Fixed point arithmetic

3
votes

I'm currently using Microchip's Fixed Point Library, but I think this applies to most fixed point libraries. It supports Q15 and Q15.16 types, respectively 16-bit and 32-bit data.

One thing I noticed is that it does not include add, subtract, multiply or divide functions.

How am I supposed to do these? Is it as simple as just adding/subtracting/multiplying/dividing them together using integer math? I can see addition and subtraction working, but multiplying or dividing wouldn't take care of the fractional part...?

2
fixed-point
If it can't add, subtract, multiply or divide, what can it do? - robert
@robert, All trig functions and inverses, exp, power, sqrt, log - as well as pretty much all floating point functions. - Thomas O
Are _Q16mac and _Q16reciprocal no use to you? `_Q15add' and '_Q16neg' should facilitate add / subtract. - Will A
@WillA, They might be, but MAC will be slower than plain old multiply and reciprocal would lose precision with large denominators. - Thomas O
@Thomas - take a look here microchip.com/forums/m450988.aspx for a divide function. Worth giving _Q16mac a go - if it's too slow it's too slow, but it may well be quick enough. - Will A

2 Answers

1
votes

The Microsoft library includes functions for adding and subtracting that deal with underflow/overflow (_Q15add and _Q15sub).

Multiplication can be implemented as an assembly function (I think the code is good - this is from memory).

C calling prototype is:

extern _Q15 Q15mpy(_Q15 a, _Q15 b);

The routine (placed in a .s source file in your project) is:

.global _Q15mpy
_Q15mpy:
mul.ss w0, w1, w2        ; signed multiple parameters, result in w2:w3
SL w2, w2            ; place most significant bit of W2 in carry
RLC w3, w0           ; rotate left carry into w3; result in W0
return                        ; return value in W0

.end

Remember to include libq.h

This routine does a left-shift of one bit rather than a right-shift of 15 bit on the result. There are no overflow concerns because Q15 numbers always have a magnitude <= 1.

0
votes

It turns out that all basic arithmetic functions are performed by using the native operators due to how the numbers are represented. e.g. divide uses the / operator and multiply the * operator, and these compile to simple 32-bit divides and multiplies.