NAME

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

^[CX] 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.

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.

^[MX] 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.

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

^[MX] 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.

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

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 expm1f() and expm1l() functions are added for alignment with the ISO/IEC 9899:1999 standard.

The expm1() function is no longer marked as an extension.

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/TC1-2008/0110 [68] is applied.

POSIX.1-2008, Technical Corrigendum 2, XSH/TC2-2008/0103 [630] 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.