#include <math.h> double erf(double x); float erff(float x); long double erfl(long double x);
These functions shall compute the error function of their argument x, defined as:
An application wishing to check for error situations should set errno to zero and call feclearexcept(FE_ALL_EXCEPT) before calling these functions. On return, if errno is non-zero or fetestexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has occurred.
If x is NaN, a NaN shall be returned.
If x is ±0, ±0 shall be returned.
If x is ±Inf, ±1 shall be returned.
If the correct value would cause underflow, a range error may occur, and erf(), erff(), and erfl() shall return an implementation-defined value no greater in magnitude than DBL_MIN, FLT_MIN, and LDBL_MIN, respectively.
If the IEC 60559 Floating-Point option is supported, 2 * x/sqrt(π) should be returned.
If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then errno shall be set to [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the underflow floating-point exception shall be raised.
The following sections are informative.
This example shows how to use erf() to compute the probability that a normal variate assumes a value in the range [x1,x2] with x1≤x2.
This example uses the constant M_SQRT1_2 which is part of the XSI option.
#include <math.h> double Phi(const double x1, const double x2) { return ( erf(x2*M_SQRT1_2) - erf(x1*M_SQRT1_2) ) / 2; }
On error, the expressions (math_errhandling & MATH_ERRNO) and (math_errhandling & MATH_ERREXCEPT) are independent of each other, but at least one of them must be non-zero.
The Base Definitions volume of POSIX.1-2017, Section 4.20, Treatment of Error Conditions for Mathematical Functions, <math.h>
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