I have the following scenario: I have an input byte (IN) with the value 0-255 in it and I want to calculate a 2-byte output word (OUT) from it which should grow in an exponential way. So IN=0 must result in OUT=0 (or near 0) and IN=255 must result in OUT=65535 (Or near that value). The results between these two min/max values must be exponential and not linear.
The results must not be exact. So if OUT is 65500 when IN is 255 then this is also ok. In C I tried the formular OUT = IN * IN and the result is ok for me. The problem is, the binary gets too large with this formular (I'm compiling for an embedded chip (AVR) with 2KB RAM). So I'm searching for a very very small Assembler code which does something similiar to OUT=IN*IN but may fit into the last few bytes I have left in the chip.
The assembler dialect and architecture doesn't matter, I hope I can get the idea anyway. C code is also fine when it can be compiled into a binary small enough.
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Yes, I mean the program code gets too large. Looks like the AVR chip doesn't have a MUL assembler command so the compiler emulates the multiplication with a loop which does multiple additions. And yes, you are right, it is a quadratic formular, not exponential. Sorry for my humble mathematical skills.
@ozo: Looks promissing, I'll check it out this evening when I have access to the AVR compiler again.
To give some numbers:
a*a needs 42 Bytes of Code. Ozo's solution with the while loop needs 12 Bytes and works great. I just added another shift-left so the result now fills the 16-bit range better (0-65280 instead of 0-32640):
out = in << 1;
while (in>>=1) out<<=1;
So if no one comes up with a solution which beats the 12 bytes I give ozo the full points ;-)
Just a (maybe obvious) comment. Ozo code doesn't calculate a*a, but rather a*2^(floor(log2(a)).
So that's actually step-wise linear between any subsequent power of 2, not quadratic as desired. For example it is linear between 128 and 255. (for a plot, see http://www.wolframalpha.co
If you prefer to actually get a*a, you can use:
for(tmp=in; in; tmp<<=1, in>>=1)
if(in & 1) out+=tmp;
}
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by: lbertaccoPosted on 2008-12-13 at 13:22:57ID: 23165501
Can you explain why OUT=IN*IN is not ok? What do you mean with "the binary gets too large"? 255*255 yields 65025 which does fit into 2 bytes.