# std::expm1

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< cpp‎ | numeric‎ | math

Defined in header `<cmath>` |  |
float expm1( float arg ); | (1) | (since C++11)
double expm1( double arg ); | (2) | (since C++11)
long double expm1( long double arg ); | (3) | (since C++11)
double expm1( Integral 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).

### Parameters

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

### Return value

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.

### 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

### 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 < arg

### Example

Run this code

    #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

### See also

exp | returns e raised to the given power (ex) (function)
exp2 (C++11) | returns 2 raised to the given power (2x) (function)
log1p (C++11) | natural logarithm (to base e) of 1 plus the given number (ln(1+x)) (function)
C documentation for expm1

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