std/core feature request: Converting floats to ints without `as`

Currently there are only two ways to cast floats to integers

1. as casts
2. to_int_unchecked

Adding explicit conversion functions could make casting a bit easier.
I would propose the functions to_int_saturating and to_int_checked.
Where to_int_saturating works like as conversions, and to_int_checked is a safe version of to_int_unchecked which returns an Option and does not accept any fractional part.

Examples:

// Saturating conversion
assert_eq!(257.64f64.to_int_saturating::<u8>(), 255);
assert_eq!(232.7f64.to_int_saturating::<u8>(), 232);

// Checked conversions
assert!(257.64f64.to_int_checked::<u8>().is_none());
assert!(232.74f64.to_int_checked::<i32>().is_none());
assert!(232.73f64.to_int_checked::<i32>().is_none());
assert_eq!(232.0f64.to_int_checked::<u8>(), Some(232));

I think the to_int_checked function would be a great new feature and using a more explicit version of as casts also helps. I think creating alterntives to as many as casts as possible is desirable.

With some pointers i might also be able to help implementing this, if there is interest in implementing this feature.

Start by reviewing the existing as conversions and to_int_unchecked behavior described in this issue, along with the proposed examples. Determine the API and semantics for to_int_saturating and to_int_checked, including fractional and out-of-range values, then define the RFC-level design and acceptance criteria.