# 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

### - (Object) modulo(numeric)

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

Equivalent to num.divmod(aNumeric).

See `Numeric#divmod`.

 ``` ``` ```# File 'numeric.c' /* * call-seq: * num.modulo(numeric) -> real * * x.modulo(y) means x-y*(x/y).floor * * Equivalent to * num.divmod(aNumeric)[1]. * * See Numeric#divmod. */ 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) +

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

Returns:

 ``` ``` ```# File 'numeric.c' /* * call-seq: * +num -> num * * Unary Plus---Returns the receiver's value. */ static VALUE num_uplus(VALUE num) { return num; }```

### - (Numeric) -

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

Returns:

 ``` ``` ```# File 'numeric.c' /* * call-seq: * -num -> numeric * * Unary Minus---Returns the receiver's value, negated. */ static VALUE num_uminus(VALUE num) { VALUE zero; zero = INT2FIX(0); do_coerce(&zero, &num, TRUE); return rb_funcall(zero, '-', 1, num); }```

### - (0?) <=>(other)

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

Returns:

• (0, nil)
 ``` ``` ```# File 'numeric.c' /* * call-seq: * num <=> other -> 0 or nil * * Returns zero if num equals other, nil * otherwise. */ static VALUE num_cmp(VALUE x, VALUE y) { if (x == y) return INT2FIX(0); return Qnil; }```

### - (Numeric) abs - (Numeric) magnitude

Returns the absolute value of num.

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

 ``` ``` ```# File 'numeric.c' /* * call-seq: * num.abs -> numeric * num.magnitude -> numeric * * Returns the absolute value of num. * * 12.abs #=> 12 * (-34.56).abs #=> 34.56 * -34.56.abs #=> 34.56 */ static VALUE num_abs(VALUE num) { if (RTEST(rb_funcall(num, '<', 1, INT2FIX(0)))) { return rb_funcall(num, rb_intern("-@"), 0); } return num; }```

### - (Object) abs2

Returns square of self.

 ``` ``` ```# File 'complex.c' /* * call-seq: * num.abs2 -> real * * Returns square of self. */ static VALUE numeric_abs2(VALUE self) { return f_mul(self, self); }```

### - (0, Float) arg - (0, Float) angle - (0, Float) phase

Returns 0 if the value is positive, pi otherwise.

 ``` ``` ```# File 'complex.c' /* * call-seq: * num.arg -> 0 or float * num.angle -> 0 or float * num.phase -> 0 or float * * Returns 0 if the value is positive, pi otherwise. */ static VALUE numeric_arg(VALUE self) { if (f_positive_p(self)) return INT2FIX(0); return rb_const_get(rb_mMath, id_PI); }```

### - (0, Float) arg - (0, Float) angle - (0, Float) phase

Returns 0 if the value is positive, pi otherwise.

 ``` ``` ```# File 'complex.c' /* * call-seq: * num.arg -> 0 or float * num.angle -> 0 or float * num.phase -> 0 or float * * Returns 0 if the value is positive, pi otherwise. */ static VALUE numeric_arg(VALUE self) { if (f_positive_p(self)) return INT2FIX(0); return rb_const_get(rb_mMath, id_PI); }```

### - (Integer) ceil

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' /* * call-seq: * num.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 */ static VALUE num_ceil(VALUE num) { return flo_ceil(rb_Float(num)); }```

### - (Array) coerce(numeric)

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' /* * call-seq: * 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] */ 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); }```

### - (Numeric) conj - (Numeric) conjugate

Returns self.

 ``` ``` ```# File 'complex.c' /* * call-seq: * num.conj -> self * num.conjugate -> self * * Returns self. */ static VALUE numeric_conj(VALUE self) { return self; }```

### - (Numeric) conj - (Numeric) conjugate

Returns self.

 ``` ``` ```# File 'complex.c' /* * call-seq: * num.conj -> self * num.conjugate -> self * * Returns self. */ static VALUE numeric_conj(VALUE self) { return self; }```

### - (Integer) denominator

Returns the denominator (always positive).

Returns:

 ``` ``` ```# File 'rational.c' /* * call-seq: * num.denominator -> integer * * Returns the denominator (always positive). */ static VALUE numeric_denominator(VALUE self) { return f_denominator(f_to_r(self)); }```

### - (Integer) div(numeric)

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).

See `Numeric#divmod`.

Returns:

 ``` ``` ```# File 'numeric.c' /* * call-seq: * num.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. */ 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); }```

### - (Array) divmod(numeric)

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' /* * call-seq: * num.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] */ static VALUE num_divmod(VALUE x, VALUE y) { return rb_assoc_new(num_div(x, y), num_modulo(x, y)); }```

### - (Boolean) eql?(numeric)

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' /* * call-seq: * num.eql?(numeric) -> true or false * * 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 */ static VALUE num_eql(VALUE x, VALUE y) { if (TYPE(x) != TYPE(y)) return Qfalse; return rb_equal(x, y); }```

### - (Float) fdiv(numeric)

Returns float division.

Returns:

 ``` ``` ```# File 'numeric.c' /* * call-seq: * num.fdiv(numeric) -> float * * Returns float division. */ static VALUE num_fdiv(VALUE x, VALUE y) { return rb_funcall(rb_Float(x), '/', 1, y); }```

### - (Integer) floor

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' /* * call-seq: * num.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 */ static VALUE num_floor(VALUE num) { return flo_floor(rb_Float(num)); }```

### - (Object) i

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

 ``` ``` ```# File 'numeric.c' /* * call-seq: * num.i -> Complex(0,num) * * Returns the corresponding imaginary number. * Not available for complex numbers. */ static VALUE num_imaginary(VALUE num) { return rb_complex_new(INT2FIX(0), num); }```

### - (0) imag - (0) imaginary

Returns zero.

• - (0) imag

Returns:

• (0)
• - (0) imaginary

Returns:

• (0)
 ``` ``` ```# File 'complex.c' /* * call-seq: * num.imag -> 0 * num.imaginary -> 0 * * Returns zero. */ static VALUE numeric_imag(VALUE self) { return INT2FIX(0); }```

### - (0) imag - (0) imaginary

Returns zero.

• - (0) imag

Returns:

• (0)
• - (0) imaginary

Returns:

• (0)
 ``` ``` ```# File 'complex.c' /* * call-seq: * num.imag -> 0 * num.imaginary -> 0 * * Returns zero. */ static VALUE numeric_imag(VALUE self) { return INT2FIX(0); }```

### - (Object) initialize_copy

:nodoc:

 ``` ``` ```# File 'numeric.c' /* :nodoc: */ 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 */ }```

### - (Boolean) integer?

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

Returns:

• (Boolean)
 ``` ``` ```# File 'numeric.c' /* * call-seq: * num.integer? -> true or false * * Returns true if num is an Integer * (including Fixnum and Bignum). */ static VALUE num_int_p(VALUE num) { return Qfalse; }```

### - (Numeric) abs - (Numeric) magnitude

Returns the absolute value of num.

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

 ``` ``` ```# File 'numeric.c' /* * call-seq: * num.abs -> numeric * num.magnitude -> numeric * * Returns the absolute value of num. * * 12.abs #=> 12 * (-34.56).abs #=> 34.56 * -34.56.abs #=> 34.56 */ static VALUE num_abs(VALUE num) { if (RTEST(rb_funcall(num, '<', 1, INT2FIX(0)))) { return rb_funcall(num, rb_intern("-@"), 0); } return num; }```

### - (Object) modulo(numeric)

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

Equivalent to num.divmod(aNumeric).

See `Numeric#divmod`.

 ``` ``` ```# File 'numeric.c' /* * call-seq: * num.modulo(numeric) -> real * * x.modulo(y) means x-y*(x/y).floor * * Equivalent to * num.divmod(aNumeric)[1]. * * See Numeric#divmod. */ 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?) nonzero?

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' /* * call-seq: * num.nonzero? -> self or nil * * 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"] */ static VALUE num_nonzero_p(VALUE num) { if (RTEST(rb_funcall(num, rb_intern("zero?"), 0, 0))) { return Qnil; } return num; }```

### - (Integer) numerator

Returns the numerator.

Returns:

 ``` ``` ```# File 'rational.c' /* * call-seq: * num.numerator -> integer * * Returns the numerator. */ static VALUE numeric_numerator(VALUE self) { return f_numerator(f_to_r(self)); }```

### - (0, Float) arg - (0, Float) angle - (0, Float) phase

Returns 0 if the value is positive, pi otherwise.

 ``` ``` ```# File 'complex.c' /* * call-seq: * num.arg -> 0 or float * num.angle -> 0 or float * num.phase -> 0 or float * * Returns 0 if the value is positive, pi otherwise. */ static VALUE numeric_arg(VALUE self) { if (f_positive_p(self)) return INT2FIX(0); return rb_const_get(rb_mMath, id_PI); }```

### - (Array) polar

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

Returns:

 ``` ``` ```# File 'complex.c' /* * call-seq: * num.polar -> array * * Returns an array; [num.abs, num.arg]. */ static VALUE numeric_polar(VALUE self) { return rb_assoc_new(f_abs(self), f_arg(self)); }```

### - (Object) quo(numeric)

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

 ``` ``` ```# File 'numeric.c' /* * call-seq: * num.quo(numeric) -> real * * Returns most exact division (rational for integers, float for floats). */ static VALUE num_quo(VALUE x, VALUE y) { return rb_funcall(rb_rational_raw1(x), '/', 1, y); }```

### - (Numeric) real

Returns self.

Returns:

 ``` ``` ```# File 'complex.c' /* * call-seq: * num.real -> self * * Returns self. */ static VALUE numeric_real(VALUE self) { return self; }```

### - (Boolean) real?

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

Returns:

• (Boolean)
 ``` ``` ```# File 'numeric.c' /* * call-seq: * num.real? -> true or false * * Returns true if num is a Real * (i.e. non Complex). */ static VALUE num_real_p(VALUE num) { return Qtrue; }```

### - (Array) rect

Returns an array; [num, 0].

Returns:

 ``` ``` ```# File 'complex.c' /* * call-seq: * num.rect -> array * * Returns an array; [num, 0]. */ static VALUE numeric_rect(VALUE self) { return rb_assoc_new(self, INT2FIX(0)); }```

### - (Array) rect

Returns an array; [num, 0].

Returns:

 ``` ``` ```# File 'complex.c' /* * call-seq: * num.rect -> array * * Returns an array; [num, 0]. */ static VALUE numeric_rect(VALUE self) { return rb_assoc_new(self, INT2FIX(0)); }```

### - (Object) remainder(numeric)

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

See `Numeric#divmod`.

 ``` ``` ```# File 'numeric.c' /* * call-seq: * num.remainder(numeric) -> real * * x.remainder(y) means x-y*(x/y).truncate * * See Numeric#divmod. */ 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); } return z; }```

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

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' /* * call-seq: * num.round([ndigits]) -> integer or 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. */ static VALUE num_round(int argc, VALUE* argv, VALUE num) { return flo_round(argc, argv, rb_Float(num)); }```

### - (Object) singleton_method_added

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

 ``` ``` ```# File 'numeric.c' /* * Trap attempts to add methods to Numeric objects. Always * raises a TypeError */ 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 */ }```

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

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``````

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

Yields:

• (i)

Returns:

 ``` ``` ```# File 'numeric.c' /* * call-seq: * num.step(limit[, step]) {|i| block } -> self * num.step(limit[, step]) -> an_enumerator * * 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 */ 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); } else { if (argc == 2) { to = argv[0]; step = argv[1]; } else { rb_raise(rb_eArgError, "wrong number of arguments (%d for 1..2)", argc); } if (rb_equal(step, INT2FIX(0))) { rb_raise(rb_eArgError, "step can't be 0"); } } if (FIXNUM_P(from) && FIXNUM_P(to) && FIXNUM_P(step)) { long i, end, diff; i = FIX2LONG(from); end = FIX2LONG(to); diff = FIX2LONG(step); if (diff > 0) { while (i <= end) { rb_yield(LONG2FIX(i)); i += diff; } } else { while (i >= end) { rb_yield(LONG2FIX(i)); i += diff; } } } else if (!ruby_float_step(from, to, step, FALSE)) { VALUE i = from; ID cmp; if (RTEST(rb_funcall(step, '>', 1, INT2FIX(0)))) { cmp = '>'; } else { cmp = '<'; } for (;;) { if (RTEST(rb_funcall(i, cmp, 1, to))) break; rb_yield(i); i = rb_funcall(i, '+', 1, step); } } return from; }```

### - (Object) to_c

Returns the value as a complex.

 ``` ``` ```# File 'complex.c' /* * call-seq: * num.to_c -> complex * * Returns the value as a complex. */ static VALUE numeric_to_c(VALUE self) { return rb_complex_new1(self); }```

### - (Integer) to_int

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

Returns:

 ``` ``` ```# File 'numeric.c' /* * call-seq: * num.to_int -> integer * * Invokes the child class's to_i method to convert * num to an integer. */ static VALUE num_to_int(VALUE num) { return rb_funcall(num, id_to_i, 0, 0); }```

### - (Integer) truncate

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

Returns:

 ``` ``` ```# File 'numeric.c' /* * call-seq: * num.truncate -> integer * * Returns num truncated to an integer. Numeric * implements this by converting its value to a float and invoking * Float#truncate. */ static VALUE num_truncate(VALUE num) { return flo_truncate(rb_Float(num)); }```

### - (Boolean) zero?

Returns `true` if num has a zero value.

Returns:

• (Boolean)
 ``` ``` ```# File 'numeric.c' /* * call-seq: * num.zero? -> true or false * * Returns true if num has a zero value. */ static VALUE num_zero_p(VALUE num) { if (rb_equal(num, INT2FIX(0))) { return Qtrue; } return Qfalse; }```