std::expm1, std::expm1f, std::expm1l
| Defined in header <cmath>
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| (1) | ||
float expm1 ( float num ); double expm1 ( double num ); |
(until C++23) | |
| /* floating-point-type */ expm1 ( /* floating-point-type */ num ); |
(since C++23) (constexpr since C++26) |
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| float expm1f( float num ); |
(2) | (since C++11) (constexpr since C++26) |
| long double expm1l( long double num ); |
(3) | (since C++11) (constexpr since C++26) |
| Additional overloads (since C++11) |
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| Defined in header <cmath>
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| template< class Integer > double expm1 ( Integer num ); |
(A) | (constexpr since C++26) |
std::expm1 for all cv-unqualified floating-point types as the type of the parameter.(since C++23)|
A) Additional overloads are provided for all integer types, which are treated as double.
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(since C++11) |
Contents |
[edit] Parameters
| num | - | floating-point or integer value |
[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, 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, 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
| (C++11)(C++11) |
returns e raised to the given power (ex) (function) |
| (C++11)(C++11)(C++11) |
returns 2 raised to the given power (2x) (function) |
| (C++11)(C++11)(C++11) |
natural logarithm (to base e) of 1 plus the given number (ln(1+x)) (function) |
| C documentation for expm1
| |
