Re: [edk2-devel] [PATCH v2 1/1] MdePkg/Base.h: Simply alignment expressions

["Marvin Häuser" <mhaeuser@posteo.de>]

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> On 16. May 2023, at 09:18, Marvin Häuser <mhaeuser@posteo.de> wrote:
> 
> 
> 
>> On 16. May 2023, at 04:22, Pedro Falcato <pedro.falcato@gmail.com> wrote:
>> 
>> On Tue, May 16, 2023 at 2:46 AM gaoliming via groups.io
>> <gaoliming=byosoft.com.cn@groups.io> wrote:
>>> 
>>> Pedro:
>>> 
>>>> -----邮件原件-----
>>>> 发件人: devel@edk2.groups.io <devel@edk2.groups.io> 代表 Pedro Falcato
>>>> 发送时间: 2023年5月15日 23:15
>>>> 收件人: devel@edk2.groups.io
>>>> 抄送: Pedro Falcato <pedro.falcato@gmail.com>; Michael D Kinney
>>>> <michael.d.kinney@intel.com>; Liming Gao <gaoliming@byosoft.com.cn>;
>>>> Zhiguang Liu <zhiguang.liu@intel.com>; Marvin Häuser
>>>> <mhaeuser@posteo.de>
>>>> 主题: [edk2-devel] [PATCH v2 1/1] MdePkg/Base.h: Simply alignment
>>>> expressions
>>>> 
>>>> Simplify ALIGN_VALUE and ALIGN_VALUE_ADDEND into simpler expressions.
>>>> 
>>>> ALIGN_VALUE can simply be a (value + (align - 1)) & ~align
>>>> expression, which works for any power of 2 alignment and generates
>>>> smaller code sequences. For instance:
>>>>     ALIGN_VALUE(15, 16) = (15 + 15) & ~16 = 16
>>>>     ALIGN_VALUE(16, 16) = (16 + 15) & ~16 = 16
>>>> 
>>>> Old codegen:
>>>>     movq    %rdi, %rax
>>>>     negq    %rax
>>>>     andl    $15, %eax
>>>>     addq    %rdi, %rax
>>>> 
>>>> New codegen:
>>>>     leaq    15(%rdi), %rax
>>>>     andq    $-16, %rax
>>>> 
>>>> ALIGN_VALUE_ADDEND can simply use a bitwise NOT of Value to get the
>>>> addend for alignment, as, for instance:
>>>>     ~15 & (16 - 1) = 1
>>>>     15 + 1 = 16
>>>> 
>>> 
>>>>     ~15 & (16 - 1) = 1
>>> Its value should be zero, not 1. I also verify the updated ALIGN_VALUE_ADDEND.
>>> Its value is incorrect. Please double check.
>> 
>> Hi Liming, you're 100% right. There was a mixup when we were
>> discussing this optimization, and I got the mental calculations wrong
>> there.
>> Two's complement is definitely what we want, as one's complement is
>> always off by one (from what we want).
>> 
>> So negation (-) works beautifully, as seen in the old codegen (we
>> figured this out from the compiler's output).
> 
> To be clear on the maths side of things:
> 
> “& (Alignment - 1U)” is equivalent to “mod Alignment” for powers of two.
> “-Value” is equivalent to “2^N - Value” once the expression is promoted to an unsigned type, where N is the precision of said type.
> 
> So, the old expression basically was “(Alignment - Value) mod Alignment” and the new expression is “(2^N - Value) mod Alignment”. By modulo laws, we can apply the mod to the operands, which for the left ones gives us “Alignment mod Alignment = 0” and “2^N mod Alignment = 0”, obviously for Alignment being a power of two. They’re trivially equivalent.

Sorry, I have to add a correction here. This assumes that 2^N >= Alignment, which somehow I took for granted, but by removing Alignment from the expression, -Value will have the precision of Value rather than the higher precision out of {Alignment, Value}, which silently changes the semantics of N and thus 2^N. For Alignment > 2^(precision of Value), this will indeed not work.

Both current issues would be resolved by some mechanism to type-promote on demand. I.e. if for ALIGN_VALUE, the sub-expression (Alignment - 1U) in ~(Alignment - 1U) was promoted to the precision of Value, and for ALIGN_VALUE_ADDEND, the sub-expression Value in -Value was promoted to the precision of Alignment, both would be correct.

Best regards,
Marvin.

> 
> If you want a more technical explanation - previously, only the lower “Alignment - 1” Bits of the result were considered. As they are 0 for Alignment, the left operand, basically you get:
> 
> Result = (Alignment - Value) & (Alignment - 1) = (Alignment - Value)[0 : Alignment - 1] = (Alignment[0 : Alignment - 1] - Value[0 : Alignment - 1])[…] = (0 - Value[…])[…]
> 
> As you can see, only the lower Alignment -1 Bits of both operands matter and they are always equal for Alignment and 0.
> 
> Best regards,
> Marvin
> 
>> 
>> Sent a v3.
>> 
>> -- 
>> Pedro


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