A compact relocation format for ELF

This article introduces CREL (previously known as RELLEB), a new relocation format offering incredible size reduction (LLVM implementation in my fork).

ELF's design emphasizes natural size and alignment guidelines for its control structures. This principle, outlined in Proceedings of the Summer 1990 USENIX Conference, ELF: An Object File to Mitigate Mischievous Misoneism, promotes ease of random access for structures like program headers, section headers, and symbols.

All data structures that the object file format defines follow the "natural" size and alignment guidelines for the relevant class. If necessary, data structures contain explicit padding to ensure 4-byte alignment for 4-byte objects, to force structure sizes to a multiple of four, etc. Data also have suitable alignment from the beginning of the file. Thus, for example, a structure containing an Elf32_Addr member will be aligned on a 4-byte boundary within the file. Other classes would have appropriately scaled definitions. To illustrate, the 64-bit class would define Elf64 Addr as an 8-byte object, aligned on an 8-byte boundary. Following the strictest alignment for each object allows the format to work on any machine in a class. That is, all ELF structures on all 32-bit machines have congruent templates. For portability, ELF uses neither bit-fields nor floating-point values, because their representations vary, even among pro- cessors with the same byte order. Of course the programs in an ELF file may use these types, but the format itself does not.

While beneficial for many control structures, the natural size guideline presents significant drawbacks for relocations. Since relocations are typically processed sequentially, they don't gain the same random-access advantages. The large 24-byte Elf64_Rela structure highlights the drawback. For a detailed comparison of relocation formats, see Exploring object file formats#Relocations.

Furthermore, Elf32_Rel and Elf32_Rela sacrifice flexibility to maintain a smaller size, limiting relocation types to a maximum of 255. This constraint has become noticeable for AArch32 and RISC-V, and especially when platform-specific relocations are needed. While the 24-bit symbol index field is less elegant, it hasn't posed significant issues in real-world use cases.

In contrast, the WebAssembly object file format uses LEB128 encoding for relocations and other constrol structures, offering a significant size advantage over ELF.

Inspired by WebAssembly, I will start discussion with a generic compression algorithm and then propose an alternative format (CREL) that addresses ELF's limitations.

Compressed relocations

While the standard SHF_COMPRESSED feature is commonly used for debug sections, its application can easily extend to relocation sections. I have developed a Clang/lld prototype that demonstrates this by compressing SHT_RELA sections.

The compressed SHT_RELA section occupies sizeof(Elf64_Chdr) + size(compressed) bytes. The implementation retains uncompressed content if compression would result in a larger size.

In scenarios with numerous smaller relocation sections (such as when using -ffunction-sections -fdata-sections), the 24-byte Elf64_Chdr header can introduce significant overhead. This observation raises the question of whether encoding Elf64_Chdr fields using ULEB128 could further optimize file sizes. With larger monolithic sections (.text, .data, .eh_frame), compression ratio would be higher as well.

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# configure-llvm is my wrapper of cmake that specifies some useful options.
configure-llvm s2-custom0 -DLLVM_TARGETS_TO_BUILD=host -DLLVM_ENABLE_PROJECTS='clang;lld'
configure-llvm s2-custom1 -DLLVM_TARGETS_TO_BUILD=host -DLLVM_ENABLE_PROJECTS='clang;lld' -DCMAKE_{C,CXX}_FLAGS=-Xclang=--compress-relocations=zstd
ninja -C /tmp/out/s2-custom0 lld
ninja -C /tmp/out/s2-custom1 lld

ruby -e 'p Dir.glob("/tmp/out/s2-custom0/**/*.o").sum{|f| File.size(f)}'  # 135996752
ruby -e 'p Dir.glob("/tmp/out/s2-custom1/**/*.o").sum{|f| File.size(f)}'  # 116424688

Relocations consume a significant portion (approximately 20.9%) of the file size. Despite the overhead of -ffunction-sections -fdata-sections, the compression technique yields a significant reduction of 14.5%!

However, dropping in-place relocation processing is a downside.

CREL relocation format

The 1990 ELF paper ELF: An Object File to Mitigate Mischievous Misoneism says "ELF allows extension and redefinition for other control structures." Let's explore CREL, a new and more compact relocation format designed to replace REL and RELA. Our emphasis is on simplicity over absolute minimal encoding. This is achieved by using a byte-oriented encoding that avoids complex compression techniques (e.g., dictionary-based compression, entropy encoder). As a byte-oriented format, CREL relocations can be further compressed by other codecs, if desired. Using CREL as relocatable files can decrease memory usage.

See the end of the article for a detailed format description.

A SHT_CREL section (preferred name: .crel<name>) holds compact relocation entries that decode to Elf32_Rela or Elf64_Rela depending on the object file class (32-bit or 64-bit). Its content begins with a ULEB128-encoded relocation count, followed by entries encoding r_offset, r_type, r_symidx, and r_addend. The entries use ULEB128 and SLEB128 exclusively and there is no endianness difference.

Here are key design choices:

Relocation count (ULEB128):

This allows for efficient retrieval of the relocation count without decoding the entire section. While a uint32_t (like SHT_HASH) could be used, ULEB128 aligns with subsequent entries, removes endianness differences, and offers a slight size advantage in most cases when the number of symbols can be encoded in one to three bytes.

Shifted offset:

64-bit data sections frequently have absolute relocations spaced 8 bytes apart. Additionally, in RISC architectures, offsets are often multiples of 2 or 4. A shift value of 2 allows delta offsets within the [0, 64) range to be encoded in a single byte, often avoiding the need for two-byte encoding. In an AArch64 -O3 build, the shifted offset technique reduces size(.crel*) by 12.8%.

Many C++ virtual tables have the first relocation at offset 0x10. In the absence of the shifted offset technique, the relocation at offset 0x10 cannot be encoded in one byte.

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Relocation section '.crel.data.rel.ro._ZTVN12_GLOBAL__N_113InlineSpillerE' at offset 0x116fe contains 5 entries:
    Offset             Info             Type               Symbol's Value  Symbol's Name + Addend
0000000000000010  0000007e00000001 R_X86_64_64            0000000000000000 _ZN4llvm7Spiller6anchorEv + 0
0000000000000018  0000000c00000001 R_X86_64_64            0000000000000000 .text._ZN12_GLOBAL__N_113InlineSpillerD2Ev + 0
0000000000000020  0000000f00000001 R_X86_64_64            0000000000000000 .text._ZN12_GLOBAL__N_113InlineSpillerD0Ev + 0
0000000000000028  0000001100000001 R_X86_64_64            0000000000000000 .text._ZN12_GLOBAL__N_113InlineSpiller5spillERN4llvm13LiveRangeEditE + 0
0000000000000030  0000001a00000001 R_X86_64_64            0000000000000000 .text._ZN12_GLOBAL__N_113InlineSpiller16postOptimizationEv + 0

The shifted offset also works really well for dynamic relocations, whose offset differences are almost always a multiple of sizeof(Elf_Addr).

Addend bit:

CREL was initially designed with explicit addends in each relocation entry. However, this approach created redundancy when I extended CREL for dynamic relocations (discussed throroughly in another section). While RELR remains an option, the goal is for CREL to be a viable alternative even without RELR. In addition, when implicit addends are used, I feel sad if one bit in every relocation entry is wasted.

To address these concerns, a single bit flag has been introduced in the CREL header:

  • addend_bit==1: The flags include a bit to signal the presence of the delta addend.
  • addend_bit==0: The flags bit is stolen to encode one more bit for the offset. The addend is implicit and not encoded within the relocation.

This bit flag effectively balances efficiency by avoiding unnecessary storage for dynamic relocations while maintaining flexibility for cases requiring explicit addend values.

Assembler produced SHT_CREL sections are supposed to always set the addend_bit bit.

Delta encoding for r_offset (ULEB128):

Section offsets can be large, and relocations are typically ordered. Storing the difference between consecutive offsets offers compression potential. In most cases, a single byte will suffice. While there are exceptions (general dynamic TLS model of s390/s390x uses a local "out-of-order" pair: R_390_PLT32DBL(offset=o) R_390_TLS_GDCALL(offset=o-2)), we are optimizing for the common case.

For ELFCLASS32, r_offsets members are calculated using modular arithmetic modulo 4294967296.

Delta encoding for r_symidx (SLEB128):

This is more for consistency and less for the benefit.

Absolute symbol indexes allow one-byte encoding for symbols in the range [0,128) and offer minor size advantage for static relocations when the symbol table is sorted by usage frequency. Delta encoding, on the other hand, might optimize for the scenario when the symbol table presents locality: neighbor symbols are frequently mutually called.

Delta symbol index enables one-byte encoding for GOT/PLT dynamic relocations when .got/.got.plt entries are ordered by symbol index. For example, R_*_GLOB_DAT and R_*_JUMP_SLOT relocations can typically be encoded with repeated 0x05 0x01 (when addend_bit==0 && shift==3, offset++, symidx++). Delta encoding has a disvantage. It can partial claim the optimization by arranging symbols in a "cold0 hot cold1" pattern. In addition, delta symbol index enables one-byte encoding for GOT/PLT dynamic relocations when .got/.got.plt entries are ordered by symbol index.

In my experiments, absolute encoding with ULEB128 results in slightly larger .o file sizes for both x86-64 and AArch64 builds.

Delta encoding for r_type (SLEB128):

Some psABIs utilize relocation types greater than 128. AArch64's static relocation types begin at 257 and dynamic relocation types begin at 1024, necessitating two bytes with ULEB128/SLEB128 encoding in the absence of delta encoding. Delta encoding allows all but the first relocation's type to be encoded in a single byte. An alternative design is to define a base type in the header and encode types relative to the base type, which would introduce slight complexity.

If the AArch32 psABI could be redesigned, allocating [0,64) for Thumb relocation types and [64,*) for ARM relocation types would optimize delta encoding even further.

While sharing a single type code for multiple relocations would be efficient, it would require reordering relocations. This conflicts with order requirements imposed by several psABIs and could complicate linker implementations.

Delta encoding for addend (SLEB128):

Encoding the delta addend offers a slight size advantage and optimizes for cases like:

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.quad .data + 0x78
.quad .data + 0x80
.quad .data + 0x88
...

Symbol index/type/addend omission

Relocations often exhibit patterns that can be exploited for size reduction:

  • Symbol index/type remain constant with varying addends, common for STT_SECTION symbols, e.g. .rodata, .eh_frame, .debug_str_offsets, .debug_names, .debug_line, and .debug_addr.
  • Type/addend remain constant with varying symbol indexes, common for non-section symbols, e.g. function calls, C++ virtual tables, and dynamic relocations.
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// Type/addend do not change.
// R_AARCH64_CALL(g0), ...
// R_X86_64_PLT32(g0-4), ...
void f() { g0(); g1(); g2(); }

We use the least significant bits of the offset member to signal the presence of symbol index, type, and addend information. This allows us to omit delta fields when they match the previous entry.

CREL steals 3 bits from the offset member. I have tried stealing just a bit and utilizing negative symbol index to signal type/addend omission, but offsets generally require fewer bits to encode and stealing bits from offsets is superior.

Omitting the symbol index information is especially beneficial for reducing debug build sizes. For example, most .debug_names relocations can be encoded using only 4 bytes (offset and delta addend), instead of the 7 bytes required otherwise.

While RISC architectures often require multiple relocations with different types to access global data, making type omission slightly less beneficial than x86, the frequent use of call instructions offers large size reduction with type omission.

With a limited number of types and frequent zero addends (except R_*_RELATIVE and R_*_IRELATIVE), dynamic relocations also benefit from type/addend omission.

I have developed a prototype at https://github.com/MaskRay/llvm-project/tree/demo-crel. CREL demonstrates superrior size reduction compared to the SHF_COMPRESSED SHT_RELA approach.

LEB128 among variable-length integer encodings

LEB128 and UTF-8 stand out as the two most commonly used byte-oriented, variable-length integer encoding schemes. Binary encodings often employ LEB128. While alternatives like PrefixVarInt (or a suffix-based variant) might excel when encoding larger integers, LEB128 offers advantages when most integers fit within one or two bytes, as it avoids the need for shift operations in the common one-byte representation.

While we could utilize zigzag encoding (i>>31) ^ (i<<1) to convert SLEB128-encoded type/addend to use ULEB128 instead, the generate code is inferior to or on par with SLEB128 for one-byte encodings on x86, AArch64, and RISC-V.

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// One-byte case for SLEB128
int64_t from_signext(uint64_t v) {
  return v < 64 ? v - 128 : v;
}

// One-byte case for ULEB128 with zig-zag encoding
int64_t from_zigzag(uint64_t z) {
  return (z >> 1) ^ -(z & 1);
}

While some variale-length integer schemes allocate more integers within the one-byte bucket, I do not believe they would lead to noticeable improvement over LEB128. For example, when I assign one extra bit to offsets (by clearing addend_bit in the header), .crel.dyn merely decreases by 2.5%.

Here is an extremely simple C decoder implementation for ULEB128 and SLEB128. The clever use of 64/128 is from Stefan O'Rear. The return type uint64_t can be changed to size_t when used in a dynamic loader. 

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static uint64_t read_leb128(unsigned char **buf, uint64_t sleb_uleb) {
  uint64_t acc = 0, shift = 0, byte;
  do {
    byte = *(*buf)++;
    acc |= (byte - 128*(byte >= sleb_uleb)) << shift;
    shift += 7;
  } while (byte >= 128);
  return acc;
}

uint64_t read_uleb128(unsigned char **buf) { return read_leb128(buf, 128); }
int64_t read_sleb128(unsigned char **buf) { return read_leb128(buf, 64); }

I have used a modified lld analyze LEB128 length distribution in a x86-64 release build of lld that enables CREL.

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zo[std::min(getULEB128Size(offset-old_offset), 3u) - 1]++;
if (b & 1) {
  auto x = readSLEB128(p); symidx += x; zs[std::min(getSLEB128Size(x), 3u) - 1]++;
}
if (b & 2) {
  auto x = readSLEB128(p); type += x; zt[std::min(getSLEB128Size(x), 3u) - 1]++;
}
if (b & 4) {
  auto x = readSLEB128(p); addend += x; za[std::min(getSLEB128Size(x), 3u) - 1]++;
}

The distribution of ULEB128/SLEB128 lengths is:

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        1       2       3+      any
offset  633056  48846   0       681902
type    187759  0       0       187759
symidx  360230  229610  879     590719
addend  191523  52293   2899    246715

80.5% LEB128 encodings are of 1 byte and 19.2% are of 2 bytes. 2-byte delta symidx members are quite common, but I do not plan to steal bits from other members to symidx.

Experiments

build format .o size size(.rel*) .o size
decrease
-O3 RELA 136012504 28235448
-O3 CREL 111583312 3806234 18.0%
aarch64 -O3 RELA 124965808 25855800
aarch64 -O3 CREL 102529784 3388307 18.0%
ppc64le -O3 RELA 129017272 26589192
ppc64le -O3 CREL 105860576 3432419 17.9%
riscv64 -O3 RELA 227189744 91396344
riscv64 -O3 CREL 149343352 13549699 34.3%
-O1 -g RELA 1506173760 340965576
-O1 -g CREL 1202445768 37237274 20.2%
-O3 -g $SPLIT RELA 549003848 104227128
-O3 -g $SPLIT CREL 459768736 14992114 16.3%

SPLIT="-gpubnames -gsplit-dwarf"

Let's compare x86_64 -O3 builds of lld. size(.crel*)/size(.rel*) = 3806234 / 28235448, 13.5%. The total .o file size has decreased by 18.0%. In addition, the maximum resident set size of the linker (also lld) using mimalloc has decreased by 4.2%.

It would be interesting to explore the potential gains of combining zstd compression with CREL.

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configure-llvm s2-custom3 -DLLVM_TARGETS_TO_BUILD=host -DLLVM_ENABLE_PROJECTS='clang;lld' -DCMAKE_{C,CXX}_FLAGS='-Wa,--crel -Xclang --compress-relocations=zstd'
ninja -C /tmp/out/s2-custom3 lld

ruby -e 'p Dir.glob("/tmp/out/s2-custom3/**/*.o").sum{|f| File.size(f)}'  # 111383192

I debated whether to name the new section SHT_RELOC (.reloc<name>) or SHT_RELLEB (.relleb<name>). Ultimately, I chose SHT_CREL because its unique name minimizes potential confusion, whereas SHT_RELOC could be confused with SHT_REL and SHT_RELA and the LEB128 part is not that strong.

Case study

Let's explore some real-world scenarios where relocation size is critical.

Marker relocations

Marker relocations are utilized to indicate certain linker optimization/relaxation is applicable. While many marker relocations are used scarcely, RISC-V relocatable files are typically filled up with R_RISCV_RELAX relocations. Their size contribution is quite substantial.

.llvm_addrsig

On many Linux targets, Clang emits a special section called .llvm_addrsig (type SHT_LLVM_ADDRSIG, LLVM address-significance table) by default to allow ld.lld --icf=safe. The .llvm_addrsig section stores symbol indexes in ULEB128 format, independent of relocations. Consequently, tools like ld -r and objcopy risk invalidate the section due to symbol table modifications.

Ideally, using relocations would allow certain operations. However, the size concern of REL/RELA in ELF hinders this approach. In contrast, lld's Mach-O port chose a relocation-based representation for __DATA,__llvm_addrsig.

If CREL is adopted, we can consider switching to the relocation representation.

.llvm.call-graph-profile

LLVM leverages a special section called .llvm.call-graph-profile (type SHT_LLVM_CALL_GRAPH_PROFILE) for both instrumentation- and sample-based profile-guided optimization (PGO). lld utilizes this information ((from_symbol, to_symbol, weight) tuples) to optimize section ordering within an input section description, enhancing cache utilization and minimizing TLB thrashing.

Similar to .llvm_addrsig, the .llvm.call-graph-profile section initially faced the symbol index invalidation problem, which was solved by switching to relocations. I opted for REL over RELA to reduce code size.

DWARF sections

In a non-split-DWARF build, .rela.debug_str_offsets and .rela.debug_addr consume a significant portion of the file size.

DWARF v5 accelerated name-based access with the introduction of the .debug_names section. However, in a clang -g -gsplit-dwarf -gpubnames generated relocatable file, the .rela.debug_names section can consume a significant portion (approximately 10%) of the file size.

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Relocation section '.crel.debug_names' at offset 0x65c0 contains 200 entries:
    Offset             Info             Type               Symbol's Value  Symbol's Name + Addend
000000000000002c  0000002f0000000a R_X86_64_32            0000000000000000 .debug_info + 0
00000000000004d8  000000320000000a R_X86_64_32            0000000000000000 .debug_str + 1ab
00000000000004dc  000000320000000a R_X86_64_32            0000000000000000 .debug_str + f61
00000000000004e0  000000320000000a R_X86_64_32            0000000000000000 .debug_str + f7f
...

This size increase has sparked discussions within the LLVM community about potentially altering the file format for linking purposes.

.debug_line and .debug_addr also contribute a lot of relocations.

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Relocation section '.crel.debug_addr' at offset 0x64f1 contains 51 entries:
    Offset             Info             Type               Symbol's Value  Symbol's Name + Addend
0000000000000008  0000004300000001 R_X86_64_64            0000000000000000 _ZN4llvm30VerifyDisableABIBreakingChecksE + 0
0000000000000010  0000002d00000001 R_X86_64_64            0000000000000000 .rodata.str1.1 + 0
0000000000000018  0000002d00000001 R_X86_64_64            0000000000000000 .rodata.str1.1 + b
0000000000000020  0000002d00000001 R_X86_64_64            0000000000000000 .rodata.str1.1 + 13
...

Relocation section '.crel.debug_line' at offset 0x69a5 contains 81 entries:
    Offset             Info             Type               Symbol's Value  Symbol's Name + Addend
0000000000000022  000000350000000a R_X86_64_32            0000000000000000 .debug_line_str + 0
0000000000000026  000000350000000a R_X86_64_32            0000000000000000 .debug_line_str + 18
000000000000002a  000000350000000a R_X86_64_32            0000000000000000 .debug_line_str + 2c
...

Many adjacent relocations share the same section symbol. CREL can compress most relocations into a few bytes depending on addend sizes (offset+=O, addend+=A).

By teaching the assembler to use implicit addends, we achieve even greater size reduction by compressing most relocations into a single byte (mostly 0x04, offset+=1<<3). However, this might harm compression in the presence of --compress-debug-sections=zstd. Personally I recommend that we don't use implicit addends.

CREL for dynamic relocations

CREL excels with static relocations, but what about the dynamic case?

A substantial part of position-independent executables (PIEs) and dynamic shared objects (DSOs) is occupied by dynamic relocations. While RELR (a compact relative relocation format) offers size-saving benefits for relative relocations, other dynamic relocations can benefit from a compact relocation format. There are a few properties:

  • There are much fewer relocation types.
  • The offsets are often adjacent by Elf_Addr. No two dynamic relocations can share the same offset.
  • Each symbol is associated with very few dynamic relocations, typically 1 or 2 (R_*_JUMP_SLOT and R_*_GLOB_DAT). When a symbol is associated with more dynamic relocations, it is typically a base class function residing in multiple C++ virtual tables, e.g. __cxa_pure_virtual. -fexperimental-relative-c++-abi-vtables would eliminate such dynamic relocations.

Android's packed relocation format (linker implementation: ld.lld --pack-dyn-relocs=android) was an earlier design that applies to all dynamic relocations at the cost of complexity. It replaces .rel.dyn/.rela.dyn but does not change the section name.

Additionally, Apple linkers and dyld use LEB128 encoding for bind opcodes.

Here is a one-liner to dump the relative relocation and non-relative relocation sizes for each shared object in a system library directory: 

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ruby -e 'Dir.glob("/usr/lib/x86_64-linux-gnu/*.so.*").each{|f| next if File.symlink?(f) || `file #{f}`!~/shared object/; s=`readelf -Wr #{f}`.lines; nr=s.count{|x|x=~/R_/&&x !~/_RELATIVE/}*24; r=s.count{|x|x=~/_RELATIVE/}*24; s=File.size(f); puts "#{f}\t#{s}\t#{r} (#{(r*100.0/s).round(2)}%)\t#{nr} (#{(nr*100.0/s).round(2)}%)" }'

I believe CREL compresses dynamic relocations well, but it is far from an optimal dynamic relocation format. A generalized RELR format would leverage the dyamic relocation properties well. Here's a possible encoding:

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// R_*_RELATIVE group
Encode(length of the group)
Encode(R_*_RELATIVE)
RELR

// R_*_GLOB_DAT/absolute address relocation group
Encode(length of the group)
Encode(R_*_GLOB_DAT)
Use RELR to encode offsets
Encode symbol indexes separately

// R_*_JUMP_SLOT group
Encode(length of the group)
Encode(R_*_JUMP_SLOT)
Use RELR to encode offsets
Encode symbol indexes separately

...

We need to enumerate all dynamic relocation types including R_*_IRELATIVE, R_*_TLSDESC used by some ports. Some R_*_TLSDESC relocations have a symbol index of zero, but the straightforward encoding does not utilize this property.

Traditionally, we have two dynamic relocation ranges for executables and shared objects (except static position-dependent executables):

  • .rela.dyn ([DT_RELA, DT_RELA + DT_RELASZ)) or .rel.dyn ([DT_REL, DT_REL + DT_RELSZ))
  • .rela.plt ([DT_JMPREL, DT_JMPREL + DT_PLTRELSZ)): Stored JUMP_SLOT relocations. DT_PLTREL specifies DT_REL or DT_RELA.

IRELATIVE relocations can be placed in either range, but preferrably in .rel[a].dyn.

Some GNU ld ports (e.g. SPARC) treat .rela.plt as a subset of .rela.dyn, introducing complexity for dynamic loaders.

CREL adoption considerations

  • New dynamic tag (DT_CREL): To identify CREL relocations, separate from existing DT_REL/DT_RELA.
  • No DT_CRELSZ: Relocation count can be derived from the CREL header.
  • Output section description .rela.dyn : { *(.rela.dyn) *(.rela.plt) } is incompatible with CREL.

Challenges with lazy binding

glibc's lazy binding scheme relies on random access to relocation entries within the DT_JMPREL table. CREL's sequential nature prevents this. However, eager binding doesn't require random access. Therefore, when -z now (eager binding) is enabled, we can:

  • Set DT_PLTREL to DT_CREL.
  • Replace .rel[a].plt with .crel.plt.

Challenges with statically linked position-dependent executables

glibc introduces additional complexity for IRELATIVE relocations in statically linked position-dependent executables. They should only contain IRELATIVE relocations and no other dynamic relocations.

glibc's csu/libc-start.c processes IRELATIVE relocations in the range [__rela_iplt_start, __rela_iplt_end) (or [__rel_iplt_start, __rel_iplt_end), determined at build time through ELF_MACHINE_IREL). While CREL relocations cannot be decoded in the middle of the section, we can still place IRELATIVE relocations in .crel.dyn because there wouldn't be any other relocation types (position-dependent executables don't have RELATIVE relocations). When CREL is enabled, we can define __crel_iplt_start and __crel_iplt_end for statically linked position-dependent executables.

If glibc only intends to support addend_bit==0, the code can simply be: 

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extern const uint8_t __crel_iplt_start[] __attribute__ ((weak));
extern const uint8_t __crel_iplt_end[] __attribute__ ((weak));
if (&__crel_iplt_start != &__crel_iplt_end) {
  const uint8_t *p = __crel_iplt_start;
  size_t offset = 0, count = read_uleb128 (&p), shift = count & 3;
  for (count >>= 3; count; count--) {
    uint8_t rel_head = *p++;
    offset += rel_head >> 2;
    if (rel_head & 128)
      offset += (read_uleb128 (&p) << 5) - 32;
    if (rel_head & 2)
      read_sleb128 (&p);
    elf_crel_irel ((ElfW (Addr) *) (offset << shift));
  }
}

Considering implicit addends for CREL

Many dynamic relocations have zero addends:

  • COPY/GLOB_DAT/JUMP_SLOT relocations only use zero addends.
  • Absolute relocations could use non-zero addends with STT_SECTION symbol, but linkers convert them to relative relocations.

Usually only RELATIVE/IRELATIVE and potentially TPREL/TPOFF might require non-zero addends. Switching from DT_RELA to DT_REL offers a minor size advantage.

I considered defining two separate dynamic tags (DT_CREL and DT_CRELA) to distinguish between implicit and explicit addends. However, this would have introduced complexity:

  • Should llvm-readelf -r dump the zero addends for DT_CRELA?
  • Should dynamic loaders support both dynamic tags?

I placed the delta addend bit next to offset bits so that it can be reused for offsets. Thanks to Stefan O'Rear's for making me believe that my original thought of reserving a single bit flag (addend_bit) within the CREL header is elegant. Dynamic loaders prioritizing simplicity can hardcode the desired addend_bit value.

ld.lld -z crel defaults to implicit addends (addend_bit==0), but the option of using in-relocation addends is available with -z crel -z rela.

DT_AARCH64_AUTH_RELR vs CREL

The AArch64 PAuth ABI introduces DT_AARCH64_AUTH_RELR as a variant of RELR for signed relocations. However, its benefit seems limited.

In a release build of Clang 16, using -z crel -z rela resulted in a .crel.dyn section size of only 1.0% of the file size. Notably, enabling implicit addends with -z crel -z rel further reduced the size to just 0.3%. While DT_AARCH64_AUTH_RELR will achieve a noticeable smaller relocation size if most relative relocations are encoded with it, the advantage seems less significant considering CREL's already compact size.

Furthermore, DT_AARCH64_AUTH_RLEL introduces additional complexity to the linker due to its 32-bit addend limitation: the in-place 64 value encodes a 32-bit schema, giving just 32 bits to the implicit addend. If the addend does not fit into 32 bits, DT_AARCH64_AUTH_RELR cannot be used. CREL with addends would avoid this complexity.

I have filed Quantifying the benefits of DT_AARCH64_AUTH_RELR.

I've implemented ld.lld -z crel to replace .rel[a].dyn and .rel[a].plt with .crel.dyn and .crel.plt. Dynamic relocations are sorted by (r_type, r_offset) to better utilize CREL.

Let's link clang-16-debug using RELA, -z pack-relative-relocs, --pack-dyn-relocs=android+relr, and -z pack-relative-relocs -z crel and analyze the results.

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% fld.lld @response.txt -o - | fllvm-readelf -S - | grep -E ' \.c?rel.?\.'
  [ 8] .rela.dyn         RELA            00000000005df318 5df318 c3a980 18   A  3   0  8
  [ 9] .rela.plt         RELA            0000000001219c98 1219c98 001f38 18  AI  3  26  8
% fld.lld @response.txt -z pack-relative-relocs -o - | fllvm-readelf -S - | grep -E ' \.c?rel.?\.'
  [ 8] .rela.dyn         RELA            00000000005df340 5df340 011088 18   A  3   0  8
  [ 9] .relr.dyn         RELR            00000000005f03c8 5f03c8 0259d0 08   A  0   0  8
  [10] .rela.plt         RELA            0000000000615d98 615d98 001f38 18  AI  3  27  8
% fld.lld @response.txt --pack-dyn-relocs=android+relr -o - | fllvm-readelf -S - | grep -E ' \.c?rel.?\.'
  [ 8] .rela.dyn         ANDROID_RELA    00000000005df318 5df318 0011fc 01   A  3   0  8
  [ 9] .relr.dyn         RELR            00000000005e0518 5e0518 0259d0 08   A  0   0  8
  [10] .rela.plt         RELA            0000000000605ee8 605ee8 001f38 18  AI  3  27  8
% fld.lld @response.txt -z pack-relative-relocs -z crel -o - | fllvm-readelf -S - | grep -E ' \.c?rel.?\.'
  [ 8] .crel.dyn         CREL            00000000005df340 5df340 000fbc 00   A  3   0  8
  [ 9] .relr.dyn         RELR            00000000005e0300 5e0300 0259d0 08   A  0   0  8
  [10] .rel.plt          REL             0000000000605cd0 605cd0 0014d0 10  AI  3  27  8
% fld.lld @response.txt -z crel -o - | fllvm-readelf -S - | grep -E ' \.c?rel.?\.'
  [ 8] .crel.dyn         CREL            00000000005df318 5df318 082c29 00   A  3   0  8
  [ 9] .rel.plt          REL             0000000000661f48 661f48 0014d0 10  AI  3  26  8
% fld.lld @response.txt -z crel -z rela -o - | fllvm-readelf -S - | grep -E ' \.c?rel.?\.'
  [ 8] .crel.dyn         CREL            00000000005df318 5df318 1b8c69 00   A  3   0  8
  [ 9] .rela.plt         RELA            0000000000797f88 797f88 001f38 18  AI  3  26  8

Analysis

  • Relative relocations usually outnumber non-relative relocations.
  • RELR significantly optimizes relative relocations, offering the largest size reduction.
  • CREL further improves the non-relative portion, compressing that portion to 5.77%, even better than Android packed relocations (6.60%)! Android's r_info sharing with RELOCATION_GROUPED_BY_INFO_FLAG has been overshadowed by our shifted offset technique.
  • The non-relative relocation advantage is less pronounced since .relr.dyn still accounts for a significant portion of the size.
  • .crel.dyn using DT_CREL (implicit addends) without RELR is more than 3x as large as RELR .relr.dyn+.rela.dyn.

Decoding ULEB128/SLEB128 would necessitate more work in the dynamic loader.

Stefan O'Rear has a [PATCH] ldso: DT_CREL compact relocation support patch for musl. In an x86-64 -O2 build, CREL support linked with -z pack-relative-relocs -z crel increases the size of libc.so by just 200 bytes (0.0256%) compared to a non-CREL build with -z pack-relative-relocs.

Linker notes

--emit-relocs and -r necessitate combining relocation sections. The output size may differ from the sum of input sections. The total relocation count must be determined, a new header written, and section content regenerated, as symbol indexes and addends may have changed. If the linker does not attempt to determine the offset shift in another relocation scan, the offset shift in the header can be set to 0. Debug sections, .eh_frame, and .gcc_except_table require special handling to rewrite relocations referencing a dead symbol to R_*_NONE. This also necessitates updating the relocation type.

--emit-relocs and -r copy CREL relocation sections (e.g. .crel.text) to the output. When .rela.text is also present, linkers are required to merge .rela.text into .crel.text.

GNU ld allows certain unknown section types:

  • [SHT_LOUSER,SHT_HIUSER] and non-SHF_ALLOC
  • [SHT_LOOS,SHT_HIOS] and non-SHF_OS_NONCONFORMING

but reports errors and stops linking for others (unless --no-warn-mismatch is specified). When linking a relocatable file using SHT_CREL, you might encounter errors like the following:

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% clang -Wa,--crel -fuse-ld=bfd a.c b.c
/usr/bin/ld.bfd: unknown architecture of input file `/tmp/a-1e0778.o' is incompatible with i386:x86-64 output
/usr/bin/ld.bfd: unknown architecture of input file `/tmp/b-9963f0.o' is incompatible with i386:x86-64 output
/usr/bin/ld.bfd: error in /tmp/a-1e0778.o(.eh_frame); no .eh_frame_hdr table will be created
/usr/bin/ld.bfd: error in /tmp/b-9963f0.o(.eh_frame); no .eh_frame_hdr table will be created
clang: error: linker command failed with exit code 1 (use -v to see invocation)

Older lld and mold do not report errors. I have filed:

In addition, when there is one .eh_frame section with CIE pieces but no relocation, _bfd_elf_parse_eh_frame will report an error.

mips64el

mips64el has an incorrect r_info: a 32-bit little-endian symbol index followed by a 32-bit big-endian type. If mips64el decides to adopt CREL, they can utilize this opportunity to fix r_info.

Data compression

I analyzed relocatable files in lld 18 (x86_64, -O3 builds) and extracted RELA and CREL relocations. I investigated the potential benefits of compressing these combined sections within the file.

It's important to consider that data compression, while beneficial for size reduction, can introduce challenges for random access and increase memory usage especially for the linker. Therefore, it might not be a suitable solution.

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with open(f'{f}.bin', 'wb') as out, \
        open(f'{f}.bin.lz4', 'wb') as out_lz4, \
        open(f'{f}.bin.zst', 'wb') as out_zstd, \
        open(f'{f}.bin.xz', 'wb') as out_xz:
    for ofile in Path(where).glob('**/*.o'):
        content = bytes()
        elf = lief.parse(str(ofile))
        for sec in elf.sections:
            if sec.name.startswith(f'.{f}'):
                out.write(sec.content)
                content += sec.content
        sub = subprocess.run(['lz4'], input=content, capture_output=True, check=True)
        out_lz4.write(sub.stdout if len(sub.stdout) < len(content) else content)
        sub = subprocess.run(['zstd'], input=content, capture_output=True, check=True)
        out_zstd.write(sub.stdout if len(sub.stdout) < len(content) else content)
        sub = subprocess.run(['xz'], input=content, capture_output=True, check=True)
        out_xz.write(sub.stdout if len(sub.stdout) < len(content) else content)

CREL, being a byte-oriented format, allows for further compression. It can be regarded as a very efficient filter before a Lempel-Ziv compressor.

Even more surprising, CREL outperforms RELA compressed with lz4 (level 9) and zstd (level 6).

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% stat -c '%s %n' *.bin*
3808775 crel.bin
2855535 crel.bin.lz4
2184912 crel.bin.xz
2319041 crel.bin.zst
28238016 rela.bin
9679414 rela.bin.lz4
2835180 rela.bin.xz
4281547 rela.bin.zst

Dynamic relocations are also worth investigating. 

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ld.lld @response.txt -z now --pack-dyn-relocs=relr -o clang.relr
ld.lld @response.txt -z now --pack-dyn-relocs=android+relr -o clang.relr+android
ld.lld @response.txt -z now --pack-dyn-relocs=relr -z crel -o clang.relr+crel
llvm-objcopy --dump-section .rela.dyn=reladyn clang.relr /dev/null
llvm-objcopy --dump-section .crel.dyn=creldyn clang.relr+crel /dev/null
llvm-objcopy --dump-section .rela.dyn=androiddyn clang.relr+android /dev/null
xz -fk reladyn androiddyn creldyn
zstd -fk reladyn androiddyn creldyn
% stat -c '%s %n' reladyn* androiddyn* creldyn*
69768 reladyn
4236 reladyn.xz
4449 reladyn.zst
4604 androiddyn
1484 androiddyn.xz
1481 androiddyn.zst
3980 creldyn
1344 creldyn.xz
1367 creldyn.zst

Interestingly, both zstd and LZMA2's default levels on RELA outperform Android's packed relocation format. Even better, CREL outperforms them both!

The results do not suggest that we add a Lempel-Ziv compressor to CREL. It would significantly increase complexity and decoder memory usage. The filesystem's transparent compression can handle this for us conveniently.

CREL proposal for the generic ABI

The latest revision has been proposed at https://groups.google.com/g/generic-abi/c/yb0rjw56ORw/m/qQWVkGpuAQAJ. I have also created:

In https://www.sco.com/developers/gabi/latest/ch4.sheader.html, make the following changes.

In Figure 4-9: Section Types,sh_type, append a row

SHT_CREL | 20

Add text:

SHT_CREL - The section holds compact relocation entries with explicit addends. An object file may have multiple relocation sections. See ''Relocation'' below for details.

In Figure 4-16: Special Sections, append

.crelname | SHT_CREL | see below

Change the text below:

.relname, .relaname, and .crelname

These sections hold relocation information, as described in ''Relocation''. If the file has a loadable segment that includes relocation, the sections' attributes will include the SHF_ALLOC bit; otherwise, that bit will be off. Conventionally, name is supplied by the section to which the relocations apply. Thus a relocation section for .text normally would have the name .rel.text, .rela.text, or .crel.text.

In Figure 4-23: Relocation Entries, add:

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typedef struct {
  Elf32_Addr r_offset;
  Elf32_Word r_symidx;
  Elf32_Word r_type;
  Elf32_Sxword r_addend;
} Elf32_Crel;

typedef struct {
  Elf64_Addr r_offset;
  Elf64_Word r_symidx;
  Elf64_Word r_type;
  Elf64_Sxword r_addend;
} Elf64_Crel;

Add text above "A relocation section references two other sections":

A SHT_CREL section holds compact relocation entries that decode to Elf32_Crel or Elf64_Crel depending on the object file class (32-bit or 64-bit). Its content begins with a ULEB128-encoded value count * 8 + addend_bit * 4 + shift (35-bit or 67-bit unsigned), where:

  • count: Relocation count (32-bit or 64-bit unsigned).
  • addend_bit: 1 indicates that relocation entries encode addends. 0 indicates implicit addends (stored in the location to be modified).
  • shift: The shift value (0 to 3) applies to delta_offset in relocation entries.

Relocation entries (which encode r_offset, r_symidx, r_type, and r_addend) follow the header. Note: r_info in traditional REL/RELA formats has been split into r_symidx and r_type, allowing uint32_t relocation types for ELFCLASS32 as well.

  • Delta offset and flags (ULEB128): Holds delta_offset * (addend_bit ? 8 : 4) + flags (35-bit or 67-bit unsigned), where:
    • delta_offset: Difference in r_offset from the previous entry (truncated to Elf32_Addr or Elf64_Addr), right shifted by shift.
    • flags: 0 to 7 if addend_bit is 1; otherwise 0 to 3.
    • flags & 1: Indicate if delta symbol index is present.
    • flags & 2: Indicate if delta type is present.
    • flags & 4: Indicate if delta addend is present.
  • Delta symbol index (SLEB128, if present): The difference in symbol index from the previous entry, truncated to a 32-bit signed integer.
  • Delta type (SLEB128, if present): The difference in relocation type from the previous entry, truncated to a 32-bit signed integer.
  • Delta addend (SLEB128, if present): The difference in addend from the previous entry, truncated to a 32-bit or 64-bit signed integer depending on the object file class.

ULEB128 or SLEB128 encoded values use the canonical representation (i.e., the shortest byte sequence). For the first relocation entry, the previous offset, symbol index, type, and addend members are treated as zero.

Encoding/decoding delta offset and flags does not need multi-precision arithmetic. We can just unroll and special case the first iteration. The header can be encoded/decoded in a similar way. An implementation can assume that the relocation count cannot be larger than 2**61 and simplify the code.

Example C++ encoder:

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// encodeULEB128(uint64_t, raw_ostream &os);
// encodeSLEB128(int64_t, raw_ostream &os);

const uint8_t addendBit = config->isRela ? 4 : 0, flagBits = config->isRela ? 3 : 2;
Elf_Addr offsetMask = 8, offset = 0, addend = 0;
uint32_t symidx = 0, type = 0;
for (const Elf_Crel &rel : relocs)
  offsetMask |= rel.r_offset;
int shift = std::countr_zero(offsetMask)
encodeULEB128(relocs.size() * 8 + addendBit + shift, os);
for (const Elf_Crel &rel : relocs) {
  Elf_Addr deltaOffset = (rel.r_offset - offset) >> shift;
  uint8_t b = (deltaOffset << flagBits) + (symidx != rel.r_symidx) +
              (type != rel.r_type ? 2 : 0) + (addend != rel.r_addend ? 4 : 0);
  if (deltaOffset < (0x80 >> flagBits)) {
    os << char(b);
  } else {
    os << char(b | 0x80);
    encodeULEB128(deltaOffset >> (7 - flagBits), os);
  }
  if (b & 1) {
    encodeSLEB128(static_cast<int32_t>(rel.r_symidx - symidx), os);
    symidx = rel.r_symidx;
  }
  if (b & 2) {
    encodeSLEB128(static_cast<int32_t>(rel.r_type - type), os);
    type = rel.r_type;
  }
  if (b & 4 & addendBit) {
    encodeSLEB128(std::make_signed_t<Elf_Addr>(rel.r_addend - addend), os);
    addend = rel.r_addend;
  }
}

Example C++ decoder:

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// uint64_t decodeULEB128(uint8_t *&p);
// int64_t decodeSLEB128(uint8_t *&p);

const auto hdr = decodeULEB128(p);
const size_t count = hdr / 8, flagBits = hdr & 4 ? 3 : 2, shift = hdr % 4;
Elf_Addr offset = 0, addend = 0;
uint32_t symidx = 0, type = 0;
for (size_t i = 0; i != count; ++i) {
  const uint8_t b = *p++;
  offset += b >> flagBits;
  if (b >= 0x80)
    offset += (decodeULEB128(p) << (7 - flagBits)) - (0x80 >> flagBits);
  if (b & 1)
    symidx += decodeSLEB128(p);
  if (b & 2)
    type += decodeSLEB128(p);
  if (b & 4 & hdr)
    addend += decodeSLEB128(p);
  rels[i] = {offset << shift, symidx, type, addend};
}

Both encoder and decoder can be simplified if the desired addend_bit is hardcoded, making flagBits an integer literal.

In Figure 5-10: Dynamic Array Tags, d_tag, add:

DT_CREL | 38 | d_ptr | optional | optional

Add text below:

  • DT_CREL - This element is similar to DT_REL, except its table uses the CREL format. The relocation count can be inferred from the header.

Update DT_PLTREL and DT_PLTRELSZ:

  • DT_PLTRELSZ: This element holds the total size, in bytes, of the relocation entries associated with the procedure linkage table. If an entry of type DT_JMPREL is present and the DT_PLTREL entry value is DT_REL or DT_RELA, a DT_PLTRELSZ must accompany it.
  • DT_PLTREL: This member specifies the type of relocation entry to which the procedure linkage table refers. The d_val member holds DT_REL, DT_RELA, or DT_CREL, as appropriate. All relocations in a procedure linkage table must use the same relocation type.

Abandonded proposal RELLEB (last revision)

A SHT_CREL section holds compact relocation entries that decode to Elf32_Crel or Elf64_Crel depending on the object file class (32-bit or 64-bit). Its content begins with a ULEB128-encoded relocation count, followed by entries encoding r_offset, r_symidx, r_type, and r_addend. Note that the r_info member in traditional REL/RELA formats has been split into separate r_symidx and r_type members, allowing uint32_t relocation types for ELFCLASS32 as well.

In the following description, Elf_Addr/Elf_SAddr denote uint32_t/int32_t for ELFCLASS32 or uint64_t/int64_t for ELFCLASS64.

  • First member (ULEB128): Holds 2 * delta_offset + eq (33-bit or 65-bit unsigned), where:
    • delta_offset: Difference in r_offset from the previous entry (Elf_Addr).
    • eq: Indicates if the symbol index/type match the previous entry (1 for match, 0 otherwise).
  • Second Member (SLEB128) if eq is 1:
    • Difference in r_addend from the previous entry (Elf_SAddr).
  • Second Member (SLEB128) if eq is 0:
    • If type and addend match the previous entry, the encoded value is the symbol index; type and addend are omitted.
    • Otherwise, the bitwise NOT of the encoded value (33-bit signed) is the symbol index; delta type and delta addend follow:
      • Delta type (SLEB128): The difference in relocation type from the previous entry (32-bit signed).
      • Delta addend (SLEB128): The difference in r_addend relative to the previous entry (signed Elf_Addr).

The bitwise NOT of symbol index 0xffffffff is -0x100000000 (33-bit) instead of 0 (32-bit).

Encoder in pseudo-code: 

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Elf_Addr offset = 0, addend = 0;
uint32_t symidx = 0, type = 0;
encodeULEB128(relocs.size());
for (const Reloc &rel : relocs) {
  if (symidx == rel.r_symidx && type == rel.r_type) {
    // Symbol index/type match the previous entry. Encode the addend.
    encodeULEB128(2 * uint128_t(rel.r_offset - offset) + 1); // at most 65-bit
    encodeSLEB128(rel.r_addend - addend);
  } else {
    encodeULEB128(2 * uint128_t(rel.r_offset - offset)); // at most 65-bit
    if (type == rel.r_type && addend == rel.r_addend) {
      // Type/addend match the previous entry. Encode the symbol index.
      encodeSLEB128(rel.r_symidx);
    } else {
      // No optimization is applied. Encode symbol index, type, and addend.
      encodeSLEB128(~static_cast<int64_t>(symidx));
      encodeSLEB128(static_cast<int32_t>(rel.type - type));
      type = rel.r_type;
      encodeSLEB128(static_cast<Elf_SAddr>(rel.r_addend - addend));
      addend = rel.r_addend;
    }
    symidx = rel.r_symidx;
  }
}

Encoding/decoding a unsigned 65-bit does not need multi-precision arithmetic. We can just unroll and special case the first iteration. Example C++ encoder:

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// encodeULEB128(uint64_t, raw_ostream &os);
// encodeSLEB128(int64_t, raw_ostream &os);

Elf_Addr offset = 0, addend = 0;
uint32_t symidx = 0, type = 0;
encodeULEB128(relocs.size(), os);
for (const Reloc &rel : relocs) {
  auto deltaOffset = static_cast<uint64_t>(rel.r_offset - offset);
  offset = rel.r_offset;
  uint8_t odd = outSymidx == symidx && outType == type, b = deltaOffset * 2 + odd;
  if (deltaOffset < 0x40) {
    os << char(b);
  } else {
    os << char(b | 0x80);
    encodeULEB128(deltaOffset >> 6, os);
  }
  symidx = rel.symidx;
  if (!odd && type == rel.type && addend == rel.addend) {
    encodeSLEB128(symidx, os);
  } else {
    if (!odd) {
      encodeSLEB128(~static_cast<int64_t>(symidx), os);
      encodeSLEB128(static_cast<int32_t>(rel.type - type), os);
      type = rel.type;
    }
    encodeSLEB128(std::make_signed_t<uint>(rel.addend - addend), os);
    addend = rel.addend;
  }
}

Example C++ decoder:

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// uint64_t decodeULEB128(uint8_t *&p);
// int64_t decodeSLEB128(uint8_t *&p);

size_t count = decodeULEB128(p);
Elf_Addr offset = 0, addend = 0;
uint32_t symidx = 0, type = 0;
for (size_t i = 0; i != count; ++i) {
  const uint8_t b = *p++;
  offset += b >> 1;
  if (b >= 0x80)
    offset += (decodeULEB128(p) << 6) - 0x40;
  int64_t x = decodeSLEB128(p);
  if (b & 1) {
    addend += x;
  } else {
    if (x < 0) {
      x = ~x;
      type += decodeSLEB128(p);
      addend += decodeSLEB128(p);
    }
    symidx = x;
  }
  rels[i] = {offset, symidx, type, addend};
}