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mostComplicatedWayToDoSomethingSimple
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This is a snippet from the code review conducted during the public inquiry of the ongoing UK Post Office scandal.
Yes, the Horizon software that contains this code is still in use today.
This makes me want to scream
I have only two words: Ave Maria.
I’m still a noob, can you explain how this code functions and what a more optimized approach would be, and why?
So, if d is smaller than 0 (sad), then we take the absolute value of it (so far, so good).
But if d is greater or equal than 0 (if d is not strictly less than 0, then it is either 0 or greater), then it is subtracted by its doubled value.
E.g. with d = -4, we have a 4. If d = 4, then the returned value is 4 - (4 * 2) = -4.
Basically, it is a very convoluted way to return the flipped sign value, whereas the function could be as simple as:
ReverseSign = -d
Which is a valid operation in pretty much all languages. No condition checks done, no arithmetic. Just flip the damned sign using the negative sign operator.
But the function shown is a joke on many levels also.
- The fancy part for the case d >= 0 also applies for d < 0. -4 - (-4 × 2) = -4 + 8 = 4. Dev visibly was too flabbergasted by the positive value case for some reason.
- The Abs function for if d is negative actually needs more lines of code than flipping the sign around. Shortest abs function I can do is:
if (d >=0) return d else return -d
That dev is, like, bad and pretty inefficient. He uses bells, whistles and abs calls for a one-liner task
Thank you
The fancy part for the case d >= 0 also applies for d < 0. -4 - (-4 × 2) = -4 + 8 = 4. Dev visibly was too flabbergasted by the positive value case for some reason.
The Abs function for if d is negative actually needs more lines of code than flipping the sign around. Shortest abs function I can do is:
if (d >=0) return d else return -d
what do you mean by this ? If d<0 then it falls into the first if case, and Abs should guarantee position number right ?
There's no need to even do the first case or check to see if d < 0 as the second case will work for d < 0 && d >= 0.
the whole function could have been:
return -d
or
return d * -1
depending on what is supported in the language.
no I get that you can just flip the sign, I was trying to understand his two points about "the function shown is a joke on many levels"
sure it's a joke but "-4 - (-4 × 2) = -4 + 8 = 4" <--- this should never happen even in that function
I think he was trying to say that the programmer didn't realize that d = d - (d * 2) worked for negative numbers as well as positive numbers, which is why they had a specific case for negative numbers, making it even worse. Not only did they come up with a convoluted way to reverse the sign of a positive number, they didn't realize their convoluted method would work for negative numbers as well and added a special case for them, adding another level to the joke.
oh okay nevermind I get that so you don't need d = Abs(d) line
Also, if d is more than half the maximum value of the type, doubling d will cause it to overflow, which can have nasty memory issues or unexpected crashes
ReverseSign = -d
Out of curiosity, I can understand making a function for a piece of code you will use many times to shorten the overall code and make it more readable.
But is it really necessary to write a function to flip the sign value? It seems so easy and painless, like you wrote a single line of code.
> bankruptcy, imprisonment, suicide
so nobody bothered to check whether the bills actually make sense?
Fujitsu were logging into the backend and modifying the numbers to make things square up.
Multiple lead engineers quit Fujitsu and whistle blew about it. They were thrown under the bus too. There's no reason the UK government should be taking the financial hit for this. The people who helped cover it up inside the government and fujitsu should be rotting in jail and Fujitsu should be on the hook for billions in damages to the UK government in order to roll out a new system and to compensatethe families affected.
If you want more background there were two fantastic productions that kept this in the public view in the UK.
BBC Panorama - Scandal at the Post Office https://m.youtube.com/watch?v=d4UYP8JP61A
And a dramatisation made more recently about the people affected, which brought it back into the public eye.
https://tv.apple.com/ca/show/mr-bates-vs-the-post-office/umc.cmc.6fyn4tqnvb2n3xl5ify1to8qx.
It should be noted that once it did jump back into the public eye it became clear the government and Fujitsu were still deflecting and covering up and most people due compensation still hadn't got any.
I heard a quote from one of the jail postmasters along the lines of 'I went to jail for a crime I didn't commit. Why has no one gone to jail for crimes they have been proven to have committed?'
Because that postmaster was poor and swore an oath to the public. Rich people only swears to shareholders.
Fujitsu
is it a black company?
Iirc some postmasters tried to prove their innocence by keeping paper logs along side the digital system.
Royal mail and Fujitsu rejected their appeals stating that the digital system is correct as it cannot make mistakes...
rejected their appeals stating that the digital system is correct as it cannot make mistakes
"Stop me if you've heard this one before..."
And also swore in court that it couldn’t be modified manually by anyone. Which was a lie as well
That's the reverse of how my boss got cheated out of extra hours : he was in IT so OF COURSE he could hack into the timetracking clock and the automated reports were wrong.
Allegedly there were people in a master control room somewhere at Fujitsu who were quietly monitoring all the installed instances of the software on post office computers and simply logging directly in to them through a back-door and manually rewriting individual register values buried god-knows-where in the guts of the running code whenever a problem arose. There are stories of postmasters literally seeing erroneous financial transactions being "corrected" (and, in some cases, actually being made even worse) on the screens right in front of them whilst they were calling tech support on the phone, and then being personally blamed for their accounts not adding up.
geeez I have no idea who reviewed this but not even the juniorest of my juniors would dare to write such abominations
How... how did someone think "mmm, ho do I calculate -x? Oh right, I do x-2x"
Literally how, were they high or something?
lines of code being the measure of productivity
But x=-x is equal amount of lines as x=x-2x.
Were they paid by line length?
And if it had to be addition, "x=1-x-1" would have been better.
Why not 0-x? xD
Of course there was a better way :D
That entire snippet is weirdly complex and stupid to the point you have to believe it's malicious. There's just no way you can complicate middle school arithmatics that much. An 8yo with no concept of coding or negative numbers would come up with a better solution. Anyones first instinct would already be correct, so this is either malicious or written by someone who needs to set a phone alarm to not forget to breathe.
Brutal
People who have been lobotomized and/or have never seen a programming book or university from the inside.
The worst part of the story is not the roll out of the faulty software, the reason that lead to imprisonment, bankruptcy and suicide is the denial of the problem by the post office fearing public scrutiny so they swept every report of faulty accounting by the horizon software under the rug and forced the post masters running the indivual shops to financially cover the faulty accounting
probably loc was a measure of productivity,
lgtm, pull request approved
I wonder, is obfuscatory code like this an effort to make decompiling and reverse-engineering from binaries more challenging?
"paid by the line of code"
More like "billed by the line of code"
No, this looks to be so simple to be an obfuscation attemp.
This is 9PM on a friday code
I wonder about this too, what could be the point of doing this, it's not weird shenanigans because their language or whatever doesn't support negating a number because they're doing it in the actual function. This isn't bad code, it was written like this on purpose. Tho I can't figure out the purpose, why would they want to protect reverse engineering a negating function ?
Conceivably you might have requirements to, say, log when a value is being double negated or something? Where you’d want the operation to be a function call rather than inlined, so you have somewhere to insert breakpoints, etc.
But in isolation the existence of this function makes zero sense.
The compiler is smarter than your attempts to make your code look confusing.
Maybe, but did the guy who wrote this crap know that?
I'm sure there are easier ways to do that.
The reasoning is probably much simpler that you're imagining: it passes the unit tests.
Wait, is that VB??
Looks like it might be Ada
I just checked. Horizon was written in VB6.
I thought it was bad before..... and then it gets worse
One of the most important and impactful computer systems in the UK was written in VB6. Awesome.
Bad code is bad code. There's nothing inherently wrong with VB6 other than the low barrier to entry leads to a lot more low quality code from amateurs. Like the code here.
Not specifying a type for d leaves it as a Variant (under the hood, a giant struct/union with all sorts of arcane rules around the implicit conversions flying around here). If you're going to modify a variable passed by reference, you should make that clear, because I doubt everyone calling this function even realizes their input variable is being modified such that b = ReverseSign(a) will leave a = b. The return type also becomes a Variant as it's unspecified. Then the mathematical problems of the approach. Then the lack of error handling.
Lots of VB6 apps have reliably served business critical purposes right up through now. Some people don't like programming being accessible to people not entirely devoted to it, so they form irrational hatred of BASIC languages despite them being a wonderful tool for some purposes.
This reads like they got some VBScript kiddie writing bad websites to write his first compiled application.
Fun fact, for a Variant in VB6, 'Null', 'Empty', 'Nothing', and '0' are all entirely different things, and all different from whether a null pointer was passed (only possible from another language or with some clever tricks).
In my professional life I am aware of a few large and critical systems written in VB. Some were originally classic ASP websites that have been continuously used and updated. I don't think it's particularly rare.
Probably was something else before vb6, some mainframe 4GL. I would guess this was the only was to do it at the time and then it has just been translated for 30 years.
https://en.m.wikipedia.org/wiki/British_Post_Office_scandal Wiki page on the scandal for those curious
If d is greater than 0, d = 0-d surely?
Doesn't matter if d is positive, negative or 0. To reverse the sign, you always just do -d, (aka 0-d).
If d is positive, -d is a negative number
If d is negative, -d is a positive number
If d is 0, 0-0 is still 0.
Ah great shout
Depending on the language, -0 can still be a thing. I believe any language that implements IEEE754 for floaties is suscepticle to this pitfall.
This misses the (actual problem) of -0, which some systems treated differently from 0. 0-d is the right approach.
You completely missed the point
d *= -1
Even easier.
d = -d
It's called unary negation in many languages
I kind of expected that to not work, but I have no idea what language that is, so I don’t know whether mine works either lol
The whole function should have been
return -d
If that somehow doesn't work(idk if there are language like that)
return d*-1
What about Abs(d)?
abs always returns positive. This is converting +d to -d and -d to +d
Ah, I guess I should go work for Fujitsu then
IM DYING
Wow, you've actually managed to introduce a bug here! Congratulations -- I think Fujitsu may have a job waiting for you!
d = strtoint("-" + inttostr(d))
It passes the unit tests!
(meanwhile, unit tests only input positive numbers)
Is this gonna be the new "is_even" meme?
when you work is measured by the number of lines you write
This looks like it was written by someone who has absolutely no understanding of computer arithmetic.
Sometimes this happens to me when I'm trying to improve a MVP function into something that actually works with what I'm trying to do
And then I say "what the fuck is wrong with me" when I notice it
I literally wrote this exact basic function in MARIE for my 400 level advanced topics in programming: compilers class last semester. This is because its a toy assembly language and doesn't have any instruction to flip sign. Even the multiply was plural additions. Anyway, got 100% on the assignment and bonus marks for clean code practices. Game recognizes game, lol, jk. This context is totally different.
the fact that this bug ruined so many lives is a lesson to us all and not actually funny. Its one of the few times i really cant laugh at something like this because how fujitsu acted, and how they covered this up directly, and were absolute dickheads brings our own profession to shame. Never again.
Why is nobody talking about d < o?? They're casually comparing d to some global variable o which they assume is 0...
I think it's just a bad font. Looking at the "2" (the only other digit in the code): it is also smaller than all the other characters in the code.
I think it is a 0 (I hope!) ..if you look at the next page the date is 14/05/01 and has the same font as that 0.. weird font seems almost like old typewriters ones
Oh fuck, oh sweet Jesus fuck, you're right! Unless what we're seeing here is one hell of a misprint, some knuckle-dragging imbecile actually used the letter "o" as a variable name! In a book-keeping program written for a whole fucking national institution that doesn't just deliver the post, but also provides actual high-street banking services, often to some of the most old and vulnerable!!
There are no more words. There is only horror. I need to lie down.
It's just a bad (for code) font.
I defy you to show me any font ever created that renders the numeral zero so that it is indistinguishable from a lower-case "o." And if any such thing truly does exist, that also makes me incandescently angry.
EDIT: Wait, holy crap, you may actually be right, because it also renders the numeral two the same size as a lower-case letter. Incandescently angry it is, then; that's even worse than a misprint! Thanks for pointing that out, this debacle is just incompetence and craziness all the way down.
That’s even worse that they would write code in such a terrible font!
Sure maybe. It's still dumb lol 😭
In defence of Fujitsu I think this was actually International Computers Limited as the Horizon contract was awarded to them some time before Fujitsu bought them. So we can't blame the Japanese for this goof.
I think the press likes to blame it on Fujitsu through a mix of racism and avoiding admitting it's our fault. How much the Japanese parent was involved is somewhere between slim and none.
Fujitsu don't need defending on this.
From the wiki (with links to the references):
Business applications on Legacy Horizon (including EPOSS, the accounting application) were written by Fujitsu. The history and poor state of the EPOSS software is described in 2001 in an internal Fujitsu document "Report on the EPOSS PinICL TaskForce".
EPOSS, the component of Horizon that this snippet is auditing and the source of faults that ruined the lives of innocent people, was written by Fujitsu.
Your hearts in the right place but Fujitsu should've done much better, from the wiki:
"At the Inquiry in 2024, it was revealed that Fujitsu was aware that the Horizon software contained bugs as early as 1999, but this was not disclosed to the subpostmasters or to the courts in which prosecutions were conducted"
Yep, ICL Pathway, as it says on the doc in the screenshot.
ICL was bought by Fujitsu in 1998. Horizon "conceived in 1996". You are absolutely spot on to mention this.
If d < o Then
Obviously, that o is undefined. It could be anything from the number 461 to the string "potatoes". You can never know for sure with these pesky undefined variables.
When I was playing around with sound shaders, you often wanted to move the wave but keep it's sign and amplitude. So a ton of sng = sing(f); amp = abs(f) and then you do some math on it like amp+=0.2; before assembling it again f_out = amp*sign; and yes errors were all over the place.
After a whole someone told me that tanh(x) = smoothsign(x) and that really opened some mind eyes.
They made this terrible function, but no one tested it ?
The problem with testing is that if it passes the tests, you can still incorrectly assume the function works perfectly.
I first thought they wanted to reverse the number symbols. Which sounds pretty tricky to pull off efficiently, especially if you still want to be able to use them as a number later.
But no, they just want the negative number equivelent.
I think asking ai is the most complicated way to do something simple because first you gotta teach the linear algebra box on the entire internet, then tune it for useful responses. After all that you can ask it to write a function to detect if a number is odd or even
This looks obviously like a compiler optimization to me. Turning -1*d into d - (d << 1) doesn’t seem that strange at all. d * 2 could overflow, but if the overflow wraps (which is the default behavior in VB .NET) the code is still correct.
ie if we’re dealing with 8 bit signed integers and d =100, 2 * d =-56, d - 2d = 156 which wraps to -100. Come on guys.
Is too complicated for sure. But it does work. Is this the bug that caused suicides?
It wasn't this code, but the truth is much much worse. The hosting company was actively changing submitted values in the database whilst assuring users that this was impossible. And then laying the blame at the users door.
There should be people in prison for this and not the poor souls who did through no fault of their own. It's the greatest miscarriage of justice in British history.
ITV did an amazing dramatisation of it all at the start of of 2024. Look up Mr Bates vs The Post Office.
It only works most of the time.
D*2 can overflow, and presumably you can get other precision errors from the unnecessary operations
Maybe, it could've overflowed.
I remember this from when Ars Technica wrote about it. We talked about it at work.
I’ve seen people getting written up and/or put on PIP from a prod misconfiguration that caused tens of thousands $ of financial loss during the few minutes prod ran buggy… And then there’s this debacle.
Is this Visual Basic? Makes me wonder if in some ancient version of it simple negation on some obscure data type, that maybe they themselves made up, straight up did not work and instead of thinking about it they did this, but I honestly have no idea I coded in VB.NET only when convinced at gun point at my first job.
Or they could have overloaded some of these calculations and added some secondary business logic and so they had to use this, or could not use the simple d = -d. Honestly I don't believe this was gross incompetence, negligence, or malicious intent.
Ah, yes, the literal government-destroying function
This single handedly caused a controversy so potent, the government had to try and hide this entire thing for years, and Fujitsu refuse to even talk about it like the Japanese company they are
numer * (-1) ? What was its meaning?
I'm really new to programming.
The correct code would be something like that?
``` def reverse(n):
return n if n < 0 else -n
print(reverse(5)) ```
def reverse(n): return -n
would suffice. Your code won't reverse negative integers.
I didn't know that. Thanks!
The person had to flip just one bit. Wtf!!
Check what happens when d is 1
Wonderfull ! If you have nothing to do you write code like this to show your effort in solving problems.
return -d; duh?
Based on the comments this actually seems to be real. This is so bad that it makes me smile when I think of my own code.
when `d = ~(d-1)` is just too obscure
[deleted]
you're making a lot of assumptions
So reverse sign of 5 is -20. Got it.
yeah, no.
that d*2 could overflow
Surely that's the actual bug that got people killed.
Nobody directly died, but the accounting software messed up. Money was missing and the British post office went to Fujitsu and they swore up and down that it couldn’t possibly be due to bugs in their software. So on that basis they blamed (and in some cases charged with criminal fraud) a bunch of post office managers thinking they embezzled the money.
But actually the software was buggy as fuck and they ruined a bunch of people’s reputations because Fujitsu was incompetent. Several wrongly convicted people committed suicide. https://en.m.wikipedia.org/wiki/British_Post_Office_scandal
Nonetheless, that sort of "look at how clever I am" usage of elaborate mathematical juggling to essentially achieve a single bit flip is awfully reminsicent of the infamous THERAC-25, which did directly kill people due to a nasty combination of terrible design and code flaws, one of which was indeed an arithmetic overflow.
Oh yeah, whoever did this seems grossly incompetent.
Honestly, I'm still unsure whether the code we see here could have been produced merely by colossal incompetence, or whether it is the result of active, wilful perversity.
100%. I don’t know if I am smart enough to write something this convoluted. Like, why? What purpose could it possibly serve? Was the coder getting paid by the character? If so, I could think of much more profitable ways to write this.
In another comment I mentioned that you might want a function like this if you, say, need to log or track different financial operations. That way you have somewhere to, say, insert a breakpoint or tracepoint whenever you try to negate a negative value. A negation operator would likely be inlined.
Obviously the way they’re doing the actual math operation there is awful, though.
where was the *code review* to stop this jank getting to prod?
Code reviews assume the reviewer knows what they’re doing…
That is why I don't write medical or financial software.
Twos complement makes it more complex than that... But just multiplying by -1 would replace that whole function, in all cases, with fewer bugs while running faster and using less memory.
There's no need to do any of that mess.
you can't just bit flip the sign digit
Yeah it’s not a single bit flip, but I don’t know of any language that isn’t capable of handling the sign flip with a single operation equivalent to
x = -x. Even assembly languages can domvnor equivalent.In languages with two's complement integers, the minimum integer of a given size has no additive inverse in that same size. E.g. in C, an
intcan fitINT_MINbut not-INT_MIN. The fix is to check if the number to be inverted isINT_MINand if so error. Otherwise just negate, all other values are safe. Or use the checked APIs that got added in C23.if you have an
INT_MINinside a non-const variable at any point during execution, you've got more problems than just negation~x + 1that's flipping every bit
Assuming two's complement, which is standard for computers today, that is the representation of
-xFujitsu are hiring
I'd go work on their HR software. If their business practices are this bad, pulling an office space style scam shouldn't be too difficult.
negating a number is not a single bit flip..
It is on floats (don't use floats for money).
Depends how you represent the number.
If you're using one's complement integers in production in 2025, God help you.
Bit flip won't work on ints in U2 coding.
The bigger problem with THERAC (beyond the overflow problem) was an unusual race condition when saving new settings - unusual bc it involved a component physically moving in meatspace.
Because nurses and technicians got more familiar with the system over time, they started navigating screens and inputting data faster and faster. Eventually, they could change all the settings faster than the machine would save them (settings were saved on a clock loop) - the screen would display the right numbers, but the change wasn’t saved when they left that screen. Because the different lenses are physical objects that rotate in and out of the path of the beam, it was possible for an operator to input the correct dose and then return to the main screen to rotate the lens tray so quickly that the machine would have dangerous settings.
Oh, it was a perfect shitstorm of rotten code and bad design decisions interacting to create an absolute time-bomb. Turns out the control software was always awful and capable of intermittently sending commands to the machine that would deliver a lethal dose of ionising radiation if the operator entered and then amended the settings too quickly, but the hardware interlocks in the earlier models effectively silently prevented this from doing any harm; they merely locked up the machine and required a restart, issuing a cryptic numerical error message that gave no obvious indication to the operators (who apparently didn't even have access to documentation as to what all the error codes meant!) that the computer had just attempted to kill the patient.
Then the developers apparently decided that because the earlier models had such a good record for safety, they could save some money by removing the interlocks on the model 25...
At least 13 people died as a direct result of this. This bug impacted the Country greatly. Post Masters here are often just wee old Ladies out in the sticks.
https://www.nytimes.com/2025/07/10/world/europe/uk-post-office-scandal-report.html
Post Office has the far greater blame IMO because their role as a prosecutor conferred many responsibilities they failed to meet, which would have avoided many deaths.
In over seven hundred cases the post office prosecuted people sending many to prison, many more were financially ruined trying to avoid prosecution.
The Post Office had access to keystroke data which would have been exonerating in many cases which they didn't disclose because their contract made it too expensive.
As the scandal began coming to light a memo was written internally suggesting minutes of meetings related to it were destroyed believing (wrongly) that meant they didn't have to disclose it.
Of the relative few who had convictions quashed by appeal (the majority of victims had their convictions quashed by an absolutely extraordinary act of parliament because the appeal court had not the resources to hear so many cases) some had already died believing the shadow of this legal atrocity had condemned them to ignobility.
Some committed suicide. Lives were doubtless shortened.
The full judgment in a combined appeal for only 39 of the hundreds directly harmed and thousands indirectly is available and explains the truly horrific details: https://www.judiciary.uk/wp-content/uploads/2022/07/Hamilton-Others-v-Post-Office-judgment-230421.pdf
Yeah, the whole thing was a clusterfuck at every level. By no means did I mean to make it sound like the post office was blameless. Courts giving criminal convictions on pretty flimsy evidence was awful too.
UK courts have juries though? Why would jurors vote that people are guilty on such flimsy evidence?
"Nobody directly died"
13 people literally killed themselves over it
When you say “got people killed” I think more of things like https://en.m.wikipedia.org/wiki/Therac-25.
The whole thing was handled amazingly badly at every level. It’s hard to envision ‘bugs in this financial software being written by the lowest bidder will result in people committing suicide’ up front.
So people died as stated in the page above
Someone did commint s*icide from the stress and damage from the software.
As I wrote:
My bad, I didn't notice that. I misread.
I had heard a different story. Fujitsu wanted to fix it based on reports from small offices, but the head of those offices refused to admit the system may be faulty?
“The” bug was a combo of ui refresh delay and form re-submit logic resulting in cash to till deposits being double counted.
That is to say, cashiers would get given £100, type 100, hit enter, see nothing happens, and hit enter again, till balance would be 200, but cash in till 100, and the postmaster accused of taking the difference.
So form submission errors 101
Nope the type of bug that caused so much havoc was the system was throwing around XML messages without any kind of validation that messages were being received or kept unique.
For instance if a branch received £4k the sub post master would log that in the system. Say everything is going slow so he hits the button 3 times as users are likely to do. The post office would register a £12k debt against the branch rather than a £4k debt. There was no unique ID to ensure the transaction wasn't replayed. There was no guarantee of any kind of response to confirm everything had been processed.
Shit infrastructure on this level permeated everything. Though the real crime was that the post office was allowed to prosecute people themselves and went out of their way to hide evidence of Horizons many failings. It would have taken about 30 minutes of investigation to disprove most of the claims.
One sub post master was accused of stealing from an ATM. The ATM in question had a full log of all the transactions which it also propagated to the Horizon system. The Horizon log was incomplete and had missed multiple withdrawals. It would have taken an hour comparing the logs of the two systems to find the issue.
Yeah, guy should have known that the right way to do it is
d = 2(d/2.0 - d)Smh my head
At least your solution never produces odd amounts.
Or it could be the reassignment of
d. Not sure if whatever this language is, passes everything by reference, but in that case, it could be the bug.Why could it overflow
If D is more than half of the max value allowed then doubling it would overflow.
In two's complement it still works. Worst that could be said (EDIT: regarding correctness) is that it relies on signed overflow which may not be defined in the language they wrote it in, but it's not like better programs haven't also relied on that too.
EDIT: One thing to note when comparing it to the simple function that just returns
-dis that in the case whered == INT_MIN, this function may actually be safer. Since this function delegates toabsfor negative inputs, it handles theINT_MINcase according to howeverabshandles theINT_MINcase. Ifabswere to, say, throw an exception when called withINT_MIN, then the function in the OP would too, which may be safer than silently failing as the simpler version might. In some senses, this may actually make the function more correct than just-d.How big of a number had to be used as input for it to overflow ? Surely the post offices aren't making transactions that huge. Something I read on the thread is that there was a lot of double counting as there was no response to form submission and people would hit submit multiple times which would all go through. This sounds like a much more plausible reason for the problems, no ? I don't know this case well, so any more info is welcome.
It can't d is positive so it's not possibleEdit: nevermind you can make it negative if the second to last, leftmost bit is set 🤦♂️
Are you sure ? In the case that d>(MAX_INT/2), wouldn't d*2 overflow and cause d-(d*2) != -d?
Honestly, if it's causing this much confusion, guesswork and debate as to what, precisely, it's even supposed to do, then it's direfully bad code regardless of any cleverly subtle functionality it may or may not turn out to have.
It would still result in
d-(d*2) == -dElementary operations in a value of a given width are equivalent to the same operations in a wider value, ignoring whatever happens to the extra bits. Thus, starting with a width-w unsigned integer
dwith value strictly less than2^(w-1), extenddto width w+1, and then calculate2^w + d - 2*d. The result is2^w-dbecause this never overflows so cancellation can happen normally.dhere is guaranteed to be such that2^w-d>=2^(w-1), which means that when we restrict2^w-dto width w, we get a value that represents-din two's complement.Not sqrt, it's less than half of max UNSIGNED int. Multiplication by 2 is equivalent to left shifting the bits by 1. So to overflow the leftmost bit needs to be 1. In two's compliment, positive integers have their leftmost bit as 0 by definition (1 for negative) so its impossible to overflow a positive signed number by multiplying by 2.given an 8 bit signed integer:
01000000 = 64
01000000 << 1 = 10000000
10000000 = -128
-128 ≡ 128 mod 256
64 - (-128) = 192 ≡ -64 mod 256
In the end it still works out in 2s complement arithmetic, only case that will fail is ReverseSign(-128) where d*2 overflows to 0, but that's kinda a given considering 128 can't be represented in an 8 bit signed int.
By overflow he means go negative. Which most of us would count as overflow when we talk about signed variables.