mathn
mathn is a library for changing the way Ruby does math. If you need more precise rounding with multiple division or exponentiation operations, then mathn is the right tool.
Without mathn:
3 / 2 => 1 # Integer
With mathn:
3 / 2 => 3/2 # Rational
mathn features late rounding and lacks truncation of intermediate results:
Without mathn:
20 / 9 * 3 * 14 / 7 * 3 / 2 # => 18
With mathn:
20 / 9 * 3 * 14 / 7 * 3 / 2 # => 20
When you require 'mathn', the libraries for Prime, CMath, Matrix and Vector are also loaded.
Copyright
Author: Keiju ISHITSUKA (SHL Japan Inc.)
The top-level number class.
- #
- A
- C
- D
- E
- F
- I
- M
- N
- P
- Q
- R
- S
- T
- Z
Source: show
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.
Source: show
static VALUE
num_uplus(VALUE num)
{
return num;
}
Unary Minus—Returns the receiver's value, negated.
Source: show
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.
Source: show
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.
Source: show
static VALUE
num_abs(VALUE num)
{
if (negative_int_p(num)) {
return rb_funcall(num, rb_intern("-@"), 0);
}
return num;
}
Returns square of self.
Source: show
static VALUE
numeric_abs2(VALUE self)
{
return f_mul(self, self);
}
Returns 0 if the value is positive, pi otherwise.
Source: show
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.
Source: show
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
Source: show
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]
Source: show
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);
}
num.conjugate → self Link
Returns self.
Source: show
static VALUE
numeric_conj(VALUE self)
{
return self;
}
Returns self.
Source: show
static VALUE
numeric_conj(VALUE self)
{
return self;
}
Returns the denominator (always positive).
Source: show
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.
Source: show
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+rThe 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]
Source: show
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
Source: show
static VALUE
num_eql(VALUE x, VALUE y)
{
if (TYPE(x) != TYPE(y)) return Qfalse;
return rb_equal(x, y);
}
Returns float division.
Source: show
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
Source: show
static VALUE
num_floor(VALUE num)
{
return flo_floor(rb_Float(num));
}
Returns the corresponding imaginary number. Not available for complex numbers.
Source: show
static VALUE
num_imaginary(VALUE num)
{
return rb_complex_new(INT2FIX(0), num);
}
num.imaginary → 0 Link
Returns zero.
Source: show
static VALUE
numeric_imag(VALUE self)
{
return INT2FIX(0);
}
Returns zero.
Source: show
static VALUE
numeric_imag(VALUE self)
{
return INT2FIX(0);
}
Numerics are immutable values, which should not be copied.
Any attempt to use this method on a Numeric will raise a TypeError.
Source: show
static VALUE
num_init_copy(VALUE x, VALUE y)
{
rb_raise(rb_eTypeError, "can't copy %s", rb_obj_classname(x));
UNREACHABLE;
}
Returns true if num is an Integer (including Fixnum
and Bignum).
(1.0).integer? #=> false
(1).integer? #=> true
Source: show
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
#magnitude is an alias of #abs.
Source: show
static VALUE
num_abs(VALUE num)
{
if (negative_int_p(num)) {
return rb_funcall(num, rb_intern("-@"), 0);
}
return num;
}
Source: show
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"]
Source: show
static VALUE
num_nonzero_p(VALUE num)
{
if (RTEST(rb_funcall(num, rb_intern("zero?"), 0, 0))) {
return Qnil;
}
return num;
}
Returns the numerator.
Source: show
static VALUE
numeric_numerator(VALUE self)
{
return f_numerator(f_to_r(self));
}
Returns 0 if the value is positive, pi otherwise.
Source: show
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].
Source: show
static VALUE
numeric_polar(VALUE self)
{
return rb_assoc_new(f_abs(self), f_arg(self));
}
num.quo(flo) → flo Link
Returns most exact division (rational for integers, float for floats).
Source: show
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.
Source: show
static VALUE
numeric_real(VALUE self)
{
return self;
}
Returns true if num is a Real number. (i.e. not
Complex).
Source: show
static VALUE
num_real_p(VALUE num)
{
return Qtrue;
}
num.rectangular → array Link
Returns an array; [num, 0].
Source: show
static VALUE
numeric_rect(VALUE self)
{
return rb_assoc_new(self, INT2FIX(0));
}
Returns an array; [num, 0].
Source: show
static VALUE
numeric_rect(VALUE self)
{
return rb_assoc_new(self, INT2FIX(0));
}
x.remainder(y) means x-y*(x/y).truncateSee #divmod.
Source: show
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.
Source: show
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.
Source: show
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 \"%s\" for %s",
rb_id2name(mid),
rb_obj_classname(x));
UNREACHABLE;
}
num.step(by: step, to: limit]) → an_enumerator
num.step(limit=nil, step=1) {|i| block } → self
num.step(limit=nil, step=1) → an_enumerator Link
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, integer 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)+ 1Where the n is the following:
n = (limit - num)/stepOtherwise, 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 3.11828182845905Source: show
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.
Source: show
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
Source: show
static VALUE
num_to_int(VALUE num)
{
return rb_funcall(num, id_to_i, 0, 0);
}