Textbook errors in binary searching (1988)
dl.acm.org
dl.acm.org
Famously, Jon Bentley's book "Programming Pearls" binary search contained an overflow error. See "Extra, Extra - Read All About It: Nearly All Binary Searches and Mergesorts are Broken" at https://ai.googleblog.com/2006/06/extra-extra-read-all-about... which includes:
> Fast forward to 2006. I was shocked to learn that the binary search program that Bentley proved correct and subsequently tested in Chapter 5 of Programming Pearls contains a bug. Once I tell you what it is, you will understand why it escaped detection for two decades. Lest you think I'm picking on Bentley, let me tell you how I discovered the bug: The version of binary search that I wrote for the JDK contained the same bug. It was reported to Sun recently when it broke someone's program, after lying in wait for nine years or so.
This bug can manifest itself for arrays whose length (in elements) is 2^30 or greater (roughly a billion elements). This was inconceivable back in the '80s, when Programming Pearls was written, but it is common these days at Google and other places.
If you're using a 32-bit system, which has only 2^32 bytes in its address space, of which half is typically taken up by the OS kernel, leaving 2^31 bytes for your process, you can see just how strange this is; you would only be able to have an element size of 1 byte, for 2 would fill up the whole 2^31 bytes of address space and leave no room at all for code, and the memory manager would need to let you allocate a whole 1GB block --- and that's not even considering why you would ever want to binary search an array that large at once.
Of course, to use a 32-bit element count on a 64-bit system is itself a more valid bug, but otherwise the "bug" would appear at 2^63 elements --- clearly well beyond the capacities of computers today (x86-64 has only 48 bits virtual address space), or for that matter the size of anything which would be practically binary searchable.
Thus IMHO this is really more of a curiosity along the lines of "you'll run out of memory if you try to ask for too much", and you're probably doing something either exotic or just plain wrong if you need to fill up the machine's address space with a single data structure.
Yes, when people point out this bug, it seems crazy. Who does a binary search of 1GB of sorted data which only contains values from 0...255 (or -128...127). I mean it is a bug, but it's also the wrong data structure for that data...
> to use a 32-bit element count on a 64-bit system is itself a more valid bug
Yes, this one is real. Even ignoring the binary search algorithm, I cringe whenever I see people use "int" as a loop index. 2 gig arrays were very common in the work I used to do.
I also cringe when I see people used unsigned (size_t) loop indices, but that's a deeper topic.
Using ssize_t is pretty reasonable, and you're not going to overflow ssize_t for loop indices except in some very pathological cases on a 32 bit architecture.
If the arithmetic argument doesn't convince you, here's another one: write a correct loop (using size_t) which traverses your array in reverse order. Here is a broken example which would be fine with ssize_t:
for (size_t ii = len - 1; ii >= 0; --ii) {
}Edit: I guess that wasn't the point of your example (that it may not be easily recognisable as a bug?)
One correct way would be
for (size_t i = len; i > 0; --i) {
// use i-1 as the array index
} size_t i = len
while (i-- > 0) {
// use i as the array index
}While you see it as a curiosity, I see it as being in the same family as the Ariane 5 launch failure. https://en.wikipedia.org/wiki/Cluster_(spacecraft)#Launch_fa... . Software which was "proven" to be correct - original Bentley code or the Ariane 4 inertial reference software - was reused in a new context - in JDK on systems with over 2^32 elements or on the Ariane 5 with its greater horizontal acceleration.
The change of expected environments in both cases lead to overflow.
He added a feature and suddenly the temperature reading was just garbage. Taking the feature out fixed it. Nothing about the added code appeared to be capable of causing the problem.
Had him stumped till he started stepping through the binary search itself. The cause was adding the feature pushed the table location over the 32767 boundary. Bug was the code added two 16 bit pointers and did a right shift without carry.
d'oh!
mid = ((unsigned int)low + (unsigned int)high)) >> 1;
Max 32-bit unsigned int is (1<<32)-1.
Therefore, if 'low' and 'high' are non-negative 32-bit signed integers, it is impossible for their sum, when the values are first cast to 32-bit unsigned integers, to produce a carry.