How to round up the result of integer division

Question

I m thinking in particular of how to display pagination controls  when using a language such as C  or Java   If I have x items which I want to display in chunks of y per page  how many pages will be needed

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I had a similar need where I needed to convert Minutes to hours  amp  minutes  What I used was   int hrs   0  int mins   0   float tm   totalmins   if   tm  gt  60     hrs    int   tm   60    mins    int   tm -  hrs   60     System out println  Total time in Hours  amp  Minutes       hrs         mins

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Another alternative is to use the mod   function  or       If there is a non-zero remainder then increment the integer result of the division

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HOW TO ROUND UP THE RESULT OF INTEGER DIVISION IN C  I was interested to know what the best way is to do this in C  since I need to do this in a loop up to nearly 100k times  Solutions posted by others using Math are ranked high in the answers  but in testing I found them slow  Jarod Elliott proposed a better tactic in checking if mod produces anything  int result    int1   int2   if  int1   int2    0    result       I ran this in a loop 1 million times and it took 8ms  Here is the code using Math  int result    int Math Ceiling  double int1    double int2    Which ran at 14ms in my testing  considerably longer

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The integer math solution that Ian provided is nice  but suffers from an integer overflow bug  Assuming the variables are all int  the solution could be rewritten to use long math and avoid the bug   int pageCount    -1L   records   recordsPerPage    recordsPerPage   If records is a long  the bug remains  The modulus solution does not have the bug

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A generic method  whose result you can iterate over may be of interest   public static Object     chunk Object   src  int chunkSize         int overflow   src length chunkSize      int numChunks    src length chunkSize     overflow gt 0 1 0       Object     dest   new Object numChunks               for  int i 0  i lt numChunks  i              dest i    new Object   i lt numChunks-1    overflow  0    chunkSize   overflow            System arraycopy src  i chunkSize  dest i   0  dest i  length              return dest

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Found an elegant solution   int pageCount    records   recordsPerPage - 1    recordsPerPage    Source  Number Conversion  Roland Backhouse  2001

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For records    0  rjmunro s solution gives 1   The correct solution is 0   That said  if you know that records   0  and I m sure we ve all assumed recordsPerPage   0   then rjmunro solution gives correct results and does not have any of the overflow issues   int pageCount   0  if  records  gt  0        pageCount      records - 1    recordsPerPage    1        no else required   All the integer math solutions are going to be more efficient than any of the floating point solutions

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You ll want to do floating point division  and then use the ceiling function  to round up the value to the next integer

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A variant of Nick Berardi s answer that avoids a branch   int q   records   recordsPerPage  r   records   recordsPerPage  int pageCount   q -  -r  gt  gt   Integer SIZE - 1      Note   -r  gt  gt   Integer SIZE - 1   consists of the sign bit of r  repeated 32 times  thanks to sign extension of the  gt  gt  operator    This evaluates to 0 if r is zero or negative  -1 if r is positive   So subtracting it from q has the effect of adding 1 if records   recordsPerPage  gt  0

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Converting to floating point and back seems like a huge waste of time at the CPU level   Ian Nelson s solution   int pageCount    records   recordsPerPage - 1    recordsPerPage    Can be simplified to   int pageCount    records - 1    recordsPerPage   1    AFAICS  this doesn t have the overflow bug that Brandon DuRette pointed out  and because it only uses it once  you don t need to store the recordsPerPage specially if it comes from  an expensive function to fetch the value from a config file or something   I e  this might be inefficient  if config fetch value used a database lookup or something   int pageCount    records   config fetch value  records per page   - 1    config fetch value  records per page      This creates a variable you don t really need  which probably has  minor  memory implications and is just too much typing   int recordsPerPage   config fetch value  records per page   int pageCount    records   recordsPerPage - 1    recordsPerPage    This is all one line  and only fetches the data once   int pageCount    records - 1    config fetch value  records per page     1

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For C  the solution is to cast the values to a double  as Math Ceiling takes a double    int nPages    int Math Ceiling  double nItems    double nItemsPerPage     In java you should do the same with Math ceil

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This should give you what you want   You will definitely want x items divided by y items per page  the problem is when uneven numbers come up  so if there is a partial page we also want to add one page   int x   number of items  int y   items per page      with out library int pages   x y    x   y  gt  0   1   0      with library int pages    int Math Ceiling  double x    double y

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Alternative to remove branching in testing for zero   int pageCount    records   recordsPerPage - 1    recordsPerPage    records    0     Not sure if this will work in C   should do in C C

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I do the following  handles any overflows   var totalPages   totalResults IsDivisble recordsperpage    totalResults  recordsperpage    totalResults  recordsperpage    1    And use this extension for if there s 0 results   public static bool IsDivisble this int x  int n               return  x n     0      Also  for the current page number  wasn t asked but could be useful    var currentPage    int  Math Ceiling recordsperpage  double  recordsperpage    1

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In need of an extension method        public static int DivideUp this int dividend  int divisor                return  dividend    divisor - 1     divisor          No checks here  overflow  DivideByZero  etc   feel free to add if you like  By the way  for those worried about method invocation overhead  simple functions like this might be inlined by the compiler anyways  so I don t think that s where to be concerned  Cheers   P S  you might find it useful to be aware of this as well  it gets the remainder         int remainder       int result   Math DivRem dividend  divisor  out remainder

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The following should do rounding better than the above solutions  but at the expense of performance  due to floating point calculation of 0 5 rctDenominator    uint64 t integerDivide  const uint64 t amp  rctNumerator  const uint64 t amp  rctDenominator          Ensure  5 upwards is rounded up  otherwise integer division just truncates - ie gives no remainder    return  rctDenominator    0    0    rctNumerator    int  0 5 rctDenominator     rctDenominator

[c#] How to round up the result of integer division?

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