IEEE Std 1003.1, 2013 Edition

Copyright © 2001-2013 The IEEE and The Open Group

expm1, expm1f, expm1l - compute exponential functions

#include <math.h>

double expm1(doublex);

float expm1f(floatx);

long double expm1l(long doublex);

^{[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

e-1.0.^{x}An application wishing to check for error situations should set

errnoto zero and callfeclearexcept(FE_ALL_EXCEPT) before calling these functions. On return, iferrnois non-zero orfetestexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has occurred.

Upon successful completion, these functions return

e-1.0.^{x}If the correct value would cause overflow, a range error shall occur and

expm1(),expm1f(), andexpm1l() shall return the value of the macro HUGE_VAL, HUGE_VALF, and HUGE_VALL, respectively.

^{[MX]}Ifxis NaN, a NaN shall be returned.If

xis ±0, ±0 shall be returned.If

xis -Inf, -1 shall be returned.If

xis +Inf,xshall be returned.If

xis subnormal, a range error may occur

^{[MXX]}andxshould be returned.

^{[MX]}Ifxis not returned,expm1(),expm1f(), andexpm1l() shall return an implementation-defined value no greater in magnitude than DBL_MIN, FLT_MIN, and LDBL_MIN, respectively.

These functions shall fail if:

- Range Error
- The result overflows.
If the integer expression (

math_errhandling& MATH_ERRNO) is non-zero, thenerrnoshall 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 ofxis subnormal.If the integer expression (

math_errhandling& MATH_ERRNO) is non-zero, thenerrnoshall be set to [ERANGE]. If the integer expression (math_errhandling& MATH_ERREXCEPT) is non-zero, then the underflow floating-point exception shall be raised.

None.

The value of

expm1(x) may be more accurate thanexp(x)-1.0 for small values ofx.The

expm1() andlog1p() functions are useful for financial calculations of ((1+x)^{n}-1)/x, namely:expm1(n* log1p(x))/xwhen

xis 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 <ximpliesexpm1(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.

None.

None.

exp,feclearexcept,fetestexcept,ilogb,log1pXBD

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

First released in Issue 4, Version 2.

Moved from X/OPEN UNIX extension to BASE.

The

expm1f() andexpm1l() 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.

POSIX.1-2008, Technical Corrigendum 1, XSH/TC1-2008/0110 [68] is applied.

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