# expm1

## 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.
    


## 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



           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.1‐2017 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.
    
           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
           and _x_ should be returned.
    
           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 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.
    
           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.
    


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