Generate random numbers uniformly over an entire range

Question

I need to generate random numbers within a specified interval   max min    Also  the random numbers should be uniformly distributed over the interval  not located to a particular point   Currenly I am generating as   for int i 0  i lt 6  i          DWORD random   rand    max-min 1    min      From my tests  random numbers are generated around one point only   Example min   3604607  max   7654607    Random numbers generated   3631594 3609293 3630000 3628441 3636376 3621404   From answers below  OK  RAND MAX is 32767  I am on C   Windows platform  Is there any other method to generate random numbers with a uniform distribution

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If you want numbers to be uniformly distributed over the range, you should break your range up into a number of equal sections that represent the number of points you need. Then get a random number with a min/max for each section.

As another note, you should probably not use rand() as it's not very good at actually generating random numbers. I don't know what platform you're running on, but there is probably a better function you can call like random().

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Solution   double  rand      RAND MAX 1      max-min 1    min  Warning  Don t forget due to stretching and possible precision errors  even if RAND MAX were large enough   you ll only be able to generate evenly distributed  bins  and not all numbers in  min max       Solution  Bigrand  Warning  Note that this doubles the bits  but still won t be able to generate all numbers in your range in general  i e   it is not necessarily true that BigRand   will generate all numbers between in its range     Info  Your approach  modulo  is  fine  as long as the range of rand   exceeds your interval range and rand   is  uniform   The error for at most the first max - min numbers is 1  RAND MAX  1    Also  I suggest to switch to the new random packagee in C  11 too  which offers better and more varieties of implementations than rand

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Of course  the following code won t give you random numbers but pseudo random number  Use the following code   define QUICK RAND m n  m     std  rand        n  -  m    1       For example   int myRand   QUICK RAND 10  20     You must call   srand time 0        Initialize random number generator    otherwise the numbers won t be near random

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By their nature  a small sample of random numbers doesn t have to be uniformly distributed   They re random  after all   I agree that if a random number generator is generating numbers that consistently appear to be grouped  then there is probably something wrong with it   But keep in mind that randomness isn t necessarily uniform   Edit  I added  small sample  to clarify

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The solution given by man 3 rand for a number between 1 and 10 inclusive is   j   1    int   10 0    rand      RAND MAX   1 0       In your case  it would be   j   min    int    max-min 1     rand      RAND MAX   1 0       Of course  this is not perfect randomness or uniformity as some other messages are pointing out  but this is enough for most cases

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If you want numbers to be uniformly distributed over the range, you should break your range up into a number of equal sections that represent the number of points you need. Then get a random number with a min/max for each section.

As another note, you should probably not use rand() as it's not very good at actually generating random numbers. I don't know what platform you're running on, but there is probably a better function you can call like random().

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Why rand is a bad idea Most of the answers you got here make use of the rand function and the modulus operator  That method may not generate numbers uniformly  it depends on the range and the value of RAND MAX   and is therefore discouraged  C  11 and generation over a range With C  11 multiple other options have risen  One of which fits your requirements  for generating a random number in a range  pretty nicely  std  uniform int distribution  Here s an example  const int range from    0  const int range to      10  std  random device                  rand dev  std  mt19937                        generator rand dev     std  uniform int distribution lt int gt   distr range from  range to    std  cout  lt  lt  distr generator   lt  lt    n    And here s the running example  Template function may help some  template lt typename T gt  T random T range from  T range to        std  random device                  rand dev      std  mt19937                        generator rand dev         std  uniform int distribution lt T gt     distr range from  range to       return distr generator      Other random generators The  lt random gt  header offers innumerable other random number generators with different kind of distributions including Bernoulli  Poisson and normal  How can I shuffle a container  The standard provides std  shuffle  which can be used as follows  std  vector lt int gt  vec    4  8  15  16  23  42    std  random device random dev  std  mt19937       generator random dev      std  shuffle vec begin    vec end    generator    The algorithm will reorder the elements randomly  with a linear complexity  Boost Random Another alternative  in case you don t have access to a C  11  compiler  is to use Boost Random  Its interface is very similar to the C  11 one

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Check what RAND MAX is on your system -- I m guessing it is only 16 bits  and your range is too big for it   Beyond that see this discussion on  Generating Random Integers within a Desired Range and the notes on using  or not  the C rand   function

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Why rand is a bad idea Most of the answers you got here make use of the rand function and the modulus operator  That method may not generate numbers uniformly  it depends on the range and the value of RAND MAX   and is therefore discouraged  C  11 and generation over a range With C  11 multiple other options have risen  One of which fits your requirements  for generating a random number in a range  pretty nicely  std  uniform int distribution  Here s an example  const int range from    0  const int range to      10  std  random device                  rand dev  std  mt19937                        generator rand dev     std  uniform int distribution lt int gt   distr range from  range to    std  cout  lt  lt  distr generator   lt  lt    n    And here s the running example  Template function may help some  template lt typename T gt  T random T range from  T range to        std  random device                  rand dev      std  mt19937                        generator rand dev         std  uniform int distribution lt T gt     distr range from  range to       return distr generator      Other random generators The  lt random gt  header offers innumerable other random number generators with different kind of distributions including Bernoulli  Poisson and normal  How can I shuffle a container  The standard provides std  shuffle  which can be used as follows  std  vector lt int gt  vec    4  8  15  16  23  42    std  random device random dev  std  mt19937       generator random dev      std  shuffle vec begin    vec end    generator    The algorithm will reorder the elements randomly  with a linear complexity  Boost Random Another alternative  in case you don t have access to a C  11  compiler  is to use Boost Random  Its interface is very similar to the C  11 one

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You should look at RAND MAX for your particular compiler environment  I think you would see these results if rand   is producing a random 16-bit number   you seem to be assuming it will be a 32-bit number    I can t promise this is the answer  but please post your value of RAND MAX  and a little more detail on your environment

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The solution given by man 3 rand for a number between 1 and 10 inclusive is   j   1    int   10 0    rand      RAND MAX   1 0       In your case  it would be   j   min    int    max-min 1     rand      RAND MAX   1 0       Of course  this is not perfect randomness or uniformity as some other messages are pointing out  but this is enough for most cases

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This is not the code  but this logic may help you   static double rnd void       return  1 0    RAND MAX   1 0      double  rand           static void InitBetterRnd unsigned int seed        register int i      srand  seed        for  i   0  i  lt  POOLSIZE  i             pool i    rnd                 This function returns a number between 0 and 1  static double rnd0 1 void         static int i   POOLSIZE-1      double r       i    int  POOLSIZE pool i        r   pool i       pool i    rnd        return  r

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If you are able to  use Boost  I have had good luck with their random library   uniform int should do what you want

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If you are concerned about randomness and not about speed  you should use a secure random number generation method  There are several ways to do this    The easiest one being to use OpenSSL s Random Number Generator   You can also write your own using an encryption algorithm  like AES   By picking a seed and an IV and then continuously re-encrypting the output of the encryption function  Using OpenSSL is easier  but less manly

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If you want numbers to be uniformly distributed over the range, you should break your range up into a number of equal sections that represent the number of points you need. Then get a random number with a min/max for each section.

As another note, you should probably not use rand() as it's not very good at actually generating random numbers. I don't know what platform you're running on, but there is probably a better function you can call like random().

User · Answer

By their nature  a small sample of random numbers doesn t have to be uniformly distributed   They re random  after all   I agree that if a random number generator is generating numbers that consistently appear to be grouped  then there is probably something wrong with it   But keep in mind that randomness isn t necessarily uniform   Edit  I added  small sample  to clarify

User · Answer

If you want numbers to be uniformly distributed over the range, you should break your range up into a number of equal sections that represent the number of points you need. Then get a random number with a min/max for each section.

As another note, you should probably not use rand() as it's not very good at actually generating random numbers. I don't know what platform you're running on, but there is probably a better function you can call like random().

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This should provide a uniform distribution over the range  low  high  without using floats  as long as the overall range is less than RAND MAX   uint32 t rand range low uint32 t low  uint32 t high        uint32 t val         only for 0  lt  range  lt   RAND MAX     assert low  lt  high       assert high - low  lt   RAND MAX        uint32 t range   high-low      uint32 t scale   RAND MAX range      do           val   rand          while  val  gt   scale   range      since scale is truncated  pick a new val until it s lower than scale range     return val scale   low      and for values greater than RAND MAX you want something like  uint32 t rand range uint32 t low  uint32 t high        assert high gt low       uint32 t val      uint32 t range   high-low      if  range  lt  RAND MAX          return rand range low low  high       uint32 t scale   range RAND MAX      do           val   rand     rand range 0  scale    RAND MAX     scale the initial range in RAND MAX steps  then add an offset to get a uniform interval       while  val  gt   range       return val   low      This is roughly how std  uniform int distribution does things

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I just found this on the Internet  This should work   DWORD random     min    rand    RAND MAX   1 0      max  -  min    1

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I just found this on the Internet  This should work   DWORD random     min    rand    RAND MAX   1 0      max  -  min    1

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If you are concerned about randomness and not about speed  you should use a secure random number generation method  There are several ways to do this    The easiest one being to use OpenSSL s Random Number Generator   You can also write your own using an encryption algorithm  like AES   By picking a seed and an IV and then continuously re-encrypting the output of the encryption function  Using OpenSSL is easier  but less manly

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This should provide a uniform distribution over the range  low  high  without using floats  as long as the overall range is less than RAND MAX   uint32 t rand range low uint32 t low  uint32 t high        uint32 t val         only for 0  lt  range  lt   RAND MAX     assert low  lt  high       assert high - low  lt   RAND MAX        uint32 t range   high-low      uint32 t scale   RAND MAX range      do           val   rand          while  val  gt   scale   range      since scale is truncated  pick a new val until it s lower than scale range     return val scale   low      and for values greater than RAND MAX you want something like  uint32 t rand range uint32 t low  uint32 t high        assert high gt low       uint32 t val      uint32 t range   high-low      if  range  lt  RAND MAX          return rand range low low  high       uint32 t scale   range RAND MAX      do           val   rand     rand range 0  scale    RAND MAX     scale the initial range in RAND MAX steps  then add an offset to get a uniform interval       while  val  gt   range       return val   low      This is roughly how std  uniform int distribution does things

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edit  Warning  Do not use rand   for statistics  simulation  cryptography or anything serious      It s good enough to make numbers look random for a typical human in a hurry  no more    See  Jefffrey s reply for better options  or this answer for  crypto-secure random numbers     Generally  the high bits show a better distribution than the low bits  so the recommended way to generate random numbers of a range for simple purposes is     double  rand      RAND MAX 1      max-min 1    min   Note  make sure RAND MAX 1 does not overflow  thanks Demi     The division generates a random number in the interval  0  1    stretch  this to the required range  Only when max-min 1 gets close to RAND MAX you need a  BigRand    function like posted by Mark Ransom   This also avoids some slicing problems due to the modulo  which can worsen your numbers even more     The built-in random number generator isn t guaranteed to have a the quality required for statistical simulations  It is OK for numbers to  look random  to a human  but for a serious application  you should take something better - or at least check its properties  uniform distribution is usually good  but values tend to correlate  and the sequence is deterministic   Knuth has an excellent  if hard-to-read  treatise on random number generators  and I recently found LFSR to be excellent and darn simple to implement  given its properties are OK for you

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By their nature  a small sample of random numbers doesn t have to be uniformly distributed   They re random  after all   I agree that if a random number generator is generating numbers that consistently appear to be grouped  then there is probably something wrong with it   But keep in mind that randomness isn t necessarily uniform   Edit  I added  small sample  to clarify

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By their nature  a small sample of random numbers doesn t have to be uniformly distributed   They re random  after all   I agree that if a random number generator is generating numbers that consistently appear to be grouped  then there is probably something wrong with it   But keep in mind that randomness isn t necessarily uniform   Edit  I added  small sample  to clarify

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If RAND MAX is 32767  you can double the number of bits easily   int BigRand         assert INT MAX  RAND MAX 1   gt  RAND MAX       return rand      RAND MAX 1    rand

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Of course  the following code won t give you random numbers but pseudo random number  Use the following code   define QUICK RAND m n  m     std  rand        n  -  m    1       For example   int myRand   QUICK RAND 10  20     You must call   srand time 0        Initialize random number generator    otherwise the numbers won t be near random

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Check what RAND MAX is on your system -- I m guessing it is only 16 bits  and your range is too big for it   Beyond that see this discussion on  Generating Random Integers within a Desired Range and the notes on using  or not  the C rand   function

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edit  Warning  Do not use rand   for statistics  simulation  cryptography or anything serious      It s good enough to make numbers look random for a typical human in a hurry  no more    See  Jefffrey s reply for better options  or this answer for  crypto-secure random numbers     Generally  the high bits show a better distribution than the low bits  so the recommended way to generate random numbers of a range for simple purposes is     double  rand      RAND MAX 1      max-min 1    min   Note  make sure RAND MAX 1 does not overflow  thanks Demi     The division generates a random number in the interval  0  1    stretch  this to the required range  Only when max-min 1 gets close to RAND MAX you need a  BigRand    function like posted by Mark Ransom   This also avoids some slicing problems due to the modulo  which can worsen your numbers even more     The built-in random number generator isn t guaranteed to have a the quality required for statistical simulations  It is OK for numbers to  look random  to a human  but for a serious application  you should take something better - or at least check its properties  uniform distribution is usually good  but values tend to correlate  and the sequence is deterministic   Knuth has an excellent  if hard-to-read  treatise on random number generators  and I recently found LFSR to be excellent and darn simple to implement  given its properties are OK for you

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If you are able to  use Boost  I have had good luck with their random library   uniform int should do what you want

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If you are able to  use Boost  I have had good luck with their random library   uniform int should do what you want

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You should look at RAND MAX for your particular compiler environment  I think you would see these results if rand   is producing a random 16-bit number   you seem to be assuming it will be a 32-bit number    I can t promise this is the answer  but please post your value of RAND MAX  and a little more detail on your environment

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If you are able to  use Boost  I have had good luck with their random library   uniform int should do what you want

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edit  Warning  Do not use rand   for statistics  simulation  cryptography or anything serious      It s good enough to make numbers look random for a typical human in a hurry  no more    See  Jefffrey s reply for better options  or this answer for  crypto-secure random numbers     Generally  the high bits show a better distribution than the low bits  so the recommended way to generate random numbers of a range for simple purposes is     double  rand      RAND MAX 1      max-min 1    min   Note  make sure RAND MAX 1 does not overflow  thanks Demi     The division generates a random number in the interval  0  1    stretch  this to the required range  Only when max-min 1 gets close to RAND MAX you need a  BigRand    function like posted by Mark Ransom   This also avoids some slicing problems due to the modulo  which can worsen your numbers even more     The built-in random number generator isn t guaranteed to have a the quality required for statistical simulations  It is OK for numbers to  look random  to a human  but for a serious application  you should take something better - or at least check its properties  uniform distribution is usually good  but values tend to correlate  and the sequence is deterministic   Knuth has an excellent  if hard-to-read  treatise on random number generators  and I recently found LFSR to be excellent and darn simple to implement  given its properties are OK for you

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This is the solution I came up with    include   lt stdlib h gt    int32 t RandomRange int32 t min  int32 t max        return  rand      max - min   1     RAND MAX   1     min      This is a bucket solution  conceptually similar to the solutions that use rand     RAND MAX to get a floating point range between 0-1 and then round that into a bucket  However  it uses purely integer math  and takes advantage of integer division flooring to round down the value to the nearest bucket   It makes a few assumptions  First  it assumes that RAND MAX    max - min   1  will always fit within an int32 t  If RAND MAX is 32767 and 32 bit int calculations are used  the the maximum range you can have is 32767  If your implementation has a much larger RAND MAX  you can overcome this by using a larger integer  like int64 t  for the calculation  Secondly  if int64 t is used but RAND MAX is still 32767  at ranges greater than RAND MAX you will start to get  holes  in the possible output numbers  This is probably the biggest issue with any solution derived from scaling rand     Testing over a huge number of iterations nevertheless shows this method to be very uniform for small ranges  However  it is possible  and likely  that mathematically this has some small bias and possibly develops issues when the range approaches RAND MAX  Test it for yourself and decide if it meets your needs

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You should look at RAND MAX for your particular compiler environment  I think you would see these results if rand   is producing a random 16-bit number   you seem to be assuming it will be a 32-bit number    I can t promise this is the answer  but please post your value of RAND MAX  and a little more detail on your environment

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The solution given by man 3 rand for a number between 1 and 10 inclusive is   j   1    int   10 0    rand      RAND MAX   1 0       In your case  it would be   j   min    int    max-min 1     rand      RAND MAX   1 0       Of course  this is not perfect randomness or uniformity as some other messages are pointing out  but this is enough for most cases

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If RAND MAX is 32767  you can double the number of bits easily   int BigRand         assert INT MAX  RAND MAX 1   gt  RAND MAX       return rand      RAND MAX 1    rand

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The solution given by man 3 rand for a number between 1 and 10 inclusive is   j   1    int   10 0    rand      RAND MAX   1 0       In your case  it would be   j   min    int    max-min 1     rand      RAND MAX   1 0       Of course  this is not perfect randomness or uniformity as some other messages are pointing out  but this is enough for most cases

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I just found this on the Internet  This should work   DWORD random     min    rand    RAND MAX   1 0      max  -  min    1

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I d like to complement Angry Shoe s and peterchen s excellent answers with a short overview of the state of the art in 2015   Some good choices  randutils  The randutils library  presentation  is an interesting novelty  offering a simple interface and  declared  robust random capabilities  It has the disadvantages that it adds a dependence on your project and  being new  it has not been extensively tested  Anyway  being free  MIT license  and header-only  I think it s worth a try   Minimal sample  a die roll   include  lt iostream gt   include  randutils hpp  int main         randutils  mt19937 rng rng      std  cout  lt  lt  rng uniform 1 6   lt  lt    n       Even if one is not interested in the library  the website  http   www pcg-random org   provides many interesting articles about the theme of random number generation in general and the C   library in particular   Boost Random  Boost Random  documentation  is the library which inspired C  11 s  lt random gt   with whom shares much of the interface  While theoretically also being an external dependency  Boost has by now a status of  quasi-standard  library  and its Random module could be regarded as the classical choice for good-quality random number generation  It features two advantages with respect to the C  11 solution    it is more portable  just needing compiler support for C  03 its random device uses system-specific methods to offer seeding of good quality   The only small flaw is that the module offering random device is not header-only  one has to compile and link boost random   Minimal sample  a die roll   include  lt iostream gt   include  lt boost random hpp gt   include  lt boost nondet random hpp gt   int main         boost  random  random device                  rand dev      boost  random  mt19937                        generator rand dev         boost  random  uniform int distribution lt  gt      distr 1  6        std  cout  lt  lt  distr generator   lt  lt    n       While the minimal sample does its work well  real programs should use a pair of improvements    make mt19937 a thread local  the generator is quite plump    2 KB  and is better not allocated on the stack seed mt19937 with more than one integer  the Mersenne Twister has a big state and can take benefit of more entropy during initialization    Some not-so-good choices  The C  11 library  While being the most idiomatic solution  the  lt random gt  library does not offer much in exchange for the complexity of its interface even for the basic needs  The flaw is in std  random device  the Standard does not mandate any minimal quality for its output  as long as entropy   returns 0  and  as of 2015  MinGW  not the most used compiler  but hardly an esoterical choice  will always print 4 on the minimal sample    Minimal sample  a die roll   include  lt iostream gt   include  lt random gt  int main         std  random device                  rand dev      std  mt19937                        generator rand dev         std  uniform int distribution lt int gt   distr 1  6        std  cout  lt  lt  distr generator   lt  lt    n       If the implementation is not rotten  this solution should be equivalent to the Boost one  and the same suggestions apply   Godot s solution  Minimal sample  a die roll   include  lt iostream gt   include  lt random gt   int main         std  cout  lt  lt  std  randint 1 6       This is a simple  effective and neat solution  Only defect  it will take a while to compile     about two years  providing C  17 is released on time and the experimental randint function is approved into the new Standard  Maybe by that time also the guarantees on the seeding quality will improve   The worse-is-better solution  Minimal sample  a die roll   include  lt cstdlib gt   include  lt ctime gt   include  lt iostream gt   int main         std  srand std  time nullptr        std  cout  lt  lt   std  rand     6   1       The old C solution is considered harmful  and for good reasons  see the other answers here or this detailed analysis   Still  it has its advantages  is is simple  portable  fast and honest  in the sense it is known that the random numbers one gets are hardly decent  and therefore one is not tempted to use them for serious purposes   The accounting troll solution  Minimal sample  a die roll   include  lt iostream gt   int main         std  cout  lt  lt  9       http   dilbert com strip 2001-10-25     While 9 is a somewhat unusual outcome for a regular die roll  one has to admire the excellent combination of good qualities in this solution  which manages to be the fastest  simplest  most cache-friendly and most portable one  By substituting 9 with 4 one gets a perfect generator for any kind of Dungeons and Dragons die  while still avoiding the symbol-laden values 1  2 and 3  The only small flaw is that  because of the bad temper of Dilbert s accounting trolls  this program actually engenders undefined behavior

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Check what RAND MAX is on your system -- I m guessing it is only 16 bits  and your range is too big for it   Beyond that see this discussion on  Generating Random Integers within a Desired Range and the notes on using  or not  the C rand   function

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I d like to complement Angry Shoe s and peterchen s excellent answers with a short overview of the state of the art in 2015   Some good choices  randutils  The randutils library  presentation  is an interesting novelty  offering a simple interface and  declared  robust random capabilities  It has the disadvantages that it adds a dependence on your project and  being new  it has not been extensively tested  Anyway  being free  MIT license  and header-only  I think it s worth a try   Minimal sample  a die roll   include  lt iostream gt   include  randutils hpp  int main         randutils  mt19937 rng rng      std  cout  lt  lt  rng uniform 1 6   lt  lt    n       Even if one is not interested in the library  the website  http   www pcg-random org   provides many interesting articles about the theme of random number generation in general and the C   library in particular   Boost Random  Boost Random  documentation  is the library which inspired C  11 s  lt random gt   with whom shares much of the interface  While theoretically also being an external dependency  Boost has by now a status of  quasi-standard  library  and its Random module could be regarded as the classical choice for good-quality random number generation  It features two advantages with respect to the C  11 solution    it is more portable  just needing compiler support for C  03 its random device uses system-specific methods to offer seeding of good quality   The only small flaw is that the module offering random device is not header-only  one has to compile and link boost random   Minimal sample  a die roll   include  lt iostream gt   include  lt boost random hpp gt   include  lt boost nondet random hpp gt   int main         boost  random  random device                  rand dev      boost  random  mt19937                        generator rand dev         boost  random  uniform int distribution lt  gt      distr 1  6        std  cout  lt  lt  distr generator   lt  lt    n       While the minimal sample does its work well  real programs should use a pair of improvements    make mt19937 a thread local  the generator is quite plump    2 KB  and is better not allocated on the stack seed mt19937 with more than one integer  the Mersenne Twister has a big state and can take benefit of more entropy during initialization    Some not-so-good choices  The C  11 library  While being the most idiomatic solution  the  lt random gt  library does not offer much in exchange for the complexity of its interface even for the basic needs  The flaw is in std  random device  the Standard does not mandate any minimal quality for its output  as long as entropy   returns 0  and  as of 2015  MinGW  not the most used compiler  but hardly an esoterical choice  will always print 4 on the minimal sample    Minimal sample  a die roll   include  lt iostream gt   include  lt random gt  int main         std  random device                  rand dev      std  mt19937                        generator rand dev         std  uniform int distribution lt int gt   distr 1  6        std  cout  lt  lt  distr generator   lt  lt    n       If the implementation is not rotten  this solution should be equivalent to the Boost one  and the same suggestions apply   Godot s solution  Minimal sample  a die roll   include  lt iostream gt   include  lt random gt   int main         std  cout  lt  lt  std  randint 1 6       This is a simple  effective and neat solution  Only defect  it will take a while to compile     about two years  providing C  17 is released on time and the experimental randint function is approved into the new Standard  Maybe by that time also the guarantees on the seeding quality will improve   The worse-is-better solution  Minimal sample  a die roll   include  lt cstdlib gt   include  lt ctime gt   include  lt iostream gt   int main         std  srand std  time nullptr        std  cout  lt  lt   std  rand     6   1       The old C solution is considered harmful  and for good reasons  see the other answers here or this detailed analysis   Still  it has its advantages  is is simple  portable  fast and honest  in the sense it is known that the random numbers one gets are hardly decent  and therefore one is not tempted to use them for serious purposes   The accounting troll solution  Minimal sample  a die roll   include  lt iostream gt   int main         std  cout  lt  lt  9       http   dilbert com strip 2001-10-25     While 9 is a somewhat unusual outcome for a regular die roll  one has to admire the excellent combination of good qualities in this solution  which manages to be the fastest  simplest  most cache-friendly and most portable one  By substituting 9 with 4 one gets a perfect generator for any kind of Dungeons and Dragons die  while still avoiding the symbol-laden values 1  2 and 3  The only small flaw is that  because of the bad temper of Dilbert s accounting trolls  this program actually engenders undefined behavior

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If RAND MAX is 32767  you can double the number of bits easily   int BigRand         assert INT MAX  RAND MAX 1   gt  RAND MAX       return rand      RAND MAX 1    rand

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Solution   double  rand      RAND MAX 1      max-min 1    min  Warning  Don t forget due to stretching and possible precision errors  even if RAND MAX were large enough   you ll only be able to generate evenly distributed  bins  and not all numbers in  min max       Solution  Bigrand  Warning  Note that this doubles the bits  but still won t be able to generate all numbers in your range in general  i e   it is not necessarily true that BigRand   will generate all numbers between in its range     Info  Your approach  modulo  is  fine  as long as the range of rand   exceeds your interval range and rand   is  uniform   The error for at most the first max - min numbers is 1  RAND MAX  1    Also  I suggest to switch to the new random packagee in C  11 too  which offers better and more varieties of implementations than rand

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I just found this on the Internet  This should work   DWORD random     min    rand    RAND MAX   1 0      max  -  min    1

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edit  Warning  Do not use rand   for statistics  simulation  cryptography or anything serious      It s good enough to make numbers look random for a typical human in a hurry  no more    See  Jefffrey s reply for better options  or this answer for  crypto-secure random numbers     Generally  the high bits show a better distribution than the low bits  so the recommended way to generate random numbers of a range for simple purposes is     double  rand      RAND MAX 1      max-min 1    min   Note  make sure RAND MAX 1 does not overflow  thanks Demi     The division generates a random number in the interval  0  1    stretch  this to the required range  Only when max-min 1 gets close to RAND MAX you need a  BigRand    function like posted by Mark Ransom   This also avoids some slicing problems due to the modulo  which can worsen your numbers even more     The built-in random number generator isn t guaranteed to have a the quality required for statistical simulations  It is OK for numbers to  look random  to a human  but for a serious application  you should take something better - or at least check its properties  uniform distribution is usually good  but values tend to correlate  and the sequence is deterministic   Knuth has an excellent  if hard-to-read  treatise on random number generators  and I recently found LFSR to be excellent and darn simple to implement  given its properties are OK for you

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If you are concerned about randomness and not about speed  you should use a secure random number generation method  There are several ways to do this    The easiest one being to use OpenSSL s Random Number Generator   You can also write your own using an encryption algorithm  like AES   By picking a seed and an IV and then continuously re-encrypting the output of the encryption function  Using OpenSSL is easier  but less manly

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This is not the code  but this logic may help you   static double rnd void       return  1 0    RAND MAX   1 0      double  rand           static void InitBetterRnd unsigned int seed        register int i      srand  seed        for  i   0  i  lt  POOLSIZE  i             pool i    rnd                 This function returns a number between 0 and 1  static double rnd0 1 void         static int i   POOLSIZE-1      double r       i    int  POOLSIZE pool i        r   pool i       pool i    rnd        return  r

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Check what RAND MAX is on your system -- I m guessing it is only 16 bits  and your range is too big for it   Beyond that see this discussion on  Generating Random Integers within a Desired Range and the notes on using  or not  the C rand   function

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If RAND MAX is 32767  you can double the number of bits easily   int BigRand         assert INT MAX  RAND MAX 1   gt  RAND MAX       return rand      RAND MAX 1    rand

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You should look at RAND MAX for your particular compiler environment  I think you would see these results if rand   is producing a random 16-bit number   you seem to be assuming it will be a 32-bit number    I can t promise this is the answer  but please post your value of RAND MAX  and a little more detail on your environment

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If you are concerned about randomness and not about speed  you should use a secure random number generation method  There are several ways to do this    The easiest one being to use OpenSSL s Random Number Generator   You can also write your own using an encryption algorithm  like AES   By picking a seed and an IV and then continuously re-encrypting the output of the encryption function  Using OpenSSL is easier  but less manly

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This is the solution I came up with    include   lt stdlib h gt    int32 t RandomRange int32 t min  int32 t max        return  rand      max - min   1     RAND MAX   1     min      This is a bucket solution  conceptually similar to the solutions that use rand     RAND MAX to get a floating point range between 0-1 and then round that into a bucket  However  it uses purely integer math  and takes advantage of integer division flooring to round down the value to the nearest bucket   It makes a few assumptions  First  it assumes that RAND MAX    max - min   1  will always fit within an int32 t  If RAND MAX is 32767 and 32 bit int calculations are used  the the maximum range you can have is 32767  If your implementation has a much larger RAND MAX  you can overcome this by using a larger integer  like int64 t  for the calculation  Secondly  if int64 t is used but RAND MAX is still 32767  at ranges greater than RAND MAX you will start to get  holes  in the possible output numbers  This is probably the biggest issue with any solution derived from scaling rand     Testing over a huge number of iterations nevertheless shows this method to be very uniform for small ranges  However  it is possible  and likely  that mathematically this has some small bias and possibly develops issues when the range approaches RAND MAX  Test it for yourself and decide if it meets your needs

[c++] Generate random numbers uniformly over an entire range

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