Support scientific notation in BigDecimal#to_s

[HertzDevil]

Resolves #9578.

# before
BigDecimal.new(Float32::MAX)          # => 340282350000000000000000000000000000000
BigDecimal.new(Float32::MIN_POSITIVE) # => 0.000000000000000000000000000000000000011754944

# after
BigDecimal.new(Float32::MAX)          # => 3.4028235e+38
BigDecimal.new(Float32::MIN_POSITIVE) # => 1.1754944e-38

The code here is very similar to #10632 and Float::Printer#internal. If both are merged we should think about refactoring them into a single implementation.

[straight-shoota]

This doesn't break any formal API, but it's still a significant change in behaviour. I you expect ˋ0ˋ to stringify as ˋ0ˋ, returning ˋ0.0ˋ breaks that.

So... do we have to wait for 2.0 with this?

[straight-shoota]

Suggested change

	if buffer[0]? == 45 # '-'
	if buffer[0]? === '-'

I'm pretty sure this doen't add any significant overhead and saves you from annotating the character in a comment ;)

[sevk]

“===” different from ruby syntax ？

[HertzDevil]

Some additional clarification: unlike #10632 (comment), fixed precision formatting is actually possible for BigDecimals converted from Floats, but the current constructor doesn't work because it relies on Float#to_s, and any BigDecimals created this way are inherently lossy. Instead the float must be decomposed manually:

require "big"

struct BigDecimal
  def **(other : Int) : BigDecimal
    return (to_big_r ** other).to_big_d if other < 0 # #10892
    BigDecimal.new(@value ** other, @scale * other)
  end

  def self.exact(float : Float32)
    mantissa, exponent = Math.frexp(float)
    Math.ldexp(mantissa, Float32::MANT_DIGITS).to_i * 2.to_big_d ** (exponent - Float32::MANT_DIGITS)
  end

  def self.exact(float : Float64)
    mantissa, exponent = Math.frexp(float)
    Math.ldexp(mantissa, Float64::MANT_DIGITS).to_i * 2.to_big_d ** (exponent - Float64::MANT_DIGITS)
  end
end

# Before:
BigDecimal.exact(Float32::MAX)          # => 340282346638528859811704183484516925440
BigDecimal.new(Float32::MAX)            # => 340282350000000000000000000000000000000
BigDecimal.exact(Float32::MIN_POSITIVE) # => 0.0000000000000000000000000000000000000117549435082228750796873653722224567781866555677208752146087936
BigDecimal.new(Float32::MIN_POSITIVE)   # => 0.000000000000000000000000000000000000011754944

# After:
BigDecimal.exact(Float32::MAX)          # => 3.4028234663852885981170418348451692544e+38
BigDecimal.new(Float32::MAX)            # => 3.4028235e+38
BigDecimal.exact(Float32::MIN_POSITIVE) # => 1.17549435082228750796873653722224567781866555677208752146087936e-38
BigDecimal.new(Float32::MIN_POSITIVE)   # => 1.1754944e-38

Like the corresponding PR for BigFloat, this patch never changes the number of significant digits in the output of BigDecimal#to_s.

[beta-ziliani]

I don't think there were complains about pushing #10632, so I think we can follow suit here. Sorry Quinton that it took this long, and thanks! 🙇