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Boundary checking on signed value using bit test

 
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evsource



Joined: 21 Nov 2006
Posts: 129

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Boundary checking on signed value using bit test
PostPosted: Tue May 25, 2010 5:49 pm     Reply with quote
I'm trying to do a fast boundary check on a value that keeps increasing with every iteration of the loop. The magnitude that the value increases with each iteration is fixed. So I should be able to do the following to keep the accumulating_number variable from going much above 8192 and below -8192:

Code:
if(!bit_test(accumulating_number,13)) accumulating_number += error;


Both accumulating_number and error are declared as signed int16's.

But, when error is consistently negative, it grows well beyond the -8192. I haven't seen any values less than -32768, but they are almost always -32xxx.

As long as I do the following code, it works fine (but the above is *much* faster):

Code:

accumulating_number += error;
if(accumulating_number > 8192) accumulating_number = 8192;
else if(accumulating_number < -8192) accumulating_number = -8192;


Any ideas? I'm baffled.
PCM programmer



Joined: 06 Sep 2003
Posts: 21708

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PostPosted: Tue May 25, 2010 8:54 pm     Reply with quote
If you're in doubt about how something works, make a little test program
to study the boundary conditions. This code will do your negated bit 13
test, and step through values that are near to 8192 and -8192. You can
run it in MPLAB simulator, with "UART1" sending the printf output to the
MPLAB Output Window so you can see the results:
Quote:

8190 (1ffe): Negated Bit 13 test = 1
8191 (1fff): Negated Bit 13 test = 1
8192 (2000): Negated Bit 13 test = 0
8193 (2001): Negated Bit 13 test = 0
8194 (2002): Negated Bit 13 test = 0

-8190 (e002): Negated Bit 13 test = 0
-8191 (e001): Negated Bit 13 test = 0
-8192 (e000): Negated Bit 13 test = 0
-8193 (dfff): Negated Bit 13 test = 1
-8194 (dffe): Negated Bit 13 test = 1

Test program:
Code:

#include <18F452.h>
#fuses XT,NOWDT,PUT,BROWNOUT,NOLVP
#use delay(clock=4000000)
#use rs232(baud=9600, xmit=PIN_C6, rcv=PIN_C7, ERRORS)
 
//======================================
void main(void)
{
signed int16 acc_number;

for(acc_number = 8190; acc_number < 8195; acc_number++)
   {
    printf("%ld (%lx): ", acc_number, acc_number);

    printf("Negated Bit 13 test = %u", !bit_test(acc_number,13));
   
    printf("\r");
   }

printf("\r");

for(acc_number = -8190; acc_number > -8195; acc_number--)
   {
    printf("%ld (%lx): ", acc_number, acc_number);

    printf("Negated Bit 13 test = %u", !bit_test(acc_number,13));
   
    printf("\r");
   }

while(1);
}

How to use "UART1" in MPLAB:
http://www.ccsinfo.com/forum/viewtopic.php?t=40045
Ttelmah



Joined: 11 Mar 2010
Posts: 19504

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PostPosted: Wed May 26, 2010 2:15 am     Reply with quote
PCM programmer has shown how to 'see' what is happening. The reason, is in how -ve numbers are stored. Remember -1, is 0xFFFF.
Your test can be done in a number of ways:
Code:

accumulating_number += error;
if ((bit_test(accumulating_number,15)?\
bit_test(accumulating_number,13):!bit_test(accumulating_number,13))

Or:
Code:

if (!(bit_test(accumulating_number,13)^bit_test(accumulating_number,13)))

Or (obviously), performing the test on the abs value.

Best Wishes
evsource



Joined: 21 Nov 2006
Posts: 129

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PostPosted: Wed May 26, 2010 9:14 am     Reply with quote
Ttelmah wrote:
PCM programmer has shown how to 'see' what is happening. The reason, is in how -ve numbers are stored. Remember -1, is 0xFFFF.


Thanks Ttelmah and PCM programmer. Ttelmah, you weeded out my innocence (stupidity might be an interchangeable word here! Confused ). I had the mistaken idea that the negative representation of the number was identical to the positive number, only with the sign bit flipped. Back to two's compliment 101.

I see my mistake now. As you said, easy enough to fix:

Code:

if((!bit_test(accumulating_number,15) && !bit_test(accumulating_number,13)) || (bit_test(accumulating_number,15) && bit_test(accumulating_number,13)) ) accumulating_number += error;


Probably some ways to optimize further for speed, if it's known whether the error will tend more towards being positive or negative.
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