Constant and/or function for the implicit digit of the mantissa for floats

Proposal

Adding a constant or function that represents where the implicit digit of the mantissa of normal floating point numbers would be if it was explicit. (This is equivalent to the lowest bit of the exponent), and/or a method that would return constant if it was called on a normal value, zero otherwise.

Problem statement

Rust provides constants¹ and functions for performing bitwise operations on floats, but doesn't include a constant/function for getting the implicit bit.

¹The only one on stable is MANTISSA_DIGITS, but BITS, MANTISSA_MASK, EXPONENT_MASK, and SIGN_MASK are in the process of stabilization and constants for the exponent bias, signal bit and payload, have been proposed. See related work for links to the tracking issues/ACPs.

Motivating examples or use cases

The implementation of many if not most, that are written to compute a mathematic function and perform bitwise ops require introducing the implied bit on normal values in order to compute their result. Both the function and the constant provide methods of generating this value.

I personally would use this to implement arithmetic where the rounding mode can be specified.

Solution sketch

impl f64 {
    /// <docs>
    pub const IMPLICIT_BIT: u64 = 0x0010_0000_0000_0000;
    /// <docs>
    pub fn get_implied_bit(self) -> u64 {
        f64::IMPLICIT_BIT * x.is_normal() as u64
    }
}

Alternatives

Function vs constant vs both vs neither.
I generally think the constant would work better as bits will likely have already been moved off of float registers to moving it back to the function (and then possibly moving it back to the regular registers so you can actually perform is_normal) would be a waste, as well as the fact that it is ill-defined on infinities and NaNs.

Links and related work

• bit masks for the parts of non-nan floats: https://github.com/rust-lang/rust/issues/154064
• bits constant for floats: https://github.com/rust-lang/rust/issues/151073
• exp bias constant: #784
• bit mask for the parts of nans: #795

Start by reading the proposal and its related issues #154064, #151073, #784, and #795 to understand the surrounding float-constant work. The issue does not name implementation files or tests; done requires resolving whether a constant, function, both, or neither belongs in the API and defining the accepted behavior for normal values and non-normal values.