/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)

 loglogflogl (C99)(C99) computes natural (base-e) logarithm ($${\small \ln{x} }$$ln(x)) (function) log10log10flog10l (C99)(C99) computes common (base-10) logarithm ($${\small \log_{10}{x} }$$log10(x)) (function) log2log2flog2l (C99)(C99)(C99) computes base-2 logarithm ($${\small \log_{2}{x} }$$log2(x)) (function) expm1expm1fexpm1l (C99)(C99)(C99) computes e raised to the given power, minus one ($${\small e^x-1}$$ex-1) (function) C++ documentation for log1p