std::expm1

C++

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Named requirements

Language support library

Concepts library (C++20)

Diagnostics library

Utilities library

Strings library

Containers library

Algorithms library

Iterators library

Numerics library

Input/output library

Localizations library

Regular expressions library (C++11)

Atomic operations library (C++11)

Thread support library (C++11)

Filesystem library (C++17)

Technical Specifications

Numerics library

Common mathematical functions

Special mathematical functions

Floating-point environment (C++11)

Complex numbers

Numeric arrays

Pseudo-random number generation

Compile-time rational arithmetic (C++11)

Numeric algorithms

gcd (C++17)

lcm (C++17)

Generic numeric operations

iota (C++11)

accumulate

inner_product

adjacent_difference

partial_sum

reduce (C++17)

transform_reduce (C++17)

inclusive_scan (C++17)

exclusive_scan (C++17)

transform_inclusive_scan (C++17)

transform_exclusive_scan (C++17)

Bit operations

bit_cast (C++20)

ispow2 (C++20)

ceil2 (C++20)

floor2 (C++20)

log2p1 (C++20)

Common mathematical functions

Functions
Basic operations
abs(int)labsllabsimaxabs (C++11) abs(float)fabs divldivlldivimaxdiv (C++11) fmod	remainder (C++11) remquo (C++11) fma (C++11) fmax (C++11) fmin (C++11) fdim (C++11) nannanfnanl (C++11)(C++11)(C++11)
Exponential functions
exp exp2 (C++11) expm1 (C++11)	log log10 log1p (C++11) log2 (C++11)
Power functions
sqrt cbrt (C++11)	hypot (C++11) pow
Trigonometric and hyperbolic functions
sin cos tan asin acos atan atan2	sinh cosh tanh asinh (C++11) acosh (C++11) atanh (C++11)

Error and gamma functions
erf (C++11) erfc (C++11)	lgamma (C++11) tgamma (C++11)
Nearest integer floating point operations
ceil floor roundlroundllround (C++11)(C++11)(C++11)	trunc (C++11) nearbyint (C++11) rintlrintllrint (C++11)(C++11)(C++11)
Floating point manipulation functions
ldexp scalbnscalbln (C++11)(C++11) ilogb (C++11) logb (C++11)	frexp modf nextafternexttoward (C++11)(C++11) copysign (C++11)
Classification/Comparison
fpclassify (C++11) isfinite (C++11) isinf (C++11) isnan (C++11) isnormal (C++11) signbit (C++11)	isgreater (C++11) isgreaterequal (C++11) isless (C++11) islessequal (C++11) islessgreater (C++11) isunordered (C++11)
Macro constants
HUGE_VALFHUGE_VALHUGE_VALL (C++11)(C++11) INFINITY (C++11) NAN (C++11) math_errhandlingMATH_ERRNOMATH_ERREXCEPT (C++11)	FP_NORMALFP_SUBNORMALFP_ZEROFP_INFINITEFP_NAN (C++11)(C++11)(C++11)(C++11)(C++11)

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( 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).

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)