std::frexp,...std::frexpl(3)

Okay bestie, welcome to the std::frexp,...std::frexpl(3) page from the C++ Standard Libary manual — yes, that manual name is literally exactly as written, and we're keeping it. This is the float-splitting squad, and they're about to make normalized fractions make sense. 💅✨

🎀 NAME 🎀

std::frexp, std::frexpf, std::frexpl — the whole iconic trio, no cap.

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✨ Synopsis ✨

First up, the header tea: these live in <cmath>.

Main character declarations:

float       frexp ( float num, int* exp );
double      frexp ( double num, int* exp );                  (until C++23)
long double frexp ( long double num, int* exp );
constexpr /* floating-point-type */
            frexp ( /* floating-point-type */ num,           (since C++23)
int* exp );                                          (1)
float       frexpf( float num, int* exp );               (2) (since C++11)
                                                                     (constexpr since C++23)
long double frexpl( long double num, int* exp );         (3) (since C++11)
                                                                     (constexpr since C++23)

Additional overloads (since C++11):

Defined in header <cmath> — yes, again, because of course. 🫶

template< class Integer >                                (A)
(constexpr since C++23)
double      frexp ( Integer num, int* exp );

1-3) Decomposes given floating point value num into a normalized fraction and an integral exponent of two.

The library provides overloads of std::frexp for all cv-unqualified floating-point types as the type of the parameter num. (since C++23)

A) Additional overloads are provided for all integer types, which are treated as double. (since C++11)

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🌸 Parameters 🌸

• num — floating-point or integer value.
• exp — pointer to integer value to store the exponent to.

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💖 Return value 💖

If num is zero, returns zero and stores zero in *exp.

Otherwise (if num is not zero), if no errors occur, returns the value x in the range (-1, -0.5], [0.5, 1) and stores an integer value in *exp such that x×2(*exp) == num.

🚨 If the value to be stored in *exp is outside the range of int, the behavior is unspecified. That's unspecified behavior, bestie — not a vibe.

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🚨 Error handling 🚨

Good news: this function is not subject to any errors specified in math_errhandling.

If the implementation supports IEEE floating-point arithmetic (IEC 60559), here's the tea:

• If num is ±0, it is returned, unmodified, and 0 is stored in *exp.
• If num is ±∞, it is returned, and an unspecified value is stored in *exp.
• If num is NaN, NaN is returned, and an unspecified value is stored in *exp.
• No floating-point exceptions are raised.
• If FLT_RADIX is 2 (or a power of 2), the returned value is exact, the current rounding mode is ignored.

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🧚 Notes 🧚

On a binary system (where FLT_RADIX is 2), std::frexp may be implemented as

{
    *exp = (value == 0) ? 0 : (int)(1 + std::logb(value));
    return std::scalbn(value, -(*exp));
}

The function std::frexp, together with its dual, std::ldexp, can be used to manipulate the representation of a floating-point number without direct bit manipulations.

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::frexp(num, exp) has the same effect as std::frexp(static_cast<double>(num), exp).

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🍓 Example 🍓

Compares different floating-point decomposition functions:

#include <cmath>
#include <iostream>
#include <limits>

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';
}

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

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🌈 See also 🌈

• ldexp, ldexpf, ldexpl — multiplies a number by 2 raised to an integral power (function); ldexpf and ldexpl carry (C++11) markers.
• logb, logbf, logbl — extracts exponent of the number (function); the (C++11) markers are on these too.
• ilogb, ilogbf, ilogbl — extracts exponent of the number (function); yep, (C++11) markers again.
• modf, modff, modfl — decomposes a number into integer and fractional parts (function); (C++11) markers where the original says so.
• C documentation for frexp — the C side has a page too.

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💖 and that's the whole page, bestie! Source: http://cppreference.com · version/date: 2024.06.10 · page: std::frexp,...std::frexpl(3). Now go split some floats, mwah! 💖