_mm_testc_ps and _mm_testc_pd vs _mm_testc_si128

As you know, the first two are AVX-specific intrinsics and the second is a SSE4.1 intrinsic. Both sets of intrinsics can be used to check for equality of 2 floating-point vectors. My specific use case is:

_mm_cmpeq_ps or _mm_cmpeq_pd, followed by
_mm_testc_ps or _mm_testc_pd on the result, with an appropriate mask

But AVX provides equivalents for "legacy" intrinsics, so I might be able to use _mm_testc_si128, after a cast of the result to __m128i. My questions are, which of the two use cases results in better performance and where I can find out what legacy SSE instructions are provided by AVX.

Oops, I didn't read the question carefully. You're talking about using these after a cmpeqps. They're always slower than movmskps / test if you already have a mask. cmpps / ptest / jcc is 4 uops. cmpps / movmskps eax, xmm0 / test eax,eax / jnz is 3 uops. (test/jnz fuse into a single uop). Also, none of the instructions are multi-uop, so no decode bottlenecks.

Only use ptest / vtestps/pd when you can take full advantage of the AND or ANDN operation to avoid an earlier step. I've posted answers before where I compared ptest vs. an alternative. I think I did find one case once where ptest was a win, but it's hard to use. Yup, found it: someone wanted an FP compare that was true for NaN == NaN. It's one of the only times I've ever found a use for the carry flag result of ptest.

If the high element of a compare result is "garbage", then you can still ignore it cheaply with movmskps:

_mm_movemask_ps(vec) & 0b0111 == 0  // tests for none of the first three being true

This is totally free. The x86 test instruction works a lot like ptest: You can use it with an immediate mask instead of to test a register against itself. (It actually has a tiny cost: one extra byte of machine code, because test eax, 3 is one byte longer than test eax, eax, but they run identically.).

See the x86 wiki for links to guides (Agner Fog's guide is good for perf analysis at the instruction level). There's an AVX version of every legacy SSE instruction, but some are only 128 bits wide. They all get an extra operand (so the dest doesn't have to be one of the src regs), which saves on mov instructions to copy registers.

Answer to a question you didn't ask:

Neither _mm_testc_ps nor _mm_testc_si128 can be used to compare floats for equality. vtestps is like ptest, but only operates on the sign bits of each float element.

They all compute (~x) & y (on sign bits or on the full register), which doesn't tell you whether they're equal, or even whether the sign bits are equal.

Note that even checking for bitwise equality of floats (with pcmpeqd) isn't the same as cmpeqps (which implements C's == operator), because -0.0 isn't bitwise equal to 0.0. And two bitwise-identical NaNs aren't equal to each other. The comparison is unordered (which means not equal) if either or both operand is NaN.