BigFloat prints differently from Float(32|64) in scientific notation

[fredrikekre]

BigFloats always include the + for the exponent and leading 0s but e.g. Float64 does not:

julia> big"1e6"
1.0e+06

julia> 1e6
1.0e6

Noticed by @pjaap in fredrikekre/Runic.jl#13 (comment).

[tgross35]

There is also a discrepancy with %a formatting:

julia> @printf "%a" 4.5
0x1.2p+2
julia> @printf "%a" big(4.5)
0x4.8p+0

It would be nicer if bigfloat normalized the same as regular floats, i.e. always starting with a leading 0x1 rather than any hex digit.

[Seelengrab]

Do we do our own printing for BigFloat, or do we forward to GMP?

[tgross35]

Ah, it looks like it is MPFR doing the formatting

julia/stdlib/Printf/src/Printf.jl

Lines 490 to 521 in ac79b9f

	_snprintf(ptr, siz, str, arg) =
	@ccall "libmpfr".mpfr_snprintf(ptr::Ptr{UInt8}, siz::Csize_t, str::Ptr{UInt8};
	arg::Ref{BigFloat})::Cint
	# Arbitrary constant for a maximum number of bytes we want to output for a BigFloat.
	# 8KiB seems like a reasonable default. Larger BigFloat representations should probably
	# use a custom printing routine. Printing values with results larger than this ourselves
	# seems like a dangerous thing to do.
	const __BIG_FLOAT_MAX__ = 8192
	function fmt(buf, pos, arg, spec::Spec{T}) where {T <: Floats}
	leftalign, plus, space, zero, hash, width, prec =
	spec.leftalign, spec.plus, spec.space, spec.zero, spec.hash, spec.width, spec.precision
	x = tofloat(arg)
	if x isa BigFloat
	if isfinite(x)
	GC.@preserve buf begin
	siz = length(buf) - pos + 1
	str = string(spec; modifier="R")
	required_length = _snprintf(pointer(buf, pos), siz, str, x)
	if required_length > siz
	required_length > __BIG_FLOAT_MAX__ &&
	throw(ArgumentError("The given BigFloat requires $required_length bytes to be printed, which is more than the maximum of $__BIG_FLOAT_MAX__ bytes supported."))
	resize!(buf, required_length + 1)
	required_length = _snprintf(pointer(buf, pos), required_length + 1, str, x)
	end
	required_length > 0 || throw(ArgumentError("The given BigFloat would produce less than the maximum allowed number of bytes $__BIG_FLOAT_MAX__, but still couldn't be printed fully for an unknown reason."))
	return pos + required_length
	end
	end
	x = Float64(x)
	end

, the dotnet docs have an example that confirms mpfr's behavior https://machinecognitis.github.io/Math.Mpfr.Native/html/8c4f26fd-509c-6557-1907-76d9d7ed7475.htm.