# 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 *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.*

## 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>**

## Copyright

Portions of this text are reprinted and reproduced in electronic form from IEEE Std 1003.1, 2013 Edition, Standard for Information Technology -- Portable Operating System Interface (POSIX), The Open Group Base Specifications Issue 7, Copyright (C) 2013 by the Institute of Electrical and Electronics Engineers, Inc and The Open Group. (This is POSIX.1-2008 with the 2013 Technical Corrigendum 1 applied.) 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.unix.org/online.html .