u128

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

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.

convert this to a number using the given base. If negative, add "-" as
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

create binary representation

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.

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.

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.

test divisibility by other

bitwise and, or and xor operations

multiplication, with check for overflow

exponentiation for positive exponent

'zero ** zero' is permitted and results in 'one'.

exponentiation with overflow checking semantics

'zero **? zero' is permitted and results in 'one'.

exponentiation with saturating semantics

'zero **^ zero' is permitted and results in 'one'.

exponentiation with wrap-around semantics

'zero **° zero' is permitted and results in 'one'.

addition, with check for overflow

subtraction, with check for overflow

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

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

create a fraction

shift operations (unsigned)

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

create octal representation

create octal representation with given number of digits.

count the number of 1 bits in the binary representation of this
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

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.

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: '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.

negation, with check for overflow

preconditions used in 'numeric' for basic operations: true if the
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 larger than zero

count the number of trailing zeros in this integer.

would negation cause an overflow?

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

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

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.

equality

the value corresponding to v in whatever integer implementation we have,
maximum in case of overflow

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

=>

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 *'

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.

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`.

identity element for 'infix +'