# log1p 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.

log1p, log1pf, log1pl — compute a natural logarithm

## Synopsis

```
#include <math.h>
double log1p(double
```*x*);
float log1pf(float *x*);
long double log1pl(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 log_{e}(1.0 + *x*).

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 shall return the natural logarithm of 1.0 + *x*.

If *x* is -1, a pole error shall occur and *log1p*(), *log1pf*(), and *log1pl*() shall return -HUGE_VAL, -HUGE_VALF, and -HUGE_VALL, respectively.

For finite values of *x* that are less than -1, or if *x* is -Inf, a domain error shall occur, and either a NaN (if supported), or an implementation-defined value shall be returned.

If *x* is NaN, a NaN shall be returned.

If *x* is ±0, or +Inf, *x* shall be returned.

If *x* is subnormal, a range error may occur

and *x* should be returned.

If *x* is not returned, *log1p*(), *log1pf*(), and *log1pl*() 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:

- Domain Error
The finite value of

*x*is less than -1, or*x*is -Inf.If the integer expression (

*math_errhandling*& MATH_ERRNO) is non-zero, then*errno*shall be set to**[EDOM]**. If the integer expression (*math_errhandling*& MATH_ERREXCEPT) is non-zero, then the invalid floating-point exception shall be raised.- Pole Error
The value of

*x*is -1.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 divide-by-zero 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

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

*feclearexcept()*, *fetestexcept()*, *log()*

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 .