Difference between revisions of "cpp/numeric/math/log1p"
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{{cpp/numeric/math/navbar}} | {{cpp/numeric/math/navbar}} | ||
{{dcl begin}} | {{dcl begin}} | ||
| − | {{dcl header | cmath}} | + | {{dcl header|cmath}} |
| − | {{dcl | since=c++11 |num=1| | + | {{dcl|since=c++11|num=1| |
float log1p ( float arg ); | float log1p ( float arg ); | ||
float log1pf( float arg ); | float log1pf( float arg ); | ||
}} | }} | ||
| − | {{dcl | since=c++11 |num=2| | + | {{dcl|since=c++11|num=2| |
double log1p ( double arg ); | double log1p ( double arg ); | ||
}} | }} | ||
| − | {{dcl | since=c++11 |num=3| | + | {{dcl|since=c++11|num=3| |
long double log1p ( long double arg ); | long double log1p ( long double arg ); | ||
long double log1pl( long double arg ); | long double log1pl( long double arg ); | ||
}} | }} | ||
| − | {{dcl | since=c++11 |num=4| | + | {{dcl|since=c++11|num=4| |
double log1p ( IntegralType arg ); | double log1p ( IntegralType arg ); | ||
}} | }} | ||
{{dcl end}} | {{dcl end}} | ||
| − | @1-3@ Computes the natural (base {{c|e}}) logarithm of {{c|1+arg}}. This function is more precise than the expression {{c|std::log(1+arg)}} if {{tt|arg}} is close to zero. | + | @1-3@ Computes the natural (base {{c|e}}) logarithm of {{c|1 + arg}}. This function is more precise than the expression {{c|std::log(1 + arg)}} if {{tt|arg}} is close to zero. |
@4@ A set of overloads or a function template accepting an argument of any [[cpp/types/is_integral|integral type]]. Equivalent to {{v|2}} (the argument is cast to {{c|double}}). | @4@ A set of overloads or a function template accepting an argument of any [[cpp/types/is_integral|integral type]]. Equivalent to {{v|2}} (the argument is cast to {{c|double}}). | ||
===Parameters=== | ===Parameters=== | ||
{{par begin}} | {{par begin}} | ||
| − | {{par | arg | value of floating-point or [[cpp/types/is_integral|Integral type]]}} | + | {{par|arg|value of floating-point or [[cpp/types/is_integral|Integral type]]}} |
{{par end}} | {{par end}} | ||
| Line 95: | Line 95: | ||
FE_DIVBYZERO raised | FE_DIVBYZERO raised | ||
}} | }} | ||
| − | |||
===See also=== | ===See also=== | ||
{{dsc begin}} | {{dsc begin}} | ||
| − | {{dsc inc | cpp/numeric/math/dsc log}} | + | {{dsc inc|cpp/numeric/math/dsc log}} |
| − | {{dsc inc | cpp/numeric/math/dsc log10}} | + | {{dsc inc|cpp/numeric/math/dsc log10}} |
| − | {{dsc inc | cpp/numeric/math/dsc log2}} | + | {{dsc inc|cpp/numeric/math/dsc log2}} |
| − | {{dsc inc | cpp/numeric/math/dsc expm1}} | + | {{dsc inc|cpp/numeric/math/dsc expm1}} |
| − | {{dsc see c | c/numeric/math/log1p}} | + | {{dsc see c|c/numeric/math/log1p}} |
{{dsc end}} | {{dsc end}} | ||
{{langlinks|de|es|fr|it|ja|pt|ru|zh}} | {{langlinks|de|es|fr|it|ja|pt|ru|zh}} | ||
Revision as of 15:31, 14 March 2023
| Defined in header <cmath>
|
||
| float log1p ( float arg ); float log1pf( float arg ); |
(1) | (since C++11) |
| double log1p ( double arg ); |
(2) | (since C++11) |
| long double log1p ( long double arg ); long double log1pl( long double arg ); |
(3) | (since C++11) |
| double log1p ( IntegralType arg ); |
(4) | (since C++11) |
1-3) Computes the natural (base e) logarithm of 1 + arg. This function is more precise than the expression std::log(1 + arg) if
arg is close to zero.4) A set of overloads or a function template accepting an argument of any integral type. Equivalent to (2) (the argument is cast to double).
Contents |
Parameters
| arg | - | value of floating-point or Integral type |
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 std::expm1 and std::log1p are useful for financial calculations, for example, when calculating small daily interest rates: (1+x)n-1 can be expressed as std::expm1(n * std::log1p(x)). These functions also simplify writing accurate inverse hyperbolic functions.
Example
Run this code
#include <cerrno> #include <cfenv> #include <cmath> #include <cstring> #include <iostream> // #pragma STDC FENV_ACCESS ON int main() { std::cout << "log1p(0) = " << log1p(0) << '\n' << "Interest earned in 2 days on $100, compounded daily at 1%\n" << " on a 30/360 calendar = " << 100*expm1(2*log1p(0.01/360)) << '\n' << "log(1+1e-16) = " << std::log(1+1e-16) << ", but log1p(1e-16) = " << std::log1p(1e-16) << '\n'; // special values std::cout << "log1p(-0) = " << std::log1p(-0.0) << '\n' << "log1p(+Inf) = " << std::log1p(INFINITY) << '\n'; // error handling errno = 0; std::feclearexcept(FE_ALL_EXCEPT); std::cout << "log1p(-1) = " << std::log1p(-1) << '\n'; if (errno == ERANGE) std::cout << " errno == ERANGE: " << std::strerror(errno) << '\n'; if (std::fetestexcept(FE_DIVBYZERO)) std::cout << " FE_DIVBYZERO raised\n"; }
Possible output:
log1p(0) = 0
Interest earned in 2 days on $100, compounded daily at 1%
on a 30/360 calendar = 0.00555563
log(1+1e-16) = 0, but log1p(1e-16) = 1e-16
log1p(-0) = -0
log1p(+Inf) = inf
log1p(-1) = -inf
errno == ERANGE: Result too large
FE_DIVBYZERO raisedSee also
| (C++11)(C++11) |
computes natural (base e) logarithm (ln(x)) (function) |
| (C++11)(C++11) |
computes common (base 10) logarithm (log10(x)) (function) |
| (C++11)(C++11)(C++11) |
base 2 logarithm of the given number (log2(x)) (function) |
| (C++11)(C++11)(C++11) |
returns e raised to the given power, minus one (ex-1) (function) |
| C documentation for log1p
| |
