CODEWITHSUNDEEP
performancex86floating-pointsimdavx
BeeOnRope
BeeOnRope

Reputation: 64875

Floating point compare of absolute values in AVX

I would like to compare two vectors of doubles based on their absolute values.

That is, the vector equivalent of the following:

if (fabs(x) < fabs(y)) {
    ...
}

Is there anything better than just taking the absolute value of each side and following up with a _mm256_cmp_pd?

Interested in all of AVX, AVX2, and AVX-512 flavors.

Upvotes: 5

Views: 984

Answers (1)

wim
wim

Reputation: 3930

With AVX-512 you can save one µop. Instead of 2xvandpd+vcmppd you can use vpternlogq+vpcmpuq. Note that the solution below assumes that the numbers are not a NaN.

IEEE-754 floating point numbers have the nice property that they are encoded such that if x[62:0] integer_less_than y[62:0], then as a floating point: abs(x)<abs(y).

So, instead of setting both sign bits to 0, we can copy the sign bit of x to the sign bit of y and compare the result as an unsigned integer. In the (untested) code below, for negative x both xi[63] and yi_sgnx[63] are 1, while for positive x, both xi[63] and yi_sgnx[63] are 0. So the unsigned integer compare actually compares xi[62:0] with yi[62:0], which is just what we need for the comparison abs(x)<abs(y).

The vpternlog instruction is suitable for copying the sign bit, see here or here. I'm not sure if the constants z and 0xCA are chosen correctly.

__mmask8 cmplt_via_ternlog(__m512d x, __m512d y){
    __m512i xi        = _mm512_castpd_si512(x);                                       
    __m512i yi        = _mm512_castpd_si512(x);                                       
    __m512i z         = _mm512_set1_epi64(0x7FFFFFFFFFFFFFFFull);
    __m512i yi_sgnx   = _mm512_ternarylogic_epi64(z, yi, xi, 0xCA);
    return _mm512_cmp_epu64_mask(xi, yi_sgnx, 1);   /* _CMPINT_LT  */
}

Upvotes: 3

Related Questions