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Difference between revisions of "cpp/numeric/math/logb"

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{{cpp/title|logb|logbf|logbl}}
 
{{cpp/title|logb|logbf|logbl}}
 
{{cpp/numeric/math/navbar}}
 
{{cpp/numeric/math/navbar}}
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{{dcl begin}}
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{{cpp/numeric/math/declarations
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{{dcl header|cmath}}
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|family=logb
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{{dcl rev multi|num=1|since1=c++11|dcl1=
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|param1=num
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float      logb ( float num );
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|constexpr_since=23
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double      logb ( double num );
+
|desc=Extracts the value of the unbiased radix-independent exponent from the floating-point argument {{c|num}}, and returns it as a floating-point value.
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long double logb ( long double num );
+
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|since2=c++23|dcl2=
+
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constexpr /* floating-point-type */
+
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            logb ( /* floating-point-type */ num );
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}}
 
}}
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{{dcl|num=2|since=c++11|notes={{mark|constexpr since C++23}}|
 
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float      logbf( float num );
 
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}}
 
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{{dcl|num=3|since=c++11|notes={{mark|constexpr since C++23}}|
 
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long double logbl( long double num );
 
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}}
 
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{{dcl h|[[#Notes|Additional overloads]]}}
 
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{{dcl header|cmath}}
 
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{{dcl|num=A|since=c++11|notes={{mark|constexpr since C++23}}|
 
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template< class Integer >
 
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double      logb ( Integer num );
 
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}}
 
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{{dcl end}}
 
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@1-3@ Extracts the value of the unbiased radix-independent exponent from the floating-point argument {{c|num}}, and returns it as a floating-point value.{{rev inl|since=c++23| The library provides overloads of {{tt|std::logb}} for all cv-unqualified floating-point types as the type of the parameter {{c|num}}.}}
 
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@A@ Additional overloads are provided for all integer types, which are treated as {{c/core|double}}.
 
  
 
Formally, the unbiased exponent is the signed integral part of {{math|log{{su|b=r}}{{!}}num{{!}}}} (returned by this function as a floating-point value), for non-zero {{c|num}}, where {{c|r}} is {{c|std::numeric_limits<T>::radix}} and {{tt|T}} is the floating-point type of {{c|num}}. If {{c|num}} is subnormal, it is treated as though it was normalized.
 
Formally, the unbiased exponent is the signed integral part of {{math|log{{su|b=r}}{{!}}num{{!}}}} (returned by this function as a floating-point value), for non-zero {{c|num}}, where {{c|r}} is {{c|std::numeric_limits<T>::radix}} and {{tt|T}} is the floating-point type of {{c|num}}. If {{c|num}} is subnormal, it is treated as though it was normalized.
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If the implementation supports IEEE floating-point arithmetic (IEC 60559),
 
If the implementation supports IEEE floating-point arithmetic (IEC 60559),
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* If {{c|num}} is ±0, -∞ is returned and {{lc|FE_DIVBYZERO}} is raised
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* If {{c|num}} is ±0, -∞ is returned and {{lc|FE_DIVBYZERO}} is raised.
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* If {{c|num}} is ±∞, +∞ is returned
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* If {{c|num}} is ±∞, +∞ is returned.
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* If {{c|num}} is NaN, NaN is returned
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* If {{c|num}} is NaN, NaN is returned.
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* In all other cases, the result is exact ({{lc|FE_INEXACT}} is never raised) and [[cpp/numeric/fenv/FE_round|the current rounding mode]] is ignored
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* In all other cases, the result is exact ({{lc|FE_INEXACT}} is never raised) and [[cpp/numeric/fenv/FE_round|the current rounding mode]] is ignored.
  
 
===Notes===
 
===Notes===
−
[http://pubs.opengroup.org/onlinepubs/9699919799/functions/logb.html POSIX requires] that a pole error occurs if {{c|num}} is ±0.
+
[https://pubs.opengroup.org/onlinepubs/9699919799/functions/logb.html POSIX requires] that a pole error occurs if {{c|num}} is ±0.
  
−
The value of the exponent returned by {{tt|std::logb}} is always 1 less than the exponent returned by {{lc|std::frexp}} because of the different normalization requirements: for the exponent {{c|e}} returned by {{tt|std::logb}}, {{math|{{!}}num*r{{su|p=-e}}{{!}}}} is between 1 and {{c|r}} (typically between {{c|1}} and {{c|2}}), but for the exponent {{c|e}} returned by {{lc|std::frexp}}, {{math|{{!}}num*2{{su|p=-e}}{{!}}}} is between {{c|0.5}} and {{c|1}}.
+
The value of the exponent returned by {{tt|std::logb}} is always 1 less than the exponent returned by {{lc|std::frexp}} because of the different normalization requirements: for the exponent {{c|e}} returned by {{tt|std::logb}}, {{math|{{!}}num*r{{su|p=-e}}{{!}}}} is between {{c|1}} and {{c|r}} (typically between {{c|1}} and {{c|2}}), but for the exponent {{c|e}} returned by {{lc|std::frexp}}, {{math|{{!}}num*2{{su|p=-e}}{{!}}}} is between {{c|0.5}} and {{c|1}}.
  
 
{{cpp/numeric/math/additional integer overload note|logb}}
 
{{cpp/numeric/math/additional integer overload note|logb}}
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#include <iostream>
 
#include <iostream>
 
#include <limits>
 
#include <limits>
−
 
+
// #pragma STDC FENV_ACCESS ON
−
#pragma STDC FENV_ACCESS ON
+
  
 
int main()
 
int main()

Latest revision as of 21:46, 15 October 2023

 
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Defined in header <cmath>
(1)
float       logb ( float num );

double      logb ( double num );

long double logb ( long double num );
 (until C++23)
constexpr /* floating-point-type */
            logb ( /* floating-point-type */ num );
 (since C++23)
float       logbf( float num );
 (2) (since C++11)
(constexpr since C++23)
long double logbl( long double num );
 (3) (since C++11)
(constexpr since C++23)
Additional overloads (since C++11)
Defined in header <cmath>
template< class Integer >
double      logb ( Integer num );
 (A) (constexpr since C++23)
1-3) Extracts the value of the unbiased radix-independent exponent from the floating-point argument num, and returns it as a floating-point value. The library provides overloads of std::logb for all cv-unqualified floating-point types as the type of the parameter.(since C++23)
A) Additional overloads are provided for all integer types, which are treated as double.
 (since C++11)

Formally, the unbiased exponent is the signed integral part of logr|num| (returned by this function as a floating-point value), for non-zero num, where r is std::numeric_limits<T>::radix and T is the floating-point type of num. If num is subnormal, it is treated as though it was normalized.

Contents

[edit] Parameters

num - floating-point or integer value

[edit] Return value

If no errors occur, the unbiased exponent of num is returned as a signed floating-point value.

If a domain error occurs, an implementation-defined value is returned.

If a pole error occurs, -HUGE_VAL, -HUGE_VALF, or -HUGE_VALL is returned.

[edit] Error handling

Errors are reported as specified in math_errhandling.

Domain or range error may occur if num is zero.

If the implementation supports IEEE floating-point arithmetic (IEC 60559),

  • If num is ±0, -∞ is returned and FE_DIVBYZERO is raised.
  • If num is ±∞, +∞ is returned.
  • If num is NaN, NaN is returned.
  • In all other cases, the result is exact (FE_INEXACT is never raised) and the current rounding mode is ignored.

[edit] Notes

POSIX requires that a pole error occurs if num is ±0.

The value of the exponent returned by std::logb is always 1 less than the exponent returned by std::frexp because of the different normalization requirements: for the exponent e returned by std::logb, |num*r-e| is between 1 and r (typically between 1 and 2), but for the exponent e returned by std::frexp, |num*2-e| is between 0.5 and 1.

The additional overloads are not required to be provided exactly as (A). They only need to be sufficient to ensure that for their argument num of integer type, std::logb(num) has the same effect as std::logb(static_cast<double>(num)).

[edit] Example

Compares different floating-point decomposition functions:

Run this code
#include <cfenv>
#include <cmath>
#include <iostream>
#include <limits>
// #pragma STDC FENV_ACCESS ON
 
int main()
{
    double f = 123.45;
    std::cout << "Given the number " << f << " or " << std::hexfloat
              << f << std::defaultfloat << " in hex,\n";
 
    double f3;
    double f2 = std::modf(f, &f3);
    std::cout << "modf() makes " << f3 << " + " << f2 << '\n';
 
    int i;
    f2 = std::frexp(f, &i);
    std::cout << "frexp() makes " << f2 << " * 2^" << i << '\n';
 
    i = std::ilogb(f);
    std::cout << "logb()/ilogb() make " << f / std::scalbn(1.0, i) << " * "
              << std::numeric_limits<double>::radix
              << "^" << std::ilogb(f) << '\n';
 
    // error handling
    std::feclearexcept(FE_ALL_EXCEPT);
 
    std::cout << "logb(0) = " << std::logb(0) << '\n';
    if (std::fetestexcept(FE_DIVBYZERO))
        std::cout << "    FE_DIVBYZERO raised\n";
}

Possible output: 

Given the number 123.45 or 0x1.edccccccccccdp+6 in hex,
modf() makes 123 + 0.45
frexp() makes 0.964453 * 2^7
logb()/ilogb() make 1.92891 * 2^6
logb(0) = -Inf
    FE_DIVBYZERO raised

[edit] See also

(C++11)(C++11)
 decomposes a number into significand and base-2 exponent
(function) [edit]
(C++11)(C++11)(C++11)
 extracts exponent of the number
(function) [edit]
(C++11)(C++11)(C++11)(C++11)(C++11)(C++11)
 multiplies a number by FLT_RADIX raised to a power
(function) [edit]
C documentation for logb
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