/C

# log1p, log1pf, log1pl

Defined in header `<math.h>`
`float       log1pf( float arg );`
(1) (since C99)
`double      log1p( double arg );`
(2) (since C99)
`long double log1pl( long double arg );`
(3) (since C99)
Defined in header `<tgmath.h>`
`#define log1p( arg )`
(4) (since C99)
1-3) Computes the natural (base `e`) logarithm of `1+arg`. This function is more precise than the expression `log(1+arg)` if `arg` is close to zero.
4) Type-generic macro: If `arg` has type `long double`, `log1pl` is called. Otherwise, if `arg` has integer type or the type `double`, `log1p` is called. Otherwise, `log1pf` is called.

### Parameters

 arg - floating point value

### Return value

If no errors occur ln(1+arg) is returned.

If a domain error occurs, an implementation-defined value is returned (NaN where supported).

If a pole error 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.

Domain error occurs if `arg` is less than -1.

Pole error may occur if `arg` is -1.

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 and `FE_DIVBYZERO` is raised.
• If the argument is less than -1, NaN is returned and `FE_INVALID` is raised.
• If the argument is +∞, +∞ is returned
• If the argument is NaN, NaN is returned

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.

### 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("log1p(0) = %f\n", log1p(0));
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("log(1+1e-16) = %g, but log1p(1e-16) = %g\n",
log(1+1e-16), log1p(1e-16));
// special values
printf("log1p(-0) = %f\n", log1p(-0.0));
printf("log1p(+Inf) = %f\n", log1p(INFINITY));
//error handling
errno = 0; feclearexcept(FE_ALL_EXCEPT);
printf("log1p(-1) = %f\n", log1p(-1));
if(errno == ERANGE) perror("    errno == ERANGE");
if(fetestexcept(FE_DIVBYZERO)) puts("    FE_DIVBYZERO raised");
}```

Possible output:

```log1p(0) = 0.000000
Interest earned in 2 days on \$100, compounded daily at 1%
on a 30/360 calendar = 0.005556
log(1+1e-16) = 0, but log1p(1e-16) = 1e-16
log1p(-0) = -0.000000
log1p(+Inf) = Inf
log1p(-1) = -Inf
errno == ERANGE: Result too large
FE_DIVBYZERO raised```
• C11 standard (ISO/IEC 9899:2011):
• 7.12.6.9 The log1p functions (p: 245)
• 7.25 Type-generic math <tgmath.h> (p: 373-375)
• F.10.3.9 The log1p functions (p: 522)
• C99 standard (ISO/IEC 9899:1999):
• 7.12.6.9 The log1p functions (p: 226)
• 7.22 Type-generic math <tgmath.h> (p: 335-337)
• F.9.3.9 The log1p functions (p: 459)