Inlining of a recursive function - c++

Question

When I try to compile this code:
#include <iostream>
#include <limits.h>
// End recursive template-expansion of function select below.
template <typename Type>
static inline constexpr Type select(unsigned index)
{ return Type(); }
// Select one of the items passed to it.
// e.g. select(0, a, b, c) = a; select(1, a, b, c) = b; etc.
template <typename Type, typename... Params>
[[gnu::always_inline]]
static inline constexpr Type select(unsigned index, Type value, Params... values)
{ return index == 0 ? value : select<Type>(index - 1, values...); }
template <typename Type>
[[gnu::always_inline]]
static inline constexpr Type reflect_mask_helper_1(Type mask, Type shift, Type value)
{ return ((value & mask) >> shift) | ((value << shift) & mask); }
template <typename Type>
[[gnu::always_inline]]
static inline constexpr Type reflect_mask_helper_0(unsigned i, Type value)
{
return i == 0
? value
: reflect_mask_helper_0(
i - 1,
reflect_mask_helper_1<Type>(
select(i - 1, 0xaaaaaaaaaaaaaaaa, 0xcccccccccccccccc, 0xf0f0f0f0f0f0f0f0,
0xff00ff00ff00ff00, 0xffff0000ffff0000, 0xffffffff00000000),
1 << (i - 1),
value));
}
template <typename Type>
[[gnu::flatten]]
static inline constexpr Type reflect_mask(Type value)
{ return reflect_mask_helper_0(__builtin_ctz(sizeof(Type) * CHAR_BIT), value); }
int main(void) {
for (int i = 0; i < 65536; i++) {
std::cout << reflect_mask<uint16_t>(i) << std::endl;
}
}
gcc gives me an error saying the function reflect_mask_helper_0 cannot be inlined because it is recursive. However, the function select is also recursive, but gcc inlines it without complaining. What am I missing here?
(I need it to be recursive, since constexpr functions cannot contain loops under C++11.)
Error message:
% g++ test.cpp -O3 -march=native -c
test.cpp: In function ‘constexpr Type reflect_mask_helper_0(unsigned int, Type) [with Type = short unsigned int]’:
test.cpp:23:30: error: inlining failed in call to always_inline ‘constexpr Type reflect_mask_helper_0(unsigned int, Type) [with Type = short unsigned int]’: recursive inlining
23 | static inline constexpr Type reflect_mask_helper_0(unsigned i, Type value)
| ^~~~~~~~~~~~~~~~~~~~~
test.cpp:27:28: note: called from here
27 | : reflect_mask_helper_0(
| ~~~~~~~~~~~~~~~~~~~~~^
28 | i - 1,
| ~~~~~~
29 | reflect_mask_helper_1<Type>(
| ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
30 | select(i - 1, 0xaaaaaaaaaaaaaaaa, 0xcccccccccccccccc, 0xf0f0f0f0f0f0f0f0,
| ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
31 | 0xff00ff00ff00ff00, 0xffff0000ffff0000, 0xffffffff00000000),
| ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
32 | 1 << (i - 1),
| ~~~~~~~~~~~~~
33 | value));
| ~~~~~~~
test.cpp: In function ‘int main()’:
test.cpp:23:30: error: inlining failed in call to always_inline ‘constexpr Type reflect_mask_helper_0(unsigned int, Type) [with Type = short unsigned int]’: recursive inlining
23 | static inline constexpr Type reflect_mask_helper_0(unsigned i, Type value)
| ^~~~~~~~~~~~~~~~~~~~~
test.cpp:27:28: note: called from here
27 | : reflect_mask_helper_0(
| ~~~~~~~~~~~~~~~~~~~~~^
28 | i - 1,
| ~~~~~~
29 | reflect_mask_helper_1<Type>(
| ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
30 | select(i - 1, 0xaaaaaaaaaaaaaaaa, 0xcccccccccccccccc, 0xf0f0f0f0f0f0f0f0,
| ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
31 | 0xff00ff00ff00ff00, 0xffff0000ffff0000, 0xffffffff00000000),
| ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
32 | 1 << (i - 1),
| ~~~~~~~~~~~~~
33 | value));
| ~~~~~~~

Answer 1

select doesn't actually calls itself. It pops the front of the type list it received and then calls another specialization of select<Type, ...>. The trailing parameter pack is different. Since that "recursion" is essentially a finite set of nested function calls (different functions), GCC can see right through it, regardless of the run-time parameter.
But reflect_mask_helper_0 does call itself, with the same template arguments, indefinitely. GCC has no way to tell how deep this run-time recursion will go at run-time. Recall that a constexpr function is still a regular function that must be invocable at run-time.

Answer 2

If you check out the resulting assembly code, if you remove the always_inline and flatten attributes, you can see that gcc actually inlines everything correctly.
So, this issue is a QoI thing. Maybe, at that point, when always_inline handled, it cannot be inlined (hence the error message), but gcc decides to inline it afterwards anyways.
Btw., you can finetune gcc, and with a little modification to your code, gcc can compile it:
pass --param max-early-inliner-iterations=3 to gcc
remove the flatten attribute (no idea, why it matters...)
(So, actually, this issue has nothing to do with recursive calls - from the compiler standpoint, it doesn't matter whether the function is recursive, or not, it just follows the flow of the code - to a certain extent, of course. Here, recursive depth is just 4, it is not too hard to follow for a compiler)

Answer 3

Here’s the solution I’ve found, thanks to grek40’s comment and to StoryTeller’s answer.
(As for my previous problem with the unused function template instance left in the compiled binary, I solved it by compiling the original code — without the gnu::always_inline and gnu::flatten attributes — with the arguments -ffunction-sections -fdata-sections -Wl,--gc-sections.)
Now reflect_mask_helper_0 is inside a struct (because C++ doesn’t allow partial specialization of function templates), and the i parameter of the function became the Index parameter of the struct template.
#include <iostream>
#include <limits.h>
// End recursive template-expansion of function select below.
template <typename Type>
static inline constexpr Type select(unsigned index)
{ return Type(); }
// Select one of the items passed to it.
// e.g. select(0, a, b, c) = a; select(1, a, b, c) = b; etc.
template <typename Type, typename... Params>
[[gnu::always_inline]]
static inline constexpr Type select(unsigned index, Type value, Params... values)
{ return index == 0 ? value : select<Type>(index - 1, values...); }
template <typename Type>
[[gnu::always_inline]]
static inline constexpr Type reflect_mask_helper_1(Type mask, Type shift, Type value)
{ return ((value & mask) >> shift) | ((value << shift) & mask); }
template <typename Type, unsigned Index>
struct reflect_mask_helper_0
{
[[gnu::always_inline]]
static inline constexpr Type invoke(Type value)
{
return reflect_mask_helper_0<Type, Index - 1>::call(
reflect_mask_helper_1<Type>(
static_cast<Type>(select(Index - 1,
0xaaaaaaaaaaaaaaaa, 0xcccccccccccccccc, 0xf0f0f0f0f0f0f0f0,
0xff00ff00ff00ff00, 0xffff0000ffff0000, 0xffffffff00000000)),
1 << (Index - 1),
value));
}
};
template <typename Type>
struct reflect_mask_helper_0<Type, 0>
{
[[gnu::always_inline]]
static inline constexpr Type invoke(Type value) { return value; }
};
template <typename Type>
static inline constexpr Type reflect_mask(Type value)
{ return reflect_mask_helper_0<Type, __builtin_ctz(sizeof(Type) * CHAR_BIT)>::invoke(value); }
int main(void) {
for (int i = 0; i < 65536; i++) {
std::cout << reflect_mask<uint16_t>(i) << std::endl;
}
}