EXPM1(3) Library Functions Manual EXPM1(3)

NAME

expm1 expm1f expm1l — compute exponential functions

SYNOPSIS

#include <math.h>

double expm1(double x);
float expm1f(float x);
long double expm1l(long double x);

DESCRIPTION

[CX] 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.

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.

[MX] 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 [MXX] and x should be returned.

[MX] 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.

ERRORS

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: [MX] 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.

EXAMPLES

None.

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(3) 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.