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expm1, expm1f, expm1l

From cppreference.com
< c‎ | numeric‎ | math
 
 
 
Common mathematical functions
Functions
Basic operations
(C99)
(C99)
(C99)
(C99)
(C99)
(C99)(C99)(C99)
Exponential functions
(C99)
expm1
(C99)
(C99)
(C99)
Power functions
(C99)
(C99)
Trigonometric and hyperbolic functions
(C99)
(C99)
(C99)
Error and gamma functions
(C99)
(C99)
(C99)
(C99)
Nearest integer floating point operations
(C99)(C99)(C99)
(C99)
(C99)(C99)(C99)
Floating point manipulation functions
(C99)(C99)
(C99)
(C99)
Classification
(C99)
(C99)
(C99)
Macro constants
 
Defined in header <math.h>
float       expm1f( float arg );
(1) (since C99)
double      expm1( double arg );
(2) (since C99)
long double expm1l( long double arg );
(3) (since C99)
Defined in header <tgmath.h>
#define expm1( arg )
(4) (since C99)
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) Type-generic macro: If arg has type long double, expm1l is called. Otherwise, if arg has integer type or the type double, expm1 is called. Otherwise, expm1f is called.

Contents

[edit] Parameters

arg - floating point value

[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 expm1 and log1p are useful for financial calculations, for example, when calculating small daily interest rates: (1+x)n
-1
can be expressed as expm1(n * 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

#include <stdio.h>
#include <math.h>
#include <float.h>
#include <errno.h>
#include <fenv.h>
#pragma STDC FENV_ACCESS ON
int main(void)
{
    printf("expm1(1) = %f\n", expm1(1));
    printf("Interest earned in 2 days on $100, compounded daily at 1%%\n"
           " on a 30/360 calendar = %f\n",
           100*expm1(2*log1p(0.01/360)));
    printf("exp(1e-16)-1 = %g, but expm1(1e-16) = %g\n",
           exp(1e-16)-1, expm1(1e-16));
    // special values
    printf("expm1(-0) = %f\n", expm1(-0.0));
    printf("expm1(-Inf) = %f\n", expm1(-INFINITY));
    //error handling
    errno = 0; feclearexcept(FE_ALL_EXCEPT);
    printf("expm1(710) = %f\n", expm1(710));
    if(errno == ERANGE) perror("    errno == ERANGE");
    if(fetestexcept(FE_OVERFLOW)) puts("    FE_OVERFLOW raised");
}

Possible output:

expm1(1) = 1.718282
Interest earned in 2 days on $100, compounded daily at 1%
 on a 30/360 calendar = 0.005556
exp(1e-16)-1 = 0, but expm1(1e-16) = 1e-16
expm1(-0) = -0.000000
expm1(-Inf) = -1.000000
expm1(710) = inf
    errno == ERANGE: Result too large
    FE_OVERFLOW raised

[edit] See also

(C99)(C99)
computes e raised to the given power (ex)
(function) [edit]
(C99)(C99)(C99)
computes 2 raised to the given power (2x)
(function) [edit]
(C99)(C99)(C99)
computes natural (base-e) logarithm of 1 plus the given number (ln(1+x))
(function) [edit]