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 puts 1.object_id == a.object_id #=> true
There can only ever be one instance of the integer 1, for example. Ruby ensures this by preventing instantiation and duplication.
Integer.new(1) #=> NoMethodError: undefined method `new' for Integer:Class 1.dup #=> TypeError: can't dup Fixnum
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 #=> true
static VALUE
num_modulo(VALUE x, VALUE y)
{
return rb_funcall(x, '-', 1,
rb_funcall(y, '*', 1,
rb_funcall(x, id_div, 1, y)));
}
static VALUE
num_uplus(VALUE num)
{
return num;
}
Unary Plus—Returns the receiver’s value.
static VALUE
num_uminus(VALUE num)
{
VALUE zero;
zero = INT2FIX(0);
do_coerce(&zero, &num, TRUE);
return rb_funcall(zero, '-', 1, num);
}
Unary Minus—Returns the receiver’s value, negated.
static VALUE
num_cmp(VALUE x, VALUE y)
{
if (x == y) return INT2FIX(0);
return Qnil;
}
Returns zero if number equals other, otherwise nil is returned if the two values are incomparable.
static VALUE
num_abs(VALUE num)
{
if (negative_int_p(num)) {
return rb_funcall(num, idUMinus, 0);
}
return num;
}
Returns the absolute value of num.
12.abs #=> 12 (-34.56).abs #=> 34.56 -34.56.abs #=> 34.56
Numeric#magnitude is an alias of Numeric#abs.
static VALUE
numeric_abs2(VALUE self)
{
return f_mul(self, self);
}
Returns square of self.
static VALUE
numeric_arg(VALUE self)
{
if (f_positive_p(self))
return INT2FIX(0);
return rb_const_get(rb_mMath, id_PI);
}
Returns 0 if the value is positive, pi otherwise.
static VALUE
num_ceil(VALUE num)
{
return flo_ceil(rb_Float(num));
}
Returns the smallest possible Integer that is greater than or equal to num.
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_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);
}
If a numeric is the same type as num, returns an array containing numeric and num. Otherwise, returns an array with both a numeric 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
numeric_conj(VALUE self)
{
return self;
}
Returns self.
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(rb_funcall(x, '/', 1, y), rb_intern("floor"), 0);
}
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(numeric)[0].
See Numeric#divmod.
static VALUE
num_divmod(VALUE x, VALUE y)
{
return rb_assoc_new(num_div(x, y), num_modulo(x, y));
}
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_eql(VALUE x, VALUE y)
{
if (TYPE(x) != TYPE(y)) return Qfalse;
return rb_equal(x, y);
}
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_fdiv(VALUE x, VALUE y)
{
return rb_funcall(rb_Float(x), '/', 1, y);
}
Returns float division.
static VALUE
num_floor(VALUE num)
{
return flo_floor(rb_Float(num));
}
Returns the largest integer less than or equal to num.
Numeric implements this by converting an Integer to a Float and invoking Float#floor.
1.floor #=> 1 (-1).floor #=> -1
static VALUE
num_imaginary(VALUE num)
{
return rb_complex_new(INT2FIX(0), num);
}
Returns the corresponding imaginary number. Not available for complex numbers.
static VALUE
numeric_imag(VALUE self)
{
return INT2FIX(0);
}
Returns zero.
static VALUE
num_init_copy(VALUE x, VALUE y)
{
rb_raise(rb_eTypeError, "can't copy %"PRIsVALUE, rb_obj_class(x));
UNREACHABLE;
}
static VALUE
num_int_p(VALUE num)
{
return Qfalse;
}
static VALUE
num_negative_p(VALUE num)
{
return negative_int_p(num) ? Qtrue : Qfalse;
}
Returns true if num is less than 0.
static VALUE
num_nonzero_p(VALUE num)
{
if (RTEST(rb_funcallv(num, rb_intern("zero?"), 0, 0))) {
return Qnil;
}
return num;
}
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
numeric_numerator(VALUE self)
{
return f_numerator(f_to_r(self));
}
Returns the numerator.
static VALUE
numeric_polar(VALUE self)
{
return rb_assoc_new(f_abs(self), f_arg(self));
}
Returns an array; [num.abs, num.arg].
static VALUE
num_positive_p(VALUE num)
{
const ID mid = '>';
if (FIXNUM_P(num)) {
if (method_basic_p(rb_cFixnum))
return (SIGNED_VALUE)num > (SIGNED_VALUE)INT2FIX(0) ? Qtrue : Qfalse;
}
else if (RB_TYPE_P(num, T_BIGNUM)) {
if (method_basic_p(rb_cBignum))
return BIGNUM_POSITIVE_P(num) && !rb_bigzero_p(num) ? Qtrue : Qfalse;
}
return compare_with_zero(num, mid);
}
Returns true if num is greater than 0.
static VALUE
numeric_quo(VALUE x, VALUE y)
{
if (RB_TYPE_P(y, T_FLOAT)) {
return f_fdiv(x, y);
}
#ifdef CANON
if (canonicalization) {
x = rb_rational_raw1(x);
}
else
#endif
{
x = rb_convert_type(x, T_RATIONAL, "Rational", "to_r");
}
return rb_funcall(x, '/', 1, y);
}
Returns most exact division (rational for integers, float for floats).
static VALUE
numeric_real(VALUE self)
{
return self;
}
Returns self.
static VALUE
num_real_p(VALUE num)
{
return Qtrue;
}
Returns true if num is a Real number. (i.e. not Complex).
static VALUE
numeric_rect(VALUE self)
{
return rb_assoc_new(self, INT2FIX(0));
}
Returns an array; [num, 0].
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;
}
x.remainder(y) means x-y*(x/y).truncate
See Numeric#divmod.
static VALUE
num_round(int argc, VALUE* argv, VALUE num)
{
return flo_round(argc, argv, rb_Float(num));
}
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_sadded(VALUE x, VALUE name)
{
ID mid = rb_to_id(name);
/* ruby_frame = ruby_frame->prev; */ /* pop frame for "singleton_method_added" */
rb_remove_method_id(rb_singleton_class(x), mid);
rb_raise(rb_eTypeError,
"can't define singleton method \"%"PRIsVALUE"\" for %"PRIsVALUE,
rb_id2str(mid),
rb_obj_class(x));
UNREACHABLE;
}
static VALUE
num_step(int argc, VALUE *argv, VALUE from)
{
VALUE to, step;
int desc, inf;
RETURN_SIZED_ENUMERATOR(from, argc, argv, num_step_size);
desc = num_step_scan_args(argc, argv, &to, &step);
if (RTEST(rb_num_coerce_cmp(step, INT2FIX(0), id_eq))) {
inf = 1;
}
else if (RB_TYPE_P(to, T_FLOAT)) {
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)) {
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;
}
Invokes the given block with the sequence of numbers starting at num, incremented by step (defaulted to 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), where limit is defaulted to infinity.
In the recommended keyword argument style, either or both of step and limit (default infinity) can be omitted. In the fixed position argument style, zero as a step (i.e. num.step(limit, 0)) is not allowed for historical compatibility reasons.
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 the following expression:
floor(n + n*epsilon)+ 1
Where the n is the following:
n = (limit - num)/step
Otherwise, the loop starts at num, uses either the less-than (<) or greater-than (>) operator to compare the counter against limit, and increments itself using the + operator.
If no block is given, an Enumerator is returned instead.
For example:
p 1.step.take(4) p 10.step(by: -1).take(4) 3.step(to: 5) { |i| print i, " " } 1.step(10, 2) { |i| print i, " " } Math::E.step(to: Math::PI, by: 0.2) { |f| print f, " " }
Will produce:
[1, 2, 3, 4] [10, 9, 8, 7] 3 4 5 1 3 5 7 9 2.71828182845905 2.91828182845905 3.11828182845905
static VALUE
numeric_to_c(VALUE self)
{
return rb_complex_new1(self);
}
Returns the value as a complex.
static VALUE
num_to_int(VALUE num)
{
return rb_funcallv(num, id_to_i, 0, 0);
}
Invokes the child class’s to_i method to convert num to an integer.
1.0.class => Float 1.0.to_int.class => Fixnum 1.0.to_i.class => Fixnum
static VALUE
num_truncate(VALUE num)
{
return flo_truncate(rb_Float(num));
}
Returns num truncated to an Integer.
Numeric implements this by converting its value to a Float and invoking Float#truncate.
static VALUE
num_zero_p(VALUE num)
{
if (rb_equal(num, INT2FIX(0))) {
return Qtrue;
}
return Qfalse;
}
Returns true if num has a zero value.