The Open Group Base Specifications Issue 7
IEEE Std 1003.1, 2013 Edition
Copyright © 2001-2013 The IEEE and The Open Group

#### 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.1-2008 defers to the ISO C standard.

> These functions shall compute ex-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 ex-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.

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

> [MX] 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.

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.

> 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.

#### RATIONALE

> None.

#### FUTURE DIRECTIONS

> None.

#### SEE ALSO

> exp, feclearexcept, fetestexcept, ilogb, log1p

> XBD 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.

End of informative text.

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