Float Exp Bias Constants

[Apersoma]

Proposal

Constants that specify the bias used by the encoding of the exponent for the given float type.

Problem statement

To actually figure out what the exponent of a float is given its binary representation you need to know the bias of the exponent.

Motivating examples or use cases

Implementing a function like ilog2, custom floating point conversions.

Solution sketch

impl f64 {
     pub const EXPONENT_BIAS: u64 = 1024;
}

Alternatives

Implementing functions that set or return the exponent. Much less versatile and can result in unecessary moves between fpu and regular registers.

Links and related work

#753

What happens now?

This issue contains an API change proposal (or ACP) and is part of the libs-api team feature lifecycle. Once this issue is filed, the libs-api team will review open proposals as capability becomes available. Current response times do not have a clear estimate, but may be up to several months.

Possible responses

The libs team may respond in various different ways. First, the team will consider the problem (this doesn't require any concrete solution or alternatives to have been proposed):

• We think this problem seems worth solving, and the standard library might be the right place to solve it.
• We think that this probably doesn't belong in the standard library.

Second, if there's a concrete solution:

• We think this specific solution looks roughly right, approved, you or someone else should implement this. (Further review will still happen on the subsequent implementation PR.)
• We're not sure this is the right solution, and the alternatives or other materials don't give us enough information to be sure about that. Here are some questions we have that aren't answered, or rough ideas about alternatives we'd want to see discussed.

[Apersoma]

@tgross35 I know you said you'd want this when you reviewed rust-lang/rust#154372 (comment)

[tgross35]

I think this would be nice to have to go with the other soft float helpers. Two notes:

1. Probably EXPONENT_BIAS for the naming
2. u32 is fine for all types, even binary256 only has 19 exponent bits

There's also an argument that this should be a signed integer because you're often using it with signed unbiased exponent. Personally I am used to working with the constant as a u32, though.

[joshtriplett]

Could we get some examples of code that would use this? Asking because the most obvious code we could think of would want this as a signed value:

• Mask and shift to extract the exponent bits.
• .cast_signed().
• Subtract this bias.

(For similar reasons, we felt like this should have the same size as the type.)

[cuviper]

(For similar reasons, we felt like this should have the same size as the type.)

I would expect the same type as MIN_EXP and MAX_EXP, which is i32 for all float primitives.

[tgross35]

Could we get some examples of code that would use this? Asking because the most obvious code we could think of would want this as a signed value:

* Mask and shift to extract the exponent bits.
* `.cast_signed()`.
* Subtract this bias.

Often you can avoid a unbias+rebias trip and offsets relative to the bias can be used (e.g. fixed powers of 2), so there isn't any need to switch to signed numbers. Getting the signed exponent seems like something that would be wrapped in a helper function using based on the library's needs, e.g. it may be part of normalization or just frexp.

No particularly strong feelings though.

(For similar reasons, we felt like this should have the same size as the type.)

In addition to what Josh said, full-width range isn't needed and it's nicer to have a single size when working with generic/shared code or anything involving multiple float types.