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u128
u128
u128 -- 128-bit unsigned integer values
Fields
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
this integer as an array of bytes (little endian)
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
create binary representation with given number of digits.
create decimal representation
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 u128 fit into an 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
create hexadecimal representation with given number of digits.
find the highest 1 bit in this integer and return integer with
this single bit set or 0 if this is 0.
this single bit set or 0 if this is 0.
test divisibility by other
bitwise and, or and xor operations
(other num.this.wrap_around.this) => num.this.wrap_around.this[Inherited from wrap_around][Contains abstract features]¶
(other num.this.wrap_around.this)
=>
num.this.wrap_around.this[Inherited from wrap_around]
[Contains abstract features]
¶multiplication, with check for overflow
(other num.this.wrap_around.this) => num.this.wrap_around.this[Inherited from wrap_around][Contains abstract features]¶
(other num.this.wrap_around.this)
=>
num.this.wrap_around.this[Inherited from wrap_around]
[Contains abstract features]
¶exponentiation for positive exponent
'zero ** zero' is permitted and results in 'one'.
'zero ** zero' is permitted and results in 'one'.
(other num.this.wrap_around.this) => option num.this.wrap_around.this[Inherited from wrap_around][Contains abstract features]¶
(other num.this.wrap_around.this)
=>
option num.this.wrap_around.this[Inherited from wrap_around]
[Contains abstract features]
¶exponentiation with overflow checking semantics
'zero **? zero' is permitted and results in 'one'.
'zero **? zero' is permitted and results in 'one'.
(other num.this.wrap_around.this) => num.this.wrap_around.this[Inherited from wrap_around][Contains abstract features]¶
(other num.this.wrap_around.this)
=>
num.this.wrap_around.this[Inherited from wrap_around]
[Contains abstract features]
¶exponentiation with saturating semantics
'zero **^ zero' is permitted and results in 'one'.
'zero **^ zero' is permitted and results in 'one'.
(other num.this.wrap_around.this) => num.this.wrap_around.this[Inherited from wrap_around][Contains abstract features]¶
(other num.this.wrap_around.this)
=>
num.this.wrap_around.this[Inherited from wrap_around]
[Contains abstract features]
¶exponentiation with wrap-around semantics
'zero **° zero' is permitted and results in 'one'.
'zero **° zero' is permitted and results in 'one'.
(other num.this.wrap_around.this) => option num.this.wrap_around.this[Inherited from wrap_around][Contains abstract features]¶
(other num.this.wrap_around.this)
=>
option num.this.wrap_around.this[Inherited from wrap_around]
[Contains abstract features]
¶(other num.this.wrap_around.this) => num.this.wrap_around.this[Inherited from wrap_around][Contains abstract features]¶
(other num.this.wrap_around.this)
=>
num.this.wrap_around.this[Inherited from wrap_around]
[Contains abstract features]
¶(other num.this.wrap_around.this) => num.this.wrap_around.this[Inherited from wrap_around][Contains abstract features]¶
(other num.this.wrap_around.this)
=>
num.this.wrap_around.this[Inherited from wrap_around]
[Contains abstract features]
¶addition, with check for overflow
(other num.this.wrap_around.this) => option num.this.wrap_around.this[Inherited from wrap_around][Contains abstract features]¶
(other num.this.wrap_around.this)
=>
option num.this.wrap_around.this[Inherited from wrap_around]
[Contains abstract features]
¶(other num.this.wrap_around.this) => num.this.wrap_around.this[Inherited from wrap_around][Contains abstract features]¶
(other num.this.wrap_around.this)
=>
num.this.wrap_around.this[Inherited from wrap_around]
[Contains abstract features]
¶(other num.this.wrap_around.this) => num.this.wrap_around.this[Inherited from wrap_around][Contains abstract features]¶
(other num.this.wrap_around.this)
=>
num.this.wrap_around.this[Inherited from wrap_around]
[Contains abstract features]
¶subtraction, with check for overflow
(other num.this.wrap_around.this) => option num.this.wrap_around.this[Inherited from wrap_around][Contains abstract features]¶
(other num.this.wrap_around.this)
=>
option num.this.wrap_around.this[Inherited from wrap_around]
[Contains abstract features]
¶(other num.this.wrap_around.this) => num.this.wrap_around.this[Inherited from wrap_around][Contains abstract features]¶
(other num.this.wrap_around.this)
=>
num.this.wrap_around.this[Inherited from wrap_around]
[Contains abstract features]
¶(through has_interval.this) => interval has_interval.this[Inherited from has_interval][Contains abstract features]¶
(through has_interval.this)
=>
interval has_interval.this[Inherited from has_interval]
[Contains abstract features]
¶defining an integer interval from this to other, both inclusive
special cases of interval a..b:
a < b: the interval from a to b, both inclusive
a == b: the interval containing only one element, a
a > b: an empty interval
special cases of interval a..b:
a < b: the interval from a to b, both inclusive
a == b: the interval containing only one element, a
a > b: an empty interval
division and remainder with check for div-by-zero
preconditions used in 'numeric' for basic operations: true if the
operation is permitted for the given values
operation is permitted for the given values
(other integer.this) => num.fraction integer.this[Inherited from integer][Contains abstract features]¶
(other integer.this)
=>
num.fraction integer.this[Inherited from integer]
[Contains abstract features]
¶create a fraction
shift operations (unsigned)
(other integer.this) => num.fraction integer.this[Inherited from integer][Contains abstract features]¶
(other integer.this)
=>
num.fraction integer.this[Inherited from integer]
[Contains abstract features]
¶create a fraction via unicode fraction slash \u2044 '⁄ '
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
wrap_arounds are assumed to be a bound set by default, so
this returns true unless redefined by an implementation
create octal representation with given number of digits.
count the number of 1 bits in the binary representation of this
integer.
integer.
would addition + other cause an overflow or underflow?
would exponentiation 'this ** other' cause an overflow?
would multiplication * other cause an overflow or underflow?
would subtraction - other cause an overflow or underflow?
an infinite integer Sequence starting from this up to the maximum value
has_interval.this.max
has_interval.this.max
an infinite integer Sequence starting from this up to the maximum value
has_interval.this.max
NYI: CLEANUP: Eventually remove `postfix ..` or `postfix ..∞` in favor of the
other one, for now this is here to show that `∞` is a legal symbol in an operator.
has_interval.this.max
NYI: CLEANUP: Eventually remove `postfix ..` or `postfix ..∞` in favor of the
other one, for now this is here to show that `∞` is a legal symbol in an operator.
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.
negation, with check for overflow
preconditions used in 'numeric' for basic operations: true if the
operation is permitted for the given values
operation is permitted for the given values
overflow checking operations
saturating operations
neg, add, sub, mul with wrap-around semantics
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
count the number of trailing zeros in this integer.
would negation cause an overflow?
Type Functions
returns the number in whose bit representation all bits are ones
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
how many bytes does this integer use?
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.
(a u128, b u128) => bool[Redefinition of property.orderable.type.equality][Contains abstract features]¶
(a u128, b u128)
=>
bool[Redefinition of property.orderable.type.equality]
[Contains abstract features]
¶equality
the value corresponding to v in whatever integer implementation we have,
maximum in case of overflow
maximum in case of overflow
(a u128.this.type) => u64[Redefinition of property.hashable.type.hash_code][Contains abstract features]¶
(a u128.this.type)
=>
u64[Redefinition of property.hashable.type.hash_code]
[Contains abstract features]
¶create hash code from this number
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
total order
maximum
minimum
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`.
identity element for 'infix +'
0.094dev (2025-06-18 15:08:51 GIT hash 89cffc23ae669b0898a5564fefbf793fcb8e5ca7 built by fridi@fzen)