# C/C++ fast absolute difference between two series

i am interested in generating efficient c/c++ code to get the differences between two time series.
More precise: The time series values are stored as uint16_t arrays with fixed and equal length == 128.

I am good with a pure c as well as a pure c++ implementation. My code examples are in c++

My intentions are:

``````Let A,B and C be discrete time series of length l with a value-type of uint16_t.
Vn[n<l]: Cn = |An - Bn|;
``````

What i can think of in pseudo code:

``````for index i:
if a[i] > b[i]:
c[i] = a[i] - b[i]
else:
c[i] = b[i] - a[i]
``````

Or in c/c++

``````for(uint8_t idx = 0; idx < 128; idx++){
c[i] = a[i] > b[i] ? a[i] - b[i] : b[i] - a[i];
}
``````

But i really dont like the if/else statement in the loop.
I am okay with looping – this can be unrolled by the compiler.
Somewhat like:

``````void getBufDiff(const uint16_t (&a)[], const uint16_t (&b)[], uint16_t (&c)[]) {
#pragma unroll 16
for (uint8_t i = 0; i < 128; i++) {
c[i] = a[i] > b[i] ? a[i] - b[i] : b[i] - a[i];
}
#end pragma
}
``````

What i am looking for is a ‘magic code’ which speeds up the if/else and gets me the absolute difference between the two unsigned values.

I am okay with a +/- 1 precision (In case this would allow some bit-magic to happen). I am also okay with changing the data-type to get faster results. And i am also okay with dropping the loop for something else.

So something like:

``````void getBufDiff(const uint16_t (&a)[], const uint16_t (&b)[], uint16_t (&c)[]) {
#pragma unroll 16
for (uint8_t i = 0; i < 128; i++) {
c[i] = magic_code_for_abs_diff(a[i],b[i]);
}
#end pragma
}
``````

Did try XORing the two values. Gives proper results only for one of the cases.

EDIT 2:

Did a quick test on different approaches on my Laptop.

For 250000000 entrys this is the performance (256 rounds):

``````c[i] = a[i] > b[i] ? a[i] - b[i] : b[i] - a[i];  ~500ms
c[i] = std::abs(a[i] - b[i]);                    ~800ms
c[i] = ((a[i] - b[i]) + ((a[i] - b[i]) >> 15)) ^ (i >> 15) ~425ms
uint16_t tmp = (a[i] - b[i]); c[i] = tmp * ((tmp > 0) - (tmp < 0)); ~600ms
uint16_t ret = { a[i] - b[i], b[i] - a[i] };c[i] = ret[a[i] < b[i]] ~900ms
c[i] = ((a[i] - b[i]) >> 31 | 1) * (a[i] - b[i]); ~375ms
c[i] = ((a[i] - b[i])) ^ ((a[i] - b[i]) >> 15) ~425ms
``````

### >Solution :

Since you write "I am okay with a +/- 1 precision", you can use a XOR-solution: instead of `abs(x)`, do `x ^ (x >> 15)`. This will give an off-by-1 result for negative values.

If you want to calculate the correct result even for negative values, use the other answer (with `x >> 15` correction).

In any case, this XOR-trick only works if overflow is impossible. The compiler can’t replace `abs` by code which uses XOR because of that.