The advantage works both ways: it's also nice if your normal integer vector instructions can be used to accelerate memcmp, without needing an extra opcode or instruction flag to specifically support parallel lexographical comparison. Note that if the vector units only support signed integers, then you only need an exclusive-or to flip all of the sign bits in order to get lexographical sorting, and that vector exclusive-or has important real-word use cases for hash functions and so-called add-shift-xor encryption algorithms like ChaCha20.
Alternatively, if you're going to include a dedicated lexographical comparison instruction for strcmp/memcmp (like x86 REP CMPS), a fast implementation will need less dedicated circuitry if your processor natively supports big-endian operations for other instructions.
Big-endian use in mainframes likely evolved from big-endian BCD numeric fields on punch card sorting/tabulating machines, where big-endianness was an advantage in that the normal lexographic sorting would put constant-width numeric fields in numerical order.
LEB128 is a little-endian variable-length encoding. That's what the LE stands for.
UTF-8 is a big-endian variable-length encoding. The most significant bits are packed in the earlier bytes, so that lexographic ordering comes out correctly.
I'm really alluding to something like LEB128-encoding uint64_ts, except big-endian and putting all of the continuation flags at the beginning of the encoding, so a single switch on the first byte gives you the encoded length and it also sorts correctly lexographically.
> Xor does not flip two's complement sign correctly
Re-read what I wrote. I wasn't talking about flipping the sign bit in order to negate the numeric value. I was talking about flipping the sign bit to get correct lexographic text ordering on a machine that can only do signed comparisons.
> since the machine arithmetic will behave exactly the same way (with few exceptions).
I was talking about _exactly_ one of these exceptions... comparing two values. For simplicity, let's pretend we have a 16-bit BE CPU that can only perform signed comparisons, and we want to lexographically compare two 4-byte arrays: [ 41 4F 4F 4F ] vs. [ C1 81 4F 4F ] we perform the first load to compare 0x414F (16719) vs. 0xC181 (-15999) in order to get the correct lexographical ordering in all cases, we need to invert the sense of the sign bit. Flipping the sign bit in these two cases gives 0xC14F (-16049) vs 0x8181 (33153).
In all cases, flipping the sign bit allows one to perform unsigned comparison on a CPU that can only perform signed comparisons. For an W-bit word, you end up subtracting (W-1)^2 from all values with the most significant bit unset and adding (W-1)^2 to all values with the most significant bit set. I understand this doesn't negate the values. That's not the point. The point is to perform unsigned comparison on a CPU that doesn't natively support it.
Hah, so it's literally because we write numbers with most significant digit on the left, which is the opposite to logical ordering?
I presume the only advantage to BE today is compatibility then...
I'm not saying big-endian is universally better. I'm just saying there are real-world advantages.
Note there are more than two endiannesses, where the most common middle-endian variant is big-endian order of 16-bit words, but little-endian order within those 16-bit words.
As for linguistic quirks, there's no obvious universal connection between writing order for text, the order digits are written, and the way numbers are pronounced, so I'm not sure what you're getting at. Arabic is written right-to-left, but they still write the most significant digit on the left. However, I've read that Arabic writers line-break numbers (when forced) by placing the most significant digits on the upper line and the least significant digits on the lower line, so it's not a clear-cut case of Arabic writing numbers in little-endian order right-to-left. I'm not sure about Arabic number pronunciation. I do know that German pronunciation is middle-endian: 256 is "two hundred six-and-fifty", despite the digit writing order being big-endian in German. I met a German guy who incorrectly swaps digits if you talk to him in English while he's doing mental math... forcing him to process English somehow also swaps digit orders in his head.
As for strings, GCC/Clang are great at vectorizing normal byte-oriented code. It doesn't matter if it generates or you hand code VPCMPEQB vs. VPCMPEQQ either, since they appear to have the exact same latency. Modern compilers have also been moving in the direction of punishing folks who do things like `* (uint32_t * )p`, due to aliasing rules rather than endianness. Rob Pike had an amusing blog post on this subject: https://commandcenter.blogspot.com/2012/04/byte-order-fallac...
Back when I worked on Google's indexing system (2006-2010), one of the stages keyed documents by URL (with the host name in DNS order: com.google.www) followed by a big-endian timestamp. This put records for the same domain together, and put successive crawls for the same URL in chronological order. This improved compression ratios in our BigTable tablets, and finding the latest crawled version of <URL> was just a search for the largest key <= <URL><MAX_TIMESTAMP>.
> It doesn't matter if it generates or you hand code VPCMPEQB vs. VPCMPEQQ either, since they appear to have the exact same latency.
But with VPCMPEQB, you need to have 8 times as many conditional branches as CPCMPEQQ (in the naive case) in order to turn your vectorized comparison into a memcmp result. Note that VCMPEQ* don't modify any flags, so you can't just JE/JNE after your VCMPEQ*. Now, via some vector permutes, shifts, and bitwise-ors, you can cut down on the number of conditional branches. However, it's still more processing than if you can load / compare your vector registers in lexographical order.
> But with VPCMPEQB, you need to have 8 times as many conditional branches as CPCMPEQQ in order to turn your vectorized comparison into a memcmp result
Not at all. It doesn't require any branches, other than the loop itself. Here's the trick everyone uses, for the simple case of finding one character, e.g. NUL:
0: add $vectorlen,i
pmovdqa mem,vector
pcmpeqb query,vector
pmovmskb vector,bitmask
bsf bitmask,offset
jz 0b
add offset,i
ret
The whole point is you just memcmp the whole key byte array instead of having to parse out the fields. If the timestamp is in little-endian order, then memcmp won't give you chronological ordering on the timestamp suffix.
In the case of pcmpeqb / pmovmskb / bsf, I was explicitly talking about memcmp, not finding the first same or differing byte. I don't want to get too bogged down in specific architectures vs. the more general pros/cons of byte orders themselves... but... there's pcmpeq and pcmpgt, but no pcmpne. That's fine, so to implement memcmp, you'd just xor with -1 before bsf to find the index of the first different byte and then explicitly compare the differing byte. So far so good, except that Intel explicitly designed AVX to scale up to 1024-bit vectors, at which pmovmskb can't pack 128 bits into a GP register. Fine, so use pcmpeqw/pmovmskw instead of pcmpeqb/pmovmskb, but then once you have the offset of the first differing uint16_t, you can't just do a native-endian comparison on the two uint16_ts. If the x86 were big-endian, then bsf with 64-bit GP registers would scale all the way up to 4096-bit vector registers without requiring an extra bit extractions or bswap instructions. It's fundamentally an advantage that a native-endian 64 bit subtraction performs an 8 byte lexographical comparison on big-endian machines.
Granted, the advantage is tiny, but this whole rabbit hole discussion was in reply to "I presume the __only__ advantage to BE today is compatibility then..." (emphasis mine) in [https://news.ycombinator.com/item?id=22660000]
As you have to read an entire positional number to be able to get even its magnitude; the only “advantage” I can see of LE over BE in natural languages is that at least rtl can get odd/even immediately. Then again in ltr you can get sign immediately. In real life human use neither “advantage” is compelling.