The Intel Manual says:
DC F8+i ---> FDIV ST(i), ST(0)

What the excerpt you quoted shows, one of the operands needs to be ST(0). If the first one is not, the second one must be:

Wow! I did not see this.
Thank you!

All of the legacy FP instructions can only encode a single register.

If you wanted to have Fop st(i),st(j) then you need a way to encode two registers, i & j.

The newer MMX instructions and up can encode a second register.

You mean SSE2 instruction set for packed doubles and floats. I wanted to use those, but they do not have ATAN2 or LOG operations. I suppose I can use a mixed set.

Yes. All the MMX, SSE, SSE2, ..., AVX512 are not stack based and have at least two registers in the encoding, a source and a destination.

But there are no native trigonometric instructions outside of the legacy FP. If you are doing many trig ops then it might be more efficient overall to use an SSE+ based algorithm. It depends upon what you need them for.

Also, computing trigonometric functions with FPU is actually laid with traps.

Interesting link, Tomasz. Thanks.
I have a client - they use C++ legacy app to scan a ~20Gb file with float point values and do some statistics and it is slow.
I'll just compare the results from my new FPU code and their legacy app and just see if they match.
So, where I can find some resources on how to make FPATAN equivalent using SSE+?

Had a few old transcendental function implementations sitting around. Just posted them, they use double precision radian values, think accuracy is up to 4 places. They use Gregory's series and Maclaurin's series on the sine/cosine:

https://github.com/hpdporg/datap/blob/bfbe7544ba6e8aadbfa2b1d8b8cc021677458860/src/main/asm/Numeric/Transcendental.inc#L228

And tests/usage:

https://github.com/hpdporg/datap/blob/master/src/test/cpp/Numeric/Transcendental.cpp

The range of input values may be limited to just small values, but shows some of the SSE instructions and the values I've tested in that range seem correct when using a calculator.

Thank you.