Class: Decimal

Inherits:
Object
  • Object
show all
Extended by:
DecimalSupport
Includes:
Comparable, AuxiliarFunctions
Defined in:
lib/decimal/decimal.rb

Overview

Decimal arbitrary precision floating point number. This implementation of Decimal is based on the Decimal module of Python, written by Eric Price, Facundo Batista, Raymond Hettinger, Aahz and Tim Peters.

Defined Under Namespace

Modules: AuxiliarFunctions Classes: Clamped, Context, ConversionSyntax, DivisionByZero, DivisionImpossible, DivisionUndefined, Error, Exception, Inexact, InvalidContext, InvalidOperation, Overflow, Rounded, Subnormal, Underflow

Constant Summary collapse

ROUND_HALF_EVEN = 
:half_even
ROUND_HALF_DOWN = 
:half_down
ROUND_HALF_UP = 
:half_up
ROUND_FLOOR = 
:floor
ROUND_CEILING = 
:ceiling
ROUND_DOWN = 
:down
ROUND_UP = 
:up
ROUND_05UP = 
:up05
EXCEPTIONS = 
FlagValues(Clamped, InvalidOperation, DivisionByZero, Inexact, Overflow, Underflow,
Rounded, Subnormal, DivisionImpossible, ConversionSyntax)
DefaultContext =

the DefaultContext is the base for new contexts; it can be changed.

Decimal::Context.new(
:exact=>false, :precision=>28, :rounding=>:half_even,
:emin=> -999999999, :emax=>+999999999,
:flags=>[],
:traps=>[DivisionByZero, Overflow, InvalidOperation],
:ignored_flags=>[],
:capitals=>true,
:clamp=>true)
BasicContext = 
Decimal::Context.new(DefaultContext,
:precision=>9, :rounding=>:half_up,
:traps=>[DivisionByZero, Overflow, InvalidOperation, Clamped, Underflow],
:flags=>[])
ExtendedContext = 
Decimal::Context.new(DefaultContext,
:precision=>9, :rounding=>:half_even,
:traps=>[], :flags=>[], :clamp=>false)

Class Attribute Summary collapse

Class Method Summary collapse

Instance Method Summary collapse

Methods included from DecimalSupport

FlagValues

Methods included from AuxiliarFunctions

_convert, _dexp, _div_nearest, _dlog, _dlog10, _dpower, _iexp, _ilog, _log10_digits, _log10_lb, _nbits, _normalize, _parser, _rshift_nearest, _sqrt_nearest, dexp

Constructor Details

#initialize(*args) ⇒ Decimal

A decimal value can be defined by:

  • A String containing a text representation of the number

  • An Integer

  • A Rational

  • Another Decimal value.

  • A sign, coefficient and exponent (either as separate arguments, as an array or as a Hash with symbolic keys). This is the internal representation of Decimal, as returned by Decimal#split. The sign is +1 for plus and -1 for minus; the coefficient and exponent are integers, except for special values which are defined by :inf, :nan or :snan for the exponent.

An optional Context can be passed as the last argument to override the current context; also a hash can be passed to override specific context parameters. The Decimal() admits the same parameters and can be used as a shortcut for Decimal creation.



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# File 'lib/decimal/decimal.rb', line 1165

def initialize(*args)
  context = nil
  if args.size>0 && args.last.instance_of?(Context)
    context ||= args.pop
  elsif args.size>1 && args.last.instance_of?(Hash)
    context ||= args.pop
  elsif args.size==1 && args.last.instance_of?(Hash)
    arg = args.last
    args = [arg[:sign], args[:coefficient], args[:exponent]]
    arg.delete :sign
    arg.delete :coefficient
    arg.delete :exponent
    context ||= arg
  end
  args = args.first if args.size==1 && args.first.is_a?(Array)

  context = Decimal.define_context(context)

  case args.size
  when 3
    # internal representation
    @sign, @coeff, @exp = args
    # TO DO: validate

  when 2
    # signed integer and scale
    @coeff, @exp = args
    if @coeff < 0
      @sign = -1
      @coeff = -@coeff
    else
      @sign = +1
    end

  when 1
    arg = args.first
    case arg

    when Decimal
      @sign, @coeff, @exp = arg.split

    when *context.coercible_types
      v = context._coerce(arg)
      @sign, @coeff, @exp = v.is_a?(Decimal) ? v.split : v

    when String
      if arg.strip != arg
        @sign,@coeff,@exp = context.exception(ConversionSyntax, "no trailing or leading whitespace is permitted").split
        return
      end
      m = _parser(arg)
      if m.nil?
        @sign,@coeff,@exp = context.exception(ConversionSyntax, "Invalid literal for Decimal: #{arg.inspect}").split
        return
      end
      @sign =  (m.sign == '-') ? -1 : +1
      if m.int || m.onlyfrac
        if m.int
          intpart = m.int
          fracpart = m.frac
        else
          intpart = ''
          fracpart = m.onlyfrac
        end
        @exp = m.exp.to_i
        if fracpart
          @coeff = (intpart+fracpart).to_i
          @exp -= fracpart.size
        else
          @coeff = intpart.to_i
        end
      else
        if m.diag
          # NaN
          @coeff = (m.diag.nil? || m.diag.empty?) ? nil : m.diag.to_i
          @coeff = nil if @coeff==0
           if @coeff
             max_diag_len = context.maximum_nan_diagnostic_digits
             if max_diag_len && @coeff >= Decimal.int_radix_power(max_diag_len)
                @sign,@coeff,@exp = context.exception(ConversionSyntax, "diagnostic info too long in NaN").split
               return
             end
           end
          @exp = m.signal ? :snan : :nan
        else
          # Infinity
          @coeff = 0
          @exp = :inf
        end
      end
    else
      raise TypeError, "invalid argument #{arg.inspect}"
    end
  else
    raise ArgumentError, "wrong number of arguments (#{args.size} for 1, 2 or 3)"
  end
end

Class Attribute Details

.base_coercible_types ⇒ Object (readonly)

Returns the value of attribute base_coercible_types.



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# File 'lib/decimal/decimal.rb', line 36

def base_coercible_types
  @base_coercible_types
end

.base_conversions ⇒ Object (readonly)

Returns the value of attribute base_conversions.



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# File 'lib/decimal/decimal.rb', line 37

def base_conversions
  @base_conversions
end

Class Method Details

.context(*args, &blk) ⇒ Object

The current context (thread-local). If arguments are passed they are interpreted as in Decimal.define_context() to change the current context. If a block is given, this method is a synonym for Decimal.local_context().



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# File 'lib/decimal/decimal.rb', line 1003

def Decimal.context(*args, &blk)
  if blk
    # setup a local context
    local_context(*args, &blk)
  elsif args.empty?
    # return the current context
    self._context = DefaultContext.dup if _context.nil?
    _context
  else
    # change the current context
    # TODO: consider doing _context = ... here
    # so we would have Decimal.context = c that assigns a duplicate of c
    # and Decimal.context c to set alias c
    Decimal.context = define_context(*args)
  end
end

.Context(*args) ⇒ Object

Context constructor; 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.

See Context#new() for the valid options



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# File 'lib/decimal/decimal.rb', line 955

def Decimal.Context(*args)
  case args.size
    when 0
      base = DefaultContext
    when 1
      arg = args.first
      if arg.instance_of?(Context)
        base = arg
        options = nil
      elsif arg.instance_of?(Hash)
        base = DefaultContext
        options = arg
      else
        raise TypeError,"invalid argument for Decimal.Context"
      end
    when 2
      base = args.first
      options = args.last
    else
      raise ArgumentError,"wrong number of arguments (#{args.size} for 0, 1 or 2)"
  end

  if options.nil? || options.empty?
    base
  else
    Context.new(base, options)
  end

end

.context=(c) ⇒ Object

Change the current context (thread-local).



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# File 'lib/decimal/decimal.rb', line 1021

def Decimal.context=(c)
  self._context = c.dup
end

.define_context(*options) ⇒ Object

Define a context by passing either of:

  • A Context object

  • A hash of options (or nothing) to alter a copy of the current context.

  • A Context object and a hash of options to alter a copy of it



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# File 'lib/decimal/decimal.rb', line 989

def Decimal.define_context(*options)
  context = options.shift if options.first.instance_of?(Context)
  if context && options.empty?
    context
  else
    context ||= Decimal.context
    Context(context, *options)
  end
end

.Flags(*values) ⇒ Object 



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# File 'lib/decimal/decimal.rb', line 282

def self.Flags(*values)
  DecimalSupport::Flags(EXCEPTIONS,*values)
end

.infinity(sign = +1) ⇒ Object

A decimal infinite number with the specified sign



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# File 'lib/decimal/decimal.rb', line 1061

def Decimal.infinity(sign=+1)
  Decimal.new([sign, 0, :inf])
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/decimal/decimal.rb', line 68

def self.int_div_radix_power(x,n)
  x / (10**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/decimal/decimal.rb', line 62

def self.int_mult_radix_power(x,n)
  x * (10**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/decimal/decimal.rb', line 56

def self.int_radix_power(n)
  10**n
end

.local_context(*args) ⇒ Object

Defines a scope with a local context. A context can be passed which will be set a the current context for the scope; also a hash can be passed with options to apply to the local scope. Changes done to the current context are reversed when the scope is exited.



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# File 'lib/decimal/decimal.rb', line 1029

def Decimal.local_context(*args)
  keep = Decimal.context # use this so _context is initialized if necessary
  Decimal.context = define_context(*args) # this dups the assigned context
  result = yield _context
  # TODO: consider the convenience of copying the flags from Decimal.context to keep
  # This way a local context does not affect the settings of the previous context,
  # but flags are transferred.
  # (this could be done always or be controlled by some option)
  #   keep.flags = Decimal.context.flags
  # Another alternative to consider: logically or the flags:
  #   keep.flags ||= Decimal.context.flags # (this requires implementing || in Flags)
  self._context = keep
  result
end

.nan ⇒ Object

A decimal NaN (not a number)



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# File 'lib/decimal/decimal.rb', line 1066

def Decimal.nan()
  Decimal.new([+1, nil, :nan])
end

.radix ⇒ Object

Numerical base of Decimal.



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# File 'lib/decimal/decimal.rb', line 51

def self.radix
  10
end

.zero(sign = +1) ⇒ Object

A decimal number with value zero and the specified sign



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# File 'lib/decimal/decimal.rb', line 1056

def Decimal.zero(sign=+1)
  Decimal.new([sign, 0, 0])
end

Instance Method Details

#%(other, context = nil) ⇒ Object

Modulo of two decimal numbers



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# File 'lib/decimal/decimal.rb', line 1407

def %(other, context=nil)
  _bin_op :%, :modulo, other, context
end

#*(other, context = nil) ⇒ Object

Multiplication of two decimal numbers



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# File 'lib/decimal/decimal.rb', line 1397

def *(other, context=nil)
  _bin_op :*, :multiply, other, context
end

#**(other, context = nil) ⇒ Object

Power



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# File 'lib/decimal/decimal.rb', line 1412

def **(other, context=nil)
  _bin_op :**, :power, other, context
end

#+(other, context = nil) ⇒ Object

Addition of two decimal numbers



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# File 'lib/decimal/decimal.rb', line 1387

def +(other, context=nil)
  _bin_op :+, :add, other, context
end

#+@(context = nil) ⇒ Object

Unary plus operator



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# File 'lib/decimal/decimal.rb', line 1381

def +@(context=nil)
  #(context || Decimal.context).plus(self)
  _pos(context)
end

#-(other, context = nil) ⇒ Object

Subtraction of two decimal numbers



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# File 'lib/decimal/decimal.rb', line 1392

def -(other, context=nil)
  _bin_op :-, :subtract, other, context
end

#-@(context = nil) ⇒ Object

Unary minus operator



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# File 'lib/decimal/decimal.rb', line 1375

def -@(context=nil)
  #(context || Decimal.context).minus(self)
  _neg(context)
end

#/(other, context = nil) ⇒ Object

Division of two decimal numbers



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# File 'lib/decimal/decimal.rb', line 1402

def /(other, context=nil)
  _bin_op :/, :divide, other, context
end

#<=>(other) ⇒ Object

Internal comparison operator: returns -1 if the first number is less than the second, 0 if both are equal or +1 if the first is greater than the secong.



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# File 'lib/decimal/decimal.rb', line 2206

def <=>(other)
  case other
  when *Decimal.context.coercible_types_or_decimal
    other = Decimal(other)
    if self.special? || other.special?
      if self.nan? || other.nan?
        1
      else
        self_v = self.finite? ? 0 : self.sign
        other_v = other.finite? ? 0 : other.sign
        self_v <=> other_v
      end
    else
      if self.zero?
        if other.zero?
          0
        else
          -other.sign
        end
      elsif other.zero?
        self.sign
      elsif other.sign < self.sign
        +1
      elsif self.sign < other.sign
        -1
      else
        self_adjusted = self.adjusted_exponent
        other_adjusted = other.adjusted_exponent
        if self_adjusted == other_adjusted
          self_padded,other_padded = self.coefficient,other.coefficient
          d = self.exponent - other.exponent
          if d>0
            self_padded *= Decimal.int_radix_power(d)
          else
            other_padded *= Decimal.int_radix_power(-d)
          end
          (self_padded <=> other_padded)*self.sign
        elsif self_adjusted > other_adjusted
          self.sign
        else
          -self.sign
        end
      end
    end
  else
    if !self.nan? && defined? other.coerce
      x, y = other.coerce(self)
      x <=> y
    else
      nil
    end
  end
end

#==(other) ⇒ Object 



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# File 'lib/decimal/decimal.rb', line 2259

def ==(other)
  (self<=>other) == 0
end

#_abs(round = true, context = nil) ⇒ Object

Returns a copy with positive sign



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# File 'lib/decimal/decimal.rb', line 3091

def _abs(round=true, context=nil)
  return copy_abs if not round

  if special?
    ans = _check_nans(context)
    return ans if ans
  end
  if sign>0
    ans = _neg(context)
  else
    ans = _pos(context)
  end
  ans
end

#_check_nans(context = nil, other = nil) ⇒ Object

Check if the number or other is NaN, signal if sNaN or return NaN; return nil if none is NaN.



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# File 'lib/decimal/decimal.rb', line 2988

def _check_nans(context=nil, other=nil)
  #self_is_nan = self.nan?
  #other_is_nan = other.nil? ? false : other.nan?
  if self.nan? || (other && other.nan?)
    context = Decimal.define_context(context)
    return context.exception(InvalidOperation, 'sNaN', self) if self.snan?
    return context.exception(InvalidOperation, 'sNaN', other) if other && other.snan?
    return self._fix_nan(context) if self.nan?
    return other._fix_nan(context)
  else
    return nil
  end
end

#_fix(context) ⇒ Object

Round if it is necessary to keep within precision.



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# File 'lib/decimal/decimal.rb', line 3107

def _fix(context)
  return self if context.exact?

  if special?
    if nan?
      return _fix_nan(context)
    else
      return Decimal.new(self)
    end
  end

  etiny = context.etiny
  etop  = context.etop
  if zero?
    exp_max = context.clamp? ? etop : context.emax
    new_exp = [[@exp, etiny].max, exp_max].min
    if new_exp!=@exp
      context.exception Clamped
      return Decimal.new([sign,0,new_exp])
    else
      return Decimal.new(self)
    end
  end

  nd = number_of_digits
  exp_min = nd + @exp - context.precision
  if exp_min > etop
    context.exception Inexact
    context.exception Rounded
    return context.exception(Overflow, 'above Emax', sign)
  end

  self_is_subnormal = exp_min < etiny

  if self_is_subnormal
    context.exception Subnormal
    exp_min = etiny
  end

  if @exp < exp_min
    context.exception Rounded
    # dig is the digits number from 0 (MS) to number_of_digits-1 (LS)
    # dg = numberof_digits-dig is from 1 (LS) to number_of_digits (MS)
    dg = exp_min - @exp # dig = number_of_digits + exp - exp_min
    if dg > number_of_digits # dig<0
      d = Decimal.new([sign,1,exp_min-1])
      dg = number_of_digits # dig = 0
    else
      d = Decimal.new(self)
    end
    changed = d._round(context.rounding, dg)
    coeff = Decimal.int_div_radix_power(d.coefficient, dg)
    coeff += 1 if changed==1
    ans = Decimal.new([sign, coeff, exp_min])
    if changed!=0
      context.exception Inexact
      if self_is_subnormal
        context.exception Underflow
        if ans.zero?
          context.exception Clamped
        end
      elsif ans.number_of_digits == context.precision+1
        if ans.exponent< etop
          ans = Decimal.new([ans.sign, Decimal.int_div_radix_power(ans.coefficient,1), ans.exponent+1])
        else
          ans = context.exception(Overflow, 'above Emax', d.sign)
        end
      end
    end
    return ans
  end

  if context.clamp? &&  @exp>etop
    context.exception Clamped
    self_padded = Decimal.int_mult_radix_power(@coeff, @exp-etop)
    return Decimal.new([sign,self_padded,etop])
  end

  return Decimal.new(self)

end

#_fix_nan(context) ⇒ Object

adjust payload of a NaN to the context



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# File 'lib/decimal/decimal.rb', line 3190

def _fix_nan(context)
  if  !context.exact?
    payload = @coeff
    payload = nil if payload==0

    max_payload_len = context.maximum_nan_diagnostic_digits

    if number_of_digits > max_payload_len
        payload = payload.to_s[-max_payload_len..-1].to_i
        return Decimal([@sign, payload, @exp])
    end
  end
  Decimal(self)
end

#_neg(context = nil) ⇒ Object

Returns copy with sign inverted



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# File 'lib/decimal/decimal.rb', line 3061

def _neg(context=nil)
  if special?
    ans = _check_nans(context)
    return ans if ans
  end
  if zero?
    ans = copy_abs
  else
    ans = copy_negate
  end
  context = Decimal.define_context(context)
  ans._fix(context)
end

#_pos(context = nil) ⇒ Object

Returns a copy with precision adjusted



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# File 'lib/decimal/decimal.rb', line 3076

def _pos(context=nil)
  if special?
    ans = _check_nans(context)
    return ans if ans
  end
  if zero?
    ans = copy_abs
  else
    ans = Decimal.new(self)
  end
  context = Decimal.define_context(context)
  ans._fix(context)
end

#_rescale(exp, rounding) ⇒ Object

Rescale so that the exponent is exp, either by padding with zeros or by truncating digits, using the given rounding mode.

Specials are returned without change. This operation is quiet: it raises no flags, and uses no information from the context.

exp = exp to scale to (an integer) rounding = rounding mode



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# File 'lib/decimal/decimal.rb', line 3011

def _rescale(exp, rounding)

  return Decimal.new(self) if special?
  return Decimal.new([sign, 0, exp]) if zero?
  return Decimal.new([sign, @coeff*Decimal.int_radix_power(self.exponent - exp), exp]) if self.exponent > exp
  #nd = number_of_digits + self.exponent - exp
  nd = exp - self.exponent
  if number_of_digits < nd
    slf = Decimal.new([sign, 1, exp-1])
    nd = number_of_digits
  else
    slf = Decimal.new(self)
  end
  changed = slf._round(rounding, nd)
  coeff = Decimal.int_div_radix_power(@coeff, nd)
  coeff += 1 if changed==1
  Decimal.new([slf.sign, coeff, exp])

end

#_watched_rescale(exp, context, watch_exp) ⇒ Object 



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# File 'lib/decimal/decimal.rb', line 3031

def _watched_rescale(exp, context, watch_exp)
  if !watch_exp
    ans = _rescale(exp, context.rounding)
    context.exception(Rounded) if ans.exponent > self.exponent
    context.exception(Inexact) if ans != self
    return ans
  end

  if exp < context.etiny || exp > context.emax
    return context.exception(InvalidOperation, "target operation out of bounds in quantize/rescale")
  end

  return Decimal.new([@sign, 0, exp])._fix(context) if zero?

  self_adjusted = adjusted_exponent
  return context.exception(InvalidOperation,"exponent of quantize/rescale result too large for current context") if self_adjusted > context.emax
  return context.exception(InvalidOperation,"quantize/rescale has too many digits for current context") if (self_adjusted - exp + 1 > context.precision) && !context.exact?

  ans = _rescale(exp, context.rounding)
  return context.exception(InvalidOperation,"exponent of rescale result too large for current context") if ans.adjusted_exponent > context.emax
  return context.exception(InvalidOperation,"rescale result has too many digits for current context") if (ans.number_of_digits > context.precision) && !context.exact?
  if ans.exponent > self.exponent
    context.exception(Rounded)
    context.exception(Inexact) if ans!=self
  end
  context.exception(Subnormal) if !ans.zero? && (ans.adjusted_exponent < context.emin)
  return ans._fix(context)
end

#abs(context = nil) ⇒ Object

Absolute value



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# File 'lib/decimal/decimal.rb', line 1578

def abs(context=nil)
  if special?
    ans = _check_nans(context)
    return ans if ans
  end
  sign<0 ? _neg(context) : _pos(context)
end

#add(other, context = nil) ⇒ Object

Addition



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# File 'lib/decimal/decimal.rb', line 1417

def add(other, context=nil)

  context = Decimal.define_context(context)
  other = _convert(other)

  if self.special? || other.special?
    ans = _check_nans(context,other)
    return ans if ans

    if self.infinite?
      if self.sign != other.sign && other.infinite?
        return context.exception(InvalidOperation, '-INF + INF')
      end
      return Decimal(self)
    end

    return Decimal(other) if other.infinite?
  end

  exp = [self.exponent, other.exponent].min
  negativezero = (context.rounding == ROUND_FLOOR && self.sign != other.sign)

  if self.zero? && other.zero?
    sign = [self.sign, other.sign].max
    sign = -1 if negativezero
    ans = Decimal.new([sign, 0, exp])._fix(context)
    return ans
  end

  if self.zero?
    exp = [exp, other.exponent - context.precision - 1].max unless context.exact?
    return other._rescale(exp, context.rounding)._fix(context)
  end

  if other.zero?
    exp = [exp, self.exponent - context.precision - 1].max unless context.exact?
    return self._rescale(exp, context.rounding)._fix(context)
  end

  op1, op2 = _normalize(self, other, context.precision)

  result_sign = result_coeff = result_exp = nil
  if op1.sign != op2.sign
    return ans = Decimal.new([negativezero ? -1 : +1, 0, exp])._fix(context) if op1.coefficient == op2.coefficient
    op1,op2 = op2,op1 if op1.coefficient < op2.coefficient
    result_sign = op1.sign
    op1,op2 = op1.copy_negate, op2.copy_negate if result_sign < 0
  elsif op1.sign < 0
    result_sign = -1
    op1,op2 = op1.copy_negate, op2.copy_negate
  else
    result_sign = +1
  end

  if op2.sign == +1
    result_coeff = op1.coefficient + op2.coefficient
  else
    result_coeff = op1.coefficient - op2.coefficient
  end

  result_exp = op1.exponent

  return Decimal([result_sign, result_coeff, result_exp])._fix(context)

end

#adjusted_exponent ⇒ Object

Exponent of the magnitude of the most significant digit of the operand



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# File 'lib/decimal/decimal.rb', line 2293

def adjusted_exponent
  if special?
    0
  else
    @exp + number_of_digits - 1
  end
end

#ceil(opt = {}) ⇒ Object

General ceiling operation (as for Float) with same options for precision as Decimal#round()



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# File 'lib/decimal/decimal.rb', line 2568

def ceil(opt={})
  opt[:rounding] = :ceiling
  round opt
end

#coefficient ⇒ Object

Significand as an integer, unsigned



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# File 'lib/decimal/decimal.rb', line 2334

def coefficient
  @coeff
end

#coerce(other) ⇒ Object

Used internally to convert numbers to be used in an operation to a suitable numeric type



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# File 'lib/decimal/decimal.rb', line 1350

def coerce(other)
  case other
    when *Decimal.context.coercible_types_or_decimal
      [Decimal(other),self]
    when Float
      [other, self.to_f]
    else
      super
  end
end

#compare(other, context = nil) ⇒ Object

Compares like <=> but returns a Decimal value.



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# File 'lib/decimal/decimal.rb', line 2274

def compare(other, context=nil)

  other = _convert(other)

  if self.special? || other.special?
    ans = _check_nans(context, other)
    return ans if ans
  end

  return Decimal(self <=> other)

end

#convert_to(type, context = nil) ⇒ Object

Convert to other numerical type.



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# File 'lib/decimal/decimal.rb', line 2056

def convert_to(type, context=nil)
  context = Decimal.define_context(context)
  context.convert_to(type, self)
end

#copy_abs ⇒ Object

Returns a copy of with the sign set to +



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# File 'lib/decimal/decimal.rb', line 2353

def copy_abs
  Decimal.new([+1,@coeff,@exp])
end

#copy_negate ⇒ Object

Returns a copy of with the sign inverted



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# File 'lib/decimal/decimal.rb', line 2358

def copy_negate
  Decimal.new([-@sign,@coeff,@exp])
end

#copy_sign(other) ⇒ Object

Returns a copy of with the sign of other



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# File 'lib/decimal/decimal.rb', line 2363

def copy_sign(other)
  Decimal.new([other.sign, @coeff, @exp])
end

#digits ⇒ Object

Digits of the significand as an array of integers



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# File 'lib/decimal/decimal.rb', line 2288

def digits
  @coeff.to_s.split('').map{|d| d.to_i}
end

#div(other, context = nil) ⇒ Object

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



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# File 'lib/decimal/decimal.rb', line 1845

def div(other, context=nil)
  context = Decimal.define_context(context)
  other = _convert(other)

  ans = _check_nans(context,other)
  return [ans,ans] if ans

  sign = self.sign * other.sign

  if self.infinite?
    return context.exception(InvalidOperation, 'INF // INF') if other.infinite?
    return Decimal.infinity(sign)
  end

  if other.zero?
    if self.zero?
      return context.exception(DivisionUndefined, '0 // 0')
    else
      return context.exception(DivisionByZero, 'x // 0', sign)
    end
  end
  return self._divide_floor(other, context).first
end

#divide(other, context = nil) ⇒ Object

Division



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# File 'lib/decimal/decimal.rb', line 1527

def divide(other, context=nil)
  context = Decimal.define_context(context)
  other = _convert(other)
  resultsign = self.sign * other.sign
  if self.special? || other.special?
    ans = _check_nans(context,other)
    return ans if ans
    if self.infinite?
      return context.exception(InvalidOperation,"(+-)INF/(+-)INF") if other.infinite?
      return Decimal.infinity(resultsign)
    end
    if other.infinite?
      context.exception(Clamped,"Division by infinity")
      return Decimal.new([resultsign, 0, context.etiny])
    end
  end

  if other.zero?
    return context.exception(DivisionUndefined, '0 / 0') if self.zero?
    return context.exception(DivisionByZero, 'x / 0', resultsign)
  end

  if self.zero?
    exp = self.exponent - other.exponent
    coeff = 0
  else
    prec = context.exact? ? self.number_of_digits + 4*other.number_of_digits : context.precision # this assumes radix==10
    shift = other.number_of_digits - self.number_of_digits + prec + 1
    exp = self.exponent - other.exponent - shift
    if shift >= 0
      coeff, remainder = (self.coefficient*Decimal.int_radix_power(shift)).divmod(other.coefficient)
    else
      coeff, remainder = self.coefficient.divmod(other.coefficient*Decimal.int_radix_power(-shift))
    end
    if remainder != 0
      return context.exception(Inexact) if context.exact?
      coeff += 1 if (coeff%(Decimal.radix/2)) == 0
    else
      ideal_exp = self.exponent - other.exponent
      while (exp < ideal_exp) && ((coeff % Decimal.radix)==0)
        coeff /= Decimal.radix
        exp += 1
      end
    end

  end
  return Decimal([resultsign, coeff, exp])._fix(context)

end

#divide_int(other, context = nil) ⇒ Object

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



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# File 'lib/decimal/decimal.rb', line 1820

def divide_int(other, context=nil)
  context = Decimal.define_context(context)
  other = _convert(other)

  ans = _check_nans(context,other)
  return ans if ans

  sign = self.sign * other.sign

  if self.infinite?
    return context.exception(InvalidOperation, 'INF // INF') if other.infinite?
    return Decimal.infinity(sign)
  end

  if other.zero?
    if self.zero?
      return context.exception(DivisionUndefined, '0 // 0')
    else
      return context.exception(DivisionByZero, 'x // 0', sign)
    end
  end
  return self._divide_truncate(other, context).first
end

#divmod(other, context = nil) ⇒ Object

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



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# File 'lib/decimal/decimal.rb', line 1786

def divmod(other, context=nil)
  context = Decimal.define_context(context)
  other = _convert(other)

  ans = _check_nans(context,other)
  return [ans,ans] if ans

  sign = self.sign * other.sign

  if self.infinite?
    if other.infinite?
      ans = context.exception(InvalidOperation, 'divmod(INF,INF)')
      return [ans,ans]
    else
      return [Decimal.infinity(sign), context.exception(InvalidOperation, 'INF % x')]
    end
  end

  if other.zero?
    if self.zero?
      ans = context.exception(DivisionUndefined, 'divmod(0,0)')
      return [ans,ans]
    else
      return [context.exception(DivisionByZero, 'x // 0', sign),
               context.exception(InvalidOperation, 'x % 0')]
    end
  end

  quotient, remainder = self._divide_floor(other, context)
  return [quotient, remainder._fix(context)]
end

#divrem(other, context = nil) ⇒ Object

General Decimal Arithmetic Specification integer division and remainder:

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



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# File 'lib/decimal/decimal.rb', line 1753

def divrem(other, context=nil)
  context = Decimal.define_context(context)
  other = _convert(other)

  ans = _check_nans(context,other)
  return [ans,ans] if ans

  sign = self.sign * other.sign

  if self.infinite?
    if other.infinite?
      ans = context.exception(InvalidOperation, 'divmod(INF,INF)')
      return [ans,ans]
    else
      return [Decimal.infinity(sign), context.exception(InvalidOperation, 'INF % x')]
    end
  end

  if other.zero?
    if self.zero?
      ans = context.exception(DivisionUndefined, 'divmod(0,0)')
      return [ans,ans]
    else
      return [context.exception(DivisionByZero, 'x // 0', sign),
               context.exception(InvalidOperation, 'x % 0')]
    end
  end

  quotient, remainder = self._divide_truncate(other, context)
  return [quotient, remainder._fix(context)]
end

#eql?(other) ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/decimal/decimal.rb', line 2268

def eql?(other)
  return false unless other.is_a?(Decimal)
  reduce.split == other.reduce.split
end

#even? ⇒ Boolean

returns true if is an even integer

Returns:

  • (Boolean) 


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# File 'lib/decimal/decimal.rb', line 2386

def even?
  # integral? && ((to_i%2)==0)
  if finite?
    if @exp>0 || @coeff==0
      true
    else
      if @exp <= -number_of_digits
        false
      else
        m = Decimal.int_radix_power(-@exp)
        if (@coeff % m) == 0
          # ((@coeff / m) % 2) == 0
          ((@coeff / m) & 1) == 0
        else
          false
        end
      end
    end
  else
    false
  end
end

#exp(context = nil) ⇒ Object

Exponential function



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# File 'lib/decimal/decimal.rb', line 2868

def exp(context=nil)
  context = Decimal.define_context(context)

  # exp(NaN) = NaN
  ans = _check_nans(context)
  return ans if ans

  # exp(-Infinity) = 0
  return Decimal.zero if self.infinite? && (self.sign == -1)

  # exp(0) = 1
  return Decimal(1) if self.zero?

  # exp(Infinity) = Infinity
  return Decimal(self) if self.infinite?

  # the result is now guaranteed to be inexact (the true
  # mathematical result is transcendental). There's no need to
  # raise Rounded and Inexact here---they'll always be raised as
  # a result of the call to _fix.
  return context.exception(Inexact, 'Inexact exp') if context.exact?
  p = context.precision
  adj = self.adjusted_exponent

  # we only need to do any computation for quite a small range
  # of adjusted exponents---for example, -29 <= adj <= 10 for
  # the default context.  For smaller exponent the result is
  # indistinguishable from 1 at the given precision, while for
  # larger exponent the result either overflows or underflows.
  if self.sign == +1 and adj > ((context.emax+1)*3).to_s.length
    # overflow
    ans = Decimal(+1, 1, context.emax+1)
  elsif self.sign == -1 and adj > ((-context.etiny+1)*3).to_s.length
    # underflow to 0
    ans = Decimal(+1, 1, context.etiny-1)
  elsif self.sign == +1 and adj < -p
    # p+1 digits; final round will raise correct flags
    ans = Decimal(+1, Decimal.int_radix_power(p)+1, -p)
  elsif self.sign == -1 and adj < -p-1
    # p+1 digits; final round will raise correct flags
    ans = Decimal(+1, Decimal.int_radix_power(p+1)-1, -p-1)
  else
    # general case
    c = self.coefficient
    e = self.exponent
    c = -c if self.sign == -1

    # compute correctly rounded result: increase precision by
    # 3 digits at a time until we get an unambiguously
    # roundable result
    extra = 3
    coeff = exp = nil
    loop do
      coeff, exp = _dexp(c, e, p+extra)
      break if (coeff % (5*10**(coeff.to_s.length-p-1)))!=0
      extra += 3
    end
    ans = Decimal(+1, coeff, exp)
  end

  # at this stage, ans should round correctly with *any*
  # rounding mode, not just with ROUND_HALF_EVEN
  Decimal.context(context, :rounding=>:half_even) do |local_context|
    ans = ans._fix(local_context)
    context.flags = local_context.flags
  end

  return ans
end

#exponent ⇒ Object

Exponent of the significand as an integer.



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# File 'lib/decimal/decimal.rb', line 2339

def exponent
  @exp
end

#finite? ⇒ Boolean

Returns whether the number is finite

Returns:

  • (Boolean) 


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# File 'lib/decimal/decimal.rb', line 1298

def finite?
  !special?
end

#floor(opt = {}) ⇒ Object

General floor operation (as for Float) with same options for precision as Decimal#round()



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# File 'lib/decimal/decimal.rb', line 2575

def floor(opt={})
  opt[:rounding] = :floor
  round opt
end

#fma(other, third, context = nil) ⇒ Object

Fused multiply-add.

Computes (self*other+third) with no rounding of the intermediate product self*other.



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# File 'lib/decimal/decimal.rb', line 2590

def fma(other, third, context=nil)
  context = Decimal.define_context(context)
  other = _convert(other)
  third = _convert(third)
  if self.special? || other.special?
    return context.exception(InvalidOperation, 'sNaN', self) if self.snan?
    return context.exception(InvalidOperation, 'sNaN', other) if other.snan?
    if self.nan?
      product = self
    elsif other.nan?
      product = other
    elsif self.infinite?
      return context.exception(InvalidOperation, 'INF * 0 in fma') if other.zero?
      product = Decimal.infinity(self.sign*other.sign)
    elsif other.infinite?
      return context.exception(InvalidOperation, '0 * INF  in fma') if self.zero?
      product = Decimal.infinity(self.sign*other.sign)
    end
  else
    product = Decimal.new([self.sign*other.sign,self.coefficient*other.coefficient, self.exponent+other.exponent])
  end
  return product.add(third, context)
end

#fractional_exponent ⇒ Object

Exponent as though the significand were a fraction (the decimal point before its first digit)



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# File 'lib/decimal/decimal.rb', line 2307

def fractional_exponent
  scientific_exponent + 1
end

#hash ⇒ Object 



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# File 'lib/decimal/decimal.rb', line 2264

def hash
  ([Decimal]+reduce.split).hash # TODO: optimize
end

#infinite? ⇒ Boolean

Returns whether the number is infinite

Returns:

  • (Boolean) 


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# File 'lib/decimal/decimal.rb', line 1293

def infinite?
  @exp == :inf
end

#inspect ⇒ Object 



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# File 'lib/decimal/decimal.rb', line 2196

def inspect
  if $DEBUG
    "Decimal('#{self}') [coeff:#{@coeff.inspect} exp:#{@exp.inspect} s:#{@sign.inspect}]"
  else
    "Decimal('#{self}')"
  end
end

#integral? ⇒ Boolean

Returns true if the value is an integer

Returns:

  • (Boolean) 


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# File 'lib/decimal/decimal.rb', line 2368

def integral?
  if finite?
    if @exp>=0 || @coeff==0
      true
    else
      if @exp <= -number_of_digits
        false
      else
        m = Decimal.int_radix_power(-@exp)
        (@coeff % m) == 0
      end
    end
  else
    false
  end
end

#integral_exponent ⇒ Object

Exponent of the significand as an integer. Synonym of exponent



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# File 'lib/decimal/decimal.rb', line 2323

def integral_exponent
  # fractional_exponent - number_of_digits
  @exp
end

#integral_significand ⇒ Object

Significand as an integer, unsigned. Synonym of coefficient



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# File 'lib/decimal/decimal.rb', line 2318

def integral_significand
  @coeff
end

#ln(context = nil) ⇒ Object

Returns the natural (base e) logarithm



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# File 'lib/decimal/decimal.rb', line 2939

def ln(context=nil)
  context = Decimal.define_context(context)

  # ln(NaN) = NaN
  ans = _check_nans(context)
  return ans if ans

  # ln(0.0) == -Infinity
  return Decimal.infinity(-1) if self.zero?

  # ln(Infinity) = Infinity
  return Decimal.infinity if self.infinite? && self.sign == +1

  # ln(1.0) == 0.0
  return Decimal.zero if self == Decimal(1)

  # ln(negative) raises InvalidOperation
  return context.exception(InvalidOperation, 'ln of a negative value') if self.sign==-1

  # result is irrational, so necessarily inexact
  return context.exception(Inexact, 'Inexact exp') if context.exact?

  c = self.coefficient
  e = self.exponent
  p = context.precision

  # correctly rounded result: repeatedly increase precision by 3
  # until we get an unambiguously roundable result
  places = p - self._ln_exp_bound + 2 # at least p+3 places
  coeff = nil
  loop do
    coeff = _dlog(c, e, places)
    # assert coeff.to_s.length-p >= 1
    break if (coeff % (5*10**(coeff.abs.to_s.length-p-1))) != 0
    places += 3
  end
  ans = Decimal((coeff<0) ? -1 : +1, coeff.abs, -places)

  Decimal.context(context, :rounding=>:half_even) do |local_context|
    ans = ans._fix(local_context)
    context.flags = local_context.flags
  end
  return ans
end

#log10(context = nil) ⇒ Object

Returns the base 10 logarithm



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# File 'lib/decimal/decimal.rb', line 2818

def log10(context=nil)
  context = Decimal.define_context(context)

  # log10(NaN) = NaN
  ans = _check_nans(context)
  return ans if ans

  # log10(0.0) == -Infinity
  return Decimal.infinity(-1) if self.zero?

  # log10(Infinity) = Infinity
  return Decimal.infinity if self.infinite? && self.sign == +1

  # log10(negative or -Infinity) raises InvalidOperation
  return context.exception(InvalidOperation, 'log10 of a negative value') if self.sign == -1

  digits = self.digits
  # log10(10**n) = n
  if digits.first == 1 && digits[1..-1].all?{|d| d==0}
    # answer may need rounding
    ans = Decimal(self.exponent + digits.size - 1)
    return ans if context.exact?
  else
    # result is irrational, so necessarily inexact
    return context.exception(Inexact, "Inexact power") if context.exact?
    c = self.coefficient
    e = self.exponent
    p = context.precision

    # correctly rounded result: repeatedly increase precision
    # until result is unambiguously roundable
    places = p-self._log10_exp_bound+2
    coeff = nil
    loop do
      coeff = _dlog10(c, e, places)
      # assert coeff.abs.to_s.length-p >= 1
      break if (coeff % (5*10**(coeff.abs.to_s.length-p-1)))!=0
      places += 3
    end
    ans = Decimal(coeff<0 ? -1 : +1, coeff.abs, -places)
  end

  Decimal.context(context, :rounding=>:half_even) do |local_context|
    ans = ans._fix(local_context)
    context.flags = local_context.flags
  end
  return ans
end

#logb(context = nil) ⇒ Object

Returns the exponent of the magnitude of the most significant digit.

The result is the integer which is the exponent of the magnitude of the most significant digit of the number (as though it were truncated to a single digit while maintaining the value of that digit and without limiting the resulting exponent).



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# File 'lib/decimal/decimal.rb', line 2027

def logb(context=nil)
  context = Decimal.define_context(context)
  ans = _check_nans(context)
  return ans if ans
  return Decimal.infinity if infinite?
  return context.exception(DivisionByZero,'logb(0)',-1) if zero?
  Decimal.new(adjusted_exponent)
end

#minus(context = nil) ⇒ Object

Unary prefix minus operator



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# File 'lib/decimal/decimal.rb', line 1592

def minus(context=nil)
  _neg(context)
end

#modulo(other, context = nil) ⇒ Object

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



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# File 'lib/decimal/decimal.rb', line 1871

def modulo(other, context=nil)
  context = Decimal.define_context(context)
  other = _convert(other)

  ans = _check_nans(context,other)
  return ans if ans

  #sign = self.sign * other.sign

  if self.infinite?
    return context.exception(InvalidOperation, 'INF % x')
  elsif other.zero?
    if self.zero?
      return context.exception(DivisionUndefined, '0 % 0')
    else
      return context.exception(InvalidOperation, 'x % 0')
    end
  end

  return self._divide_floor(other, context).last._fix(context)
end

#multiply(other, context = nil) ⇒ Object

Multiplication



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# File 'lib/decimal/decimal.rb', line 1498

def multiply(other, context=nil)
  context = Decimal.define_context(context)
  other = _convert(other)
  resultsign = self.sign * other.sign
  if self.special? || other.special?
    ans = _check_nans(context,other)
    return ans if ans

    if self.infinite?
      return context.exception(InvalidOperation,"(+-)INF * 0") if other.zero?
      return Decimal.infinity(resultsign)
    end
    if other.infinite?
      return context.exception(InvalidOperation,"0 * (+-)INF") if self.zero?
      return Decimal.infinity(resultsign)
    end
  end

  resultexp = self.exponent + other.exponent

  return Decimal([resultsign, 0, resultexp])._fix(context) if self.zero? || other.zero?
  #return Decimal([resultsign, other.coefficient, resultexp])._fix(context) if self.coefficient==1
  #return Decimal([resultsign, self.coefficient, resultexp])._fix(context) if other.coefficient==1

  return Decimal([resultsign, other.coefficient*self.coefficient, resultexp])._fix(context)

end

#nan? ⇒ Boolean

Returns whether the number is not actualy one (NaN, not a number).

Returns:

  • (Boolean) 


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# File 'lib/decimal/decimal.rb', line 1278

def nan?
  @exp==:nan || @exp==:snan
end

#next_minus(context = nil) ⇒ Object

Largest representable number smaller than itself



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# File 'lib/decimal/decimal.rb', line 1597

def next_minus(context=nil)
  context = Decimal.define_context(context)
  if special?
    ans = _check_nans(context)
    return ans if ans
    if infinite?
      return Decimal.new(self) if @sign == -1
      # @sign == +1
      if context.exact?
         return context.exception(InvalidOperation, 'Exact +INF next minus')
      else
        return Decimal.new(+1, context.maximum_significand, context.etop)
      end
    end
  end

  return context.exception(InvalidOperation, 'Exact next minus') if context.exact?

  result = nil
  Decimal.local_context(context) do |local|
    local.rounding = :floor
    local.ignore_all_flags
    result = self._fix(local)
    if result == self
      result = self - Decimal(+1, 1, local.etiny-1)
    end
  end
  result
end

#next_plus(context = nil) ⇒ Object

Smallest representable number larger than itself



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# File 'lib/decimal/decimal.rb', line 1628

def next_plus(context=nil)
  context = Decimal.define_context(context)

  if special?
    ans = _check_nans(context)
    return ans if ans
    if infinite?
      return Decimal.new(self) if @sign == +1
      # @sign == -1
      if context.exact?
         return context.exception(InvalidOperation, 'Exact -INF next plus')
      else
        return Decimal.new(-1, context.maximum_significand, context.etop)
      end
    end
  end

  return context.exception(InvalidOperation, 'Exact next plus') if context.exact?

  result = nil
  Decimal.local_context(context) do |local|
    local.rounding = :ceiling
    local.ignore_all_flags
    result = self._fix(local)
    if result == self
      result = self + Decimal(+1, 1, local.etiny-1)
    end
  end
  result

end

#next_toward(other, context = nil) ⇒ Object

Returns the number closest to self, in the direction towards other.



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# File 'lib/decimal/decimal.rb', line 1661

def next_toward(other, context=nil)
  context = Decimal.define_context(context)
  other = _convert(other)
  ans = _check_nans(context,other)
  return ans if ans

  return context.exception(InvalidOperation, 'Exact next_toward') if context.exact?

  comparison = self <=> other
  return self.copy_sign(other) if comparison == 0

  if comparison == -1
    result = self.next_plus(context)
  else # comparison == 1
    result = self.next_minus(context)
  end

  # decide which flags to raise using value of ans
  if result.infinite?
    context.exception Overflow, 'Infinite result from next_toward', result.sign
    context.exception Rounded
    context.exception Inexact
  elsif result.adjusted_exponent < context.emin
    context.exception Underflow
    context.exception Subnormal
    context.exception Rounded
    context.exception Inexact
    # if precision == 1 then we don't raise Clamped for a
    # result 0E-etiny.
    context.exception Clamped if result.zero?
  end

  result
end

#nonzero? ⇒ Boolean

Returns whether the number not zero

Returns:

  • (Boolean) 


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# File 'lib/decimal/decimal.rb', line 1308

def nonzero?
  special? || @coeff>0
end

#normal?(context = nil) ⇒ Boolean

Returns whether the number is normal

Returns:

  • (Boolean) 


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# File 'lib/decimal/decimal.rb', line 1320

def normal?(context=nil)
  return false if special? || zero?
  context = Decimal.define_context(context)
  (context.emin <= self.adjusted_exponent) &&  (self.adjusted_exponent <= context.emax)
end

#normalize(context = nil) ⇒ Object

normalizes so that the coefficient has precision digits (this is not the old GDA normalize function)



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# File 'lib/decimal/decimal.rb', line 2007

def normalize(context=nil)
  context = Decimal.define_context(context)
  return Decimal(self) if self.special? || self.zero?
  return context.exception(InvalidOperation, "Normalize in exact context") if context.exact?
  return context.exception(Subnormal, "Cannot normalize subnormal") if self.subnormal?
  min_normal_coeff = Decimal.int_radix_power(context.precision-1)
  sign, coeff, exp = self._fix(context).split
  while coeff < min_normal_coeff
    coeff *= Decimal.radix
    exp -= 1
  end
  Decimal(sign, coeff, exp)
end

#number_class(context = nil) ⇒ Object

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

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



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# File 'lib/decimal/decimal.rb', line 1329

def number_class(context=nil)
  return "sNaN" if snan?
  return "NaN" if nan?
  if infinite?
    return '+Infinity' if @sign==+1
    return '-Infinity' # if @sign==-1
  end
  if zero?
    return '+Zero' if @sign==+1
    return '-Zero' # if @sign==-1
  end
  context = Decimal.define_context(context)
  if subnormal?(context)
    return '+Subnormal' if @sign==+1
    return '-Subnormal' # if @sign==-1
  end
  return '+Normal' if @sign==+1
  return '-Normal' if @sign==-1
end

#number_of_digits ⇒ Object

Number of digits in the significand



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# File 'lib/decimal/decimal.rb', line 2312

def number_of_digits
  # digits.size
  @coeff.to_s.size
end

#odd? ⇒ Boolean

returns true if is an odd integer

Returns:

  • (Boolean) 


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# File 'lib/decimal/decimal.rb', line 2410

def odd?
  # integral? && ((to_i%2)==1)
  # integral? && !even?
  if finite?
    if @exp>0 || @coeff==0
      false
    else
      if @exp <= -number_of_digits
        false
      else
        m = Decimal.int_radix_power(-@exp)
        if (@coeff % m) == 0
          # ((@coeff / m) % 2) == 1
          ((@coeff / m) & 1) == 1
        else
          false
        end
      end
    end
  else
    false
  end
end

#plus(context = nil) ⇒ Object

Unary prefix plus operator



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# File 'lib/decimal/decimal.rb', line 1587

def plus(context=nil)
  _pos(context)
end

#power(other, modulo = nil, context = nil) ⇒ Object

Raises to the power of x, to modulo if given.

With two arguments, compute self**other. If self is negative then other must be integral. The result will be inexact unless other is integral and the result is finite and can be expressed exactly in ‘precision’ digits.

With three arguments, compute (self**other) % modulo. For the three argument form, the following restrictions on the arguments hold:

- all three arguments must be integral
- other must be nonnegative
- at least one of self or other must be nonzero
- modulo must be nonzero and have at most 'precision' digits

The result of a.power(b, modulo) is identical to the result that would be obtained by computing (a**b) % modulo with unbounded precision, but is computed more efficiently. It is always exact.



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# File 'lib/decimal/decimal.rb', line 2634

def power(other, modulo=nil, context=nil)

  if context.nil? && (modulo.is_a?(Context) || modulo.is_a?(Hash))
    context = modulo
    modulo = nil
  end

  return self.power_modulo(other, modulo, context) if modulo

  context = Decimal.define_context(context)
  other = _convert(other)

  ans = _check_nans(context, other)
  return ans if ans

  # 0**0 = NaN (!), x**0 = 1 for nonzero x (including +/-Infinity)
  if other.zero?
    if self.zero?
      return context.exception(InvalidOperation, '0 ** 0')
    else
      return Decimal(1)
    end
  end

  # result has sign -1 iff self.sign is -1 and other is an odd integer
  result_sign = +1
  _self = self
  if _self.sign == -1
    if other.integral?
      result_sign = -1 if !other.even?
    else
      # -ve**noninteger = NaN
      # (-0)**noninteger = 0**noninteger
      unless self.zero?
        return context.exception(InvalidOperation, 'x ** y with x negative and y not an integer')
      end
    end
    # negate self, without doing any unwanted rounding
    _self = self.copy_negate
  end

  # 0**(+ve or Inf)= 0; 0**(-ve or -Inf) = Infinity
  if _self.zero?
    return (other.sign == +1) ? Decimal(result_sign, 0, 0) : Decimal.infinity(result_sign)
  end

  # Inf**(+ve or Inf) = Inf; Inf**(-ve or -Inf) = 0
  if _self.infinite?
    return (other.sign == +1) ? Decimal.infinity(result_sign) : Decimal(result_sign, 0, 0)
  end

  # 1**other = 1, but the choice of exponent and the flags
  # depend on the exponent of self, and on whether other is a
  # positive integer, a negative integer, or neither
  if _self == Decimal(1)
    return _self if context.exact?
    if other.integral?
      # exp = max(self._exp*max(int(other), 0),
      # 1-context.prec) but evaluating int(other) directly
      # is dangerous until we know other is small (other
      # could be 1e999999999)
      if other.sign == -1
        multiplier = 0
      elsif other > context.precision
        multiplier = context.precision
      else
        multiplier = other.to_i
      end

      exp = _self.exponent * multiplier
      if exp < 1-context.precision
        exp = 1-context.precision
        context.exception Rounded
      end
    else
      context.exception Rounded
      context.exception Inexact
      exp = 1-context.precision
    end

    return Decimal(result_sign, Decimal.int_radix_power(-exp), exp)
  end

  # compute adjusted exponent of self
  self_adj = _self.adjusted_exponent

  # self ** infinity is infinity if self > 1, 0 if self < 1
  # self ** -infinity is infinity if self < 1, 0 if self > 1
  if other.infinite?
    if (other.sign == +1) == (self_adj < 0)
      return Decimal(result_sign, 0, 0)
    else
      return Decimal.infinity(result_sign)
    end
  end

  # from here on, the result always goes through the call
  # to _fix at the end of this function.
  ans = nil

  # crude test to catch cases of extreme overflow/underflow.  If
  # log10(self)*other >= 10**bound and bound >= len(str(Emax))
  # then 10**bound >= 10**len(str(Emax)) >= Emax+1 and hence
  # self**other >= 10**(Emax+1), so overflow occurs.  The test
  # for underflow is similar.
  bound = _self._log10_exp_bound + other.adjusted_exponent
  if (self_adj >= 0) == (other.sign == +1)
    # self > 1 and other +ve, or self < 1 and other -ve
    # possibility of overflow
    if bound >= context.emax.to_s.length
      ans = Decimal(result_sign, 1, context.emax+1)
    end
  else
    # self > 1 and other -ve, or self < 1 and other +ve
    # possibility of underflow to 0
    etiny = context.etiny
    if bound >= (-etiny).to_s.length
      ans = Decimal(result_sign, 1, etiny-1)
    end
  end

  # try for an exact result with precision +1
  if ans.nil?
    if context.exact?
      if other.adjusted_exponent < 100
        test_precision = _self.number_of_digits*other.to_i+1
      else
        test_precision = _self.number_of_digits+1
      end
    else
      test_precision = context.precision + 1
    end
    ans = _self._power_exact(other, test_precision)
    if !ans.nil? && (result_sign == -1)
      ans = Decimal(-1, ans.coefficient, ans.exponent)
    end
  end

  # usual case: inexact result, x**y computed directly as exp(y*log(x))
  if !ans.nil?
    return ans if context.exact?
  else
    return context.exception(Inexact, "Inexact power") if context.exact?

    p = context.precision
    xc = _self.coefficient
    xe = _self.exponent
    yc = other.coefficient
    ye = other.exponent
    yc = -yc if other.sign == -1

    # compute correctly rounded result:  start with precision +3,
    # then increase precision until result is unambiguously roundable
    extra = 3
    coeff, exp = nil, nil
    loop do
      coeff, exp = _dpower(xc, xe, yc, ye, p+extra)
      #break if (coeff % Decimal.int_mult_radix_power(5,coeff.to_s.length-p-1)) != 0
      break if (coeff % (5*10**(coeff.to_s.length-p-1))) != 0
      extra += 3
    end
    ans = Decimal(result_sign, coeff, exp)
  end

  # the specification says that for non-integer other we need to
  # raise Inexact, even when the result is actually exact.  In
  # the same way, we need to raise Underflow here if the result
  # is subnormal.  (The call to _fix will take care of raising
  # Rounded and Subnormal, as usual.)
  if !other.integral?
    context.exception Inexact
    # pad with zeros up to length context.precision+1 if necessary
    if ans.number_of_digits <= context.precision
      expdiff = context.precision+1 - ans.number_of_digits
      ans = Decimal(ans.sign, Decimal.int_mult_radix_power(ans.coefficient, expdiff), ans.exponent-expdiff)
    end
    context.exception Underflow if ans.adjusted_exponent < context.emin
  end
  # unlike exp, ln and log10, the power function respects the
  # rounding mode; no need to use ROUND_HALF_EVEN here
  ans._fix(context)
end

#qnan? ⇒ Boolean

Returns whether the number is a quite NaN (non-signaling)

Returns:

  • (Boolean) 


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# File 'lib/decimal/decimal.rb', line 1283

def qnan?
  @exp == :nan
end

#quantize(exp, context = nil, watch_exp = true) ⇒ Object

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



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# File 'lib/decimal/decimal.rb', line 2453

def quantize(exp, context=nil, watch_exp=true)
  exp = _convert(exp)
  context = Decimal.define_context(context)
  if self.special? || exp.special?
    ans = _check_nans(context, exp)
    return ans if ans
    if exp.infinite? || self.infinite?
      return Decimal.new(self) if exp.infinite? && self.infinite?
      return context.exception(InvalidOperation, 'quantize with one INF')
    end
  end
  exp = exp.exponent
  _watched_rescale(exp, context, watch_exp)
end

#reduce(context = nil) ⇒ 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/decimal/decimal.rb', line 1982

def reduce(context=nil)
  context = Decimal.define_context(context)
  if special?
    ans = _check_nans(context)
    return ans if ans
  end
  dup = _fix(context)
  return dup if dup.infinite?

  return Decimal.new([dup.sign, 0, 0]) if dup.zero?

  exp_max = context.clamp? ? context.etop : context.emax
  end_d = nd = dup.number_of_digits
  exp = dup.exponent
  coeff = dup.coefficient
  dgs = dup.digits
  while (dgs[end_d-1]==0) && (exp < exp_max)
    exp += 1
    end_d -= 1
  end
  return Decimal.new([dup.sign, coeff/Decimal.int_radix_power(nd-end_d), exp])
end

#remainder(other, context = nil) ⇒ Object

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



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# File 'lib/decimal/decimal.rb', line 1894

def remainder(other, context=nil)
  context = Decimal.define_context(context)
  other = _convert(other)

  ans = _check_nans(context,other)
  return ans if ans

  #sign = self.sign * other.sign

  if self.infinite?
    return context.exception(InvalidOperation, 'INF % x')
  elsif other.zero?
    if self.zero?
      return context.exception(DivisionUndefined, '0 % 0')
    else
      return context.exception(InvalidOperation, 'x % 0')
    end
  end

  return self._divide_truncate(other, context).last._fix(context)
end

#remainder_near(other, context = nil) ⇒ Object

General Decimal Arithmetic Specification remainder-near:

x - y*round_half_even(x/y)



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# File 'lib/decimal/decimal.rb', line 1918

def remainder_near(other, context=nil)
  context = Decimal.define_context(context)
  other = _convert(other)

  ans = _check_nans(context,other)
  return ans if ans

  sign = self.sign * other.sign

  if self.infinite?
    return context.exception(InvalidOperation, 'remainder_near(INF,x)')
  elsif other.zero?
    if self.zero?
      return context.exception(DivisionUndefined, 'remainder_near(0,0)')
    else
      return context.exception(InvalidOperation, 'remainder_near(x,0)')
    end
  end

  if other.infinite?
    return Decimal.new(self)._fix(context)
  end

  ideal_exp = [self.exponent, other.exponent].min
  if self.zero?
    return Decimal([self.sign, 0, ideal_exp])._fix(context)
  end

  expdiff = self.adjusted_exponent - other.adjusted_exponent
  if (expdiff >= context.precision+1) && !context.exact?
    return context.exception(DivisionImpossible)
  elsif expdiff <= -2
    return self._rescale(ideal_exp, context.rounding)._fix(context)
  end

    self_coeff = self.coefficient
    other_coeff = other.coefficient
    de = self.exponent - other.exponent
    if de >= 0
      self_coeff = Decimal.int_mult_radix_power(self_coeff, de)
    else
      other_coeff = Decimal.int_mult_radix_power(other_coeff, -de)
    end
    q, r = self_coeff.divmod(other_coeff)
    if 2*r + (q&1) > other_coeff
      r -= other_coeff
      q += 1
    end

    return context.exception(DivisionImpossible) if q >= Decimal.int_radix_power(context.precision) && !context.exact?

    sign = self.sign
    if r < 0
      sign = -sign
      r = -r
    end

  return Decimal.new([sign, r, ideal_exp])._fix(context)

end

#rescale(exp, context = nil, watch_exp = true) ⇒ Object

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



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# File 'lib/decimal/decimal.rb', line 2436

def rescale(exp, context=nil, watch_exp=true)
  context = Decimal.define_context(context)
  exp = _convert(exp)
  if self.special? || exp.special?
    ans = _check_nans(context, exp)
    return ans if ans
    if exp.infinite? || self.infinite?
      return Decimal.new(self) if exp.infinite? && self.infinite?
      return context.exception(InvalidOperation, 'rescale with one INF')
    end
  end
  return context.exception(InvalidOperation,"exponent of rescale is not integral") unless exp.integral?
  exp = exp.to_i
  _watched_rescale(exp, context, watch_exp)
end

#round(opt = {}) ⇒ Object

General rounding.

With an integer argument this acts like Float#round: the parameter specifies the number of fractional digits (or digits to the left of the decimal point if negative).

Options can be passed as a Hash instead; valid options are:

  • :rounding method for rounding (see Context#new())

The precision can be specified as:

  • :places number of fractional digits as above.

  • :exponent specifies the exponent corresponding to the digit to be rounded (exponent == -places)

  • :precision or :significan_digits is the number of digits

  • :power 10^exponent, value of the digit to be rounded, should be passed as a type convertible to Decimal.

  • :index 0-based index of the digit to be rounded

  • :rindex right 0-based index of the digit to be rounded

The default is :places=>0 (round to integer).

Example: ways of specifiying the rounding position

number:     1   2   3   4  .  5    6    7    8
:places    -3  -2  -1   0     1    2    3    4
:exponent   3   2   1   0    -1   -2   -3   -4
:precision  1   2   3   4     5    6    7    8
:power    1E3 1E2  10   1   0.1 1E-2 1E-3 1E-4
:index      0   1   2   3     4    5    6    7
:index      7   6   5   4     3    2    1    0



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# File 'lib/decimal/decimal.rb', line 2537

def round(opt={})
  opt = { :places=>opt } if opt.kind_of?(Integer)
  r = opt[:rounding] || :half_up
  as_int = false
  if v=(opt[:precision] || opt[:significant_digits])
    prec = v
  elsif v=(opt[:places])
    prec = adjusted_exponent + 1 + v
  elsif v=(opt[:exponent])
    prec = adjusted_exponent + 1 - v
  elsif v=(opt[:power])
    prec = adjusted_exponent + 1 - Decimal(v).adjusted_exponent
  elsif v=(opt[:index])
    prec = i+1
  elsif v=(opt[:rindex])
    prec = number_of_digits - v
  else
    prec = adjusted_exponent + 1
    as_int = true
  end
  dg = number_of_digits-prec
  changed = _round(r, dg)
  coeff = Decimal.int_div_radix_power(@coeff, dg)
  exp = @exp + dg
  coeff += 1 if changed==1
  result = Decimal(@sign, coeff, exp)
  return as_int ? result.to_i : result
end

#same_quantum?(other) ⇒ Boolean

Return true if has the same exponent as other.

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/decimal/decimal.rb', line 2474

def same_quantum?(other)
  other = _convert(other)
  if self.special? || other.special?
    return (self.nan? && other.nan?) || (self.infinite? && other.infinite?)
  end
  return self.exponent == other.exponent
end

#scaleb(other, context = nil) ⇒ Object

Adds a value to the exponent.



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# File 'lib/decimal/decimal.rb', line 2037

def scaleb(other, context=nil)

  context = Decimal.define_context(context)
  other = _convert(other)
  ans = _check_nans(context, other)
  return ans if ans
  return context.exception(InvalidOperation) if other.infinite? || other.exponent != 0
  unless context.exact?
    liminf = -2 * (context.emax + context.precision)
    limsup =  2 * (context.emax + context.precision)
    i = other.to_i
    return context.exception(InvalidOperation) if !((liminf <= i) && (i <= limsup))
  end
  return Decimal.new(self) if infinite?
  return Decimal.new(@sign, @coeff, @exp+i)._fix(context)

end

#scientific_exponent ⇒ Object

Synonym for Decimal#adjusted_exponent()



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# File 'lib/decimal/decimal.rb', line 2302

def scientific_exponent
  adjusted_exponent
end

#sign ⇒ Object

Sign of the number: +1 for plus / -1 for minus.



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# File 'lib/decimal/decimal.rb', line 2329

def sign
  @sign
end

#snan? ⇒ Boolean

Returns whether the number is a signaling NaN

Returns:

  • (Boolean) 


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# File 'lib/decimal/decimal.rb', line 1288

def snan?
  @exp == :snan
end

#special? ⇒ Boolean

Returns whether the number is a special value (NaN or Infinity).

Returns:

  • (Boolean) 


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# File 'lib/decimal/decimal.rb', line 1273

def special?
  @exp.instance_of?(Symbol)
end

#split ⇒ Object

Returns the internal representation of the number, composed of:

  • a sign which is +1 for plus and -1 for minus

  • a coefficient (significand) which is a nonnegative integer

  • an exponent (an integer) or :inf, :nan or :snan for special values

The value of non-special numbers is sign*coefficient*10^exponent



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# File 'lib/decimal/decimal.rb', line 1268

def split
  [@sign, @coeff, @exp]
end

#sqrt(context = nil) ⇒ Object

Square root



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# File 'lib/decimal/decimal.rb', line 1697

def sqrt(context=nil)
  context = Decimal.define_context(context)
  if special?
    ans = _check_nans(context)
    return ans if ans
    return Decimal.new(self) if infinite? && @sign==+1
  end
  return Decimal.new([@sign, 0, @exp/2])._fix(context) if zero?
  return context.exception(InvalidOperation, 'sqrt(-x), x>0') if @sign<0
  prec = context.precision + 1
  e = (@exp >> 1)
  if (@exp & 1)!=0
    c = @coeff*Decimal.radix
    l = (number_of_digits >> 1) + 1
  else
    c = @coeff
    l = (number_of_digits+1) >> 1
  end
  shift = prec - l
  if shift >= 0
    c = Decimal.int_mult_radix_power(c, (shift<<1))
    exact = true
  else
    c, remainder = c.divmod(Decimal.int_radix_power((-shift)<<1))
    exact = (remainder==0)
  end
  e -= shift

  n = Decimal.int_radix_power(prec)
  while true
    q = c / n
    break if n <= q
    n = ((n + q) >> 1)
  end
  exact = exact && (n*n == c)

  if exact
    if shift >= 0
      n = Decimal.int_div_radix_power(n, shift)
    else
      n = Decimal.int_mult_radix_power(n, -shift)
    end
    e += shift
  else
    return context.exception(Inexact) if context.exact?
    n += 1 if (n%5)==0
  end
  ans = Decimal.new([+1,n,e])
  Decimal.local_context(:rounding=>:half_even) do
    ans = ans._fix(context)
  end
  return ans
end

#subnormal?(context = nil) ⇒ Boolean

Returns whether the number is subnormal

Returns:

  • (Boolean) 


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# File 'lib/decimal/decimal.rb', line 1313

def subnormal?(context=nil)
  return false if special? || zero?
  context = Decimal.define_context(context)
  self.adjusted_exponent < context.emin
end

#subtract(other, context = nil) ⇒ Object

Subtraction



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# File 'lib/decimal/decimal.rb', line 1485

def subtract(other, context=nil)

  context = Decimal.define_context(context)
  other = _convert(other)

  if self.special? || other.special?
    ans = _check_nans(context,other)
    return ans if ans
  end
  return add(other.copy_negate, context)
end

#to_f ⇒ Object

Conversion to Float



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# File 'lib/decimal/decimal.rb', line 2144

def to_f
  if special?
    if @exp==:inf
      @sign/0.0
    else
      0.0/0.0
    end
  else
    # to_rational.to_f
    # to_s.to_f
    @sign*@coeff*(10.0**@exp)
  end
end

#to_i ⇒ Object

Ruby-style to integer conversion.



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# File 'lib/decimal/decimal.rb', line 2062

def to_i
  if special?
    if nan?
      #return Decimal.context.exception(InvalidContext)
      Decimal.context.exception InvalidContext
      return nil
    end
    raise Error, "Cannot convert infinity to Integer"
  end
  if @exp >= 0
    return @sign*Decimal.int_mult_radix_power(@coeff,@exp)
  else
    return @sign*Decimal.int_div_radix_power(@coeff,-@exp)
  end
end

#to_int_scale ⇒ Object

Return the value of the number as an signed integer and a scale.



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# File 'lib/decimal/decimal.rb', line 2344

def to_int_scale
  if special?
    nil
  else
    [@sign*integral_significand, integral_exponent]
  end
end

#to_integral_exact(context = nil) ⇒ Object

Rounds to a nearby integer. May raise Inexact or Rounded.



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# File 'lib/decimal/decimal.rb', line 2483

def to_integral_exact(context=nil)
  context = Decimal.define_context(context)
  if special?
    ans = _check_nans(context)
    return ans if ans
    return Decimal.new(self)
  end
  return Decimal.new(self) if @exp >= 0
  return Decimal.new([@sign, 0, 0]) if zero?
  context.exception Rounded
  ans = _rescale(0, context.rounding)
  context.exception Inexact if ans != self
  return ans
end

#to_integral_value(context = nil) ⇒ Object

Rounds to a nearby integer. Doesn’t raise Inexact or Rounded.



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# File 'lib/decimal/decimal.rb', line 2499

def to_integral_value(context=nil)
  context = Decimal.define_context(context)
  if special?
    ans = _check_nans(context)
    return ans if ans
    return Decimal.new(self)
  end
  return Decimal.new(self) if @exp >= 0
  return _rescale(0, context.rounding)
end

#to_r ⇒ Object

Conversion to Rational. Conversion of special values will raise an exception under Ruby 1.9



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# File 'lib/decimal/decimal.rb', line 2130

def to_r
  if special?
    num = (@exp == :inf) ? @sign : 0
    Rational.respond_to?(:new!) ? Rational.new!(num,0) : Rational(num,0)
  else
    if @exp < 0
      Rational(@sign*@coeff, Decimal.int_radix_power(-@exp))
    else
      Rational(Decimal.int_mult_radix_power(@sign*@coeff,@exp), 1)
    end
  end
end

#to_s(eng = false, context = nil) ⇒ Object

Ruby-style to string conversion.



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# File 'lib/decimal/decimal.rb', line 2079

def to_s(eng=false,context=nil)
  # (context || Decimal.context).to_string(self)
  context = Decimal.define_context(context)
  sgn = sign<0 ? '-' : ''
  if special?
    if @exp==:inf
      "#{sgn}Infinity"
    elsif @exp==:nan
      "#{sgn}NaN#{@coeff}"
    else # exp==:snan
      "#{sgn}sNaN#{@coeff}"
    end
  else
    ds = @coeff.to_s
    n_ds = ds.size
    exp = integral_exponent
    leftdigits = exp + n_ds
    if exp<=0 && leftdigits>-6
      dotplace = leftdigits
    elsif !eng
      dotplace = 1
    elsif @coeff==0
      dotplace = (leftdigits+1)%3 - 1
    else
      dotplace = (leftdigits-1)%3 + 1
    end

    if dotplace <=0
      intpart = '0'
      fracpart = '.' + '0'*(-dotplace) + ds
    elsif dotplace >= n_ds
      intpart = ds + '0'*(dotplace - n_ds)
      fracpart = ''
    else
      intpart = ds[0...dotplace]
      fracpart = '.' + ds[dotplace..-1]
    end

    if leftdigits == dotplace
      e = ''
    else
      e = (context.capitals ? 'E' : 'e') + "%+d"%(leftdigits-dotplace)
    end

    sgn + intpart + fracpart + e

  end
end

#truncate(opt = {}) ⇒ Object

General truncate operation (as for Float) with same options for precision as Decimal#round()



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# File 'lib/decimal/decimal.rb', line 2582

def truncate(opt={})
  opt[:rounding] = :down
  round opt
end

#ulp(context = nil) ⇒ 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/decimal/decimal.rb', line 2160

def ulp(context = nil)
  context = Decimal.define_context(context)

  return context.exception(InvalidOperation, "ulp in exact context") if context.exact?

  if self.nan?
    return Decimal(self)
  elsif self.infinite?
    # The ulp here is context.maximum_finite - context.maximum_finite.next_minus
    return Decimal(+1, 1, context.etop)
  elsif self.zero? || self.adjusted_exponent <= context.emin
    # This is the ulp value for self.abs <= context.minimum_normal*Decimal.context
    # Here we use it for self.abs < context.minimum_normal*Decimal.context;
    #  because of the simple exponent check; the remaining cases are handled below.
    return context.minimum_nonzero
  else
    # The next can compute the ulp value for the values that
    #   self.abs > context.minimum_normal && self.abs <= context.maximum_finite
    # The cases self.abs < context.minimum_normal*Decimal.context have been handled above.

    # assert self.normal? && self.abs>context.minimum_nonzero
    norm = self.normalize
    exp = norm.integral_exponent
    sig = norm.integral_significand

    # Powers of the radix, r**n, are between areas with different ulp values: r**(n-p-1) and r**(n-p)
    # (p is context.precision).
    # This method and the ulp definitions by Muller, Kahan and Harrison assign the smaller ulp value
    # to r**n; the definition by Goldberg assigns it to the larger ulp.
    # The next line selects the smaller ulp for powers of the radix:
    exp -= 1 if sig == Decimal.int_radix_power(context.precision-1)

    return Decimal(+1, 1, exp)
  end
end

#zero? ⇒ Boolean

Returns whether the number is zero

Returns:

  • (Boolean) 


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# File 'lib/decimal/decimal.rb', line 1303

def zero?
  @coeff==0 && !special?
end