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) |
arg is close to zero.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
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.
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 raisedReferences
- 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)
See also
| (C99)(C99) |
computes natural (base-e) logarithm (ln(x)) (function) |
| (C99)(C99) |
computes common (base-10) logarithm (log10(x)) (function) |
| (C99)(C99)(C99) |
computes base-2 logarithm (log2(x)) (function) |
| (C99)(C99)(C99) |
computes e raised to the given power, minus one (ex-1) (function) |