class Numeric
Numeric is the class from which all higher-level numeric classes should inherit.
Numeric allows instantiation of heap-allocated objects. Other core numeric classes such asInteger are implemented as immediates, which means that eachInteger is a single immutable object which is always passed by value.
a =11.object_id==a.object_id#=> true
There can only ever be one instance of the integer1, for example. Ruby ensures this by preventing instantiation. If duplication is attempted, the same instance is returned.
Integer.new(1)#=> NoMethodError: undefined method `new' for Integer:Class1.dup#=> 11.object_id==1.dup.object_id#=> true
For this reason, Numeric should be used when defining other numeric classes.
Classes which inherit from Numeric must implementcoerce, which returns a two-memberArray containing an object that has been coerced into an instance of the new class andself (seecoerce).
Inheriting classes should also implement arithmetic operator methods (+,-,* and/) and the<=> operator (seeComparable). These methods may rely oncoerce to ensure interoperability with instances of other numeric classes.
classTally<Numericdefinitialize(string)@string =stringenddefto_s@stringenddefto_i@string.sizeenddefcoerce(other) [self.class.new('|'*other.to_i),self]enddef<=>(other)to_i<=>other.to_ienddef+(other)self.class.new('|'* (to_i+other.to_i))enddef-(other)self.class.new('|'* (to_i-other.to_i))enddef*(other)self.class.new('|'* (to_i*other.to_i))enddef/(other)self.class.new('|'* (to_i/other.to_i))endendtally =Tally.new('||')putstally*2#=> "||||"putstally>1#=> true
What’s Here¶↑
First, what’s elsewhere. Class Numeric:
Inherits fromclass Object.
Includesmodule Comparable.
Here, class Numeric provides methods for:
Querying¶↑
finite?: Returns true unlessselfis infinite or not a number.infinite?: Returns -1,nilor +1, depending on whetherselfis-Infinity<tt>, finite, or <tt>+Infinity.integer?: Returns whetherselfis an integer.negative?: Returns whetherselfis negative.nonzero?: Returns whetherselfis not zero.positive?: Returns whetherselfis positive.real?: Returns whetherselfis a real value.zero?: Returns whetherselfis zero.
Comparing¶↑
<=>: Returns:-1 if
selfis less than the given value.0 if
selfis equal to the given value.1 if
selfis greater than the given value.nilifselfand the given value are not comparable.
eql?: Returns whetherselfand the given value have the same value and type.
Converting¶↑
%(aliased asmodulo): Returns the remainder ofselfdivided by the given value.-@: Returns the value ofself, negated.abs(aliased asmagnitude): Returns the absolute value ofself.abs2: Returns the square ofself.angle(aliased asargandphase): Returns 0 ifselfis positive, Math::PI otherwise.ceil: Returns the smallest number greater than or equal toself, to a given precision.coerce: Returns array[coerced_self, coerced_other]for the given other value.conj(aliased asconjugate): Returns the complex conjugate ofself.denominator: Returns the denominator (always positive) of theRationalrepresentation ofself.div: Returns the value ofselfdivided by the given value and converted to an integer.divmod: Returns array[quotient, modulus]resulting from dividingselfthe given divisor.fdiv: Returns theFloatresult of dividingselfby the given divisor.floor: Returns the largest number less than or equal toself, to a given precision.i: Returns theComplexobjectComplex(0, self). the given value.imaginary(aliased asimag): Returns the imaginary part of theself.numerator: Returns the numerator of theRationalrepresentation ofself; has the same sign asself.polar: Returns the array[self.abs, self.arg].quo: Returns the value ofselfdivided by the given value.real: Returns the real part ofself.rect(aliased asrectangular): Returns the array[self, 0].remainder: Returnsself-arg*(self/arg).truncatefor the givenarg.round: Returns the value ofselfrounded to the nearest value for the given a precision.to_int: Returns theIntegerrepresentation ofself, truncating if necessary.truncate: Returnsselftruncated (toward zero) to a given precision.
Other¶↑
Public Instance Methods
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static VALUEnum_modulo(VALUE x, VALUE y){ VALUE q = num_funcall1(x, id_div, y); return rb_funcall(x, '-', 1, rb_funcall(y, '*', 1, q));}Returnsself moduloother as a real number.
Of the Core and Standard Library classes, onlyRational uses this implementation.
ForRationalr and real numbern, these expressions are equivalent:
r%nr-n*(r/n).floorr.divmod(n)[1]
SeeNumeric#divmod.
Examples:
r =Rational(1,2)# => (1/2)r2 =Rational(2,3)# => (2/3)r%r2# => (1/2)r%2# => (1/2)r%2.0# => 0.5r =Rational(301,100)# => (301/100)r2 =Rational(7,5)# => (7/5)r%r2# => (21/100)r%-r2# => (-119/100)(-r)%r2# => (119/100)(-r)%-r2# => (-21/100)
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static VALUEnum_uminus(VALUE num){ VALUE zero; zero = INT2FIX(0); do_coerce(&zero, &num, TRUE); return num_funcall1(zero, '-', num);}Unary Minus—Returns the receiver, negated.
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static VALUEnum_cmp(VALUE x, VALUE y){ if (x == y) return INT2FIX(0); return Qnil;}Returns zero ifself is the same asother,nil otherwise.
No subclass in the Ruby Core or Standard Library uses this implementation.
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static VALUEnum_abs(VALUE num){ if (rb_num_negative_int_p(num)) { return num_funcall0(num, idUMinus); } return num;}Returns the absolute value ofself.
12.abs#=> 12(-34.56).abs#=> 34.56-34.56.abs#=> 34.56
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static VALUEnumeric_abs2(VALUE self){ return f_mul(self, self);}Returns the square ofself.
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static VALUEnumeric_arg(VALUE self){ if (f_positive_p(self)) return INT2FIX(0); return DBL2NUM(M_PI);}Returns zero ifself is positive, Math::PI otherwise.
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static VALUEnum_ceil(int argc, VALUE *argv, VALUE num){ return flo_ceil(argc, argv, rb_Float(num));}Returns the smallest float or integer that is greater than or equal toself, as specified by the given ‘ndigits`, which must be aninteger-convertible object.
Equivalent toself.to_f.ceil(ndigits).
Related:floor,Float#ceil.
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static VALUEnum_clone(int argc, VALUE *argv, VALUE x){ return rb_immutable_obj_clone(argc, argv, x);}Returnsself.
Raises an exception if the value forfreeze is neithertrue nornil.
Related:Numeric#dup.
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static VALUEnum_coerce(VALUE x, VALUE y){ if (CLASS_OF(x) == CLASS_OF(y)) return rb_assoc_new(y, x); x = rb_Float(x); y = rb_Float(y); return rb_assoc_new(y, x);}Returns a 2-element array containing two numeric elements, formed from the two operandsself andother, of a common compatible type.
Of the Core and Standard Library classes,Integer,Rational, andComplex use this implementation.
Examples:
i =2# => 2i.coerce(3)# => [3, 2]i.coerce(3.0)# => [3.0, 2.0]i.coerce(Rational(1,2))# => [0.5, 2.0]i.coerce(Complex(3,4))# Raises RangeError.r =Rational(5,2)# => (5/2)r.coerce(2)# => [(2/1), (5/2)]r.coerce(2.0)# => [2.0, 2.5]r.coerce(Rational(2,3))# => [(2/3), (5/2)]r.coerce(Complex(3,4))# => [(3+4i), ((5/2)+0i)]c =Complex(2,3)# => (2+3i)c.coerce(2)# => [(2+0i), (2+3i)]c.coerce(2.0)# => [(2.0+0i), (2+3i)]c.coerce(Rational(1,2))# => [((1/2)+0i), (2+3i)]c.coerce(Complex(3,4))# => [(3+4i), (2+3i)]
Raises an exception if any type conversion fails.
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static VALUEnumeric_denominator(VALUE self){ return f_denominator(f_to_r(self));}Returns the denominator (always positive).
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static VALUEnum_div(VALUE x, VALUE y){ if (rb_equal(INT2FIX(0), y)) rb_num_zerodiv(); return rb_funcall(num_funcall1(x, '/', y), rb_intern("floor"), 0);}Returns the quotientself/other as an integer (viafloor), using method/ in the derived class ofself. (Numeric itself does not define method/.)
Of the Core and Standard Library classes, OnlyFloat andRational use this implementation.
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static VALUEnum_divmod(VALUE x, VALUE y){ return rb_assoc_new(num_div(x, y), num_modulo(x, y));}Returns a 2-element array[q, r], where
q = (self/other).floor# Quotientr =self%other# Remainder
Of the Core and Standard Library classes, onlyRational uses this implementation.
Examples:
Rational(11,1).divmod(4)# => [2, (3/1)]Rational(11,1).divmod(-4)# => [-3, (-1/1)]Rational(-11,1).divmod(4)# => [-3, (1/1)]Rational(-11,1).divmod(-4)# => [2, (-3/1)]Rational(12,1).divmod(4)# => [3, (0/1)]Rational(12,1).divmod(-4)# => [-3, (0/1)]Rational(-12,1).divmod(4)# => [-3, (0/1)]Rational(-12,1).divmod(-4)# => [3, (0/1)]Rational(13,1).divmod(4.0)# => [3, 1.0]Rational(13,1).divmod(Rational(4,11))# => [35, (3/11)]
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static VALUEnum_eql(VALUE x, VALUE y){ if (TYPE(x) != TYPE(y)) return Qfalse; if (RB_BIGNUM_TYPE_P(x)) { return rb_big_eql(x, y); } return rb_equal(x, y);}Returnstrue ifself andother are the same type and have equal values.
Of the Core and Standard Library classes, onlyInteger,Rational, andComplex use this implementation.
Examples:
1.eql?(1)# => true1.eql?(1.0)# => false1.eql?(Rational(1,1))# => false1.eql?(Complex(1,0))# => false
Methodeql? is different from== in thateql? requires matching types, while== does not.
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static VALUEnum_fdiv(VALUE x, VALUE y){ return rb_funcall(rb_Float(x), '/', 1, y);}Returns the quotientself/other as a float, using method/ in the derived class ofself. (Numeric itself does not define method/.)
Of the Core and Standard Library classes, onlyBigDecimal uses this implementation.
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# File numeric.rb, line 48deffinite?trueend
Returnstrue ifself is a finite number,false otherwise.
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static VALUEnum_floor(int argc, VALUE *argv, VALUE num){ return flo_floor(argc, argv, rb_Float(num));}Returns the largest float or integer that is less than or equal toself, as specified by the given ‘ndigits`, which must be aninteger-convertible object.
Equivalent toself.to_f.floor(ndigits).
Related:ceil,Float#floor.
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static VALUEnum_imaginary(VALUE num){ return rb_complex_new(INT2FIX(0), num);}ReturnsComplex(0, self):
2.i# => (0+2i)-2.i# => (0-2i)2.0.i# => (0+2.0i)Rational(1,2).i# => (0+(1/2)*i)Complex(3,4).i# Raises NoMethodError.
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# File numeric.rb, line 58definfinite?nilend
Returnsnil, -1, or 1 depending on whetherself is finite,-Infinity, or+Infinity.
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# File numeric.rb, line 39definteger?falseend
Returnstrue ifself is anInteger.
1.0.integer?# => false1.integer?# => true
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static VALUEnum_negative_p(VALUE num){ return RBOOL(rb_num_negative_int_p(num));}Returnstrue ifself is less than 0,false otherwise.
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static VALUEnum_nonzero_p(VALUE num){ if (RTEST(num_funcall0(num, rb_intern("zero?")))) { return Qnil; } return num;}Returnsself ifself is not a zero value,nil otherwise; uses methodzero? for the evaluation.
The returnedself allows the method to be chained:
a =%w[z Bb bB bb BB a aA Aa AA A]a.sort {|a,b| (a.downcase<=>b.downcase).nonzero?||a<=>b }# => ["A", "a", "AA", "Aa", "aA", "BB", "Bb", "bB", "bb", "z"]
Of the Core and Standard Library classes,Integer,Float,Rational, andComplex use this implementation.
Related:zero?
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static VALUEnumeric_numerator(VALUE self){ return f_numerator(f_to_r(self));}Returns the numerator.
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static VALUEnumeric_polar(VALUE self){ VALUE abs, arg; if (RB_INTEGER_TYPE_P(self)) { abs = rb_int_abs(self); arg = numeric_arg(self); } else if (RB_FLOAT_TYPE_P(self)) { abs = rb_float_abs(self); arg = float_arg(self); } else if (RB_TYPE_P(self, T_RATIONAL)) { abs = rb_rational_abs(self); arg = numeric_arg(self); } else { abs = f_abs(self); arg = f_arg(self); } return rb_assoc_new(abs, arg);}Returns array[self.abs, self.arg].
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static VALUEnum_positive_p(VALUE num){ const ID mid = '>'; if (FIXNUM_P(num)) { if (method_basic_p(rb_cInteger)) return RBOOL((SIGNED_VALUE)num > (SIGNED_VALUE)INT2FIX(0)); } else if (RB_BIGNUM_TYPE_P(num)) { if (method_basic_p(rb_cInteger)) return RBOOL(BIGNUM_POSITIVE_P(num) && !rb_bigzero_p(num)); } return rb_num_compare_with_zero(num, mid);}Returnstrue ifself is greater than 0,false otherwise.
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VALUErb_numeric_quo(VALUE x, VALUE y){ if (RB_TYPE_P(x, T_COMPLEX)) { return rb_complex_div(x, y); } if (RB_FLOAT_TYPE_P(y)) { return rb_funcallv(x, idFdiv, 1, &y); } x = rb_convert_type(x, T_RATIONAL, "Rational", "to_r"); return rb_rational_div(x, y);}Returns the most exact division (rational for integers, float for floats).
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# File numeric.rb, line 18defreal?trueend
Returnstrue ifself is a real number (i.e. notComplex).
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static VALUEnum_remainder(VALUE x, VALUE y){ if (!rb_obj_is_kind_of(y, rb_cNumeric)) { do_coerce(&x, &y, TRUE); } VALUE z = num_funcall1(x, '%', y); if ((!rb_equal(z, INT2FIX(0))) && ((rb_num_negative_int_p(x) && rb_num_positive_int_p(y)) || (rb_num_positive_int_p(x) && rb_num_negative_int_p(y)))) { if (RB_FLOAT_TYPE_P(y)) { if (isinf(RFLOAT_VALUE(y))) { return x; } } return rb_funcall(z, '-', 1, y); } return z;}Returns the remainder after dividingself byother.
Of the Core and Standard Library classes, onlyFloat andRational use this implementation.
Examples:
11.0.remainder(4)# => 3.011.0.remainder(-4)# => 3.0-11.0.remainder(4)# => -3.0-11.0.remainder(-4)# => -3.012.0.remainder(4)# => 0.012.0.remainder(-4)# => 0.0-12.0.remainder(4)# => -0.0-12.0.remainder(-4)# => -0.013.0.remainder(4.0)# => 1.013.0.remainder(Rational(4,1))# => 1.0Rational(13,1).remainder(4)# => (1/1)Rational(13,1).remainder(-4)# => (1/1)Rational(-13,1).remainder(4)# => (-1/1)Rational(-13,1).remainder(-4)# => (-1/1)
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static VALUEnum_round(int argc, VALUE* argv, VALUE num){ return flo_round(argc, argv, rb_Float(num));}Returnsself rounded to the nearest value with a precision ofdigits decimal digits.
Numeric implements this by convertingself to aFloat and invokingFloat#round.
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static VALUEnum_step(int argc, VALUE *argv, VALUE from){ VALUE to, step; int desc, inf; if (!rb_block_given_p()) { VALUE by = Qundef; num_step_extract_args(argc, argv, &to, &step, &by); if (!UNDEF_P(by)) { step = by; } if (NIL_P(step)) { step = INT2FIX(1); } else if (rb_equal(step, INT2FIX(0))) { rb_raise(rb_eArgError, "step can't be 0"); } if ((NIL_P(to) || rb_obj_is_kind_of(to, rb_cNumeric)) && rb_obj_is_kind_of(step, rb_cNumeric)) { return rb_arith_seq_new(from, ID2SYM(rb_frame_this_func()), argc, argv, num_step_size, from, to, step, FALSE); } return SIZED_ENUMERATOR_KW(from, 2, ((VALUE [2]){to, step}), num_step_size, FALSE); } desc = num_step_scan_args(argc, argv, &to, &step, TRUE, FALSE); if (rb_equal(step, INT2FIX(0))) { inf = 1; } else if (RB_FLOAT_TYPE_P(to)) { double f = RFLOAT_VALUE(to); inf = isinf(f) && (signbit(f) ? desc : !desc); } else inf = 0; if (FIXNUM_P(from) && (inf || FIXNUM_P(to)) && FIXNUM_P(step)) { long i = FIX2LONG(from); long diff = FIX2LONG(step); if (inf) { for (;; i += diff) rb_yield(LONG2FIX(i)); } else { long end = FIX2LONG(to); if (desc) { for (; i >= end; i += diff) rb_yield(LONG2FIX(i)); } else { for (; i <= end; i += diff) rb_yield(LONG2FIX(i)); } } } else if (!ruby_float_step(from, to, step, FALSE, FALSE)) { VALUE i = from; if (inf) { for (;; i = rb_funcall(i, '+', 1, step)) rb_yield(i); } else { ID cmp = desc ? '<' : '>'; for (; !RTEST(rb_funcall(i, cmp, 1, to)); i = rb_funcall(i, '+', 1, step)) rb_yield(i); } } return from;}Generates a sequence of numbers; with a block given, traverses the sequence.
Of the Core and Standard Library classes,Integer,Float, andRational use this implementation.
A quick example:
squares = []1.step(by:2,to:10) {|i|squares.push(i*i) }squares# => [1, 9, 25, 49, 81]
The generated sequence:
Begins with
self.Continues at intervals of
by(which may not be zero).Ends with the last number that is within or equal to
to; that is, less than or equal totoifbyis positive, greater than or equal totoifbyis negative. Iftoisnil, the sequence is of infinite length.
If a block is given, calls the block with each number in the sequence; returnsself. If no block is given, returns anEnumerator::ArithmeticSequence.
Keyword Arguments
With keyword argumentsby andto, their values (or defaults) determine the step and limit:
# Both keywords given.squares = []4.step(by:2,to:10) {|i|squares.push(i*i) }# => 4squares# => [16, 36, 64, 100]cubes = []3.step(by:-1.5,to:-3) {|i|cubes.push(i*i*i) }# => 3cubes# => [27.0, 3.375, 0.0, -3.375, -27.0]squares = []1.2.step(by:0.2,to:2.0) {|f|squares.push(f*f) }squares# => [1.44, 1.9599999999999997, 2.5600000000000005, 3.24, 4.0]squares = []Rational(6/5).step(by:0.2,to:2.0) {|r|squares.push(r*r) }squares# => [1.0, 1.44, 1.9599999999999997, 2.5600000000000005, 3.24, 4.0]# Only keyword to given.squares = []4.step(to:10) {|i|squares.push(i*i) }# => 4squares# => [16, 25, 36, 49, 64, 81, 100]# Only by given.# Only keyword by givensquares = []4.step(by:2) {|i|squares.push(i*i);breakifi>10 }squares# => [16, 36, 64, 100, 144]# No block given.e =3.step(by:-1.5,to:-3)# => (3.step(by: -1.5, to: -3))e.class# => Enumerator::ArithmeticSequence
Positional Arguments
With optional positional argumentsto andby, their values (or defaults) determine the step and limit:
squares = []4.step(10,2) {|i|squares.push(i*i) }# => 4squares# => [16, 36, 64, 100]squares = []4.step(10) {|i|squares.push(i*i) }squares# => [16, 25, 36, 49, 64, 81, 100]squares = []4.step {|i|squares.push(i*i);breakifi>10 }# => nilsquares# => [16, 25, 36, 49, 64, 81, 100, 121]
Implementation Notes
If all the arguments are integers, the loop operates using an integer counter.
If any of the arguments are floating point numbers, all are converted to floats, and the loop is executedfloor(n + n*Float::EPSILON) + 1 times, wheren = (limit - self)/step.
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static VALUEnumeric_to_c(VALUE self){ return rb_complex_new1(self);}Returnsself as aComplex object.
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static VALUEnum_to_int(VALUE num){ return num_funcall0(num, id_to_i);}Returnsself as an integer; converts using methodto_i in the derived class.
Of the Core and Standard Library classes, onlyRational andComplex use this implementation.
Examples:
Rational(1,2).to_int# => 0Rational(2,1).to_int# => 2Complex(2,0).to_int# => 2Complex(2,1).to_int# Raises RangeError (non-zero imaginary part)
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static VALUEnum_truncate(int argc, VALUE *argv, VALUE num){ return flo_truncate(argc, argv, rb_Float(num));}Returnsself truncated (toward zero) to a precision ofdigits decimal digits.
Numeric implements this by convertingself to aFloat and invokingFloat#truncate.