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i16

i16

i16 -- 16-bit signed integer values

Value 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|)|`.

NYI: CLEANUP: Due to #3081, we need `postfix |` as the first operation, should be
`prefix |` first

Functions

§
:
Any
 => 
numeric.this 
[Inherited from  numeric]
absolute value
§
:
Any
 => 
array u8 
[Inherited from  wrap_around]
this integer as an array of bytes (little endian)
conversion to u32, i64 and u64, with range check
§
:
Any
 => 
String 
[Inherited from  integer]
convert this to a decimal number in a string. If negative, add "-" as
the first character.

redefines:

§(base u32)
:
encodings
 => 
String 
[Inherited from  integer]
convert this to a number using the given base. If negative, add "-" as
the first character.
§(len i32, base u32)
:
Any
 => 
String 
[Inherited from  integer]
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
§
:
Any
 => 
u8 
[Redefinition of numeric.as_u8]

redefines:

§
:
Any
 => 
String 
[Inherited from  integer]
create binary representation
§(len i32)
:
Any
 => 
String 
[Inherited from  integer]
create binary representation with given number of digits.
§
:
Any
 => 
String 
[Inherited from  integer]
create decimal representation
§(len i32)
:
Any
 => 
String 
[Inherited from  integer]
create decimal representation with given number of digits.
§
:
Any
 => 
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.
§
:
Any
 => 
bool 
[Redefinition of numeric.fits_in_u8]
does this i16 fit into an u8?

redefines:

§(b integer.this)
:
Any
 => 
integer.this 
[Inherited from  integer]
greatest common divisor of this and b

note that this assumes zero to be divisible by any positive integer.
§
:
Any
 => 
String 
[Inherited from  integer]
create hexadecimal representation
§(len i32)
:
Any
 => 
String 
[Inherited from  integer]
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 zero.
§(other i16)
:
Any
 => 
i16 
[Redefinition of numeric.infix %]

redefines:

§(other integer.this)
:
Any
 => 
bool 
[Inherited from  integer]

redefines:

§(other integer.this)
:
Any
 => 
bool 
[Inherited from  integer]
test divisibility by other
§(other i16)
:
Any
 => 
i16 
[Redefinition of integer.infix &]
bitwise and, or and xor operations

redefines:

multiplication, with check for overflow

redefines:


redefines:

exponentiation for positive exponent

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

redefines:


redefines:

exponentiation with overflow checking semantics

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

redefines:

exponentiation with saturating semantics

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

redefines:

exponentiation with wrap-around semantics

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

redefines:


redefines:

§(other i16)
:
Any
 => 
i16 
[Redefinition of num.wrap_around.infix *°]
addition, with check for overflow

redefines:


redefines:


redefines:


redefines:

§(other i16)
:
Any
 => 
i16 
[Redefinition of num.wrap_around.infix +°]
subtraction, with check for overflow

redefines:


redefines:


redefines:


redefines:

§(other i16)
:
Any
 => 
i16 
[Redefinition of num.wrap_around.infix -°]
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
§(other i16)
:
Any
 => 
i16 
[Redefinition of numeric.infix /]
division and remainder with check for div-by-zero

redefines:

§(other integer.this)
:
Any
 => 
bool 
[Inherited from  integer]
preconditions used in 'numeric' for basic operations: true if the
operation is permitted for the given values

redefines:

create a fraction
§(other i16)
:
Any
 => 
i16 
[Redefinition of integer.infix <<]

redefines:

§(other i16)
:
Any
 => 
i16 
[Redefinition of integer.infix >>]
shift operations (signed)

redefines:

§(other i16)
:
Any
 => 
i16 
[Redefinition of integer.infix ^]

redefines:

§(other i16)
:
Any
 => 
i16 
[Redefinition of integer.infix |]

redefines:

create a fraction via unicode fraction slash \u2044 '⁄ '
§
:
Any
 => 
bool 
[Inherited from  wrap_around]
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

redefines:

§
:
Any
 => 
bool 
[Inherited from  wrap_around]
§
:
Any
 => 
bool 
[Inherited from  wrap_around]
§
:
Any
 => 
bool 
[Inherited from  numeric]
§
:
Any
 => 
bool 
[Inherited from  numeric]
§
:
Any
 => 
u8 
[Redefinition of integer.low8bits]
casting to unsigned, adding 1<<16 if negative

redefines:

§
:
Any
 => 
String 
[Inherited from  integer]
create octal representation
§(len i32)
:
Any
 => 
String 
[Inherited from  integer]
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.
§
:
Any
 => 
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.
§
:
Any
 => 
numeric.this 
[Inherited from  numeric]
basic operations: 'prefix +' (identity)
§
:
Any
 => 
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.
negation, with check for overflow

redefines:

§
:
Any
 => 
bool 
[Inherited from  wrap_around]
preconditions used in 'numeric' for basic operations: true if the
operation is permitted for the given values

redefines:

overflow checking operations

redefines:

saturating operations

redefines:

neg, add, sub, mul with wrap-around semantics
bitwise NOT

redefines:

§
:
Any
 => 
integer.this 
[Inherited from  integer]
bitwise NOT (Unicode alias)
§
:
Any
 => 
i32 
[Inherited from  numeric]
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?

Value Types

§
:
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|)|`.

NYI: CLEANUP: Due to #3081, we need `postfix |` as the first operation, should be
`prefix |` first

Type Features

returns the number in whose bit representation all bits are ones
§
:
Any
 is
 
[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:

§
:
Any
 is
 
[Inherited from  wrap_around]
how many bytes does this integer use?
§
:
Any
 is
 
[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:

§(a i16, b i16)
:
Any
 is
 
[Redefinition of numeric.type.equality]
equality
§(v u32)
:
Any
 is
 
[Inherited from  numeric]
the value corresponding to v in whatever integer implementation we have,
maximum in case of overflow
§(a i16.this.type)
:
Any
 is
 
create hash code from this number
§(T 
type
)
:
Any
 is
 
[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

it is most useful in conjunction preconditions or `if` statements as in

pair(a,b T) is

=>

or

val(n T) is

§(a i16, b i16)
:
Any
 is
 
[Redefinition of numeric.type.lteq]
total order
maximum
minimum
§
:
Any
 is
 
[Inherited from  Type]
name of this type, including type parameters, e.g. 'option (list i32)'.
§
:
Any
 is
 
[Redefinition of numeric.type.one]
identity element for 'infix *'

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.
§
:
Any
 is
 
[Inherited from  numeric]
the constant '10' in whatever integer implementation we have, maximum in case of overflow
§
:
Any
 is
 
[Inherited from  numeric]
the constant '2' in whatever integer implementation we have, maximum in case of overflow
§
:
Any
 is
 
[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`.
§
:
Any
 is
 
[Redefinition of numeric.type.zero]
identity element for 'infix +'

redefines: