class Numeric
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. If duplication is attempted, the same instance is returned.
Integer.new(1) #=> NoMethodError: undefined method `new' for Integer:Class
1.dup #=> 1
1.object_id == 1.dup.object_id #=> true
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
Public Instance Methods
modulo(numeric) → real Show source
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));
}x.modulo(y) means x-y*(x/y).floorEquivalent to num.divmod(numeric)[1].
See #divmod.
+num → num Show source
static VALUE
num_uplus(VALUE num)
{
return num;
}Unary Plus—Returns the receiver's value.
-num → numeric Show source
static VALUE
num_uminus(VALUE num)
{
VALUE zero;
zero = INT2FIX(0);
do_coerce(&zero, &num, TRUE);
return num_funcall1(zero, '-', num);
}Unary Minus—Returns the receiver's value, negated.
number <=> other → 0 or nil Show source
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.
abs → numeric Show source
static VALUE
num_abs(VALUE num)
{
if (negative_int_p(num)) {
return num_funcall0(num, idUMinus);
}
return num;
}Returns the absolute value of num.
12.abs #=> 12
(-34.56).abs #=> 34.56
-34.56.abs #=> 34.56
#magnitude is an alias of #abs.
abs2 → real Show source
static VALUE
numeric_abs2(VALUE self)
{
return f_mul(self, self);
}Returns square of self.
angle → 0 or float Show source
static VALUE
numeric_arg(VALUE self)
{
if (f_positive_p(self))
return INT2FIX(0);
return DBL2NUM(M_PI);
}Returns 0 if the value is positive, pi otherwise.
arg → 0 or float Show source
static VALUE
numeric_arg(VALUE self)
{
if (f_positive_p(self))
return INT2FIX(0);
return DBL2NUM(M_PI);
}Returns 0 if the value is positive, pi otherwise.
ceil([ndigits]) → integer or float Show source
static VALUE
num_ceil(int argc, VALUE *argv, VALUE num)
{
return flo_ceil(argc, argv, 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
coerce(numeric) → array Show source
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]
conj → self Show source
conjugate → self
static VALUE
numeric_conj(VALUE self)
{
return self;
}Returns self.
conjugate → self Show source
static VALUE
numeric_conj(VALUE self)
{
return self;
}Returns self.
denominator → integer Show source
static VALUE
numeric_denominator(VALUE self)
{
return f_denominator(f_to_r(self));
}Returns the denominator (always positive).
div(numeric) → integer Show source
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);
}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 #divmod.
divmod(numeric) → array Show source
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 | -3.5Examples
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]
eql?(numeric) → true or false Show source
static VALUE
num_eql(VALUE x, VALUE y)
{
if (TYPE(x) != TYPE(y)) return Qfalse;
if (RB_TYPE_P(x, T_BIGNUM)) {
return rb_big_eql(x, y);
}
return rb_equal(x, y);
}Returns true if num and numeric are the same type and have equal values. Contrast this with Numeric#==, which performs type conversions.
1 == 1.0 #=> true
1.eql?(1.0) #=> false
(1.0).eql?(1.0) #=> true
68719476736.eql?(68719476736.0) #=> false
fdiv(numeric) → float Show source
static VALUE
num_fdiv(VALUE x, VALUE y)
{
return rb_funcall(rb_Float(x), '/', 1, y);
}Returns float division.
finite? → true or false Show source
static VALUE
num_finite_p(VALUE num)
{
return Qtrue;
}Return true if num is finite number, oterwise returns false.
floor([ndigits]) → integer or float Show source
static VALUE
num_floor(int argc, VALUE *argv, VALUE num)
{
return flo_floor(argc, argv, 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
i → Complex(0,num) Show source
static VALUE
num_imaginary(VALUE num)
{
return rb_complex_new(INT2FIX(0), num);
}Returns the corresponding imaginary number. Not available for complex numbers.
imag → 0 Show source
imaginary → 0
static VALUE
numeric_imag(VALUE self)
{
return INT2FIX(0);
}Returns zero.
imaginary → 0 Show source
static VALUE
numeric_imag(VALUE self)
{
return INT2FIX(0);
}Returns zero.
infinite? → nil or 1 or -1 Show source
static VALUE
num_infinite_p(VALUE num)
{
return Qnil;
}Returns values corresponding to the value of num's magnitude:
finite-
nil -Infinity-
-1 -
+
Infinity -
+
1
integer? → true or false Show source
static VALUE
num_int_p(VALUE num)
{
return Qfalse;
}Returns true if num is an Integer.
(1.0).integer? #=> false
(1).integer? #=> true
magnitude → numeric Show source
static VALUE
num_abs(VALUE num)
{
if (negative_int_p(num)) {
return num_funcall0(num, idUMinus);
}
return num;
}Returns the absolute value of num.
12.abs #=> 12
(-34.56).abs #=> 34.56
-34.56.abs #=> 34.56
#magnitude is an alias of #abs.
modulo(numeric) → real Show source
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));
}x.modulo(y) means x-y*(x/y).floorEquivalent to num.divmod(numeric)[1].
See #divmod.
negative? → true or false Show source
static VALUE
num_negative_p(VALUE num)
{
return negative_int_p(num) ? Qtrue : Qfalse;
}Returns true if num is less than 0.
nonzero? → self or nil Show source
static VALUE
num_nonzero_p(VALUE num)
{
if (RTEST(num_funcall0(num, rb_intern("zero?")))) {
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"]
numerator → integer Show source
static VALUE
numeric_numerator(VALUE self)
{
return f_numerator(f_to_r(self));
}Returns the numerator.
phase → 0 or float Show source
static VALUE
numeric_arg(VALUE self)
{
if (f_positive_p(self))
return INT2FIX(0);
return DBL2NUM(M_PI);
}Returns 0 if the value is positive, pi otherwise.
polar → array Show source
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);
}Returns an array; [num.abs, num.arg].
positive? → true or false Show source
static VALUE
num_positive_p(VALUE num)
{
const ID mid = '>';
if (FIXNUM_P(num)) {
if (method_basic_p(rb_cInteger))
return (SIGNED_VALUE)num > (SIGNED_VALUE)INT2FIX(0) ? Qtrue : Qfalse;
}
else if (RB_TYPE_P(num, T_BIGNUM)) {
if (method_basic_p(rb_cInteger))
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.
quo(int_or_rat) → rat Show source
quo(flo) → flo
static VALUE
numeric_quo(VALUE x, VALUE y)
{
if (RB_FLOAT_TYPE_P(y)) {
return rb_funcall(x, rb_intern("fdiv"), 1, y);
}
#ifdef CANON
if (canonicalization) {
x = rb_rational_raw1(x);
}
else
#endif
{
x = rb_convert_type(x, T_RATIONAL, "Rational", "to_r");
}
return nurat_div(x, y);
}Returns most exact division (rational for integers, float for floats).
real → self Show source
static VALUE
numeric_real(VALUE self)
{
return self;
}Returns self.
real? → true or false Show source
static VALUE
num_real_p(VALUE num)
{
return Qtrue;
}Returns true if num is a Real number. (i.e. not Complex).
rect → array Show source
rectangular → array
static VALUE
numeric_rect(VALUE self)
{
return rb_assoc_new(self, INT2FIX(0));
}Returns an array; [num, 0].
rectangular → array Show source
static VALUE
numeric_rect(VALUE self)
{
return rb_assoc_new(self, INT2FIX(0));
}Returns an array; [num, 0].
remainder(numeric) → real Show source
static VALUE
num_remainder(VALUE x, VALUE y)
{
VALUE z = num_funcall1(x, '%', 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).truncateSee #divmod.
round([ndigits]) → integer or float Show source
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;
}Trap attempts to add methods to Numeric objects. Always raises a TypeError.
Numerics should be values; singleton_methods should not be added to them.
step(by: step, to: limit) {|i| block } → self Show source
step(by: step, to: limit) → an_enumerator
step(limit=nil, step=1) {|i| block } → self
step(limit=nil, step=1) → an_enumerator
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 (rb_equal(step, INT2FIX(0))) {
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 to_c → complex Show source
static VALUE
numeric_to_c(VALUE self)
{
return rb_complex_new1(self);
}Returns the value as a complex.
to_int → integer Show source
static VALUE
num_to_int(VALUE num)
{
return num_funcall0(num, id_to_i);
}Invokes the child class's to_i method to convert num to an integer.
1.0.class => Float
1.0.to_int.class => Integer
1.0.to_i.class => Integer truncate([ndigits]) → integer or float Show source
static VALUE
num_truncate(int argc, VALUE *argv, VALUE num)
{
return flo_truncate(argc, argv, rb_Float(num));
}Returns num truncated to an Integer.
Numeric implements this by converting its value to a Float and invoking Float#truncate.
zero? → true or false Show source
static VALUE
num_zero_p(VALUE num)
{
if (FIXNUM_P(num)) {
if (FIXNUM_ZERO_P(num)) {
return Qtrue;
}
}
else if (RB_TYPE_P(num, T_BIGNUM)) {
if (rb_bigzero_p(num)) {
/* this should not happen usually */
return Qtrue;
}
}
else if (rb_equal(num, INT2FIX(0))) {
return Qtrue;
}
return Qfalse;
}Returns true if num has a zero value.
Ruby Core © 1993–2017 Yukihiro Matsumoto
Licensed under the Ruby License.
Ruby Standard Library © contributors
Licensed under their own licenses.