Class: Flt::Num::ContextBase

Inherits:
Object
  • Object
show all
Defined in:
lib/flt/num.rb,
lib/flt/complex.rb

Overview

Base class for Context classes.

Derived classes will implement Floating-Point contexts for the specific floating-point types (DecNum, BinNum)

Direct Known Subclasses

BinNum::Context, DecNum::Context

Constant Summary collapse

CONDITION_MAP = 
{
  #ConversionSyntax=>InvalidOperation,
  #DivisionImpossible=>InvalidOperation,
  DivisionUndefined=>InvalidOperation,
  InvalidContext=>InvalidOperation
}

Instance Attribute Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(num_class, *options) ⇒ ContextBase

If an options hash is passed, the options are applied to the default context; if a Context is passed as the first argument, it is used as the base instead of the default context.

The valid options are:

  • :rounding : one of :half_even, :half_down, :half_up, :floor, :ceiling, :down, :up, :up05

  • :precision : number of digits (or 0 for exact precision)

  • :exact : if true precision is ignored and Inexact conditions are trapped,

    if :quiet it set exact precision but no trapping;

  • :traps : a Flags object with the exceptions to be trapped

  • :flags : a Flags object with the raised flags

  • :ignored_flags : a Flags object with the exceptions to be ignored

  • :emin, :emax : minimum and maximum adjusted exponents

  • :elimit : the exponent limits can also be defined by a single value; if positive it is taken as emax and emin=1-emax; otherwiae it is taken as emin and emax=1-emin. Such limits comply with IEEE 754-2008

  • :capitals : (true or false) to use capitals in text representations

  • :clamp : (true or false) enables clamping

See also the context constructor method Flt::Num.Context().



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# File 'lib/flt/num.rb', line 395

def initialize(num_class, *options)
  @num_class = num_class

  if options.first.kind_of?(ContextBase)
    base = options.shift
    copy_from base
  else
    @exact = false
    @rounding = @emin = @emax = nil
    @capitals = false
    @clamp = false
    @ignored_flags = Num::Flags()
    @traps = Num::Flags()
    @flags = Num::Flags()
    @coercible_type_handlers = num_class.base_coercible_types.dup
    @conversions = num_class.base_conversions.dup
    @angle = :rad # angular units: :rad (radians) / :deg (degrees) / :grad (gradians)
  end
  assign options.first

end

Instance Attribute Details

#angle ⇒ Object

Returns the value of attribute angle.



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# File 'lib/flt/num.rb', line 480

def angle
  @angle
end

#capitals ⇒ Object

Returns the value of attribute capitals.



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# File 'lib/flt/num.rb', line 480

def capitals
  @capitals
end

#clamp ⇒ Object

Returns the value of attribute clamp.



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# File 'lib/flt/num.rb', line 480

def clamp
  @clamp
end

#emax ⇒ Object

Returns the value of attribute emax.



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# File 'lib/flt/num.rb', line 480

def emax
  @emax
end

#emin ⇒ Object

Returns the value of attribute emin.



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# File 'lib/flt/num.rb', line 480

def emin
  @emin
end

#flags ⇒ Object

Returns the value of attribute flags.



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# File 'lib/flt/num.rb', line 480

def flags
  @flags
end

#ignored_flags ⇒ Object

Returns the value of attribute ignored_flags.



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# File 'lib/flt/num.rb', line 480

def ignored_flags
  @ignored_flags
end

#rounding ⇒ Object

Returns the value of attribute rounding.



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# File 'lib/flt/num.rb', line 480

def rounding
  @rounding
end

#traps ⇒ Object

Returns the value of attribute traps.



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# File 'lib/flt/num.rb', line 480

def traps
  @traps
end

Instance Method Details

#_coerce(x) ⇒ Object

Internally used to convert numeric types to DecNum (or to an array [sign,coefficient,exponent])



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# File 'lib/flt/num.rb', line 1052

def _coerce(x)
  c = x.class
  while c!=Object && (h=@coercible_type_handlers[c]).nil?
    c = c.superclass
  end
  if h
    h.call(x, self)
  else
    nil
  end
end

#abs(x) ⇒ Object

Absolute value of a decimal number



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# File 'lib/flt/num.rb', line 666

def abs(x)
  _convert(x).abs(self)
end

#add(x, y) ⇒ Object

Addition of two decimal numbers



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# File 'lib/flt/num.rb', line 646

def add(x,y)
  _convert(x).add(y,self)
end

#assign(options) ⇒ Object

Alters the contexts by assigning options from a Hash. See DecNum#new() for the valid options.



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# File 'lib/flt/num.rb', line 582

def assign(options)
  if options
    @rounding = options[:rounding] unless options[:rounding].nil?
    @precision = options[:precision] unless options[:precision].nil?
    @traps = DecNum::Flags(options[:traps]) unless options[:traps].nil?
    @flags = DecNum::Flags(options[:flags]) unless options[:flags].nil?
    @ignored_flags = DecNum::Flags(options[:ignored_flags]) unless options[:ignored_flags].nil?
    if elimit=options[:elimit]
      @emin, @emax = [elimit, 1-elimit].sort
    end
    @emin = options[:emin] unless options[:emin].nil?
    @emax = options[:emax] unless options[:emax].nil?
    @capitals = options[:capitals ] unless options[:capitals ].nil?
    @clamp = options[:clamp ] unless options[:clamp ].nil?
    @exact = options[:exact ] unless options[:exact ].nil?
    @angle = options[:angle ] unless options[:angle ].nil?
    @precision += options[:extra_precision] unless options[:extra_precision].nil?
    update_precision
  end
end

#clamp? ⇒ Boolean

is clamping enabled?

Returns:

  • (Boolean) 


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# File 'lib/flt/num.rb', line 546

def clamp?
  @clamp
end

#cmath(*parameters, &blk) ⇒ Object 



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# File 'lib/flt/complex.rb', line 279

def cmath(*parameters, &blk)
  # if ComplexContext is derived from ContextBase: return ComplexContext(self).math(*parameters, &blk)
  num_class.context(self) do
    if parameters.empty?
      Flt.ComplexContext(num_class.context).instance_eval &blk
    else
      Flt.xiComplexContext(num_class.context).instance_exec *parameters, &blk
    end
  end
end

#coefficient(x) ⇒ Object 



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# File 'lib/flt/num.rb', line 1102

def coefficient(x)
  _convert(x).coefficient
end

#coercible_types ⇒ Object

Internal use: array of numeric types that be coerced to DecNum.



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# File 'lib/flt/num.rb', line 1042

def coercible_types
  @coercible_type_handlers.keys
end

#coercible_types_or_num ⇒ Object

Internal use: array of numeric types that be coerced to DecNum, including DecNum



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# File 'lib/flt/num.rb', line 1047

def coercible_types_or_num
  [num_class] + coercible_types
end

#compare(x, y) ⇒ Object

Compares like <=> but returns a DecNum value.

  • -1 if x < y

  • 0 if x == b

  • +1 if x > y

  • NaN if x or y is NaN



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# File 'lib/flt/num.rb', line 847

def compare(x,y)
  _convert(x).compare(y, self)
end

#convert_to(type, x) ⇒ Object

Convert a DecNum x to other numerical type



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# File 'lib/flt/num.rb', line 1077

def convert_to(type, x)
  converter = @conversions[type]
  if converter.nil?
    raise TypeError, "Undefined conversion from DecNum to #{type}."
  elsif converter.is_a?(Symbol)
    x.send converter
  else
    converter.call(x)
  end
end

#copy_abs(x) ⇒ Object

Returns a copy of x with the sign set to +



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# File 'lib/flt/num.rb', line 852

def copy_abs(x)
  _convert(x).copy_abs
end

#copy_from(other) ⇒ Object

Copy the state from other Context object.

Raises:

  • (TypeError) 


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# File 'lib/flt/num.rb', line 607

def copy_from(other)
  raise TypeError, "Assign #{other.num_class} context to #{self.num_class} context" if other.num_class != self.num_class
  @rounding = other.rounding
  @precision = other.precision
  @traps = other.traps.dup
  @flags = other.flags.dup
  @ignored_flags = other.ignored_flags.dup
  @emin = other.emin
  @emax = other.emax
  @capitals = other.capitals
  @clamp = other.clamp
  @exact = other.exact
  @coercible_type_handlers = other.coercible_type_handlers.dup
  @conversions = other.conversions.dup
  @angle = other.angle
end

#copy_negate(x) ⇒ Object

Returns a copy of x with the sign inverted



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# File 'lib/flt/num.rb', line 857

def copy_negate(x)
  _convert(x).copy_negate
end

#copy_sign(x, y) ⇒ Object

Returns a copy of x with the sign of y



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# File 'lib/flt/num.rb', line 862

def copy_sign(x,y)
  _convert(x).copy_sign(y)
end

#define_conversion_from(type, &blk) ⇒ Object

Define a numerical conversion from type to DecNum. The block that defines the conversion has two parameters: the value to be converted and the context and must return either a DecNum or [sign,coefficient,exponent]



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# File 'lib/flt/num.rb', line 1067

def define_conversion_from(type, &blk)
  @coercible_type_handlers[type] = blk
end

#define_conversion_to(type, &blk) ⇒ Object

Define a numerical conversion from DecNum to type as an instance method of DecNum



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# File 'lib/flt/num.rb', line 1072

def define_conversion_to(type, &blk)
  @conversions[type] = blk
end

#digits ⇒ Object

synonym for precision()



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# File 'lib/flt/num.rb', line 526

def digits
  self.precision
end

#digits=(n) ⇒ Object

synonym for precision=()



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# File 'lib/flt/num.rb', line 531

def digits=(n)
  self.precision=n
end

#div(x, y) ⇒ Object

Ruby-style integer division: (x/y).floor



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# File 'lib/flt/num.rb', line 799

def div(x,y)
  _convert(x).div(y,self)
end

#divide(x, y) ⇒ Object

Division of two decimal numbers



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# File 'lib/flt/num.rb', line 661

def divide(x,y)
  _convert(x).divide(y,self)
end

#divide_int(x, y) ⇒ Object

General Decimal Arithmetic Specification integer division: (x/y).truncate



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# File 'lib/flt/num.rb', line 814

def divide_int(x,y)
  _convert(x).divide_int(y,self)
end

#divmod(x, y) ⇒ Object

Ruby-style integer division and modulo: (x/y).floor, x - y*(x/y).floor



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# File 'lib/flt/num.rb', line 809

def divmod(x,y)
  _convert(x).divmod(y,self)
end

#divrem(x, y) ⇒ Object

General Decimal Arithmetic Specification integer division and remainder:

(x/y).truncate, x - y*(x/y).truncate



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# File 'lib/flt/num.rb', line 831

def divrem(x,y)
  _convert(x).divrem(y,self)
end

#dup ⇒ Object 



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# File 'lib/flt/num.rb', line 624

def dup
  self.class.new(self)
end

#elimit=(e) ⇒ Object

Set the exponent limits, according to IEEE 754-2008 if e > 0 it is taken as emax and emin=1-emax if e < 0 it is taken as emin and emax=1-emin



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# File 'lib/flt/num.rb', line 521

def elimit=(e)
  @emin, @emax = [e, 1-e].sort
end

#epsilon(sign = +1) ⇒ Object

This is the difference between 1 and the smallest DecNum value greater than 1: (DecNum(1).next_plus - DecNum(1))



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# File 'lib/flt/num.rb', line 963

def epsilon(sign=+1)
  return exception(InvalidOperation, "Exact context epsilon") if exact?
  Num(sign, 1, 1-precision)
end

#etiny ⇒ Object

‘tiny’ exponent (emin - precision + 1) is the minimum valid value for the (integral) exponent



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# File 'lib/flt/num.rb', line 508

def etiny
  emin - precision + 1
end

#etop ⇒ Object

top exponent (emax - precision + 1) is the maximum valid value for the (integral) exponent



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# File 'lib/flt/num.rb', line 514

def etop
  emax - precision + 1
end

#eval(&blk) ⇒ Object

Evaluate a block under a context (set up the context as a local context)

When we have a context object we can use this instead of using the context method of the numeric class, e.g.:

DecNum.context(context) { ... }

This saves verbosity, specially when numeric class is not fixed, in which case we would have to write:

context.num_class.context(context) { ... }

With this method, we simply write:

context.eval { ... }



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# File 'lib/flt/num.rb', line 427

def eval(&blk)
  # TODO: consider other names for this method; use ? apply ? local ? with ?
  num_class.context(self, &blk)
end

#exact ⇒ Object

Returns true if the precision is exact



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# File 'lib/flt/num.rb', line 572

def exact
  @exact
end

#exact=(v) ⇒ Object

Enables or disables the exact precision



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# File 'lib/flt/num.rb', line 565

def exact=(v)
  @exact = v
  update_precision
  v
end

#exact? ⇒ Boolean

Returns true if the precision is exact

Returns:

  • (Boolean) 


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# File 'lib/flt/num.rb', line 577

def exact?
  @exact
end

#exception(cond, msg = '', *params) ⇒ Object

Raises a flag (unless it is being ignores) and raises and exceptioin if the trap for it is enabled.

Raises:

  • (err.new(*params)) 


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# File 'lib/flt/num.rb', line 637

def exception(cond, msg='', *params)
  err = (CONDITION_MAP[cond] || cond)
  return err.handle(self, *params) if @ignored_flags[err]
  @flags << err # @flags[err] = true
  return cond.handle(self, *params) if !@traps[err]
  raise err.new(*params), msg
end

#exp(x) ⇒ Object

Exponential function: e**x



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# File 'lib/flt/num.rb', line 696

def exp(x)
  _convert(x).exp(self)
end

#exponent(x) ⇒ Object 



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# File 'lib/flt/num.rb', line 1106

def exponent(x)
  _convert(x).exponent
end

#fma(x, y, z) ⇒ Object

Fused multiply-add.

Computes (x*y+z) with no rounding of the intermediate product x*y.



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# File 'lib/flt/num.rb', line 838

def fma(x,y,z)
  _convert(x).fma(y,z,self)
end

#half_epsilon(sign = +1) ⇒ Object

This is the maximum relative error corresponding to 1/2 ulp:

(radix/2)*radix**(-precision) == epsilon/2

This is called “machine epsilon” in Goldberg’s “What Every Computer Scientist…”



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# File 'lib/flt/num.rb', line 997

def half_epsilon(sign=+1)
  Num(sign, num_class.radix/2, -precision)
end

#ignore_all_flags ⇒ Object

Ignore all flags if they are raised



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# File 'lib/flt/num.rb', line 490

def ignore_all_flags
  #@ignored_flags << EXCEPTIONS
  @ignored_flags.set!
end

#ignore_flags(*flags) ⇒ Object

Ignore a specified set of flags if they are raised



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# File 'lib/flt/num.rb', line 496

def ignore_flags(*flags)
  #@ignored_flags << flags
  @ignored_flags.set(*flags)
end

#infinite?(x) ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/flt/num.rb', line 1114

def infinite?(x)
  _convert(x).infinite?
end

#inspect ⇒ Object 



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# File 'lib/flt/num.rb', line 1005

def inspect
  class_name = self.class.to_s.split('::').last
  "<#{class_name}:\n" +
  instance_variables.map { |v| "  #{v}: #{instance_variable_get(v).inspect}"}.join("\n") +
  ">\n"
end

#int_div_radix_power(x, n) ⇒ Object

Divide by an integral power of the base: x/(radix**n) for x,n integer; returns an integer.



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# File 'lib/flt/num.rb', line 476

def int_div_radix_power(x,n)
  @num_class.int_div_radix_power(x,n)
end

#int_mult_radix_power(x, n) ⇒ Object

Multiply by an integral power of the base: x*(radix**n) for x,n integer; returns an integer.



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# File 'lib/flt/num.rb', line 470

def int_mult_radix_power(x,n)
  @num_class.int_mult_radix_power(x,n)
end

#int_radix_power(n) ⇒ Object

Integral power of the base: radix**n for integer n; returns an integer.



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# File 'lib/flt/num.rb', line 464

def int_radix_power(n)
  @num_class.int_radix_power(n)
end

#ln(x) ⇒ Object

Returns the natural (base e) logarithm



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# File 'lib/flt/num.rb', line 701

def ln(x)
  _convert(x).ln(self)
end

#log(x, base = nil) ⇒ Object

Ruby-style log function: arbitrary base logarithm which defaults to natural logarithm



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# File 'lib/flt/num.rb', line 706

def log(x, base=nil)
  _convert(x).log(base, self)
end

#log10(x) ⇒ Object

Returns the base 10 logarithm



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# File 'lib/flt/num.rb', line 686

def log10(x)
  _convert(x).log10(self)
end

#log2(x) ⇒ Object

Returns the base 2 logarithm



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# File 'lib/flt/num.rb', line 691

def log2(x)
  _convert(x).log10(self)
end

#logb(x) ⇒ Object

Adjusted exponent of x returned as a DecNum value.



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# File 'lib/flt/num.rb', line 745

def logb(x)
  _convert(x).logb(self)
end

#math(*parameters, &blk) ⇒ Object

Evalute a block under a context (set up the context as a local context) and inject the context methods (math and otherwise) into the block scope.

This allows the use of regular algebraic notations for math functions, e.g. exp(x) instead of x.exp



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# File 'lib/flt/num.rb', line 437

def math(*parameters, &blk)
  # TODO: consider renaming this to eval
  num_class.context(self) do
    if parameters.empty?
      num_class.context.instance_eval &blk
    else
      # needs instance_exe (available in Ruby 1.9, ActiveRecord; TODO: include implementation here)
      num_class.context.instance_exec *parameters, &blk
    end
  end
end

#maximum_coefficient ⇒ Object

Maximum integral significand value for numbers using this context’s precision.



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# File 'lib/flt/num.rb', line 1013

def maximum_coefficient
  if exact?
    exception(InvalidOperation, 'Exact maximum coefficient')
    nil
  else
    num_class.int_radix_power(precision)-1
  end
end

#maximum_finite(sign = +1) ⇒ Object

Maximum finite number



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# File 'lib/flt/num.rb', line 934

def maximum_finite(sign=+1)
  return exception(InvalidOperation, "Exact context maximum finite value") if exact?
  # equals +Num(+1, 1, emax)
  # equals Num.infinity.next_minus(self)
  Num(sign, num_class.int_radix_power(precision)-1, etop)
end

#maximum_nan_diagnostic_digits ⇒ Object

Maximum number of diagnostic digits in NaNs for numbers using this context’s precision.



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# File 'lib/flt/num.rb', line 1033

def maximum_nan_diagnostic_digits
  if exact?
    nil # ?
  else
    precision - (clamp ? 1 : 0)
  end
end

#maximum_subnormal(sign = +1) ⇒ Object

Maximum subnormal number



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# File 'lib/flt/num.rb', line 949

def maximum_subnormal(sign=+1)
  return exception(InvalidOperation, "Exact context maximum subnormal value") if exact?
  # equals mininum_normal.next_minus(self)
  Num(sign, num_class.int_radix_power(precision-1)-1, etiny)
end

#minimum_nonzero(sign = +1) ⇒ Object

Minimum nonzero positive number (minimum positive subnormal)



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# File 'lib/flt/num.rb', line 956

def minimum_nonzero(sign=+1)
  return exception(InvalidOperation, "Exact context minimum nonzero value") if exact?
  Num(sign, 1, etiny)
end

#minimum_normal(sign = +1) ⇒ Object

Minimum positive normal number



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# File 'lib/flt/num.rb', line 942

def minimum_normal(sign=+1)
  return exception(InvalidOperation, "Exact context maximum normal value") if exact?
  #Num(sign, 1, emin).normalize(self)
  Num(sign, minimum_normalized_coefficient, etiny)
end

#minimum_normalized_coefficient ⇒ Object

Minimum value of a normalized coefficient (normalized unit)



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# File 'lib/flt/num.rb', line 1023

def minimum_normalized_coefficient
  if exact?
    exception(InvalidOperation, 'Exact maximum coefficient')
    nil
  else
    num_class.int_radix_power(precision-1)
  end
end

#minus(x) ⇒ Object

Unary prefix minus operator



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# File 'lib/flt/num.rb', line 676

def minus(x)
  _convert(x)._neg(self)
end

#modulo(x, y) ⇒ Object

Ruby-style modulo: x - y*div(x,y)



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# File 'lib/flt/num.rb', line 804

def modulo(x,y)
  _convert(x).modulo(y,self)
end

#multiply(x, y) ⇒ Object

Multiplication of two decimal numbers



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# File 'lib/flt/num.rb', line 656

def multiply(x,y)
  _convert(x).multiply(y,self)
end

#nan?(x) ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/flt/num.rb', line 1110

def nan?(x)
  _convert(x).nan?
end

#next_minus(x) ⇒ Object

Returns the largest representable number smaller than x.



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# File 'lib/flt/num.rb', line 904

def next_minus(x)
  _convert(x).next_minus(self)
end

#next_plus(x) ⇒ Object

Returns the smallest representable number larger than x.



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# File 'lib/flt/num.rb', line 909

def next_plus(x)
  _convert(x).next_plus(self)
end

#next_toward(x, y) ⇒ Object

Returns the number closest to x, in the direction towards y.

The result is the closest representable number to x (excluding x) that is in the direction towards y, unless both have the same value. If the two operands are numerically equal, then the result is a copy of x with the sign set to be the same as the sign of y.



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# File 'lib/flt/num.rb', line 920

def next_toward(x, y)
  _convert(x).next_toward(y, self)
end

#normal?(x) ⇒ Boolean

Is a normal number?

Returns:

  • (Boolean) 


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# File 'lib/flt/num.rb', line 777

def normal?(x)
  _convert(x).normal?(self)
end

#normalize(x) ⇒ Object

Normalizes (changes quantum) so that the coefficient has precision digits, unless it is subnormal. For surnormal numbers the Subnormal flag is raised an a subnormal is returned with the smallest possible exponent.

This is different from reduce GDAS function which was formerly called normalize, and corresponds to the classic meaning of floating-point normalization.

Note that the number is also rounded (precision is reduced) if it had more precision than the context.



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# File 'lib/flt/num.rb', line 740

def normalize(x)
  _convert(x).normalize(self)
end

#normalized_integral_exponent(x) ⇒ Object

Exponent in relation to the significand as an integer normalized to precision digits. (minimum exponent)



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# File 'lib/flt/num.rb', line 758

def normalized_integral_exponent(x)
  x = _convert(x)
  x.exponent - (precision - x.number_of_digits)
end

#normalized_integral_significand(x) ⇒ Object

Significand normalized to precision digits x == normalized_integral_significand(x) * radix**(normalized_integral_exponent)



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# File 'lib/flt/num.rb', line 765

def normalized_integral_significand(x)
  x = _convert(x)
  x.coefficient*(num_class.int_radix_power(precision - x.number_of_digits))
end

#Num(*args) ⇒ Object

Constructor for the associated numeric class



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# File 'lib/flt/num.rb', line 455

def Num(*args)
  num_class.Num(*args)
end

#num_class ⇒ Object

This gives access to the numeric class (Flt::Num-derived) this context is for.



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# File 'lib/flt/num.rb', line 450

def num_class
  @num_class
end

#number_class(x) ⇒ Object

Classifies a number as one of ‘sNaN’, ‘NaN’, ‘-Infinity’, ‘-Normal’, ‘-Subnormal’, ‘-Zero’,

'+Zero', '+Subnormal', '+Normal', '+Infinity'



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# File 'lib/flt/num.rb', line 789

def number_class(x)
  _convert(x).number_class(self)
end

#plus(x) ⇒ Object

Unary prefix plus operator



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# File 'lib/flt/num.rb', line 671

def plus(x)
  _convert(x).plus(self)
end

#power(x, y, modulo = nil) ⇒ Object

Power. See DecNum#power()



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# File 'lib/flt/num.rb', line 681

def power(x,y,modulo=nil)
  _convert(x).power(y,modulo,self)
end

#prec ⇒ Object

synonym for precision()



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# File 'lib/flt/num.rb', line 536

def prec
  self.precision
end

#prec=(n) ⇒ Object

synonym for precision=()



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# File 'lib/flt/num.rb', line 541

def prec=(n)
  self.precision = n
end

#precision ⇒ Object

Number of digits of precision



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# File 'lib/flt/num.rb', line 560

def precision
  @precision
end

#precision=(n) ⇒ Object

Set the number of digits of precision. If 0 is set the precision turns to be exact.



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# File 'lib/flt/num.rb', line 552

def precision=(n)
  @precision = n
  @exact = false unless n==0
  update_precision
  n
end

#quantize(x, y, watch_exp = true) ⇒ Object

Quantize x so its exponent is the same as that of y.



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# File 'lib/flt/num.rb', line 873

def quantize(x, y, watch_exp=true)
  _convert(x).quantize(y, self, watch_exp)
end

#radix ⇒ Object 



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# File 'lib/flt/num.rb', line 459

def radix
  @num_class.radix
end

#reduce(x) ⇒ Object

Reduces an operand to its simplest form by removing trailing 0s and incrementing the exponent. (formerly called normalize in GDAS)



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# File 'lib/flt/num.rb', line 728

def reduce(x)
  _convert(x).reduce(self)
end

#regard_flags(*flags) ⇒ Object

Stop ignoring a set of flags, if they are raised



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# File 'lib/flt/num.rb', line 502

def regard_flags(*flags)
  @ignored_flags.clear(*flags)
end

#remainder(x, y) ⇒ Object

General Decimal Arithmetic Specification remainder: x - y*divide_int(x,y)



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# File 'lib/flt/num.rb', line 819

def remainder(x,y)
  _convert(x).remainder(y,self)
end

#remainder_near(x, y) ⇒ Object

General Decimal Arithmetic Specification remainder-near

x - y*round_half_even(x/y)



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# File 'lib/flt/num.rb', line 825

def remainder_near(x,y)
  _convert(x).remainder_near(y,self)
end

#rescale(x, exp, watch_exp = true) ⇒ Object

Rescale x so that the exponent is exp, either by padding with zeros or by truncating digits.



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# File 'lib/flt/num.rb', line 868

def rescale(x, exp, watch_exp=true)
  _convert(x).rescale(exp, self, watch_exp)
end

#same_quantum?(x, y) ⇒ Boolean

Return true if x and y have the same exponent.

If either operand is a special value, the following rules are used:

  • return true if both operands are infinities

  • return true if both operands are NaNs

  • otherwise, return false.

Returns:

  • (Boolean) 


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# File 'lib/flt/num.rb', line 883

def same_quantum?(x,y)
  _convert(x).same_quantum?(y)
end

#scaleb(x, y) ⇒ Object

Adds the second value to the exponent of the first: x*(radix**y)

y must be an integer



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# File 'lib/flt/num.rb', line 752

def scaleb(x, y)
  _convert(x).scaleb(y,self)
end

#sign(x) ⇒ Object 



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# File 'lib/flt/num.rb', line 1098

def sign(x)
  _convert(x).sign
end

#split(x) ⇒ Object

Simply calls x.split; implemented to ease handling Float and BigDecimal as Nums withoug having to add methods like split to those classes.



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# File 'lib/flt/num.rb', line 1090

def split(x)
  _convert(x).split
end

#sqrt(x) ⇒ Object

Square root of a decimal number



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# File 'lib/flt/num.rb', line 794

def sqrt(x)
  _convert(x).sqrt(self)
end

#strict_epsilon(sign = +1) ⇒ Object

The strict epsilon is the smallest value that produces something different from 1 wehen added to 1. It may be smaller than the general epsilon, because of the particular rounding rules used.



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# File 'lib/flt/num.rb', line 971

def strict_epsilon(sign=+1)
  return exception(InvalidOperation, "Exact context strict epsilon") if exact?
  # assume radix is even (num_class.radix%2 == 0)
  case rounding
  when :down, :floor
    # largest epsilon: 0.0...10 (precision digits shown to the right of the decimal point)
    exp = 1-precision
    coeff = 1
  when :half_even, :half_down
    # next largest:    0.0...050...1 (+precision-1 additional digits here)
    exp = 1-2*precision
    coeff = 1 + num_class.int_radix_power(precision)/2
  when :half_up
    # next largest:    0.0...05 (precision digits shown to the right of the decimal point)
    exp = 1-2*precision
    coeff = num_class.int_radix_power(precision)/2
  when :up, :ceiling, :up05
    # smallest epsilon
    return minimum_nonzero(sign)
  end
  return Num(sign, coeff, exp)
end

#subnormal?(x) ⇒ Boolean

Is a subnormal number?

Returns:

  • (Boolean) 


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# File 'lib/flt/num.rb', line 782

def subnormal?(x)
  _convert(x).subnormal?(self)
end

#subtract(x, y) ⇒ Object

Subtraction of two decimal numbers



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# File 'lib/flt/num.rb', line 651

def subtract(x,y)
  _convert(x).subtract(y,self)
end

#to_eng_string(x) ⇒ Object

Converts a number to a string, using engineering notation



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# File 'lib/flt/num.rb', line 721

def to_eng_string(x)
  to_string x, true
end

#to_int_scale(x) ⇒ Object 



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# File 'lib/flt/num.rb', line 1094

def to_int_scale(x)
  _convert(x).to_int_scale
end

#to_integral_exact(x) ⇒ Object

Rounds to a nearby integer.

See also: DecNum#to_integral_value(), which does exactly the same as this method except that it doesn’t raise Inexact or Rounded.



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# File 'lib/flt/num.rb', line 891

def to_integral_exact(x)
  _convert(x).to_integral_exact(self)
end

#to_integral_value(x) ⇒ Object

Rounds to a nearby integerwithout raising inexact, rounded.

See also: DecNum#to_integral_exact(), which does exactly the same as this method except that it may raise Inexact or Rounded.



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# File 'lib/flt/num.rb', line 899

def to_integral_value(x)
  _convert(x).to_integral_value(self)
end

#to_normalized_int_scale(x) ⇒ Object

Returns both the (signed) normalized integral significand and the corresponding exponent



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# File 'lib/flt/num.rb', line 771

def to_normalized_int_scale(x)
  x = _convert(x)
  [x.sign*normalized_integral_significand(x), normalized_integral_exponent(x)]
end

#to_s ⇒ Object 



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# File 'lib/flt/num.rb', line 1001

def to_s
  inspect
end

#to_sci_string(x) ⇒ Object

Converts a number to a string, using scientific notation



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# File 'lib/flt/num.rb', line 716

def to_sci_string(x)
  to_string x, false
end

#to_string(x, eng = false) ⇒ Object

Converts a number to a string



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# File 'lib/flt/num.rb', line 711

def to_string(x, eng=false)
  _convert(x)._fix(self).to_s(eng, self)
end

#ulp(x = nil, mode = :low) ⇒ Object

ulp (unit in the last place) according to the definition proposed by J.M. Muller in “On the definition of ulp(x)” INRIA No. 5504



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# File 'lib/flt/num.rb', line 926

def ulp(x=nil, mode=:low)
  x ||= 1
  _convert(x).ulp(self, mode)
end

#zero?(x) ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/flt/num.rb', line 1118

def zero?(x)
  _convert(x).zero?
end