# expm1 - Man Page

compute exponential functions

## 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.

## Synopsis

#include <math.h> double expm1(doublex); float expm1f(floatx); long double expm1l(long doublex);

## 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 *e*^{x}-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 *e*^{x}-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.*

## 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*() 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.

## Rationale

None.

## Future Directions

None.

## See Also

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

The Base Definitions volume of POSIX.1-2017, *Section 4.20*, *Treatment of Error Conditions for Mathematical Functions*, <math.h>

## Copyright

Portions of this text are reprinted and reproduced in electronic form from IEEE Std 1003.1-2017, Standard for Information Technology -- Portable Operating System Interface (POSIX), The Open Group Base Specifications Issue 7, 2018 Edition, Copyright (C) 2018 by the Institute of Electrical and Electronics Engineers, Inc and The Open Group. In the event of any discrepancy between this version and the original IEEE and The Open Group Standard, the original IEEE and The Open Group Standard is the referee document. The original Standard can be obtained online at http://www.opengroup.org/unix/online.html .

Any typographical or formatting errors that appear in this page are most likely to have been introduced during the conversion of the source files to man page format. To report such errors, see https://www.kernel.org/doc/man-pages/reporting_bugs.html .