Constrain a 16 bit signed value between 0 and 4095 using Bit Manipulation only (without branching)

Question

I want to constrain the value of a signed short variable between 0 and 4095, after which I take the most significant 8 bits as my final value for use elsewhere. Right now I'm doing it in a basic manner as below:

short color     = /* some external source */;
/* 
 * I get the color value as a 16 bit signed integer from an
 * external source I cannot trust. 16 bits are being used here
 * for higher precision.
 */

if ( color < 0 ) {
    color = 0;
}
else if ( color > 4095 ) {
    color = 4095;
}

unsigned char color8bit  = 0xFF & (color >> 4);
/*
 * color8bit is my final value which I would actually use
 * in my application.
 */

Is there any way this can be done using bit manipulation only, i.e. without using any conditionals? It might help quite a bit in speeding things up as this operation is happening thousands of time in the code.

The following won't help as it doesn't take care of edge cases such as negative values and overflows:

unsigned char color8bit = 0xFF & (( 0x0FFF & color ) >> 4 );

Edit: Adam Rosenfield's answer is the one which takes the correct approach but its incorrectly implemented. ouah's answer gives correct results but takes a different approach that what I originally intended to find out.

This is what I ended up using:

const static short min = 0;
const static short max = 4095;
color = min ^ (( min ^ color ) & -( min < color ));
color = max ^ (( color ^ max ) & -( color < max ));
unsigned char color8bit = 0xFF & (( 0x0FFF & color ) >> 4 );

Answer 1

Yes, see these bit-twiddling hacks:

short color = ...;
color = color ^ (color & -(color < 0));  // color = max(color, 0)
color = 4096 ^ ((color ^ 4096) & -(color < 4096));  // color = min(color, 4096)

unsigned char color8bit  = 0xFF & (color >> 4);

Whether this actually turns out to be faster, I don't know -- you should profile. Most modern x86 and x86-64 chips these days support "conditional move" instructions (cmov) which conditionally store a value depending on the EFLAGS status bits, and optimizing compilers will often produce these instructions from ternary expressions like color >= 0 ? color : 0. Those will likely be fastest, but they won't run on older x86 chips.

Answer 2

You can do the following:

BYTE data[0x10000] = { ..... };

BYTE byte_color = data[(unsiged short)short_color];

In your days 64kb table is not something outrageous and may be acceptable. The number of assembler commands in this variant of code will be absolute minimum compared to other possible approaches.