# 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.

Author: Keiju ISHITSUKA (SHL Japan Inc.)

Document-class: FloatDomainError

Raised when attempting to convert special float values (in particular infinite or NaN) to numerical classes which don't support them.

``````Float::INFINITY.to_r
``````

raises the exception:

``FloatDomainError: Infinity``
Methods
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Included Modules
Instance Public methods
num.modulo(numeric) → real
``x.modulo(y) means x-y*(x/y).floor``

Equivalent to num.divmod(aNumeric).

See `Numeric#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)));
}```
+num → num

Unary Plusâ€”Returns the receiver's value.

```static VALUE
num_uplus(VALUE num)
{
return num;
}```
-num → numeric

Unary Minusâ€”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);
}```
number <=> other → 0 or nil

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;
}```
num.abs → numeric

Returns the absolute value of num.

``````12.abs         #=> 12
(-34.56).abs   #=> 34.56
-34.56.abs     #=> 34.56
``````
```static VALUE
num_abs(VALUE num)
{
if (negative_int_p(num)) {
return rb_funcall(num, rb_intern("-@"), 0);
}
return num;
}```
num.abs2 → real

Returns square of self.

```static VALUE
numeric_abs2(VALUE self)
{
return f_mul(self, self);
}```
num.angle → 0 or float

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);
}```
num.arg → 0 or float

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);
}```
num.ceil → integer

Returns the smallest `Integer` greater than or equal to num. Class `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));
}```
num.coerce(numeric) → array

If aNumeric is the same type as num, returns an array containing aNumeric and num. Otherwise, returns an array with both aNumeric 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);
}```
num.conj → self
num.conjugate → self

Returns self.

```static VALUE
numeric_conj(VALUE self)
{
return self;
}```
num.conjugate → self

Returns self.

```static VALUE
numeric_conj(VALUE self)
{
return self;
}```
num.denominator → integer

Returns the denominator (always positive).

```static VALUE
numeric_denominator(VALUE self)
{
return f_denominator(f_to_r(self));
}```
num.div(numeric) → integer

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(aNumeric).

See `Numeric#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);
}```
num.divmod(numeric) → array

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));
}```
num.eql?(numeric) → true or false

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);
}```
num.fdiv(numeric) → float

Returns float division.

```static VALUE
num_fdiv(VALUE x, VALUE y)
{
return rb_funcall(rb_Float(x), '/', 1, y);
}```
num.floor → integer

Returns the largest integer less than or equal to num. `Numeric` implements this by converting anInteger 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));
}```
num.i → Complex(0,num)

Returns the corresponding imaginary number. Not available for complex numbers.

```static VALUE
num_imaginary(VALUE num)
{
return rb_complex_new(INT2FIX(0), num);
}```
num.imag → 0
num.imaginary → 0

Returns zero.

```static VALUE
numeric_imag(VALUE self)
{
return INT2FIX(0);
}```
num.imaginary → 0

Returns zero.

```static VALUE
numeric_imag(VALUE self)
{
return INT2FIX(0);
}```
num.integer? → true or false

Returns `true` if `num` is an Integer (including Fixnum and Bignum).

``````(1.0).integer? #=> false
(1).integer?   #=> true
``````
```static VALUE
num_int_p(VALUE num)
{
return Qfalse;
}```
num.magnitude → numeric

Returns the absolute value of num.

``````12.abs         #=> 12
(-34.56).abs   #=> 34.56
-34.56.abs     #=> 34.56
``````
```static VALUE
num_abs(VALUE num)
{
if (negative_int_p(num)) {
return rb_funcall(num, rb_intern("-@"), 0);
}
return num;
}```
num.modulo(numeric) → real
``x.modulo(y) means x-y*(x/y).floor``

Equivalent to num.divmod(aNumeric).

See `Numeric#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)));
}```
num.nonzero? → self or nil

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;
}```
num.numerator → integer

Returns the numerator.

```static VALUE
numeric_numerator(VALUE self)
{
return f_numerator(f_to_r(self));
}```
num.phase → 0 or float

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);
}```
num.polar → array

Returns an array; [num.abs, num.arg].

```static VALUE
numeric_polar(VALUE self)
{
return rb_assoc_new(f_abs(self), f_arg(self));
}```
num.quo(numeric) → real

Returns most exact division (rational for integers, float for floats).

```static VALUE
num_quo(VALUE x, VALUE y)
{
return rb_funcall(rb_rational_raw1(x), '/', 1, y);
}```
num.real → self

Returns self.

```static VALUE
numeric_real(VALUE self)
{
return self;
}```
num.real? → true or false

Returns `true` if num is a `Real` (i.e. non `Complex`).

```static VALUE
num_real_p(VALUE num)
{
return Qtrue;
}```
num.rect → array

Returns an array; [num, 0].

```static VALUE
numeric_rect(VALUE self)
{
return rb_assoc_new(self, INT2FIX(0));
}```
num.rect → array

Returns an array; [num, 0].

```static VALUE
numeric_rect(VALUE self)
{
return rb_assoc_new(self, INT2FIX(0));
}```
num.remainder(numeric) → real
``x.remainder(y) means x-y*(x/y).truncate``

See `Numeric#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;
}```
num.round([ndigits]) → integer or float

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));
}```
singleton_method_added(p1)

Trap attempts to add methods to `Numeric` objects. Always raises a `TypeError`

```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" */
/* Numerics should be values; singleton_methods should not be added to them */
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;
}```
num.step(limit[, step]) {|i| block } → self
num.step(limit[, step]) → an_enumerator

Invokes block with the sequence of numbers starting at num, incremented by step (default 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). 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*epsilon)+ 1 times, where n = (limit - num)/step. Otherwise, the loop starts at num, uses either the `<` or `>` operator to compare the counter against limit, and increments itself using the `+` operator.

If no block is given, an enumerator is returned instead.

``````1.step(10, 2) { |i| print i, " " }
Math::E.step(Math::PI, 0.2) { |f| print f, " " }
``````

produces:

``````1 3 5 7 9
2.71828182845905 2.91828182845905 3.11828182845905``````
```static VALUE
num_step(int argc, VALUE *argv, VALUE from)
{
VALUE to, step;

RETURN_SIZED_ENUMERATOR(from, argc, argv, num_step_size);
if (argc == 1) {
to = argv[0];
step = INT2FIX(1);
}
else {
rb_check_arity(argc, 1, 2);
to = argv[0];
step = argv[1];
if (rb_equal(step, INT2FIX(0))) {
rb_raise(rb_eArgError, "step can't be 0");
}
}

if (FIXNUM_P(from) && FIXNUM_P(to) && FIXNUM_P(step)) {
long i, end, diff;

i = FIX2LONG(from);
end = FIX2LONG(to);
diff = FIX2LONG(step);

if (diff > 0) {
while (i <= end) {
rb_yield(LONG2FIX(i));
i += diff;
}
}
else {
while (i >= end) {
rb_yield(LONG2FIX(i));
i += diff;
}
}
}
else if (!ruby_float_step(from, to, step, FALSE)) {
VALUE i = from;
ID cmp;

if (positive_int_p(step)) {
cmp = '>';
}
else {
cmp = '<';
}
for (;;) {
if (RTEST(rb_funcall(i, cmp, 1, to))) break;
rb_yield(i);
i = rb_funcall(i, '+', 1, step);
}
}
return from;
}```
num.to_c → complex

Returns the value as a complex.

```static VALUE
numeric_to_c(VALUE self)
{
return rb_complex_new1(self);
}```
num.to_int → integer

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);
}```
num.truncate → integer

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));
}```
num.zero? → true or false

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;
}```