Class: Nio::RepDec

Inherits:
Object
  • Object
show all
Includes:
StateEquivalent
Defined in:
lib/nio/repdec.rb,
lib/nio/fmt.rb

Overview

RepDec handles repeating decimals (repeating numerals actually)

Defined Under Namespace

Classes: Opt

Constant Summary collapse

DEF_OPT = 
Opt.new

Instance Attribute Summary collapse

Class Method Summary collapse

Instance Method Summary collapse

Methods included from StateEquivalent

#===, #eql?, #hash

Constructor Details

#initialize(b = 10) ⇒ RepDec

Returns a new instance of RepDec.



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# File 'lib/nio/repdec.rb', line 134

def initialize(b=10)
  setZ(b)
end

Instance Attribute Details

#d ⇒ Object

protected



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# File 'lib/nio/repdec.rb', line 474

def d
  @d
end

#ip ⇒ Object

protected



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# File 'lib/nio/repdec.rb', line 474

def ip
  @ip
end

#rep_i ⇒ Object

protected



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# File 'lib/nio/repdec.rb', line 474

def rep_i
  @rep_i
end

#sign ⇒ Object

protected



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# File 'lib/nio/repdec.rb', line 474

def sign
  @sign
end

Class Method Details

.group_digits(digits, opt) ⇒ Object 



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# File 'lib/nio/repdec.rb', line 480

def RepDec.group_digits(digits, opt)
  if opt.grp_sep!=nil && opt.grp_sep!='' && opt.grp.length>0
    grouped = ''
    i = 0
    while digits.length>0
      l = opt.grp[i]
      l = digits.length if l>digits.length
      grouped = opt.grp_sep + grouped if grouped.length>0
      grouped = digits[-l,l] + grouped
      digits = digits[0,digits.length-l]
      i += 1 if i<opt.grp.length-1
    end
    grouped
  else
   digits
  end
end

.maximum_number_of_digits ⇒ Object

Return the maximum number of digits that RepDec objects can handle.



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# File 'lib/nio/repdec.rb', line 389

def RepDec.maximum_number_of_digits
  @max_d
end

.maximum_number_of_digits=(n) ⇒ Object

Change the maximum number of digits that RepDec objects can handle.



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# File 'lib/nio/repdec.rb', line 384

def RepDec.maximum_number_of_digits=(n)
  @max_d = [n,2048].max
end

.parse(str, opt = DEF_OPT) ⇒ Object 



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# File 'lib/nio/repdec.rb', line 211

def RepDec.parse(str, opt=DEF_OPT)
  sgn,i_str,f_str,ri,detect_rep = nil,nil,nil,nil,nil

  i = 0;
  l = str.length;

  detect_rep = false;

  
  i += 1 while i<str.length && str[i,1] =~/\s/
  
  
  neg = false;

  neg = true if str[i,1]=='-'
  i += 1 if str[i,1]=='-' || str[i,1]=='+'
  

  i += 1 while i<str.length && str[i,1] =~/\s/
  

  str.upcase!
  if str[i,opt.nan_txt.size]==opt.nan_txt.upcase
    i_str = :indeterminate;
  elsif str[i,opt.inf_txt.size]==opt.inf_txt.upcase
    i_str = neg ? :neginfinity : :posinfinity;
  end
  
  unless i_str
    i_str = "0";
    while i<l && str[i,1]!=opt.dec_sep
      break if str[i,opt.auto_rep.length]==opt.auto_rep && opt.auto_rep!=''
      i_str += str[i,1] if str[i,1]!=opt.grp_sep
      i += 1;
    end
    sgn = neg ? -1 : +1
    i += 1; # skip the decimal separator
  end
  
  unless i_str.kind_of?(Symbol)
    j = 0;
    f_str = ''
    while i<l
      ch = str[i,1];
      if ch==opt.begin_rep then
        ri = j;
      elsif ch==opt.end_rep then
        i = l;
      elsif ch==opt.auto_rep[0,1] then
        detect_rep = true;
        i = l;
      else
        f_str << ch
        j += 1;
      end
      i += 1;
    end
  end
  return [sgn,i_str,f_str,ri,detect_rep]
end

Instance Method Details

#==(c) ⇒ Object 



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# File 'lib/nio/repdec.rb', line 370

def ==(c)
  a = copy;
  b = c.copy;
  a.normalize!
  b.normalize!
  return a.ip==b.ip && a.d==b.d && a.rep_i==b.rep_i
end

#copy ⇒ Object 



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# File 'lib/nio/repdec.rb', line 364

def copy()
  c = clone
  c.d = d.clone
  return c;
end

#getQ(opt = DEF_OPT) ⇒ Object

Raises:



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# File 'lib/nio/repdec.rb', line 433

def getQ(opt=DEF_OPT)
  raise RepDecError,"Base mismatch: #{opt.digits.radix} when #{@radix} was expected." if opt.digits_defined? && @radix!=opt.digits.radix
  
  if !ip.is_a?(Integer) then
    y = 0;
    x=0 if ip==:indeterminate;
    x=1 if ip==:posinfinity
    x=-1 if ip==:neginfinity
    return x,y;
  end if

  
  n = @d.length
  a = @ip
  b = a
  for i in 0...n
    a*=@radix
    a+=@d[i];
    if @rep_i!=nil && i<@rep_i
      b *= @radix
      b += @d[i];
    end
  end

  x = a
  x -= b if @rep_i!=nil

  y = @radix**n
  y -= @radix**@rep_i if @rep_i!=nil

  d = Nio.gcd(x,y)
  x /= d
  y /= d

  x = -x if @sign<0

  return x,y;
end

#getS(nrep = 0, opt = DEF_OPT) ⇒ Object

Raises:



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# File 'lib/nio/repdec.rb', line 272

def getS(nrep=0, opt=DEF_OPT)
  raise RepDecError,"Base mismatch: #{opt.digits.radix} when #{@radix} was expected." if opt.digits_defined? && @radix!=opt.digits.radix
   
   if !ip.is_a?(Integer) then
     str=opt.nan_txt if ip==:indeterminate;
     str=opt.inf_txt if ip==:posinfinity
     str='-'+opt.inf_txt if ip==:neginfinity
     return str;
   end
   
   s = "";
   s += '-' if @sign<0
   s += RepDec.group_digits(@ip.to_s(@radix),opt);
   s += opt.dec_sep if @d.length>0;
   for i in 0...@d.length
     break if nrep>0 && @rep_i==i;
     s += opt.begin_rep if i==@rep_i;
     s << opt.digits.digit_char(@d[i])
   end;
   if nrep>0 then
     if @rep_i!=nil then
        nrep += 1;
        nrep.times do
          for i in @rep_i...@d.length
           s << opt.digits.digit_char(@d[i])
          end
        end
        
        check = RepDec.new;
        check.setS s+opt.auto_rep, opt;
        #print " s=",s,"\n"
        #print " self=",self.to_s,"\n"
        while check!=self
          for i in @rep_i...@d.length
            s << opt.digits.digit_char(@d[i])
          end
          check.setS s+opt.auto_rep, opt;
        end
        
        s += opt.auto_rep;
     end
   else
     s += opt.end_rep if @rep_i!=nil;
   end
   return s;
end

#normalize!(remove_trailing_zeros = true) ⇒ Object 



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# File 'lib/nio/repdec.rb', line 323

def normalize!(remove_trailing_zeros=true)
  if ip.is_a?(Integer)
    if @rep_i!=nil && @rep_i==@d.length-1 && @d[@rep_i]==(@radix-1) then
      @d.pop;
      @rep_i = nil;
      
      i = @d.length-1;
      carry = 1;
      while carry>0 && i>=0
        @d[i] += carry;
        carry = 0;
        if @d[i]>(@radix) then
          carry = 1;
          @d[i]=0;
          @d.pop if i==@d.length;
        end
        i -= 1;
      end
      @ip += carry;
      
    end
    
    if @rep_i!=nil && @rep_i>=@d.length
      @rep_i = nil
    end
    
    if @rep_i!=nil && @rep_i>=0
      unless @d[@rep_i..-1].find {|x| x!=0}
        @d = @d[0...@rep_i]
        @rep_i = nil
      end
    end
    if @rep_i==nil && remove_trailing_zeros
      while @d[@d.length-1]==0
        @d.pop
      end
    end
    
  end
end

#setQ(x, y, opt = DEF_OPT) ⇒ Object 



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# File 'lib/nio/repdec.rb', line 393

def setQ(x,y, opt=DEF_OPT)
  @radix = opt.digits.radix if opt.digits_defined?
  xy_sign = x==0 ? 0 : x<0 ? -1 : +1;
  xy_sign = -xy_sign if y<0;
  @sign = xy_sign
  x = x.abs;
  y = y.abs;

  @d = [];
  @rep_i = nil;
  
  if y==0 then
    if x==0 then
      @ip = :indeterminate
    else
      @ip = xy_sign==-1 ? :neginfinity : :posinfinity
    end
    return self
  end
  
  k = {};
  @ip = x.div(y) #x/y;
  x -= @ip*y;
  i = 0;
  ended = false;

  max_d = opt.max_d
  while x>0 && @rep_i==nil && (max_d<=0 || i<max_d)
    @rep_i = k[x]
    if @rep_i.nil? then
      k[x] = i;
      x *= @radix
      d,x = x.divmod(y)
      @d.push d
      i += 1;
    end
  end
  self
end

#setS(str, opt = DEF_OPT) ⇒ Object 



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# File 'lib/nio/repdec.rb', line 147

def setS(str, opt=DEF_OPT)
  setZ(opt.digits_defined? ? opt.digits.radix : @radix);
  sgn,i_str,f_str,ri,detect_rep = RepDec.parse(str,opt)
  if i_str.kind_of?(Symbol)
    @ip = i_str
  else
    @ip = i_str.to_i(@radix); # this assumes conventional digits
  end
  @sign = sgn
  @rep_i = ri if ri
  f_str.each_byte{|b| @d.push opt.digits.digit_value(b)} unless f_str.nil?

  if detect_rep then
    
    for l in 1..(@d.length/2)
      l = @d.length/2 + 1 - l;
      if @d[-l..-1]==@d[-2*l...-l]
        
        for m in 1..l
          if l.modulo(m)==0 then
            reduce_l = true;
            for i in 2..l/m
              if @d[-m..-1]!=@d[-i*m...-i*m+m] then
                 reduce_l = false;
                 break;
              end
            end
            if reduce_l then
               l = m
               break
            end
          end
        end
        
        
        @rep_i = @d.length - 2*l;
        l.times { @d.pop }
        
        
        while @d.length >= 2*l && @d[-l..-1]==@d[-2*l...-l]
          
          @rep_i = @d.length - 2*l;
          l.times { @d.pop }
          
        end
        
        break
      end
    end
    
  end

  
  if @rep_i!=nil then
    if @d.length==@rep_i+1 && @d[@rep_i]==0 then
      @rep_i = nil;
      @d.pop;
    end
  end
  @d.pop while @d[@d.length-1]==0
  
  self
end

#setZ(b = 10) ⇒ Object 



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# File 'lib/nio/repdec.rb', line 138

def setZ(b=10)
   @ip    = 0;
   @d     = [];
   @rep_i = nil;
   @sign  = 0;
   @radix = b;
   self
end

#to_NeutralNum(base_dgs = nil) ⇒ Object 



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# File 'lib/nio/fmt.rb', line 360

def to_NeutralNum(base_dgs=nil)
  num = NeutralNum.new
  if !ip.is_a?(Integer)
    
    case ip
      when :indeterminate
        num.set_special :nan
      when :posinfinity
        num.set_special :inf,'+'
      when :neginfinity
        num.set_special :inf,'-'
      else
        num = nil
    end
    
  else
    base_dgs ||= DigitsDef.base(@radix)
    # assert base_dgs.radix == @radix
    signch = sign<0 ? '-' : '+'
    decimals = ip.to_s(@radix)
    dec_pos = decimals.length
    d.each {|dig| decimals << base_dgs.digit_char(dig) }
    rep_pos = rep_i==nil ? decimals.length : dec_pos + rep_i
    num.set signch, decimals, dec_pos, rep_pos, base_dgs
  end
  return num
end

#to_s ⇒ Object 



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# File 'lib/nio/repdec.rb', line 319

def to_s()
  getS
end