функции ошибок (error functions)
Пролог (Prolog)
This manual page is part of the POSIX Programmer's Manual. The
Linux implementation of this interface may differ (consult the
corresponding Linux manual page for details of Linux behavior),
or the interface may not be implemented on Linux.
Имя (Name)
erf, erff, erfl — error functions
Синопсис (Synopsis)
#include <math.h>
double erf(double x);
float erff(float x);
long double erfl(long double x);
Описание (Description)
The functionality described on this reference page is aligned
with the ISO C standard. Any conflict between the requirements
described here and the ISO C standard is unintentional. This
volume of POSIX.1‐2017 defers to the ISO C standard.
These functions shall compute the error function of their
argument x, defined as:
√_2π_x0∫e^ −t^2 dt
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.
Возвращаемое значение (Return value)
Upon successful completion, these functions shall return the
value of the error function.
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.
Ошибки (Error)
These functions may fail if:
Range Error The result underflows.
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.
Примеры (Examples)
Computing the Probability for a Normal Variate
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;
}
Использование в приложениях (Application usage)
Underflow occurs when |x| < DBL_MIN * (sqrt(π)/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.
Обоснование (Rationale)
None.
Будущие направления (Future directions)
None.
Смотри также (See also)
erfc(3p), feclearexcept(3p), fetestexcept(3p), isnan(3p)
The Base Definitions volume of POSIX.1‐2017, Section 4.20,
Treatment of Error Conditions for Mathematical Functions,
math.h(0p)
