role Real
Error ReportCollection examples

Non-complex number

Common role for non-Complex numbers.

# Methods

## method Bridge

Defined as:

Default implementation coerces the invocant to Num and that's the behavior of this method in core Real types. This method primarily exist to make it easy to implement custom Real types by users, with the `Bridge` method returning one of the core `Real` types (NOT necessarily a Num) that best represent the custom `Real` type. In turn, this lets all the core operators and methods obtain a usable value they can work with.

As an example, we can implement a custom `Temperature` type. It has a unit of measure and the value, which are given during instantiation. We can implement custom operators or conversion methods that work with this type. When it comes to regular mathematical operators, however, we can simply use the `.Bridge` method to convert the `Temperature` to Kelvin expressed in one of the core numeric types:

As we can see from the last two lines of the output, the type of the bridged result is not forced to be any particular core type. It is a Rat, when we instantiated `Temperature` with a `Rat` or when conversion was involved, and it is an Int when we instantiated `Temperature` with an Int.

## method Complex

Converts the number to a `Complex` with the number converted to a `Num` as its real part and 0e0 as the imaginary part.

## method Rat

Converts the number to a `Rat` with the precision `\$epsilon`.

## method Real

Defined as:

The `:D` variant simply returns the invocant. The `:U` variant issues a warning about using an uninitialized value in numeric context and then returns `self.new`.

## routine rand

Returns a pseudo-random number between zero (inclusive) and the number (non-inclusive). The `Bridge` method is used to coerce the `Real` to a numeric that supports rand method.

The term form returns a pseudo-random `Num` between 0e0 (inclusive) and 1e0 (non-inclusive.)

## method sign

Returns `-1` if the number is negative, `0` if it is zero and `1` otherwise.

## method round

Rounds the number to scale `\$scale`. If `\$scale` is 1, rounds to an integer. If scale is `0.1`, rounds to one digit after the radix point (period or comma), etc.

## method floor

Return the largest integer not greater than the number.

## method ceiling

Returns the smallest integer not less than the number.

## method truncate

Rounds the number towards zero.

## method polymod

Returns the remainders after applying sequentially all divisors in the `@mods` argument; the last element of the array will be the last remainder.

`10 xx 8` is simply an array with eight number 10s; the first division by 10 will return `1` as a remainder, while the rest, up to the last, will return 0. With 8 divisors, as above, the result will have one more elements, in this case for the last remainder.

## method base

Converts the number to a string, using `\$base` as base. For `\$base` larger than ten, capital Latin letters are used.

The optional `\$digits` argument asks for that many digits of fraction (which may not be negative). If omitted, a reasonable default is chosen based on type. For Int this default is 0. For Num, the default is 8. For Rational, the number of places is scaled to the size of the denominator, with a minimum of 6.

A special value of `Whatever` (`*`) can be given as `\$digits`, which functions the same as when `\$digits` is not specified for all `Real` types except the `Rationals`. For `Rationals`, the `Whatever` indicates that you wish all of the possible digits of the fractional part, but use caution: since there's no detection of repeating fractional parts (the algorithm will eventually stop after generating 2**63 digits).

The final digit produced is always rounded.

For reverse operation, see `parse-base`