sqrt

kyosu::sqrt = {}

inlineconstexpr

Computes a square root value.

Defined in Header

#include <kyosu/functions.hpp>

Callable Signatures

namespace kyosu
{
   template<eve::floating_ordered_value T>     constexpr T sqrt(T z) noexcept; //1
   template<kyosu::concepts::complex T>        constexpr T sqrt(T z) noexcept; //2
   template<kyosu::concepts::cayley_dickson T> constexpr T sqrt(T z) noexcept; //3
}

Parameters

• z: Value to for which square root is computed.

Return value

1. a real typed input z is treated as if kyosu::complex(z) was entered.
2. Returns the elementwise the square root of z, in the range of the right half-plane, including the imaginary axis ( \([0, +\infty]\) along the real axis and \([-\infty, +\infty]\) along the imaginary axis.)
   • The function is continuous onto the branch cut taking into account the sign of imaginary part
   • eve::sqrt(kyosu::conj(z)) == kyosu::conj(kyosu::sqrt(z))
   • If z is \(\pm0\), the result is \(+0\)
   • If z is \(x+i \infty\), the result is \(\infty+i \infty\) even if x is \(NaN\)
   • If z is \(x,NaN\), the result is \(NaN,NaN\) (unless x is \(\pm\infty\))
   • If z is \(-\infty+i y\), the result is \(+0+i \infty\) for finite positive y
   • If z is \(+\infty+i y\), the result is \(+\infty+i 0\) for finite positive y
   • If z is \(-\infty+i NaN\), the result is \(NaN \pm i \infty\) (sign of imaginary part unspecified)
   • If z is \(+\infty+i NaN\), the result is \(+\infty+i NaN\)
   • If z is \(NaN+i y\), the result is \(NaN+i NaN\)
   • If z is \(NaN+i NaN\), the result is \(NaN+i NaN\)

1. Returns a square root of z.

Example

#include <kyosu/kyosu.hpp>
#include <eve/wide.hpp>
#include <iostream>
 
int main()
{
  using kyosu::sqrt;
  using kyosu::complex_t;
  using kyosu::quaternion_t;
 
  std::cout << "Real:        ";
  std::cout << 72.9f << " -> " << sqrt(72.9f) << "\n";
 
  std::cout << "Complex:     ";
  std::cout << kyosu::complex_t<float>(3.5f,-2.9f) << " -> " << sqrt(kyosu::complex_t<float>(3.5f,-2.9f)) << "\n";
 
  std::cout << "Quaternion:  ";
  std::cout << kyosu::quaternion_t<double>(1.,2.,3.,4.) << " -> " << sqrt(kyosu::quaternion_t<double>(1.,2.,3.,4.)) << "\n";
 
  std::cout << "SIMD:        ";
  using wc_t = eve::wide<kyosu::complex_t<double>, eve::fixed<2>>;
  std::cout << wc_t(kyosu::complex_t<double>(1.3,-3.7)) << " -> " << sqrt(wc_t(kyosu::complex_t<double>(1.3,-3.7))) << "\n";
 
  return 0;
}