I need to detect the overflowing of an unsigned long.
This variable holds the amount of milliseconds since the device is running (it's an Arduino). Doing sizeof(unsigned long), I have come to see it's indeed a 32-bit number. Now, since it increments every millisecond, which means the device will run for about 49 days before this value overflows.
Since it's for a home system, it isn't really advisable. Now what I'm using the number for, is comparing if the current time is larger than the previous time plus an amount of debouncing.
if(timeChanged + amountOfMs < currentTime){ ... }
Needless to say, once overflow occurs this isn't going to work anymore. What's an efficient way to solve this? I've thought about also having a second-timer as well to check if the milliseconds one has overflowed, but in the end I'll have the same problem.
This rollover issue seems to cause quite a bit of confusion...
The right answer is that you need not worry about the millis() rollover, as long as you do your calculation properly.
This is bad:
if (timeChanged + amountOfMs < currentTime) { ... }
This is good (rollover-safe):
if (currentTime - timeChanged > amountOfMs) { ... }
The reason it works is that arithmetics with unsigned integers (unsigned long in your case) reliably works modulo max+1 (ULONG_MAX+1 is 232). Thus, currentTime, timeChanged and their difference always have the correct value, modulo 232. As long as you test your button more often than once every 49 days (which is likely) the difference will be in the range of an unsigned long, and your test will be correct.
Let put it another way: if millis() rolls over between timeChanged and currentTime, then the difference currentTime - timeChanged will be negative. But since the difference is actually computed with unsigned numbers, it will underflow and roll-over to the correct result. I do not like this explanation though, as it sounds like an error compensating another error. The truth is: if you think of unsigned numbers in terms of modular arithmetics, there is no error anywhere.
This is such a common mistake (and one that I've made myself) that the Arduino Playground has a nice, thorough, and correct answer. See https://playground.arduino.cc/Code/TimingRollover
You can create a new if loop checking the condition : if(currentTime == 0xFFFFFFFE)
If this is the condition, next millisecond will overflow your variable. So at this point you can manually reset it to zero and goto loop where it starts from zero.
This might or might not help your situation. I can't say for sure because you haven't shared any further details about your code.
Define two variables, I'm going to call them 'now' and 'lastNow'.
unsigned long now;
unsigned long lastNow = 0;
In your loop you can now do this:
now = millis();
if (now < lastNow) {
// rollover!
}
lastNow = now;
Nice and reliable regardless of how frequently (or infrequently) you loop.
Related
This is a question about an SO question; I don't think it belongs in meta despite being sp by definition, but if someone feels it should go to math, cross-validated, etc., please let me know.
Background:
#ForceBru asked this question about how to generate a 64 bit random number using rand(). #nwellnhof provided an answer that was accepted that basically takes the low 15 bits of 5 random numbers (because MAXRAND is apparently only guaranteed to be 15bits on at least some compilers) and glues them together and then drops the first 11 bits (15*5-64=11). #NikBougalis made a comment that while this seems reasonable, it won't pass many statistical tests of randomnes. #Foon (me) asked for a citation or an example of a test that it would fail. #NikBougalis replied with an answer that didn't elucidate me; #DavidSwartz suggested running it against dieharder.
So, I ran dieharder. I ran it against the algorithm in question
unsigned long long llrand() {
unsigned long long r = 0;
for (int i = 0; i < 5; ++i) {
r = (r << 15) | (rand() & 0x7FFF);
}
return r & 0xFFFFFFFFFFFFFFFFULL;
}
For comparison, I also ran it against just rand() and just 8bits of rand() at at time.
void rand_test()
{
int x;
srand(1);
while(1)
{
x = rand();
fwrite(&x,sizeof(x),1,stdout);
}
void rand_byte_test()
{
srand(1);
while(1)
{
x = rand();
c = x % 256;
fwrite(&c,sizeof(c),1,stdout);
}
}
The algorithm under question came back with two tests showing weakenesses for rgb_lagged_sum for ntuple=28 and one of the sts_serials for ntuple=8.
The just using rand() failed horribly on many tests, presumably because I'm taking a number that has 15 bits of randomness and passing it off as 32 bits of randomness.
The using the low 8 bits of rand() at a time came back as weak for rgb_lagged_sum with ntuple 2, and (edit) failed dab_monobit, with tuple 12
My question(s) is:
Am I interpretting the results for 8 bits of randomly correctly, namely that given that one of the tests (which was marked as "good"; for the record, it also came back as weak for one of the dieharder tests marked "suspect"), came as weak and one as failed, rand()'s randomness should be suspected.
Am I interpretting the results for the algorithm under test correctly (namely that this should also be marginally suspected)
Given the description of what the tests that came back as weak do (e.g for sts_serial looks at whether the distribution of bit patterns of a certain size is valid), should I be able to determine what the bias likely is
If 3, since I'm not, can someone point out what I should be seeing?
Edit: understood that rand() isn't guaranteed to be great. Also, I tried to think what values would be less likely, and surmised zero, maxvalue, or repeated numbers might be... but doing a test of 1000000000 tries, the ratio is very near the expected value of 1 out of every 2^15 times (e.g., in 1000000000 runs, we saw 30512 zeros, 30444 max, and 30301 repeats, and bc says that 30512 * 2^15 is 999817216; other runs had similar ratios including cases where max and/or repeat was larger than zeros.
When you run dieharder the column you really need to watch is the p-value column.
The p-value column essentially says: "This is the probability that real random numbers could have produced this result." You want it to be uniformly distributed between 0 and 1.
You'll also want to run it multiple times on suspect cases. For instance, if you have a column with a p-value of (for instance) .03 then if you re-run it, you still have .03 (rather than some higher value) then you can have a high confidence that your random number generator performs poorly on that test and it's not just a 3% fluke. However, if you get a high value, then you're probably looking at a statistical fluke. But it cuts both ways.
Ultimately, knowing facts about random or pseudorandom processes is difficult. But armed with dieharder you have approximate knowledge of many things.
I'm programming a PLC with some legacy software (RSLogix 500, don't ask) and it does not natively support a modulus operation, but I need one. I do not have access to: modulus, integer division, local variables, a truncate operation (though I can hack it with rounding). Furthermore, all variables available to me are laid out in tables sorted by data type. Finally, it should work for floating point decimals, for example 12345.678 MOD 10000 = 2345.678.
If we make our equation:
dividend / divisor = integer quotient, remainder
There are two obvious implementations.
Implementation 1:
Perform floating point division: dividend / divisor = decimal quotient. Then hack together a truncation operation so you find the integer quotient. Multiply it by the divisor and find the difference between the dividend and that, which results in the remainder.
I don't like this because it involves a bunch of variables of different types. I can't 'pass' variables to a subroutine, so I just have to allocate some of the global variables located in multiple different variable tables, and it's difficult to follow. Unfortunately, 'difficult to follow' counts, because it needs to be simple enough for a maintenance worker to mess with.
Implementation 2:
Create a loop such that while dividend > divisor divisor = dividend - divisor. This is very clean, but it violates one of the big rules of PLC programming, which is to never use loops, since if someone inadvertently modifies an index counter you could get stuck in an infinite loop and machinery would go crazy or irrecoverably fault. Plus loops are hard for maintenance to troubleshoot. Plus, I don't even have looping instructions, I have to use labels and jumps. Eww.
So I'm wondering if anyone has any clever math hacks or smarter implementations of modulus than either of these. I have access to + - * /, exponents, sqrt, trig functions, log, abs value, and AND/OR/NOT/XOR.
How many bits are you dealing with? You could do something like:
if dividend > 32 * divisor dividend -= 32 * divisor
if dividend > 16 * divisor dividend -= 16 * divisor
if dividend > 8 * divisor dividend -= 8 * divisor
if dividend > 4 * divisor dividend -= 4 * divisor
if dividend > 2 * divisor dividend -= 2 * divisor
if dividend > 1 * divisor dividend -= 1 * divisor
quotient = dividend
Just unroll as many times as there are bits in dividend. Make sure to be careful about those multiplies overflowing. This is just like your #2 except it takes log(n) instead of n iterations, so it is feasible to unroll completely.
If you don't mind overly complicating things and wasting computer time you can calculate modulus with periodic trig functions:
atan(tan(( 12345.678 -5000)*pi/10000))*10000/pi+5000 = 2345.678
Seriously though, subtracting 10000 once or twice (your "implementation 2") is better. The usual algorithms for general floating point modulus require a number of bit-level manipulations that are probably unfeasible for you. See for example http://www.netlib.org/fdlibm/e_fmod.c (The algorithm is simple but the code is complex because of special cases and because it is written for IEEE 754 double precision numbers assuming there is no 64-bit integer type)
This all seems completely overcomplicated. You have an encoder index that rolls over at 10000 and objects rolling along the line whose positions you are tracking at any given point. If you need to forward project stop points or action points along the line, just add however many inches you need and immediately subtract 10000 if your target result is greater than 10000.
Alternatively, or in addition, you always get a new encoder value every PLC scan. In the case where the difference between the current value and last value is negative you can energize a working contact to flag the wrap event and make appropriate corrections for any calculations on that scan. (**or increment a secondary counter as below)
Without knowing more about the actual problem it is hard to suggest a more specific solution but there are certainly better solutions. I don't see a need for MOD here at all. Furthermore, the guys on the floor will thank you for not filling up the machine with obfuscated wizard stuff.
I quote :
Finally, it has to work for floating point decimals, for example
12345.678 MOD 10000 = 2345.678
There is a brilliant function that exists to do this - it's a subtraction. Why does it need to be more complicated than that? If your conveyor line is actually longer than 833 feet then roll a second counter that increments on a primary index roll-over until you've got enough distance to cover the ground you need.
For example, if you need 100000 inches of conveyor memory you can have a secondary counter that rolls over at 10. Primary encoder rollovers can be easily detected as above and you increment the secondary counter each time. Your working encoder position, then, is 10000 times the counter value plus the current encoder value. Work in the extended units only and make the secondary counter roll over at whatever value you require to not lose any parts. The problem, again, then reduces to a simple subtraction (as above).
I use this technique with a planetary geared rotational part holder, for example. I have an encoder that rolls over once per primary rotation while the planetary geared satellite parts (which themselves rotate around a stator gear) require 43 primary rotations to return to an identical starting orientation. With a simple counter that increments (or decrements, depending on direction) at the primary encoder rollover point it gives you a fully absolute measure of where the parts are at. In this case, the secondary counter rolls over at 43.
This would work identically for a linear conveyor with the only difference being that a linear conveyor can go on for an infinite distance. The problem then only needs to be limited by the longest linear path taken by the worst-case part on the line.
With the caveat that I've never used RSLogix, here is the general idea (I've used generic symbols here and my syntax is probably a bit wrong but you should get the idea)
With the above, you end up with a value ENC_EXT which has essentially transformed your encoder from a 10k inch one to a 100k inch one. I don't know if your conveyor can run in reverse, if it can you would need to handle the down count also. If the entire rest of your program only works with the ENC_EXT value then you don't even have to worry about the fact that your encoder only goes to 10k. It now goes to 100k (or whatever you want) and the wraparound can be handled with a subtraction instead of a modulus.
Afterword :
PLCs are first and foremost state machines. The best solutions for PLC programs are usually those that are in harmony with this idea. If your hardware is not sufficient to fully represent the state of the machine then the PLC program should do its best to fill in the gaps for that missing state information with the information it has. The above solution does this - it takes the insufficient 10000 inches of state information and extends it to suit the requirements of the process.
The benefit of this approach is that you now have preserved absolute state information, not just for the conveyor, but also for any parts on the line. You can track them forward and backward for troubleshooting and debugging and you have a much simpler and clearer coordinate system to work with for future extensions. With a modulus calculation you are throwing away state information and trying to solve individual problems in a functional way - this is often not the best way to work with PLCs. You kind of have to forget what you know from other programming languages and work in a different way. PLCs are a different beast and they work best when treated as such.
You can use a subroutine to do exactly what you are talking about. You can tuck the tricky code away so the maintenance techs will never encounter it. It's almost certainly the easiest for you and your maintenance crew to understand.
It's been a while since I used RSLogix500, so I might get a couple of terms wrong, but you'll get the point.
Define a Data File each for your floating points and integers, and give them symbols something along the lines of MOD_F and MOD_N. If you make these intimidating enough, maintenance techs leave them alone, and all you need them for is passing parameters and workspace during your math.
If you really worried about them messing up the data tables, there are ways to protect them, but I have forgotten what they are on a SLC/500.
Next, defined a subroutine, far away numerically from the ones in use now, if possible. Name it something like MODULUS. Again, maintenance guys almost always stay out of SBRs if they sound like programming names.
In the rungs immediately before your JSR instruction, load the variables you want to process into the MOD_N and MOD_F Data Files. Comment these rungs with instructions that they load data for MODULUS SBR. Make the comments clear to anyone with a programming background.
Call your JSR conditionally, only when you need to. Maintenance techs do not bother troubleshooting non-executing logic, so if your JSR is not active, they will rarely look at it.
Now you have your own little walled garden where you can write your loop without maintenance getting involved with it. Only use those Data Files, and don't assume the state of anything but those files is what you expect. In other words, you cannot trust indirect addressing. Indexed addressing is OK, as long as you define the index within your MODULUS JSR. Do not trust any incoming index. It's pretty easy to write a FOR loop with one word from your MOD_N file, a jump and a label. Your whole Implementation #2 should be less than ten rungs or so. I would consider using an expression instruction or something...the one that lets you just type in an expression. Might need a 504 or 505 for that instruction. Works well for combined float/integer math. Check the results though to make sure the rounding doesn't kill you.
After you are done, validate your code, perfectly if possible. If this code ever causes a math overflow and faults the processor, you will never hear the end of it. Run it on a simulator if you have one, with weird values (in case they somehow mess up the loading of the function inputs), and make sure the PLC does not fault.
If you do all that, no one will ever even realize you used regular programming techniques in the PLC, and you will be fine. AS LONG AS IT WORKS.
This is a loop based on the answer by #Keith Randall, but it also maintains the result of the division by substraction. I kept the printf's for clarity.
#include <stdio.h>
#include <limits.h>
#define NBIT (CHAR_BIT * sizeof (unsigned int))
unsigned modulo(unsigned dividend, unsigned divisor)
{
unsigned quotient, bit;
printf("%u / %u:", dividend, divisor);
for (bit = NBIT, quotient=0; bit-- && dividend >= divisor; ) {
if (dividend < (1ul << bit) * divisor) continue;
dividend -= (1ul << bit) * divisor;
quotient += (1ul << bit);
}
printf("%u, %u\n", quotient, dividend);
return dividend; // the remainder *is* the modulo
}
int main(void)
{
modulo( 13,5);
modulo( 33,11);
return 0;
}
I've been reading up on the Y2038 problem and I understand that time_t will eventually revert to the lowest representable negative number because it'll try to "increment" the sign bit.
According to that Wikipedia page, changing time_t to an unsigned integer cannot be done because it would break programs that handle early dates. (Which makes sense.)
However, I don't understand why it wasn't made an unsigned integer in the first place. Why not just store January 1, 1970 as zero rather than some ridiculous negative number?
Because letting it start at signed −2,147,483,648 is equivalent to letting it start at unsigned 0. It doesn't change the range of a values a 32 bit integer can hold - a 32 bit integer can hold 4,294,967,296 different states. The problem isn't the starting point, the problem is the maximum value which can be held by the integer. Only way to mitigate the problem is to upgrade to 64 bit integers.
Also (as I just realized that): 1970 was set as 0, so we could reach back in time as well. (reaching back to 1901 seemed to be sufficient at the time). If they went unsigned, the epoch would've begun at 1901 to be able to reach back from 1970, and we would have the same problem again.
There's a more fundamental problem here than using unsigned values. If we used unsigned values, then we'd get only one more bit of timekeeping. This would have a definitely positive impact - it would double the amount of time we could keep - but then we'd have a problem much later on in the future. More generally, for any fixed-precision integer value, we'd have a problem along these lines.
When UNIX was being developed in the 1970s, having a 60 year clock sounded fine, though clearly a 120-year clock would have been better. If they had used more bits, then we'd have a much longer clock - say 1000 years - but after that much time elapsed we'd be right back in the same bind and would probably think back and say "why didn't they use more bits?"
Because not all systems have to deal purely with "past" and "future" values. Even in the 70s, when Unix was created and the time system defined, they had to deal with dates back in the 60s or earlier. So, a signed integer made sense.
Once everyone switches to 64bit time_t's, we won't have to worry about a y2038k type problem for another 2billion or so 136-year periods.
Just as background, I'm building an application in Cocoa. This application existed originally in C++ in another environment. I'd like to do as much as possible in Objective-C.
My questions are:
1)
How do I compute, as an integer, the number of milliseconds between now and the previous time I remembered as now?
2)
When used in an objective-C program, including time.h, what are the units of
clock()
Thank you for your help.
You can use CFAbsoluteTimeGetCurrent() but bear in mind the clock can change between two calls and can screw you over. If you want to protect against that you should use CACurrentMediaTime().
The return type of these is CFAbsoluteTime and CFTimeInterval respectively, which are both double by default. So they return the number of seconds with double precision. If you really want an integer you can use mach_absolute_time() found in #include <mach/mach_time.h> which returns a 64 bit integer. This needs a bit of unit conversion, so check out this link for example code. This is what CACurrentMediaTime() uses internally so it's probably best to stick with that.
Computing the difference between two calls is obviously just a subtraction, use a variable to remember the last value.
For the clock function see the documentation here: clock(). Basically you need to divide the return value by CLOCKS_PER_SEC to get the actual time.
How do I compute, as an integer, the number of milliseconds between now and the previous time I remembered as now?
Is there any reason you need it as an integral number of milliseconds? Asking NSDate for the time interval since another date will give you a floating-point number of seconds. If you really do need milliseconds, you can simply multiply by that by 1000 to get a floating-point number of milliseconds. If you really do need an integer, you can round or truncate the floating-point value.
If you'd like to do it with integers from start to finish, use either UpTime or mach_absolute_time to get the current time in absolute units, then use AbsoluteToNanoseconds to convert that to a real-world unit. Obviously, you'll have to divide that by 1,000,000 to get milliseconds.
QA1398 suggests mach_absolute_time, but UpTime is easier, since it returns the same type AbsoluteToNanoseconds uses (no “pointer fun” as shown in the technote).
AbsoluteToNanoseconds returns an UnsignedWide, which is a structure. (This stuff dates back to before Mac machines could handle scalar 64-bit values.) Use the UnsignedWideToUInt64 function to convert it to a scalar. That just leaves the subtraction, which you'll do the normal way.
I'm just curious and can't find the answer anywhere. Usually, we use an integer for a counter in a loop, e.g. in C/C++:
for (int i=0; i<100; ++i)
But we can also use a short integer or even a char. My question is: Does it change the performance? It's a few bytes less so the memory savings are negligible. It just intrigues me if I do any harm by using a char if I know that the counter won't exceed 100.
Probably using the "natural" integer size for the platform will provide the best performance. In C++ this is usually int. However, the difference is likely to be small and you are unlikely to find that this is the performance bottleneck.
Depends on the architecture. On the PowerPC, there's usually a massive performance penalty involved in using anything other than int (or whatever the native word size is) -- eg, don't use short or char. Float is right out, too.
You should time this on your particular architecture because it varies, but in my test cases there was ~20% slowdown from using short instead of int.
I can't provide a citation, but I've heard that you often do incur a little performance overhead by using a short or char.
The memory savings are nonexistant since it's a temporary stack variable. The memory it lives in will almost certainly already be allocated, and you probably won't save anything by using something shorter because the next variable will likely want to be aligned to a larger boundary anyway.
You can use whatever legal type you want in a for; it doesn't have to be integral or even built in. For example, you can use iterators as well:
for( std::vector<std::string>::iterator s = myStrings.begin(); myStrings.end() != s; ++s )
{
...
}
Whether or not it will have an impact on performance comes down to a question of how the operators you use are implemented. So in the above example that means end(), operator!=() and operator++().
This is not really an answer. I'm just exploring what Crashworks said about the PowerPC. As others have pointed out already, using a type that maps to the native word size should yield the shortest code and the best performance.
$ cat loop.c
extern void bar();
void foo()
{
int i;
for (i = 0; i < 42; ++i)
bar();
}
$ powerpc-eabi-gcc -S -O3 -o - loop.c
.
.
.L5:
bl bar
addic. 31,31,-1
bge+ 0,.L5
It is quite different with short i, instead of int i, and looks like won't perform as well either.
.L5:
bl bar
addi 3,31,1
extsh 31,3
cmpwi 7,31,41
ble+ 7,.L5
No, it really shouldn't impact performance.
It probably would have been quicker to type in a quick program (you did the most complex line already) and profile it, than ask this question here. :-)
FWIW, in languages that use bignums by default (Python, Lisp, etc.), I've never seen a profile where a loop counter was the bottleneck. Checking the type tag is not that expensive -- a couple instructions at most -- but probably bigger than the difference between a (fix)int and a short int.
Probably not as long as you don't do it with a float or a double. Since memory is cheap you would probably be best off just using an int.
An unsigned or size_t should, in theory, give you better results ( wow, easy people, we are trying to optimise for evil, and against those shouting 'premature' nonsense. It's the new trend ).
However, it does have its drawbacks, primarily the classic one: screw-up.
Google devs seems to avoid it to but it is pita to fight against std or boost.
If you compile your program with optimization (e.g., gcc -O), it doesn't matter. The compiler will allocate an integer register to the value and never store it in memory or on the stack. If your loop calls a routine, gcc will allocate one of the variables r14-r31 which any called routine will save and restore. So use int, because that causes the least surprise to whomever reads your code.