Are all integer overflows equal?

Background: I’ve been relearning Rust (more about that in a separate post, some time later), and in doing so, I chose to implement the low-level parts of git (I’ll touch the why in that separate post I just promised).

Disclaimer: It’s friday. This is not entirely(?) a serious post.

So, I was looking at Documentation/technical/index-format.txt, and saw:

32-bit number of index entries.

What? The index/staging area can’t handle more than ~4.3 billion files?

There I was, writing Rust code to write out the index.

try!(out.write_u32::<NetworkOrder>(self.entries.len()));

(For people familiar with the byteorder crate and wondering what NetworkOrder is, I have a use byteorder::BigEndian as NetworkOrder)

And the Rust compiler rightfully barfed:

error: mismatched types:
 expected `u32`,
    found `usize` [E0308]

And there I was, wondering: “mmmm should I just add as u32 and silently truncate or … hey what does git do?”

And it turns out, git uses an unsigned int to track the number of entries in the first place, so there is no truncation happening.

Then I thought “but what happens when cache_nr reaches the max?”

Well, it turns out there’s only one obvious place where the field is incremented.

What? Holy coffin nails, Batman! No overflow check?

Wait a second, look 3 lines above that:

ALLOC_GROW(istate->cache, istate->cache_nr + 1, istate->cache_alloc);

Yeah, obviously, if you’re incrementing cache_nr, you already have that many entries in memory. So, how big would that array be?

        struct cache_entry **cache;

So it’s an array of pointers, assuming 64-bits pointers, that’s … ~34.3 GB. But, all those cache_nr entries are in memory too. How big is a cache entry?

struct cache_entry {
        struct hashmap_entry ent;
        struct stat_data ce_stat_data;
        unsigned int ce_mode;
        unsigned int ce_flags;
        unsigned int ce_namelen;
        unsigned int index;     /* for link extension */
        unsigned char sha1[20];
        char name[FLEX_ARRAY]; /* more */
};

So, 4 ints, 20 bytes, and as many bytes as necessary to hold a path. And two inline structs. How big are they?


struct hashmap_entry {
        struct hashmap_entry *next;
        unsigned int hash;
};

struct stat_data {
        struct cache_time sd_ctime;
        struct cache_time sd_mtime;
        unsigned int sd_dev;
        unsigned int sd_ino;
        unsigned int sd_uid;
        unsigned int sd_gid;
        unsigned int sd_size;
};

Woohoo, nested structs.

struct cache_time {
        uint32_t sec;
        uint32_t nsec;
};

So all in all, we’re looking at 1 + 2 + 2 + 5 + 4 32-bit integers, 1 64-bits pointer, 2 32-bits padding, 20 bytes of sha1, for a total of 92 bytes, not counting the variable size for file paths.

The average path length in mozilla-central, which only has slightly over 140 thousands of them, is 59 (including the terminal NUL character).

Let’s conservatively assume our crazy repository would have the same average, making the average cache entry 151 bytes.

But memory allocators usually allocate more than requested. In this particular case, with the default allocator on GNU/Linux, it’s 156 (weirdly enough, it’s 152 on my machine).

156 times 4.3 billion… 670 GB. Plus the 34.3 from the array of pointers: 704.3 GB. Of RAM. Not counting the memory allocator overhead of handling that. Or all the other things git might have in memory as well (which apparently involves a hashmap, too, but I won’t look at that, I promise).

I think one would have run out of memory before hitting that integer overflow.

Interestingly, looking at Documentation/technical/index-format.txt again, the on-disk format appears smaller, with 62 bytes per file instead of 92, so the corresponding index file would be smaller. (And in version 4, paths are prefix-compressed, so paths would be smaller too).

But having an index that large supposes those files are checked out. So let’s say I have an empty ext4 file system as large as possible (which I’m told is 2^60 bytes (1.15 billion gigabytes)). Creating a small empty ext4 tells me at least 10 inodes are allocated by default. I seem to remember there’s at least one reserved for the journal, there’s the top-level directory, and there’s lost+found ; there apparently are more. Obviously, on that very large file system, We’d have a git repository. git init with an empty template creates 9 files and directories, so that’s 19 more inodes taken. But git init doesn’t create an index, and doesn’t have any objects. We’d thus have at least one file for our hundreds of gigabyte index, and at least 2 who-knows-how-big files for the objects (a pack and its index). How many inodes does that leave us with?

The Linux kernel source tells us the number of inodes in an ext4 file system is stored in a 32-bits integer.

So all in all, if we had an empty very large file system, we’d only be able to store, at best, 2^32 – 22 files… And we wouldn’t even be able to get cache_nr to overflow.

… while following the rules. Because the index can keep files that have been removed, it is actually possible to fill the index without filling the file system. After hours (days? months? years? decades?*) of running

seq 0 4294967296 | while read i; do touch $i; git update-index --add $i; rm $i; done

One should be able to reach the integer overflow. But that’d still require hundreds of gigabytes of disk space and even more RAM.

  • At the rate it was possible to add files to the index when I tried (yeah, I tried), for a few minutes, and assuming a constant rate, the estimate is close to 2 years. But the time spent reading and writing the index file increases linearly with its size, so the longer it’d run, the longer it’d take.

Ok, it’s actually much faster to do it hundreds of thousand files at a time, with something like:

seq 0 100000 4294967296 | while read i; do j=$(seq $i $(($i + 99999))); touch $j; git update-index --add $j; rm $j; done

At the rate the first million files were added, still assuming a constant rate, it would take about a month on my machine. Considering reading/writing a list of a million files is a thousand times faster than reading a list of a billion files, assuming linear increase, we’re still talking about decades, and plentiful RAM. Fun fact: after leaving it run for 5 times as much as it had run for the first million files, it hasn’t even done half more…

One could generate the necessary hundreds-of-gigabytes index manually, that wouldn’t be too hard, and assuming it could be done at about 1 GB/s on a good machine with a good SSD, we’d be able to craft a close-to-explosion index within a few minutes. But we’d still lack the RAM to load it.

So, here is the open question: should I report that integer overflow?

Wow, that was some serious procrastination.

Edit: Epilogue: Actually, oops, there is a separate integer overflow on the reading side that can trigger a buffer overflow, that doesn’t actually require a large index, just a crafted header, demonstrating that yes, not all integer overflows are equal.

2016-07-08 13:18:34+0900

p.d.o, p.m.o

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One Response to “Are all integer overflows equal?”

  1. Ludovic Says:

    “So, here is the open question: should I report that integer overflow?”

    You just did , didn’t you :)

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