#include <math.h> double expm1(double x); float expm1f(float x); long double expm1l(long double x);
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.
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.
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:
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.
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.
The Base Definitions volume of POSIX.1-2008, Section 4.19, Treatment of Error Conditions for Mathematical Functions, <math.h>
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