[PATCH v1 3/6] libstdc++: Improve low-rank layout_{left, right}::stride.
Luc Grosheintz
luc.grosheintz@gmail.com
Wed Jul 30 08:56:29 GMT 2025
On 7/28/25 13:04, Tomasz Kaminski wrote:
> On Mon, Jul 28, 2025 at 10:24 AM Tomasz Kaminski <tkaminsk@redhat.com>
> wrote:
>
>>
>>
>>
>> On Mon, Jul 28, 2025 at 10:03 AM Luc Grosheintz <luc.grosheintz@gmail.com>
>> wrote:
>>
>>>
>>>
>>> On 7/28/25 08:02, Tomasz Kaminski wrote:
>>>> On Sun, Jul 27, 2025 at 2:47 PM Luc Grosheintz <
>>> luc.grosheintz@gmail.com>
>>>> wrote:
>>>>
>>>>> The methods layout_{left,right}::mapping::stride are defined
>>>>> as
>>>>>
>>>>> \prod_{i = 0}^r E[i]
>>>>> \prod_{i = r+1}^n E[i]
>>>>>
>>>>> This is computed as the product of a pre-comupted static product and
>>> the
>>>>> product of the required dynamic extents.
>>>>>
>>>>> Disassembly shows that even for low-rank extents, i.e. rank == 1 and
>>>>> rank == 2, with at least one dynamic extent, the generated code loads
>>>>> two values; and then runs the loop over at most one element, e.g.
>>>>>
>>>>> 220: 48 8b 0c f5 00 00 00 mov rcx,QWORD PTR [rsi*8+0x0]
>>>>> 227: 00
>>>>> 228: 48 8b 04 f5 00 00 00 mov rax,QWORD PTR [rsi*8+0x0]
>>>>> 22f: 00
>>>>> 230: 48 c1 e1 02 shl rcx,0x2
>>>>> 234: 74 1a je 250 <stride_left_d5+0x30>
>>>>> 236: 48 01 f9 add rcx,rdi
>>>>> 239: 0f 1f 80 00 00 00 00 nop DWORD PTR [rax+0x0]
>>>>> 240: 48 63 17 movsxd rdx,DWORD PTR [rdi]
>>>>> 243: 48 83 c7 04 add rdi,0x4
>>>>> 247: 48 0f af c2 imul rax,rdx
>>>>> 24b: 48 39 f9 cmp rcx,rdi
>>>>> 24e: 75 f0 jne 240 <stride_left_d5+0x20>
>>>>> 250: c3 ret
>>>>>
>>>>> If there's no dynamic extents, it simply loads the precomputed product
>>>>> of static extents.
>>>>>
>>>>> For rank == 1 the answer is constant `1`; for rank == 2 it's either 1
>>> or
>>>>> extents.extent(k), with k == 0 for layout_left and k == 1 for
>>>>> layout_right.
>>>>>
>>>>> Consider,
>>>>>
>>>>> using Ed = std::extents<int, dyn>;
>>>>> int stride_left_d(const std::layout_left::mapping<Ed>& m, size_t r)
>>>>> { return m.stride(r); }
>>>>>
>>>>> using E3d = std::extents<int, 3, dyn>;
>>>>> int stride_left_3d(const std::layout_left::mapping<E3d>& m, size_t
>>> r)
>>>>> { return m.stride(r); }
>>>>>
>>>>> using Ed5 = std::extents<int, dyn, 5>;
>>>>> int stride_left_d5(const std::layout_left::mapping<Ed5>& m, size_t
>>> r)
>>>>> { return m.stride(r); }
>>>>>
>>>>> The optimized code for these three cases is:
>>>>>
>>>>> 0000000000000060 <stride_left_d>:
>>>>> 60: b8 01 00 00 00 mov eax,0x1
>>>>> 65: c3 ret
>>>>>
>>>>> 0000000000000090 <stride_left_3d>:
>>>>> 90: 48 83 fe 01 cmp rsi,0x1
>>>>> 94: 19 c0 sbb eax,eax
>>>>> 96: 83 e0 fe and eax,0xfffffffe
>>>>> 99: 83 c0 03 add eax,0x3
>>>>> 9c: c3 ret
>>>>>
>>>>> 00000000000000a0 <stride_left_d5>:
>>>>> a0: b8 01 00 00 00 mov eax,0x1
>>>>> a5: 48 85 f6 test rsi,rsi
>>>>> a8: 74 02 je ac <stride_left_d5+0xc>
>>>>> aa: 8b 07 mov eax,DWORD PTR [rdi]
>>>>> i ac: c3 ret
>>>>>
>>>>> For rank == 1 it simply returns 1 (as expected). For rank == 2, it
>>>>> either implements a branchless formula, or conditionally loads one
>>>>> value. In all cases involving a dynamic extent this seems like it's
>>>>> always doing clearly less work, both in terms of computation and loads.
>>>>>
>>>>> For rank == 2, it trades loading one value for a branchless sequence of
>>>>> four instructions that don't require loading any values.
>>>>>
>>>> I will put this optimization into the __fwd_prod and __rev_pord
>>> functions,
>>>> so it will be applied for all uses. This will also avoid us creating
>>> this
>>>> caching
>>>> tables for such small ranks.
>>>
>>> The problem is that we don't have the same amount of information in
>>> the stride and __fwd_prod. The valid values for __r are 1, ..., rank;
>>> for __fwd_prod it's inclusive, while in stride it's exclusive. Therefore,
>>> we can do the optimization with one comparison less in stride than in
>>> __fwd_prod.
>>>
>> Make sense, and I am OK having this optimization there. However, out of
>> curiosity, if we put always_inline on the __fwd_prod, wouldn't compiler be
>> able
>> to eliminate __rank == __i. Also once we have separate call to __size, we
>> could
>> put assertions (just as a comment) that for __fwd_prod and __rev_prod __r
>> is
>> required to be smaller than rank().
>>
> I think I would pursue that direction, and have similar if constexpr in the
> __size function:
> __rank == 0 -> 1
> __rank == 1 -> extent(0)
> __rank == 2 -> extent(0) * extent(1)
> __rank == rank_dynamic() -> __ext_prod with __sta_ext == 1
> otherwise -> use __sta_extr.
We know that __size is optimized very aggressively and effectively. On
-O2 everything is inlined and no symbols are created, no static storage
is needed to compute __size. This is regardless of rank.
The following:
using E1 = std::extents<int, dyn>;
int size1(const std::mdspan<double, E1>& md)
{ return md.size(); }
using E2 = std::extents<int, 3, 5, dyn, dyn, 7, dyn, 11>;
int size2(const std::mdspan<double, E2>& md)
{ return md.size(); }
using E3 = std::extents<int, 3, dyn>;
int size3(const std::mdspan<double, E3>& md)
{ return md.size(); }
when compiled with -O2 -c size.o
$ nm size.o
0000000000000000 T size1
0000000000000010 T size2
0000000000000030 T size3
$ objdump -h size.o
size.o: file format elf64-x86-64
Sections:
Idx Name Size VMA LMA File off Algn
0 .text 00000037 0000000000000000 0000000000000000 00000040 2**4
CONTENTS, ALLOC, LOAD, READONLY, CODE
1 .data 00000000 0000000000000000 0000000000000000 00000077 2**0
CONTENTS, ALLOC, LOAD, DATA
2 .bss 00000000 0000000000000000 0000000000000000 00000077 2**0
ALLOC
3 .comment 0000002b 0000000000000000 0000000000000000 00000077 2**0
CONTENTS, READONLY
4 .note.GNU-stack 00000000 0000000000000000 0000000000000000 000000a2 2**0
CONTENTS, READONLY
5 .note.gnu.property 00000030 0000000000000000 0000000000000000 000000a8 2**3
CONTENTS, ALLOC, LOAD, READONLY, DATA
6 .eh_frame 00000058 0000000000000000 0000000000000000 000000d8 2**3
CONTENTS, ALLOC, LOAD, RELOC, READONLY, DATA
$ objdump -d size.o
0000000000000000 <size1>:
0: 8b 07 mov (%rdi),%eax
2: c3 ret
3: 66 66 2e 0f 1f 84 00 data16 cs nopw 0x0(%rax,%rax,1)
a: 00 00 00 00
e: 66 90 xchg %ax,%ax
0000000000000010 <size2>:
10: 48 63 07 movslq (%rdi),%rax
13: 48 63 57 04 movslq 0x4(%rdi),%rdx
17: 48 0f af c2 imul %rdx,%rax
1b: 0f af 47 08 imul 0x8(%rdi),%eax
1f: 69 c0 83 04 00 00 imul $0x483,%eax,%eax
25: c3 ret
26: 66 2e 0f 1f 84 00 00 cs nopw 0x0(%rax,%rax,1)
2d: 00 00 00
0000000000000030 <size3>:
30: 48 63 07 movslq (%rdi),%rax
33: 8d 04 40 lea (%rax,%rax,2),%eax
36: c3 ret
Hence, I'm not sure where I need to look to find the cost of not putting
the constexpr-if in __size. If I can see why it's slower, I'm happy to
add them. However, since I've looked and can't see a cost, I'm reluctant
to add them because they require test coverage for each branch (otherwise
they're never compiled and could contain complete non-sense).
>
>>
>>> I purposefully checked mdspan::size (part of the previous commit); and
>>> on optimized builds it fully unrolls the loop and does everything
>>> automatically, meaning it doesn't need help and we're not repeating
>>> the same optimization several times.
>>>
>>> As for avoiding the tables for small ranks, we can refactor _RevProd
>>> as follows:
>>>
>>> template<size_t... _Extents>
>>> struct _RevProd
>>> {
>>> size_t _S_value(size_t i)
>>> { return _S_data[i]; }
>>>
>>> private:
>>> array _S_data = consteval ...;
>>> }
>>>
>>> and use partial specialization to eliminate _S_data.
>>>
>>>>
>>>>>
>>>>> libstdc++-v3/ChangeLog:
>>>>>
>>>>> * include/std/mdspan (layout_left::mapping::stride): Optimize
>>>>> for rank <= 2.
>>>>> (layout_right::mapping::stride): Ditto.
>>>>>
>>>>> Signed-off-by: Luc Grosheintz <luc.grosheintz@gmail.com>
>>>>> ---
>>>>> libstdc++-v3/include/std/mdspan | 14 ++++++++++++--
>>>>> 1 file changed, 12 insertions(+), 2 deletions(-)
>>>>>
>>>>> diff --git a/libstdc++-v3/include/std/mdspan
>>>>> b/libstdc++-v3/include/std/mdspan
>>>>> index 06ccf3e3827..f288af96cdb 100644
>>>>> --- a/libstdc++-v3/include/std/mdspan
>>>>> +++ b/libstdc++-v3/include/std/mdspan
>>>>> @@ -652,7 +652,12 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION
>>>>> requires (extents_type::rank() > 0)
>>>>> {
>>>>> __glibcxx_assert(__i < extents_type::rank());
>>>>> - return __mdspan::__fwd_prod(_M_extents, __i);
>>>>> + if constexpr (extents_type::rank() == 1)
>>>>> + return 1;
>>>>> + else if constexpr (extents_type::rank() == 2)
>>>>> + return __i == 0 ? 1 : _M_extents.extent(0);
>>>>> + else
>>>>> + return __mdspan::__fwd_prod(_M_extents, __i);
>>>>> }
>>>>>
>>>>> template<typename _OExtents>
>>>>> @@ -797,7 +802,12 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION
>>>>> requires (extents_type::rank() > 0)
>>>>> {
>>>>> __glibcxx_assert(__i < extents_type::rank());
>>>>> - return __mdspan::__rev_prod(_M_extents, __i);
>>>>> + if constexpr (extents_type::rank() == 1)
>>>>> + return 1;
>>>>> + else if constexpr (extents_type::rank() == 2)
>>>>> + return __i == 0 ? _M_extents.extent(1) : 1;
>>>>> + else
>>>>> + return __mdspan::__rev_prod(_M_extents, __i);
>>>>> }
>>>>>
>>>>> template<typename _OExtents>
>>>>> --
>>>>> 2.50.0
>>>>>
>>>>>
>>>>
>>>
>>>
>
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