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      erf, erff, erfl

      From cppreference.com
      <c‎ |numeric‎ |math
       
       
       
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      Defined in header<math.h>
      float       erff(float arg);
      		 (1)(since C99)
      double      erf(double arg);
      		 (2)(since C99)
      longdouble erfl(longdouble arg);
      		 (3)(since C99)
      Defined in header<tgmath.h>
      #define erf( arg )
      		 (4)(since C99)
      1-3) Computes theerror function ofarg.
      4) Type-generic macro: Ifarg has typelongdouble,erfl is called. Otherwise, ifarg has integer type or the typedouble,erf is called. Otherwise,erff is called.

      Contents

      [edit]Parameters

      arg - floating-point value

      [edit]Return value

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

      [edit]Example

      Run this code
      #include <math.h>#include <stdio.h> double phi(double x1,double x2){return(erf(x2/sqrt(2))- erf(x1/sqrt(2)))/2;} int main(void){puts("normal variate probabilities:");for(int n=-4; n<4;++n)printf("[%2d:%2d]: %5.2f%%\n", n, n+1,100* phi(n, n+1)); puts("special values:");printf("erf(-0) = %f\n", erf(-0.0));printf("erf(Inf) = %f\n", erf(INFINITY));}

      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) = -0.000000erf(Inf) = 1.000000

      [edit]References

      • C11 standard (ISO/IEC 9899:2011):
      • 7.12.8.1 The erf functions (p: 249)
      • 7.25 Type-generic math <tgmath.h> (p: 373-375)
      • F.10.5.1 The erf functions (p: 525)
      • C99 standard (ISO/IEC 9899:1999):
      • 7.12.8.1 The erf functions (p: 230)
      • 7.22 Type-generic math <tgmath.h> (p: 335-337)
      • F.9.5.1 The erf functions (p: 462)

      [edit]See also

      (C99)(C99)(C99)
      		 computes 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=c/numeric/math/erf&oldid=172080"
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