вычислить функцию gamma () (compute gamma() function)
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)
tgamma, tgammaf, tgammal — compute gamma() function
Синопсис (Synopsis)
#include <math.h>
double tgamma(double x);
float tgammaf(float x);
long double tgammal(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 Γ(x) where Γ(x) is defined as ∞0∫e^
−tt^ x−1dt.
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
gamma of x.
If x is a negative integer, a domain error may occur and either a
NaN (if supported) or an implementation-defined value shall be
returned. On systems that support the IEC 60559 Floating-Point
option, a domain error shall occur and a NaN shall be returned.
If x is ±0, tgamma(), tgammaf(), and tgammal() shall return
±HUGE_VAL, ±HUGE_VALF, and ±HUGE_VALL, respectively. On systems
that support the IEC 60559 Floating-Point option, a pole error
shall occur; otherwise, a pole error may occur.
If the correct value would cause overflow, a range error shall
occur and tgamma(), tgammaf(), and tgammal() shall return
±HUGE_VAL, ±HUGE_VALF, or ±HUGE_VALL, respectively, with the same
sign as the correct value of the function.
If the correct value would cause underflow, and is not
representable, a range error may occur, and tgamma(), tgammaf(),
and tgammal() shall return 0.0, or (if IEC 60559 Floating-Point
is not supported) an implementation-defined value no greater in
magnitude than DBL_MIN, FLT_MIN, and LDBL_MIN, respectively.
If the correct value would cause underflow, and is representable,
a range error may occur and the correct value shall be returned.
If x is subnormal and 1/x is representable, 1/x should be
returned.
If x is NaN, a NaN shall be returned.
If x is +Inf, x shall be returned.
If x is -Inf, a domain error shall occur, and a NaN shall be
returned.
Ошибки (Error)
These functions shall fail if:
Domain Error
The value of x is a negative integer, or x is -Inf.
If the integer expression (math_errhandling &
MATH_ERRNO) is non-zero, then errno shall be set to
[EDOM]. If the integer expression (math_errhandling
& MATH_ERREXCEPT) is non-zero, then the invalid
floating-point exception shall be raised.
Pole Error The value of x is zero.
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 divide-by-zero floating-point exception shall be
raised.
Range Error The value overflows.
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 overflow floating-point exception shall be
raised.
These functions may fail if:
Domain Error
The value of x is a negative integer.
If the integer expression (math_errhandling &
MATH_ERRNO) is non-zero, then errno shall be set to
[EDOM]. If the integer expression (math_errhandling
& MATH_ERREXCEPT) is non-zero, then the invalid
floating-point exception shall be raised.
Pole Error The value of x is zero.
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 divide-by-zero floating-point exception shall be
raised.
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)
None.
Использование в приложениях (Application usage)
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)
This function is named tgamma() in order to avoid conflicts with
the historical gamma() and lgamma() functions.
Будущие направления (Future directions)
It is possible that the error response for a negative integer
argument may be changed to a pole error and a return value of
±Inf.
Смотри также (See also)
feclearexcept(3p), fetestexcept(3p), lgamma(3p)
The Base Definitions volume of POSIX.1‐2017, Section 4.20,
Treatment of Error Conditions for Mathematical Functions,
math.h(0p)
