> On 16. May 2023, at 04:22, Pedro Falcato <[email protected]> wrote:
>
> On Tue, May 16, 2023 at 2:46 AM gaoliming via groups.io
> <[email protected]> wrote:
>>
>> Pedro:
>>
>>> -----邮件原件-----
>>> 发件人: [email protected] <[email protected]> 代表 Pedro Falcato
>>> 发送时间: 2023年5月15日 23:15
>>> 收件人: [email protected]
>>> 抄送: Pedro Falcato <[email protected]>; Michael D Kinney
>>> <[email protected]>; Liming Gao <[email protected]>;
>>> Zhiguang Liu <[email protected]>; Marvin Häuser
>>> <[email protected]>
>>> 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
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