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
Whatâs Here¶ ↑
First, whatâs elsewhere. Class Numeric:
Inherits from class Object.
Includes module Comparable.
Here, class Numeric provides methods for:
Querying¶ ↑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.
-@
Returns the value of self, negated.
abs2
Returns the square of self.
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.
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.
floor
Returns the largest number less than or equal to self, to a given precision.
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.
truncate
Returns self truncated (toward zero) to a given precision.
clone
Returns self; does not allow freezing.
step
Invokes the given block with the sequence of specified numbers.
self % other → real_numeric click to toggle source
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:
c % n c-n*(c/n).floor c.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
Numeric#modulo is an alias for Numeric#%.
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));
}
+self → self click to toggle source
Returns self.
static VALUE
num_uplus(VALUE num)
{
return num;
}
-self → numeric click to toggle source
Unary MinusâReturns the receiver, negated.
static VALUE
num_uminus(VALUE num)
{
VALUE zero;
zero = INT2FIX(0);
do_coerce(&zero, &num, TRUE);
return num_funcall1(zero, '-', num);
}
self <=> other → zero or nil click to toggle source
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_cmp(VALUE x, VALUE y)
{
if (x == y) return INT2FIX(0);
return Qnil;
}
abs → numeric click to toggle source
Returns the absolute value of self.
12.abs (-34.56).abs -34.56.abs
Numeric#magnitude is an alias for Numeric#abs.
static VALUE
num_abs(VALUE num)
{
if (rb_num_negative_int_p(num)) {
return num_funcall0(num, idUMinus);
}
return num;
}
abs2 → real click to toggle source
Returns square of self.
static VALUE
numeric_abs2(VALUE self)
{
return f_mul(self, self);
}
angle → 0 or float
Returns 0 if the value is positive, pi otherwise.
arg → 0 or float click to toggle source
Returns 0 if the value is positive, pi otherwise.
static VALUE
numeric_arg(VALUE self)
{
if (f_positive_p(self))
return INT2FIX(0);
return DBL2NUM(M_PI);
}
ceil(digits = 0) → integer or float click to toggle source
Returns the smallest number that is greater than or equal to self with a precision of digits decimal digits.
Numeric implements this by converting self to a Float and invoking Float#ceil.
static VALUE
num_ceil(int argc, VALUE *argv, VALUE num)
{
return flo_ceil(argc, argv, rb_Float(num));
}
clone(freeze: true) → self click to toggle source
Returns self.
Raises an exception if the value for freeze is neither true nor nil.
Related: Numeric#dup.
static VALUE
num_clone(int argc, VALUE *argv, VALUE x)
{
return rb_immutable_obj_clone(argc, argv, x);
}
coerce(other) → array click to toggle source
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
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
Returns self.
conjugate -> self click to toggle source
Returns self.
static VALUE
numeric_conj(VALUE self)
{
return self;
}
denominator → integer click to toggle source
Returns the denominator (always positive).
static VALUE
numeric_denominator(VALUE self)
{
return f_denominator(f_to_r(self));
}
div(other) → integer click to toggle source
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, Float, Rational, and Complex use this implementation.
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);
}
divmod(other) → array click to toggle source
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_divmod(VALUE x, VALUE y)
{
return rb_assoc_new(num_div(x, y), num_modulo(x, y));
}
dup → self click to toggle source
Returns self.
Related: Numeric#clone.
static VALUE
num_dup(VALUE x)
{
return x;
}
eql?(other) → true or false click to toggle source
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_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);
}
fdiv(other) → float click to toggle source
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.
static VALUE
num_fdiv(VALUE x, VALUE y)
{
return rb_funcall(rb_Float(x), '/', 1, y);
}
finite? → true or false click to toggle source
Returns true if num is a finite number, otherwise returns false.
def finite? return true end
floor(digits = 0) → integer or float click to toggle source
Returns the largest number that is less than or equal to self with a precision of digits decimal digits.
Numeric implements this by converting self to a Float and invoking Float#floor.
static VALUE
num_floor(int argc, VALUE *argv, VALUE num)
{
return flo_floor(argc, argv, rb_Float(num));
}
i → complex click to toggle source
Returns Complex(0, self):
2.i -2.i 2.0.i Rational(1, 2).i Complex(3, 4).i
static VALUE
num_imaginary(VALUE num)
{
return rb_complex_new(INT2FIX(0), num);
}
imaginary -> 0 click to toggle source
Returns zero.
static VALUE
numeric_imag(VALUE self)
{
return INT2FIX(0);
}
infinite? → -1, 1, or nil click to toggle source
Returns nil, -1, or 1 depending on whether the value is finite, -Infinity, or +Infinity.
def infinite? return nil end
integer? → true or false click to toggle source
Returns true if num is an Integer.
1.0.integer? 1.integer?
def integer? return false end
modulo(p1)
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:
c % n c-n*(c/n).floor c.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
Numeric#modulo is an alias for Numeric#%.
negative? → true or false click to toggle source
Returns true if self is less than 0, false otherwise.
static VALUE
num_negative_p(VALUE num)
{
return RBOOL(rb_num_negative_int_p(num));
}
nonzero? → self or nil click to toggle source
Returns self if self is not a zero value, nil otherwise; uses method zero? 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 }
Of the Core and Standard Library classes, Integer, Float, Rational, and Complex use this implementation.
static VALUE
num_nonzero_p(VALUE num)
{
if (RTEST(num_funcall0(num, rb_intern("zero?")))) {
return Qnil;
}
return num;
}
numerator → integer click to toggle source
Returns the numerator.
static VALUE
numeric_numerator(VALUE self)
{
return f_numerator(f_to_r(self));
}
phase → 0 or float
Returns 0 if the value is positive, pi otherwise.
polar → array click to toggle source
Returns an array; [num.abs, num.arg].
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);
}
positive? → true or false click to toggle source
Returns true if self is greater than 0, false otherwise.
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);
}
quo(int_or_rat) → rat click to toggle source
quo(flo) → flo
Returns the most exact division (rational for integers, float for floats).
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);
}
real → self click to toggle source
Returns self.
static VALUE
numeric_real(VALUE self)
{
return self;
}
real? → true or false click to toggle source
Returns true if num is a real number (i.e. not Complex).
def real? return true end
rect → array
Returns an array; [num, 0].
rectangular -> array click to toggle source
Returns an array; [num, 0].
static VALUE
numeric_rect(VALUE self)
{
return rb_assoc_new(self, INT2FIX(0));
}
remainder(other) → real_number click to toggle source
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_remainder(VALUE x, VALUE y)
{
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;
}
round(digits = 0) → integer or float click to toggle source
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_round(int argc, VALUE* argv, VALUE num)
{
return flo_round(argc, argv, rb_Float(num));
}
step(to = nil, by = 1) {|n| ... } → self click to toggle source
step(to = nil, by = 1) → enumerator
step(to = nil, by: 1) {|n| ... } → self
step(to = nil, by: 1) → enumerator
step(by: 1, to: ) {|n| ... } → self
step(by: 1, to: ) → enumerator
step(by: , to: nil) {|n| ... } → self
step(by: , to: nil) → enumerator
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 # => [1, 9, 25, 49, 81]
The generated sequence:
- Begins with +self+.
- Continues at intervals of +step+ (which may not be zero).
- Ends with the last number that is within or equal to +limit+;
that is, less than or equal to +limit+ if +step+ is positive,
greater than or equal to +limit+ if +step+ is negative.
If +limit+ is not given, 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.
<b>Keyword Arguments</b>
With keyword arguments +by+ and +to+,
their values (or defaults) determine the step and limit:
# Both keywords given.
squares = []
4.step(by: 2, to: 10) {|i| squares.push(i*i) } # => 4
squares # => [16, 36, 64, 100]
cubes = []
3.step(by: -1.5, to: -3) {|i| cubes.push(i*i*i) } # => 3
cubes # => [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) } # => 4
squares # => [16, 25, 36, 49, 64, 81, 100]
# Only by given.
# Only keyword by given
squares = []
4.step(by:2) {|i| squares.push(i*i); break if i > 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
<b>Positional Arguments</b>
With optional positional arguments +limit+ and +step+,
their values (or defaults) determine the step and limit:
squares = []
4.step(10, 2) {|i| squares.push(i*i) } # => 4
squares # => [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); break if i > 10 } # => nil
squares # => [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 executed <i>floor(n + n*Float::EPSILON) + 1</i> times, where <i>n = (limit - self)/step</i>.
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 (by != Qundef) {
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;
}
to_c → complex click to toggle source
Returns the value as a complex.
static VALUE
numeric_to_c(VALUE self)
{
return rb_complex_new1(self);
}
to_int → integer click to toggle source
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)
static VALUE
num_to_int(VALUE num)
{
return num_funcall0(num, id_to_i);
}
truncate(digits = 0) → integer or float click to toggle source
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_truncate(int argc, VALUE *argv, VALUE num)
{
return flo_truncate(argc, argv, rb_Float(num));
}
zero? → true or false click to toggle source
Returns true if zero has a zero value, false otherwise.
Of the Core and Standard Library classes, only Rational and Complex use this implementation.
static VALUE
num_zero_p(VALUE num)
{
return rb_equal(num, INT2FIX(0));
}
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