std::sqrt, std::sqrtf, std::sqrtl

 

C++

Language

Standard Library Headers

Freestanding and hosted implementations

Named requirements

Language support library

Concepts library (C++20)

Diagnostics library

Utilities library

Strings library

Containers library

Iterators library

Ranges library (C++20)

Algorithms library

Numerics library

Input/output library

Localizations library

Regular expressions library (C++11)

Atomic operations library (C++11)

Thread support library (C++11)

Filesystem library (C++17)

Technical Specifications

 

Numerics library

Common mathematical functions

Mathematical special functions (C++17)

Mathematical constants (C++20)

Floating-point environment (C++11)

Complex numbers

Numeric arrays

Pseudo-random number generation

Compile-time rational arithmetic (C++11)

Numeric algorithms

gcd (C++17)

lcm (C++17)

Interpolations

midpoint (C++20)

lerp (C++20)

Generic numeric operations

iota (C++11)

accumulate

inner_product

adjacent_difference

partial_sum

reduce (C++17)

transform_reduce (C++17)

inclusive_scan (C++17)

exclusive_scan (C++17)

transform_inclusive_scan (C++17)

transform_exclusive_scan (C++17)

Bit operations

bit_cast (C++20)

has_single_bit (C++20)

bit_ceil (C++20)

bit_floor (C++20)

bit_width (C++20)

rotl (C++20)

rotr (C++20)

countl_zero (C++20)

countl_one (C++20)

countr_zero (C++20)

countr_one (C++20)

popcount (C++20)

endian (C++20)

 

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)
Exponential functions
exp exp2 (C++11) expm1 (C++11)	log log10 log1p (C++11) log2 (C++11)
Power functions
sqrt cbrt (C++11)	hypot (C++11) pow
Trigonometric and hyperbolic functions
sin cos tan asin acos atan atan2	sinh cosh tanh asinh (C++11) acosh (C++11) atanh (C++11)

Error and gamma functions
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)
Classification/Comparison
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       sqrt ( float arg );
float       sqrtf( float arg );			(since C++11)
double      sqrt ( double arg );		(2)
		(3)
long double sqrt ( long double arg );
long double sqrtl( long double arg );				(since C++11)
double      sqrt ( IntegralType arg );			(4)	(since C++11)

1-3) Computes the square root of arg.

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).

Parameters

arg

-

Value of a floating-point or integral type

Return value

If no errors occur, square root of arg (\({\small \sqrt{arg} }\)√arg), is returned.

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

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 zero.

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

• If the argument is less than -0, FE_INVALID is raised and NaN is returned.
• If the argument is +∞ or ±0, it is returned, unmodified.
• If the argument is NaN, NaN is returned

Notes

std::sqrt is required by the IEEE standard to be exact. The only other operations required to be exact are the arithmetic operators and the function std::fma. After rounding to the return type (using default rounding mode), the result of std::sqrt is indistinguishable from the infinitely precise result. In other words, the error is less than 0.5 ulp. Other functions, including std::pow, are not so constrained.

Example

Run this code

#include <iostream>
#include <cmath>
#include <cerrno>
#include <cfenv>
#include <cstring>
 
#pragma STDC FENV_ACCESS ON
 
int main()
{
    // normal use
    std::cout << "sqrt(100) = " << std::sqrt(100) << '\n'
              << "sqrt(2) = " << std::sqrt(2) << '\n'
              << "golden ratio = " << (1+std::sqrt(5))/2 << '\n';
    // special values
    std::cout << "sqrt(-0) = " << std::sqrt(-0.0) << '\n';
    // error handling
    errno = 0;
    std::feclearexcept(FE_ALL_EXCEPT);
    std::cout << "sqrt(-1.0) = " << std::sqrt(-1) << '\n';
    if(errno == EDOM)
        std::cout << "    errno = EDOM " << std::strerror(errno) << '\n';
    if(std::fetestexcept(FE_INVALID))
        std::cout << "    FE_INVALID raised\n";
}

Possible output:

sqrt(100) = 10
sqrt(2) = 1.41421
golden ratio = 1.61803
sqrt(-0) = -0
sqrt(-1.0) = -nan
    errno = EDOM Numerical argument out of domain
    FE_INVALID raised

See also

powpowfpowl (C++11)(C++11)	raises a number to the given power (\(\small{x^y}\)xy) (function)
cbrtcbrtfcbrtl (C++11)(C++11)(C++11)	computes cubic 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 given numbers (\(\scriptsize{\sqrt{x^2+y^2} }\)√x2 +y2 ) (function)
sqrt(std::complex)	complex square root in the range of the right half-plane (function template)
sqrt(std::valarray)	applies the function std::sqrt to each element of valarray (function template)