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integer

integer

§
:
numeric
 is
 
[Contains abstract features]

integer -- abstract ancestor of integer numbers

integer is the abstract ancestor of integer numbers that provides operations
from numeric plus a division remainder operation %, bitwise logical operations,
shift operations and gcd. Also, integers can be used to build fractions.

Value Constructors

§
:
Any
 is
 
[Inherited from  numeric]
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

§
:
Any
 => 
numeric.this 
[Inherited from  numeric]
absolute value
§
:
Any
 => 
String 
[Redefinition of Any.as_string]
convert this to a decimal number in a string. If negative, add "-" as
the first character.

redefines:

convert this to a number using the given base. If negative, add "-" as
the first character.
§(len i32, base u32)
:
Any
 => 
String
convert this to a number using the given base. If negative, add "-" as
the first character. Extend with leading "0" until the length is at
least len
§
:
Any
 => 
u8 
[Inherited from  numeric]
 
[Abstract feature]
this numeric value as an u8
create binary representation
create binary representation with given number of digits.
create decimal representation
create decimal representation with given number of digits.
§
:
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.
§
:
Any
 => 
bool 
[Inherited from  numeric]
does this numeric value fit into an u8? This is redefined by children
of numeric that support `as_u8`.
greatest common divisor of this and b

note that this assumes zero to be divisible by any positive integer.
create hexadecimal representation
create hexadecimal representation with given number of digits.
§(other numeric.this)
:
Any
 => 
numeric.this 
[Inherited from  numeric]
 
[Abstract feature]
basic operations: 'infix %' (division remainder)
§(other integer.this)
:
Any
 => 
bool 
[Redefinition of numeric.infix %!]

redefines:

test divisibility by other
§(other integer.this)
:
Any
 => 
integer.this 
[Abstract feature]
bitwise operations
§(other numeric.this)
:
Any
 => 
numeric.this 
[Inherited from  numeric]
 
[Abstract feature]
basic operations: 'infix *' (multiplication)
§(other numeric.this)
:
Any
 => 
bool 
[Inherited from  numeric]
§(other numeric.this)
:
Any
 => 
numeric.this 
[Inherited from  numeric]
 
[Abstract feature]
basic operations: 'infix **' (exponentiation)
§(other numeric.this)
:
Any
 => 
bool 
[Inherited from  numeric]
§(other numeric.this)
:
Any
 => 
num_option numeric.this 
[Inherited from  numeric]
 
[Abstract feature]
§(other numeric.this)
:
Any
 => 
numeric.this 
[Inherited from  numeric]
 
[Abstract feature]
§(other numeric.this)
:
Any
 => 
numeric.this 
[Inherited from  numeric]
§(other numeric.this)
:
Any
 => 
numeric.this 
[Inherited from  numeric]
 
[Abstract feature]
basic operations: 'infix +' (addition)
§(other numeric.this)
:
Any
 => 
bool 
[Inherited from  numeric]
§(other numeric.this)
:
Any
 => 
numeric.this 
[Inherited from  numeric]
§(other numeric.this)
:
Any
 => 
numeric.this 
[Inherited from  numeric]
 
[Abstract feature]
basic operations: 'infix -' (subtraction)
§(other numeric.this)
:
Any
 => 
bool 
[Inherited from  numeric]
§(other numeric.this)
:
Any
 => 
numeric.this 
[Inherited from  numeric]
§(other numeric.this)
:
Any
 => 
numeric.this 
[Inherited from  numeric]
 
[Abstract feature]
basic operations: 'infix /' (division)
§(other integer.this)
:
Any
 => 
bool 
[Redefinition of numeric.infix /!]
preconditions used in 'numeric' for basic operations: true if the
operation is permitted for the given values

redefines:

create a fraction
§(other integer.this)
:
Any
 => 
integer.this 
[Abstract feature]
§(other integer.this)
:
Any
 => 
integer.this 
[Abstract feature]
shift operations
§(other integer.this)
:
Any
 => 
integer.this 
[Abstract feature]
§(other integer.this)
:
Any
 => 
integer.this 
[Abstract feature]
create a fraction via unicode fraction slash \u2044 '⁄ '
check if this type of integer is bounded

returns false unless redefined by a specific implementation of integer
§
:
Any
 => 
bool 
[Inherited from  numeric]
§
:
Any
 => 
bool 
[Inherited from  numeric]
create octal representation
create octal representation with given number of digits.
§
:
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.
§
:
Any
 => 
numeric.this 
[Inherited from  numeric]
basic operations: 'prefix +' (identity)
§
:
Any
 => 
bool 
[Inherited from  numeric]
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.
§
:
Any
 => 
numeric.this 
[Inherited from  numeric]
basic operations: 'prefix -' (negation)
§
:
Any
 => 
bool 
[Inherited from  numeric]
overflow checking operations
§
:
Any
 => 
numeric.this 
[Inherited from  numeric]
saturating operations
§
:
Any
 => 
integer.this 
[Abstract feature]
bitwise NOT
bitwise NOT (Unicode alias)
§
:
Any
 => 
i32 
[Inherited from  numeric]
sign function resulting in `-1`/`0`/`+1` depending on whether `numeric.this`
is less than, equal or larger than zero

Value Types

§
:
Any
 is
 
[Inherited from  numeric]
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
 
[Inherited from  numeric]
 
[Abstract feature]
equality
§(v u32)
:
Any
 is
 
[Inherited from  numeric]
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
 
[Inherited from  numeric]
 
[Abstract feature]
total order
§
:
Any
 is
 
[Inherited from  Type]
name of this type, including type parameters, e.g. 'option (list i32)'.
§
:
Any
 is
 
[Inherited from  numeric]
 
[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.
§
:
Any
 is
 
[Inherited from  numeric]
the constant '10' in whatever integer implementation we have, maximum in case of overflow
§
:
Any
 is
 
[Inherited from  numeric]
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
 
[Inherited from  numeric]
 
[Abstract feature]
identity element for 'infix +'