How to use the PI constant in C

Question

I want to use the PI constant and trigonometric functions in some C   program  I get the trigonometric functions with include  lt math h gt   However  there doesn t seem to be a definition for PI in this header file   How can I get PI without defining it manually

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include  lt cmath gt  const long double pi   acos -1 L

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Values like M PI  M PI 2  M PI 4  etc are not standard C   so a constexpr seems a better solution  Different const expressions can be formulated that calculate the same pi and it concerns me whether they  all  provide me the full accuracy  The C   standard does not explicitly mention how to calculate pi  Therefore  I tend to fall back to defining pi manually  I would like to share the solution below which supports all kind of fractions of pi in full accuracy    include  lt ratio gt   include  lt iostream gt   template lt typename RATIO gt  constexpr double dpipart         long double const pi   3 14159265358979323846264338327950288419716939937510582097494459230781640628620899863      return static cast lt double gt  pi   RATIO  num   RATIO  den      int main         std  cout  lt  lt  dpipart lt std  ratio lt -1  6 gt  gt     lt  lt  std  endl

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Standard C   doesn t have a constant for PI   Many C   compilers define M PI in cmath  or in math h for C  as a non-standard extension   You may have to  define  USE MATH DEFINES before you can see it

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You can do this    include  lt cmath gt   ifndef M PI  define M PI  3 14159265358979323846   endif   If M PI is already defined in cmath  this won t do anything else than include cmath  If M PI isn t defined  which is the case for example in Visual Studio   it will define it  In both cases  you can use M PI to get the value of pi   This value of pi comes from Qt Creator s qmath h

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Since the official standard library doesn t define a constant PI you would have to define it yourself  So the answer to your question  How can I get PI without defining it manually   is  You don t -- or you rely on some compiler-specific extensions    If you re not concerned about portability you could check your compiler s manual for this   C   allows you to write  const double PI   std  atan 1 0  4    but the initialization of this constant is not guaranteed to be static  The G   compiler however handles those math functions as intrinsics and is able to compute this constant expression at compile-time

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I just came across this article by Danny Kalev which has a great tip for C  14 and up   template lt typename T gt  constexpr T pi   T 3 1415926535897932385     I thought this was pretty cool  though I would use the highest precision PI in there I could   especially because templates can use it based on type   template lt typename T gt  T circular area T r      return pi lt T gt    r   r    double darea  circular area 5 5    uses pi lt double gt  float farea  circular area 5 5f    uses pi lt float gt

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I would do  template lt typename T gt  T const pi   std  acos -T 1      or  template lt typename T gt  T const pi   std  arg -std  log T 2       I would not typing in p to the precision you need  What is that even supposed to mean  The precision you need is the precision of T  but we know nothing about T   You might say  What are you talking about  T will be float  double or long double  So  just type in the precision of long double  i e   template lt typename T gt  T const pi   static cast lt T gt     long double precision p        But do you really know that there won t be a new floating point type in the standard in the future with an even higher precision than long double  You don t   And that s why the first solution is beautiful  You can be quite sure that the standard would overload the trigonometric functions for a new type   And please  don t say that the evaluation of a trigonometric function at initialization is a performance penalty

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You could also use boost  which defines important math constants with maximum accuracy for the requested type  i e  float vs double      const double pi   boost  math  constants  pi lt double gt       Check out the boost documentation for more examples

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C  14 lets you do static constexpr auto pi   acos -1

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Some elegant solutions  I am doubtful that the precision of the trigonometric functions is equal to the precision of the types though  For those that prefer to write a constant value  this works for g    -  template lt class T gt  class X   public              static constexpr T PI    T  3 14159265358979323846264338327950288419  71693993751058209749445923078164062862089986280348253421170679821480865132823066  47093844609550582231725359408128481117450284102701938521105559644622948954930381  964428810975665933446128475648233786783165271201909145648566923460          256 decimal digit accuracy should be enough for any future long long long double type  If more are required visit https   www piday org million

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I would recommend just typing in pi to the precision you need   This would add no calculation time to your execution  and it would be portable without using any headers or  defines   Calculating acos or atan is always more expensive than using a precalculated value   const double PI   3 141592653589793238463  const float  PI F 3 14159265358979f

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I generally prefer defining my own  const double PI   2 acos 0 0   because not all implementations provide it for you   The question of whether this function gets called at runtime or is static ed out at compile time is usually not an issue  because it only happens once anyway

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Pi can be calculated as atan 1  4  You could calculate the value this way and cache it

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Get it from the FPU unit on chip instead   double get PI         double pi        asm               fldpi         fstp pi           return pi     double PI   get PI

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I use following in one of my common header in the project that covers all bases    define  USE MATH DEFINES  include  lt cmath gt    ifndef M PI  define M PI  3 14159265358979323846   endif   ifndef M PIl  define M PIl  3 14159265358979323846264338327950288   endif   On a side note  all of below compilers define M PI and M PIl constants if you include  lt cmath gt   There is no need to add   define  USE MATH DEFINES which is only required for VC     x86 GCC 4 4  ARM GCC 4 5  x86 Clang 3 0

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On windows  cygwin   g     I ve found it necessary to add the flag -D XOPEN SOURCE 500 for the preprocessor to process the definition of M PI in math h

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You can use that    define  USE MATH DEFINES    for C    include  lt cmath gt    define  USE MATH DEFINES    for C  include  lt math h gt    Math Constants are not defined in Standard C C    To use them  you must first define  USE MATH DEFINES and then include cmath or math h

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C  20 std  numbers  pi At last  it has arrived  http   eel is c  draft numbers main cpp  include  lt numbers gt     std  numbers  include  lt iomanip gt   include  lt iostream gt   int main         std  cout  lt  lt  std  fixed  lt  lt  std  setprecision 20       std  cout  lt  lt   quot float        quot   lt  lt  std  numbers  pi v lt float gt   lt  lt  std  endl      std  cout  lt  lt   quot double       quot   lt  lt  std  numbers  pi  lt  lt  std  endl      std  cout  lt  lt   quot long double  quot   lt  lt  std  numbers  pi v lt long double gt   lt  lt  std  endl      std  cout  lt  lt   quot exact        quot   lt  lt   quot 3 141592653589793238462643383279502884197169399375105820974944 quot   lt  lt  std  endl     where the exact result was calculated with  echo  quot scale 60  4 a 1  quot    BC LINE LENGTH 0 bc -l  as per  How can I calculate pi using Bash command Compile and run  g  -10 -ggdb3 -O0 -std c  20 -Wall -Wextra -pedantic -o main out main cpp   main out  Output  float       3 14159274101257324219 double      3 14159265358979311600 long double 3 14159265358979323851 exact       3 141592653589793238462643383279502884197169399375105820974944  Tested on Ubuntu 20 04 amd64  GCC 10 2 0 The accepted proposal describes   5 0     Headers     headers  In the table  tab cpp library headers   a new  lt math gt  header needs to be added        namespace std   namespace math     template lt typename T  gt  inline constexpr T pi v   unspecified     inline constexpr double pi   pi v lt double gt     There is also a std  numbers  e of course  -  How to calculate Euler constant or Euler powered in C    These constants use the C  14 variable template feature  C  14 Variable Templates  what is their purpose  Any usage example  In earlier versions of the draft  the constant was under std  math  pi  http   www open-std org jtc1 sc22 wg21 docs papers 2019 p0631r7 pdf

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From the Posix man page of math h      The   lt math h gt   header  shall  provide for the following constants   The    values are of type double and are accurate within the precision of  the    double type      M PI   Value of pi     M PI 2 Value of pi 2     M PI 4 Value of pi 4     M 1 PI Value of 1 pi     M 2 PI Value of 2 pi     M 2 SQRTPI           Value of 2  sqrt pi

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On some  especially older  platforms  see the comments below  you might need to   define  USE MATH DEFINES   and then include the necessary header file    include  lt math h gt    and the value of pi can be accessed via   M PI   In my math h  2014  it is defined as      define M PI           3 14159265358979323846     pi      but check your math h for more  An extract from the  old  math h  in 2009       Define  USE MATH DEFINES before including math h to expose these macro    definitions for common math constants   These are placed under an  ifdef    since these commonly-defined names are not part of the C C   standards        However    on newer platforms  at least on my 64 bit Ubuntu 14 04  I do not need to define the  USE MATH DEFINES  On  recent  Linux platforms there are long double values too provided as a GNU Extension     define M PIl          3 141592653589793238462643383279502884L    pi

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Rather than writing   define  USE MATH DEFINES   I would recommend using -D USE MATH DEFINES or  D USE MATH DEFINES depending on your compiler   This way you are assured that even in the event of someone including the header before you do  and without the  define  you will still have the constants instead of an obscure compiler error that you will take ages to track down

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