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Defined in header <math.h> | ||
float log1pf(float arg); | (1) | (since C99) |
double log1p(double arg); | (2) | (since C99) |
longdouble log1pl(longdouble arg); | (3) | (since C99) |
Defined in header <tgmath.h> | ||
#define log1p( arg ) | (4) | (since C99) |
log1pl is called. Otherwise, ifarg has integer type or the typedouble,log1p is called. Otherwise,log1pf is called.Contents |
| arg | - | floating-point value |
If no errors occurln(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.
Errors are reported as specified inmath_errhandling.
Domain error occurs ifarg is less than-1.
Pole error may occur ifarg is-1.
If the implementation supports IEEE floating-point arithmetic (IEC 60559),
The functionsexpm1 andlog1p are useful for financial calculations, for example, when calculating small daily interest rates:(1+x)n
-1 can be expressed asexpm1(n* log1p(x)). These functions also simplify writing accurate inverse hyperbolic functions.
#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 valuesprintf("log1p(-0) = %f\n", log1p(-0.0));printf("log1p(+Inf) = %f\n", log1p(INFINITY)); // error handlingerrno=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) = 0.000000Interest earned in 2 days on $100, compounded daily at 1% on a 30/360 calendar = 0.005556log(1+1e-16) = 0, but log1p(1e-16) = 1e-16log1p(-0) = -0.000000log1p(+Inf) = Inflog1p(-1) = -Inf errno == ERANGE: Result too large FE_DIVBYZERO raised
(C99)(C99) | computes natural (base-e) logarithm (\({\small \ln{x} }\)ln(x)) (function)[edit] |
(C99)(C99) | computes common (base-10) logarithm (\({\small \log_{10}{x} }\)log10(x)) (function)[edit] |
(C99)(C99)(C99) | computes base-2 logarithm (\({\small \log_{2}{x} }\)log2(x)) (function)[edit] |
(C99)(C99)(C99) | computese raised to the given power, minus one (\({\small e^x-1}\)ex-1) (function)[edit] |
C++ documentation forlog1p | |
