Random float number generation

Question

How do I generate random floats in C     I thought I could take the integer rand and divide it by something  would that be adequate enough

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Take a look at Boost Random  You could do something like this   float gen random float float min  float max        boost  mt19937 rng      boost  uniform real lt float gt  u min  max       boost  variate generator lt boost  mt19937 amp   boost  uniform real lt float gt   gt  gen rng  u       return gen        Play around  you might do better passing the same mt19937 object around instead of constructing a new one every time  but hopefully you get the idea

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If you know that your floating point format is IEEE 754  almost all modern CPUs including Intel and ARM  then you can build a random floating point number from a random integer using bit-wise methods  This should only be considered if you do not have access to C  11 s random or Boost Random which are both much better   float rand float            returns a random value in the range  0 0-1 0          start with a bit pattern equating to 1 0     uint32 t pattern   0x3f800000          get 23 bits of random integer     uint32 t random23   0x7fffff  amp   rand    lt  lt  8   rand             replace the mantissa  resulting in a number  1 0-2 0      pattern    random23          convert from int to float without undefined behavior     assert sizeof float     sizeof uint32 t        char buffer sizeof float        memcpy buffer   amp pattern  sizeof float        float f      memcpy  amp f  buffer  sizeof float         return f - 1 0      This will give a better distribution than one using division

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drand48 3  is the POSIX standard way  GLibC also provides a reentrant version  drand48 r 3    The function was declared obsolete in SVID 3 but no adequate alternative was provided so IEEE Std 1003 1-2013 still includes it and has no notes that it s going anywhere anytime soon   In Windows  the standard way is CryptGenRandom

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rand   return a int between 0 and RAND MAX    To get a random number between 0 0 and 1 0  first cast the int return by rand   to a float  then divide by RAND MAX

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If you are using C   and not C  then remember that in technical report 1  TR1  and in the C  0x draft they have added facilities for a random number generator in the  header file  I believe it is identical to the Boost Random library and definitely more flexible and  modern  than the C library function  rand   This syntax offers the ability to choose a generator  like the mersenne twister mt19937  and then choose a distribution  normal  bernoulli  binomial etc     Syntax is as follows  shameless borrowed from this site       include  lt iostream gt     include  lt random gt            std  tr1  mt19937 eng      a core engine class    std  tr1  normal distribution lt float gt  dist          for  int i   0  i  lt  10    i                std  cout  lt  lt  dist eng   lt  lt  std  endl

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In modern c   you may use the  lt random gt  header that came with c  11  To get random float s you can use std  uniform real distribution lt  gt    You can use a function to generate the numbers and if you don t want the numbers to be the same all the time  set the engine and distribution to be  static  Example   float get random         static std  default random engine e      static std  uniform real distribution lt  gt  dis 0  1      rage 0 - 1     return dis e       It s ideal to place the float s in a container such as std  vector   int main         std  vector lt float gt  nums      for  int i    i    5    i     Generate 5 random floats         nums emplace back get random          for  const auto amp  i   nums  std  cout  lt  lt  i  lt  lt           Example output   0 0518757 0 969106 0 0985112 0 0895674 0 895542

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On some systems  Windows with VC springs to mind  currently   RAND MAX is ridiculously small  i   e  only 15 bit  When dividing by RAND MAX you are only generating a mantissa of 15 bit instead of the 23 possible bits  This may or may not be a problem for you  but you re missing out some values in that case   Oh  just noticed that there was already a comment for that problem  Anyway  here s some code that might solve this for you   float r    float   rand    lt  lt  15   rand     amp    1  lt  lt  24  - 1      1  lt  lt  24     Untested  but might work  -

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C  11 gives you a lot of new options with random  The canonical paper on this topic would be N3551  Random Number Generation in C  11  To see why using rand   can be problematic see the rand   Considered Harmful presentation material by Stephan T  Lavavej given during the GoingNative 2013 event  The slides are in the comments but here is a direct link   I also cover boost as well as using rand since legacy code may still require its support   The example below is distilled from the cppreference site and uses the std  mersenne twister engine engine and the std  uniform real distribution which generates numbers in the  0 10  interval  with other engines and distributions commented out  see it live     include  lt iostream gt   include  lt iomanip gt   include  lt string gt   include  lt map gt   include  lt random gt   int main         std  random device rd                 Engines             std  mt19937 e2 rd           std  knuth b e2 rd           std  default random engine e2 rd                     Distribtuions            std  uniform real distribution lt  gt  dist 0  10         std  normal distribution lt  gt  dist 2  2         std  student t distribution lt  gt  dist 5         std  poisson distribution lt  gt  dist 2         std  extreme value distribution lt  gt  dist 0 2        std  map lt int  int gt  hist      for  int n   0  n  lt  10000    n              hist std  floor dist e2                for  auto p   hist            std  cout  lt  lt  std  fixed  lt  lt  std  setprecision 1   lt  lt  std  setw 2                     lt  lt  p first  lt  lt       lt  lt  std  string p second 200        lt  lt    n             output will be similar to the following   0      1      2      3      4       5      6       7      8       9        The output will vary depending on which distribution you choose  so if we decided to go with std  normal distribution with a value of 2 for both mean and stddev e g  dist 2  2  instead the output would be similar to this  see it live    -6  -5  -4  -3  -2    -1       0          1            2            3          4       5     6   7   8   9    The following is a modified version of some of the code presented in N3551  see it live      include  lt algorithm gt   include  lt array gt   include  lt iostream gt   include  lt random gt   std  default random engine  amp  global urng          static std  default random engine u        return u      void randomize          static std  random device rd        global urng   seed  rd         int main           Manufacture a deck of cards    using card   int    std  array lt card 52 gt  deck      std  iota deck begin    deck end    0      randomize           std  shuffle deck begin    deck end    global urng          Display each card in the shuffled deck    auto suit       card c     return  SHDC  c   13        auto rank       card c     return  AKQJT98765432  c   13         for  card c   deck         std  cout  lt  lt       lt  lt  rank c   lt  lt  suit c       std  cout  lt  lt  std  endl      Results will look similar to      5H 5S AS 9S 4D 6H TH 6D KH 2S QS 9H 8H 3D KC TD 7H 2D KS 3C TC 7D 4C QH QC QD JD AH JC AC KD 9D 5C 2H 4H 9C 8C JH 5D 4S 7C AD 3S 8S TS 2C 8D 3H 6C JS 7S 6S   Boost  Of course Boost Random is always an option as well  here I am using boost  random  uniform real distribution    include  lt iostream gt   include  lt iomanip gt   include  lt string gt   include  lt map gt   include  lt boost random mersenne twister hpp gt   include  lt boost random uniform real distribution hpp gt   int main         boost  random  mt19937 gen      boost  random  uniform real distribution lt  gt  dist 0  10        std  map lt int  int gt  hist      for  int n   0  n  lt  10000    n              hist std  floor dist gen                for  auto p   hist            std  cout  lt  lt  std  fixed  lt  lt  std  setprecision 1   lt  lt  std  setw 2                     lt  lt  p first  lt  lt       lt  lt  std  string p second 200        lt  lt    n             rand    If you must use rand   then we can go to the C FAQ for a guides on How can I generate floating-point random numbers    which basically gives an example similar to this for generating an on the interval  0 1     include  lt stdlib h gt   double randZeroToOne         return rand      RAND MAX   1        and to generate a random number in the range from  M N    double randMToN double M  double N        return M    rand       RAND MAX    N-M

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In my opinion the above answer do give some  random  float  but none of them is truly a random float  i e  they miss a part of the float representation   Before I will rush into my implementation lets first have a look at the ANSI IEEE standard format for floats    sign  1-bit    e  8-bits      f  23-bit      the number represented by this word is  -1   sign    2 e   1 f  note the the  e  number is a biased  with a bias of 127  number thus ranging from -127 to 126  The most simple  and actually most random  function is to just write the data of a random int into a float  thus  int tmp   rand    float f    float    float   amp tmp     note that if you do float f    float rand    it will convert the integer into a float  thus 10 will become 10 0   So now if you want to limit the maximum value you can do something like  not sure if this works   int tmp   rand    float f      float   amp tmp   tmp    unsigned int f          note float to int conversion  tmp    max number  f -  tmp    but if you look at the structure of the float you can see that the maximum value of a float is  approx  2 127 which is way larger as the maximum value of an int  2 32  thus ruling out a significant part of the numbers that can be represented by a float  This is my final implementation          Function generates a random float using the upper bound float to determine     the upper bound for the exponent and for the fractional part      param min exp sets the minimum number  closest to 0  to 1   e min exp  min -127      param max exp sets the maximum number to 2   e max exp  max 126      param sign flag if sign flag   0 the random number is always positive  if                  sign flag   1 then the sign bit is random as well     return a random float     float randf int min exp  int max exp  char sign flag        assert min exp  lt   max exp        int min exp mod   min exp   126       int sign mod   sign flag   1      int frac mod    1  lt  lt  23        int s   rand     sign mod      note x   1   0     int e    rand     max exp    min exp mod      int f   rand     frac mod       int tmp    s  lt  lt  31     e  lt  lt  23    f       float r    float    float    amp tmp             uncomment if you want to see the structure of the float           printf   x   x   x   x   f n    s  lt  lt  31    e  lt  lt  23   f  tmp  r        return r      using this function randf 0  8  0  will return a random number between 0 0 and 255 0

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rand   can be used to generate pseudo-random numbers in C     In combination with RAND MAX and a little math  you can generate random numbers in any arbitrary interval you choose   This is sufficient for learning purposes and toy programs   If you need truly random numbers with normal distribution  you ll need to employ a more advanced method     This will generate a number from 0 0 to 1 0  inclusive   float r   static cast  lt float gt   rand      static cast  lt float gt   RAND MAX     This will generate a number from 0 0 to some arbitrary float  X   float r2   static cast  lt float gt   rand       static cast  lt float gt   RAND MAX X      This will generate a number from some arbitrary LO to some arbitrary HI   float r3   LO   static cast  lt float gt   rand       static cast  lt float gt   RAND MAX  HI-LO         Note that the rand   function will often not be sufficient if you need truly random numbers     Before calling rand    you must first  seed  the random number generator by calling srand     This should be done once during your program s run -- not once every time you call rand     This is often done like this   srand  static cast  lt unsigned gt   time 0       In order to call rand or srand you must  include  lt cstdlib gt    In order to call time  you must  include  lt ctime gt

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For C    it can generate real float numbers within the range specified by dist variable   include  lt random gt     If it doesnt work then use    include  lt tr1 random gt   include  lt iostream gt   using namespace std   typedef std  tr1  ranlux64 base 01 Myeng   typedef std  tr1  normal distribution lt double gt  Mydist   int main             Myeng eng          eng seed  unsigned int  time NULL      initializing generator to January 1  1970          Mydist dist 1 10            dist reset       discard any cached values         for  int i   0  i  lt  10  i                        std  cout  lt  lt   a random value       lt  lt   int dist eng   lt  lt  std  endl                    return  0

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I wasn t satisfied by any of the answers so far so I wrote a new random float function   It makes bitwise assumptions about the float data type   It still needs a rand   function with at least 15 random bits     Returns a random number in the range  0 0f  1 0f    Every   bit of the mantissa is randomized  float rnd void       Generate a random number in the range  0 5f  1 0f     unsigned int ret   0x3F000000    0x7FFFFF  amp    rand    lt  lt  8    rand        unsigned short coinFlips       If the coin is tails  return the number  otherwise     divide the random number by two by decrementing the     exponent and keep going  The exponent starts at 63      Each loop represents 15 random bits  a k a   coin flips      define RND INNER LOOP         if  coinFlips  amp  1   break        coinFlips  gt  gt   1        ret -  0x800000   for          coinFlips   rand        RND INNER LOOP    RND INNER LOOP    RND INNER LOOP          At this point  the exponent is 60  45  30  15  or 0        If the exponent is 0  then the number equals 0 0f      if     ret  amp  0x3F800000    return 0 0f      RND INNER LOOP    RND INNER LOOP    RND INNER LOOP        RND INNER LOOP    RND INNER LOOP    RND INNER LOOP        RND INNER LOOP    RND INNER LOOP    RND INNER LOOP        RND INNER LOOP    RND INNER LOOP    RND INNER LOOP          return    float     amp ret

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include  lt cstdint gt   include  lt cstdlib gt   include  lt ctime gt   using namespace std      single precision float offers 24bit worth of linear distance from 1 0f to 0 0f    float getval            rand   has min 16bit  but we need a 24bit random number         uint least32 t r    rand    amp  0xffff      rand    amp  0x00ff   lt  lt  16          5 9604645E-8 is  1f - 0 99999994f   0 99999994f is the first value less than 1f         return  double r   5 9604645E-8     int main         srand time NULL          I couldn t post two answers  so here is the second solution   log2 random numbers  massive bias towards 0 0f but it s truly a random float 1 0f to 0 0f    include  lt cstdint gt   include  lt cstdlib gt   include  lt ctime gt   using namespace std   float getval          union UNION           uint32 t i          float f        r         3 because it s 0011  the first bit is the float s sign         Clearing the second bit eliminates values  gt  1 0f              r i    rand     amp  0xffff      rand     amp  0x3fff   lt  lt  16       return r f     int main          srand  time  NULL

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Call the code with two float values  the code works in any range   float rand FloatRange float a  float b        return   b - a      float rand     RAND MAX     a

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