The Open Group Base Specifications Issue 8
IEEE Std 1003.1-2024
Copyright © 2001-2024 The IEEE and The Open Group

NAME

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

[CX] [Option Start] 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.1-2024 defers to the ISO C standard. [Option End]

These functions shall compute loge(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, [MX] [Option Start]  or if x is -Inf, [Option End] a domain error shall occur, and [MX] [Option Start]  either a NaN (if supported), or [Option End]  an implementation-defined value shall be returned.

[MX] [Option Start] If x is NaN, a NaN shall be returned.

If x is ±0, or +Inf, x shall be returned. [Option End]

[MXX] [Option Start] If x is subnormal, x should be returned.
[Option End] [MX] [Option Start] If x is subnormal, a range error may occur and, 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. [Option End]

ERRORS

These functions shall fail if:

Domain Error
The finite value of x is less than -1, [MX] [Option Start]  or x is -Inf. [Option End]

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
[MX] [Option Start] 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. [Option End]


The following sections are informative.

EXAMPLES

None.

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.

RATIONALE

None.

FUTURE DIRECTIONS

None.

SEE ALSO

feclearexcept , fetestexcept , log

XBD 4.23 Treatment of Error Conditions for Mathematical Functions , <math.h>

CHANGE HISTORY

First released in Issue 4, Version 2.

Issue 5

Moved from X/OPEN UNIX extension to BASE.

Issue 6

The normative text is updated to avoid use of the term "must" for application requirements.

The log1p() function is no longer marked as an extension.

The log1pf() and log1pl() functions are added for alignment with the ISO/IEC 9899:1999 standard.

The DESCRIPTION, RETURN VALUE, ERRORS, and APPLICATION USAGE sections are revised to align with the ISO/IEC 9899:1999 standard.

IEC 60559:1989 standard floating-point extensions over the ISO/IEC 9899:1999 standard are marked.

Issue 7

POSIX.1-2008, Technical Corrigendum 1, XSH/TC1-2008/0364 [68] is applied.

Issue 8

Austin Group Defect 1382 is applied, rearranging the text describing the behavior when x is subnormal to avoid the need for two shading changes.

End of informative text.

 

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