log1p, log1pf, log1pl
Defined in header <math.h>
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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>
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#define log1p( arg ) |
(4) | (since C99) |
log1pl
is called. Otherwise, if arg has integer type or the type double, log1p
is called. Otherwise, log1pf
is called.Contents |
[edit] Parameters
arg | - | floating-point value |
[edit] 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.
[edit] 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.
[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.
[edit] Example
#include <errno.h> #include <fenv.h> #include <float.h> #include <math.h> #include <stdio.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
[edit] References
- C23 standard (ISO/IEC 9899:2024):
- 7.12.6.9 The log1p functions (p: TBD)
- 7.25 Type-generic math <tgmath.h> (p: TBD)
- F.10.3.9 The log1p functions (p: TBD)
- C17 standard (ISO/IEC 9899:2018):
- 7.12.6.9 The log1p functions (p: TBD)
- 7.25 Type-generic math <tgmath.h> (p: TBD)
- F.10.3.9 The log1p functions (p: TBD)
- 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)
[edit] 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) |
C++ documentation for log1p
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