Defined in header `<cmath>` | ||
---|---|---|

float expm1 ( float arg ); float expm1f( float arg ); | (1) | (since C++11) |

double expm1 ( double arg ); | (2) | (since C++11) |

long double expm1 ( long double arg ); long double expm1l( long double arg ); | (3) | (since C++11) |

double expm1 ( IntegralType arg ); | (4) | (since C++11) |

1-3) Computes the *e* (Euler's number,

`2.7182818`

) raised to the given power `arg`

, minus `1.0`

. This function is more accurate than the expression `std::exp(arg)-1.0`

if `arg`

is close to zero.
4) A set of overloads or a function template accepting an argument of any integral type. Equivalent to 2) (the argument is cast to

`double`

).arg | - | value of floating-point or Integral type |

If no errors occur earg

-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.

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

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 < arg.

#include <iostream> #include <cmath> #include <cerrno> #include <cstring> #include <cfenv> #pragma STDC FENV_ACCESS ON int main() { std::cout << "expm1(1) = " << std::expm1(1) << '\n' << "Interest earned in 2 days on 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 on $100, compounded daily at 1% on a 30/360 calendar = 0.00555563 exp(1e-16)-1 = 0 expm1(1e-16) = 1e-16 expm1(-0) = -0 expm1(-Inf) = -1 expm1(710) = inf errno == ERANGE: Result too large FE_OVERFLOW raised

(C++11)(C++11) | returns e raised to the given power (e^{x}) (function) |

(C++11)(C++11)(C++11) | returns 2 raised to the given power (2^{x}) (function) |

(C++11)(C++11)(C++11) | natural logarithm (to base e) of 1 plus the given number (ln(1+x)) (function) |

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