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
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).floor.
Equivalent to num.divmod(numeric)[1].
See Numeric#divmod.
static VALUE num_abs(VALUE num) { if (rb_num_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
Numeric#magnitude is an alias for Numeric#abs.
static VALUE
num_ceil(int argc, VALUE *argv, VALUE num)
{
return flo_ceil(argc, argv, rb_Float(num));
} 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_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 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_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 Numeric#divmod.
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_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
static VALUE
num_floor(int argc, VALUE *argv, VALUE num)
{
return flo_floor(argc, argv, rb_Float(num));
} 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.
Returns true if num is an Integer.
1.0.integer? #=> false 1.integer? #=> true
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_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"]
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].
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 true if num is greater than 0.
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);
} Returns the most exact division (rational for integers, float for floats).
Returns true if num is a real number (i.e. not Complex).
Returns an array; [num, 0].
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;
} 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));
} 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_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(from, 2, ((VALUE [2]){to, step}), 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;
} 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_truncate(int argc, VALUE *argv, VALUE num)
{
return flo_truncate(argc, argv, rb_Float(num));
} 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.
Ruby Core © 1993–2020 Yukihiro Matsumoto
Licensed under the Ruby License.
Ruby Standard Library © contributors
Licensed under their own licenses.