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      erfc, erfcf, erfcl

      From cppreference.com
      <c‎ |numeric‎ |math
       
       
       
      Common mathematical functions
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      erfc
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      Defined in header<math.h>
      float       erfcf(float arg);
      		 (1)(since C99)
      double      erfc(double arg);
      		 (2)(since C99)
      longdouble erfcl(longdouble arg);
      		 (3)(since C99)
      Defined in header<tgmath.h>
      #define erfc( arg )
      		 (4)(since C99)
      1-3) Computes thecomplementary error function ofarg, that is1.0-erf(arg), but without loss of precision for largearg.
      4) Type-generic macro: Ifarg has typelongdouble,erfcl is called. Otherwise, ifarg has integer type or the typedouble,erfc is called. Otherwise,erfcf is called.

      Contents

      [edit]Parameters

      arg - floating-point value

      [edit]Return value

      If no errors occur, value of the complementary error function ofarg, that is\(\frac{2}{\sqrt{\pi} }\int_{arg}^{\infty}{e^{-{t^2} }\mathsf{d}t}\)
      2
      √π
      ∫∞
      arg      e-t2
      dt       or\({\small 1-\operatorname{erf}(arg)}\)1-erf(arg), is returned.

      If a range error occurs due to underflow, the correct result (after rounding) 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 is returned.
      • If the argument is -∞, 2 is returned.
      • If the argument is NaN, NaN is returned.

      [edit]Notes

      For the IEEE-compatible typedouble, underflow is guaranteed ifarg >26.55.

      [edit]Example

      Run this code
      #include <math.h>#include <stdio.h> double normalCDF(double x)// Phi(-∞, x) aka N(x){return erfc(-x/sqrt(2))/2;} int main(void){puts("normal cumulative distribution function:");for(double n=0; n<1; n+=0.1)printf("normalCDF(%.2f) %5.2f%%\n", n,100* normalCDF(n)); printf("special values:\n""erfc(-Inf) = %f\n""erfc(Inf) = %f\n",           erfc(-INFINITY),           erfc(INFINITY));}

      Output:

      normal cumulative distribution function:normalCDF(0.00) 50.00%normalCDF(0.10) 53.98%normalCDF(0.20) 57.93%normalCDF(0.30) 61.79%normalCDF(0.40) 65.54%normalCDF(0.50) 69.15%normalCDF(0.60) 72.57%normalCDF(0.70) 75.80%normalCDF(0.80) 78.81%normalCDF(0.90) 81.59%normalCDF(1.00) 84.13%special values:erfc(-Inf) = 2.000000erfc(Inf) = 0.000000

      [edit]References

      • C23 standard (ISO/IEC 9899:2024):
      • 7.12.8.2 The erfc functions (p: 249-250)
      • 7.25 Type-generic math <tgmath.h> (p: 373-375)
      • F.10.5.2 The erfc functions (p: 525)
      • C17 standard (ISO/IEC 9899:2018):
      • 7.12.8.2 The erfc functions (p: 249-250)
      • 7.25 Type-generic math <tgmath.h> (p: 373-375)
      • F.10.5.2 The erfc functions (p: 525)
      • C11 standard (ISO/IEC 9899:2011):
      • 7.12.8.2 The erfc functions (p: 249-250)
      • 7.25 Type-generic math <tgmath.h> (p: 373-375)
      • F.10.5.2 The erfc functions (p: 525)
      • C99 standard (ISO/IEC 9899:1999):
      • 7.12.8.2 The erfc functions (p: 230)
      • 7.22 Type-generic math <tgmath.h> (p: 335-337)
      • F.9.5.2 The erfc functions (p: 462)

      [edit]See also

      (C99)(C99)(C99)
      		 computes error function
      (function)[edit]

      [edit]External links

      Weisstein, Eric W. "Erfc." From MathWorld — A Wolfram Web Resource.
      Retrieved from "https://en.cppreference.com/mwiki/index.php?title=c/numeric/math/erfc&oldid=172079"
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