feat(bb/avm): use flat tuple for univariate/value containers (#16191)

Uses a flat tuple (tuplet) instead of `std::tuple` for the largest
containers (tuples of univariates). This takes compilation time for the
AVM from ~`4m43s` to ~`3m46s` on x86.

It takes tuple instantiation/recursion times from minutes to
milliseconds.

WARNING: There seems to be a change in initialization semantics, see
comments. This uncovered several sites where univariates and values were
not being set to 0.

------------

Biggest offenders in terms of template instantiations are still
- bb::RelationUtils<bb::avm2::AvmFlavor>::add_nested_tuples
-
bb::SumcheckProverRound<bb::avm2::AvmFlavor>::accumulate_relation_univariates
- bb::SumcheckProverRound<bb::avm2::AvmFlavor>::batch_over_relations
 - bb::RelationUtils<bb::avm2::AvmFlavor>::scale_univariates
-
bb::SumcheckProverRound<bb::avm2::AvmFlavor>::extend_and_batch_univariates

but a lot of work would be needed to solve those. Probably some type
erasure over univariates is needed.

Author: fcarreiro

barretenberg/cpp/src/CMakeLists.txt

@@ -14,6 +14,8 @@ set(CMAKE_LIBRARY_OUTPUT_DIRECTORY ${CMAKE_BINARY_DIR}/lib)
 # To preserve the warning, but prevent them from causing the build to fail,
 # use the flag `-Wno-error=${ERROR_NAME}`
 add_compile_options(-Werror -Wall -Wextra -Wconversion -Wsign-conversion -Wfatal-errors)
+# Needed until https://github.com/codeinred/tuplet/issues/37 is solved.
+add_compile_options(-Wno-missing-braces)
 
 if(CMAKE_CXX_COMPILER_ID MATCHES "Clang")
     add_compile_options(-fcolor-diagnostics -fconstexpr-steps=100000000)

barretenberg/cpp/src/barretenberg/common/tuple.hpp

@@ -0,0 +1,30 @@
+#pragma once
+
+#include "barretenberg/common/tuplet.hpp"
+
+namespace bb {
+
+namespace flat_tuple = ::tuplet;
+
+} // namespace bb
+
+namespace std {
+
+template <size_t I, class... T> constexpr decltype(auto) get(::tuplet::tuple<T...>&& t) noexcept
+{
+    return ::tuplet::get<I>(static_cast<::tuplet::tuple<T...>&&>(t));
+}
+template <size_t I, class... T> constexpr decltype(auto) get(::tuplet::tuple<T...>& t) noexcept
+{
+    return ::tuplet::get<I>(static_cast<::tuplet::tuple<T...>&>(t));
+}
+template <size_t I, class... T> constexpr decltype(auto) get(const ::tuplet::tuple<T...>& t) noexcept
+{
+    return ::tuplet::get<I>(static_cast<const ::tuplet::tuple<T...>&>(t));
+}
+template <size_t I, class... T> constexpr decltype(auto) get(const ::tuplet::tuple<T...>&& t) noexcept
+{
+    return ::tuplet::get<I>(static_cast<const ::tuplet::tuple<T...>&&>(t));
+}
+
+} // namespace std