Math constant PI value in C

Question

Calculating PI value is one of the complex problem and wikipedia talks about the approximations done for it and says it s difficult to calculate PI accurately    How does C calculate PI  Does it calculate it every time or is it using a less accurate fixed value

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Just define    define M PI acos -1 0    It should give you exact PI number that math functions are working with  So if they change PI value they are working with in tangent or cosine or sine  then your program should be always up-to-dated

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In C Pi is defined in math h   define M PI 3 14159265358979323846

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Depending on the library you are using the standard GNU C Predefined Mathematical Constants are here    https   www gnu org software libc manual html node Mathematical-Constants html  You already have them so why redefine them  Your system desktop calculators probably have them and are even more accurate so you could but just be sure you re not conflicting with existing defined ones to save on compile warnings as they tend to get defaults for things like that  Enjoy

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anyway you have not a unlimited accuracy so C define a constant in this way     define PI 3 14159265358979323846   import math h to use this

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I don t know exactly how C calculates PI directly as I m more familiar with C   than C  however  you could either have a predefined C macro or const such as     define PI 3 14159265359      const float PI   3 14159265359      const double PI   3 14159265359         If your machine os  amp  compiler supports the long double    const long double PI   3 14159265359         or you could calculate it with either of these two formulas    define M PI acos -1 0    define M PI  4 0   atan 1 0       tan pi 4    1 or acos -1    IMHO I m not 100  certain but I think atan   is cheaper than acos

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The closest thing C does to  computing p  in a way that s directly visible to applications is acos -1  or similar  This is almost always done with polynomial rational approximations for the function being computed  either in C  or by the FPU microcode    However  an interesting issue is that computing the trigonometric functions  sin  cos  and tan  requires reduction of their argument modulo 2p  Since 2p is not a diadic rational  and not even rational   it cannot be represented in any floating point type  and thus using any approximation of the value will result in catastrophic error accumulation for large arguments  e g  if x is 1e12  and 2 M PI differs from 2p by e  then fmod x 2 M PI  differs from the correct value of 2p by up to 1e12 e p times the correct value of x mod 2p  That is to say  it s completely meaningless   A correct implementation of C s standard math library simply has a gigantic very-high-precision representation of p hard coded in its source to deal with the issue of correct argument reduction  and uses some fancy tricks to make it not-quite-so-gigantic   This is how most all C versions of the sin cos tan functions work  However  certain implementations  like glibc  are known to use assembly implementations on some cpus  like x86  and don t perform correct argument reduction  leading to completely nonsensical outputs   Incidentally  the incorrect asm usually runs about the same speed as the correct C code for small arguments

[c] Math constant PI value in C

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