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

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 ); float expm1f( float arg );	(1)	(since C++11)
double expm1 ( double arg );	(2)	(since C++11)
long double expm1 ( long double arg ); long double expm1l( 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 $e arg -1$ 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

Language
Standard Library Headers
Freestanding and hosted implementations
Named requirements
Language support library
Concepts library (C++20)
Diagnostics library
Utilities library
Strings library
Containers library
Iterators library
Ranges library (C++20)
Algorithms 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

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)
Interpolations
midpoint (C++20)
lerp (C++20)
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)