=begin
 
> お題：与えられた正の整数nを2進数～16進数に変換して表示する。
> 11進数以降の10以上を表す文字はABCDEFを使用。
> （10=A, 11=B, 12=C, 13=D, 14=E, 15=F）
> 例：12進数の11 ---> B
 
整数だと面白くないので実数でやる。
検査のために逆関数も作っとく。
2進数～64進数の Base64もどき。
 
# 1/3の3進とか、Piの2進とかやってみたかった。
 
=end
 
Nstr = *'0'..'9', *'A'..'Z', *'a'..'z', '+', '/'	# Base64 もどき
Nidx = {}
Nstr.each_with_index{|ch,idx| Nidx[ch] = idx }
 
 
def fbase( bs, n )
	return nil	if bs < 2 || bs > Nstr.size
	str = ''
	sgn = (n < 0)? '-' : ''
	n = n.abs
	fr = n - n.to_i
	n = n.to_i
	begin
		n, r = n.divmod( bs )
		str << Nstr[r]
	end while n != 0
 
	fdig = Math.log( 10 ** 8, bs ).to_i + 1
 
	fstr = '.'
	begin
		fr *= bs
		fstr << Nstr[fr.to_i]
		fr -= fr.to_i
		fdig -= 1
	end while fr != 0 && fdig > 0
	fstr.sub!( /0+$/, '' )
	fstr = ''	if fstr == '.'
 
	"#{sgn}#{str.reverse}#{fstr}"
end
 
def revfbase( bs, str )
	return nil	if bs < 2 || bs > Nstr.size
	fstr = ''
	if str =~ /^(.*)\.(.*)$/
		str = $1
		fstr = $2
	end
	sg = 1
	if str[0] == '-'
		sg = -1
		str = str[1..-1]
	end
	n = 0
	m = 1
	str.reverse.each_char{|ch|
		unless Nidx[ch]
			warn "*** #{ch} ***"
			return ''
		end
		n += m * Nidx[ch]
		m *= bs
	}
	m = 1
	fstr.each_char{|ch|
		unless Nidx[ch]
			warn "*** #{ch} ***"
			return ''
		end
		m = m.fdiv(bs)
		n += m * Nidx[ch]
	}
	sg * n
end
 
def ftest( bs, n )
	return	if bs < 2 || bs > Nstr.size
	print "%20s : " % n
	ans = fbase(  bs, n )
	print "#{'%2d' % bs} : #{'%20s' % ans}"
	str = revfbase( bs, ans )
	print " : #{'%20s' % str}"
	if n != str.to_f
		print " : #{'%.1e' % [n - str.to_f]}"
	end
	puts
end
 
 
	ftest(  2, 123456 )
	ftest( 10, 123456 )
	ftest( 16, 123456 )
	ftest( 64, 123456 )
	ftest( 10, -123456 )
	ftest(  2, -123456 )
 
	ftest(  2, 0 )
	ftest(  2, 2.5 )
	ftest(  2, 0.5 )
	ftest(  2, 0.25 )
	ftest(  2, 0.125 )
	ftest(  2, -0.125 )
	ftest(  2, 0.75 )
 
	ftest(  2, 1.41421356 )
	ftest(  2, 3.1415926 )
	ftest(  3, 3.1415926 )
	ftest( 10, 3.1415926 )
	ftest( 16, 3.1415926 )
	ftest( 64, 3.1415926 )
 
	ftest( 16, 10.75 )
 
	ftest(  3, 1.fdiv(3) )
	ftest(  6, 1.fdiv(3) )
	ftest(  9, 1.fdiv(3) )
	ftest( 63, 1.fdiv(3) )
 

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