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numeric

numeric

§
:
hashable,orderable
 is
 
[Contains abstract features]

numeric -- parent of all numeric features

Value Constructors

absolute value using `|a|` built from a `prefix |` and `postfix |` as an operator
alias of `a.abs`

Due to the low precedence of `|`, this works also on expressions like `|a-b|`, even
with spaces `| a-b |`, `|a - b|`, `| a-b|` or `|a-b |`.

Nesting, however, does not work, e.g, `| - |a| |`, this requires parentheses `|(- |a|)|`.

NYI: CLEANUP: Due to #3081, we need `postfix |` as the first operation, should be
`prefix |` first

Functions

absolute value
§
:
Any
 => 
String 
[Inherited from  Any]
create a String from this instance. Unless redefined, `a.as_string` will
create `"instance[T]"` where `T` is the dynamic type of `a`
§
:
Any
 => 
u8 
[Abstract feature]
this numeric value as an u8
§
:
Any
 => 
Type 
[Inherited from  Any]
Get the dynamic type of this instance. For value instances `x`, this is
equal to `type_of x`, but for `x` with a `ref` type `x.dynamic_type` gives
the actual runtime type, while `type_of x` results in the static
compile-time type.

There is no dynamic type of a type instance since this would result in an
endless hierarchy of types. So for Type values, dynamic_type is redefined
to just return Type.type.
does this numeric value fit into an u8? This is redefined by children
of numeric that support `as_u8`.
§(other numeric.this)
:
Any
 => 
numeric.this 
[Abstract feature]
basic operations: 'infix %' (division remainder)
§(other numeric.this)
:
Any
 => 
numeric.this 
[Abstract feature]
basic operations: 'infix *' (multiplication)
§(other numeric.this)
:
Any
 => 
numeric.this 
[Abstract feature]
basic operations: 'infix **' (exponentiation)
§(other numeric.this)
:
Any
 => 
numeric.this 
[Abstract feature]
§(other numeric.this)
:
Any
 => 
numeric.this 
[Abstract feature]
basic operations: 'infix +' (addition)
§(other numeric.this)
:
Any
 => 
numeric.this 
[Abstract feature]
basic operations: 'infix -' (subtraction)
§(other numeric.this)
:
Any
 => 
numeric.this 
[Abstract feature]
basic operations: 'infix /' (division)
§
:
Any
 => 
String 
[Inherited from  Any]
convenience prefix operator to create a string from a value.

This permits usage of `$` as a prefix operator in a similar way both
inside and outside of constant strings: $x and "$x" will produce the
same string.
basic operations: 'prefix +' (identity)
preconditions for basic operations: true if the operation's result is
representable and defined for the given values

default implementations all return `true` such that children have to
redefine these only for partial operations such as those resulting in
an overflow or that are undefined like a division by zero for most
types.
basic operations: 'prefix -' (negation)
overflow checking operations
saturating operations
sign function resulting in `-1`/`0`/`+1` depending on whether `numeric.this`
is less than, equal or larger than zero

Value Types

absolute value using `|a|` built from a `prefix |` and `postfix |` as an operator
alias of `a.abs`

Due to the low precedence of `|`, this works also on expressions like `|a-b|`, even
with spaces `| a-b |`, `|a - b|`, `| a-b|` or `|a-b |`.

Nesting, however, does not work, e.g, `| - |a| |`, this requires parentheses `|(- |a|)|`.

NYI: CLEANUP: Due to #3081, we need `postfix |` as the first operation, should be
`prefix |` first

Type Features

§
:
Any
 is
 
[Inherited from  Type]
string representation of this type to be used for debugging.

result has the form "Type of '<name>'", but this might change in the future

redefines:

§
:
Any
 is
 
[Inherited from  Type]
There is no dynamic type of a type instance since this would result in an
endless hierarchy of types, so dynamic_type is redefined to just return
Type.type here.

redefines:

§(a numeric.this.type, b numeric.this.type)
:
Any
 is
  
[Abstract feature]
equality
the value corresponding to v in whatever integer implementation we have,
maximum in case of overflow
§(a property.hashable.this.type)
:
Any
 is
 
[Inherited from  hashable]
 
[Abstract feature]
create hash code for this instance

This should satisfy the following condition:

(T.equality a b) : (T.hash_code a = T.hash_code b)
§(T 
type
)
:
Any
 is
 
[Inherited from  Type]
Is this type assignable to a type parameter with constraint `T`?

The result of this is a compile-time constant that can be used to specialize
code for a particular type.

is_of_integer_type(n T : numeric) => T : integer
say (is_of_integer_type 1234) # true
say (is_of_integer_type 3.14) # false

it is most useful in conjunction preconditions or `if` statements as in

pair(a,b T) is

=>

or

val(n T) is

§(a numeric.this.type, b numeric.this.type)
:
Any
 is
  
[Abstract feature]
total order
§
:
Any
 is
 
[Inherited from  Type]
name of this type, including type parameters, e.g. 'option (list i32)'.
§
:
Any
 is
 
[Abstract feature]
identity element for 'infix *'
monoid of numeric with infix * operation. Will create product of all elements
it is applied to.
monoid of numeric with infix *^ operation. Will create product of all elements
it is applied to, stopping at max/min value in case of overflow.
monoid of numeric with infix + operation. Will create sum of all elements it
is applied to.
monoid of numeric with infix +^ operation. Will create sum of all elements it
is applied to, stopping at max/min value in case of overflow.
the constant '10' in whatever integer implementation we have, maximum in case of overflow
the constant '2' in whatever integer implementation we have, maximum in case of overflow
§
:
Any
 is
 
[Inherited from  Any]
Get a type as a value.

This is a feature with the effect equivalent to Fuzion's `expr.type` call tail.
It is recommended to use `expr.type` and not `expr.type_value`.

`type_value` is here to show how this can be implemented and to illustrate the
difference to `dynamic_type`.
§
:
Any
 is
 
[Abstract feature]
identity element for 'infix +'
last changed: 2024-09-18