Class: Flt::Num
- Extended by:
- AuxiliarFunctions, Support
- Includes:
- Comparable, AuxiliarFunctions, Support::AuxiliarFunctions
- Defined in:
- lib/flt/num.rb,
lib/flt/complex.rb
Overview
ComplexContext
Defined Under Namespace
Modules: AuxiliarFunctions Classes: Clamped, ContextBase, 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)
Constants included from AuxiliarFunctions
AuxiliarFunctions::EXP_INC, AuxiliarFunctions::LOG10_LB_CORRECTION, AuxiliarFunctions::LOG10_MULT, AuxiliarFunctions::LOG2_LB_CORRECTION, AuxiliarFunctions::LOG2_MULT, AuxiliarFunctions::LOG_PREC_INC, AuxiliarFunctions::LOG_RADIX_EXTRA, AuxiliarFunctions::LOG_RADIX_INC
Constants included from Support::AuxiliarFunctions
Support::AuxiliarFunctions::NBITS_BLOCK, Support::AuxiliarFunctions::NBITS_LIMIT, Support::AuxiliarFunctions::NDIGITS_BLOCK, Support::AuxiliarFunctions::NDIGITS_LIMIT
Class Attribute Summary collapse
-
._base_coercible_types ⇒ Object
readonly
Returns the value of attribute _base_coercible_types.
-
._base_conversions ⇒ Object
readonly
Returns the value of attribute _base_conversions.
Class Method Summary collapse
- .[](*args) ⇒ Object
- .base_coercible_types ⇒ Object
- .base_conversions ⇒ Object
- .ccontext(*args) ⇒ Object
-
.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.
-
.context(*args, &blk) ⇒ Object
The current context (thread-local).
-
.context=(c) ⇒ Object
Change the current context (thread-local).
-
.define_context(*options) ⇒ Object
Define a context by passing either of: * A Context object (of the same type) * A hash of options (or nothing) to alter a copy of the current context.
- .Flags(*values) ⇒ Object
-
.infinity(sign = +1) ⇒ Object
A floating-point infinite number with the specified sign.
- .int_div_radix_power(x, n) ⇒ Object
- .int_mult_radix_power(x, n) ⇒ Object
- .int_radix_power(n) ⇒ Object
-
.local_context(*args) ⇒ Object
Defines a scope with a local context.
- .math(*args, &blk) ⇒ Object
-
.nan ⇒ Object
A floating-point NaN (not a number).
-
.Num(*args) ⇒ Object
Num is the general constructor that can be invoked on specific Flt::Num-derived classes.
- .num_class ⇒ Object
-
.one_half ⇒ Object
One half: 1/2.
-
.set_context(*args) ⇒ Object
Modify the current context, e.g.
-
.zero(sign = +1) ⇒ Object
A floating-point number with value zero and the specified sign.
Instance Method Summary collapse
-
#%(other, context = nil) ⇒ Object
Modulo of two decimal numbers.
-
#*(other, context = nil) ⇒ Object
Multiplication of two decimal numbers.
-
#**(other, context = nil) ⇒ Object
Power.
-
#+(other, context = nil) ⇒ Object
Addition of two decimal numbers.
-
#+@(context = nil) ⇒ Object
Unary plus operator.
-
#-(other, context = nil) ⇒ Object
Subtraction of two decimal numbers.
-
#-@(context = nil) ⇒ Object
Unary minus operator.
-
#/(other, context = nil) ⇒ Object
Division of two decimal numbers.
- #<(other) ⇒ Object
-
#<=(other) ⇒ Object
For MRI this is unnecesary, but it is needed for Rubinius because of the coercion done in Numeric#< etc.
-
#<=>(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.
- #==(other) ⇒ Object
- #>(other) ⇒ Object
- #>=(other) ⇒ Object
-
#_abs(round = true, context = nil) ⇒ Object
Returns a copy with positive sign.
-
#_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.
-
#_fix(context) ⇒ Object
Round if it is necessary to keep within precision.
-
#_fix_nan(context) ⇒ Object
adjust payload of a NaN to the context.
-
#_neg(context = nil) ⇒ Object
Returns copy with sign inverted.
-
#_pos(context = nil) ⇒ Object
Returns a copy with precision adjusted.
-
#_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.
- #_watched_rescale(exp, context, watch_exp) ⇒ Object
-
#abs(context = nil) ⇒ Object
Absolute value.
-
#add(other, context = nil) ⇒ Object
Addition.
-
#adjusted_exponent ⇒ Object
Exponent of the magnitude of the most significant digit of the operand.
-
#ceil(opt = {}) ⇒ Object
General ceiling operation (as for Float) with same options for precision as Flt::Num#round().
-
#coefficient ⇒ Object
Significand as an integer, unsigned.
-
#coerce(other) ⇒ Object
Used internally to convert numbers to be used in an operation to a suitable numeric type.
-
#compare(other, context = nil) ⇒ Object
Compares like <=> but returns a Num value.
-
#convert_to(type, context = nil) ⇒ Object
Convert to other numerical type.
-
#copy_abs ⇒ Object
Returns a copy of with the sign set to +.
-
#copy_negate ⇒ Object
Returns a copy of with the sign inverted.
-
#copy_sign(other) ⇒ Object
Returns a copy of with the sign of other.
-
#digits ⇒ Object
Digits of the significand as an array of integers.
-
#div(other, context = nil) ⇒ Object
Ruby-style integer division: (x/y).floor.
-
#divide(other, context = nil) ⇒ Object
Division.
-
#divide_int(other, context = nil) ⇒ Object
General Decimal Arithmetic Specification integer division: (x/y).truncate.
-
#divmod(other, context = nil) ⇒ Object
Ruby-style integer division and modulo: (x/y).floor, x - y*(x/y).floor.
-
#divrem(other, context = nil) ⇒ Object
General Decimal Arithmetic Specification integer division and remainder: (x/y).truncate, x - y*(x/y).truncate.
- #eql?(other) ⇒ Boolean
-
#even? ⇒ Boolean
returns true if is an even integer.
-
#exp(context = nil) ⇒ Object
Exponential function.
-
#exponent ⇒ Object
Exponent of the significand as an integer.
-
#finite? ⇒ Boolean
Returns whether the number is finite.
-
#floor(opt = {}) ⇒ Object
General floor operation (as for Float) with same options for precision as Flt::Num#round().
-
#fma(other, third, context = nil) ⇒ Object
Fused multiply-add.
-
#fraction_part ⇒ Object
Fraction part (as a Num).
-
#fractional_exponent ⇒ Object
Exponent as though the significand were a fraction (the decimal point before its first digit).
- #hash ⇒ Object
-
#infinite? ⇒ Boolean
Returns whether the number is infinite.
-
#initialize(*args) ⇒ Num
constructor
A floating point-number value can be defined by: * A String containing a text representation of the number * An Integer * A Rational * For binary floating point: a Float * A Value of a type for which conversion is defined in the context.
- #inspect ⇒ Object
-
#integer_part ⇒ Object
Integer part (as a Num).
-
#integral? ⇒ Boolean
Returns true if the value is an integer.
-
#integral_exponent ⇒ Object
Exponent of the significand as an integer.
-
#integral_significand ⇒ Object
Significand as an integer, unsigned.
-
#ln(context = nil) ⇒ Object
Returns the natural (base e) logarithm.
-
#log(b = nil, context = nil) ⇒ Object
Ruby-style logarithm of arbitrary base, e (natural base) by default.
-
#log10(context = nil) ⇒ Object
Returns the base 10 logarithm.
-
#log2(context = nil) ⇒ Object
Returns the base 2 logarithm.
-
#logb(context = nil) ⇒ Object
Returns the exponent of the magnitude of the most significant digit.
-
#minus(context = nil) ⇒ Object
Unary prefix minus operator.
-
#modulo(other, context = nil) ⇒ Object
Ruby-style modulo: x - y*div(x,y).
-
#multiply(other, context = nil) ⇒ Object
Multiplication.
-
#nan? ⇒ Boolean
Returns whether the number is not actualy one (NaN, not a number).
-
#next_minus(context = nil) ⇒ Object
Largest representable number smaller than itself.
-
#next_plus(context = nil) ⇒ Object
Smallest representable number larger than itself.
-
#next_toward(other, context = nil) ⇒ Object
Returns the number closest to self, in the direction towards other.
-
#nonzero? ⇒ Boolean
Returns whether the number not zero.
-
#normal?(context = nil) ⇒ Boolean
Returns whether the number is normal.
-
#normalize(context = nil) ⇒ Object
Normalizes (changes quantum) so that the coefficient has precision digits, unless it is subnormal.
- #num_class ⇒ Object
-
#number_class(context = nil) ⇒ Object
Classifies a number as one of ‘sNaN’, ‘NaN’, ‘-Infinity’, ‘-Normal’, ‘-Subnormal’, ‘-Zero’, ‘+Zero’, ‘+Subnormal’, ‘+Normal’, ‘+Infinity’.
-
#number_of_digits ⇒ Object
Number of digits in the significand.
-
#odd? ⇒ Boolean
returns true if is an odd integer.
-
#plus(context = nil) ⇒ Object
Unary prefix plus operator.
-
#power(other, modulo = nil, context = nil) ⇒ Object
Raises to the power of x, to modulo if given.
-
#qnan? ⇒ Boolean
Returns whether the number is a quite NaN (non-signaling).
-
#quantize(exp, context = nil, watch_exp = true) ⇒ Object
Quantize so its exponent is the same as that of y.
-
#rationalize(tol = nil) ⇒ Object
Approximate conversion to Rational within given tolerance.
-
#reduce(context = nil) ⇒ Object
Reduces an operand to its simplest form by removing trailing 0s and incrementing the exponent.
-
#reduced_exponent ⇒ Object
Exponent corresponding to the integral significand with all trailing digits removed.
-
#remainder(other, context = nil) ⇒ Object
General Decimal Arithmetic Specification remainder: x - y*divide_int(x,y).
-
#remainder_near(other, context = nil) ⇒ Object
General Decimal Arithmetic Specification remainder-near: x - y*round_half_even(x/y).
-
#rescale(exp, context = nil, watch_exp = true) ⇒ Object
Rescale so that the exponent is exp, either by padding with zeros or by truncating digits.
-
#round(opt = {}) ⇒ Object
General rounding.
-
#same_quantum?(other) ⇒ Boolean
Return true if has the same exponent as other.
-
#scaleb(other, context = nil) ⇒ Object
Adds a value to the exponent.
-
#scientific_exponent ⇒ Object
Synonym for Num#adjusted_exponent().
-
#sign ⇒ Object
Sign of the number: +1 for plus / -1 for minus.
-
#snan? ⇒ Boolean
Returns whether the number is a signaling NaN.
-
#special? ⇒ Boolean
Returns whether the number is a special value (NaN or Infinity).
-
#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.
-
#sqrt(context = nil) ⇒ Object
Square root.
-
#subnormal?(context = nil) ⇒ Boolean
Returns whether the number is subnormal.
-
#subtract(other, context = nil) ⇒ Object
Subtraction.
-
#to_f ⇒ Object
Conversion to Float.
-
#to_i ⇒ Object
Ruby-style to integer conversion.
-
#to_int_scale ⇒ Object
Return the value of the number as an signed integer and a scale.
-
#to_integral_exact(context = nil) ⇒ Object
Rounds to a nearby integer.
-
#to_integral_value(context = nil) ⇒ Object
Rounds to a nearby integer.
-
#to_r ⇒ Object
Conversion to Rational.
-
#to_s(*args) ⇒ Object
Convert to a text literal in the specified base (10 by default).
-
#truncate(opt = {}) ⇒ Object
General truncate operation (as for Float) with same options for precision as Flt::Num#round().
-
#ulp(context = nil, mode = :low) ⇒ Object
ulp (unit in the last place) according to the definition proposed by J.M.
-
#zero? ⇒ Boolean
Returns whether the number is zero.
Methods included from Support
FlagValues, adjust_digits, simplified_round_mode
Methods included from AuxiliarFunctions
_convert, _div_nearest, _exp, _iexp, _ilog, _log, _log_radix_digits, _log_radix_lb, _log_radix_mult, _normalize, _number_of_digits, _parser, _power, _rshift_nearest, _sqrt_nearest, log10_lb, log2_lb
Methods included from Support::AuxiliarFunctions
_nbits, _ndigits, detect_float_rounding
Constructor Details
#initialize(*args) ⇒ Num
A floating point-number value can be defined by:
-
A String containing a text representation of the number
-
An Integer
-
A Rational
-
For binary floating point: a Float
-
A Value of a type for which conversion is defined in the context.
-
Another floating-point value of the same type.
-
A sign, coefficient and exponent (either as separate arguments, as an array or as a Hash with symbolic keys), or a signed coefficient and an exponent. This is the internal representation of Num, as returned by Num#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 after the value-definint argument to override the current context and options can be passed in a last hash argument; alternatively context options can be overriden by options of the hash argument.
When the number is defined by a numeric literal (a String), it can be followed by a symbol that specifies the mode used to convert the literal to a floating-point value:
-
:free is currently the default for all cases. The precision of the input literal (including trailing zeros) is preserved and the precision of the context is ignored. When the literal is in the same base as the floating-point radix, (which, by default, is the case for DecNum only), the literal is preserved exactly in floating-point. Otherwise, all significative digits that can be derived from the literal are generanted, significative meaning here that if the digit is changed and the value converted back to a literal of the same base and precision, the original literal will not be obtained.
-
:short is a variation of :free in which only the minimun number of digits that are necessary to produce the original literal when the value is converted back with the same original precision; namely, given an input in base b1, its :short representation in base 2 is the shortest number in base b2 such that when converted back to base b2 with the same precision that the input had, the result is identical to the input:
short = Num[b2].new(input, :short, base: b1) Num[b1].context.precision = precision_of_inpu Num[b1].new(short.to_s(base: b2), :fixed, base: b2)) == Num[b1].new(input, :free, base: b1)
-
:fixed will round and normalize the value to the precision specified by the context (normalize meaning that exaclty the number of digits specified by the precision will be generated, even if the original literal has fewer digits.) This may fail returning NaN (and raising Inexact) if the context precision is :exact, but not if the floating-point radix is a multiple of the input base.
Options that can be passed for construction from literal:
-
:base is the numeric base of the input, 10 by default.
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# File 'lib/flt/num.rb', line 1472 def initialize(*args) = args.pop if args.last.is_a?(Hash) context = args.pop if args.size>0 && (args.last.kind_of?(ContextBase) || args.last.nil?) context ||= && .delete(:context) mode = args.pop if args.last.is_a?(Symbol) && ![:inf, :nan, :snan].include?(args.last) args = args.first if args.size==1 && args.first.is_a?(Array) if args.empty? && args = [.delete(:sign)||+1, .delete(:coefficient) || 0, .delete(:exponent) || 0] end mode ||= && .delete(:mode) base = ( && .delete(:base)) context = if context.nil? && && !.empty? context = 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 num_class @sign, @coeff, @exp = arg.split when *context.coercible_types v = context._coerce(arg) @sign, @coeff, @exp = v.is_a?(Num) ? 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, :base => base) if m.nil? @sign,@coeff,@exp = context.exception(ConversionSyntax, "Invalid literal for DecNum: #{arg.inspect}").split return end @sign = (m.sign == '-') ? -1 : +1 if m.int || m.onlyfrac sign = @sign if m.int intpart = m.int fracpart = m.frac else intpart = '' fracpart = m.onlyfrac end fracpart ||= '' base = m.base exp = m.exp.to_i coeff = (intpart+fracpart).to_i(base) if m.exp_base && m.exp_base != base # The exponent uses a different base; # compute exponent in base; assume base = exp_base**k k = Math.log(base, m.exp_base).round exp -= fracpart.size*k base = m.exp_base else exp -= fracpart.size end if false # Old behaviour: use :fixed format when num_class.radix != base # Advantages: # * Behaviour similar to Float: BinFloat(txt) == Float(txt) mode ||= ((num_class.radix == base) ? :free : :fixed) else # New behaviour: the default is always :free # Advantages: # * Is coherent with construction of DecNum from decimal literal: # preserve precision of the literal with independence of context. mode ||= :free end if mode == :free && base == num_class.radix # simple case, the job is already done # # :free mode with same base must not be handled by the Reader; # note that if we used the Reader for the same base case in :free mode, # an extra 'significative' digit would be added, because that digit # is significative in the sense that (under non-directed rounding, # and with the significance interpretation of Reader wit the all-digits option) # it's not free to take any value without affecting the value of # the other digits: e.g. input: '0.1', the result of :free # conversion with the Reader is '0.10' because de last digit is not free; # if it was 9 for example the actual value would round to '0.2' with the input # precision given here. # # On the other hand, :short, should be handled by the Reader even when # the input and output bases are the same because we want to find the shortest # number that can be converted back to the input with the same input precision. else rounding = context.rounding reader = Support::Reader.new(:mode=>mode) ans = reader.read(context, rounding, sign, coeff, exp, base) context.exception(Inexact,"Inexact decimal to radix #{num_class.radix} conversion") if !reader.exact? if !reader.exact? && context.exact? sign, coeff, exp = num_class.nan.split else sign, coeff, exp = ans.split end end @sign, @coeff, @exp = sign, coeff, exp 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 >= context.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/flt/num.rb', line 174 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/flt/num.rb', line 175 def _base_conversions @_base_conversions end |
Class Method Details
.[](*args) ⇒ Object
Num can be use to obtain a floating-point numeric class with radix base, so that, for example, Num is equivalent to BinNum and Num to DecNum.
If the base does not correspond to one of the predefined classes (DecNum, BinNum), a new class is dynamically generated.
The [] operator can also be applied to classes derived from Num to act as a constructor (short hand for .new):
Flt::Num[10]['0.1'] # same as FLt::DecNum['0.1'] or Flt.DecNum('0.1') or Flt::DecNum.new('0.1')
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# File 'lib/flt/num.rb', line 4609 def [](*args) return self.Num(*args) if self!=Num # && self.ancestors.include?(Num) raise RuntimeError, "Invalid number of arguments (#{args.size}) for Num.[]; 1 expected." unless args.size==1 base = args.first case base when 10 DecNum when 2 BinNum else class_name = "Base#{base}Num" unless Flt.const_defined?(class_name) cls = Flt.const_set class_name, Class.new(Num) { def initialize(*args) super(*args) end } = class <<cls;self;end .send :define_method, :radix do base end cls.const_set :Context, Class.new(Num::ContextBase) cls::Context.send :define_method, :initialize do |*| super(cls, *) end default_digits = 10 default_elimit = 100 cls.const_set :DefaultContext, cls::Context.new( :exact=>false, :precision=>default_digits, :rounding=>:half_even, :elimit=>default_elimit, :flags=>[], :traps=>[DivisionByZero, Overflow, InvalidOperation], :ignored_flags=>[], :capitals=>true, :clamp=>true, :angle=>:rad ) end Flt.const_get class_name end end |
.base_coercible_types ⇒ Object
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# File 'lib/flt/num.rb', line 176 def base_coercible_types Num._base_coercible_types end |
.base_conversions ⇒ Object
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# File 'lib/flt/num.rb', line 179 def base_conversions Num._base_conversions end |
.ccontext(*args) ⇒ Object
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# File 'lib/flt/complex.rb', line 274 def self.ccontext(*args) ComplexContext(self.context(*args)) 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.
Note that this method should be called on concrete floating point types such as Flt::DecNum and Flt::BinNum, and not in the abstract base class Flt::Num.
See Flt::Num::ContextBase#new() for the valid options
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# File 'lib/flt/num.rb', line 1265 def self.Context(*args) case args.size when 0 base = self::DefaultContext when 1 arg = args.first if arg.instance_of?(self::Context) base = arg = nil elsif arg.instance_of?(Hash) base = self::DefaultContext = arg else raise TypeError,"invalid argument for #{num_class}.Context" end when 2 base = args.first = args.last else raise ArgumentError,"wrong number of arguments (#{args.size} for 0, 1 or 2)" end if .nil? || .empty? base else self::Context.new(base, ) end end |
.context(*args, &blk) ⇒ Object
The current context (thread-local). If arguments are passed they are interpreted as in Num.define_context() and an altered copy of the current context is returned. If a block is given, this method is a synonym for Num.local_context().
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# File 'lib/flt/num.rb', line 1319 def self.context(*args, &blk) if blk # setup a local context local_context(*args, &blk) elsif args.empty? # return the current context ctxt = self._context self._context = ctxt = self::DefaultContext.dup if ctxt.nil? ctxt else # Return a modified copy of the current context if args.first.kind_of?(ContextBase) self.define_context(*args) else self.define_context(self.context, *args) end end end |
.context=(c) ⇒ Object
Change the current context (thread-local).
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# File 'lib/flt/num.rb', line 1339 def self.context=(c) self._context = c.dup end |
.define_context(*options) ⇒ Object
Define a context by passing either of:
-
A Context object (of the same type)
-
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/flt/num.rb', line 1299 def self.define_context(*) context = .shift if .first.instance_of?(self::Context) if context && .empty? context else context ||= self.context self.Context(context, *) end end |
.Flags(*values) ⇒ Object
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# File 'lib/flt/num.rb', line 397 def self.Flags(*values) Flt::Support::Flags(EXCEPTIONS,*values) end |
.infinity(sign = +1) ⇒ Object
A floating-point infinite number with the specified sign
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# File 'lib/flt/num.rb', line 1399 def infinity(sign=+1) new [sign, 0, :inf] end |
.int_div_radix_power(x, n) ⇒ Object
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# File 'lib/flt/num.rb', line 1421 def int_div_radix_power(x,n) n < 0 ? (x * self.radix**(-n) ) : (x / self.radix**n) end |
.int_mult_radix_power(x, n) ⇒ Object
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# File 'lib/flt/num.rb', line 1417 def int_mult_radix_power(x,n) n < 0 ? (x / self.radix**(-n)) : (x * self.radix**n) end |
.int_radix_power(n) ⇒ Object
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# File 'lib/flt/num.rb', line 1413 def int_radix_power(n) self.radix**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/flt/num.rb', line 1352 def self.local_context(*args) begin keep = self.context # use this so _context is initialized if necessary self.context = define_context(*args) # this dups the assigned context result = yield _context ensure # TODO: consider the convenience of copying the flags from DecNum.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 = DecNum.context.flags # Another alternative to consider: logically or the flags: # keep.flags ||= DecNum.context.flags # (this requires implementing || in Flags) self._context = keep result end end |
.math(*args, &blk) ⇒ Object
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# File 'lib/flt/num.rb', line 1425 def math(*args, &blk) self.context.math(*args, &blk) end |
.nan ⇒ Object
A floating-point NaN (not a number)
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# File 'lib/flt/num.rb', line 1404 def nan() new [+1, nil, :nan] end |
.Num(*args) ⇒ Object
Num is the general constructor that can be invoked on specific Flt::Num-derived classes.
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# File 'lib/flt/num.rb', line 1626 def Num(*args) if args.size==1 && args.first.instance_of?(self) args.first else new(*args) end end |
.num_class ⇒ Object
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# File 'lib/flt/num.rb', line 1387 def num_class self end |
.one_half ⇒ Object
One half: 1/2
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# File 'lib/flt/num.rb', line 1409 def one_half new '0.5' end |
.set_context(*args) ⇒ Object
Modify the current context, e.g. DecNum.set_context(:precision=>10)
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# File 'lib/flt/num.rb', line 1344 def self.set_context(*args) self.context = define_context(*args) end |
.zero(sign = +1) ⇒ Object
A floating-point number with value zero and the specified sign
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# File 'lib/flt/num.rb', line 1394 def zero(sign=+1) new [sign, 0, 0] end |
Instance Method Details
#%(other, context = nil) ⇒ Object
Modulo of two decimal numbers
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# File 'lib/flt/num.rb', line 1779 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/flt/num.rb', line 1769 def *(other, context=nil) _bin_op :*, :multiply, other, context end |
#**(other, context = nil) ⇒ Object
Power
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# File 'lib/flt/num.rb', line 1784 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/flt/num.rb', line 1759 def +(other, context=nil) _bin_op :+, :add, other, context end |
#+@(context = nil) ⇒ Object
Unary plus operator
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# File 'lib/flt/num.rb', line 1753 def +@(context=nil) #(context || num_class.context).plus(self) _pos(context) end |
#-(other, context = nil) ⇒ Object
Subtraction of two decimal numbers
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# File 'lib/flt/num.rb', line 1764 def -(other, context=nil) _bin_op :-, :subtract, other, context end |
#-@(context = nil) ⇒ Object
Unary minus operator
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# File 'lib/flt/num.rb', line 1747 def -@(context=nil) #(context || num_class.context).minus(self) _neg(context) end |
#/(other, context = nil) ⇒ Object
Division of two decimal numbers
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# File 'lib/flt/num.rb', line 1774 def /(other, context=nil) _bin_op :/, :divide, other, context end |
#<(other) ⇒ Object
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# File 'lib/flt/num.rb', line 2811 def <(other) (self<=>other) < 0 end |
#<=(other) ⇒ Object
For MRI this is unnecesary, but it is needed for Rubinius because of the coercion done in Numeric#< etc.
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# File 'lib/flt/num.rb', line 2808 def <=(other) (self<=>other) <= 0 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/flt/num.rb', line 2750 def <=>(other) case other when *num_class.context.coercible_types_or_num other = Num(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 *= num_class.int_radix_power(d) else other_padded *= num_class.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/flt/num.rb', line 2803 def ==(other) (self<=>other) == 0 end |
#>(other) ⇒ Object
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# File 'lib/flt/num.rb', line 2817 def >(other) (self<=>other) > 0 end |
#>=(other) ⇒ Object
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# File 'lib/flt/num.rb', line 2814 def >=(other) (self<=>other) >= 0 end |
#_abs(round = true, context = nil) ⇒ Object
Returns a copy with positive sign
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# File 'lib/flt/num.rb', line 3557 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/flt/num.rb', line 3453 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 = 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/flt/num.rb', line 3573 def _fix(context) return self if context.exact? if special? if nan? return _fix_nan(context) else return Num(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 Num(sign,0,new_exp) else return Num(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 = Num(sign,1,exp_min-1) dg = number_of_digits # dig = 0 else d = Num(self) end changed = d._round(context.rounding, dg) coeff = num_class.int_div_radix_power(d.coefficient, dg) coeff += 1 if changed==1 ans = Num(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 = Num(ans.sign, num_class.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 = num_class.int_mult_radix_power(@coeff, @exp-etop) return Num(sign,self_padded,etop) end return Num(self) end |
#_fix_nan(context) ⇒ Object
adjust payload of a NaN to the context
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# File 'lib/flt/num.rb', line 3656 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 num_class.Num([@sign, payload, @exp]) end end Num(self) end |
#_neg(context = nil) ⇒ Object
Returns copy with sign inverted
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# File 'lib/flt/num.rb', line 3527 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 = define_context(context) ans._fix(context) end |
#_pos(context = nil) ⇒ Object
Returns a copy with precision adjusted
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# File 'lib/flt/num.rb', line 3542 def _pos(context=nil) if special? ans = _check_nans(context) return ans if ans end if zero? ans = copy_abs else ans = Num(self) end context = 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/flt/num.rb', line 3476 def _rescale(exp, rounding) return Num(self) if special? return Num(sign, 0, exp) if zero? return Num(sign, @coeff*num_class.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 = Num(sign, 1, exp-1) nd = number_of_digits else slf = num_class.new(self) end changed = slf._round(rounding, nd) coeff = num_class.int_div_radix_power(@coeff, nd) coeff += 1 if changed==1 Num(slf.sign, coeff, exp) end |
#_watched_rescale(exp, context, watch_exp) ⇒ Object
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# File 'lib/flt/num.rb', line 3497 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 Num(@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/flt/num.rb', line 2024 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/flt/num.rb', line 1789 def add(other, context=nil) context = 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 Num(self) end return Num(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 = Num([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 = Num(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 Num(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/flt/num.rb', line 2847 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 Flt::Num#round()
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# File 'lib/flt/num.rb', line 3143 def ceil(opt={}) opt[:rounding] = :ceiling round opt end |
#coefficient ⇒ Object
Significand as an integer, unsigned
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# File 'lib/flt/num.rb', line 2893 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/flt/num.rb', line 1722 def coerce(other) case other when *num_class.context.coercible_types_or_num [Num(other),self] when Float [other, self.to_f] else super end end |
#compare(other, context = nil) ⇒ Object
Compares like <=> but returns a Num value.
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# File 'lib/flt/num.rb', line 2833 def compare(other, context=nil) other = _convert(other) if self.special? || other.special? ans = _check_nans(context, other) return ans if ans end return Num(self <=> other) end |
#convert_to(type, context = nil) ⇒ Object
Convert to other numerical type.
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# File 'lib/flt/num.rb', line 2635 def convert_to(type, context=nil) context = 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/flt/num.rb', line 2927 def copy_abs Num(+1,@coeff,@exp) end |
#copy_negate ⇒ Object
Returns a copy of with the sign inverted
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# File 'lib/flt/num.rb', line 2932 def copy_negate Num(-@sign,@coeff,@exp) end |
#copy_sign(other) ⇒ Object
Returns a copy of with the sign of other
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# File 'lib/flt/num.rb', line 2937 def copy_sign(other) sign = other.respond_to?(:sign) ? other.sign : ((other < 0) ? -1 : +1) Num(sign, @coeff, @exp) end |
#digits ⇒ Object
Digits of the significand as an array of integers
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# File 'lib/flt/num.rb', line 2872 def digits @coeff.to_s(num_class.radix).split('').map{|d| d.to_i} # TODO: optimize in derivided classes end |
#div(other, context = nil) ⇒ Object
Ruby-style integer division: (x/y).floor
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# File 'lib/flt/num.rb', line 2236 def div(other, context=nil) context = 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 num_class.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/flt/num.rb', line 1898 def divide(other, context=nil) context = 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 num_class.infinity(resultsign) end if other.infinite? context.exception(Clamped,"Division by infinity") return num_class.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 shift = other.number_of_digits - self.number_of_digits + prec shift += 1 exp = self.exponent - other.exponent - shift if shift >= 0 coeff, remainder = (self.coefficient*num_class.int_radix_power(shift)).divmod(other.coefficient) else coeff, remainder = self.coefficient.divmod(other.coefficient*num_class.int_radix_power(-shift)) end if remainder != 0 return context.exception(Inexact) if context.exact? # result is not exact; adjust to ensure correct rounding if num_class.radix == 10 # perform 05up rounding so the the final rounding will be correct coeff += 1 if (coeff%5) == 0 else # since we will round to less digits and there is a remainder, we just need # to append some nonzero digit; but we must avoid producing a tie (adding a single # digit whose value is radix/2), so we append two digits, 01, that will be rounded away coeff = num_class.int_mult_radix_power(coeff, 2) + 1 exp -= 2 end else # result is exact; get as close to idaal exponent as possible ideal_exp = self.exponent - other.exponent while (exp < ideal_exp) && ((coeff % num_class.radix)==0) coeff /= num_class.radix exp += 1 end end end return Num(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/flt/num.rb', line 2211 def divide_int(other, context=nil) context = 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 num_class.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/flt/num.rb', line 2177 def divmod(other, context=nil) context = 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 [num_class.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/flt/num.rb', line 2144 def divrem(other, context=nil) context = 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 [num_class.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
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# File 'lib/flt/num.rb', line 2827 def eql?(other) return false unless other.is_a?(num_class) reduce.split == other.reduce.split end |
#even? ⇒ Boolean
returns true if is an even integer
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# File 'lib/flt/num.rb', line 2961 def even? # integral? && ((to_i%2)==0) if finite? if @exp>0 || @coeff==0 true else if @exp <= -number_of_digits false else m = num_class.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/flt/num.rb', line 2480 def exp(context=nil) context = num_class.define_context(context) # exp(NaN) = NaN ans = _check_nans(context) return ans if ans # exp(-Infinity) = 0 return num_class.zero if self.infinite? && (self.sign == -1) # exp(0) = 1 return Num(1) if self.zero? # exp(Infinity) = Infinity return Num(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 if self.sign == +1 and adj > _number_of_digits((context.emax+1)*3) # overflow ans = Num(+1, 1, context.emax+1) elsif self.sign == -1 and adj > _number_of_digits((-context.etiny+1)*3) # underflow to 0 ans = Num(+1, 1, context.etiny-1) elsif self.sign == +1 and adj < -p # p+1 digits; final round will raise correct flags ans = Num(+1, num_clas.int_radix_power(p)+1, -p) elsif self.sign == -1 and adj < -p-1 # p+1 digits; final round will raise correct flags ans = Num(+1, num_clas.int_radix_power(p+1)-1, -p-1) else # general case x_sign = self.sign x = self.copy_sign(+1) i, lasts, s, fact, num = 0, 0, 1, 1, 1 elim = [context.emax, -context.emin, 10000].max xprec = num_class.radix==10 ? 3 : 4 num_class.local_context(context, :extra_precision=>xprec, :rounding=>:half_even, :elimit=>elim) do while s != lasts lasts = s i += 1 fact *= i num *= x s += num / fact end s = num_class.Num(1)/s if x_sign<0 end ans = s end # at this stage, ans should round correctly with *any* # rounding mode, not just with ROUND_HALF_EVEN num_class.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/flt/num.rb', line 2898 def exponent @exp end |
#finite? ⇒ Boolean
Returns whether the number is finite
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# File 'lib/flt/num.rb', line 1670 def finite? !special? end |
#floor(opt = {}) ⇒ Object
General floor operation (as for Float) with same options for precision as Flt::Num#round()
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# File 'lib/flt/num.rb', line 3150 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/flt/num.rb', line 3165 def fma(other, third, context=nil) context =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 = num_class.infinity(self.sign*other.sign) elsif other.infinite? return context.exception(InvalidOperation, '0 * INF in fma') if self.zero? product = num_class.infinity(self.sign*other.sign) end else product = Num(self.sign*other.sign,self.coefficient*other.coefficient, self.exponent+other.exponent) end return product.add(third, context) end |
#fraction_part ⇒ Object
Fraction part (as a Num)
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# File 'lib/flt/num.rb', line 2911 def fraction_part ans = _check_nans return ans if ans self - self.integer_part 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/flt/num.rb', line 2861 def fractional_exponent scientific_exponent + 1 end |
#hash ⇒ Object
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# File 'lib/flt/num.rb', line 2823 def hash ([num_class]+reduce.split).hash # TODO: optimize end |
#infinite? ⇒ Boolean
Returns whether the number is infinite
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# File 'lib/flt/num.rb', line 1665 def infinite? @exp == :inf end |
#inspect ⇒ Object
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# File 'lib/flt/num.rb', line 2739 def inspect class_name = num_class.to_s.split('::').last if $DEBUG "#{class_name}('#{self}') [coeff:#{@coeff.inspect} exp:#{@exp.inspect} s:#{@sign.inspect} radix:#{num_class.radix}]" else "#{class_name}('#{self}')" end end |
#integer_part ⇒ Object
Integer part (as a Num)
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# File 'lib/flt/num.rb', line 2903 def integer_part ans = _check_nans return ans if ans return_as_num = {:places=>0} self.sign < 0 ? self.ceil(return_as_num) : self.floor(return_as_num) end |
#integral? ⇒ Boolean
Returns true if the value is an integer
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# File 'lib/flt/num.rb', line 2943 def integral? if finite? if @exp>=0 || @coeff==0 true else if @exp <= -number_of_digits false else m = num_class.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/flt/num.rb', line 2882 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/flt/num.rb', line 2877 def integral_significand @coeff end |
#ln(context = nil) ⇒ Object
Returns the natural (base e) logarithm
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# File 'lib/flt/num.rb', line 2547 def ln(context=nil) context = num_class.define_context(context) # ln(NaN) = NaN ans = _check_nans(context) return ans if ans # ln(0.0) == -Infinity return num_class.infinity(-1) if self.zero? # ln(Infinity) = Infinity return num_class.infinity if self.infinite? && self.sign == +1 # ln(1.0) == 0.0 return num_class.zero if self == Num(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? elim = [context.emax, -context.emin, 10000].max xprec = num_class.radix==10 ? 3 : 4 num_class.local_context(context, :extra_precision=>xprec, :rounding=>:half_even, :elimit=>elim) do one = num_class.Num(1) x = self if (expo = x.adjusted_exponent)<-1 || expo>=2 x = x.scaleb(-expo) else expo = nil end x = (x-one)/(x+one) x2 = x*x ans = x d = ans i = one last_ans = nil while ans != last_ans last_ans = ans x = x2*x i += 2 d = x/i ans += d end ans *= 2 if expo ans += num_class.Num(num_class.radix).ln*expo end end num_class.context(context, :rounding=>:half_even) do |local_context| ans = ans._fix(local_context) context.flags = local_context.flags end return ans end |
#log(b = nil, context = nil) ⇒ Object
Ruby-style logarithm of arbitrary base, e (natural base) by default
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# File 'lib/flt/num.rb', line 2609 def log(b=nil, context=nil) if b.nil? self.ln(context) elsif b==10 self.log10(context) elsif b==2 self.log2(context) else context = num_class.define_context(context) +num_class.context(:extra_precision=>3){self.ln(context)/num_class[b].ln(context)} end end |
#log10(context = nil) ⇒ Object
Returns the base 10 logarithm
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# File 'lib/flt/num.rb', line 2623 def log10(context=nil) context = num_class.define_context(context) num_class.context(:extra_precision=>3){self.ln/num_class.Num(10).ln} end |
#log2(context = nil) ⇒ Object
Returns the base 2 logarithm
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# File 'lib/flt/num.rb', line 2629 def log2(context=nil) context = num_class.define_context(context) num_class.context(context, :extra_precision=>3){self.ln()/num_class.Num(2).ln} 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/flt/num.rb', line 2448 def logb(context=nil) context = define_context(context) ans = _check_nans(context) return ans if ans return num_class.infinity if infinite? return context.exception(DivisionByZero,'logb(0)',-1) if zero? Num(adjusted_exponent)._fix(context) end |
#minus(context = nil) ⇒ Object
Unary prefix minus operator
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# File 'lib/flt/num.rb', line 2038 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/flt/num.rb', line 2262 def modulo(other, context=nil) context = 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/flt/num.rb', line 1869 def multiply(other, context=nil) context = 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 num_class.infinity(resultsign) end if other.infinite? return context.exception(InvalidOperation,"0 * (+-)INF") if self.zero? return num_class.infinity(resultsign) end end resultexp = self.exponent + other.exponent return Num(resultsign, 0, resultexp)._fix(context) if self.zero? || other.zero? #return Num(resultsign, other.coefficient, resultexp)._fix(context) if self.coefficient==1 #return Num(resultsign, self.coefficient, resultexp)._fix(context) if other.coefficient==1 return Num(resultsign, other.coefficient*self.coefficient, resultexp)._fix(context) end |
#nan? ⇒ Boolean
Returns whether the number is not actualy one (NaN, not a number).
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# File 'lib/flt/num.rb', line 1650 def nan? @exp==:nan || @exp==:snan end |
#next_minus(context = nil) ⇒ Object
Largest representable number smaller than itself
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# File 'lib/flt/num.rb', line 2043 def next_minus(context=nil) context = define_context(context) if special? ans = _check_nans(context) return ans if ans if infinite? return Num(self) if @sign == -1 # @sign == +1 if context.exact? return context.exception(InvalidOperation, 'Exact +INF next minus') else return Num(+1, context.maximum_coefficient, context.etop) end end end return context.exception(InvalidOperation, 'Exact next minus') if context.exact? result = nil num_class.local_context(context) do |local| local.rounding = :floor local.ignore_all_flags result = self._fix(local) if result == self result = self - Num(+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/flt/num.rb', line 2074 def next_plus(context=nil) context = define_context(context) if special? ans = _check_nans(context) return ans if ans if infinite? return Num(self) if @sign == +1 # @sign == -1 if context.exact? return context.exception(InvalidOperation, 'Exact -INF next plus') else return Num(-1, context.maximum_coefficient, context.etop) end end end return context.exception(InvalidOperation, 'Exact next plus') if context.exact? result = nil num_class.local_context(context) do |local| local.rounding = :ceiling local.ignore_all_flags result = self._fix(local) if result == self result = self + Num(+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/flt/num.rb', line 2107 def next_toward(other, context=nil) context = 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
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# File 'lib/flt/num.rb', line 1680 def nonzero? special? || @coeff>0 end |
#normal?(context = nil) ⇒ Boolean
Returns whether the number is normal
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# File 'lib/flt/num.rb', line 1692 def normal?(context=nil) return false if special? || zero? context = define_context(context) (context.emin <= self.adjusted_exponent) && (self.adjusted_exponent <= context.emax) end |
#normalize(context = nil) ⇒ 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 2422 def normalize(context=nil) context = define_context(context) return Num(self) if self.special? || self.zero? || context.exact? sign, coeff, exp = self._fix(context).split if self.subnormal? context.exception Subnormal if exp > context.etiny coeff = num_class.int_mult_radix_power(coeff, exp - context.etiny) exp = context.etiny end else min_normal_coeff = context.minimum_normalized_coefficient while coeff < min_normal_coeff coeff = num_class.int_mult_radix_power(coeff, 1) exp -= 1 end end Num(sign, coeff, exp) end |
#num_class ⇒ Object
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# File 'lib/flt/num.rb', line 1382 def num_class self.class 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/flt/num.rb', line 1701 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 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/flt/num.rb', line 2866 def number_of_digits # digits.size @coeff.is_a?(Integer) ? @coeff.to_s(num_class.radix).size : 0 end |
#odd? ⇒ Boolean
returns true if is an odd integer
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# File 'lib/flt/num.rb', line 2985 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 = num_class.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/flt/num.rb', line 2033 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 may be computed more efficiently. It is always exact.
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# File 'lib/flt/num.rb', line 3269 def power(other, modulo=nil, context=nil) if context.nil? && (modulo.kind_of?(ContextBase) || modulo.is_a?(Hash)) context = modulo modulo = nil end context = num_class.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 Num(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) ? Num(result_sign, 0, 0) : num_class.infinity(result_sign) end # Inf**(+ve or Inf) = Inf; Inf**(-ve or -Inf) = 0 if _self.infinite? return (other.sign == +1) ? num_class.infinity(result_sign) : Num(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 == Num(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 Num(result_sign, num_class.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 Num(result_sign, 0, 0) else return num_class.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 # log_radix(self)*other >= radix**bound and bound >= len(str(Emax)) # then radixs**bound >= radix**len(str(Emax)) >= Emax+1 and hence # self**other >= radix**(Emax+1), so overflow occurs. The test # for underflow is similar. bound = _self._log_radix_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 >= _number_of_digits(context.emax) ans = Num(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 >= _number_of_digits(-etiny) ans = Num(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 # ???? 4 ? ... 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 = Num(-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 = _power(xc, xe, yc, ye, p+extra) break if (coeff % (num_class.int_radix_power(_number_of_digits(coeff)-p)/2)) != 0 # base 2: (coeff % (10**(_number_of_digits(coeff)-p-1))) != 0 extra += 3 end ans = Num(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 = Num(ans.sign, num_class.int_mult_radix_power(ans.coefficient, expdiff), ans.exponent-expdiff) end context.exception Underflow if ans.adjusted_exponent < context.emin end ans = ans % modulo if modulo # 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)
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# File 'lib/flt/num.rb', line 1655 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/flt/num.rb', line 3028 def quantize(exp, context=nil, watch_exp=true) exp = _convert(exp) context = define_context(context) if self.special? || exp.special? ans = _check_nans(context, exp) return ans if ans if exp.infinite? || self.infinite? return Num(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 |
#rationalize(tol = nil) ⇒ Object
Approximate conversion to Rational within given tolerance
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# File 'lib/flt/num.rb', line 2673 def rationalize(tol=nil) tol ||= Flt.Tolerance(Rational(1,2),:ulps) case tol when Integer Rational(*Support::Rationalizer.max_denominator(self, tol, num_class)) else Rational(*Support::Rationalizer[tol].rationalize(self)) end 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/flt/num.rb', line 2373 def reduce(context=nil) context = define_context(context) if special? ans = _check_nans(context) return ans if ans end dup = _fix(context) return dup if dup.infinite? return Num(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 Num(dup.sign, coeff/num_class.int_radix_power(nd-end_d), exp) end |
#reduced_exponent ⇒ Object
Exponent corresponding to the integral significand with all trailing digits removed. Does not use any context; equals the value of self.reduce.exponent (but as an integer rather than a Num) except for special values and when the number is rounded under the context or exceeds its limits.
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# File 'lib/flt/num.rb', line 2399 def reduced_exponent if self.special? || self.zero? 0 else exp = self.exponent dgs = self.digits nd = dgs.size # self.number_of_digits while dgs[nd-1]==0 exp += 1 nd -= 1 end exp end end |
#remainder(other, context = nil) ⇒ Object
General Decimal Arithmetic Specification remainder: x - y*divide_int(x,y)
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# File 'lib/flt/num.rb', line 2285 def remainder(other, context=nil) context = 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/flt/num.rb', line 2309 def remainder_near(other, context=nil) context = 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 Num(self)._fix(context) end ideal_exp = [self.exponent, other.exponent].min if self.zero? return Num(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 = num_class.int_mult_radix_power(self_coeff, de) else other_coeff = num_class.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 >= num_class.int_radix_power(context.precision) && !context.exact? sign = self.sign if r < 0 sign = -sign r = -r end return Num(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/flt/num.rb', line 3011 def rescale(exp, context=nil, watch_exp=true) context = 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 Num(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 Num.
-
: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
:rindex 7 6 5 4 3 2 1 0
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# File 'lib/flt/num.rb', line 3112 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 - num_class.Num(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 = num_class.int_div_radix_power(@coeff, dg) exp = @exp + dg coeff += 1 if changed==1 result = Num(@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.
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# File 'lib/flt/num.rb', line 3049 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/flt/num.rb', line 2458 def scaleb(other, context=nil) context = 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 Num(self) if infinite? return Num(@sign, @coeff, @exp+i)._fix(context) end |
#scientific_exponent ⇒ Object
Synonym for Num#adjusted_exponent()
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# File 'lib/flt/num.rb', line 2856 def scientific_exponent adjusted_exponent end |
#sign ⇒ Object
Sign of the number: +1 for plus / -1 for minus.
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# File 'lib/flt/num.rb', line 2888 def sign @sign end |
#snan? ⇒ Boolean
Returns whether the number is a signaling NaN
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# File 'lib/flt/num.rb', line 1660 def snan? @exp == :snan end |
#special? ⇒ Boolean
Returns whether the number is a special value (NaN or Infinity).
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# File 'lib/flt/num.rb', line 1645 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/flt/num.rb', line 1640 def split [@sign, @coeff, @exp] end |
#sqrt(context = nil) ⇒ Object
Square root
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# File 'lib/flt/num.rb', line 1961 def sqrt(context=nil) context = define_context(context) if special? ans = _check_nans(context) return ans if ans return Num(self) if infinite? && @sign==+1 end return Num(@sign, 0, @exp/2)._fix(context) if zero? return context.exception(InvalidOperation, 'sqrt(-x), x>0') if @sign<0 prec = context.precision + 1 # express the number in radix**2 base e = (@exp >> 1) if (@exp & 1)!=0 c = @coeff*num_class.radix l = (number_of_digits >> 1) + 1 else c = @coeff l = (number_of_digits+1) >> 1 end shift = prec - l if shift >= 0 c = num_class.int_mult_radix_power(c, (shift<<1)) exact = true else c, remainder = c.divmod(num_class.int_radix_power((-shift)<<1)) exact = (remainder==0) end e -= shift n = num_class.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 = num_class.int_div_radix_power(n, shift) else n = num_class.int_mult_radix_power(n, -shift) end e += shift else return context.exception(Inexact) if context.exact? # result is not exact; adjust to ensure correct rounding if num_class.radix == 10 n += 1 if (n%5)==0 else n = num_class.int_mult_radix_power(n, 2) + 1 e -= 2 end end ans = Num(+1,n,e) num_class.local_context(:rounding=>:half_even) do ans = ans._fix(context) end return ans end |
#subnormal?(context = nil) ⇒ Boolean
Returns whether the number is subnormal
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# File 'lib/flt/num.rb', line 1685 def subnormal?(context=nil) return false if special? || zero? context = define_context(context) self.adjusted_exponent < context.emin end |
#subtract(other, context = nil) ⇒ Object
Subtraction
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# File 'lib/flt/num.rb', line 1856 def subtract(other, context=nil) context = 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/flt/num.rb', line 2684 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*(num_class.radix.to_f**@exp)).to_f end end |
#to_i ⇒ Object
Ruby-style to integer conversion.
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# File 'lib/flt/num.rb', line 2641 def to_i if special? if nan? #return context.exception(InvalidContext) num_class.context.exception InvalidContext return nil end raise Error, "Cannot convert infinity to Integer" end if @exp >= 0 return @sign*num_class.int_mult_radix_power(@coeff,@exp) else return @sign*num_class.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/flt/num.rb', line 2918 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/flt/num.rb', line 3058 def to_integral_exact(context=nil) context = define_context(context) if special? ans = _check_nans(context) return ans if ans return Num(self) end return Num(self) if @exp >= 0 return Num(@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/flt/num.rb', line 3074 def to_integral_value(context=nil) context = define_context(context) if special? ans = _check_nans(context) return ans if ans return Num(self) end return Num(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/flt/num.rb', line 2659 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, num_class.int_radix_power(-@exp)) else Rational(num_class.int_mult_radix_power(@sign*@coeff,@exp), 1) end end end |
#to_s(*args) ⇒ Object
Convert to a text literal in the specified base (10 by default).
If the output base is the floating-point radix, the rendered value is the exact value of the number, showing trailing zeros up to the stored precision.
With bases different from the radix, the floating-point number is treated as an approximation with a precision of number_of_digits, representing any value within its rounding range. In that case, this method always renders that aproximated value in other base without introducing additional precision.
The resulting text numeral is such that it has as few digits as possible while preserving the original while if converted back to the same type of floating-point value with the same context precision that the original number had (number_of_digits).
To render the exact value of a Num x in a different base b this can be used
Flt::Num.convert_exact(x, b).to_s(:base=>b)
Or, to represent a BinNum x in decimal:
x.to_decimal_exact(:exact=>true).to_s
Options: :base output base, 10 by default
:rounding is used to override the context rounding, but it’s main use is specify :nearest as the rounding-mode, which means that the text literal will have enough digits to be converted back to self in any round-to_nearest rounding mode. Otherwise only enough digits for conversion in a specific rounding mode are produced.
:all_digits if true all significant digits are shown. A digit is considered as significant here if when used on input, cannot arbitrarily change its value and preserve the parsed value of the floating point number. Using all_digits will show trailing zeros up to the precision of the floating-point, so the output will preserve the input precision. With all_digits and the :down rounding-mod (truncation), the result will be the exact value floating-point value in the output base (if it is conmensurable with the floating-point base).
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# File 'lib/flt/num.rb', line 3224 def to_s(*args) eng=false context=nil # admit legacy arguments eng, context in that order if [true,false].include?(args.first) eng = args.shift end if args.first.is_a?(Num::ContextBase) context = args.shift end # admit also :eng to specify the eng mode if args.first == :eng eng = true args.shift end raise TypeError, "Invalid arguments to #{num_class}#to_s" if args.size>1 || (args.size==1 && !args.first.is_a?(Hash)) # an admit arguments through a final parameters Hash = args.first || {} context = .delete(:context) if .has_key?(:context) eng = .delete(:eng) if .has_key?(:eng) format(context, .merge(:eng=>eng)) end |
#truncate(opt = {}) ⇒ Object
General truncate operation (as for Float) with same options for precision as Flt::Num#round()
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# File 'lib/flt/num.rb', line 3157 def truncate(opt={}) opt[:rounding] = :down round opt end |
#ulp(context = 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 If the mode parameter has the value :high the Golberg ulp is computed instead; which is different on the powers of the radix (which are the borders between areas of different ulp-magnitude)
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# File 'lib/flt/num.rb', line 2703 def ulp(context = nil, mode=:low) context = define_context(context) return context.exception(InvalidOperation, "ulp in exact context") if context.exact? if self.nan? return Num(self) elsif self.infinite? # The ulp here is context.maximum_finite - context.maximum_finite.next_minus return Num(+1, 1, context.etop) elsif self.zero? || self.adjusted_exponent <= context.emin # This is the ulp value for self.abs <= context.minimum_normal*num_class.context # Here we use it for self.abs < context.minimum_normal*num_class.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*num_class.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 (so ulp varies with adjusted_exponent). # The next line selects the smaller ulp for powers of the radix: exp -= 1 if sig == num_class.int_radix_power(context.precision-1) if mode == :low return Num(+1, 1, exp) end end |
#zero? ⇒ Boolean
Returns whether the number is zero
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# File 'lib/flt/num.rb', line 1675 def zero? @coeff==0 && !special? end |