by Jon Ripley, August 2006
BBC BASIC for Windows provides a pseudo-random number generator for use in BASIC programs but has no built-in support for generating pseudo-random numbers from assembly language programs. This article contains code to add support for generating pseudo-random numbers from assembly language that can be added to any program.
The following routine generates a 32-bit pseudo-random number when called, the pseudo-random number is returned in the eax register:
.seed dd 1 :dd 0
.Rand
mov eax, &4C957F2D ; |
mul dword [seed] ; |
push edx ; |
mov edx, [seed] ; |
imul ebx, edx, &5851F42D ; |\
pop edx ; | - seed = seed * &5851F42D4C957F2D
add edx, ebx ; |/
mov ebx, [seed+4] ; |
imul ebx, ebx, &4C957F2D ; |
add edx, ebx ; |
add eax, 1 ; seed = seed + 1
adc edx, 0
mov [seed], eax ; store the new seed
mov [seed+4], edx
shrd eax, edx, 21 ; shift right 21 bits
ret ; return
The following routine generates a pseudo-random number in the range 1 to N:
.RandRange
call Rand ; get random number
mov ebx, [esp+4] ; read range limit
xor edx,edx ; clear edx register
div ebx ; do integer division; eax / ebx
mov eax,edx ; read remainder of division
inc eax ; add one
ret 4 ; restore stack and return
Call RandRange using code similar to the following:
push N%
call RandRange
The pseudo-random number is returned in eax. Here N% can be a register eax, read from a pointer to a 4 byte block in memory [addr], a BASIC constant N% defined at assemble time, a BASIC variable [^N%] or a numeric constant 1234. If the assembler reports a “Size needed” error add the dword prefix to the pushed parameter.
To change the range of numbers returned to 0 to N remove the 'inc eax' instruction.
The following routine generates a pseudo-random number in the range 0.0 to 1.0, exclusive of 1.0:
.RandFloat
call Rand ; get random number
and eax, &7FFFFFFF ; clear top bit
push eax ; push random number on stack
call Rand ; get random number
push eax ; push random number on stack
push &80000000 ; \ Put &8000000000000000
push 0 ; / on the stack
fild qword [esp] ; load &8000000000000000
fild qword [esp+8] ; load random number
fdivrp st1,st0 ; divide random number by &8000000000000000
fabs ; convert result to absolute value
mov eax,[esp+20] ; read location to store result
fstp qword [eax] ; store result
add esp,16 ; free local variables
ret 4 ; restore stack and return
To call this routine use code similar to the following:
push ^N#
call RandFloat
The result is stored in the memory pointed to by the parameter. Here ^N# is a pointer to a 64-bit floating point BASIC variable but can be a pointer to an 8 byte block of memory [addr]. If the assembler reports a “Size needed” error add the dword prefix to the pushed parameter.
The following routine is called to seed the pseudo-random number generator with a 64-bit seed:
.RandSeed
mov eax, [esp+4] ; load new seed
mov edx, [esp+8]
mov dword [seed], eax ; store new seed
mov dword [seed+4], edx
ret 8 ; restore stack and return
To seed the random number generator use the following code:
push hN
push lN
call RandSeed
Here we pass a 64-bit integer value to seed the pseudo-random number, hN is the top 32-bits of the seed and lN is the bottom 32-bits of the seed. By default the seed is set to the value of TIME when the code was assembled. If the assembler reports a “Size needed” error add the dword prefix to the pushed parameter.
These routines may be called from BASIC, instead of using the RND function, if you really want to:
result% = USR Rand :REM Return a pseudo-random number in result% SYS RandFloat, ^N# :REM Return a pseudo-random float in N# SYS RandRange, N TO result% :REM Return a range limited pseudo-random number in result% SYS RandSeed, TIME, TIME :REM Seed the pseudo-random generator using TIME
The multiplier 6364136223846793005 was obtained from Knuth, D.E., "The Art of Computer Programming," Vol 2, Seminumerical Algorithms, Third edition, Addison-Wesley, 1998, p. 106 (line 26) & p. 108.