Class: Abst::MPQS

Inherits:
Object
  • Object
show all
Defined in:
lib/include/prime_mpqs.rb

Constant Summary collapse

@@kronecker_table = 
nil
@@fixed_factor_base = 
[-1, 2, 3, 5, 7, 11, 13].freeze
@@fixed_factor_base_log = 
([nil] + @@fixed_factor_base[1..-1].map {|p| Math.log(p)}).freeze
@@mpqs_parameter_map = 
[[100,20]] * 9 + [
[100, 20],		# 9 -digits
[100, 21],		# 10
[100, 22],		# 11
[100, 24],		# 12
[100, 26],		# 13
[100, 29],		# 14
[100, 32],		# 15
[200, 35],		# 16
[300, 40],		# 17
[300, 60],		# 18
[300, 80],		# 19
[300, 100],		# 20
[300, 100],		# 21
[300, 120],		# 22
[300, 140],		# 23
[600, 160],		# 24
[900, 180],		# 25
[1000, 200],	# 26
[1000, 220],	# 27
[2000, 240],	# 28
[2000, 260],	# 29
[2000, 325],	# 30
[2000, 355],	# 31
[2000, 375],	# 32
[3000, 400],	# 33
[2000, 425],	# 34
[2000, 550],	# 35
[3000, 650],	# 36
[5000, 750],	# 37
[4000, 850],	# 38
[4000, 950],	# 39
[5000, 1000],	# 40
[14000, 1150],	# 41
[15000, 1300],	# 42
[15000, 1600],	# 43
[15000, 1900],	# 44
[15000, 2200],	# 45
[20000, 2500],	# 46
[25000, 2500],	# 47
[27500, 2700],	# 48
[30000, 2800],	# 49
[35000, 2900],	# 50
[40000, 3000],	# 51
[50000, 3200],	# 52
[50000, 3500]]

Class Method Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(n, thread_num) ⇒ MPQS

Returns a new instance of MPQS.



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# File 'lib/include/prime_mpqs.rb', line 76

def initialize(n, thread_num)
#@@proc_time[:init] -= Time.now.to_i + Time.now.usec.to_f / 10 ** 6
	@original_n = n
	@thread_num = [thread_num, 1].max
	@big_prime = {}
	@big_prime_mutex = Mutex.new

	decide_multiplier(n)
	decide_parameter
	select_factor_base
	some_precomputations

	@d = Abst.isqrt(Abst.isqrt(@n >> 1) / @sieve_range)
	@d -= (@d & 3) + 1

	@matrix_left = []
	@matrix_right = []
	@mask = 1
	@check_list = Array.new(@factor_base_size)
#@@proc_time[:init] += Time.now.to_i + Time.now.usec.to_f / 10 ** 6
end

Class Method Details

.kronecker_table ⇒ Object

@@proc_time = Hash.new(0) def self.get_times return @@proc_time end



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# File 'lib/include/prime_mpqs.rb', line 62

def self.kronecker_table
	unless @@kronecker_table
		target = [3, 5, 7, 11, 13]
		@@kronecker_table = 4.times.map{Hash.new}
		(17..3583).each_prime do |p|
			k = target.map {|b| Abst.kronecker_symbol(p, b)}
			@@kronecker_table[(p & 6) >> 1][k] ||= p
		end
		@@kronecker_table[0][[1, 1, 1, 1, 1]] = 1
	end

	return @@kronecker_table
end

Instance Method Details

#decide_multiplier(n) ⇒ Object 



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# File 'lib/include/prime_mpqs.rb', line 98

def decide_multiplier(n)
	t = [3, 5, 7, 11, 13].map {|p| Abst.kronecker_symbol(n, p)}
	multiplier = self.class.kronecker_table[(n & 6) >> 1][t]
	@n = n * multiplier
end

#decide_parameter ⇒ Object 



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# File 'lib/include/prime_mpqs.rb', line 104

def decide_parameter
	digit = Math.log(@n, 10).floor
	parameter = @@mpqs_parameter_map[digit] ? @@mpqs_parameter_map[digit].dup : @@mpqs_parameter_map.last.dup
	parameter[0] = (parameter[0] * 2).floor
	@sieve_range, @factor_base_size = parameter
	@sieve_range_2 = @sieve_range << 1
end

#eliminate_big_primes(sieve_rslt) ⇒ Object 



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# File 'lib/include/prime_mpqs.rb', line 263

def eliminate_big_primes(sieve_rslt)
	sieve_rslt_with_big_prime = sieve_rslt.select{|f, re, d, r| 1 != re}
	sieve_rslt.select!{|f, re, d, r| 1 == re}

	temp_f = sieve_rslt.map(&:first)
	temp_r = sieve_rslt.map(&:last)
	temp_big = sieve_rslt.map{|f, re, d, r| d}
	sieve_rslt_with_big_prime.each do |f, re, d, r|
		unless @big_prime[re]
			@big_prime[re] = [f, r, d]
		else
			temp_f << (@big_prime[re][0].zip(f).map{|e1, e2| e1 + e2})
			temp_big << (re * d * @big_prime[re][2])
			temp_r << (r * @big_prime[re][1])
		end
	end

	return temp_f, temp_big, temp_r
end

#find_factor ⇒ Object 



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# File 'lib/include/prime_mpqs.rb', line 138

def find_factor
	if 1 == @thread_num
		find_factor_single_thread
	else
		sieve_thread_num = [@thread_num - 2, 1].max
		find_factor_multi_thread(sieve_thread_num)
	end
end

#find_factor_multi_thread(sieve_thread_num) ⇒ Object 



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# File 'lib/include/prime_mpqs.rb', line 193

def find_factor_multi_thread(sieve_thread_num)
	queue_poly = SizedQueue.new(sieve_thread_num)
	queue_sieve_rslt = SizedQueue.new(sieve_thread_num)

	# Create thread make polynomials
	th_make_poly = Thread.new do
		loop { queue_poly.push next_poly }
	end

	thg_sieve = ThreadGroup.new
	# Create threads for sieve
	sieve_thread_num.times do
		thread = Thread.new do
			loop do
				a, b, c, d = queue_poly.shift

#temp = Time.now.to_i + Time.now.usec.to_f / 10 ** 6
				# Sieve
				rslt = sieve(a, b, c, d)
#@@proc_time[:sieve] += Time.now.to_i + Time.now.usec.to_f / 10 ** 6 - temp

				queue_sieve_rslt.push rslt unless rslt.empty?
			end
		end
		thg_sieve.add thread
	end

	r_list = []
	factorization = []
	big_prime_sup = []
	loop do
		sieve_rslt = queue_sieve_rslt.shift
		next if sieve_rslt.empty?

#temp = Time.now.to_i + Time.now.usec.to_f / 10 ** 6
		f, big, r = eliminate_big_primes(sieve_rslt)
		next if f.empty?

#p [factorization.size, r_list.size, big_prime_sup.size]
		# Gaussian elimination
		factorization.concat f
		r_list.concat r
		big_prime_sup.concat big

		eliminated = gaussian_elimination(f)
#@@proc_time[:gaussian] += Time.now.to_i + Time.now.usec.to_f / 10 ** 6 - temp
		eliminated.each do |row|
			x = y = 1
			f = Array.new(@factor_base_size, 0)
			factorization.size.times do |i|
				next if row[i] == 0
				x = x * r_list[i] % @n
				f = f.zip(factorization[i]).map{|e1, e2| e1 + e2}
				y = y * big_prime_sup[i] % @n
			end

			2.upto(@factor_base_size - 1) do |i|
				y = y * Abst.power(@factor_base[i], f[i] >> 1, @n) % @n
			end
			y = (y << (f[1] >> 1)) % @n

			z = Abst.lehmer_gcd(x - y, @original_n)
			return z if 1 < z and z < @original_n
		end
	end
ensure
	thg_sieve.list.each {|th| th.kill}
	th_make_poly.kill
end

#find_factor_single_thread ⇒ Object 



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# File 'lib/include/prime_mpqs.rb', line 147

def find_factor_single_thread
	r_list = []
	factorization = []
	big_prime_sup = []

	loop do
		# Create polynomial
		a, b, c, d = next_poly

		# Sieve
#temp = Time.now.to_i + Time.now.usec.to_f / 10 ** 6
		sieve_rslt = sieve(a, b, c, d)
#@@proc_time[:sieve] += Time.now.to_i + Time.now.usec.to_f / 10 ** 6 - temp
		next if sieve_rslt.empty?
		f, big, r = eliminate_big_primes(sieve_rslt)
		next if f.empty?

		# Gaussian elimination
		factorization += f
		r_list += r
		big_prime_sup += big

#@@proc_time[:gaussian] -= Time.now.to_i + Time.now.usec.to_f / 10 ** 6
		eliminated = gaussian_elimination(f)
#@@proc_time[:gaussian] += Time.now.to_i + Time.now.usec.to_f / 10 ** 6
		eliminated.each do |row|
			x = y = 1
			f = Array.new(@factor_base_size, 0)
			factorization.size.times do |i|
				next if row[i] == 0
				x = x * r_list[i] % @n
				f = f.zip(factorization[i]).map{|e1, e2| e1 + e2}
				y = y * big_prime_sup[i] % @n
			end

			2.upto(@factor_base_size - 1) do |i|
				y = y * Abst.power(@factor_base[i], f[i] >> 1, @n) % @n
			end
			y = (y << (f[1] >> 1)) % @n

			z = Abst.lehmer_gcd(x - y, @original_n)
			return z if 1 < z and z < @original_n
		end
	end
end

#gaussian_elimination(m) ⇒ Object 



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# File 'lib/include/prime_mpqs.rb', line 385

def gaussian_elimination(m)
	elim_start = @matrix_left.size
	temp = Array.new(m.size)
	m.size.times do |i|
		temp[i] = @mask
		@mask <<= 1
	end
	rslt = @matrix_right += temp
	m = @matrix_left.concat(m.map{|row| row.reverse_each.map{|i| i[0]}})

	height = m.size
	width = @factor_base_size

	i = 0
	width.times do |j|
		unless @check_list[j]
			# Find non-zero entry
			row = nil
			elim_start.upto(height - 1) do |i2|
				if 1 == m[i2][j]
					row = i2
					break
				end
			end
			next unless row

			@check_list[j] = row

			# Swap?
			if i < row
				m.insert(i, m.delete_at(row))
				rslt.insert(i, rslt.delete_at(row))
			end

			elim_start += 1
		end

		# Eliminate
		m_i = m[i]
		(row ? (row + 1) : elim_start).upto(height - 1) do |i2|
			next if m[i2][j] == 0

			m_i2 = m[i2]
			(j + 1).upto(width - 1) do |j2|
				m_i2[j2] ^= 1 if 1 == m_i[j2]
			end
			rslt[i2] ^= rslt[i]
		end

		i += 1
	end

	t = height - i
	m.pop(t)
	return rslt.pop(t)
end

#next_d ⇒ Object 



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# File 'lib/include/prime_mpqs.rb', line 298

def next_d
	d = @d + 4
	if d < Abst.primes_list.last
		plist = Abst.primes_list
		(d..plist.last).each_prime do |p|
			return p if p[1] == 1 and Abst.kronecker_symbol(@n, p) == 1
		end
		d += 4
	end

	loop do
		return d if Abst.kronecker_symbol(@n, d) == 1 and Abst.power(@n, d >> 1, d) == 1
		d += 4
	end
end

#next_poly ⇒ Object

Return

a, b,c



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# File 'lib/include/prime_mpqs.rb', line 284

def next_poly
#temp = Time.now.to_i + Time.now.usec.to_f / 10 ** 6
	@d = d = next_d
	a = d ** 2
	h1 = Abst.power(@n, (d >> 2) + 1, d)
	h2 = ((@n - h1 ** 2) / d) * Abst.extended_lehmer_gcd(h1 << 1, d)[0] % d
	b = h1 + h2 * d
	b = a - b if b.even?
	c = ((b ** 2 - @n) >> 2) / a

#@@proc_time[:make_poly_2] += Time.now.to_i + Time.now.usec.to_f / 10 ** 6 - temp
	return a, b, c, d
end

#select_factor_base ⇒ Object 



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# File 'lib/include/prime_mpqs.rb', line 112

def select_factor_base
	@factor_base = @@fixed_factor_base.dup
	(17..INFINITY).each_prime do |p|
		if 1 == Abst.kronecker_symbol(@n, p)
			@factor_base.push(p)
			break if @factor_base_size <= @factor_base.size
		end
	end
end

#sieve(a, b, c, d) ⇒ Object 



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# File 'lib/include/prime_mpqs.rb', line 314

def sieve(a, b, c, d)
	a2 = a << 1
	lo = -(b / a2) - @sieve_range + 1

	sieve = Array.new(@sieve_range_2, 0)

#temp = Time.now.to_i + Time.now.usec.to_f / 10 ** 6
	# Sieve by 2
	#		0.upto(@sieve_range_2 - 1) do |i|
	#			count = 1
	#			count += 1 while sieve[i][2][count] == 0
	#			sieve[i][1] += @factor_base_log[1] * count
	#		end

	# Sieve by 3, 5, 7, 11, ...
	#		2.upto(@factor_base_size - 1) do |i|
	4.upto(@factor_base_size - 1) do |i|
		p = @factor_base[i]
		a_inverse = Abst.extended_lehmer_gcd(a2, p ** @power_limit[i])[0]
		pe = 1
		e = 1

		power_limit_i = @power_limit[i]
		factor_base_log_i = @factor_base_log[i]
		mod_sqrt_cache_i = @mod_sqrt_cache[i]
		while e <= power_limit_i
			pe *= p
			sqrt = mod_sqrt_cache_i[e]

			t = sqrt
			s = ((t - b) * a_inverse - lo) % pe
			s.step(@sieve_range_2 - 1, pe) do |j|
				sieve[j] += factor_base_log_i
			end

			t = pe - sqrt
			s = ((t - b) * a_inverse - lo) % pe
			s.step(@sieve_range_2 - 1, pe) do |j|
				sieve[j] += factor_base_log_i
			end

			e += 1
		end
	end
#@@proc_time[:sieve_a] += Time.now.to_i + Time.now.usec.to_f / 10 ** 6 - temp

#temp = Time.now.to_i + Time.now.usec.to_f / 10 ** 6
	# select trial division target
	td_target = []
	sieve.each.with_index do |sum_of_log, idx|
		if @closenuf < sum_of_log
			x = idx + lo
			t = a * x
			td_target.push([(t << 1) + b, (t + b) * x + c])
		end
	end
#@@proc_time[:sieve_slct] += Time.now.to_i + Time.now.usec.to_f / 10 ** 6 - temp

	# trial division on factor base
	rslt = []
#temp = Time.now.to_i + Time.now.usec.to_f / 10 ** 6
	td_target.each do |r, s|
		f, re = trial_division_on_factor_base(s, @factor_base)
		f[1] += 2
		rslt.push [f, re, d, r]
	end
#@@proc_time[:sieve_td] += Time.now.to_i + Time.now.usec.to_f / 10 ** 6 - temp

	return rslt
end

#some_precomputations ⇒ Object 



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# File 'lib/include/prime_mpqs.rb', line 122

def some_precomputations
	size  = @@fixed_factor_base_log.size
	@factor_base_log = @@fixed_factor_base_log + @factor_base[size..-1].map {|p| Math.log(p)}

	@power_limit = Array.new(@factor_base_size)
	@mod_sqrt_cache = Array.new(@factor_base_size)
	2.upto(@factor_base_size - 1) do |i|
		p = @factor_base[i]
		@power_limit[i] = (@factor_base_log.last / @factor_base_log[i]).floor
		@mod_sqrt_cache[i] = [nil] + Abst.mod_sqrt(@n, p, @power_limit[i], true)
	end

	target = Math.log(@n) / 2 + Math.log(@sieve_range) - 1
	@closenuf = target - 1.8 * Math.log(@factor_base.last)
end

#trial_division_on_factor_base(n, factor_base) ⇒ Object 



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# File 'lib/include/prime_mpqs.rb', line 442

def trial_division_on_factor_base(n, factor_base)
	factor = Array.new(@factor_base_size, 0)
	if n < 0
		factor[0] = 1
		n = -n
	end

	div_count = 1
	div_count += 1 while n[div_count] == 0
	factor[1] = div_count
	n >>= div_count

	i = 2
	while i < @factor_base_size
		d = factor_base[i]
		q, r = n.divmod(d)
		if 0 == r
			n = q
			div_count = 1
			loop do
				q, r = n.divmod(d)
				break unless 0 == r

				n = q
				div_count += 1
			end

			factor[i] = div_count
		end

		i += 1
	end

	return factor, n
end