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Showing content from https://docs.ruby-lang.org/en/3.4/RubyVM/../Numeric.html below:

class Numeric - Documentation for Ruby 3.4

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 as Integer are implemented as immediates, which means that each Integer is a single immutable object which is always passed by value.

a = 1
1.object_id == a.object_id   

There can only ever be one instance of the integer 1, for example. Ruby ensures this by preventing instantiation. If duplication is attempted, the same instance is returned.

Integer.new(1)                   
1.dup                            
1.object_id == 1.dup.object_id   

For this reason, Numeric should be used when defining other numeric classes.

Classes which inherit from Numeric must implement coerce, which returns a two-member Array containing an object that has been coerced into an instance of the new class and self (see coerce).

Inheriting classes should also implement arithmetic operator methods (+, -, * and /) and the <=> operator (see Comparable). These methods may rely on coerce to ensure interoperability with instances of other numeric classes.

class Tally < Numeric
  def initialize(string)
    @string = string
  end

  def to_s
    @string
  end

  def to_i
    @string.size
  end

  def coerce(other)
    [self.class.new('|' * other.to_i), self]
  end

  def <=>(other)
    to_i <=> other.to_i
  end

  def +(other)
    self.class.new('|' * (to_i + other.to_i))
  end

  def -(other)
    self.class.new('|' * (to_i - other.to_i))
  end

  def *(other)
    self.class.new('|' * (to_i * other.to_i))
  end

  def /(other)
    self.class.new('|' * (to_i / other.to_i))
  end
end

tally = Tally.new('||')
puts tally * 2            
puts tally > 1            

First, what’s elsewhere. Class Numeric:

• Inherits from class Object.

• Includes module Comparable.

Here, class Numeric provides methods for:

• Querying

• Comparing

• Converting

• Other

• finite?: Returns true unless self is infinite or not a number.

• infinite?: Returns -1, nil or +1, depending on whether self is -Infinity<tt>, finite, or <tt>+Infinity.

• integer?: Returns whether self is an integer.

• negative?: Returns whether self is negative.

• nonzero?: Returns whether self is not zero.

• positive?: Returns whether self is positive.

• real?: Returns whether self is a real value.

• zero?: Returns whether self is zero.

• <=>: Returns:

  • -1 if self is less than the given value.

  • 0 if self is equal to the given value.

  • 1 if self is greater than the given value.

  • nil if self and the given value are not comparable.

• eql?: Returns whether self and the given value have the same value and type.

• % (aliased as modulo): Returns the remainder of self divided by the given value.

• -@: Returns the value of self, negated.

• abs (aliased as magnitude): Returns the absolute value of self.

• abs2: Returns the square of self.

• angle (aliased as arg and phase): Returns 0 if self is positive, Math::PI otherwise.

• ceil: Returns the smallest number greater than or equal to self, to a given precision.

• coerce: Returns array [coerced_self, coerced_other] for the given other value.

• conj (aliased as conjugate): Returns the complex conjugate of self.

• denominator: Returns the denominator (always positive) of the Rational representation of self.

• div: Returns the value of self divided by the given value and converted to an integer.

• divmod: Returns array [quotient, modulus] resulting from dividing self the given divisor.

• fdiv: Returns the Float result of dividing self by the given divisor.

• floor: Returns the largest number less than or equal to self, to a given precision.

• i: Returns the Complex object Complex(0, self). the given value.

• imaginary (aliased as imag): Returns the imaginary part of the self.

• numerator: Returns the numerator of the Rational representation of self; has the same sign as self.

• polar: Returns the array [self.abs, self.arg].

• quo: Returns the value of self divided by the given value.

• real: Returns the real part of self.

• rect (aliased as rectangular): Returns the array [self, 0].

• remainder: Returns self-arg*(self/arg).truncate for the given arg.

• round: Returns the value of self rounded to the nearest value for the given a precision.

• to_c: Returns the Complex representation of self.

• to_int: Returns the Integer representation of self, truncating if necessary.

• truncate: Returns self truncated (toward zero) to a given precision.

• clone: Returns self; does not allow freezing.

• dup (aliased as +@): Returns self.

• step: Invokes the given block with the sequence of specified numbers.

static VALUE
num_modulo(VALUE x, VALUE y)
{
    VALUE q = num_funcall1(x, id_div, y);
    return rb_funcall(x, '-', 1,
                      rb_funcall(y, '*', 1, q));
}

Returns self modulo other as a real number.

Of the Core and Standard Library classes, only Rational uses this implementation.

For Rational r and real number n, these expressions are equivalent:

r % n
r-n*(r/n).floor
r.divmod(n)[1]

See Numeric#divmod.

Examples:

r = Rational(1, 2)    
r2 = Rational(2, 3)   
r % r2                
r % 2                 
r % 2.0               

r = Rational(301,100) 
r2 = Rational(7,5)    
r % r2                
r % -r2               
(-r) % r2             
(-r) %-r2             

static VALUE
num_uminus(VALUE num)
{
    VALUE zero;

    zero = INT2FIX(0);
    do_coerce(&zero, &num, TRUE);

    return num_funcall1(zero, '-', num);
}

Unary Minus—Returns the receiver, negated.

static VALUE
num_cmp(VALUE x, VALUE y)
{
    if (x == y) return INT2FIX(0);
    return Qnil;
}

Returns zero if self is the same as other, nil otherwise.

No subclass in the Ruby Core or Standard Library uses this implementation.

static VALUE
num_abs(VALUE num)
{
    if (rb_num_negative_int_p(num)) {
        return num_funcall0(num, idUMinus);
    }
    return num;
}

Returns the absolute value of self.

12.abs        
(-34.56).abs  
-34.56.abs    

static VALUE
numeric_abs2(VALUE self)
{
    return f_mul(self, self);
}

Returns the square of self.

static VALUE
numeric_arg(VALUE self)
{
    if (f_positive_p(self))
        return INT2FIX(0);
    return DBL2NUM(M_PI);
}

Returns zero if self is positive, Math::PI otherwise.

static VALUE
num_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 to self, as specified by the given ‘ndigits`, which must be an integer-convertible object.

Equivalent to self.to_f.ceil(ndigits).

Related: floor, Float#ceil.

static VALUE
num_clone(int argc, VALUE *argv, VALUE x)
{
    return rb_immutable_obj_clone(argc, argv, x);
}

Returns self.

Raises an exception if the value for freeze is neither true nor nil.

Related: Numeric#dup.

static VALUE
num_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 operands self and other, of a common compatible type.

Of the Core and Standard Library classes, Integer, Rational, and Complex use this implementation.

Examples:

i = 2                    
i.coerce(3)              
i.coerce(3.0)            
i.coerce(Rational(1, 2)) 
i.coerce(Complex(3, 4))  

r = Rational(5, 2)       
r.coerce(2)              
r.coerce(2.0)            
r.coerce(Rational(2, 3)) 
r.coerce(Complex(3, 4))  

c = Complex(2, 3)        
c.coerce(2)              
c.coerce(2.0)            
c.coerce(Rational(1, 2)) 
c.coerce(Complex(3, 4))  

Raises an exception if any type conversion fails.

static VALUE
numeric_denominator(VALUE self)
{
    return f_denominator(f_to_r(self));
}

Returns the denominator (always positive).

static VALUE
num_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 quotient self/other as an integer (via floor), using method / in the derived class of self. (Numeric itself does not define method /.)

Of the Core and Standard Library classes, Only Float and Rational use this implementation.

static VALUE
num_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                  
r = self % other                        

Of the Core and Standard Library classes, only Rational uses this implementation.

Examples:

Rational(11, 1).divmod(4)               
Rational(11, 1).divmod(-4)              
Rational(-11, 1).divmod(4)              
Rational(-11, 1).divmod(-4)             

Rational(12, 1).divmod(4)               
Rational(12, 1).divmod(-4)              
Rational(-12, 1).divmod(4)              
Rational(-12, 1).divmod(-4)             

Rational(13, 1).divmod(4.0)             
Rational(13, 1).divmod(Rational(4, 11)) 

static VALUE
num_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);
}

Returns true if self and other are the same type and have equal values.

Of the Core and Standard Library classes, only Integer, Rational, and Complex use this implementation.

Examples:

1.eql?(1)              
1.eql?(1.0)            
1.eql?(Rational(1, 1)) 
1.eql?(Complex(1, 0))  

Method eql? is different from == in that eql? requires matching types, while == does not.

static VALUE
num_fdiv(VALUE x, VALUE y)
{
    return rb_funcall(rb_Float(x), '/', 1, y);
}

Returns the quotient self/other as a float, using method / in the derived class of self. (Numeric itself does not define method /.)

Of the Core and Standard Library classes, only BigDecimal uses this implementation.

Returns true if self is a finite number, false otherwise.

static VALUE
num_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 to self, as specified by the given ‘ndigits`, which must be an integer-convertible object.

Equivalent to self.to_f.floor(ndigits).

Related: ceil, Float#floor.

static VALUE
num_imaginary(VALUE num)
{
    return rb_complex_new(INT2FIX(0), num);
}

Returns Complex(0, self):

2.i              
-2.i             
2.0.i            
Rational(1, 2).i 
Complex(3, 4).i  

Returns nil, -1, or 1 depending on whether self is finite, -Infinity, or +Infinity.

Returns true if self is an Integer.

1.0.integer? 
1.integer?   

static VALUE
num_negative_p(VALUE num)
{
    return RBOOL(rb_num_negative_int_p(num));
}

Returns true if self is less than 0, false otherwise.

static VALUE
num_nonzero_p(VALUE num)
{
    if (RTEST(num_funcall0(num, rb_intern("zero?")))) {
        return Qnil;
    }
    return num;
}

Returns +self+ if +self+ is not a zero value, +nil+ otherwise;
uses method <tt>zero?</tt> for the evaluation.

The returned +self+ 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, and Complex use this implementation.

Related: zero?

static VALUE
numeric_numerator(VALUE self)
{
    return f_numerator(f_to_r(self));
}

Returns the numerator.

static VALUE
numeric_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].

static VALUE
num_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);
}

Returns true if self is greater than 0, false otherwise.

VALUE
rb_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).

Returns true if self is a real number (i.e. not Complex).

static VALUE
num_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 dividing self by other.

Of the Core and Standard Library classes, only Float and Rational use this implementation.

Examples:

11.0.remainder(4)              
11.0.remainder(-4)             
-11.0.remainder(4)             
-11.0.remainder(-4)            

12.0.remainder(4)              
12.0.remainder(-4)             
-12.0.remainder(4)             
-12.0.remainder(-4)            

13.0.remainder(4.0)            
13.0.remainder(Rational(4, 1)) 

Rational(13, 1).remainder(4)   
Rational(13, 1).remainder(-4)  
Rational(-13, 1).remainder(4)  
Rational(-13, 1).remainder(-4) 

static VALUE
num_round(int argc, VALUE* argv, VALUE num)
{
    return flo_round(argc, argv, rb_Float(num));
}

Returns self rounded to the nearest value with a precision of digits decimal digits.

Numeric implements this by converting self to a Float and invoking Float#round.

static VALUE
num_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, and Rational use this implementation.

A quick example:

squares = []
1.step(by: 2, to: 10) {|i| squares.push(i*i) }
squares 

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 to to if by is positive, greater than or equal to to if by is negative. If to is nil, the sequence is of infinite length.

If a block is given, calls the block with each number in the sequence; returns self. If no block is given, returns an Enumerator::ArithmeticSequence.

Keyword Arguments

With keyword arguments by and to, their values (or defaults) determine the step and limit:

squares = []
4.step(by: 2, to: 10) {|i| squares.push(i*i) }    
squares 
cubes = []
3.step(by: -1.5, to: -3) {|i| cubes.push(i*i*i) } 
cubes   
squares = []
1.2.step(by: 0.2, to: 2.0) {|f| squares.push(f*f) }
squares 

squares = []
Rational(6/5).step(by: 0.2, to: 2.0) {|r| squares.push(r*r) }
squares 


squares = []
4.step(to: 10) {|i| squares.push(i*i) }           
squares 



squares = []
4.step(by:2) {|i| squares.push(i*i); break if i > 10 }
squares 


e = 3.step(by: -1.5, to: -3) 
e.class                      

Positional Arguments

With optional positional arguments to and by, their values (or defaults) determine the step and limit:

squares = []
4.step(10, 2) {|i| squares.push(i*i) }    
squares 
squares = []
4.step(10) {|i| squares.push(i*i) }
squares 
squares = []
4.step {|i| squares.push(i*i); break if i > 10 }  
squares 

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 executed floor(n + n*Float::EPSILON) + 1 times, where n = (limit - self)/step.

static VALUE
numeric_to_c(VALUE self)
{
    return rb_complex_new1(self);
}

Returns self as a Complex object.

static VALUE
num_to_int(VALUE num)
{
    return num_funcall0(num, id_to_i);
}

Returns self as an integer; converts using method to_i in the derived class.

Of the Core and Standard Library classes, only Rational and Complex use this implementation.

Examples:

Rational(1, 2).to_int 
Rational(2, 1).to_int 
Complex(2, 0).to_int  
Complex(2, 1).to_int  

static VALUE
num_truncate(int argc, VALUE *argv, VALUE num)
{
    return flo_truncate(argc, argv, rb_Float(num));
}

Returns self truncated (toward zero) to a precision of digits decimal digits.

Numeric implements this by converting self to a Float and invoking Float#truncate.

static VALUE
num_zero_p(VALUE num)
{
    return rb_equal(num, INT2FIX(0));
}

Returns true if zero has a zero value, false otherwise.

Of the Core and Standard Library classes, only Rational and Complex use this implementation.

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