class Numeric
The top-level number class.
Public Instance Methods
x.modulo(y) means x-y*(x/y).floor
Equivalent to num.divmod(numeric)[1].
See #divmod.
static VALUE
num_modulo(VALUE x, VALUE y)
{
return rb_funcall(x, '-', 1,
rb_funcall(y, '*', 1,
rb_funcall(x, rb_intern("div"), 1, y)));
}
Unary Plus—Returns the receiver's value.
static VALUE
num_uplus(VALUE num)
{
return num;
}
Unary Minus—Returns the receiver's value, negated.
static VALUE
num_uminus(VALUE num)
{
VALUE zero;
zero = INT2FIX(0);
do_coerce(&zero, &num, TRUE);
return rb_funcall(zero, '-', 1, num);
}
Returns zero if number equals other, otherwise
nil is returned if the two values are incomparable.
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
#magnitude is an alias of #abs.
static VALUE
num_abs(VALUE num)
{
if (negative_int_p(num)) {
return rb_funcall(num, rb_intern("-@"), 0);
}
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 rb_const_get(rb_mMath, id_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 rb_const_get(rb_mMath, id_PI);
}
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_ceil(VALUE num)
{
return flo_ceil(rb_Float(num));
}
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
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 #divmod.
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);
}
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_divmod(VALUE x, VALUE y)
{
return rb_assoc_new(num_div(x, y), num_modulo(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_eql(VALUE x, VALUE y)
{
if (TYPE(x) != TYPE(y)) return Qfalse;
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 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_floor(VALUE num)
{
return flo_floor(rb_Float(num));
}
Returns the corresponding imaginary number. Not available for complex numbers.
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 the absolute value of num.
12.abs #=> 12 (-34.56).abs #=> 34.56 -34.56.abs #=> 34.56
#magnitude is an alias of #abs.
static VALUE
num_abs(VALUE num)
{
if (negative_int_p(num)) {
return rb_funcall(num, rb_intern("-@"), 0);
}
return num;
}
x.modulo(y) means x-y*(x/y).floor
Equivalent to num.divmod(numeric)[1].
See #divmod.
static VALUE
num_modulo(VALUE x, VALUE y)
{
return rb_funcall(x, '-', 1,
rb_funcall(y, '*', 1,
rb_funcall(x, rb_intern("div"), 1, y)));
}
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(rb_funcall(num, rb_intern("zero?"), 0, 0))) {
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 rb_const_get(rb_mMath, id_PI);
}
Returns an array; [num.abs, num.arg].
static VALUE
numeric_polar(VALUE self)
{
return rb_assoc_new(f_abs(self), f_arg(self));
}
Returns most exact division (rational for integers, float for floats).
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 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 #divmod.
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;
}
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_round(int argc, VALUE* argv, VALUE num)
{
return flo_round(argc, argv, rb_Float(num));
}
Trap attempts to add methods to Numeric objects. Always raises a TypeError.
Numerics should be values; singleton_methods should not be added to them.
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;
}
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
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;
}
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 => Fixnum 1.0.to_i.class => Fixnum
static VALUE
num_to_int(VALUE num)
{
return rb_funcall(num, id_to_i, 0, 0);
}
Returns num truncated to an Integer.
Numeric implements this by converting its value to a Float and invoking Float#truncate.
static VALUE
num_truncate(VALUE num)
{
return flo_truncate(rb_Float(num));
}
Returns true if num has a zero value.
static VALUE
num_zero_p(VALUE num)
{
if (rb_equal(num, INT2FIX(0))) {
return Qtrue;
}
return Qfalse;
}