sqrt_newton_()

template<typename F>

F fl::detail::sqrt_newton_ ( F value )

inline

Definition at line 232 of file math.cpp.hpp.

                                            {
    if (value <= F(0)) return F(0);
    // Initial estimate: x_0 = value / 2. Pure-arithmetic, no bit-cast needed.
    // Newton converges quadratically so 5-6 iterations is plenty even from a
    // crude start.
    F x = value;
    if (x > F(1)) x = F(1) + (x - F(1)) * F(0.5);  // bias toward 1 for fast convergence
    for (int i = 0; i < 6; ++i) {
        if (x == F(0)) break;
        x = F(0.5) * (x + value / x);
    }
    return x;
}

References fl::FL_NO_EXCEPT, fl::type_rank< T >::value, and fl::x.

Referenced by fl::asin_impl_double(), fl::asin_impl_float(), fl::hypot_impl_double(), fl::hypot_impl_float(), fl::sqrt_impl_double(), and fl::sqrt_impl_float().

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