# Class: Numeric

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

## Overview

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`.

 ``` 428 429 430 431 432 433 434``` ```# File 'numeric.c', line 428 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:

 ``` 327 328 329 330 331``` ```# File 'numeric.c', line 327 static VALUE num_uplus(VALUE num) { return num; }```

### #- ⇒ Numeric

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

Returns:

 ``` 355 356 357 358 359 360 361 362 363 364``` ```# File 'numeric.c', line 355 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)
 ``` 1033 1034 1035 1036 1037 1038``` ```# File 'numeric.c', line 1033 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
``````

 ``` 547 548 549 550 551 552 553 554``` ```# File 'numeric.c', line 547 static VALUE num_abs(VALUE num) { if (negative_int_p(num)) { return rb_funcall(num, rb_intern("[email protected]"), 0); } return num; }```

### #abs2 ⇒ Object

Returns square of self.

 ``` 1970 1971 1972 1973 1974``` ```# File 'complex.c', line 1970 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.

 ``` 1986 1987 1988 1989 1990 1991 1992``` ```# File 'complex.c', line 1986 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.

 ``` 1986 1987 1988 1989 1990 1991 1992``` ```# File 'complex.c', line 1986 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:

 ``` 1709 1710 1711 1712 1713``` ```# File 'numeric.c', line 1709 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:

 ``` 204 205 206 207 208 209 210 211 212``` ```# File 'numeric.c', line 204 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 ⇒ self #conjugate ⇒ self

Returns self.

• #conjself

Returns:

• (self)
• #conjugateself

Returns:

• (self)
 ``` 2025 2026 2027 2028 2029``` ```# File 'complex.c', line 2025 static VALUE numeric_conj(VALUE self) { return self; }```

### #conj ⇒ self #conjugate ⇒ self

Returns self.

• #conjself

Returns:

• (self)
• #conjugateself

Returns:

• (self)
 ``` 2025 2026 2027 2028 2029``` ```# File 'complex.c', line 2025 static VALUE numeric_conj(VALUE self) { return self; }```

### #denominator ⇒ Integer

Returns the denominator (always positive).

Returns:

 ``` 1767 1768 1769 1770 1771``` ```# File 'rational.c', line 1767 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:

 ``` 408 409 410 411 412 413``` ```# File 'numeric.c', line 408 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:

 ``` 501 502 503 504 505``` ```# File 'numeric.c', line 501 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)

Returns:

• (Boolean)
 ``` 1017 1018 1019 1020 1021 1022 1023``` ```# File 'numeric.c', line 1017 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:

 ``` 387 388 389 390 391``` ```# File 'numeric.c', line 387 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:

 ``` 1687 1688 1689 1690 1691``` ```# File 'numeric.c', line 1687 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:

 ``` 341 342 343 344 345``` ```# File 'numeric.c', line 341 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)
 ``` 1958 1959 1960 1961 1962``` ```# File 'complex.c', line 1958 static VALUE numeric_imag(VALUE self) { return INT2FIX(0); }```

### #imag ⇒ 0 #imaginary ⇒ 0

Returns zero.

• #imag0

Returns:

• (0)
• #imaginary0

Returns:

• (0)
 ``` 1958 1959 1960 1961 1962``` ```# File 'complex.c', line 1958 static VALUE numeric_imag(VALUE self) { return INT2FIX(0); }```

### #initialize_copy ⇒ Object

:nodoc:

 ``` 311 312 313 314 315 316 317 318``` ```# File 'numeric.c', line 311 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)); UNREACHABLE; }```

### #integer? ⇒ Boolean

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

Returns:

• (Boolean)

Returns:

• (Boolean)
 ``` 529 530 531 532 533``` ```# File 'numeric.c', line 529 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
``````

 ``` 547 548 549 550 551 552 553 554``` ```# File 'numeric.c', line 547 static VALUE num_abs(VALUE num) { if (negative_int_p(num)) { return rb_funcall(num, rb_intern("[email protected]"), 0); } return num; }```

### #modulo(numeric) ⇒ Object

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

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

See `Numeric#divmod`.

 ``` 428 429 430 431 432 433 434``` ```# File 'numeric.c', line 428 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? ⇒ self?

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:

• (self, nil)

Returns:

• (Boolean)
 ``` 586 587 588 589 590 591 592 593``` ```# File 'numeric.c', line 586 static VALUE num_nonzero_p(VALUE num) { if (RTEST(rb_funcall(num, rb_intern("zero?"), 0, 0))) { return Qnil; } return num; }```

### #numerator ⇒ Integer

Returns the numerator.

Returns:

 ``` 1755 1756 1757 1758 1759``` ```# File 'rational.c', line 1755 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.

 ``` 1986 1987 1988 1989 1990 1991 1992``` ```# File 'complex.c', line 1986 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:

 ``` 2012 2013 2014 2015 2016``` ```# File 'complex.c', line 2012 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).

 ``` 373 374 375 376 377``` ```# File 'numeric.c', line 373 static VALUE num_quo(VALUE x, VALUE y) { return rb_funcall(rb_rational_raw1(x), '/', 1, y); }```

### #real ⇒ self

Returns self.

Returns:

• (self)
 ``` 1945 1946 1947 1948 1949``` ```# File 'complex.c', line 1945 static VALUE numeric_real(VALUE self) { return self; }```

### #real? ⇒ Boolean

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

Returns:

• (Boolean)

Returns:

• (Boolean)
 ``` 515 516 517 518 519``` ```# File 'numeric.c', line 515 static VALUE num_real_p(VALUE num) { return Qtrue; }```

### #rect ⇒ Array

Returns an array; [num, 0].

Returns:

 ``` 2000 2001 2002 2003 2004``` ```# File 'complex.c', line 2000 static VALUE numeric_rect(VALUE self) { return rb_assoc_new(self, INT2FIX(0)); }```

### #rect ⇒ Array

Returns an array; [num, 0].

Returns:

 ``` 2000 2001 2002 2003 2004``` ```# File 'complex.c', line 2000 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`.

 ``` 445 446 447 448 449 450 451 452 453 454 455 456 457 458``` ```# File 'numeric.c', line 445 static VALUE num_remainder(VALUE x, VALUE y) { VALUE z = rb_funcall(x, '%', 1, y); if ((!rb_equal(z, INT2FIX(0))) && ((negative_int_p(x) && positive_int_p(y)) || (positive_int_p(x) && negative_int_p(y)))) { return rb_funcall(z, '-', 1, y); } return z; }```

### #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:

 ``` 1725 1726 1727 1728 1729``` ```# File 'numeric.c', line 1725 static VALUE num_round(int argc, VALUE* argv, VALUE num) { return flo_round(argc, argv, rb_Float(num)); }```

### #singleton_method_added ⇒ Object

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

 ``` 295 296 297 298 299 300 301 302 303 304 305 306 307 308``` ```# File 'numeric.c', line 295 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)); UNREACHABLE; }```

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

Yields:

• (i)

Returns:

• (self)
 ``` 1866 1867 1868 1869 1870 1871 1872 1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 1886 1887 1888 1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 1921 1922``` ```# File 'numeric.c', line 1866 static VALUE num_step(int argc, VALUE *argv, VALUE from) { VALUE to, step; RETURN_SIZED_ENUMERATOR(from, argc, argv, num_step_size); if (argc == 1) { to = argv[0]; step = INT2FIX(1); } else { rb_check_arity(argc, 1, 2); to = argv[0]; step = argv[1]; 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 (positive_int_p(step)) { cmp = '>'; } else { cmp = '<'; } for (;;) { if (RTEST(rb_funcall(i, cmp, 1, to))) break; rb_yield(i); i = rb_funcall(i, '+', 1, step); } } return from; }```

### #to_c ⇒ Object

Returns the value as a complex.

 ``` 1509 1510 1511 1512 1513``` ```# File 'complex.c', line 1509 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:

 ``` 603 604 605 606 607``` ```# File 'numeric.c', line 603 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:

 ``` 1740 1741 1742 1743 1744``` ```# File 'numeric.c', line 1740 static VALUE num_truncate(VALUE num) { return flo_truncate(rb_Float(num)); }```

### #zero? ⇒ Boolean

Returns `true` if num has a zero value.

Returns:

• (Boolean)

Returns:

• (Boolean)
 ``` 564 565 566 567 568 569 570 571``` ```# File 'numeric.c', line 564 static VALUE num_zero_p(VALUE num) { if (rb_equal(num, INT2FIX(0))) { return Qtrue; } return Qfalse; }```