sqrt

kyosu::sqrt = eve::functor<sqrt_t>

inlineconstexpr

Computes a square root value.

Header file

#include <kyosu/functions.hpp>

Callable Signatures

namespace kyosu
{
   //  regular call
   template<kyosu::concepts::cayley_dickson_like T> constexpr complexify_t<T> sqrt(T z) noexcept;
 
   // semantic modifyers
   template<concepts::real T> constexpr complexify_t<T> sqrt[real_only](T z) noexcept;
}

Parameters

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

Return value

• A real typed input z is treated as if complex(z) was entered, unless the option real_only is used in which case the parameter must be a floating_value, the real part of the result will the same as an eve::sqrt implying a Nan result if the result is not real.
• for complex inpur, 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 \(NaN+i NaN\)

Returns a square root of z.

External references

• C++ standard reference: complex cosh
• Wolfram MathWorld: Square Root
• Wikipedia: Square root

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;
}