 10 Random
24368
8854
28772
16122
11064
24190
23724
6690
14784
21222

From a Free Cell Deal solution <lang Csharp> using System; using System.Collections.Generic; using System.Linq; using System.Text;

namespace FreeCellDeals {

   public class LCG
   {
       private int _state;
       public bool Microsoft { get; set;}
       public bool BSD
       {
           get
           {
               return !Microsoft;
           }
           set
           {
               Microsoft = !value;
           }
       }

       public LCG(bool microsoft = true)
       {
           _state = (int)DateTime.Now.Ticks;
           Microsoft = microsoft;
       }

       public LCG(int n, bool microsoft = true)
       {
           _state = n;
           Microsoft = microsoft;
       }

       public int Next()
       {
           if (BSD)
           {
               return _state = (1103515245 * _state + 12345) & int.MaxValue;
           }
           return ((_state = 214013 * _state + 2531011) & int.MaxValue) >> 16;
       }

       public IEnumerable<int> Seq()
       {
           while (true)
           {
               yield return Next();
           }
       }
   }

   class Program
   {
       static void Main()
       {
           LCG ms = new LCG(0, true);
           LCG bsd = new LCG(0,false);
           Console.WriteLine("Microsoft");
           ms.Seq().Take(10).ToList().ForEach(Console.WriteLine);
           Console.WriteLine("\nBSD");
           bsd.Seq().Take(10).ToList().ForEach(Console.WriteLine);
           Console.ReadKey();
       }
   }

} </lang> Output:

C++

<lang cpp>#include <iostream>

//-------------------------------------------------------------------------------------------------- using namespace std;

//-------------------------------------------------------------------------------------------------- class mRND { public:

   void seed( unsigned int s ) { _seed = s; }

protected:

   mRND() : _seed( 0 ), _a( 0 ), _c( 0 ), _m( 2147483648 ) {}
   int rnd() { return( _seed = ( _a * _seed + _c ) % _m ); }

   int _a, _c;
   unsigned int _m, _seed;

}; //-------------------------------------------------------------------------------------------------- class MS_RND : public mRND { public:

   MS_RND()  { _a = 214013; _c = 2531011; }
   int rnd() { return mRND::rnd() >> 16; }

}; //-------------------------------------------------------------------------------------------------- class BSD_RND : public mRND { public:

   BSD_RND() { _a = 1103515245; _c = 12345; }
   int rnd() { return mRND::rnd(); }

}; //-------------------------------------------------------------------------------------------------- int main( int argc, char* argv[] ) {

   BSD_RND bsd_rnd;
   MS_RND ms_rnd;

   cout << "MS RAND:" << endl << "========" << endl;
   for( int x = 0; x < 10; x++ )

cout << ms_rnd.rnd() << endl;

   cout << endl  << "BSD RAND:" << endl << "=========" << endl;
   for( int x = 0; x < 10; x++ )

cout << bsd_rnd.rnd() << endl;

   cout << endl << endl;
   system( "pause" );
   return 0;

} //--------------------------------------------------------------------------------------------------</lang> Output:

C++11

Works with: C++11

<lang cpp>#include <iostream>

include <random>

int main() {

 std::linear_congruential_engine<std::uint_fast32_t, 1103515245, 12345, 1 << 31> bsd_rand(0);
 std::linear_congruential_engine<std::uint_fast32_t, 214013, 2531011, 1 << 31> ms_rand(0);

 std::cout << "BSD RAND:" << std::endl << "========" << std::endl;
 for (int i = 0; i < 10; i++) {
   std::cout << bsd_rand() << std::endl;
 }
 std::cout << std::endl;
 std::cout << "MS RAND:" << std::endl << "========" << std::endl;
 for (int i = 0; i < 10; i++) {
   std::cout << (ms_rand() >> 16) << std::endl;
 }
 
 return 0;

}</lang> Output:

Clojure

(defn iterator [a b]

 (fn[x] (mod (+ (* a x) b) (bit-shift-left 1 31))))

(def bsd (drop 1 (iterate (iterator 1103515245 12345) 0)))

(def ms (drop 1 (for [x (iterate (iterator 214013 2531011) 0)] (bit-shift-right x 16))))

(take 10 bsd) ;-> (12345 1406932606 654583775 1449466924 229283573 1109335178 1051550459 1293799192 794471793 551188310) (take 10 ms) ;-> (38 7719 21238 2437 8855 11797 8365 32285 10450 30612)

</lang>

Common Lisp

<lang lisp>(defun make-rng (&key (seed 0) (mode nil))

 "returns an RNG according to :seed and :mode keywords
 default mode: bsd
 default seed: 0 (should be 1 actually)"
 (if (eql mode 'ms)
   #'(lambda ()

(ash (setf seed (mod (+ (* 214013 seed) 2531011) (expt 2 31))) -16))

   #'(lambda () (setf seed (mod (+ (* seed 1103515245) 12345) (expt 2 31))))))

(let ((rng (make-rng)))

     (dotimes (x 10) (format t "BSD: ~d~%" (funcall rng))))

(let ((rng (make-rng :mode 'ms :seed 1)))

     (dotimes (x 10) (format t "MS: ~d~%" (funcall rng))))</lang>

Another solution could be: <lang lisp>(defun linear-random (seed &key (times 1) (bounds (expt 2 31)) (multiplier 1103515245) (adder 12345) (divisor 1) (max 2147483647) (min 0))

 (loop for candidate = seed then (mod (+ (* multiplier candidate) adder) bounds)
    for result = candidate then (floor (/ candidate divisor))
    when (and (< result max) (> result min)) collect result into valid-numbers
    when (> (length valid-numbers) times) return result))</lang>

Which defaults to the BSD formula, but can be customized to any formula with keyword arguments, for example: <lang lisp>(format t "Count:~15tBSD:~30tMS:~%~{~{~a~15t~a~30t~a~%~}~}"

       (loop for i from 0 upto 5 collect
            (list i
                  (linear-random 0 :times i)
                  (linear-random 0 :times i :multiplier 214013 :adder 2531011 :max 32767 :divisor (expt 2 16)))))</lang>

Outputs:

Count:         BSD:           MS:
0              12345          38
1              1406932606     7719
2              654583775      21238
3              1449466924     2437
4              229283573      8855
5              1109335178     11797

D

<lang d>struct LinearCongruentialGenerator {

   enum uint RAND_MAX = (1U << 31) - 1;
   uint seed = 0;

   uint randBSD() pure nothrow @nogc {
       seed = (seed * 1_103_515_245 + 12_345) & RAND_MAX;
       return seed;
   }

   uint randMS() pure nothrow @nogc {
       seed = (seed * 214_013 + 2_531_011) & RAND_MAX;
       return seed >> 16;
   }

}

void main() {

   import std.stdio;

   LinearCongruentialGenerator rnd;

   foreach (immutable i; 0 .. 10)
       writeln(rnd.randBSD);
   writeln;

   rnd.seed = 0;
   foreach (immutable i; 0 .. 10)
       writeln(rnd.randMS);

}</lang> Output:

dc

dc has no bitwise operations, so this program uses the modulus operator (2147483648 %) and division (65536 /). Fortunately, dc numbers cannot overflow to negative, so the modulus calculation involves only non-negative integers.

For BSD rand(): <lang dc>[*

* lrx -- (random number from 0 to 2147483647)
*
* Returns a number from the BSD rand() sequence.
* Seeded by storing a seed in register R.
*]sz

[lR 1103515245 * 12345 + 2147483648 % d sR]sr

[* Set seed to 1, then print the first 3 random numbers. *]sz 1 sR lrx psz lrx psz lrx psz</lang>

1103527590
377401575
662824084

For Microsoft rand(): <lang dc>[*

* lrx -- (random number from 0 to 32767)
*
* Returns a number from the Microsoft rand() sequence.
* Seeded by storing a seed in register R.
*]sz

[lR 214013 * 2531011 + 2147483648 % d sR 65536 /]sr

[* Set seed to 1, then print the first 3 random numbers. *]sz 1 sR lrx psz lrx psz lrx psz</lang>

41
18467
6334

EDSAC order code

The first version of this solution had trouble with the "sandwich digit". As pointed out by Wilkes, Wheeler & Gill (1951 edition, page 26), a 35-bit constant cannot be loaded via pseudo-orders if the middle bit (sandwich digit) is 1. One workaround, adopted in the EDSAC solution to the Babbage Problem, is to use the negative of the constant instead. The alternative, which WWG evidently preferred and which is used in the LCG solution posted here, is to load 35-bit constants via the library subroutine R9.

The task doesn't specify what random seed is to be used. This program uses 1, with results identical to those from the Elixir program. <lang edsac>

[Linear congruential generators for pseudo-random numbers.
 EDSAC program, Initial Orders 2.]

[Library subroutine R9, to read integer constants at load time.
 See Wilkes, Wheeler & Gill, 1951 edition, pages 98 & 148.]
 ..PK
 T 56 K [must be loaded at 56]
 GKT20FVDL8FA40DUDTFI40FA40FS39FG@S2FG23FA5@T5@E4@

[Modification of library subroutine P7.
 Prints non-negative integer, up to 10 digits, right-justified.
 55 locations, load at even address.
 Set up to be called with 'G N', so that caller needn't know its address.
 See Wilkes, Wheeler & Gill, 1951 edition, page 18.]
           T  46 K  [location corresponding to N parameter]
           P  72 F  [load subroutine at 72]
           E  25 K  TN
 GKA3FT42@A47@T31@ADE10@T31@A48@T31@SDTDH44#@NDYFLDT4DS43@TF
 H17@S17@A43@G23@UFS43@T1FV4DAFG50@SFLDUFXFOFFFSFL4FT4DA49@T31@
 A1FA43@G20@XFP1024FP610D@524D!FO46@O26@XFO46@SFL8FT4DE39@

[BSD linear congruential generator.
 Call with 'G B' to initialize, passing seed in 0D.
 Call with 'G 1 B' to get next value, returned in 0D.]
           T  53 K  [location corresponding to B parameter]
           P 140 F  [load subroutine at 140]
           E  25 K  TB GK
     [0]   G  10 @  [jump to initialize]
     [1]   G  15 @  [jump to get next value]
     [2]   PF  PF   [mask, 2^31 - 1]
     [4]   PF  PF   [multiplier]
     [6]   PF  PF   [added constant]
        [Call R9 to set the 3 preceding constants at load time.]
           E69KT2#@
           2147483647F1103515245F12345#
           T8Z
     [8]   PF  PF    [current state]

        [Initialize; caller places seed in 0D]
    [10]   A    3 F  [make jump back to caller]
           T   14 @  [plant in code]
           A      D  [load seed passed by caller]
           T    8#@  [store as initial state]
    [14]   Z      F  [overwritten by jump back to caller]

        [Get next value from BSD; return it in 0D]
    [15]   A    3 F  [make jump back to caller]
           T   28 @  [plant in code, acc := 0]
           H    4#@  [mult reg := multiplier]
           V    8#@  [acc := state * multiplier]
           LF  LF  L64F  [shift 34 left, done as 13 + 13 + 8]
           A    6#@  [add the constant]
           T      D  [temp store in 0D]
           H    2#@  [mult reg := mask]
           C      D  [acc := result modulo 2^31]
           U    8#@  [update state]
           T      D  [also to 0D for caller]
    [28]   Z      F  [overwritten by jump back to caller]

[Microsoft linear congruential generator.
 Call with 'G M' to initialize, passing seed in 0D.
 Call with 'G 1 M' to get next value, returned in 0D.
 Very similar to code for BSD, so given in condensed form.]
 T47KP180FE25KTMGKG10@G15@PFPFPFPFPFPFE69KT2#@
        2147483647F214013F2531011# [the 3 constants]
 T8ZPFPFA3FT14@ADT8#@ZFA3FT30@H4#@V8#@LFLFL64FA6#@TDH2#@CDU8#@
[Unlike BSD, MS returns the state divided by 2^16]
           RF  RD  [shift 16 right, done as 15 + 1]
           T    D  [to 0D for caller]
    [30]   Z    F  [overwritten by jump back to caller]

[Main routine]
           T  220 K  [load at 220]
           G      K  [set theta parameter as usual]
     [0]   PF    PF  [35-bit seed]
        [Use library subroutine R9 to set seed]
           E69K T#@
           1#        [non-negative seed followed by '#']
           T2Z
     [2]   P      F  [negative counter for loop]
     [3]   P   10 F  [to print first 10 values]
        [Characters for printing]
     [4]   B      F
     [5]   D      F
     [6]   E      F
     [7]   M      F
     [8]   S      F
     [9]   C      F  [colon when in figures mode]
    [10]   K 2048 F  [set letters on teleprinter]
    [11]   #      F  [set figures on teleprinter]
    [12]   @      F  [carriage return]
    [13]   &      F  [line feed]
    [14]   K 4096 F  [null]

       [Enter with acc = 0]
       [Print 'SEED:' and then the seed]
    [15]   O10@ O8@ O6@ O6@ O5@ O11@ O9@
           A     #@  [load seed]
           T      D  [store in 0D for printing]
    [24]   A   24 @  [pass return address]
           G      N  [call print subroutine]
           O12@ O13@ [print new line]

        [Initialize the BSD generator]
           A     #@  [load seed]
           T      D  [pass seed in 0D]
    [30]   A   30 @  [pass return address]
           G      B  [call BSD initializer]
           O10@ O4@ O8@ O5@ O11@ O9@ O12@ O13@  [print 'BSD:']
           S    3 @  [load negative of count]
        [Loop printing values from BSD generator]
    [41]   T    2 @  [update negative counter]
    [42]   A   42 @  [pass return address]
           G    1 B  [call BSD to get next value in 0D]
    [44]   A   44 @  [pass return address]
           G      N  [call print subroutine]
           O12@ O13@ [print new line]
           A    2 @  [load negative counter]
           A    2 F  [increment]
           G   41 @  [loop until counter = 0]

[Microsoft LCG, very similar to BSD, so given in condensed form]
 A#@TDA53@GMO10@O7@O8@O11@O9@O12@O13@S3@T2@A64@G1MA66@GNO12@O13@A2@A2FG63@

           O   14 @  [print null to flush teleprinter buffer]
           Z      F  [stop]
           E   15 Z  [define entry point]
           P      F  [acc = 0 on entry]

</lang>

Output:

SEED:          1
BSD:
 1103527590
  377401575
  662824084
 1147902781
 2035015474
  368800899
 1508029952
  486256185
 1062517886
  267834847
MS:
         41
      18467
       6334
      26500
      19169
      15724
      11478
      29358
      26962
      24464

Elixir

<lang elixir>defmodule LCG do

 def ms_seed(seed) do
   Process.put(:ms_state, seed)
   ms_rand
   Process.put(:ms_seed, seed)
 end
 
 def ms_rand do
   state = Process.get(:ms_state)
   state2 = rem(214013 * state + 2531011, 2147483648)
   Process.put(:ms_state, state2)
   div(state, 65536)
 end
 
 def bsd_seed(seed) do
   Process.put(:bsd_state, seed)
   Process.put(:bsd_seed, seed)
 end
 
 def bsd_rand do
   state = Process.get(:bsd_state)
   state2 = rem(1103515245 * state + 12345, 2147483648)
   Process.put(:bsd_state, state2)
   state2
 end

end

Enum.each([0,1], fn i ->

 IO.puts "\nRandom seed: #{i}\n        BSD      MS"
 LCG.bsd_seed(i)
 LCG.ms_seed(i)
 Enum.each(1..10, fn _ ->
   :io.format "~11w~8w~n", [LCG.bsd_rand, LCG.ms_rand]
 end)

end)</lang>

Output:

Random seed: 0
        BSD      MS
      12345      38
 1406932606    7719
  654583775   21238
 1449466924    2437
  229283573    8855
 1109335178   11797
 1051550459    8365
 1293799192   32285
  794471793   10450
  551188310   30612

Random seed: 1
        BSD      MS
 1103527590      41
  377401575   18467
  662824084    6334
 1147902781   26500
 2035015474   19169
  368800899   15724
 1508029952   11478
  486256185   29358
 1062517886   26962
  267834847   24464

Erlang

Translation of: Elixir

<lang erlang>-module(lcg). -export([bsd_seed/1, ms_seed/1, bsd_rand/0, ms_rand/0]).

bsd_seed(Seed) -> put(bsd_state, Seed). ms_seed(Seed) -> put(ms_state, Seed).

bsd_rand() ->

 State = (get(bsd_state) * 1103515245 + 12345) rem 2147483648,
 put(bsd_state,State),
 State.

ms_rand() ->

 State = (get(ms_state) * 214013 + 2531011) rem 2147483648,
 put(ms_state,State),
 State div 65536.

main(_) ->

 bsd_seed(0), 
 ms_seed(0), 
 io:fwrite("~10s~c~5s~n", ["BSD", 9, "MS"]),
 lists:map(fun(_) -> io:fwrite("~10w~c~5w~n", [bsd_rand(),9,ms_rand()]) end, lists:seq(1,10)).</lang>

Output:

       BSD         MS
     12345         38
1406932606       7719
 654583775      21238
1449466924       2437
 229283573       8855
1109335178      11797
1051550459       8365
1293799192      32285
 794471793      10450
 551188310      30612

ERRE

ERRE doesn't generate the proper output from the BSD constants; it uses double-precision floating point, which is not enough for some of the intermediate products: for exact computation you can use MULPREC program. The BSD series deviates starting with the third value (see sample output below). <lang ERRE>PROGRAM RNG

!$DOUBLE

DIM CARDS%[52]

PROCEDURE XRANDOM(SEED->XRND)

  POW31=2^31
  POW16=2^16
  SEED=SEED*214013+2531011
  SEED=SEED-POW31*INT(SEED/POW31)
  XRND=INT(SEED/POW16)

END PROCEDURE

PROCEDURE YRANDOM(SEED->YRND)

  POW31=2^31
  SEED=SEED*1103515245+12345
  SEED=SEED-POW31*INT(SEED/POW31)
  YRND=SEED

END PROCEDURE

BEGIN

   PRINT(CHR$(12);)
   SEED=0  PRINT("BSD:")
   FOR I%=1 TO 10 DO
      YRANDOM(SEED->YRND)
      PRINT(TAB(10);YRND)
   END FOR
   SEED=0  PRINT("MSD:")
   FOR I%=1 TO 10 DO
      XRANDOM(SEED->XRND)
      PRINT(TAB(10);XRND)
   END FOR

END PROGRAM</lang>

Output:

F#

<lang fsharp>module lcg =

   let bsd seed =
       let state = ref seed
       (fun (_:unit) ->
           state := (1103515245 * !state + 12345) &&& System.Int32.MaxValue
           !state)

   let ms seed =
       let state = ref seed
       (fun (_:unit) ->
           state := (214013 * !state + 2531011) &&& System.Int32.MaxValue
           !state / (1<<<16))

</lang>

let rndBSD = lcg.bsd 0;; 
let BSD=[for n in [0 .. 9] -> rndBSD()];;

let rndMS = lcg.ms 0;; 
let MS=[for n in [0 .. 9] -> rndMS()];;

val BSD : int list =
  [12345; 1406932606; 654583775; 1449466924; 229283573; 1109335178; 1051550459;
   1293799192; 794471793; 551188310]
val MS : int list =
  [38; 7719; 21238; 2437; 8855; 11797; 8365; 32285; 10450; 30612]

Forth

<lang forth>1 31 lshift 1- constant MAX-RAND-BSD 1 15 lshift 1- constant MAX-RAND-MS

variable seed \ seed variable

(random) seed @ * + dup seed ! ; ( -- n)

BSDrandom MAX-RAND-BSD 12345 1103515245 (random) and ;

MSrandom MAX-RAND-MS 2531011 214013 (random) 16 rshift and ;

test-random

 1 seed ! cr ." BSD (seed=1)" cr
 5 0 do BSDrandom . cr loop
 1 seed ! cr ." MS  (seed=1)" cr
 5 0 do MSrandom . cr loop

test-random</lang>

Output:

BSD (seed=1)
1103527590
377401575
662824084
1147902781
2035015474

MS  (seed=1)
41
18467
6334
26500
19169

Fortran

Works with: Fortran version 90 and later

<lang fortran>module lcgs

 implicit none

 integer, parameter :: i64 = selected_int_kind(18)
 integer, parameter :: a1 = 1103515245, a2 = 214013
 integer, parameter :: c1 = 12345, c2 = 2531011
 integer, parameter :: div = 65536
 integer(i64), parameter :: m = 2147483648_i64  ! need to go to 64 bits because
                                                ! of the use of signed integers

contains

function bsdrand(seed)

 integer :: bsdrand
 integer, optional, intent(in) :: seed
 integer(i64) :: x = 0
 
 if(present(seed)) x = seed
 x = mod(a1 * x + c1, m)
 bsdrand = x

end function

function msrand(seed)

 integer :: msrand
 integer, optional, intent(in) :: seed
 integer(i64) :: x = 0

 if(present(seed)) x = seed 
 x = mod(a2 * x + c2, m)
 msrand = x / div

end function end module

program lcgtest

 use lcgs
 implicit none
 integer :: i
 
 write(*, "(a)") "      BSD            MS"
 do i = 1, 10
   write(*, "(2i12)") bsdrand(), msrand()
 end do

end program</lang> Output

      BSD            MS
       12345          38
  1406932606        7719
   654583775       21238
  1449466924        2437
   229283573        8855
  1109335178       11797
  1051550459        8365
  1293799192       32285
   794471793       10450
   551188310       30612

FreeBASIC

<lang freebasic>' version 04-11-2016 ' compile with: fbc -s console

' to seed BSD_lcg(seed > -1) ' to get random number BSD_lcg(-1) or BSD_lcg() or just BSD_lcg Function BSD_lcg(seed As UInteger = -1) As UInteger

   Static As UInteger bsd_state

   If seed <> -1 Then
       bsd_state = seed Mod 2 ^ 31
   Else
       bsd_state = (1103515245 * bsd_state + 12345) Mod 2 ^ 31
   End If

   Return bsd_state

End Function

' to seed ms_lcg(seed > -1) ' to get random number ms_lcg(-1) or ms_lcg() or just ms_lcg Function ms_lcg(seed As Integer = -1) As UInteger

   Static As UInteger ms_state

   If seed <> -1 Then
       ms_state = seed Mod 2 ^ 31
   Else
       ms_state = (214013 * ms_state + 2531011) Mod 2 ^ 31
   End If

   Return ms_state Shr 16

End Function

' ------=< MAIN >=------

Dim As Long i

Print "MS generator" ' ms_lcg(0) ' state = 0 at the start of the program For i = 1 To 10

   Print Using "###########"; ms_lcg

   Print Using "###########"; BSD_lcg

Output:

MS generator
         38
       7719
      21238
       2437
       8855
      11797
       8365
      32285
      10450
      30612

BSD generator
      12345
 1406932606
  654583775
 1449466924
  229283573
 1109335178
 1051550459
 1293799192
  794471793
  551188310

Go

<lang go>package main

import "fmt"

// basic linear congruential generator func lcg(a, c, m, seed uint32) func() uint32 {

   r := seed
   return func() uint32 {
       r = (a*r + c) % m
       return r
   }

}

// microsoft generator has extra division step func msg(seed uint32) func() uint32 {

   g := lcg(214013, 2531011, 1<<31, seed)
   return func() uint32 {
       return g() / (1 << 16)
   }

}

func example(seed uint32) {

   fmt.Printf("\nWith seed = %d\n", seed)
   bsd := lcg(1103515245, 12345, 1<<31, seed)
   msf := msg(seed)
   fmt.Println("       BSD  Microsoft")
   for i := 0; i < 5; i++ {
       fmt.Printf("%10d    %5d\n", bsd(), msf())
   }

}

func main() {

   example(0)
   example(1)

}</lang> Output:

With seed = 0
       BSD  Microsoft
     12345       38
1406932606     7719
 654583775    21238
1449466924     2437
 229283573     8855

With seed = 1
       BSD  Microsoft
1103527590       41
 377401575    18467
 662824084     6334
1147902781    26500
2035015474    19169

Haskell

<lang haskell>bsd = tail . iterate (\n -> (n * 1103515245 + 12345) `mod` 2^31) msr = map (`div` 2^16) . tail . iterate (\n -> (214013 * n + 2531011) `mod` 2^31)

main = do print $ take 10 $ bsd 0 -- can take seeds other than 0, of course print $ take 10 $ msr 0</lang>

Icon and Unicon

The following LCRNG's behave in the same way maintaining the state (seed) from round to round. There is an srand procedure for each lcrng that maintains the seed state and allows the user to assign a new state. <lang Icon>link printf

procedure main()

  printf("       BSD        MS\n")
  every 1 to 10 do 
     printf("%10s %10s\n",rand_BSD(),rand_MS())

end

procedure srand_BSD(x) #: seed random static seed

  return seed := \x | \seed | 0   # parm or seed or zero if none

end

procedure rand_BSD() #: lcrng

  return srand_BSD((1103515245 * srand_BSD() + 12345) % 2147483648)

end

procedure srand_MS(x) #: seed random static seed

  return seed := \x | \seed | 0   # parm or seed or zero if none

end

procedure rand_MS() #: lcrng

  return ishift(srand_MS((214013 * srand_MS() + 2531011) % 2147483648),-16)

end</lang>

Library: Icon Programming Library

printf.icn provides printf

J

Solution: <lang j>lcg=: adverb define

0 m lcg y                     NB. default seed of 0

'a c mod'=. x: m
}. (mod | c + a * ])^:(<y+1) x

)

rand_bsd=: (1103515245 12345 , <.2^31) lcg rand_ms=: (2^16) <.@:%~ (214013 2531011 , <.2^31) lcg</lang> Example Use: <lang j> rand_bsd 10 12345 1406932606 654583775 1449466924 229283573 1109335178 1051550459 1293799192 794471793 551188310

  654583775 rand_bsd 4

1449466924 229283573 1109335178 1051550459

  rand_ms 10

38 7719 21238 2437 8855 11797 8365 32285 10450 30612

  1 rand_ms 5                  NB. seed of 1

41 18467 6334 26500 19169</lang>

Java

Works with: Java version 8

<lang java>import java.util.stream.IntStream; import static java.util.stream.IntStream.iterate;

public class LinearCongruentialGenerator {

   final static int mask = (1 << 31) - 1;

   public static void main(String[] args) {
       System.out.println("BSD:");
       randBSD(0).limit(10).forEach(System.out::println);

       System.out.println("\nMS:");
       randMS(0).limit(10).forEach(System.out::println);
   }

   static IntStream randBSD(int seed) {
       return iterate(seed, s -> (s * 1_103_515_245 + 12_345) & mask).skip(1);
   }

   static IntStream randMS(int seed) {
       return iterate(seed, s -> (s * 214_013 + 2_531_011) & mask).skip(1)
               .map(i -> i >> 16);
   }

}</lang>

jq

Currently, jq arithmetic is based on IEEE 754 64-bit numbers. As a result, it is trivial to implement the Microsoft linear congruential generator (LCG), but the BSD generator requires some kind of "big integer" support. In this section, therefore, we first present functions to support the Microsoft LCG, and then present functions to support the LCG on the assumption that a suitable jq "BigInt" library is available.

Microsoft LCG

<lang jq># 15-bit integers generated using the same formula as rand()

from the Microsoft C Runtime.
Input: [ count, state, rand ]

def next_rand_Microsoft:

 .[0] as $count | .[1] as $state
 | ( (214013 * $state) + 2531011) % 2147483648 # mod 2^31
 | [$count+1 , ., (. / 65536 | floor) ];

Generate the first n pseudo-random numbers:

def rand_Microsoft(seed; n):

 [0,seed]
 | next_rand_Microsoft  # the seed is not so random
 | recurse(if .[0] < n then next_rand_Microsoft else empty end)
 | .[2];</lang>

Example:

rand_Microsoft(1;5)

Output:

BSD LCG

The following code has been tested with the "BigInt" library at [1]. <lang jq># BSD rand()

Input: [count, previous]

def next_rand_berkeley:

 long_multiply("1103515245" ; .[1]|tostring) as $lm
 | long_add( $lm; "12345") as $la
 # mod 2^31
 | [.[0] + 1, (long_mod( $la; "2147483648") | tonumber) ];

Generate n values

def rand_berkeley(seed; n):

 [0, seed]
 | next_rand_berkeley # skip the seed itself
 | recurse(if .[0] < n then next_rand_berkeley else empty end)
 | .[1];</lang>

Example:

rand_berkeley(1;5)

Output:

Julia

getlgc creates a linear congruential generator as a closure. This function is used to create the two generators called for by the task. <lang julia>using Printf

function getlgc(r::Integer, a::Integer, c::Integer, m::Integer, sh::Integer)

   state = r
   return function lgcrand()
       state = mod(a * state + c, m)
       return state >> sh
   end

end

seed, nrep = 0, 10 bsdrand = getlgc(seed, 1103515245, 12345, 2 ^ 31, 0)

println("The first $nrep results for a BSD rand seeded with $seed:") for _ in 1:nrep

   @printf("%14d\n", bsdrand())

end

msrand = getlgc(seed, 214013, 2531011, 2 ^ 31, 16)

println("\nThe first $nrep results for a M\$ rand seeded with $seed:") for _ in 1:nrep

   @printf("%14d\n", msrand())

end</lang>

Output:

The first 10 results for a BSD rand seeded with 0:
         12345
    1406932606
     654583775
    1449466924
     229283573
    1109335178
    1051550459
    1293799192
     794471793
     551188310

The first 10 results for a M$ rand seeded with 0:
            38
          7719
         21238
          2437
          8855
         11797
          8365
         32285
         10450
         30612

K

<lang K> bsd:{1_ y{((1103515245*x)+12345)!(_2^31)}\x}

  ms:{1_(y{_(((214013*x)+2531011)!(_2^31))}\x)%(_2^16)}

  bsd[0;10]

12345 1406932606 654583775 1449466924 229283573 1109335178 1051550459 1293799192 794471793 551188310

  ms[0;10]

38 7719 21238 2437 8855 11797 8365 32285 10450 30612</lang>

Kotlin

<lang scala>// version 1.1.3

class Lcg(val a: Long, val c: Long, val m: Long, val d: Long, val s: Long) {

   private var state = s
   
   fun nextInt(): Long {
       state = (a * state + c) % m
       return state / d
   }

}

fun main(args: Array<String>) {

   println("First 10 BSD random numbers - seed 0")
   val bsd = Lcg(1103515245, 12345, 1 shl 31, 1, 0)
   for (i in 1..10) println("${bsd.nextInt()}")
   println("\nFirst 10 MSC random numbers - seed 0")
   val msc = Lcg(214013, 2531011, 1 shl 31, 1 shl 16, 0)
   for (i in 1..10) println("${msc.nextInt()}")

}</lang>

Output:

First 10 BSD random numbers - seed 0
12345
1406932606
654583775
1449466924
229283573
1109335178
1051550459
1293799192
794471793
551188310

First 10 MSC random numbers - seed 0
38
7719
21238
2437
8855
11797
8365
32285
10450
30612

Liberty BASIC

<lang lb> 'by default these are 0 global BSDState global MSState

for i = 1 to 10

   print randBSD()

next i

print

for i = 1 to 10

   print randMS()

next i

function randBSD()

   randBSD = (1103515245 * BSDState + 12345) mod (2 ^ 31)
   BSDState = randBSD

end function

function randMS()

   MSState = (214013 * MSState + 2531011) mod (2 ^ 31)
   randMS = int(MSState / 2 ^ 16)

end function </lang>

Logo

Note that, perhaps ironically, UCB Logo, as of version 6.0, doesn't generate the proper output from the BSD constants; it uses double-precision floating point, which is not enough for some of the intermediate products. In UCBLogo, the BSD series deviates starting with the third value (see sample output below).

<lang Logo>; Configuration parameters for Microsoft and BSD implementations make "LCG_MS [214013 2531011 65536 2147483648] make "LCG_BSD [1103515245 12345 1 2147483648]

Default seed is 0

make "_lcg_value 0

set the seed

to lcg_seed :seed

 make "_lcg_value :seed

end

generate the next number in the series using the given parameters

to lcg_rand [:config :LCG_MS]

 local "a local "c local "d local "m
 foreach [a c d m] [
   make ? item # :config
 ]
 make "_lcg_value (modulo (sum (product :a :_lcg_value) :c) :m)
 output int quotient :_lcg_value :d

end

foreach (list :LCG_BSD :LCG_MS) [

 lcg_seed 0
 repeat 10 [
   print (lcg_rand ?)
 ]
 print []

] bye</lang>

Output:

UCBLogo output for the BSD section:

Lua

Works with: Lua version 5.3

This requires Lua 5.3 or later because previous versions didn't have support for large integers or integral arithmetic operations.

<lang lua>local RNG = {

 new = function(class, a, c, m, rand) 
   local self = setmetatable({}, class)
   local state = 0
   self.rnd = function() 
     state = (a * state + c) % m
     return rand and rand(state) or state
   end
   self.seed = function(new_seed)
     state = new_seed % m
   end
   return self
 end

}

bsd = RNG:new(1103515245, 12345, 1<<31) ms = RNG:new(214013, 2531011, 1<<31, function(s) return s>>16 end)

print"BSD:" for _ = 1,10 do

 print(("\t%10d"):format(bsd.rnd()))

end print"Microsoft:" for _ = 1,10 do

 print(("\t%10d"):format(ms.rnd()))

end </lang>

Output:

Mathematica

<lang Mathematica>BSDrand[x_] := Mod[x*1103515245 + 12345, 2147483648] NestList[BSDrand, 0, 10] -> {0, 12345, 1406932606, 654583775, 1449466924, 229283573, 1109335178, 1051550459, 1293799192, 794471793, 551188310}

MSrand[x_] := Mod[x*214013 + 2531011, 2147483648] BitShiftRight[ NestList[MSrand, 0, 10], 16] -> {0, 38, 7719, 21238, 2437, 8855, 11797, 8365, 32285, 10450, 30612}</lang>

Maxima

<lang maxima>seed: 0$ ms_rand() := quotient(seed: mod(214013 * seed + 2531011, 2147483648), 65536)$ makelist(ms_rand(), 20); /* see http://oeis.org/A096558 */

[38, 7719, 21238, 2437, 8855, 11797, 8365, 32285, 10450, 30612, 5853, 28100, 1142, 281, 20537, 15921, 8945, 26285, 2997, 14680]

seed: 0$ bsd_rand() := seed: mod(1103515245 * seed + 12345, 2147483648)$ makelist(bsd_rand(), 20); /* see http://www.randomwalk.de/scimath/prngseqs.txt */

[12345, 1406932606, 654583775, 1449466924, 229283573, 1109335178, 1051550459, 1293799192, 794471793, 551188310, 803550167, 1772930244, 370913197, 639546082, 1381971571, 1695770928, 2121308585, 1719212846, 996984527, 1157490780]</lang>

Nim

<lang nim>proc bsdRand(seed: int): iterator: int =

 var seed = seed
 result = iterator: int =
   while true:
     seed = (1103515245 * seed + 12345) and 0x7fffffff
     yield seed

proc msvcrtRand(seed: int): iterator: int =

 var seed = seed
 result = iterator: int =
   while true:
     seed = (214013 * seed + 2531011) and 0x7fffffff
     yield seed</lang>

Oforth

Function genLCG returns a block object that, when performed, will return the next random number from the LCG.

<lang Oforth>: genLCG(a, c, m, seed) | ch |

  Channel newSize(1) dup send(seed) drop ->ch
  #[ ch receive a * c + m mod dup ch send drop ] ;</lang>

Output:

genLCG(1103515245, 12345, 2 31 pow asInteger, 0) #[ dup perform println ] times(10) drop
12345
1406932606
654583775
1449466924
229283573
1109335178
1051550459
1293799192
794471793
551188310

genLCG(214013, 2531011, 2 31 pow asInteger, 0) #[ dup perform 65536 / println ] times(10) drop
38
7719
21238
2437
8855
11797
8365
32285
10450
30612

PARI/GP

Note that up to PARI/GP version 2.4.0, random() used a linear congruential generator. <lang parigp>BSDseed=Mod(1,1<<31); MSFTseed=Mod(1,1<<31); BSD()=BSDseed=1103515245*BSDseed+12345;lift(BSDseed); MSFT()=MSFTseed=214013*MSFTseed+2531011;lift(MSFTseed)%(1<<31);</lang>

Pascal

<lang pascal>Program LinearCongruentialGenerator(output); {$mode iso} var

 x1, x2: int64;

function bsdrand: cardinal;

 const
   a = 1103515245;
   c = 12345;
   m = 2147483648;
 begin
   x1 := (a * x1 + c) mod m;
   bsdrand := x1;
 end;

function msrand: cardinal;

 const
   a = 214013;
   c = 2531011;
   m = 2147483648;
 begin
   x2 := (a * x2 + c) mod m;
   msrand := x2 div 65536;
 end;

var

 i: cardinal;

begin

 writeln('      BSD            MS');
 x1 := 0;
 x2 := 0;
 for i := 1 to 10 do
   writeln(bsdrand:12, msrand:12);

end. </lang> Output:

      BSD            MS
       12345          38
  1406932606        7719
   654583775       21238
  1449466924        2437
   229283573        8855
  1109335178       11797
  1051550459        8365
  1293799192       32285
   794471793       10450
   551188310       30612

Perl

Creates a magic scalar whose value is next in the LCG sequence when read.<lang perl>use strict; package LCG;

use overload '0+' => \&get;

use integer; sub gen_bsd { (1103515245 * shift() + 12345) % (1 << 31) }

sub gen_ms { my $s = (214013 * shift() + 2531011) % (1 << 31); $s, $s / (1 << 16) }

sub set { $_[0]->{seed} = $_[1] } # srand sub get { my $o = shift; ($o->{seed}, my $r) = $o->{meth}->($o->{seed}); $r //= $o->{seed} }

sub new { my $cls = shift; my %opts = @_; bless { seed => $opts{seed}, meth => $opts{meth} eq 'MS' ? \&gen_ms : \&gen_bsd, }, ref $cls || $cls; }

package main;

my $rand = LCG->new;

print "BSD:\n"; print "$rand\n" for 1 .. 10;

$rand = LCG->new(meth => 'MS');

print "\nMS:\n"; print "$rand\n" for 1 .. 10;</lang>output<lang>BSD: 12345 1406932606 654583775 1449466924 229283573 1109335178 1051550459 1293799192 794471793 551188310

MS: 38 7719 21238 2437 8855 11797 8365 32285 10450 30612</lang>

Phix

Library: Phix/mpfr

As per the comments, I had to resort to gmp to get BSDrnd() to work on 32-bit. <lang Phix>atom seed

include builtins/mpfr.e

function BSDrnd()

   -- oh dear, native only works on 64-bit, 
   -- as per ERRE and UCBLogo above on 32-bit...

-- seed = remainder(1103515245 * seed + 12345, #8000_0000)

   -- so, resort to gmp, with the added twist than both
   -- 1103515245 and #8000_0000 are greater than 1GB and
   -- therefore a smidge too big & need some extra help...
   mpz z = mpz_init(seed), 
       h8 = mpz_init("2147483648") -- (ie #8000_0000)
   mpz_mul_si(z,z,5)
   mpz_mul_si(z,z,1103515245/5)    -- (do in two <1GB factors)
   mpz_add_si(z,z,12345)
   mpz_fdiv_r(z,z,h8)
   seed = mpz_get_atom(z)
   return seed

end function

function MSrnd()

   seed = and_bits(seed*214013+2531011,#7FFFFFFF)
   return floor(seed/power(2,16))

end function

seed = 0 ?"BSDrnd" for i=1 to 10 do printf(1,"%d\n",BSDrnd()) end for seed = 0 ?"MSrnd" for i=1 to 10 do printf(1,"%d\n",MSrnd()) end for</lang>

Output:

PHP

Works with: PHP version 5.3+

<lang php><?php function bsd_rand($seed) {

   return function() use (&$seed) {
       return $seed = (1103515245 * $seed + 12345) % (1 << 31);
   };

}

function msvcrt_rand($seed) {

   return function() use (&$seed) {
       return ($seed = (214013 * $seed + 2531011) % (1 << 31)) >> 16;
   };

}

$lcg = bsd_rand(0); echo "BSD "; for ($i = 0; $i < 10; $i++)

   echo $lcg(), " ";

echo "\n";

$lcg = msvcrt_rand(0); echo "Microsoft "; for ($i = 0; $i < 10; $i++)

   echo $lcg(), " ";

echo "\n"; ?></lang>

PicoLisp

<lang PicoLisp>(zero *BsdSeed *MsSeed)

(de bsdRand ()

  (setq *BsdSeed
     (& (+ 12345 (* 1103515245 *BsdSeed)) `(dec (** 2 31))) ) )

(de msRand ()

  (>> 16
     (setq *MsSeed
        (& (+ 2531011 (* 214013 *MsSeed)) `(dec (** 2 31))) ) ) )</lang>

Output:

: (do 7 (printsp (bsdRand)))
12345 1406932606 654583775 1449466924 229283573 1109335178 1051550459 -> 1051550459

: (do 12 (printsp (msRand)))
38 7719 21238 2437 8855 11797 8365 32285 10450 30612 5853 28100 -> 28100

PL/I

<lang> (nofixedoverflow, nosize): LCG: procedure options (main);

  declare i fixed binary;

  put skip list ('BSD', 'MS');
  do i = 1 to 20;
     put skip list (BSD(), MS());
  end;

bsd: procedure returns (fixed binary (31));

   declare const fixed binary static initial (12345);
   declare s fixed binary (31) static initial (123456789);

   s = s * 1103515245 + const;
   s = isrl(isll(s,1), 1);
   return (s);

end bsd; ms: procedure returns (fixed binary (15));

   declare const fixed binary (31) static initial (2531011);
   declare s     fixed binary (31) static initial (123456789);

   s = s * 214013 + const;
   s = isrl(isll(s,1), 1);
   return (isrl(s,16));

end ms;

end LCG; </lang> OUTPUT:

BSD                     MS 
     231794730              13259 
    1126946331              26974 
    1757975480              13551 
     850994577              30354 
    1634557174              18709 
     707246327              15861 
    1397699428              16906 
    1035569613              21981 
    1904890498               8603 
    1335160211              12911 
    1434329552              18110 
    1273099721               3228 
    1250890958              27918 
    1016516591              17989 
    1097566972              22768 
     436938117              23599 
    1175171034               7712 
    1059748875              15601 
     308566760               7038 
     534615297              21512

PowerShell

<lang powershell> Function msstate{

   Param($current_seed)
   Return (214013*$current_seed+2531011)%2147483648}

Function randMS{

   Param($MSState)
   Return [int]($MSState/65536)}

Function randBSD{

   Param($BSDState)
   Return (1103515245*$BSDState+12345)%2147483648}

Write-Host "MS: seed=0" $seed=0 #initialize seed For($i=1;$i-le5;$i++){

   $seed = msstate($seed)
   $rand = randMS($seed)
   Write-Host $rand}

Write-Host "BSD: seed=0" $seed=0 #initialize seed For($j=1;$j-le5;$j++){

   $seed = randBSD($seed)
   Write-Host $seed}

</lang>

Output:

MS: seed=0
39
7720
21238
2437
8855
BSD: seed=0
12345
1406932606
654583775
1449466924
229283573

PureBasic

<lang purebasic>Procedure ms_LCG(seed.q = -1)

 Static state.q
 If seed >= 0
   state = seed
 Else
   state = (state * 214013 + 2531011) % (1 << 31) 
   ProcedureReturn state >> 16
 EndIf

EndProcedure

Procedure.q bsd_LCG(seed.q = -1)

 Static state.q
 If seed >= 0
   state = seed
 Else 
   state = (state * 1103515245 + 12345) % (1 << 31) 
   ProcedureReturn state
 EndIf

EndProcedure

If OpenConsole()

 Define i
 PrintN("BSD (seed = 1)")
 bsd_LCG(1)
 For i = 1 To 5
   PrintN(Str(bsd_LCG()))
 Next
 
 PrintN(#CRLF$ + "MS (seed = 1)")
 ms_LCG(1)
 For i = 1 To 5
   PrintN(Str(ms_LCG()))
 Next
  
 Print(#CRLF$ + #CRLF$ + "Press ENTER to exit"): Input()
 CloseConsole()

EndIf</lang> Sample output:

BSD (seed = 1)
1103527590
377401575
662824084
1147902781
2035015474

MS (seed = 1)
41
18467
6334
26500
19169

Python

<lang python>def bsd_rand(seed):

  def rand():
     rand.seed = (1103515245*rand.seed + 12345) & 0x7fffffff
     return rand.seed
  rand.seed = seed
  return rand

def msvcrt_rand(seed):

  def rand():
     rand.seed = (214013*rand.seed + 2531011) & 0x7fffffff
     return rand.seed >> 16
  rand.seed = seed
  return rand</lang>

Works with: Python version 3.x

<lang python>def bsd_rand(seed):

  def rand():
     nonlocal seed
     seed = (1103515245*seed + 12345) & 0x7fffffff
     return seed
  return rand

def msvcrt_rand(seed):

  def rand():
     nonlocal seed
     seed = (214013*seed + 2531011) & 0x7fffffff
     return seed >> 16
  return rand</lang>

Racket

The following solution uses generators and transcribes the mathematical formulas above directly. It does not attempt to be efficient.

lang racket

(require racket/generator)

(define (bsd-update state_n)

 (modulo (+ (* 1103515245 state_n) 12345)
         (expt 2 31)))

(define (ms-update state_n)

 (modulo (+ (* 214013 state_n) 2531011)
         (expt 2 31)))

(define ((rand update ->rand) seed)

 (generator ()
  (let loop ([state_n seed])
    (define state_n+1 (update state_n))
    (yield (->rand state_n+1))
    (loop state_n+1))))

(define bsd-rand (rand bsd-update identity)) (define ms-rand (rand ms-update (λ (x) (quotient x (expt 2 16))))) </lang>

Raku

(formerly Perl 6)

We'll define subroutines implementing the LCG algorithm for each version. We'll make them return a lazy list.

<lang perl6>constant modulus = 2**31; sub bsd {

   $^seed, ( 1103515245 * * + 12345 ) % modulus ... *

} sub ms {

   map * +> 16, (

$^seed, ( 214013 * * + 2531011 ) % modulus ... *

}

say 'BSD LCG first 10 values (first one is the seed):'; .say for bsd(0)[^10];

say "\nMS LCG first 10 values (first one is the seed):"; .say for ms(0)[^10];</lang>

BSD LCG first 10 values (first one is the seed):
0
12345
1406932606
654583775
1449466924
229283573
1109335178
1051550459
1293799192
794471793

MS LCG first 10 values (first one is the seed):
0
38
7719
21238
2437
8855
11797
8365
32285
10450

REXX

<lang rexx>/*REXX program uses a congruential generator that simulates the old BSD and MS random */ /*──────────── number generators. BSD= 0 ──► (2**31)-1 MS= 0 ──► (2**16)-1 */ numeric digits 20 /*use enough dec. digs for the multiply*/

 do seed=0  to 1                                /*perform for seed=0  and also  seed=1.*/
 bsd= seed;    ms= seed                         /*assign  SEED  to  two REXX variables.*/
 say center('seed='seed, 79, "─")               /*display the seed in a title/separator*/
                                                /* [↓]  show 20 rand #'s for each seed.*/
     do j=1  for 20                             /*generate and display 20 rand numbers.*/
     bsd = (1103515245 * bsd  +    12345)    //    2**31
     ms  = (    214013 *  ms  +  2531011)    //    2**31
     say '  state'   right(j,3)   " BSD"   right(bsd,     11)   left(, 13),
                                  " MS"    right( ms,     11)   left(,  5),
                                  " rand"  right(ms%2**16, 6)
     end   /*j*/
 end       /*seed*/                             /*stick a fork in it,  we're all done. */</lang>

output (shown at five-sixth size.)

────────────────────────────────────seed=0─────────────────────────────────────
  state   1  BSD       12345                MS     2531011        rand     38
  state   2  BSD  1406932606                MS   505908858        rand   7719
  state   3  BSD   654583775                MS  1391876949        rand  21238
  state   4  BSD  1449466924                MS   159719620        rand   2437
  state   5  BSD   229283573                MS   580340855        rand   8855
  state   6  BSD  1109335178                MS   773150046        rand  11797
  state   7  BSD  1051550459                MS   548247209        rand   8365
  state   8  BSD  1293799192                MS  2115878600        rand  32285
  state   9  BSD   794471793                MS   684884587        rand  10450
  state  10  BSD   551188310                MS  2006221698        rand  30612
  state  11  BSD   803550167                MS   383622205        rand   5853
  state  12  BSD  1772930244                MS  1841626636        rand  28100
  state  13  BSD   370913197                MS    74896543        rand   1142
  state  14  BSD   639546082                MS    18439398        rand    281
  state  15  BSD  1381971571                MS  1345953809        rand  20537
  state  16  BSD  1695770928                MS  1043415696        rand  15921
  state  17  BSD  2121308585                MS   586225427        rand   8945
  state  18  BSD  1719212846                MS  1722639754        rand  26285
  state  19  BSD   996984527                MS   196417061        rand   2997
  state  20  BSD  1157490780                MS   962080852        rand  14680
────────────────────────────────────seed=1─────────────────────────────────────
  state   1  BSD  1103527590                MS     2745024        rand     41
  state   2  BSD   377401575                MS  1210316419        rand  18467
  state   3  BSD   662824084                MS   415139642        rand   6334
  state   4  BSD  1147902781                MS  1736732949        rand  26500
  state   5  BSD  2035015474                MS  1256316804        rand  19169
  state   6  BSD   368800899                MS  1030492215        rand  15724
  state   7  BSD  1508029952                MS   752224798        rand  11478
  state   8  BSD   486256185                MS  1924036713        rand  29358
  state   9  BSD  1062517886                MS  1766988168        rand  26962
  state  10  BSD   267834847                MS  1603301931        rand  24464
  state  11  BSD   180171308                MS   373929026        rand   5705
  state  12  BSD   836760821                MS  1844513277        rand  28145
  state  13  BSD   595337866                MS  1525789900        rand  23281
  state  14  BSD   790425851                MS  1102819423        rand  16827
  state  15  BSD  2111915288                MS   652855718        rand   9961
  state  16  BSD  1149758321                MS    32201169        rand    491
  state  17  BSD  1644289366                MS   196285776        rand   2995
  state  18  BSD  1388290519                MS   782671571        rand  11942
  state  19  BSD  1647418052                MS   316395082        rand   4827
  state  20  BSD  1675546029                MS   356309989        rand   5436

Ruby

You can create multiple instances of LCG::Berkeley or LCG::Microsoft. Each instance privately keeps the original seed in @seed, and the current state in @r. Each class resembles the core Random class, but with fewer features. The .new method takes a seed. The #rand method returns the next random number. The #seed method returns the original seed.

<lang ruby>module LCG

 module Common
   # The original seed of this generator.
   attr_reader :seed

   # Creates a linear congruential generator with the given _seed_.
   def initialize(seed)
     @seed = @r = seed
   end
 end

 # LCG::Berkeley generates 31-bit integers using the same formula
 # as BSD rand().
 class Berkeley
   include Common
   def rand
     @r = (1103515245 * @r + 12345) & 0x7fff_ffff
   end
 end

 # LCG::Microsoft generates 15-bit integers using the same formula
 # as rand() from the Microsoft C Runtime.
 class Microsoft
   include Common
   def rand
     @r = (214013 * @r + 2531011) & 0x7fff_ffff
     @r >> 16
   end
 end

end</lang>

The next example sets the seed to 1, and prints the first 5 random numbers.

<lang ruby>lcg = LCG::Berkeley.new(1) p (1..5).map {lcg.rand}

prints [1103527590, 377401575, 662824084, 1147902781, 2035015474]

lcg = LCG::Microsoft.new(1) p (1..5).map {lcg.rand}

prints [41, 18467, 6334, 26500, 19169]</lang>

Run BASIC

<lang runbasic>global bsd global ms print "Num ___Bsd___";chr$(9);"__Ms_" for i = 1 to 10

   print using("##",i);using("############",bsdRnd());chr$(9);using("#####",msRnd())

next i

function bsdRnd()

   bsdRnd = (1103515245 * bsd + 12345) mod (2 ^ 31)
   bsd = bsdRnd

end function

function msRnd()

   ms = (214013 * ms + 2531011) mod (2 ^ 31)
   msRnd = int(ms / 2 ^ 16)

end function</lang>

Num  ___Bsd___	__Ms_
 1       12345	   38
 2  1406932606	 7719
 3   654583775	21238
 4  1449466924	 2437
 5   229283573	 8855
 6  1109335178	11797
 7  1051550459	 8365
 8  1293799192	32285
 9   794471793	10450
10   551188310	30612

Rust

<lang rust>extern crate rand;

pub use rand::{Rng, SeedableRng};

pub struct BsdLcg {

   state: u32,

}

impl Rng for BsdLcg {

   // Because the output is in the range [0, 2147483647], this should technically be `next_u16`
   // (the largest integer size which is fully covered, as `rand::Rng` assumes).  The `rand`
   // crate does not provide it however.  If serious usage is required, implementing this
   // function as a concatenation of two `next_u16`s (elsewhere defined) should work.
   fn next_u32(&mut self) -> u32 {
       self.state = self.state.wrapping_mul(1_103_515_245).wrapping_add(12_345);
       self.state %= 1 << 31;
       self.state
   }

}

impl SeedableRng<u32> for BsdLcg {

   fn from_seed(seed: u32) -> Self {
       Self { state: seed }
   }
   fn reseed(&mut self, seed: u32) {
       self.state = seed;
   }

}

pub struct MsLcg {

   state: u32,

}

impl Rng for MsLcg {

   // Similarly, this outputs in the range [0, 32767] and should output a `u8`.  Concatenate
   // four `next_u8`s for serious usage.
   fn next_u32(&mut self) -> u32 {
       self.state = self.state.wrapping_mul(214_013).wrapping_add(2_531_011);
       self.state %= 1 << 31;
       self.state >> 16 // rand_n = state_n / 2^16
   }

}

impl SeedableRng<u32> for MsLcg {

   fn from_seed(seed: u32) -> Self {
       Self { state: seed }
   }
   fn reseed(&mut self, seed: u32) {
       self.state = seed;
   }

}

fn main() {

   println!("~~~ BSD ~~~");
   let mut bsd = BsdLcg::from_seed(0);
   for _ in 0..10 {
       println!("{}", bsd.next_u32());
   }

   println!("~~~ MS ~~~");
   let mut ms = MsLcg::from_seed(0);
   for _ in 0..10 {
       println!("{}", ms.next_u32());
   }

   // Because we have implemented the `rand::Rng` trait, we can generate a variety of other types.
   println!("~~~ Others ~~~");
   println!("{:?}", ms.gen::<[u32; 5]>());
   println!("{}", ms.gen::<bool>());
   println!("{}", ms.gen_ascii_chars().take(15).collect::<String>());

}</lang>

Scala

<lang scala>object LinearCongruentialGenerator {

 def bsdRandom(rseed:Int):Iterator[Int]=new Iterator[Int]{
   var seed=rseed
   override def hasNext:Boolean=true
   override def next:Int={seed=(seed * 1103515245 + 12345) & Int.MaxValue; seed}
 }

 def msRandom(rseed:Int):Iterator[Int]=new Iterator[Int]{
   var seed=rseed
   override def hasNext:Boolean=true
   override def next:Int={seed=(seed * 214013 + 2531011) & Int.MaxValue; seed >> 16}
 }

 def toString(it:Iterator[Int], n:Int=20)=it take n mkString ", "

 def main(args:Array[String]){
   println("-- seed 0 --")
   println("BSD: "+ toString(bsdRandom(0)))
   println("MS : "+ toString(msRandom(0)))

   println("-- seed 1 --")
   println("BSD: "+ toString(bsdRandom(1)))
   println("MS : "+ toString( msRandom(1)))
 }

}</lang>

Output:

-- seed 0 --
BSD: 12345, 1406932606, 654583775, 1449466924, 229283573, 1109335178, 1051550459, 1293799192,
794471793, 551188310, 803550167, 1772930244, 370913197, 639546082, 1381971571, 1695770928, 
2121308585, 1719212846, 996984527, 1157490780

MS : 38, 7719, 21238, 2437, 8855, 11797, 8365, 32285, 10450, 30612, 5853, 28100, 1142, 281, 20537,
15921, 8945, 26285, 2997, 14680

-- seed 1 --
BSD: 1103527590, 377401575, 662824084, 1147902781, 2035015474, 368800899, 1508029952, 486256185,
1062517886, 267834847, 180171308, 836760821, 595337866, 790425851, 2111915288, 1149758321,
1644289366, 1388290519, 1647418052, 1675546029

MS : 41, 18467, 6334, 26500, 19169, 15724, 11478, 29358, 26962, 24464, 5705, 28145, 23281, 16827,
9961, 491, 2995, 11942, 4827, 5436

Scheme

<lang scheme>(define ((bsd-rand seed)) (set! seed (remainder (+ (* 1103515245 seed) 12345) 2147483648)) seed)

(define ((msvcrt-rand seed)) (set! seed (remainder (+ (* 214013 seed) 2531011) 2147483648)) (quotient seed 65536))

auxiliary function to get a list of 'n random numbers from generator 'r

(define (rand-list r n) = (if (zero? n) '() (cons (r) (rand-list r (- n 1)))))

(rand-list (bsd-rand 0) 10)

(12345 1406932606 654583775 1449466924 229283573 1109335178 1051550459 1293799192 794471793 551188310)

(rand-list (msvcrt-rand 0) 10)

(38 7719 21238 2437 8855 11797 8365 32285 10450 30612)</lang>

Seed7

Seed7 provides also a random number generator. The random function is overloaded for many types. E.g.: The library integer.s7i defines rand(lower, upper). The parameters specifiy the lower and upper bound of the desired random value. The library array.s7i defines rand(arr). This function selects a random element from an array.

<lang seed7>$ include "seed7_05.s7i";

 include "bigint.s7i";

var bigInteger: bsdSeed is 0_; var bigInteger: msSeed is 0_;

const func integer: bsdRand is func

 result
   var integer: bsdRand is 0;
 begin
   bsdSeed := (1103515245_ * bsdSeed + 12345_) mod 2147483648_;
   bsdRand := ord(bsdSeed);
 end func;

const func integer: msRand is func

 result
   var integer: msRand is 0;
 begin
   msSeed := (214013_ * msSeed + 2531011_) mod 2147483648_;
   msRand := ord(msSeed) mdiv 65536;
 end func;

const proc: main is func

 local
   var integer: i is 0;
 begin
   writeln("         BSD          MS");
   for i range 1 to 10 do
     writeln(bsdRand lpad 12 <& msRand lpad 12);
   end for;
 end func;</lang>

Output:

         BSD          MS
       12345          38
  1406932606        7719
   654583775       21238
  1449466924        2437
   229283573        8855
  1109335178       11797
  1051550459        8365
  1293799192       32285
   794471793       10450
   551188310       30612

SequenceL

Uses the Random library provided by SequenceL to create new Random Number Generators

<lang sequenceL> import <Utilities/Random.sl>;

main(args(2)) := let bsdRandomGenerator := newRandomGenerator(0, 0, 2147483647, bsdNext); msRandomGenerator := newRandomGenerator(0, 0, 32767, msNext);

// Create a random sequence with each one of the generators numbers := getRandomSequence([bsdRandomGenerator, msRandomGenerator], 10).Value; in "BSD Values: " ++ toString(numbers[1]) ++ "\nMS Values: " ++ toString(numbers[2]);

bsdNext(RG) := let newSeed := ((1103515245 -> int64 * RG.Seed + 12345) mod 2147483648) -> int32; in (Value : newSeed, Generator : (Seed : newSeed, RandomMin : RG.RandomMin, RandomMax : RG.RandomMax, NextFunction : RG.NextFunction));

msNext(RG) := let newSeed := ((214013 -> int64 * RG.Seed + 2531011) mod 2147483648) -> int32; in (Value : newSeed / 65536, Generator : (Seed : newSeed, RandomMin : RG.RandomMin, RandomMax : RG.RandomMax, NextFunction : RG.NextFunction)); </lang> Output

BSD Values: [12345,1406932606,654583775,1449466924,229283573,1109335178,1051550459,1293799192,794471793,551188310]
MS Values: [38,7719,21238,2437,8855,11797,8365,32285,10450,30612]

Sidef

Translation of: Ruby

<lang ruby>module LCG {

 # Creates a linear congruential generator and remembers the initial seed.
 class Common(r) {
    has seed = r
 }

 # LCG::Berkeley generates 31-bit integers using the same formula
 # as BSD rand().
 class Berkeley < Common {
   method rand {
     self.r = ((1103515245 * self.r + 12345) & 0x7fff_ffff);
   }
 }

 # LCG::Microsoft generates 15-bit integers using the same formula
 # as rand() from the Microsoft C Runtime.
 class Microsoft < Common {
   method rand {
     self.r = ((214013 * self.r + 2531011) & 0x7fff_ffff);
     self.r >> 16;
   }
 }

}

var lcg1 = LCG::Berkeley(1) say 5.of { lcg1.rand }

var lcg2 = LCG::Microsoft(1) say 5.of { lcg2.rand }</lang>

Output:

[1103527590, 377401575, 662824084, 1147902781, 2035015474]
[41, 18467, 6334, 26500, 19169]

Sparkling

<lang sparkling>var states = { "BSD": 0, "MS": 0 };

function BSD_seed(n) { states.BSD = n; }

function BSD_rand() { return states.BSD = (1103515245 * states.BSD + 12345) % (1 << 31); }

function Microsoft_seed(n) { states.MS = n; }

function Microsoft_rand() { return (states.MS = (214013 * states.MS + 2531011) % (1 << 31)) % (1 << 15); }</lang>

Output seen after seeding both generators with 0:

<lang sparkling>spn:8> Microsoft_seed(0); spn:9> Microsoft_rand() = 7875 spn:10> Microsoft_rand() = 3706 spn:11> Microsoft_rand() = 23381 spn:12> Microsoft_rand() = 8388 spn:13> Microsoft_rand() = 19575 spn:14> BSD_seed(0); spn:15> BSD_rand() = 12345 spn:16> BSD_rand() = 1406932606 spn:17> BSD_rand() = 654583775 spn:18> BSD_rand() = 1449466924 spn:19> BSD_rand() = 229283573</lang>

Stata

<lang stata>mata function rand_bsd(u) { m = 65536 u1 = floor(u/m) u2 = mod(u,m) a1 = 16838 a2 = 20077 b = 12345 u = mod((a1*u2+a2*u1)*m+a2*u2+b,2147483648) return(u) }

function rand_ms(u) { u = mod(214013*u+2531011,2147483648) return(floor(u/65536)) }

function rand_seq(f,seed,n) { a = J(n,1,.) for (i=1; i<=n; i++) a[i] = (*f)(seed) return(a) }

rand_seq(&rand_bsd(),1,10) rand_seq(&rand_ms(),0,10)</lang>

Output: compare with OEIS A096553 and A096558.

                 1
     +--------------+
   1 |  1103527590  |
   2 |   377401575  |
   3 |   662824084  |
   4 |  1147902781  |
   5 |  2035015474  |
   6 |   368800899  |
   7 |  1508029952  |
   8 |   486256185  |
   9 |  1062517886  |
  10 |   267834847  |
     +--------------+


            1
     +---------+
   1 |     38  |
   2 |   7719  |
   3 |  21238  |
   4 |   2437  |
   5 |   8855  |
   6 |  11797  |
   7 |   8365  |
   8 |  32285  |
   9 |  10450  |
  10 |  30612  |
     +---------+

Swift

<lang Swift>import Cocoa

class LinearCongruntialGenerator {

   var state = 0 //seed of 0 by default
   let a, c, m, shift: Int
   
   //we will use microsoft random by default
   init() {
       self.a = 214013
       self.c = 2531011
       self.m = Int(pow(2.0, 31.0)) //2^31 or 2147483648
       self.shift = 16
   }
   
   init(a: Int, c: Int, m: Int, shift: Int) {
       self.a = a
       self.c = c
       self.m = m //2^31 or 2147483648
       self.shift = shift
   }
   
   func seed(seed: Int) -> Void {
       state = seed;
   }
   
   func random() -> Int {
       state = (a * state + c) % m
       return state >> shift
   }

}

let microsoftLinearCongruntialGenerator = LinearCongruntialGenerator() let BSDLinearCongruntialGenerator = LinearCongruntialGenerator(a: 1103515245, c: 12345, m: 2147483648, shift: 0)

print("Microsft Rand:") for(var i = 0; i < 10; i++) {

   print(microsoftLinearCongruntialGenerator.random())

}

print("") //new line for readability print("BSD Rand:") for(var i = 0; i < 10; i++) {

   print(BSDLinearCongruntialGenerator.random())

}</lang>

Output:

Microsft Rand:

38 7719 21238 2437 8855 11797 8365 32285 10450 30612

BSD Rand: 12345 1406932606 654583775 1449466924 229283573 1109335178 1051550459 1293799192 794471793

551188310

Tcl

Using an object-oriented solution, inspired by (but not a translation of) the Ruby solution above. <lang tcl>package require Tcl 8.6

General form of a linear-congruential RNG

oo::class create LCRNG {

   variable seed A B C D
   constructor {init a b c d} {

if {$init < 1} {set init [clock clicks]} variable seed $init A $a B $b C $c D $d

   }
   method rand {} {

set seed [expr {($A * $seed + $B) % $C}] return [expr {$seed / $D}]

   }
   method srand x {

set seed $x

}

Subclass to introduce constants

oo::class create BSDRNG {

   superclass LCRNG
   constructor Template:InitialSeed -1 {

next $initialSeed 1103515245 12345 [expr {2**31}] 1

} oo::class create MSRNG {

   superclass LCRNG
   constructor Template:InitialSeed -1 {

next $initialSeed 214013 2531011 [expr {2**31}] [expr {2**16}]

}</lang> Demo code: <lang tcl>proc sample rng {foreach - {1 2 3 4 5} {lappend r [$rng rand]}; join $r ", "} puts BSD:\t\[[sample [BSDRNG new 1]]\] puts MS:\t\[[sample [MSRNG new 1]]\]</lang> Output:

BSD:	[1103527590, 377401575, 662824084, 1147902781, 2035015474]
MS:	[41, 18467, 6334, 26500, 19169]

uBasic/4tH

uBasic is an integer BASIC without any bitwise operations. That's why a trick is used when it enters the negative domain. Unfortunately, it is not portable and must be adjusted for different integer widths. This 32-bit version produces the proper result, though. <lang>w = 32 ' Change for different integer size b = 0 ' Initial BSD seed m = 0 ' Initial MS seed

Print "BSD" ' Get the first 10 numbers from BSD For i = 1 To 10

   GoSub _randBSD
   Print Pop()

Next i

Print

Print "Microsoft" ' Get the first 10 numbers from MS For i = 1 To 10

   GoSub _randMS
   Print Pop()

Next i

End

_randBSD ' ( n1 -- n2)

   Push (1103515245 * b + 12345)      ' Compensate for the sign bit
   If Tos() < 0 Then Push (Pop() - (2 ^ (w-1)))
   b = Pop() % (2 ^ 31)               ' Now we got a number less than 2^31
   Push b                             ' So we can complete the operation

Return

_randMS ' ( n1 -- n2)

   Push (214013 * m + 2531011)        ' Compensate for the sign bit
   If Tos() < 0 Then Push (Pop() - (2 ^ (w-1)))
   m =  Pop() % (2 ^ 31)              ' Now we got a number less than 2^31
   Push m / (2 ^ 16)                  ' So we can complete the operation

Return</lang>

Output:

BSD
12345
1406932606
654583775
1449466924
229283573
1109335178
1051550459
1293799192
794471793
551188310

Microsoft
38
7719
21238
2437
8855
11797
8365
32285
10450
30612

0 OK, 0:908

UNIX Shell

<lang bash>#! /bin/bash

function BSD() {

 SEED=$(((1103515245 * $SEED + 12345) % 2**31))
 echo "  $SEED"

}

function MS() {

 SEED=$(((214013 * $SEED + 2531011) % 2**31))
 echo "  $(($SEED / 2**16))"

}

function output() {

 SEED=0
 echo "$1"

 for i in {1..10}; do
   eval "$1"
 done

 echo ""

}

output BSD output MS</lang>

Output:

VBA

<lang vb>Public stateBSD As Variant Public stateMS As Variant Private Function bsd() As Long

   Dim temp As Variant
   temp = CDec(1103515245 * stateBSD + 12345)
   temp2 = temp / 2 ^ 31
   temp3 = CDec(WorksheetFunction.Floor_Precise(temp2))
   stateBSD = temp - (2 ^ 31) * temp3
   bsd = stateBSD

End Function Private Function ms() As Integer

   Dim temp As Variant
   temp = CDec(214013 * stateMS + 2531011)
   temp2 = temp / 2 ^ 31
   temp3 = CDec(WorksheetFunction.Floor_Precise(temp2))
   stateMS = temp - (2 ^ 31) * temp3
   ms = stateMS \ 2 ^ 16

End Function Public Sub main()

   stateBSD = CDec(0)
   stateMS = CDec(0)
   Debug.Print "       BSD", "   MS"
   For i = 1 To 10
       Debug.Print Format(bsd, "@@@@@@@@@@"), Format(ms, "@@@@@")
   Next i

End Sub</lang>

Output:

       BSD       MS
     12345       38
1406932606     7719
 654583775    21238
1449466924     2437
 229283573     8855
1109335178    11797
1051550459     8365
1293799192    32285
 794471793    10450
 551188310    30612

X86 Assembly

These programs are based off of the implementations described in this article: "https://software.intel.com/en-us/articles/fast-random-number-generator-on-the-intel-pentiumr-4-processor", using the Microsoft equation.

First example using integer instructions. <lang asm>;x86-64 assembly code for Microsoft Windows

Tested in windows 7 Enterprise Service Pack 1 64 bit
With the AMD FX(tm)-6300 processor
Assembled with NASM version 2.11.06
Linked to C library with gcc version 4.9.2 (x86_64-win32-seh-rev1, Built by MinGW-W64 project)

Assembled and linked with the following commands
nasm -f win64 <filename>.asm -o <filename>.obj
gcc <filename>.obj -o <filename>

Takes number of iterations to run RNG loop as command line parameter.

extern printf,puts,atoi,exit,time,malloc

section .data align 64 errmsg_argnumber: db "There should be no more than one argument.",0 align 64 errmsg_noarg: db "Number of iterations was not specified.",0 align 64 errmsg_zeroiterations: db "Zero iterations of RNG loop specified.",0

align 64 errmsg_timefail: db "Unable to retrieve calender time.",0 align 64 errmsg_mallocfail: db "Unable to allocate memory for array of random numbers.",0

align 64 fmt_random: db "The %u number generated is %d",0xa,0xd,0

section .bss

section .text global main

main:

check for argument

cmp rcx,1 jle err_noarg

ensure that only one argument was entered

cmp rcx,2 jg err_argnumber

get number of times to iterate get_random

mov rcx,[rdx + 8] call atoi

ensure that number of iterations is greater than 0

cmp rax,0 jle err_zeroiterations mov rcx,rax

calculate space needed for an array containing the random numbers

shl rcx,2

move size of array into r14

mov r14,rcx

reserve memory for array of random numbers with malloc

call malloc

cmp rax,0 jz err_mallocfail

pointer to array in r15

mov r15,rax

seed the RNG using time()

xor rcx,rcx call time

ensure that time returns valid output

cmp rax,-1 jz err_timefail

calculate address of end of array in r14

add r14,r15

pointer to array of random numbers in r15
address of end of array in r14
current address in array in rdi
multiplier in rbx
seed in rax
current random number in rcx

prepare random number generator

mov rdi,r15

mov rbx,214013

get_random:

multiply by 214013 and add 2561011 to get next state

mul ebx add eax,2531011

shr by 16 and AND with 0x7FFF to get current random number

mov ecx,eax shr ecx,16 and ecx,0x7fff

store random number in array

mov [rdi],ecx

add rdi,4 cmp rdi,r14 jl get_random

pointer to array of random numbers in r15
address of end of array in r14
current address in array in rdi
array index in rsi

xor rsi,rsi mov rdi,r15

print_random:

mov rcx,fmt_random mov rdx,rsi mov r8d,[rdi] call printf

add rsi,1 add rdi,4 cmp rdi,r14 jl print_random

xor rcx,rcx call exit

ERROR MESSAGES;;;;;;;;;;;;;;;;

err_argnumber:

mov rcx,errmsg_argnumber call puts

jmp exit_one

err_noarg:

mov rcx,errmsg_noarg call puts

jmp exit_one

err_zeroiterations:

mov rcx,errmsg_zeroiterations call puts

jmp exit_one

err_timefail:

mov rcx,errmsg_timefail call puts

jmp exit_one

err_mallocfail:

mov rcx,errmsg_mallocfail call puts

exit_one:

mov rcx,1 call exit</lang>

Second example using AVX instructions.

This example is incorrect. Please fix the code and remove this message.

Details: It will not produce output identical to that of the Microsoft rand() function.

<lang asm>;x86-64 assembly code for Microsoft Windows

Tested in windows 7 Enterprise Service Pack 1 64 bit
With the AMD FX(tm)-6300 processor
Assembled with NASM version 2.11.06
Linked to C library with gcc version 4.9.2 (x86_64-win32-seh-rev1, Built by MinGW-W64 project)

Assembled and linked with the following commands
nasm -f win64 <filename>.asm -o <filename>.obj
gcc <filename>.obj -o <filename>

Takes number of iterations to run RNG loop as command line parameter.

extern printf,puts,atoi,exit,time,_aligned_malloc

section .data align 64 errmsg_argnumber: db "There should be no more than one argument.",0 align 64 errmsg_noarg: db "Number of iterations was not specified.",0 align 64 errmsg_zeroiterations: db "Zero iterations of RNG loop specified.",0

align 64 errmsg_timefail: db "Unable to retrieve calender time.",0 align 64 errmsg_mallocfail: db "Unable to allocate memory for array of random numbers.",0

align 64 fmt_random: db "The %u number generated is %d",0xa,0xd,0

align 16 multiplier: dd 214013,17405,214013,69069 align 16 addend: dd 2531011, 10395331, 13737667, 1 align 16 mask: dd 0xffffffff,0,0xffffffff,0 align 16 masklo: dd 0x7fff,0x7fff,0x7fff,0x7fff

section .bss

section .text global main

main:

check for argument

cmp rcx,1 jle err_noarg

ensure that only one argument was entered

cmp rcx,2 jg err_argnumber

get number of times to iterate get_random

mov rcx,[rdx + 8] call atoi

ensure that number of iterations is greater than 0

cmp rax,0 jle err_zeroiterations mov rcx,rax

calculate space needed for an array containing the random numbers

shl rcx,4

move size of array into r14

mov r14,rcx

16 byte alignment boundary

mov rdx,16

reserve memory aligned to 16 byte boundary for array with _aligned_malloc

call _aligned_malloc

cmp rax,0 jz err_mallocfail

pointer to array in r15

mov r15,rax

seed the RNG using time()

xor rcx,rcx call time

ensure that time returns valid output

cmp rax,-1 jz err_timefail

pointer to array of random numbers in r15
address of end of array at in r14
states stored in xmm0

calculate address of end of array in r14

add r14,r15

load seed,seed+1,seed,seed+1 into xmm0

lea rbx,[rax - 1] shl rax,32 or rax,rbx

movq xmm0,rax vpslldq xmm1,xmm0,8 vpor xmm0,xmm0,xmm1

pointer to array of random numbers in r15
address of end of array in r14
current address in array in rdi
current states in xmm0
multiplier in xmm1
addened in xmm2
mask in xmm3
masklo in xmm4
split seed in xmm5
current set of random numbers in xmm6

prepare random number generator

mov rdi,r15

vmovdqa xmm1,[multiplier] vmovdqa xmm2,[addend] vmovdqa xmm3,[mask] vmovdqa xmm4,[masklo]

get_random:

arrange order of current states to 2,3,0,1 and store in split seed

vpshufd xmm5,xmm0,10110001b

multiply current states by multiplier

vpmulld xmm0,xmm0,xmm1

set order of multiplier to 2,3,0,1

vpshufd xmm1,xmm1,10110001b

multiply split seed by multiplier

vpmulld xmm5,xmm5,xmm1

and current states with mask

vpand xmm0,xmm0,xmm3

and current split seed with mask

vpand xmm5,xmm5,xmm3

set order of split seed to 2,3,0,1

vpshufd xmm5,xmm5,10110001b

or current states with split seed

vpor xmm0,xmm0,xmm5

add adder to current states

vpaddd xmm0,xmm0,xmm2

shift vector right by two bytes

vpsrldq xmm6,xmm0,2

and each state with 0x7fff

vpand xmm6,xmm6,xmm4

vmovdqa [rdi],xmm6

add rdi,16 cmp rdi,r14 jl get_random

pointer to array of random numbers in r15
address of end of array in r14
current address in array in rdi
array index in rsi

xor rsi,rsi mov rdi,r15

print_random:

mov rcx,fmt_random mov rdx,rsi mov r8d,[rdi] call printf

add rsi,1 add rdi,4 cmp rdi,r14 jl print_random

xor rcx,rcx call exit

ERROR MESSAGES;;;;;;;;;;;;;;;;

err_argnumber:

mov rcx,errmsg_argnumber call puts

jmp exit_one

err_noarg:

mov rcx,errmsg_noarg call puts

jmp exit_one

err_zeroiterations:

mov rcx,errmsg_zeroiterations call puts

jmp exit_one

err_timefail:

mov rcx,errmsg_timefail call puts

jmp exit_one

err_mallocfail:

mov rcx,errmsg_mallocfail call puts

exit_one:

mov rcx,1 call exit</lang>

Sample:

Integer instruction example:

F:\>lcgint.exe 20
The 0 number generated is 20272
The 1 number generated is 4467
The 2 number generated is 8618
The 3 number generated is 1587
The 4 number generated is 2687
The 5 number generated is 21398
The 6 number generated is 29522
The 7 number generated is 27724
The 8 number generated is 23875
The 9 number generated is 2399
The 10 number generated is 4086
The 11 number generated is 923
The 12 number generated is 23002
The 13 number generated is 11586
The 14 number generated is 13200
The 15 number generated is 22090
The 16 number generated is 26528
The 17 number generated is 14271
The 18 number generated is 10476
The 19 number generated is 9981

F:\>

AVX instruction example:

F:\>lcgavx.exe 5
The 0 number generated is 20370
The 1 number generated is 45
The 2 number generated is 20541
The 3 number generated is 15699
The 4 number generated is 23637
The 5 number generated is 30131
The 6 number generated is 26151
The 7 number generated is 27319
The 8 number generated is 26933
The 9 number generated is 28417
The 10 number generated is 16647
The 11 number generated is 14840
The 12 number generated is 29228
The 13 number generated is 16968
The 14 number generated is 1027
The 15 number generated is 12099
The 16 number generated is 17170
The 17 number generated is 23893
The 18 number generated is 18556
The 19 number generated is 16434

F:\>

XPL0

It's not easy just by looking at the numbers generated if they are sufficiently random. You might notice that the BSD numbers alternate odd and even, which is pretty bad. A simple but effective test is to simulate falling snowflakes.

<lang XPL0>include c:\cxpl\codes; int R;

func BSD; [R:= (1103515245*R + 12345) & $7FFF_FFFF; return R; ]; \BSD

func MSFT; [R:= (214013*R + 2531011) & $7FFF_FFFF; return R>>16; ]; \MSFT

int N; [SetVid(4); \320x200x2 graphics R:= 0; \initialize seed for N:= 0 to 5000 do

       Point(rem(BSD/180), rem(BSD/180), 3);

N:= ChIn(1); \wait for keystoke

SetVid(4); \320x200x2 graphics R:= 0; \initialize seed for N:= 0 to 5000 do

       Point(rem(MSFT/180), rem(MSFT/180), 3);

N:= ChIn(1); \wait for keystoke SetVid(3); \restore normal text mode ]</lang>

zkl

<lang zkl>var [private] seed = 0; fcn srand(s){ seed = s }

const TWO31=(1).shiftLeft(31);

//#define BSD_RAND 1

ifdef BSD_RAND

  const A=1103515245, C=12345;
  fcn rand{ seed = (seed * A + C) % TWO31 }

else // MS rand

  const A=214013, C=2531011, TWO16=(1).shiftLeft(16);
  fcn rand{ (seed = (seed * A + C) % TWO31) / TWO16 }

endif</lang>

<lang zkl>srand(0); println(rand(),",",rand(),",",rand());</lang>

Output:

MS:  38,7719,21238
BSD: 12345,1406932606,654583775