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Random Functions

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britlion

Posts: 766

Joined: Mon Apr 27, 2009 7:26 pm

Location: Slough, Berkshire, UK

Post Mon Jun 18, 2012 11:07 pm

Random Functions

Boriel has included a better random function in the code; but this passes through floating point numbers, which is potentially fairly slow - and for games we usually require integer numbers anyway!

I've written a few functions that are a possible alternative.

This is the base function that does the hard work of generating a random number from 0-255 in the A register (or as a return value, conveniently enough). This is the same random number generator that Boriel is using, incidentally. (Based pretty much wholly on Patrik Rak's stream random generator).

  Code:
FUNCTION FASTCALL randomBase () as uByte
ASM
random: ld  hl,$A280       ; xz -> yw
        ld  de,$C0DE       ; yw -> zt
        ld  (random+1),de   ; x = y, z = w
        ld  a,e             ; w = w ^ ( w << 3 )
        add a,a
        add a,a
        add a,a
        xor e
        ld  e,a
        ld  a,h             ; t = x ^ (x << 1)
        add a,a
        xor h
        ld  d,a
        rra                 ; t = t ^ (t >> 1) ^ w
        xor d
        xor e
        ld  h,l             ; y = z
        ld  l,a             ; w = t
        ld  (random+4),hl
        ;ret (Not necessary, since the compiler will add ret to the end)
END ASM
END FUNCTION


This function will update the seed value based on the current frames counter. To improve randomness, get the user to have a human interaction that can take a variable amount of time and then run this.
  Code:
SUB FASTCALL updateSeed()
REM Updates the random generator seed from the FRAMES system variable.
t()
ASM
LD A,E
EX DE,HL
LD HL,random+2
XOR (HL)
AND A
JR NZ,updateSeedNotZero
INC A
updateSeedNotZero:
LD (HL),A


LD HL,random+4
LD A,E
XOR (HL)
LD (HL),A
INC HL
LD A,D
XOR (HL)
LD (HL),A

END ASM
END SUB

The above function depends on my timer function, which gets the value in FRAMES:

  Code:
FUNCTION FASTCALL t() as uLong
asm
    DI
    LD DE,(23674)
    LD D,0
    LD HL,(23672)
    EI
end asm
end function


This function returns a value from zero to the specified limit number (limit <= 255)
  Code:
FUNCTION fastcall randomBin(limit as uByte) as uByte
ASM

AND A
RET Z ; Input zero, output zero.
LD B,A ; Save A

LD C,255
randomBinLoop:
RLA
JR C, randomBinLoopExit
RR C
JR randomBinLoop ; loop back until we find a bit.
randomBinLoopExit:

randomBinRedoCall:
call random
AND C
CP B
RET Z
JR NC, randomBinRedoCall

END ASM
END FUNCTION

it's worth noting that the issue with this is that it basically rolls a random, and if it's bigger than limit, it rolls another one. This could potentially take a while, and isn't guaranteed to be fast. Though the probability of failing to hit the zone is kept to 50%, so on average it will roll 1.5 random numbers, I think, per call. This should usually be faster than a floating point multiply, I believe.

If you do want a number a random number between 0 and 1, using FIXED is quite a lot faster than float. This routine uses randombase to do that:

  Code:
FUNCTION FASTCALL randomFixed() as FIXED
ASM
call random
push AF
call random
ld l,A
POP AF
ld h,a
ld d,0
ld e,d
END ASM
END FUNCTION


Timings:

  Code:
dim time as uLong
DIM n as uInteger
DIM variable as uByte
time=t()

for n=0 to 20000
REM One line of the following three:
'variable=rnd*128
'variable=randomFixed()*128
'variable=randomBin(128)

next n

print t()-time


20,000 loops took:

variable=rnd*128 => 1180 frames.

variable=randomFixed()*128 => 613 Frames (1.92 x faster)

variable=randomBin(128) => 74 frames. (this example is 16 x faster) (worst case averages 13x faster; best case averages 22x faster)
(This does vary by limit, but is never > 89 frames for any limit chosen. Can be as low as about 52. Average is about 64.)

All three, of course, return an integer from 0 to 127 (the last 0-128; this chosen because it's a worse case scenario for timing).

For scale, 20,000 loops calling randomBase takes 37 frames. Of course, this returns a number from 0-255 regardless, with no option to set the upper bound.
Last edited by britlion on Thu Jul 05, 2012 11:01 am, edited 5 times in total.
<<

britlion

Posts: 766

Joined: Mon Apr 27, 2009 7:26 pm

Location: Slough, Berkshire, UK

Post Tue Jun 19, 2012 12:27 am

Re: Random Functions

For those that are curious, bored, or obsessive about numbers (me) here are the relative timings for each possible output:

You can clearly see the timings increase as we cross a bit boundary (that is, limit requires more bits). This is because probability of rolling higher than the limit increases here - and decreases fairly linearly until the next bit boundary, when it jumps up.

For values at bitboundary upper limits, if you can, choose the faster route :)

Limit Frames for 20,000
0 23 (really, you want a number from 0-0? You're going to get 0! There's definitely a faster way of calculating zero...)
1 82 Faster route: baseRandom bAND 1
2 86
3 78
4 89
5 82
6 77
7 74 Faster route: baseRandom bAND 7
8 88
9 84
10 81
11 77
12 75
13 73
14 71
15 69 Faster route: baseRandom bAND 15
16 87
17 84
18 82
19 80
20 78
21 76
22 75
23 73
24 72
25 70
26 69
27 68
28 67
29 66
30 66
31 65 Faster route: baseRandom bAND 31
32 84
33 82
34 80
35 79
36 78
37 77
38 76
39 75
40 74
41 73
42 72
43 71
44 70
45 70
46 69
47 69
48 68
49 67
50 67
51 66
52 66
53 65
54 65
55 64
56 64
57 63
58 63
59 62
60 62
61 61
62 61
63 61 Faster Route: baseRandom bAND 63
64 80
65 79
66 78
67 77
68 77
69 76
70 76
71 75
72 74
73 74
74 73
75 73
76 72
77 71
78 71
79 71
80 70
81 70
82 69
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84 68
85 68
86 68
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108 60
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111 60
112 59
113 59
114 59
115 59
116 59
117 58
118 58
119 58
120 58
121 57
122 57
123 57
124 57
125 57
126 57
127 56 Faster route: baseRandom bAND 127
128 75
129 75
130 75
131 74
132 74
133 73
134 73
135 73
136 72
137 72
138 72
139 72
140 71
141 71
142 70
143 70
144 70
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249 53
250 52
251 52
252 52
253 52
254 52
255 52 Much faster to use randomBase to get 0-255.

I know. Waaay overboard. Mostly did this just to reassure myself there weren't any exceptionally slow points, or corner cases. There was a bug, which I think I've fixed :)

In short: I put this forward as a faster random number generator than using floating point numbers.
Last edited by britlion on Tue Jun 19, 2012 11:57 am, edited 1 time in total.
<<

slenkar

Posts: 282

Joined: Sun Feb 13, 2011 3:33 am

Location: Kentucky US, used to be Birmingham UK

Post Tue Jun 19, 2012 4:19 am

Re: Random Functions

so to get the fastest random number generator you have to use
randombase,
t() ,
the seed function,
and randombin

together
<<

britlion

Posts: 766

Joined: Mon Apr 27, 2009 7:26 pm

Location: Slough, Berkshire, UK

Post Tue Jun 19, 2012 11:56 am

Re: Random Functions

The time function t() and updateSeed() work together - you only need those if you want to re-seed.

randomBase gives you a number from 0-255 (very quickly)

randomBin (with an awful name. Should probably be randomLimit) gives you 0-n

You can probably see it's trivial to do other ranges.

10-20 would be randomBin(10)+10 for example.
<<

britlion

Posts: 766

Joined: Mon Apr 27, 2009 7:26 pm

Location: Slough, Berkshire, UK

Post Tue Jun 19, 2012 12:35 pm

Re: Random Functions

Of course this is only going to make a big difference if you are doing a lot of random numbers! Not worth using the space for this if it's just one or two. However some games do require a LOT of random data to be generated, and you'd see the difference using this suite.

E.g. generating a whole random landscape.
<<

boriel

Site Admin

Posts: 1463

Joined: Wed Nov 01, 2006 6:18 pm

Location: Santa Cruz de Tenerife, Spain

Post Wed Jun 20, 2012 7:01 am

Re: Random Functions

RND was made float to be 100% compatible with Sinclair BASIC. In fact, much of it slowness comes from multiplying with another float number. E.g.
  Code:
PRINT RND * 128

Not only generates an RND float number (0, 1), but also multiplies it by another float, 128. Thus much slower than the others.

I think it could be possible to put your routine in the library while taking the code fron rnd.asm (which already contains the random bit generator you use here). :?:
<<

britlion

Posts: 766

Joined: Mon Apr 27, 2009 7:26 pm

Location: Slough, Berkshire, UK

Post Wed Jun 20, 2012 4:09 pm

Re: Random Functions

boriel wrote:RND was made float to be 100% compatible with Sinclair BASIC. In fact, much of it slowness comes from multiplying with another float number. E.g.
  Code:
PRINT RND * 128

Not only generates an RND float number (0, 1), but also multiplies it by another float, 128. Thus much slower than the others.


Oh, absolutely. You did it completely right for the compiler - as I noted in the original post "going through float" is the slow part. My ugly hack here actually, rather than multiplies up numbers, even rolls a new random number until it finds one smaller than the specified limit. This, on average, is actually faster than a multiply, however. Unless there's a long string of fails.


boriel wrote:I think it could be possible to put your routine in the library while taking the code fron rnd.asm (which already contains the random bit generator you use here). :?:


Yes - I think it might. The trick is to be able to call it and be sure it's in the final code - doesn't the compiler cut it out if rnd isn't used?
I suppose an initialise routine might do the trick.

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