Function malachite_base::num::conversion::mantissa_and_exponent::sci_mantissa_and_exponent_with_rounding

pub fn sci_mantissa_and_exponent_with_rounding<T: PrimitiveUnsigned, U: PrimitiveFloat>(
    x: T, 
    rm: RoundingMode
) -> Option<(U, u64)>

Returns the scientific mantissa and exponent.

When $x$ is positive, we can write $x = 2^{e_s}m_s$, where $e_s$ is an integer and $m_s$ is a rational number with $1 \leq m_s < 2$. We represent the rational mantissa as a float. The conversion might not be exact, so we round to the nearest float using the provided rounding mode. If the rounding mode is Exact but the conversion is not exact, None is returned. $$ f(x, r) \approx (\frac{x}{2^{\lfloor \log_2 x \rfloor}}, \lfloor \log_2 x \rfloor). $$

Worst-case complexity

Constant time and additional memory.

Examples

use malachite_base::num::basic::floats::PrimitiveFloat;
use malachite_base::num::basic::unsigneds::PrimitiveUnsigned;
use malachite_base::num::conversion::mantissa_and_exponent::*;
use malachite_base::num::conversion::traits::SciMantissaAndExponent;
use malachite_base::num::float::NiceFloat;
use malachite_base::rounding_modes::RoundingMode;

fn test<T: PrimitiveUnsigned, U: PrimitiveFloat>(
    n: T,
    rm: RoundingMode,
    out: Option<(U, u64)>,
) {
    assert_eq!(
        sci_mantissa_and_exponent_with_rounding(n, rm).map(|(m, e)| (NiceFloat(m), e)),
        out.map(|(m, e)| (NiceFloat(m), e))
    );
}
test::<u32, f32>(3, RoundingMode::Down, Some((1.5, 1)));
test::<u32, f32>(3, RoundingMode::Ceiling, Some((1.5, 1)));
test::<u32, f32>(3, RoundingMode::Up, Some((1.5, 1)));
test::<u32, f32>(3, RoundingMode::Nearest, Some((1.5, 1)));
test::<u32, f32>(3, RoundingMode::Exact, Some((1.5, 1)));

test::<u32, f32>(123, RoundingMode::Floor, Some((1.921875, 6)));
test::<u32, f32>(123, RoundingMode::Down, Some((1.921875, 6)));
test::<u32, f32>(123, RoundingMode::Ceiling, Some((1.921875, 6)));
test::<u32, f32>(123, RoundingMode::Up, Some((1.921875, 6)));
test::<u32, f32>(123, RoundingMode::Nearest, Some((1.921875, 6)));
test::<u32, f32>(123, RoundingMode::Exact, Some((1.921875, 6)));

test::<u32, f32>(1000000000, RoundingMode::Nearest, Some((1.8626451, 29)));