Faster way to convert a number from range to another range

Question

According to this SO question, it is possible to convert a number range to another (linear conversion) by calculating:

NewValue = (((OldValue - OldMin) * NewRange) / OldRange) + NewMin

However, I want to know if there is another faster way to do this.

Consider a microcontroller with no division instruction, converting massive amount of a ranges to another ranges (i.e. 24-bit color/pixels from image file to 18-bit color/pixels for the LCD display) would take sometime. I was thinking is there any way to optimze this.

Answer 1

24 bit color is usually 8 x 3 (3 components, 8 bits per).

18 bit color is 6 x 3.

A simple >>2 converts the range of 8 bit values to 6 bit values, "rounding down". And shift operations are fast on most hardware.

Rounding to nearest is harder mainly because of overflow. Starrt with this:

(x+2)>>2

in a 16 bit value. The result is a value from 0 to 2^6, not 0 to 2^6-1 like you want. You'll have to detect that last case.

If you can afford the ROM, a lookup table can be used. 256 entries isn't all that many. This may be more worth considering if you want to apply gamma or other corrections.

But really, just >>2 and/or mask each component, then shift and mask into place.

int32 r = ((pix>>2)&(0x3F<<0))|((pix>>4)&(0x3F<<6))|((pix>>6)&(0x3F<<12));

Where pix is a 32 bit value storing your 24 bit pixel and r stores the 18 bit result.

This kind of optimization requires profiling in as close to a real environment as possible.