Function primitive_float_sqrt_rational 

pub fn primitive_float_sqrt_rational<T>(x: &Rational) -> T
where
    Float: PartialOrd<T>,
    for<'a> T: ExactFrom<&'a Float> + RoundingFrom<&'a Float> + PrimitiveFloat,

Computes the square root of a Rational, returning a primitive float result.

If the square root is equidistant from two primitive floats, the primitive float with fewer 1s in its binary expansion is chosen. See RoundingMode for a description of the Nearest rounding mode.

The square root of any negative number is NaN.

$$ f(x) = \sqrt{x}+\varepsilon. $$

• If $\sqrt{x}$ is infinite, zero, or NaN, $\varepsilon$ may be ignored or assumed to be 0.
• If $\sqrt{x}$ is finite and nonzero, then $|\varepsilon| < 2^{\lfloor\log_2 \sqrt{x}\rfloor-p}$, where $p$ is precision of the output (typically 24 if T is a f32 and 53 if T is a f64, but less if the output is subnormal).

Special cases:

• $f(0)=0.0$

Overflow:

• If the absolute value of the result is too large to represent, $\infty$ is returned instead.
• If the absolute value of the result is too small to represent, 0.0 is returned instead.

Since the result is never negative, negative overflow and underflow cannot occur.

Worst-case complexity

$T(m) = O(m \log m \log\log m)$

$M(m) = O(m \log m)$

where $T$ is time, $M$ is additional memory, and $m$ is x.significant_bits().

Examples

use malachite_base::num::basic::traits::Zero;
use malachite_base::num::float::NiceFloat;
use malachite_float::float::arithmetic::sqrt::primitive_float_sqrt_rational;
use malachite_q::Rational;

assert_eq!(
    NiceFloat(primitive_float_sqrt_rational::<f64>(&Rational::ZERO)),
    NiceFloat(0.0)
);
assert_eq!(
    NiceFloat(primitive_float_sqrt_rational::<f64>(
        &Rational::from_unsigneds(1u8, 3)
    )),
    NiceFloat(0.5773502691896257)
);
assert_eq!(
    NiceFloat(primitive_float_sqrt_rational::<f64>(&Rational::from(10000))),
    NiceFloat(100.0)
);
assert_eq!(
    NiceFloat(primitive_float_sqrt_rational::<f64>(&Rational::from(
        -10000
    ))),
    NiceFloat(f64::NAN)
);