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 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
x.modulo(y) means x-y*(x/y).floor.
Equivalent to num.divmod(numeric)[1].
See Numeric#divmod.
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));
}
Unary Plus—Returns the receiver.
static VALUE
num_uplus(VALUE num)
{
return num;
}
Unary Minus—Returns the receiver, negated.
static VALUE
num_uminus(VALUE num)
{
VALUE zero;
zero = INT2FIX(0);
do_coerce(&zero, &num, TRUE);
return num_funcall1(zero, '-', num);
}
Returns zero if number equals other, otherwise returns nil.
static VALUE
num_cmp(VALUE x, VALUE y)
{
if (x == y) return INT2FIX(0);
return Qnil;
}
Returns the absolute value of num.
12.abs #=> 12 (-34.56).abs #=> 34.56 -34.56.abs #=> 34.56
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;
}
Returns square of self.
static VALUE
numeric_abs2(VALUE self)
{
return f_mul(self, self);
}
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);
}
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);
}
Returns the smallest number greater than or equal to num with a precision of ndigits decimal digits (default: 0).
Numeric implements this by converting its value 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));
}
Returns the receiver. freeze cannot be false.
static VALUE
num_clone(int argc, VALUE *argv, VALUE x)
{
return rb_immutable_obj_clone(argc, argv, x);
}
If numeric is the same type as num, returns an array [numeric, num]. Otherwise, returns an array with both 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
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);
}
Returns self.
static VALUE
numeric_conj(VALUE self)
{
return self;
}
Returns self.
static VALUE
numeric_conj(VALUE self)
{
return self;
}
Returns the denominator (always positive).
static VALUE
numeric_denominator(VALUE self)
{
return f_denominator(f_to_r(self));
}
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_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);
}
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 negative 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));
}
Returns the receiver.
static VALUE
num_dup(VALUE x)
{
return x;
}
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
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 float division.
static VALUE
num_fdiv(VALUE x, VALUE y)
{
return rb_funcall(rb_Float(x), '/', 1, y);
}
Returns true if num is a finite number, otherwise returns false.
static VALUE
num_finite_p(VALUE num)
{
return Qtrue;
}
Returns the largest number less than or equal to num with a precision of ndigits decimal digits (default: 0).
Numeric implements this by converting its value 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));
}
Returns the corresponding imaginary number. Not available for complex numbers.
-42.i #=> (0-42i) 2.0.i #=> (0+2.0i)
static VALUE
num_imaginary(VALUE num)
{
return rb_complex_new(INT2FIX(0), num);
}
Returns zero.
static VALUE
numeric_imag(VALUE self)
{
return INT2FIX(0);
}
Returns zero.
static VALUE
numeric_imag(VALUE self)
{
return INT2FIX(0);
}
Returns nil, -1, or 1 depending on whether the value is finite, -Infinity, or +Infinity.
static VALUE
num_infinite_p(VALUE num)
{
return Qnil;
}
Returns true if num is an Integer.
1.0.integer? #=> false 1.integer? #=> true
static VALUE
num_int_p(VALUE num)
{
return Qfalse;
}
Returns the absolute value of num.
12.abs #=> 12 (-34.56).abs #=> 34.56 -34.56.abs #=> 34.56
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;
}
x.modulo(y) means x-y*(x/y).floor.
Equivalent to num.divmod(numeric)[1].
See Numeric#divmod.
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));
}
Returns true if num is less than 0.
static VALUE
num_negative_p(VALUE num)
{
return rb_num_negative_int_p(num) ? Qtrue : Qfalse;
}
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(num_funcall0(num, rb_intern("zero?")))) {
return Qnil;
}
return num;
}
Returns the numerator.
static VALUE
numeric_numerator(VALUE self)
{
return f_numerator(f_to_r(self));
}
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);
}
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);
}
Returns true if num is greater than 0.
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 rb_num_compare_with_zero(num, mid);
}
Returns the most exact division (rational for integers, float for floats).
VALUE
rb_numeric_quo(VALUE x, VALUE y)
{
if (RB_FLOAT_TYPE_P(y)) {
return rb_funcall(x, rb_intern("fdiv"), 1, y);
}
if (canonicalization) {
x = rb_rational_raw1(x);
}
else {
x = rb_convert_type(x, T_RATIONAL, "Rational", "to_r");
}
return rb_rational_div(x, y);
}
Returns self.
static VALUE
numeric_real(VALUE self)
{
return self;
}
Returns true if num is a real number (i.e. not Complex).
static VALUE
num_real_p(VALUE num)
{
return Qtrue;
}
Returns an array; [num, 0].
static VALUE
numeric_rect(VALUE self)
{
return rb_assoc_new(self, INT2FIX(0));
}
Returns an array; [num, 0].
static VALUE
numeric_rect(VALUE self)
{
return rb_assoc_new(self, INT2FIX(0));
}
x.remainder(y) means x-y*(x/y).truncate.
See Numeric#divmod.
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)))) {
return rb_funcall(z, '-', 1, y);
}
return z;
}
Returns num rounded to the nearest value with a precision of ndigits decimal digits (default: 0).
Numeric implements this by converting its value 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));
}
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 floor(n + n*Float::EPSILON) + 1 times, where 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. Especially, the enumerator is an Enumerator::ArithmeticSequence if both limit and step are kind of Numeric or nil.
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 2.718281828459045 2.9182818284590453 3.118281828459045
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);
}
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(from, argc, argv, num_step_size);
}
desc = num_step_scan_args(argc, argv, &to, &step, TRUE, FALSE);
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, 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;
}
Returns the value as a complex.
static VALUE
numeric_to_c(VALUE self)
{
return rb_complex_new1(self);
}
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
static VALUE
num_to_int(VALUE num)
{
return num_funcall0(num, id_to_i);
}
Returns num truncated (toward zero) to a precision of ndigits decimal digits (default: 0).
Numeric implements this by converting its value 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));
}
Returns true if num has a zero value.
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;
}