expm1, expm1f, expm1l - compute exponential functions
double expm1(double x);
float expm1f(float x);
long double expm1l(long double x);
[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 IEEE Std 1003.1-2001 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.
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 and x should be returned.
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 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.
exp(), feclearexcept(), fetestexcept(), ilogb(), log1p(), the Base Definitions volume of IEEE Std 1003.1-2001, Section 4.18, 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() 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.