std::expm1, std::expm1f, std::expm1l
<cmath>
double expm1 ( double num );
expm1 ( /*floating-point-type*/ num );
(constexpr since C++26)
(constexpr since C++26)
(constexpr since C++26)
<simd>
constexpr /*deduced-simd-t*/<V>
<cmath>
double expm1 ( Integer num );
std::expm1 for all cv-unqualified floating-point types as the type of the parameter.(since C++23)std::expm1 on v_num.- (See math-floating-point and deduced-simd-t for their definitions.)
[edit] Parameters
[edit] Return value
If no errors occur enum
-1 is returned.
If a range error due to overflow occurs, +HUGE_VAL , +HUGE_VALF, or +HUGE_VALL is returned.
If a range error occurs due to underflow, the correct result (after rounding) is returned.
[edit] Error handling
Errors are reported as specified in math_errhandling .
If the implementation supports IEEE floating-point arithmetic (IEC 60559),
- If the argument is ±0, it is returned, unmodified.
- If the argument is -∞, -1 is returned.
- If the argument is +∞, +∞ is returned.
- If the argument is NaN, NaN is returned.
[edit] Notes
The functions std::expm1 and std::log1p are useful for financial calculations, for example, when calculating small daily interest rates: (1+x)n
-1 can be expressed as std::expm1(n * std::log1p (x)). These functions also simplify writing accurate inverse hyperbolic functions.
For IEEE-compatible type double, overflow is guaranteed if 709.8 < num.
The additional overloads are not required to be provided exactly as (A). They only need to be sufficient to ensure that for their argument num of integer type, std::expm1(num) has the same effect as std::expm1(static_cast<double>(num)).
[edit] Example
#include <cerrno> #include <cfenv> #include <cmath> #include <cstring> #include <iostream> // #pragma STDC FENV_ACCESS ON int main() { std::cout << "expm1(1) = " << std::expm1(1) << '\n' << "Interest earned in 2 days on 100,ドル compounded daily at 1%\n" << " on a 30/360 calendar = " << 100 * std::expm1(2 * std::log1p (0.01 / 360)) << '\n' << "exp(1e-16)-1 = " << std::exp (1e-16) - 1 << ", but expm1(1e-16) = " << std::expm1(1e-16) << '\n'; // special values std::cout << "expm1(-0) = " << std::expm1(-0.0) << '\n' << "expm1(-Inf) = " << std::expm1(-INFINITY ) << '\n'; // error handling errno = 0; std::feclearexcept (FE_ALL_EXCEPT ); std::cout << "expm1(710) = " << std::expm1(710) << '\n'; if (errno == ERANGE ) std::cout << " errno == ERANGE: " << std::strerror (errno) << '\n'; if (std::fetestexcept (FE_OVERFLOW )) std::cout << " FE_OVERFLOW raised\n"; }
Possible output:
expm1(1) = 1.71828 Interest earned in 2 days on 100,ドル compounded daily at 1% on a 30/360 calendar = 0.00555563 exp(1e-16)-1 = 0, but expm1(1e-16) = 1e-16 expm1(-0) = -0 expm1(-Inf) = -1 expm1(710) = inf errno == ERANGE: Result too large FE_OVERFLOW raised
[edit] See also
(function) [edit]