Class: Nio::Tolerance

Inherits:
Object
  • Object
show all
Includes:
StateEquivalent
Defined in:
lib/nio/flttol.rb

Overview

This class represents floating point tolerances for Float numbers and allows comparison within the specified tolerance.

Class Method Summary collapse

Instance Method Summary collapse

Methods included from StateEquivalent

#==, #===, #eql?, #hash

Constructor Details

#initialize(t = 0.0, mode = :abs, decmode = false) ⇒ Tolerance

The tolerance mode is either :abs (absolute) :rel (relative) or :sig (significant). The last parameter is a flag to specify decimal mode for the :sig mode



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# File 'lib/nio/flttol.rb', line 113

def initialize(t=0.0, mode=:abs, decmode=false)
  set t, mode, decmode
end

Class Method Details

.big_epsilon(n = 1, mode = :sig) ⇒ Object 



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# File 'lib/nio/flttol.rb', line 366

def Tolerance.big_epsilon(n=1, mode=:sig)
  Tolerance.new.big_epsilon(n, mode)
end

.decimals(d = 0, mode = :abs, rounded = true) ⇒ Object 



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# File 'lib/nio/flttol.rb', line 357

def Tolerance.decimals(d=0, mode=:abs,rounded=true)
  Tolerance.new.decimals(d,mode,rounded)
end

.epsilon(n = 1, mode = :sig) ⇒ Object 



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# File 'lib/nio/flttol.rb', line 363

def Tolerance.epsilon(n=1, mode=:sig)
  Tolerance.new.epsilon(n, mode)
end

.fraction(f) ⇒ Object 



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# File 'lib/nio/flttol.rb', line 369

def Tolerance.fraction(f)
  Tolerance.new.fraction(f)
end

.percent(p) ⇒ Object 



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# File 'lib/nio/flttol.rb', line 372

def Tolerance.percent(p)
  Tolerance.new.percent(p)
end

.permille(p) ⇒ Object 



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# File 'lib/nio/flttol.rb', line 375

def Tolerance.permille(p)
  Tolerance.new.permille(p)
end

.sig_decimals(d = 0, mode = :abs, rounded = true) ⇒ Object 



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

def Tolerance.sig_decimals(d=0, mode=:abs,rounded=true)
  Tolerance.new.sig_decimals(d,rounded)
end

Instance Method Details

#[](x) ⇒ Object

Shortcut notation for get_value



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# File 'lib/nio/flttol.rb', line 162

def [](x)
  return x.nil? ? @t : get_value(x)
end

#apprx_i(x, result = Integer) ⇒ Object

If the argument is close to an integer it rounds it and returns it as an object of the specified class (by default, Integer)



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# File 'lib/nio/flttol.rb', line 296

def apprx_i(x,result=Integer)
  r = x.round
  return equals?(x,r) ? Nio.numeric_cast(r,result) : x
end

#apprx_i?(x) ⇒ Boolean

Returns true if the argument is approximately an integer

Returns:

  • (Boolean) 


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# File 'lib/nio/flttol.rb', line 291

def apprx_i?(x)
  equals?(x,x.round)
end

#aprx_equals?(x, y) ⇒ Boolean

Approximate equality within tolerance

Returns:

  • (Boolean) 


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# File 'lib/nio/flttol.rb', line 207

def aprx_equals?(x,y)
  
  case @mode
    when :sig
      
      if @decimal_mode
        begin
          x_exp = Math.log10(x.abs)
          #x_exp = x_exp.finite? ? x_exp.ceil : 0
          x_exp = x_exp.finite? ? x_exp.floor+1 : 0
        rescue
          x_exp = 0
        end
        begin 
          y_exp = Math.log10(y.abs)
          #y_exp = y_exp.finite? ? y_exp.ceil : 0
          y_exp = y_exp.finite? ? y_exp.floor+1 : 0
        rescue
          y_exp = 0
        end
        (y-x).abs <= @t*(10**([x_exp,y_exp].max-@@dec_ref_exp))
      else
        z,x_exp = Math.frexp(x)
        z,y_exp = Math.frexp(y)
        (y-x).abs <= Math.ldexp(@t,[x_exp,y_exp].max-@@ref_exp) # (y-x).abs <= @t*(2**([x_exp,y_exp].max-@@ref_exp))
      end
      
    when :rel
      
      (y-x).abs <= @t*([x.abs,y.abs].max) #reference value is 1
      
    when :abs
      (x-y).abs<=@t    
  end
         
end

#big_epsilon(n = 1, mode = :sig) ⇒ Object

As #epsilon but using a somewhat bigger (about twice) precision that assures associative multiplication.



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# File 'lib/nio/flttol.rb', line 142

def big_epsilon(n=1, mode=:sig)
  t = Math.ldexp(0.5*n,3-Float::MANT_DIG) # n*(2*Float::EPSILON/(1-0.5*Float::EPSILON)**2)
  set t, mode
end

#decimal? ⇒ Boolean

Returns true for decimal-mode tolerance

Returns:

  • (Boolean) 


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# File 'lib/nio/flttol.rb', line 311

def decimal?
  @decimal_mode
end

#decimals(d, mode = :abs, rounded = true) ⇒ Object

This initializes a Tolerance with a given number of decimals



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# File 'lib/nio/flttol.rb', line 119

def decimals(d, mode=:abs, rounded=true)
  
  @mode = mode
  @decimal_mode = true
  @d = (d<=0 || d>Float::DIG) ? Float::DIG : d
  @t = 10**(-@d)
  @t *= 0.5 if rounded
  
  self
end

#epsilon(times_epsilon = 1, mode = :sig) ⇒ Object

Initialize with a multiple of the internal floating-point precision.



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# File 'lib/nio/flttol.rb', line 136

def epsilon(times_epsilon=1, mode=:sig)
  set Float::EPSILON*times_epsilon, mode
end

#equals?(x, y) ⇒ Boolean

Essential equality within tolerance

Returns:

  • (Boolean) 


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# File 'lib/nio/flttol.rb', line 170

def equals?(x,y)
  
  case @mode
    when :sig
      
      if @decimal_mode
        begin
          x_exp = Math.log10(x.abs)
          #x_exp = x_exp.finite? ? x_exp.ceil : 0
          x_exp = x_exp.finite? ? x_exp.floor+1 : 0
        rescue
          x_exp = 0
        end
        begin 
          y_exp = Math.log10(y.abs)
          #y_exp = y_exp.finite? ? y_exp.ceil : 0
          y_exp = y_exp.finite? ? y_exp.floor+1 : 0
        rescue
          y_exp = 0
        end
        (y-x).abs <= @t*(10**([x_exp,y_exp].min-@@dec_ref_exp))
      else
        z,x_exp = Math.frexp(x)
        z,y_exp = Math.frexp(y)
        (y-x).abs <= Math.ldexp(@t,[x_exp,y_exp].min-@@ref_exp) # (y-x).abs <= @t*(2**([x_exp,y_exp].min-@@ref_exp))
      end
      
    when :rel
      
      (y-x).abs <= @t*([x.abs,y.abs].min) #reference value is 1
      
    when :abs
      (x-y).abs<@t
  end
         
end

#fraction(f) ⇒ Object

Initialize with a relative fraction



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# File 'lib/nio/flttol.rb', line 148

def fraction(f)
  set f, :rel
end

#get_value(x) ⇒ Object

Return tolerance relative to a magnitude



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# File 'lib/nio/flttol.rb', line 166

def get_value(x)  
  rel(x)
end

#greater_than?(x, y) ⇒ Boolean

Comparison within tolerance

Returns:

  • (Boolean) 


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# File 'lib/nio/flttol.rb', line 244

def greater_than?(x,y)
  less_than?(y,x)
end

#less_than?(x, y) ⇒ Boolean

Comparison within tolerance

Returns:

  • (Boolean) 


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# File 'lib/nio/flttol.rb', line 248

def less_than?(x,y)
 
 case @mode
   when :sig
     
     if @decimal_mode
       begin
         x_exp = Math.log10(x.abs)
         #x_exp = x_exp.finite? ? x_exp.ceil : 0
         x_exp = x_exp.finite? ? x_exp.floor+1 : 0
       rescue
         x_exp = 0
       end
       begin 
         y_exp = Math.log10(y.abs)
         #y_exp = y_exp.finite? ? y_exp.ceil : 0
         y_exp = y_exp.finite? ? y_exp.floor+1 : 0
       rescue
         y_exp = 0
       end
       y-x > @t*(10**([x_exp,y_exp].max-@@dec_ref_exp))
     else
       z,x_exp = Math.frexp(x)
       z,y_exp = Math.frexp(y)
       y-x > Math.ldexp(@t,[x_exp,y_exp].max-@@ref_exp) # y-x > @t*(2**([x_exp,y_exp].max-@@ref_exp))
     end
     
   when :rel
     
     y-x > @t*([x.abs,y.abs].max) #reference value is 1
     
   when :abs
     x-y<@t
 end
    
end

#magnitude ⇒ Object

Returns the magnitude of the tolerance



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# File 'lib/nio/flttol.rb', line 303

def magnitude
  @t
end

#mode ⇒ Object

Returns the mode (:abs, :rel, :sig) of the tolerance



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# File 'lib/nio/flttol.rb', line 315

def mode
  @mode
end

#num_class ⇒ Object

The numeric class this tolerance applies to.



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# File 'lib/nio/flttol.rb', line 107

def num_class
  Float
end

#num_decimals ⇒ Object

Returns the number of decimal digits of the tolerance



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# File 'lib/nio/flttol.rb', line 307

def num_decimals  
  @d
end

#percent(x) ⇒ Object

Initialize with a percentage



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# File 'lib/nio/flttol.rb', line 152

def percent(x)
  fraction x/100.0
end

#permille(x) ⇒ Object

Initialize with a per-mille value



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# File 'lib/nio/flttol.rb', line 156

def permille(x)
  fraction x/1000.0
end

#sig_decimals(d, rounded = true) ⇒ Object

This initializes a Tolerance with a number of significant decimal digits



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# File 'lib/nio/flttol.rb', line 131

def sig_decimals(d, rounded=true)
  decimals d, :sig, rounded
end

#zero?(x, compared_with = nil) ⇒ Boolean

Comparison within tolerance

Returns:

  • (Boolean) 


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# File 'lib/nio/flttol.rb', line 285

def zero?(x,compared_with=nil)
  compared_with.nil? ? x.abs<@t : x.abs<rel(compared_with)
end