> On 16. May 2023, at 09:18, Marvin Häuser <[email protected]> wrote:
>
>
>
>> 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.
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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