llvm dev - Nov 2015 - [lld] R_MIPS_HI16 / R_MIPS_LO16 calculation

On Sun, Nov 22, 2015 at 1:28 AM, Rui Ueyama <ruiu at google.com>
wrote:
> I'm not sure if I understand the semantics of HI16 and LO16
relocations. If
> my understanding is correct, a pair of HI16 and LO16 represents an addend
> AHL. AHL is computed by (AHI<<16) | (ALO&0xFFFF). Can't we
apply HI16 and
> LO16 relocations separately and produce the same relocation result? Do we
> have to pair them up before applying relocations?
The correct formula for the combined addend is (AHI << 16) +
(short)ALO. So the combined addend depends on both AHI and ALO
addends, therefore ALO affects result of R_MIPS_HI16 relocation.

Current version of bfd GNU linker looks up R_MIPS_LO16 relocation each
time it needs to calculate R_MIPS_HI16 relocation. It uses
`mips_elf_add_lo16_rel_addend` function for that
(https://goo.gl/P7nb76).

-- 
Simon Atanasyan

On Sun, Nov 22, 2015 at 3:05 AM, Simon Atanasyan <simon at atanasyan.com>
wrote:
> On Sun, Nov 22, 2015 at 1:28 AM, Rui Ueyama <ruiu at google.com>
wrote:
> > I'm not sure if I understand the semantics of HI16 and LO16
relocations.
> If
> > my understanding is correct, a pair of HI16 and LO16 represents an
addend
> > AHL. AHL is computed by (AHI<<16) | (ALO&0xFFFF). Can't
we apply HI16 and
> > LO16 relocations separately and produce the same relocation result? Do
we
> > have to pair them up before applying relocations?
>
> The correct formula for the combined addend is (AHI << 16) +
> (short)ALO. So the combined addend depends on both AHI and ALO
> addends, therefore ALO affects result of R_MIPS_HI16 relocation.

Does that mean it is impossible to process HI16 and LO16 separately?

If you apply only HI16 relocation, the relocation target will have a value
AHI<<16. Next time when you apply LO16 relocation to the same address,
you'll be able to see the previous result of HI16 relocation. So you
don't
have to combine them before applying relocations, no?

>
> Current version of bfd GNU linker looks up R_MIPS_LO16 relocation each
> time it needs to calculate R_MIPS_HI16 relocation. It uses
> `mips_elf_add_lo16_rel_addend` function for that
> (https://goo.gl/P7nb76).
>
> --
> Simon Atanasyan
>
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On Mon, Nov 23, 2015 at 6:39 AM, Rui Ueyama <ruiu at google.com>
wrote:
> On Sun, Nov 22, 2015 at 3:05 AM, Simon Atanasyan <simon at
atanasyan.com>
> wrote:
>>
>> On Sun, Nov 22, 2015 at 1:28 AM, Rui Ueyama <ruiu at google.com>
wrote:
>> > I'm not sure if I understand the semantics of HI16 and LO16
relocations.
>> > If
>> > my understanding is correct, a pair of HI16 and LO16 represents an
>> > addend
>> > AHL. AHL is computed by (AHI<<16) | (ALO&0xFFFF).
Can't we apply HI16
>> > and
>> > LO16 relocations separately and produce the same relocation
result? Do
>> > we
>> > have to pair them up before applying relocations?
>>
>> The correct formula for the combined addend is (AHI << 16) +
>> (short)ALO. So the combined addend depends on both AHI and ALO
>> addends, therefore ALO affects result of R_MIPS_HI16 relocation.
>
>
> Does that mean it is impossible to process HI16 and LO16 separately?
>
> If you apply only HI16 relocation, the relocation target will have a value
> AHI<<16. Next time when you apply LO16 relocation to the same
address,
> you'll be able to see the previous result of HI16 relocation. So you
don't
> have to combine them before applying relocations, no?
HI16 and LO16 applied to the different place in the code. Take a look
at the typical example below. So you have to apply the relocations
separately but calculate them together.

00000000 <main>:
   0:   3c1c0000        lui     gp,0x0
                        0: R_MIPS_HI16  _gp_disp
   4:   279c0000        addiu   gp,gp,0
                        4: R_MIPS_LO16  _gp_disp

HI16 / LO16 relocations use a combined addend AHL. The R_MIPS_LO16
uses low 16 bits of the (S + AHL) expression so HI16 addend does not
affect its result. But LO16 addend might affect the result of the HI16
relocation.

-- 
Simon Atanasyan