Implementation notes: amd64, hertz, crypto_encrypt/4hfe

Compiler output

HFE-test.cpp: In file included from HFE-test.cpp:18:
HFE-test.cpp: In file included from ./HFE.h:6:
HFE-test.cpp: ./tower.h:364:9: error: argument to '__builtin_ia32_palignr128' must be a constant integer
HFE-test.cpp:   364 |         return _mm_alignr_epi8(a1, a0, i*2);
HFE-test.cpp:       |                ^~~~~~~~~~~~~~~~~~~~~~~~~~~~
HFE-test.cpp: /usr/lib/llvm-18/lib/clang/18/include/tmmintrin.h:157:13: note: expanded from macro '_mm_alignr_epi8'
HFE-test.cpp:   157 |   ((__m128i)__builtin_ia32_palignr128((__v16qi)(__m128i)(a), \
HFE-test.cpp:       |             ^
HFE-test.cpp:   158 |                                       (__v16qi)(__m128i)(b), (n)))
HFE-test.cpp:       |                                                              ~~~
HFE-test.cpp: In file included from HFE-test.cpp:18:
HFE-test.cpp: In file included from ./HFE.h:7:
HFE-test.cpp: ./groebner.h:291:14: warning: unused variable 'y3' [-Wunused-variable]
HFE-test.cpp:   291 |         monomial<4> y3 = monomial<4>(48);
HFE-test.cpp:       |                     ^~
HFE-test.cpp: In file included from HFE-test.cpp:18:
HFE-test.cpp: In file included from ./HFE.h:9:
HFE-test.cpp: In file included from ./bqas.h:79:
HFE-test.cpp: ./transpose8.h:38:2: error: ISO C++17 does not allow 'register' storage class specifier [-Wregister]
HFE-test.cpp:    38 |         register __m128i a=s[0],b=s[1],c=s[2],d=s[3],e=s[4],f=s[5],g=s[6],h=s[7];
HFE-test.cpp:       |         ^~~~~~~~
HFE-test.cpp: ./transpose8.h:38:2: error: ISO C++17 does not allow 'register' storage class specifier [-Wregister]
HFE-test.cpp:    38 |         register __m128i a=s[0],b=s[1],c=s[2],d=s[3],e=s[4],f=s[5],g=s[6],h=s[7];
HFE-test.cpp:       |         ^~~~~~~~
HFE-test.cpp: ./transpose8.h:38:2: error: ISO C++17 does not allow 'register' storage class specifier [-Wregister]
HFE-test.cpp: ...

Compiler output

HFE-test.cpp: In file included from HFE.h:6,
HFE-test.cpp:                  from HFE-test.cpp:18:
HFE-test.cpp: tower.h:107:56: warning: dereferencing type-punned pointer will break strict-aliasing rules [-Wstrict-aliasing]
HFE-test.cpp:   107 | template <> const gftower<31,9> gftower<31,9>::one = *((gftower<31,9> *)_gf_31_56_one);
HFE-test.cpp:       |                                                       ~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
HFE-test.cpp: tower.h:107:56: warning: dereferencing type-punned pointer will break strict-aliasing rules [-Wstrict-aliasing]
HFE-test.cpp: tower.h:108:58: warning: dereferencing type-punned pointer will break strict-aliasing rules [-Wstrict-aliasing]
HFE-test.cpp:   108 | template <> const gftower<31,10> gftower<31,10>::one = *((gftower<31,10> *)_gf_31_56_one);
HFE-test.cpp:       |                                                         ~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
HFE-test.cpp: tower.h:108:58: warning: dereferencing type-punned pointer will break strict-aliasing rules [-Wstrict-aliasing]
HFE-test.cpp: tower.h:109:58: warning: dereferencing type-punned pointer will break strict-aliasing rules [-Wstrict-aliasing]
HFE-test.cpp:   109 | template <> const gftower<31,15> gftower<31,15>::one = *((gftower<31,15> *)_gf_31_56_one);
HFE-test.cpp:       |                                                         ~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
HFE-test.cpp: tower.h:109:58: warning: dereferencing type-punned pointer will break strict-aliasing rules [-Wstrict-aliasing]
HFE-test.cpp: tower.h:110:58: warning: dereferencing type-punned pointer will break strict-aliasing rules [-Wstrict-aliasing]
HFE-test.cpp:   110 | template <> const gftower<31,18> gftower<31,18>::one = *((gftower<31,18> *)_gf_31_56_one);
HFE-test.cpp:       |                                                         ~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
HFE-test.cpp: tower.h:110:58: warning: dereferencing type-punned pointer will break strict-aliasing rules [-Wstrict-aliasing]
HFE-test.cpp: tower.h:111:58: warning: dereferencing type-punned pointer will break strict-aliasing rules [-Wstrict-aliasing]
HFE-test.cpp:   111 | template <> const gftower<31,30> gftower<31,30>::one = *((gftower<31,30> *)_gf_31_56_one);
HFE-test.cpp:       |                                                         ~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
HFE-test.cpp: tower.h:111:58: warning: dereferencing type-punned pointer will break strict-aliasing rules [-Wstrict-aliasing]
HFE-test.cpp: tower.h:112:58: warning: dereferencing type-punned pointer will break strict-aliasing rules [-Wstrict-aliasing]
HFE-test.cpp:   112 | template <> const gftower<31,45> gftower<31,45>::one = *((gftower<31,45> *)_gf_31_56_one);
HFE-test.cpp:       |                                                         ~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
HFE-test.cpp: ...