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Expm1

Defined in header <cmath>.

Description

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 num.

Declarations

// 1)
/* floating-point-type */ expm1( /* floating-point-type */ num );
// 2)
float expm1f( float num );
// 3)
long double expm1l( long double num );
Additional Overloads
// 4)
template< class Integer >
double expm1 ( Integer num );

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

Examples

#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 Result
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

Expm1

Defined in header <cmath>.

Description

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 num.

Declarations

// 1)
/* floating-point-type */ expm1( /* floating-point-type */ num );
// 2)
float expm1f( float num );
// 3)
long double expm1l( long double num );
Additional Overloads
// 4)
template< class Integer >
double expm1 ( Integer num );

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

Examples

#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 Result
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