NAME¶

std::expm1,std::expm1f,std::expm1l - std::expm1,std::expm1f,std::expm1l

Synopsis¶

Defined in header <cmath>
float expm1 ( float num );

double expm1 ( double num ); (until C++23)

long double expm1 ( long double num );
/* floating-point-type */ (since C++23)
expm1 ( /* floating-point-type */ num ); (constexpr since C++26)
float expm1f( float num ); (1) (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)
Defined in header <cmath>
template< class Integer > (A) (constexpr since C++26)
double expm1 ( Integer num );

1-3) Computes the e (Euler's number, 2.7182818...) raised to the given power num,
minus 1.0. This function is more accurate than the expression std::exp(num) - 1.0 if
num is close to zero.
The library provides overloads of 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 (since C++11)
treated as double.

Parameters¶

num - floating-point or integer value

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.

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 < 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)).

Example¶

// Run this code

#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

See also¶

exp
expf returns e raised to the given power (\({\small e^x}\)e^x)
expl (function)
(C++11)
(C++11)
exp2
exp2f
exp2l returns 2 raised to the given power (\({\small 2^x}\)2^x)
(C++11) (function)
(C++11)
(C++11)
log1p
log1pf natural logarithm (to base e) of 1 plus the given number
log1pl (\({\small\ln{(1+x)}}\)ln(1+x))
(C++11) (function)
(C++11)
(C++11)
C documentation for
expm1