Function primitive_float_rem_rational 

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

Computes the remainder of a primitive float by a Rational, with the quotient rounded toward zero, correctly rounding the result to the nearest value.

The Rational modulus is used exactly. A remainder is unusually sensitive to its modulus — perturbing it by $\varepsilon$ moves the result by up to the quotient times $\varepsilon$ — so no primitive-float approximation of the modulus could produce these values. NaN or infinite x, or zero y, gives NaN.

Worst-case complexity

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

$M(n) = O(n)$

where $T$ is time, $M$ is additional memory, and $n$ is y.significant_bits().

Examples

use malachite_base::num::float::NiceFloat;
use malachite_float::float::arithmetic::rem::primitive_float_rem_rational;
use malachite_q::Rational;

// 10 mod 22/7 = 4/7
assert_eq!(
    NiceFloat(primitive_float_rem_rational(
        10.0,
        &Rational::from_signeds(22, 7)
    )),
    NiceFloat(0.5714285714285714)
);