How do I print a double value with full precision using cout

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In my earlier question I was printing a double using cout that got rounded when I wasn t expecting it   How can I make cout print a double using full precision

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C  20 std  format This great new C   library feature has the advantage of not affecting the state of std  cout as std  setprecision does   include  lt format gt   include  lt string gt   int main         std  cout  lt  lt  std  format  quot    2     3  n quot   3 1415  3 1415      Expected output  3 14 3 145  The as mentioned at https   stackoverflow com a 65329803 895245 not if you don t pass the precision explicitly it prints the shortest decimal representation with a round-trip guarantee  TODO understand in more detail how it compares to  dbl  max digits10 as shown at https   stackoverflow com a 554134 895245 with          include  lt format gt   include  lt limits gt   include  lt string gt   int main         std  cout  lt  lt  std  format  quot        n quot           3 1415926535897932384626433  dbl  max digits10      See also   Set back default floating point print precision in C   for how to restore the initial precision in pre-c  20 std  string formatting like sprintf https   en cppreference com w cpp utility format formatter Standard format specification

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printf    12f   M PI       12f means floating point  with precision of 12 digits

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In C  20 you ll be able to use std  format to do this  std  cout  lt  lt  std  format  quot    quot   M PI    Output  assuming IEEE754 double   3 141592653589793  The default floating-point format is the shortest decimal representation with a round-trip guarantee  The advantage of this method compared to the setprecision I O manipulator is that it doesn t print unnecessary digits  In the meantime you can use the  fmt  library  std  format is based on   fmt  also provides the print function that makes this even easier and more efficient  godbolt   fmt  print  quot    quot   M PI    Disclaimer  I m the author of  fmt  and C  20 std  format

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This will show the value up to two decimal places after the dot   include  lt iostream gt   include  lt iomanip gt   double d   2 0  int n   2  cout  lt  lt  fixed  lt  lt  setprecision n   lt  lt  d   See here  Fixed-point notation std  fixed  Use fixed floating-point notation Sets the floatfield format flag for the str stream to fixed  When floatfield is set to fixed  floating-point values are written using fixed-point notation  the value is represented with exactly as many digits in the decimal part as specified by the precision field  precision  and with no exponent part   std  setprecision  Set decimal precision Sets the decimal precision to be used to format floating-point values on output operations   If you re familiar with the IEEE standard for representing the floating-points  you would know that it is impossible to show floating-points with full-precision out of the scope of the standard  that is to say  it will always result in a rounding of the real value  You need to first check whether the value is within the scope  if yes  then use  cout  lt  lt  defaultfloat  lt  lt  d    std  defaultfloat  Use default floating-point notation Sets the floatfield format flag for the str stream to defaultfloat  When floatfield is set to defaultfloat  floating-point values are written using the default notation  the representation uses as many meaningful digits as needed up to the stream s decimal precision  precision   counting both the digits before and after the decimal point  if any    That is also the default behavior of cout  which means you don t use it explicitly

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The iostreams way is kind of clunky   I prefer using boost  lexical cast because it calculates the right precision for me   And it s fast  too    include  lt string gt   include  lt boost lexical cast hpp gt   using boost  lexical cast  using std  string   double d   3 14159265358979  cout  lt  lt   Pi     lt  lt  lexical cast lt string gt  d   lt  lt  endl    Output      Pi  3 14159265358979

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You can set the precision directly on std  cout and use the std  fixed format specifier   double d   3 14159265358979  cout precision 17   cout  lt  lt   Pi     lt  lt  fixed  lt  lt  d  lt  lt  endl    You can  include  lt limits gt  to get the maximum precision of a float or double    include  lt limits gt   typedef std  numeric limits lt  double  gt  dbl   double d   3 14159265358979  cout precision dbl  max digits10   cout  lt  lt   Pi     lt  lt  d  lt  lt  endl

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With ostream  precision int   cout precision  numeric limits lt double gt   digits10   1   cout  lt  lt  M PI  lt  lt        lt  lt  M E  lt  lt  endl    will yield  3 141592653589793  2 718281828459045   Why you have to say   1  I have no clue  but the extra digit you get out of it is correct

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IEEE 754 floating point values are stored using base 2 representation  Any base 2 number can be represented as a decimal  base 10  to full precision  None of the proposed answers  however  do  They all truncate the decimal value  This seems to be due to a misinterpretation of what std  numeric limits lt T gt   max digits10 represents   The value of std  numeric limits lt T gt   max digits10 is the number of base-10 digits that are necessary to uniquely represent all distinct values of the type T   In other words  It s the  worst-case  number of digits required to output if you want to roundtrip from binary to decimal to binary  without losing any information  If you output at least max digits10 decimals and reconstruct a floating point value  you are guaranteed to get the exact same binary representation you started with  What s important  max digits10 in general neither yields the shortest decimal  nor is it sufficient to represent the full precision  I m not aware of a constant in the C   Standard Library that encodes the maximum number of decimal digits required to contain the full precision of a floating point value  I believe it s something like 767 for doubles1  One way to output a floating point value with full precision would be to use a sufficiently large value for the precision  like so2  and have the library strip any trailing zeros   include  lt iostream gt   int main         double d   0 1      std  cout precision 767       std  cout  lt  lt   quot d    quot   lt  lt  d  lt  lt  std  endl     This produces the following output  that contains the full precision  d   0 1000000000000000055511151231257827021181583404541015625  Note that this has significantly more decimals than max digits10 would suggest   While that answers the question that was asked  a far more common goal would be to get the shortest decimal representation of any given floating point value  that retains all information  Again  I m not aware of any way to instruct the Standard I O library to output that value  Starting with C  17 the possibility to do that conversion has finally arrived in C   in the form of std  to chars  By default  it produces the shortest decimal representation of any given floating point value that retains the entire information  Its interface is a bit clunky  and you d probably want to wrap this up into a function template that returns something you can output to std  cout  like a std  string   e g   include  lt charconv gt   include  lt array gt   include  lt string gt   include  lt system error gt    include  lt iostream gt   include  lt cmath gt   template lt typename T gt  std  string to string T value           24 characters is the longest decimal representation of any double value     std  array lt char  24 gt  buffer         auto const res   std  to chars buffer data    buffer data     buffer size    value         if  res ec    std  errc                      Success         return std  string buffer data    res ptr                 Error     return    quot FAILED  quot        int main         auto value   0 1f        std  cout  lt  lt  to string value   lt  lt  std  endl      value   std  nextafter value  INFINITY       std  cout  lt  lt  to string value   lt  lt  std  endl      value   std  nextafter value  INFINITY       std  cout  lt  lt  to string value   lt  lt  std  endl     This would print out  using Microsoft s C   Standard Library   0 1 0 10000001 0 10000002   1 From Stephan T  Lavavej s CppCon 2019 talk titled Floating-Point  lt charconv gt   Making Your Code 10x Faster With C  17 s Final Boss   The entire talk is worth watching   2 This would also require using a combination of scientific and fixed  whichever is shorter  I m not aware of a way to set this mode using the C   Standard I O library

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Most portably      include  lt limits gt   using std  numeric limits               cout precision numeric limits lt double gt   digits10   1       cout  lt  lt  d

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Here is how to display a double with full precision   double d   100 0000000000005  int precision   std  numeric limits lt double gt   max digits10  std  cout  lt  lt  std  setprecision precision   lt  lt  d  lt  lt  std  endl    This displays      100 0000000000005    max digits10 is the number of digits that are necessary to uniquely represent all distinct double values  max digits10 represents the number of digits before and after the decimal point    Don t use set precision max digits10  with std  fixed  On fixed notation  set precision   sets the number of digits only after the decimal point  This is incorrect as max digits10 represents the number of digits before and after the decimal point   double d   100 0000000000005  int precision   std  numeric limits lt double gt   max digits10  std  cout  lt  lt  std  fixed  lt  lt  std  setprecision precision   lt  lt  d  lt  lt  std  endl    This displays incorrect result      100 00000000000049738   Note  Header files required   include  lt iomanip gt   include  lt limits gt

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By full precision  I assume mean enough precision to show the best approximation to the intended value  but it should be pointed out that double is stored using base 2 representation and base 2 can t represent something as trivial as 1 1 exactly   The only way to get the full-full precision of the actual double  with NO ROUND OFF ERROR  is to print out the binary bits  or hex nybbles   One way of doing that is using a union to type-pun the double to a integer and then printing the integer  since integers do not suffer from truncation or round-off issues   Type punning like this is not supported by the C   standard  but it is supported in C  However  most C   compilers will probably print out the correct value anyways   I think g   supports this   union       double d      uint64 t u64    x  x d   1 1  std  cout  lt  lt  std  hex  lt  lt  x u64   This will give you the 100  accurate precision of the double    and be utterly unreadable because humans can t read IEEE double format    Wikipedia has a good write up on how to interpret the binary bits  In newer C    you can do std  cout  lt  lt  std  hexfloat  lt  lt  1 1

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Here is a function that works for any floating-point type  not just double  and also puts the stream back the way it was found afterwards  Unfortunately it won t interact well with threads  but that s the nature of iostreams  You ll need these includes at the start of your file   include  lt limits gt   include  lt iostream gt   Here s the function  you could it in a header file if you use it a lot  template  lt class T gt  void printVal std  ostream amp  os  T val        auto oldFlags   os flags        auto oldPrecision   os precision         os flags oldFlags  amp   std  ios base  floatfield       os precision std  numeric limits lt T gt   digits10       os  lt  lt  val           os flags oldFlags       os precision oldPrecision      Use it like this  double d   foo    float f   bar    printVal std  cout  d   printVal std  cout  f    If you want to be able to use the normal insertion  lt  lt  operator  you can use this extra wrapper code  template  lt class T gt  struct PrintValWrapper   T val     template  lt class T gt  std  ostream amp  operator lt  lt  std  ostream amp  os  PrintValWrapper lt T gt  pvw        printVal os  pvw val       return os    template  lt class T gt  PrintValWrapper lt T gt  printIt T val        return PrintValWrapper lt T gt  val      Now you can use it like this  double d   foo    float f   bar    std  cout  lt  lt   quot The values are   quot   lt  lt  printIt d   lt  lt   quot    quot   lt  lt  printIt f   lt  lt    n

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Use std  setprecision   std  cout  lt  lt  std  setprecision  15   lt  lt  3 14159265358979  lt  lt  std  endl

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How do I print a double value with full precision using cout    Use hexfloat or use scientific and set the precision  std  cout precision std  numeric limits lt double gt   max digits10 - 1   std  cout  lt  lt  std  scientific  lt  lt   1 0 7 0  lt  lt    n       C  11 Typical output 1 4285714285714285e-01     Too many answers address only one of 1  base 2  fixed scientific layout or 3  precision   Too many answers with precision do not provide the proper value needed  Hence this answer to a old question    What base    A double is certainly encoded using base 2   A direct approach with C  11 is to print using std  hexfloat  If a non-decimal output is acceptable  we are done   std  cout  lt  lt   hexfloat     lt  lt  std  hexfloat  lt  lt  exp  -100   lt  lt    n   std  cout  lt  lt   hexfloat     lt  lt  std  hexfloat  lt  lt  exp   100   lt  lt    n      output hexfloat  0x1 a8c1f14e2af5dp-145 hexfloat  0x1 3494a9b171bf5p 144      Otherwise  fixed or scientific    A double is a floating point type  not fixed point     Do not use std  fixed as that fails to print small double as anything but 0 000   000   For large double  it prints many digits  perhaps hundreds of questionable informativeness   std  cout  lt  lt   std  fixed     lt  lt  std  fixed  lt  lt  exp  -100   lt  lt    n   std  cout  lt  lt   std  fixed     lt  lt  std  fixed  lt  lt  exp   100   lt  lt    n      output std  fixed  0 000000 std  fixed  26881171418161356094253400435962903554686976 000000    To print with full precision  first use std  scientific which will  write floating-point values in scientific notation    Notice the default of 6 digits after the decimal point  an insufficient amount  is handled in the next point   std  cout  lt  lt   std  scientific     lt  lt  std  scientific  lt  lt  exp  -100   lt  lt    n     std  cout  lt  lt   std  scientific     lt  lt  std  scientific  lt  lt  exp   100   lt  lt    n      output std  scientific  3 720076e-44 std  scientific  2 688117e 43      How much precision  how many total digits     A double encoded using the binary base 2 encodes the same precision between various powers of 2   This is often 53 bits     1 0   2 0  there are 253 different double   2 0   4 0  there are 253 different double   4 0   8 0  there are 253 different double   8 0   10 0  there are 2 8   253 different double   Yet if code prints in decimal with N significant digits  the number of combinations  1 0   10 0  is 9 10   10N     Whatever N  precision  is chosen  there will not be a one-to-one mapping between double and decimal text   If a fixed N is chosen  sometimes it will be slightly more or less than truly needed for certain double values   We could error on too few  a  below  or too many  b  below    3 candidate N   a  Use an N so when converting from text-double-text we arrive at the same text for all double   std  cout  lt  lt  dbl  digits10  lt  lt    n      Typical output 15   b  Use an N so when converting from double-text-double we arrive at the same double for all double      C  11 std  cout  lt  lt  dbl  max digits10  lt  lt    n      Typical output 17   When max digits10 is not available  note that due to base 2 and base 10 attributes  digits10   2  lt   max digits10  lt   digits10   3  we can use digits10   3 to insure enough decimal digits are printed     c  Use an N that varies with the value   This can be useful when code wants to display minimal text  N    1  or the exact value of a double  N    1000-ish in the case of denorm min    Yet since this is  work  and not likely OP s goal  it will be set aside     It is usually b  that is used to  print a double value with full precision    Some applications may prefer a  to error on not providing too much information   With  scientific   precision   sets the number of digits to print after the decimal point  so 1    precision   digits are printed   Code needs max digits10 total digits so  precision   is called with a max digits10 - 1   typedef std  numeric limits lt  double  gt  dbl  std  cout precision dbl  max digits10 - 1   std  cout  lt  lt  std  scientific  lt  lt   exp  -100   lt  lt    n   std  cout  lt  lt  std  scientific  lt  lt   exp   100   lt  lt    n      Typical output 3 7200759760208361e-44 2 6881171418161356e 43   1234567890123456  17 total digits   Similar C question

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Here is what I would use   std  cout  lt  lt  std  setprecision  std  numeric limits lt double gt   digits10   1             lt  lt  3 14159265358979            lt  lt  std  endl    Basically the limits package has traits for all the build in types  One of the traits for floating point numbers  float double long double  is the digits10 attribute  This defines the accuracy  I forget the exact terminology  of a floating point number in base 10   See  http   www cplusplus com reference std limits numeric limits html For details about other attributes

[c++] How do I print a double value with full precision using cout?

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