expm1 man page

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.

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

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.1‐2008 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.

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.

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

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.

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.

For IEEE Std 754‐1985 double, 709.8 < x implies expm1(x) has overflowed.

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.

See Also

exp(), feclearexcept(), fetestexcept(), ilogb(), log1p()

The Base Definitions volume of POSIX.1‐2008, Section 4.19, Treatment of Error Conditions for Mathematical Functions, <math.h>

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2013 IEEE/The Open Group POSIX Programmer's Manual