вычислить экспоненциальные функции (compute exponential 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)
expm1, expm1f, expm1l — compute exponential functions
Синопсис (Synopsis)
#include <math.h>
double expm1(double x);
float expm1f(float x);
long double expm1l(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 ex-1.0.
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 return ex-1.0.
If the correct value would cause overflow, a range error shall
occur and expm1(), expm1f(), and expm1l() shall return the value
of the macro HUGE_VAL, HUGE_VALF, and HUGE_VALL, respectively.
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 x is +Inf, x shall be returned.
If x is subnormal, a range error may occur
and x should be returned.
If x is not returned, expm1(), expm1f(), and expm1l() shall
return an implementation-defined value no greater in magnitude
than DBL_MIN, FLT_MIN, and LDBL_MIN, respectively.
Ошибки (Error)
These functions shall fail if:
Range Error The result 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:
Range Error The value of x is subnormal.
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)
The value of expm1(x) may be more accurate than exp(x)-1.0 for
small values of x.
The expm1() and log1p() functions are useful for financial
calculations of ((1+x)n-1)/x, namely:
expm1(n * log1p(x))/x
when x is very small (for example, when calculating small daily
interest rates). These functions also simplify writing accurate
inverse hyperbolic functions.
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)
exp(3p), feclearexcept(3p), fetestexcept(3p), ilogb(3p),
log1p(3p)
The Base Definitions volume of POSIX.1‐2017, Section 4.20,
Treatment of Error Conditions for Mathematical Functions,
math.h(0p)
