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float

float

:
numeric
 is
[Contains abstract features]
float -- floating point values


float is the abstract parent of concrete floating point features such as
f32 or f64.

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
 => 
float.this
[Abstract feature]
convert a float value to i32 dropping any fraction.
the value must be in the range of i32
 => 
i64
[Abstract feature]
convert a float value to i64 dropping any fraction.
the value must be in the range of i64
 => 
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`
 => 
u8
[Inherited from  numeric]
[Abstract feature]
this numeric value as an u8
 => 
float.this
[Abstract feature]
 => 
float.this
[Abstract feature]
ceiling: the smallest integer greater or equal to this
 => 
float.this
[Abstract feature]
 => 
float.this
[Abstract feature]
(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.
 => 
float.this
[Abstract feature]
the `val`-th power of ℇ
i.e. ℇᵛᵃˡ
 => 
i32
[Abstract feature]
the normalized exponent of this float
 => 
i32
[Abstract feature]
the biased exponent of this float
does this float value fit into an i64? This is redefined by children
of float that support `as_i64`.
 => 
bool
[Inherited from  numeric]
does this numeric value fit into an u8? This is redefined by children
of numeric that support `as_u8`.
floor: the greatest integer lower or equal to this
 => 
float.this
[Abstract feature]
(other numeric.this)
 => 
numeric.this
[Inherited from  numeric]
[Abstract feature]
basic operations: 'infix %' (division remainder)
(other numeric.this)
 => 
bool
[Inherited from  numeric]
(other numeric.this)
 => 
numeric.this
[Inherited from  numeric]
[Abstract feature]
basic operations: 'infix *' (multiplication)
(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]
(other numeric.this)
 => 
numeric.this
[Inherited from  numeric]
[Abstract feature]
basic operations: 'infix +' (addition)
(other numeric.this)
 => 
bool
[Inherited from  numeric]
(other numeric.this)
 => 
numeric.this
[Inherited from  numeric]
(other numeric.this)
 => 
numeric.this
[Inherited from  numeric]
[Abstract feature]
basic operations: 'infix -' (subtraction)
(other numeric.this)
 => 
bool
[Inherited from  numeric]
(other numeric.this)
 => 
numeric.this
[Inherited from  numeric]
(other numeric.this)
 => 
numeric.this
[Inherited from  numeric]
[Abstract feature]
basic operations: 'infix /' (division)
(other numeric.this)
 => 
bool
[Inherited from  numeric]
 => 
bool
[Abstract feature]
is not a number?
 => 
bool
[Inherited from  numeric]
 => 
bool
[Abstract feature]
is the bit denoting the sign of the number set?
this is different from smaller than zero since
there is +0, -0, NaN, etc. in floating point numbers.
 => 
bool
[Inherited from  numeric]
 => 
float.this
[Abstract feature]
logarithm with base ℇ
logarithm with base `base`
 => 
u64
[Abstract feature]
the normalized mantissa of this float
 => 
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.
 => 
numeric.this
[Inherited from  numeric]
basic operations: 'prefix -' (negation)
 => 
bool
[Inherited from  numeric]
overflow checking operations
 => 
numeric.this
[Inherited from  numeric]
saturating operations
round floating point number
ties to away (0.5 => 1; -0.5 => -1; etc.)

NYI: PERFORMANCE: this could be made faster, see here:
https://cs.opensource.google/go/go/+/refs/tags/go1.18.1:src/math/floor.go;l=79
 => 
i32
[Inherited from  numeric]
sign function resulting in `-1`/`0`/`+1` depending on whether `numeric.this`
is less than, equal or greater than zero
 => 
float.this
[Abstract feature]
 => 
float.this
[Abstract feature]
square root alias
 => 
float.this
[Abstract feature]
square root
 => 
float.this
[Abstract feature]
 => 
float.this
[Abstract feature]
 => 
bool
[Abstract feature]
true when the absolute value
is smaller than 0.001
or greater than 9_999_999

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:

(y float.this.type, x float.this.type)
 => 
float.this.type
[Abstract feature]
 => 
i32
[Abstract feature]
number of bytes required to store this value
 => 
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:

 => 
float.this.type
[Abstract feature]
(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'.
 => 
i32
[Abstract feature]
number of bits used for exponent
(val i64)
 => 
float.this.type
[Abstract feature]
convert an i64 value to a floating point value

if the value cannot be represented exactly, the result is either
the nearest higher or nearest lower value
(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)
 => 
float.this.type
infinity
(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?
the amount of bits that are used to encode the mantissa
 => 
float.this.type
[Abstract feature]
 => 
i32
[Abstract feature]
 => 
i32
[Abstract feature]
 => 
float.this.type
[Abstract feature]
 => 
String
[Inherited from  Type]
name of this type, including type parameters, e.g. 'option (list i32)'.
 => 
float.this.type
not a number
 => 
float.this.type
 => 
numeric.this.type
[Inherited from  numeric]
[Abstract feature]
identity element for 'infix *'
 => 
float.this.type
 => 
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.
 => 
float.this.type
non signaling not a number
 => 
i32
[Abstract feature]
number of bits used for mantissa,
including leading '1' that is not actually stored
number of bits required to store this value
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 +'
 => 
float.this.type
[Abstract feature]
pi 3.14...
 => 
float.this.type
[Abstract feature]
eulers number 2.72..

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)