☰
float
float
Value 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|)|`.
NYI: CLEANUP: Due to #3081, we need `postfix |` as the first operation, should be
`prefix |` first
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
convert a float value to i32 dropping any fraction.
the value must be in the range of i32
the value must be in the range of i32
convert a float value to i64 dropping any fraction.
the value must be in the range of i64
the value must be in the range of i64
create a String from this instance. Unless redefined, `a.as_string` will
create `"instance[T]"` where `T` is the dynamic type of `a`
create `"instance[T]"` where `T` is the dynamic type of `a`
ceiling: the smallest integer greater or equal to this
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.
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`.
of float that support `as_i64`.
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`.
floor: the greatest integer lower or equal to this
basic operations: 'infix %' (division remainder)
basic operations: 'infix *' (multiplication)
basic operations: 'infix **' (exponentiation)
basic operations: 'infix +' (addition)
basic operations: 'infix -' (subtraction)
basic operations: 'infix /' (division)
comparison
This provides comparison operators using IEEE semantics.
type.equality and type.lteq should be used for equivalence relations
and total ordering in the mathematical sense.
This provides comparison operators using IEEE semantics.
type.equality and type.lteq should be used for equivalence relations
and total ordering in the mathematical sense.
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.
this is different from smaller than zero since
there is +0, -0, NaN, etc. in floating point numbers.
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.
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.
round floating point number
ties to away (0.5 => 1; -0.5 => -1; etc.)
NYI this could be made faster, see here:
https://cs.opensource.google/go/go/+/refs/tags/go1.18.1:src/math/floor.go;l=79
ties to away (0.5 => 1; -0.5 => -1; etc.)
NYI this could be made faster, see here:
https://cs.opensource.google/go/go/+/refs/tags/go1.18.1:src/math/floor.go;l=79
sign function resulting in `-1`/`0`/`+1` depending on whether `numeric.this`
is less than, equal or larger than zero
is less than, equal or larger than zero
true when the absolute value
is smaller than 0.001
or greater than 9_999_999
is smaller than 0.001
or greater than 9_999_999
Value Types
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
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
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
number of bytes required to store this value
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
This provides an equivalence relation in the mathematical
sense and therefore breaks the IEEE semantics. infix = should
be used for IEEE semantics.
The equivalence relation is provided by the usual comparison
of floating-point numbers, with the definition of NaN = NaN.
This provides an equivalence relation in the mathematical
sense and therefore breaks the IEEE semantics. infix = should
be used for IEEE semantics.
The equivalence relation is provided by the usual comparison
of floating-point numbers, with the definition of NaN = NaN.
number of bits used for exponent
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
if the value cannot be represented exactly, the result is either
the nearest higher or nearest lower value
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)
infinity
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
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
is not a number?
total order
This provides a total order in the mathematical sense and
therefore breaks the IEEE semantics. infix <= should be
used for IEEE semantics.
The total order is provided by the usual comparison of
floating-point numbers, with the definition that NaN <= x,
for any x (including x = NaN).
This provides a total order in the mathematical sense and
therefore breaks the IEEE semantics. infix <= should be
used for IEEE semantics.
The total order is provided by the usual comparison of
floating-point numbers, with the definition that NaN <= x,
for any x (including x = NaN).
the amount of bits that are used to encode the mantissa
name of this type, including type parameters, e.g. 'option (list i32)'.
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.
non signaling not a number
number of bits used for mantissa,
including leading '1' that is not actually stored
including leading '1' that is not actually stored
square root
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`.
float is the abstract parent of concrete floating point features such as
f32 or f64.