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