Function partial_reduce 

pub(crate) fn partial_reduce<L: Limbs + Limbs>(
    log_2_bound: u32,
    a: L,
    b: (Choice, L),
    negative_discriminant_abs: &L,
) -> (L, (Choice, L), L)

Partially reduce a positive definite binary quadratic form.

For a positive definite binary quadratic form (a, b, c) such that:

• b^2 - 4ac = delta where delta < 0 (the form is well-defined for a negative discriminant)
• $delta \cong 1 \mod 2$
• 0 <= a (a isn’t negative, as enforced by the type system)
• floor(log_2(a)) + 1 <= log_2_bound
• floor(log_2(|b|)) + 1 <= log_2_bound
• There is an integer solution for c in b^2 - 4 a c = delta.
• ceil(log_2_bound / Limb::BITS) <= <L as AsRef::<[Limb]>>::as_ref(&a).len()
• <L as AsRef::<[Limb]>>::as_ref(&a).len() == <L as AsRef::<[Limb]>>::as_ref(&b.1).len()
• <L as AsRef::<[Limb]>>::as_ref(&negative_discriminant_abs).len() <= 2 * <L as AsRef::<[Limb]>>::as_ref(&b.1).len()
• $floor(log_2(|delta|)) + 1 < <_ as AsRef<Limb>>::as_ref(a).len() * Limb::BITS$
• $floor(log_2(a)) + 1 < <_ as AsRef<Limb>>::as_ref(a).len() * Limb::BITS$

Yield an equivalent form (a', b', c') such that:

• b'^2 <= |delta|
• (a', b', c') is reduced or b' > a'
• gcd(a, b, c) = gcd(a', b', c')

As composition is presumably programmed to compose b-bit-length numbers, where composition outputs 2 * b-bit-length numbers, this function intends to solely perform the necessary reduction such that the numbers are once again of b-bit-length (and able to be composed again). While these forms are not reduced, they may still usable for composition without performing a full reduction (which would take roughly twice as long). This allows deferring a full reduction until one needs a reduced form.

This second bound on the output, (a', b', c') is reduced or b' > a', is critical as it enables the following corollary: a'^2 < |delta|.

b.0, b'.0 are true if the value is positive.

delta is bound to be negative and specified via its absolute value in negative_discriminant_abs.