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fraction

num.fraction

(B 
type
:
integer, numerator B, denominator B)
:
numeric
 is
[Contains abstract features]
fraction


fraction provides fraction numbers based on an integer type to represent the
numerator and the denominator.

basic numeric operations +, -, * and comparison are supported. numerator and
denominator are reduced after each operation.

there are currently no checks or preconditions for overflows in the numerator
or the denominator.

Type Parameters

Fields

numerator
 B
denominator
 B

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
 => 
String
[Redefinition of  Any.as_string]

redefines:

 => 
u8
[Inherited from  numeric]
[Abstract feature]
this numeric value as an u8
 => 
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`.
(other numeric.this)
 => 
numeric.this
[Inherited from  numeric]
[Abstract feature]
basic operations: 'infix %' (division remainder)
(other numeric.this)
 => 
bool
[Inherited from  numeric]

redefines:

(other numeric.this)
 => 
bool
[Inherited from  numeric]
(other numeric.this)
 => 
numeric.this
[Inherited from  numeric]
[Abstract feature]
basic operations: 'infix **' (exponentiation)
(other numeric.this)
 => 
bool
[Inherited from  numeric]
(other numeric.this)
 => 
option numeric.this
[Inherited from  numeric]
[Abstract feature]
(other numeric.this)
 => 
numeric.this
[Inherited from  numeric]
[Abstract feature]
(other numeric.this)
 => 
numeric.this
[Inherited from  numeric]

redefines:

(other numeric.this)
 => 
bool
[Inherited from  numeric]
(other numeric.this)
 => 
numeric.this
[Inherited from  numeric]

redefines:

(other numeric.this)
 => 
bool
[Inherited from  numeric]
(other numeric.this)
 => 
numeric.this
[Inherited from  numeric]

redefines:

(other numeric.this)
 => 
bool
[Inherited from  numeric]
 => 
bool
[Inherited from  numeric]
 => 
bool
[Inherited from  numeric]
 => 
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

redefines:

 => 
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.

redefines:

 => 
bool
[Inherited from  numeric]
overflow checking operations
 => 
numeric.this
[Inherited from  numeric]
saturating operations
reduce numerator and denominator by their gcd:
 => 
i32
[Inherited from  numeric]
sign function resulting in `-1`/`0`/`+1` depending on whether `numeric.this`
is less than, equal or greater than zero

Type Functions

 => 
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:

 => 
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:

equality
(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.

is_of_integer_type(n T : numeric) => T : integer
say (is_of_integer_type 1234) # true
say (is_of_integer_type 3.14) # false
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
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it is most useful in conjunction preconditions or `if` statements as in

pair(a,b T) is
same
pre T : property.equatable
=>
a = b
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
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or

val(n T) is
# check if T is numeric, if so
# return true if n > zero,
# return nil if T is not numeric
#
more_than_zero option bool =>
if T : numeric then
n > T.zero
else
nil
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
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total order
 => 
String
[Inherited from  Type]
name of this type, including type parameters, e.g. 'option (list i32)'.
identity element for 'infix *'

redefines:

 => 
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`.
identity element for 'infix +'

redefines:

0.094dev (2025-07-10 15:41:47 GIT hash eafa42ae743de61b62f958948d7abb5fada7756f built by fridi@fzen)