reduce allocations for string(::IEEEFloat)

[oscardssmith]

julia> @time string(1.0)
  0.000004 seconds (3 allocations: 432 bytes) # before
  0.000007 seconds (3 allocations: 112 bytes) # after
julia> io = IOBuffer();
julia> @time show(io, 1.0)
  0.000014 seconds (3 allocations: 432 bytes) # before
  0.000012 seconds (1 allocation: 48 bytes) # after

mitigates #57976

[bvdmitri]

Can this PR also fix Printf.format in a similar manner? Currently it does allocate an intermediate array too and works almost in exactly same way as the show method. With the Printf.format though by using some internal API it is possible to do non-allocating printing of a number

julia> buf = Vector{UInt8}(undef, 10)
10-element Vector{UInt8}:
 0x69
 0x09
 0x00
 0x00
 0x00
 0x00
 0x00
 0x00
 0x6a
 0x09

julia> format = Printf.format"%.4f"
Printf.Format{Base.CodeUnits{UInt8, String}, Tuple{Printf.Spec{Val{'f'}}}}(UInt8[0x25, 0x2e, 0x34, 0x66], UnitRange{Int64}[1:0, 5:4], (%.4f,), 1)

julia> @time Printf.format(buf, 1, format, 1.0)
  0.000016 seconds
7

However, the signature of format is constrained to Vector and cannot use the Memory

[oscardssmith]

I think printf should be left to a separate PR. The last thing to do here, is I would appreciate someone double checking that the numbers I've put down for neededfloatdigits are correct (and ideally find the formula that generates them). I believe these are the right numbers, but my search for them wasn't exactly principled)

[vtjnash]

Extra bytes are needed (for "Float16()") if "typed && T isa Float16"

[oscardssmith]

I included this in neededfloatdigits(::Float16), but I guess it would make sense to separate it so we can allocate less when !typed

[vtjnash]

"If an IEEE 754 double-precision number is converted to a decimal string with at least 17 significant digits, and then converted back to double-precision representation, the final result must match the original number"

17 + decimal point + sign bit + "e" + second sign bit + max exponent (3) = 24?

https://en.wikipedia.org/wiki/Double-precision_floating-point_format

[vtjnash]

9 + decimal point + sign bit + "f" + second sign bit + max exponent (2) = 15

[vtjnash]

julia> extrema(i->length(string(reinterpret(Float32, i))), typemin(UInt32):typemax(UInt32))
(3, 15)

[vtjnash]

5 + decimal point + sign bit + "e" + second sign bit + max exponent (2) = 11

julia> extrema(i->length(string(reinterpret(Float16, i))), typemin(UInt16):typemax(UInt16))
(3, 11)

(so maximum = 20 with typed=true)