/C

# expm1, expm1f, expm1l

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.

### Parameters

 arg - floating point value

### 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 `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.

### 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```

### References

• C11 standard (ISO/IEC 9899:2011):
• 7.12.6.3 The expm1 functions (p: 243)
• 7.25 Type-generic math <tgmath.h> (p: 373-375)
• F.10.3.3 The expm1 functions (p: 521)
• C99 standard (ISO/IEC 9899:1999):
• 7.12.6.3 The expm1 functions (p: 223-224)
• 7.22 Type-generic math <tgmath.h> (p: 335-337)
• F.9.3.3 The expm1 functions (p: 458)

 expexpfexpl (C99)(C99) computes e raised to the given power (ex) (function) exp2exp2fexp2l (C99)(C99)(C99) computes 2 raised to the given power (2x) (function) log1plog1pflog1pl (C99)(C99)(C99) computes natural (base-e) logarithm of 1 plus the given number (ln(1+x)) (function) C++ documentation for `expm1`