# Pseudo random number generation

## About this recipe

This recipe describes a 32-bit pseudo random number generator implemented efficiently in ARM Assembly Language.

## The details

It is often necessary to generate pseudo random numbers, and the most efficient algorithms are based on shift generators with exclusive-or feedback (rather like a cyclic redundancy check generator). Unfortunately the sequence of a 32-bit generator needs more than one feedback tap to be maximal length (ie. 2^32-1 cycles before repetition), so this example uses a 33 bit register with taps at bits 33 and 20.

The basic algorithm is newbit:=bit33 EOR bit20, shift left the 33 bit number and put in newbit at the bottom; this operation is performed for all the newbits needed (ie. 32 bits). The entire operation can be coded compactly by making maximal use of the ARM's barrel shifter:

``

    ; enter with seed in R0 (32 bits), R1 (1 bit in least significant bit)
    ; R2 is used as a temporary register.
    ; on exit the new seed is in R0 and R1 as before
    ; Note that a seed of 0 will always produce a new seed of 0.
    ; All other values produce a maximal length sequence.
    ;
        TST    R1, R1, LSR #1                       ; top bit into Carry
        MOVS   R2, R0, RRX                          ; 33 bit rotate right
        ADC    R1, R1, R1                           ; carry into lsb of R1
        EOR    R2, R2, R0, LSL #12                  ; (involved!)
        EOR    R0, R2, R2, LSR #20                  ; (similarly involved!)

## Using this example

This random number generation code is provided as random.s in the examples directory. It is provided as ARM Assembly Language source which can be assembled and then linked with C modules (see recipes in Interfacing Assembly Language and C for more information).

The C test program randtest.c (also in the examples directory) can be used to demonstrate this. First set the examples directory to be your current directory, and execute the following commands to build an executable suitable for armsd:

``

    armasm random.s -o random.o -li
    armcc -c randtest.c -li -apcs 3/32bit
    armlink randtest.o random.o -o randtest

Where somewhere is the path to the lib directory of the ARM Software Development Toolkit release.

Note that in both the above commands, and the armsd command below, -li indicates that the target ARM is little endian, and -apcs 3/32bit specifies that the 32 bit variant of the ARM Procedure Call Standard should be used. These options can be omitted if the tools have already been configured appropriately.

armsd can be used to run this program as follows:

``

    > armsd -li randtest
    A.R.M. Source-level Debugger, version 4.10 (A.R.M.) [Aug 26 1992]
    ARMulator V1.20, 512 Kb RAM, MMU present, Demon 1.01, FPE, Little
    endian.
    Object program file randtest
    armsd: go
    randomnumber() returned 0b3a9965
    randomnumber() returned ac0b1672
    randomnumber() returned 6762ad4f
    randomnumber() returned 1965a731
    randomnumber() returned d6c1cef4
    randomnumber() returned f78fa802
    randomnumber() returned 8147fc15
    randomnumber() returned 3f62adfc
    randomnumber() returned b56e9da8
    randomnumber() returned b36dc5e2
    Program terminated normally at PC = 0x000082c8
          0x000082c8: 0xef000011 .... : >  swi     0x11
    armsd: quit
    Quitting
    >

## Related topics

Please refer to the index for other topics of interest.