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

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

> 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.

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