std::pow, std::powf, std::powl

 

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Common mathematical functions

Functions
Basic operations
abs(int)labsllabsimaxabs (C++11) abs(float)fabs divldivlldivimaxdiv (C++11) fmod	remainder (C++11) remquo (C++11) fma (C++11) fmax (C++11) fmin (C++11) fdim (C++11) nannanfnanl (C++11)(C++11)(C++11)
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exp exp2 (C++11) expm1 (C++11)	log log10 log1p (C++11) log2 (C++11)
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sqrt cbrt (C++11)	hypot (C++11) pow
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sin cos tan asin acos atan atan2	sinh cosh tanh asinh (C++11) acosh (C++11) atanh (C++11)

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erf (C++11) erfc (C++11)	lgamma (C++11) tgamma (C++11)
Nearest integer floating point operations
ceil floor roundlroundllround (C++11)(C++11)(C++11)	trunc (C++11) nearbyint (C++11) rintlrintllrint (C++11)(C++11)(C++11)
Floating point manipulation functions
ldexp scalbnscalbln (C++11)(C++11) ilogb (C++11) logb (C++11)	frexp modf nextafternexttoward (C++11)(C++11) copysign (C++11)
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fpclassify (C++11) isfinite (C++11) isinf (C++11) isnan (C++11) isnormal (C++11) signbit (C++11)	isgreater (C++11) isgreaterequal (C++11) isless (C++11) islessequal (C++11) islessgreater (C++11) isunordered (C++11)
Macro constants
HUGE_VALFHUGE_VALHUGE_VALL (C++11)(C++11) INFINITY (C++11) NAN (C++11) math_errhandlingMATH_ERRNOMATH_ERREXCEPT (C++11)	FP_NORMALFP_SUBNORMALFP_ZEROFP_INFINITEFP_NAN (C++11)(C++11)(C++11)(C++11)(C++11)

 

Defined in header <cmath>
	(1)
float       pow ( float base, float exp ); double      pow ( double base, double exp ); long double pow ( long double base, long double exp );			(until C++23)
/* floating-point-type */             pow ( /* floating-point-type */ base,                   /* floating-point-type */ exp )			(since C++23) (constexpr since C++26)
float       pow ( float base, int exp ); double      pow ( double base, int exp ); long double pow ( long double base, int exp );		(2)	(until C++11)
float       powf( float base, float exp );		(3)	(since C++11) (constexpr since C++26)
long double powl( long double base, long double exp );		(4)	(since C++11) (constexpr since C++26)
Additional overloads (since C++11)
Defined in header <cmath>
template< class Arithmetic1, class Arithmetic2 > /* common-floating-point-type */             pow ( Arithmetic1 base, Arithmetic2 exp );		(A)	(constexpr since C++26)

1-4) Computes the value of base raised to the power exp. The library provides overloads of std::pow for all cv-unqualified floating-point types as the type of the parameters base and exp. (since C++23)

A) Additional overloads are provided for all other combinations of arithmetic types.

(since C++11)

Parameters

base	-	base as a floating-point or integer value
exp	-	exponent as a floating-point or integer value

Return value

If no errors occur, base raised to the power of exp (baseexp
), is returned.

If a domain error occurs, an implementation-defined value is returned (NaN where supported).

If a pole error or a range error due to overflow 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.

If base is finite and negative and exp is finite and non-integer, a domain error occurs and a range error may occur.

If base is zero and exp is zero, a domain error may occur.

If base is zero and exp is negative, a domain error or a pole error may occur.

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

• pow(+0, exp), where exp is a negative odd integer, returns +∞ and raises FE_DIVBYZERO
• pow(-0, exp), where exp is a negative odd integer, returns -∞ and raises FE_DIVBYZERO
• pow(±0, exp), where exp is negative, finite, and is an even integer or a non-integer, returns +∞ and raises FE_DIVBYZERO
• pow(±0, -∞) returns +∞ and may raise FE_DIVBYZERO
• pow(+0, exp), where exp is a positive odd integer, returns +0
• pow(-0, exp), where exp is a positive odd integer, returns -0
• pow(±0, exp), where exp is positive non-integer or a positive even integer, returns +0
• pow(-1, ±∞) returns 1
• pow(+1, exp) returns 1 for any exp, even when exp is NaN
• pow(base, ±0) returns 1 for any base, even when base is NaN
• pow(base, exp) returns NaN and raises FE_INVALID if base is finite and negative and exp is finite and non-integer.
• pow(base, -∞) returns +∞ for any |base|<1
• pow(base, -∞) returns +0 for any |base|>1
• pow(base, +∞) returns +0 for any |base|<1
• pow(base, +∞) returns +∞ for any |base|>1
• pow(-∞, exp) returns -0 if exp is a negative odd integer
• pow(-∞, exp) returns +0 if exp is a negative non-integer or negative even integer
• pow(-∞, exp) returns -∞ if exp is a positive odd integer
• pow(-∞, exp) returns +∞ if exp is a positive non-integer or positive even integer
• pow(+∞, exp) returns +0 for any negative exp
• pow(+∞, exp) returns +∞ for any positive exp
• except where specified above, if any argument is NaN, NaN is returned

Notes

C++98 added overloads where exp has type int on top of C pow(), and the return type of std::pow(float, int) was float. However, the additional overloads introduced in C++11 specify that std::pow(float, int) should return double. LWG issue 550 was raised to target this conflict, and the resolution is to removed the extra int exp overloads.

Although std::pow cannot be used to obtain a root of a negative number, std::cbrt is provided for the common case where exp is 1/3.

The additional overloads are not required to be provided exactly as (A). They only need to be sufficient to ensure that for their first argument num1 and second argument num2:

If num1 or num2 has type long double, then std::pow(num1, num2) has the same effect as std::pow(static_cast<long double>(num1),          static_cast<long double>(num2)). Otherwise, if num1 and/or num2 has type double or an integer type, then std::pow(num1, num2) has the same effect as std::pow(static_cast<double>(num1),          static_cast<double>(num2)). Otherwise, if num1 or num2 has type float, then std::pow(num1, num2) has the same effect as std::pow(static_cast<float>(num1),          static_cast<float>(num2)).

(until C++23)

If num1 and num2 have arithmetic types, then std::pow(num1, num2) has the same effect as std::pow(static_cast</* common-floating-point-type */>(num1),          static_cast</* common-floating-point-type */>(num2)), where /* common-floating-point-type */ is the floating-point type with the greatest floating-point conversion rank and greatest floating-point conversion subrank between the types of num1 and num2, arguments of integer type are considered to have the same floating-point conversion rank as double. If no such floating-point type with the greatest rank and subrank exists, then overload resolution does not result in a usable candidate from the overloads provided.

(since C++23)

Example

Run this code

#include <cerrno>
#include <cfenv>
#include <cmath>
#include <cstring>
#include <iostream>
 
// #pragma STDC FENV_ACCESS ON
 
int main()
{
    // typical usage
    std::cout << "pow(2, 10) = " << std::pow(2, 10) << '\n'
              << "pow(2, 0.5) = " << std::pow(2, 0.5) << '\n'
              << "pow(-2, -3) = " << std::pow(-2, -3) << '\n';
 
    // special values
    std::cout << "pow(-1, NAN) = " << std::pow(-1, NAN) << '\n'
              << "pow(+1, NAN) = " << std::pow(+1, NAN) << '\n'
              << "pow(INFINITY, 2) = " << std::pow(INFINITY, 2) << '\n'
              << "pow(INFINITY, -1) = " << std::pow(INFINITY, -1) << '\n';
 
    // error handling
    errno = 0;
    std::feclearexcept(FE_ALL_EXCEPT);
 
    std::cout << "pow(-1, 1/3) = " << std::pow(-1, 1.0 / 3) << '\n';
    if (errno == EDOM)
        std::cout << "    errno == EDOM " << std::strerror(errno) << '\n';
    if (std::fetestexcept(FE_INVALID))
        std::cout << "    FE_INVALID raised\n";
 
    std::feclearexcept(FE_ALL_EXCEPT);
 
    std::cout << "pow(-0, -3) = " << std::pow(-0.0, -3) << '\n';
    if (std::fetestexcept(FE_DIVBYZERO))
        std::cout << "    FE_DIVBYZERO raised\n";
}

Possible output:

pow(2, 10) = 1024
pow(2, 0.5) = 1.41421
pow(-2, -3) = -0.125
pow(-1, NAN) = nan
pow(+1, NAN) = 1
pow(INFINITY, 2) = inf
pow(INFINITY, -1) = 0
pow(-1, 1/3) = -nan
    errno == EDOM Numerical argument out of domain
    FE_INVALID raised
pow(-0, -3) = -inf
    FE_DIVBYZERO raised

See also

sqrtsqrtfsqrtl (C++11)(C++11)	computes square root (\(\small{\sqrt{x} }\)√x) (function)
cbrtcbrtfcbrtl (C++11)(C++11)(C++11)	computes cube root (\(\small{\sqrt[3]{x} }\)3√x) (function)
hypothypotfhypotl (C++11)(C++11)(C++11)	computes square root of the sum of the squares of two or three (since C++17) given numbers (\(\scriptsize{\sqrt{x^2+y^2} }\)√x2 +y2 ), (\(\scriptsize{\sqrt{x^2+y^2+z^2} }\)√x2 +y2 +z2 ) (since C++17) (function)
pow(std::complex)	complex power, one or both arguments may be a complex number (function template)
pow(std::valarray)	applies the function std::pow to two valarrays or a valarray and a value (function template)