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      std::erf,std::erff,std::erfl

      From cppreference.com
      <cpp‎ |numeric‎ |math
       
       
       
      Common mathematical functions
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      Macro constants
       
      Defined in header<cmath>
      (1)
      float       erf(float num);

      double      erf(double num);

      longdouble erf(longdouble num);
      		(until C++23)
      /*floating-point-type*/
                  erf(/*floating-point-type*/ num);
      		(since C++23)
      (constexpr since C++26)
      float       erff(float num);
      		 (2)(since C++11)
      (constexpr since C++26)
      longdouble erfl(longdouble num);
      		 (3)(since C++11)
      (constexpr since C++26)
      SIMD overload(since C++26)
      Defined in header<simd>
      template</*math-floating-point*/ V>

      constexpr/*deduced-simd-t*/<V>

                  erf(const V& v_num);
      		 (S)(since C++26)
      Defined in header<cmath>
      template<class Integer>
      double      erf( Integer num);
      		 (A)(constexpr since C++26)
      1-3) Computes theerror function ofnum. The library provides overloads ofstd::erf for all cv-unqualified floating-point types as the type of the parameter.(since C++23)
      S) The SIMD overload performs an element-wisestd::erf onv_num.
      (Seemath-floating-point anddeduced-simd-t for their definitions.)
      		(since C++26)
      A) Additional overloads are provided for all integer types, which are treated asdouble.
      		(since C++11)

      Contents

      [edit]Parameters

      num - floating-point or integer value

      [edit]Return value

      If no errors occur, value of the error function ofnum, that is\(\frac{2}{\sqrt{\pi} }\int_{0}^{num}{e^{-{t^2} }\mathsf{d}t}\)
      2
      √π
      ∫num
      0      e-t2
      dt      , is returned.
      If a range error occurs due to underflow, the correct result (after rounding), that is\(\frac{2\cdot num}{\sqrt{\pi} }\)
      2*num
      √π
       is returned.

      [edit]Error handling

      Errors are reported as specified inmath_errhandling.

      If the implementation supports IEEE floating-point arithmetic (IEC 60559),

      • If the argument is ±0, ±0 is returned.
      • If the argument is ±∞, ±1 is returned.
      • If the argument is NaN, NaN is returned.

      [edit]Notes

      Underflow is guaranteed if|num|<DBL_MIN*(std::sqrt(π)/2).

      \(\operatorname{erf}(\frac{x}{\sigma \sqrt{2} })\)erf(
      x
      σ√2
      )       is the probability that a measurement whose errors are subject to a normal distribution with standard deviation\(\sigma\)σ is less than\(x\)x away from the mean value.

      The additional overloads are not required to be provided exactly as(A). They only need to be sufficient to ensure that for their argumentnum of integer type,std::erf(num) has the same effect asstd::erf(static_cast<double>(num)).

      [edit]Example

      The following example calculates the probability that a normal variate is on the interval (x1, x2):

      Run this code
      #include <cmath>#include <iomanip>#include <iostream> double phi(double x1,double x2){return(std::erf(x2/std::sqrt(2))- std::erf(x1/std::sqrt(2)))/2;} int main(){std::cout<<"Normal variate probabilities:\n"<<std::fixed<<std::setprecision(2);for(int n=-4; n<4;++n)std::cout<<'['<<std::setw(2)<< n<<':'<<std::setw(2)<< n+1<<"]: "<<std::setw(5)<<100* phi(n, n+1)<<"%\n"; std::cout<<"Special values:\n"<<"erf(-0) = "<< std::erf(-0.0)<<'\n'<<"erf(Inf) = "<< std::erf(INFINITY)<<'\n';}

      Output:

      Normal variate probabilities:[-4:-3]:  0.13%[-3:-2]:  2.14%[-2:-1]: 13.59%[-1: 0]: 34.13%[ 0: 1]: 34.13%[ 1: 2]: 13.59%[ 2: 3]:  2.14%[ 3: 4]:  0.13%Special values:erf(-0) = -0.00erf(Inf) = 1.00

      [edit]See also

      (C++11)(C++11)(C++11)
      		 complementary error function
      (function)[edit]

      [edit]External links

      Weisstein, Eric W. "Erf." From MathWorld — A Wolfram Web Resource.
      Retrieved from "https://en.cppreference.com/mwiki/index.php?title=cpp/numeric/math/erf&oldid=160724"
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