What does ordered / unordered comparison mean?

An ordered comparison checks if neither operand is NaN. Conversely, an unordered comparison checks if either operand is a NaN.

This page gives some more information on this:

• http://csapp.cs.cmu.edu/public/waside/waside-sse.pdf (section 5)

The idea here is that comparisons with NaN are indeterminate. (can’t decide the result) So an ordered/unordered comparison checks if this is (or isn’t) the case.

double a = 0.;
double b = 0.;

__m128d x = _mm_set1_pd(a / b);     //  NaN
__m128d y = _mm_set1_pd(1.0);       //  1.0
__m128d z = _mm_set1_pd(1.0);       //  1.0

__m128d c0 = _mm_cmpord_pd(x,y);    //  NaN vs. 1.0
__m128d c1 = _mm_cmpunord_pd(x,y);  //  NaN vs. 1.0
__m128d c2 = _mm_cmpord_pd(y,z);    //  1.0 vs. 1.0
__m128d c3 = _mm_cmpunord_pd(y,z);  //  1.0 vs. 1.0
__m128d c4 = _mm_cmpord_pd(x,x);    //  NaN vs. NaN
__m128d c5 = _mm_cmpunord_pd(x,x);  //  NaN vs. NaN

cout << _mm_castpd_si128(c0).m128i_i64[0] << endl;
cout << _mm_castpd_si128(c1).m128i_i64[0] << endl;
cout << _mm_castpd_si128(c2).m128i_i64[0] << endl;
cout << _mm_castpd_si128(c3).m128i_i64[0] << endl;
cout << _mm_castpd_si128(c4).m128i_i64[0] << endl;
cout << _mm_castpd_si128(c5).m128i_i64[0] << endl;

Result:

0
-1
-1
0
0
-1

Ordered return true if the operands are comparable (neither number is NaN):

• Ordered comparison of 1.0 and 1.0 gives true.
• Ordered comparison of NaN and 1.0 gives false.
• Ordered comparison of NaN and NaN gives false.

Unordered comparison is the exact opposite:

• Unordered comparison of 1.0 and 1.0 gives false.
• Unordered comparison of NaN and 1.0 gives true.
• Unordered comparison of NaN and NaN gives true.