# Class: Numeric

Inherits:
Object
show all
Includes:
Comparable
Defined in:
numeric.c

## Overview

Document-class: FloatDomainError

Raised when attempting to convert special float values (in particular infinite or NaN) to numerical classes which don't support them.

``````Float::INFINITY.to_r
``````

raises the exception:

``````FloatDomainError: Infinity
``````

## Instance Method Summary collapse

• x.modulo(y) means x-y*(x/y).floor.

• Unary Plus---Returns the receiver's value.

• Unary Minus---Returns the receiver's value, negated.

• Returns zero if num equals other, `nil` otherwise.

• Returns the absolute value of num.

• Returns square of self.

• Returns 0 if the value is positive, pi otherwise.

• Returns 0 if the value is positive, pi otherwise.

• Returns the smallest `Integer` greater than or equal to num.

• If aNumeric is the same type as num, returns an array containing aNumeric and num.

• Returns self.

• Returns self.

• Returns the denominator (always positive).

• Uses `/` to perform division, then converts the result to an integer.

• Returns an array containing the quotient and modulus obtained by dividing num by numeric.

• Returns `true` if num and numeric are the same type and have equal values.

• Returns float division.

• Returns the largest integer less than or equal to num.

• Returns the corresponding imaginary number.

• Returns zero.

• Returns zero.

• :nodoc:.

• Returns `true` if num is an `Integer` (including `Fixnum` and `Bignum`).

• Returns the absolute value of num.

• x.modulo(y) means x-y*(x/y).floor.

• Returns `self` if num is not zero, `nil` otherwise.

• Returns the numerator.

• Returns 0 if the value is positive, pi otherwise.

• Returns an array; [num.abs, num.arg].

• Returns most exact division (rational for integers, float for floats).

• Returns self.

• Returns `true` if num is a `Real` (i.e. non `Complex`).

• Returns an array; [num, 0].

• Returns an array; [num, 0].

• x.remainder(y) means x-y*(x/y).truncate.

• Rounds num to a given precision in decimal digits (default 0 digits).

• Trap attempts to add methods to `Numeric` objects.

• Invokes block with the sequence of numbers starting at num, incremented by step (default 1) on each call.

• Returns the value as a complex.

• Invokes the child class's `to_i` method to convert num to an integer.

• Returns num truncated to an integer.

• Returns `true` if num has a zero value.

## Instance Method Details

### #modulo(numeric) ⇒ Object

x.modulo(y) means x-y*(x/y).floor

Equivalent to num.`divmod(`aNumeric`)[1]`.

See `Numeric#divmod`.

 ``` ``` ```# File 'numeric.c' static VALUE num_modulo(VALUE x, VALUE y) { return rb_funcall(x, '-', 1, rb_funcall(y, '*', 1, rb_funcall(x, rb_intern("div"), 1, y))); }```

### #+ ⇒ Numeric

Returns:

 ``` ``` ```# File 'numeric.c' static VALUE num_uplus(VALUE num) { return num; }```

### #- ⇒ Numeric

Unary Minus---Returns the receiver's value, negated.

Returns:

 ``` ``` ```# File 'numeric.c' static VALUE num_uminus(VALUE num) { VALUE zero; zero = INT2FIX(0); do_coerce(&zero, &num, TRUE); return rb_funcall(zero, '-', 1, num); }```

### #<=>(other) ⇒ 0?

Returns zero if num equals other, `nil` otherwise.

Returns:

• (0, nil)
 ``` ``` ```# File 'numeric.c' static VALUE num_cmp(VALUE x, VALUE y) { if (x == y) return INT2FIX(0); return Qnil; }```

### #abs ⇒ Numeric #magnitude ⇒ Numeric

Returns the absolute value of num.

``````12.abs         #=> 12
(-34.56).abs   #=> 34.56
-34.56.abs     #=> 34.56
``````

 ``` ``` ```# File 'numeric.c' static VALUE num_abs(VALUE num) { if (RTEST(rb_funcall(num, '<', 1, INT2FIX(0)))) { return rb_funcall(num, rb_intern("-@"), 0); }```

### #abs2 ⇒ Object

Returns square of self.

 ``` ``` ```# File 'complex.c' static VALUE numeric_abs2(VALUE self) { return f_mul(self, self); }```

### #arg ⇒ 0, Float #angle ⇒ 0, Float #phase ⇒ 0, Float

Returns 0 if the value is positive, pi otherwise.

 ``` ``` ```# File 'complex.c' static VALUE numeric_arg(VALUE self) { if (f_positive_p(self)) return INT2FIX(0); return rb_const_get(rb_mMath, id_PI); }```

### #arg ⇒ 0, Float #angle ⇒ 0, Float #phase ⇒ 0, Float

Returns 0 if the value is positive, pi otherwise.

 ``` ``` ```# File 'complex.c' static VALUE numeric_arg(VALUE self) { if (f_positive_p(self)) return INT2FIX(0); return rb_const_get(rb_mMath, id_PI); }```

### #ceil ⇒ Integer

Returns the smallest `Integer` greater than or equal to num. Class `Numeric` achieves this by converting itself to a `Float` then invoking `Float#ceil`.

``````1.ceil        #=> 1
1.2.ceil      #=> 2
(-1.2).ceil   #=> -1
(-1.0).ceil   #=> -1
``````

Returns:

 ``` ``` ```# File 'numeric.c' static VALUE num_ceil(VALUE num) { return flo_ceil(rb_Float(num)); }```

### #coerce(numeric) ⇒ Array

If aNumeric is the same type as num, returns an array containing aNumeric and num. Otherwise, returns an array with both aNumeric and num represented as `Float` objects. This coercion mechanism is used by Ruby to handle mixed-type numeric operations: it is intended to find a compatible common type between the two operands of the operator.

``````1.coerce(2.5)   #=> [2.5, 1.0]
1.2.coerce(3)   #=> [3.0, 1.2]
1.coerce(2)     #=> [2, 1]
``````

Returns:

 ``` ``` ```# File 'numeric.c' 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); }```

### #conj ⇒ Numeric #conjugate ⇒ Numeric

Returns self.

 ``` ``` ```# File 'complex.c' static VALUE numeric_conj(VALUE self) { return self; }```

### #conj ⇒ Numeric #conjugate ⇒ Numeric

Returns self.

 ``` ``` ```# File 'complex.c' static VALUE numeric_conj(VALUE self) { return self; }```

### #denominator ⇒ Integer

Returns the denominator (always positive).

Returns:

 ``` ``` ```# File 'rational.c' static VALUE numeric_denominator(VALUE self) { return f_denominator(f_to_r(self)); }```

### #div(numeric) ⇒ Integer

Uses `/` to perform division, then converts the result to an integer. `numeric` does not define the `/` operator; this is left to subclasses.

Equivalent to num.`divmod(`aNumeric`)[0]`.

See `Numeric#divmod`.

Returns:

 ``` ``` ```# File 'numeric.c' static VALUE num_div(VALUE x, VALUE y) { if (rb_equal(INT2FIX(0), y)) rb_num_zerodiv(); return rb_funcall(rb_funcall(x, '/', 1, y), rb_intern("floor"), 0); }```

### #divmod(numeric) ⇒ Array

Returns an array containing the quotient and modulus obtained by dividing num by numeric. If `q, r = x.divmod(y)`, then

``````q = floor(x/y)
x = q*y+r
``````

The quotient is rounded toward -infinity, as shown in the following table:

`````` a    |  b  |  a.divmod(b)  |   a/b   | a.modulo(b) | a.remainder(b)
------+-----+---------------+---------+-------------+---------------
13   |  4  |   3,    1     |   3     |    1        |     1
------+-----+---------------+---------+-------------+---------------
13   | -4  |  -4,   -3     |  -4     |   -3        |     1
------+-----+---------------+---------+-------------+---------------
-13   |  4  |  -4,    3     |  -4     |    3        |    -1
------+-----+---------------+---------+-------------+---------------
-13   | -4  |   3,   -1     |   3     |   -1        |    -1
------+-----+---------------+---------+-------------+---------------
11.5 |  4  |   2,    3.5   |   2.875 |    3.5      |     3.5
------+-----+---------------+---------+-------------+---------------
11.5 | -4  |  -3,   -0.5   |  -2.875 |   -0.5      |     3.5
------+-----+---------------+---------+-------------+---------------
-11.5 |  4  |  -3,    0.5   |  -2.875 |    0.5      |    -3.5
------+-----+---------------+---------+-------------+---------------
-11.5 | -4  |   2,   -3.5   |   2.875 |   -3.5      |    -3.5
``````

Examples

``````11.divmod(3)         #=> [3, 2]
11.divmod(-3)        #=> [-4, -1]
11.divmod(3.5)       #=> [3, 0.5]
(-11).divmod(3.5)    #=> [-4, 3.0]
(11.5).divmod(3.5)   #=> [3, 1.0]
``````

Returns:

 ``` ``` ```# File 'numeric.c' static VALUE num_divmod(VALUE x, VALUE y) { return rb_assoc_new(num_div(x, y), num_modulo(x, y)); }```

### #eql?(numeric) ⇒ Boolean

Returns `true` if num and numeric are the same type and have equal values.

``````1 == 1.0          #=> true
1.eql?(1.0)       #=> false
(1.0).eql?(1.0)   #=> true
``````

Returns:

• (Boolean)
 ``` ``` ```# File 'numeric.c' static VALUE num_eql(VALUE x, VALUE y) { if (TYPE(x) != TYPE(y)) return Qfalse; return rb_equal(x, y); }```

### #fdiv(numeric) ⇒ Float

Returns float division.

Returns:

 ``` ``` ```# File 'numeric.c' static VALUE num_fdiv(VALUE x, VALUE y) { return rb_funcall(rb_Float(x), '/', 1, y); }```

### #floor ⇒ Integer

Returns the largest integer less than or equal to num. `Numeric` implements this by converting anInteger to a `Float` and invoking `Float#floor`.

``````1.floor      #=> 1
(-1).floor   #=> -1
``````

Returns:

 ``` ``` ```# File 'numeric.c' static VALUE num_floor(VALUE num) { return flo_floor(rb_Float(num)); }```

### #i ⇒ Complex(0]

Returns the corresponding imaginary number. Not available for complex numbers.

Returns Complex(0].

Returns:

 ``` ``` ```# File 'numeric.c' static VALUE num_imaginary(VALUE num) { return rb_complex_new(INT2FIX(0), num); }```

### #imag ⇒ 0 #imaginary ⇒ 0

Returns zero.

• #imag0

Returns:

• (0)
• #imaginary0

Returns:

• (0)
 ``` ``` ```# File 'complex.c' static VALUE numeric_imag(VALUE self) { return INT2FIX(0); }```

### #imag ⇒ 0 #imaginary ⇒ 0

Returns zero.

• #imag0

Returns:

• (0)
• #imaginary0

Returns:

• (0)
 ``` ``` ```# File 'complex.c' static VALUE numeric_imag(VALUE self) { return INT2FIX(0); }```

### #initialize_copy ⇒ Object

:nodoc:

 ``` ``` ```# File 'numeric.c' static VALUE num_init_copy(VALUE x, VALUE y) { /* Numerics are immutable values, which should not be copied */ rb_raise(rb_eTypeError, "can't copy %s", rb_obj_classname(x)); return Qnil; /* not reached */ }```

### #integer? ⇒ Boolean

Returns `true` if num is an `Integer` (including `Fixnum` and `Bignum`).

Returns:

• (Boolean)
 ``` ``` ```# File 'numeric.c' static VALUE num_int_p(VALUE num) { return Qfalse; }```

### #abs ⇒ Numeric #magnitude ⇒ Numeric

Returns the absolute value of num.

``````12.abs         #=> 12
(-34.56).abs   #=> 34.56
-34.56.abs     #=> 34.56
``````

 ``` ``` ```# File 'numeric.c' static VALUE num_abs(VALUE num) { if (RTEST(rb_funcall(num, '<', 1, INT2FIX(0)))) { return rb_funcall(num, rb_intern("-@"), 0); }```

### #modulo(numeric) ⇒ Object

x.modulo(y) means x-y*(x/y).floor

Equivalent to num.`divmod(`aNumeric`)[1]`.

See `Numeric#divmod`.

 ``` ``` ```# File 'numeric.c' static VALUE num_modulo(VALUE x, VALUE y) { return rb_funcall(x, '-', 1, rb_funcall(y, '*', 1, rb_funcall(x, rb_intern("div"), 1, y))); }```

### #nonzero? ⇒ Numeric?

Returns `self` if num is not zero, `nil` otherwise. This behavior is useful when chaining comparisons:

``````a = %w( z Bb bB bb BB a aA Aa AA A )
b = a.sort {|a,b| (a.downcase <=> b.downcase).nonzero? || a <=> b }
b   #=> ["A", "a", "AA", "Aa", "aA", "BB", "Bb", "bB", "bb", "z"]
``````

Returns:

 ``` ``` ```# File 'numeric.c' static VALUE num_nonzero_p(VALUE num) { if (RTEST(rb_funcall(num, rb_intern("zero?"), 0, 0))) { return Qnil; }```

### #numerator ⇒ Integer

Returns the numerator.

Returns:

 ``` ``` ```# File 'rational.c' static VALUE numeric_numerator(VALUE self) { return f_numerator(f_to_r(self)); }```

### #arg ⇒ 0, Float #angle ⇒ 0, Float #phase ⇒ 0, Float

Returns 0 if the value is positive, pi otherwise.

 ``` ``` ```# File 'complex.c' static VALUE numeric_arg(VALUE self) { if (f_positive_p(self)) return INT2FIX(0); return rb_const_get(rb_mMath, id_PI); }```

### #polar ⇒ Array

Returns an array; [num.abs, num.arg].

Returns:

 ``` ``` ```# File 'complex.c' static VALUE numeric_polar(VALUE self) { return rb_assoc_new(f_abs(self), f_arg(self)); }```

### #quo(numeric) ⇒ Object

Returns most exact division (rational for integers, float for floats).

 ``` ``` ```# File 'numeric.c' static VALUE num_quo(VALUE x, VALUE y) { return rb_funcall(rb_rational_raw1(x), '/', 1, y); }```

### #real ⇒ Numeric

Returns self.

Returns:

 ``` ``` ```# File 'complex.c' static VALUE numeric_real(VALUE self) { return self; }```

### #real? ⇒ Boolean

Returns `true` if num is a `Real` (i.e. non `Complex`).

Returns:

• (Boolean)
 ``` ``` ```# File 'numeric.c' static VALUE num_real_p(VALUE num) { return Qtrue; }```

### #rect ⇒ Array

Returns an array; [num, 0].

Returns:

 ``` ``` ```# File 'complex.c' static VALUE numeric_rect(VALUE self) { return rb_assoc_new(self, INT2FIX(0)); }```

### #rect ⇒ Array

Returns an array; [num, 0].

Returns:

 ``` ``` ```# File 'complex.c' static VALUE numeric_rect(VALUE self) { return rb_assoc_new(self, INT2FIX(0)); }```

### #remainder(numeric) ⇒ Object

x.remainder(y) means x-y*(x/y).truncate

See `Numeric#divmod`.

 ``` ``` ```# File 'numeric.c' static VALUE num_remainder(VALUE x, VALUE y) { VALUE z = rb_funcall(x, '%', 1, y); if ((!rb_equal(z, INT2FIX(0))) && ((RTEST(rb_funcall(x, '<', 1, INT2FIX(0))) && RTEST(rb_funcall(y, '>', 1, INT2FIX(0)))) || (RTEST(rb_funcall(x, '>', 1, INT2FIX(0))) && RTEST(rb_funcall(y, '<', 1, INT2FIX(0)))))) { return rb_funcall(z, '-', 1, y); }```

### #round([ndigits]) ⇒ Integer, Float

Rounds num to a given precision in decimal digits (default 0 digits). Precision may be negative. Returns a floating point number when ndigits is more than zero. `Numeric` implements this by converting itself to a `Float` and invoking `Float#round`.

Returns:

 ``` ``` ```# File 'numeric.c' static VALUE num_round(int argc, VALUE* argv, VALUE num) { return flo_round(argc, argv, rb_Float(num)); }```

Trap attempts to add methods to `Numeric` objects. Always raises a `TypeError`

 ``` ``` ```# File 'numeric.c' static VALUE num_sadded(VALUE x, VALUE name) { ID mid = rb_to_id(name); /* ruby_frame = ruby_frame->prev; */ /* pop frame for "singleton_method_added" */ /* Numerics should be values; singleton_methods should not be added to them */ rb_remove_method_id(rb_singleton_class(x), mid); rb_raise(rb_eTypeError, "can't define singleton method \"%s\" for %s", rb_id2name(mid), rb_obj_classname(x)); return Qnil; /* not reached */ }```

### #step(limit[, step]) {|i| ... } ⇒ Numeric #step(limit[, step]) ⇒ Object

Invokes block with the sequence of numbers starting at num, incremented by step (default 1) on each call. The loop finishes when the value to be passed to the block is greater than limit (if step is positive) or less than limit (if step is negative). 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*epsilon)+ 1 times, where n = (limit - num)/step. Otherwise, the loop starts at num, uses either the `<` or `>` operator to compare the counter against limit, and increments itself using the `+` operator.

If no block is given, an enumerator is returned instead.

``````1.step(10, 2) { |i| print i, " " }
Math::E.step(Math::PI, 0.2) { |f| print f, " " }
``````

produces:

``````1 3 5 7 9
2.71828182845905 2.91828182845905 3.11828182845905
``````

• #step(limit[, step]) {|i| ... } ⇒ Numeric

Yields:

• (i)

Returns:

 ``` ``` ```# File 'numeric.c' static VALUE num_step(int argc, VALUE *argv, VALUE from) { VALUE to, step; RETURN_ENUMERATOR(from, argc, argv); if (argc == 1) { to = argv[0]; step = INT2FIX(1); }```

### #to_c ⇒ Object

Returns the value as a complex.

 ``` ``` ```# File 'complex.c' static VALUE numeric_to_c(VALUE self) { return rb_complex_new1(self); }```

### #to_int ⇒ Integer

Invokes the child class's `to_i` method to convert num to an integer.

Returns:

 ``` ``` ```# File 'numeric.c' static VALUE num_to_int(VALUE num) { return rb_funcall(num, id_to_i, 0, 0); }```

### #truncate ⇒ Integer

Returns num truncated to an integer. `Numeric` implements this by converting its value to a float and invoking `Float#truncate`.

Returns:

 ``` ``` ```# File 'numeric.c' static VALUE num_truncate(VALUE num) { return flo_truncate(rb_Float(num)); }```

### #zero? ⇒ Boolean

Returns `true` if num has a zero value.

Returns:

• (Boolean)
 ``` ``` ```# File 'numeric.c' static VALUE num_zero_p(VALUE num) { if (rb_equal(num, INT2FIX(0))) { return Qtrue; }```