»
integer
integer
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|)|`.
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
absolute value
convert this to a decimal number in a string. If negative, add "-" as
the first character.
the first character.
convert this to a number using the given base. If negative, add "-" as
the first character.
the first character.
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
the first character. Extend with leading "0" until the length is at
least len
this numeric value as an u8
create binary representation with given number of digits.
create decimal representation with given number of digits.
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.
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`.
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.
note that this assumes zero to be divisible by any positive integer.
create hexadecimal representation with given number of digits.
(other numeric.this) => numeric.this[Inherited from numeric][Abstract feature][Contains abstract features]¶
(other numeric.this)
=>
numeric.this[Inherited from numeric]
[Abstract feature]
[Contains abstract features]
¶basic operations: 'infix %' (division remainder)
test divisibility by other
bitwise operations
(other numeric.this) => numeric.this[Inherited from numeric][Abstract feature][Contains abstract features]¶
(other numeric.this)
=>
numeric.this[Inherited from numeric]
[Abstract feature]
[Contains abstract features]
¶basic operations: 'infix *' (multiplication)
(other numeric.this) => numeric.this[Inherited from numeric][Abstract feature][Contains abstract features]¶
(other numeric.this)
=>
numeric.this[Inherited from numeric]
[Abstract feature]
[Contains abstract features]
¶basic operations: 'infix **' (exponentiation)
(other numeric.this) => option numeric.this[Inherited from numeric][Abstract feature][Contains abstract features]¶
(other numeric.this)
=>
option numeric.this[Inherited from numeric]
[Abstract feature]
[Contains abstract features]
¶(other numeric.this) => numeric.this[Inherited from numeric][Abstract feature][Contains abstract features]¶
(other numeric.this)
=>
numeric.this[Inherited from numeric]
[Abstract feature]
[Contains abstract features]
¶(other numeric.this) => numeric.this[Inherited from numeric][Abstract feature][Contains abstract features]¶
(other numeric.this)
=>
numeric.this[Inherited from numeric]
[Abstract feature]
[Contains abstract features]
¶basic operations: 'infix +' (addition)
(other numeric.this) => numeric.this[Inherited from numeric][Abstract feature][Contains abstract features]¶
(other numeric.this)
=>
numeric.this[Inherited from numeric]
[Abstract feature]
[Contains abstract features]
¶basic operations: 'infix -' (subtraction)
(other numeric.this) => numeric.this[Inherited from numeric][Abstract feature][Contains abstract features]¶
(other numeric.this)
=>
numeric.this[Inherited from numeric]
[Abstract feature]
[Contains abstract features]
¶basic operations: 'infix /' (division)
preconditions used in 'numeric' for basic operations: true if the
operation is permitted for the given values
operation is permitted for the given values
create a fraction
shift operations
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
returns false unless redefined by a specific implementation of integer
the least significant byte of this integer
create octal representation with given number of digits.
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.
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.
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
bitwise NOT
bitwise NOT (Unicode alias)
sign function resulting in `-1`/`0`/`+1` depending on whether `numeric.this`
is less than, equal or greater than zero
is less than, equal or greater than zero
Type Functions
string representation of this type to be used for debugging.
result has the form "Type of '<name>'", but this might change in the future
result has the form "Type of '<name>'", but this might change in the future
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.
endless hierarchy of types, so dynamic_type is redefined to just return
Type.type here.
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'.
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'.
the value corresponding to v in whatever integer implementation we have,
maximum in case of overflow
maximum in case of overflow
create hash code for this instance
This should satisfy the following condition:
(T.equality a b) : (T.hash_code a = T.hash_code b)
This should satisfy the following condition:
(T.equality a b) : (T.hash_code a = T.hash_code b)
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
same
pre T : property.equatable
=>
a = b
or
val(n T) is
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
same
pre T : property.equatable
=>
a = b
or
val(n T) is
(a property.partially_orderable.this.type, b property.partially_orderable.this.type) => bool[Inherited from partially_orderable][Abstract feature][Contains abstract features]¶
(a property.partially_orderable.this.type, b property.partially_orderable.this.type)
=>
bool[Inherited from partially_orderable]
[Abstract feature]
[Contains abstract features]
¶does a come before b or is equal to b?
name of this type, including type parameters, e.g. 'option (list i32)'.
identity element for 'infix *'
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
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
monoid of numeric with infix * operation. Will create product of all elements
it is applied to.
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.
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.
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.
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
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`.
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`.
0.094dev (2025-06-18 15:08:51 GIT hash 89cffc23ae669b0898a5564fefbf793fcb8e5ca7 built by fridi@fzen)
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.