Better handling of powers in modcc.

[thorstenhater]

• $x^{-1} \Rightarrow 1/x\quad \forall x$
• $x^n \Rightarrow x\cdot \dots \cdot x \quad x\in N; |x| < 5$
• $x^n \Rightarrow 1/(x\cdot \dots \cdot x) \quad x\in N; |x| < 5; x < 0$
• $b^e \Rightarrow \exp(\log(b) e)\quad \forall b, e$

The last point introduces potential errors when pow(b, e) is allowed, but log(b) is
undefined. These occur exactly when all of the following is true

• $b < 0$
• $e\in N$
• $e$, $b$ not known at compile time (since we cover these cases before)

[llandsmeer]

Just tried a build, got this:

FAILED: arbor/CMakeFiles/arbor.dir/__/mechanisms/generated/default/kdrmt_cpu.cpp.o
ccache /usr/bin/c++ -Darbor_EXPORTS_STATIC -I/home/llandsmeer/repos/pr/2061/ext/random123/include -I/home/llandsmeer/repos/pr/2061/arbor -I/home/llandsmeer/repos/pr/2061/arbor/include -I/home/llandsmeer/repos/pr/2061/build/arbor/include -O3 -DNDEBUG -fPIC -Wall -Wno-maybe-uninitialized -Wno-psabi -march=native -fvisibility=hidden -std=c++17 -MD -MT arbor/CMakeFiles/arbor.dir/__/mechanisms/generated/default/kdrmt_cpu.cpp.o -MF arbor/CMakeFiles/arbor.dir/__/mechanisms/generated/default/kdrmt_cpu.cpp.o.d -o arbor/CMakeFiles/arbor.dir/__/mechanisms/generated/default/kdrmt_cpu.cpp.o -c /home/llandsmeer/repos/pr/2061/build/mechanisms/generated/default/kdrmt_cpu.cpp
/home/llandsmeer/repos/pr/2061/build/mechanisms/generated/default/kdrmt_cpu.cpp: In function ‘void arb::default_catalogue::kernel_kdrmt::advance_state(arb_mechanism_ppack*)’:
/home/llandsmeer/repos/pr/2061/build/mechanisms/generated/default/kdrmt_cpu.cpp:155:40: error: no matching function for call to ‘log(double&)’
  155 |         assign(qt, S::exp(S::mul(S::log(_pp_var_q10), S::mul( (double)0.10000000000000001, S::sub(celsius,  (double)24.0)))));
      |                                  ~~~~~~^~~~~~~~~~~~~

[thorstenhater]

Yes, that's due to the following chain of events (NB. It also fails in CI for the same reasons)
There's no Simd::log(Simd::scalar_t) since ARB_UNARY_ARTHIMETIC doesn't define scalar versions
(BINARY does, though). You cannot simply add it since the mapping scalar_t -> vector_t is non-injective
and C++ barfs 'cannot figure out template argument T' back at you. For BINARY that's not an issue, since
the second arg fixes the vector type.

I am currently thinking on how to add that without too much hassle.

[llandsmeer]

Can confirm the build works. Runtime for the L5PC s 4.410, a 3.3x improvement.

Didn't check GH actions - rerunning now

[llandsmeer]

Symbolic differentiation test symbolic_pdiff.nonlinear, ../test/unit-modcc/test_symdiff.cpp:210: expressions: a^x; log(a)*a^x seems to have broken. Makes sense probably if we edit the definition of a power

[thorstenhater]

Yes, that's because we compare strings here

[thorstenhater]

There, should be fixed now.