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wrap_around

num.wrap_around

:
integer
 is
[Contains abstract features]
wrap_around -- abstract ancestor of wrap-around integer numbers

wrap_around is the abstract ancestor of integer numbers that have min and
max values and operations with wrap-around semantics.

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|)|`.

Functions

 => 
numeric.this
[Inherited from  numeric]
absolute value
this integer as an array of bytes (little endian)
 => 
String
[Inherited from  integer]
convert this to a decimal number in a string. If negative, add "-" as
the first character.

redefines:

(base u32)
 => 
String
[Inherited from  integer]
convert this to a number using the given base. If negative, add "-" as
the first character.
(len i32, base u32)
 => 
String
[Inherited from  integer]
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
 => 
u8
[Inherited from  numeric]
[Abstract feature]
this numeric value as an u8
 => 
String
[Inherited from  integer]
create binary representation
(len i32)
 => 
String
[Inherited from  integer]
create binary representation with given number of digits.
 => 
String
[Inherited from  integer]
create decimal representation
(len i32)
 => 
String
[Inherited from  integer]
create decimal representation with given number of digits.
(R 
type
, F 
type
: Typed_Function R, f F)
 => 
R
[Inherited from  Any]
dynamic_apply -- apply `f.call` to `Any.this`'s dynamic type and value

This can be used to perform operation on values depending on their dynamic
type.

Here is an example that takes a `Sequence Any` that may contain boxed values
of types `i32` and `f64`. We can now write a feature `get_f64` that extracts
these values converted to `f64` and build a function `sum` that sums them up
as follows:


NYI: IMPROVEMENT: #5892: If this is fixed, we could write

 => 
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.
 => 
bool
[Inherited from  numeric]
does this numeric value fit into an u8? This is redefined by children
of numeric that support `as_u8`.
(b integer.this)
 => 
integer.this
[Inherited from  integer]
greatest common divisor of this and b

note that this assumes zero to be divisible by any positive integer.
 => 
String
[Inherited from  integer]
create hexadecimal representation
(len i32)
 => 
String
[Inherited from  integer]
create hexadecimal representation with given number of digits.
(other numeric.this)
 => 
numeric.this
[Inherited from  numeric]
[Abstract feature]
basic operations: 'infix %' (division remainder)
(other integer.this)
 => 
bool
[Inherited from  integer]

redefines:

(other integer.this)
 => 
bool
[Inherited from  integer]
test divisibility by other
(other integer.this)
 => 
integer.this
[Inherited from  integer]
[Abstract feature]
bitwise operations
multiplication, with check for overflow

redefines:


redefines:

exponentiation for positive exponent

'zero ** zero' is permitted and results in 'one'.

redefines:


redefines:

exponentiation with overflow checking semantics

'zero **? zero' is permitted and results in 'one'.

redefines:

exponentiation with saturating semantics

'zero **^ zero' is permitted and results in 'one'.

redefines:

exponentiation with wrap-around semantics

'zero **° zero' is permitted and results in 'one'.

redefines:


redefines:

addition, with check for overflow

redefines:


redefines:


redefines:


redefines:

subtraction, with check for overflow

redefines:


redefines:


redefines:


redefines:

(other numeric.this)
 => 
numeric.this
[Inherited from  numeric]
[Abstract feature]
basic operations: 'infix /' (division)
(other integer.this)
 => 
bool
[Inherited from  integer]
preconditions used in 'numeric' for basic operations: true if the
operation is permitted for the given values

redefines:

create a fraction
(other integer.this)
 => 
integer.this
[Inherited from  integer]
[Abstract feature]
(other integer.this)
 => 
integer.this
[Inherited from  integer]
[Abstract feature]
shift operations
(other integer.this)
 => 
integer.this
[Inherited from  integer]
[Abstract feature]
(other integer.this)
 => 
integer.this
[Inherited from  integer]
[Abstract feature]
create a fraction via unicode fraction slash \u2044 '⁄ '
 => 
bool
[Redefinition of  integer.is_bounded]
check if this type of wrap_around is bounded

wrap_arounds are assumed to be a bound set by default, so
this returns true unless redefined by an implementation

redefines:

 => 
bool
[Inherited from  numeric]
 => 
bool
[Inherited from  numeric]
 => 
u8
[Inherited from  integer]
[Abstract feature]
the least significant byte of this integer
 => 
String
[Inherited from  integer]
create octal representation
(len i32)
 => 
String
[Inherited from  integer]
create octal representation with given number of digits.
 => 
i32
[Abstract feature]
count the number of 1 bits in the binary representation of this
integer.
(other num.wrap_around.this)
 => 
bool
[Abstract feature]
would addition wrap_around.this + other cause an overflow or underflow?
would exponentiation 'this ** other' cause an overflow?
(other num.wrap_around.this)
 => 
bool
[Abstract feature]
would multiplication wrap_around.this * other cause an overflow or underflow?
(other num.wrap_around.this)
 => 
bool
[Abstract feature]
would subtraction wrap_around.this - other cause an overflow or underflow?
 => 
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.
 => 
numeric.this
[Inherited from  numeric]
basic operations: 'prefix +' (identity)
 => 
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.
negation, with check for overflow

redefines:

 => 
bool
[Redefinition of  numeric.prefix -!]
preconditions used in 'numeric' for basic operations: true if the
operation is permitted for the given values

redefines:

overflow checking operations

redefines:

saturating operations

redefines:

neg, add, sub, mul with wrap-around semantics
bitwise NOT

redefines:

 => 
integer.this
[Inherited from  integer]
bitwise NOT (Unicode alias)
 => 
i32
[Inherited from  numeric]
sign function resulting in `-1`/`0`/`+1` depending on whether `numeric.this`
is less than, equal or greater than zero
(other num.wrap_around.this)
 => 
bool
[Abstract feature]
(other num.wrap_around.this)
 => 
bool
[Abstract feature]
(other num.wrap_around.this)
 => 
bool
[Abstract feature]
 => 
bool
[Abstract feature]
would negation -wrap_around.this cause an overflow?

Type Functions

 => 
num.wrap_around.this.type
[Abstract feature]
returns the number in whose bit representation all bits are ones
 => 
String
[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:

how many bytes does this integer use?
 => 
Type
[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 property.orderable.this.type, b property.orderable.this.type)
 => 
bool
[Inherited from  orderable]
equality implements the default equality relation for values of this type.

This relation must be

- reflexive (equality a a),
- symmetric (equality a b = equality b a), and
- transitive ((equality a b && equality b c) : equality a c).

result is true iff 'a' is considered to represent the same abstract value
as 'b'.
(v u32)
 => 
numeric.this.type
[Inherited from  numeric]
the value corresponding to v in whatever integer implementation we have,
maximum in case of overflow
(a property.hashable.this.type)
 => 
u64
[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
)
 => 
bool
[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.


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


or

(a property.partially_orderable.this.type, b property.partially_orderable.this.type)
 => 
bool
[Inherited from  partially_orderable]
[Abstract feature]
does a come before b or is equal to b?
 => 
num.wrap_around.this.type
[Abstract feature]
maximum
 => 
num.wrap_around.this.type
[Abstract feature]
minimum
 => 
String
[Inherited from  Type]
name of this type, including type parameters, e.g. 'option (list i32)'.
 => 
numeric.this.type
[Inherited from  numeric]
[Abstract feature]
identity element for 'infix *'
 => 
String
[Inherited from  Type]
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.

NYI: Redefinition allows the type feature to be distinguished from its normal counterpart, see #3913

redefines:

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.
 => 
numeric.this.type
[Inherited from  numeric]
the constant '10' in whatever integer implementation we have, maximum in case of overflow
 => 
numeric.this.type
[Inherited from  numeric]
the constant '2' in whatever integer implementation we have, maximum in case of overflow
 => 
Type
[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`.
 => 
numeric.this.type
[Inherited from  numeric]
[Abstract feature]
identity element for 'infix +'

Applicable universe features

These are features in universe, that have an argument with a type constraint that matches this features type and can therefore be used with it.
(T 
type
:
property.equatable, a T, b T)
 => 
bool
equals -- feature that compares two values using the equality relation
defined in their type
(T 
type
:
property.hashable, a T)
 => 
u64
hash of a value
(T 
type
:
property.equatable, a T, b T)
 => 
bool
infix = -- infix operation as short-hand for 'equals'
(T 
type
:
property.orderable, a T, b T)
 => 
bool
does this come strictly before other?
infix <= -- infix operation as short-hand for 'lteq'
(T 
type
:
property.orderable, a T, b T)
 => 
order
three-way comparison between this and other.

result is < 0 if this < other
result is > 0 if this > other
result is = 0 if this = other
(T 
type
:
property.equatable, a T, b T)
 => 
bool
infix = -- infix operation as short-hand for 'equals'
(T 
type
:
property.orderable, a T, b T)
 => 
bool
does this come strictly after other?
(T 
type
:
property.orderable, a T, b T)
 => 
bool
does this come after other?
is `a` contained in `Set` `s`?

This should usually be called using type inference as in

is `a` not contained in `Set` `s`?

This should usually be called using type inference as in

(T 
type
:
property.equatable, a T, b T)
 => 
bool
infix ≟ -- infix operation as short-hand for 'equals'
infix ≤ -- infix operation as short-hand for 'lteq'
(T 
type
:
property.orderable, a T, b T)
 => 
bool
does this come after other?
(T 
type
:
property.orderable, a T, b T)
 => 
order
three-way comparison between this and other.

result is < 0 if this < other
result is > 0 if this > other
result is = 0 if this = other
(T 
type
:
property.orderable, a T, b T)
 => 
bool
does this come strictly before other?
(T 
type
:
property.orderable, a T, b T)
 => 
bool
does this come strictly after other?
(T 
type
:
property.partially_orderable, a T, b T)
 => 
bool
lteq -- feature that compares two values using the lteq relation
defined in their type
(T 
type
:
property.orderable, a T, b T)
 => 
T
maximum of two values
memoize `f`.
wraps f so that f will only be called once for every unique input.

The term "memoization" was coined by Donald Michie in 1968 and
is derived from the Latin word "memorandum" ("to be remembered"),
usually truncated as "memo" in American English, and thus carries
the meaning of "turning a function into something to be remembered".
https://en.wikipedia.org/wiki/Memoization

example:

(T 
type
:
property.orderable, a T, b T)
 => 
T
minimum of two values
0.095dev (2025-09-09 14:29:31 GIT hash 98644f8f651c2101a0730cfe31c5807993b7603b built by fridi@fzen)