std::expm1
From cppreference.com
| Defined in header
<cmath>
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| float expm1( float arg );
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(1) | (since C++11) |
| double expm1( double arg );
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(2) | (since C++11) |
| long double expm1( long double arg );
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(3) | (since C++11) |
| double expm1( Integral arg );
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(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).
Contents |
[edit] Parameters
| arg | - | value of floating-point or Integral type |
[edit] 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.
[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 < arg
[edit] 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[edit] See also
| returns e raised to the given power (ex) (function) |
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| (C++11)
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returns 2 raised to the given power (2x) (function) |
| (C++11)
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natural logarithm (to base e) of 1 plus the given number (ln(1+x)) (function) |
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C documentation for expm1
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