The machinewords Module¶
Introduction¶
This chapter describes the Open Dylan implementation of machine words. It describes a number of extensions to the Dylan language, which are available from the Dylan library.
Throughout this chapter, arguments are instances of the class specified
by the argument name, unless otherwise noted. Thus, the arguments
machineword and integer are instances of <machineword>
and
<integer>
, respectively.
The class <machineword>
is a sealed subclass of <object>
,
defined in the Dylan library. The class <machineword>
represents a
limited range of integral values. The representation used has the natural
size suggested by the implementation architecture. (When running a 32 bit
OS, a <machineword>
is 32 bits wide. When running a 64 bit OS, then
<machineword>
is 64 bits wide.) The class <machineword>
is
disjoint from all other classes specified by the Dylan language.
The \\==
function compares instances of <machineword>
by value.
Useful functions from the Dylan module¶
This section describes additional methods defined in the Dylan module
that pertain to <machineword>
. Note that this section only describes
extensions to the Dylan library; for complete descriptions, you should
also refer to the Dylan Reference Manual.
Note that the Common Dylan library also has these extensions because it uses the Dylan library.

odd?
Function¶ Signature: odd? m => r
Parameters:  m – An instance of
<machineword>
Values:  r – An instance of
<boolean>
 m – An instance of

even?
Function¶ Signature: even? m => r
Parameters:  m – An instance of
<machineword>
Values:  r – An instance of
<boolean>
 m – An instance of

zero?
Function¶ Signature: zero? m => r
Parameters:  m – An instance of
<machineword>
Values:  r – An instance of
<boolean>
 m – An instance of
Note
Cannot be used as the name of a result. It is not a valid Dylan name.

positive?
Function¶ Signature: positive? m => r
Parameters:  m – An instance of
<machineword>
Values:  r – An instance of
<boolean>
 m – An instance of

negative?
Function¶ Signature: negative? m => r
Parameters:  m – An instance of
<machineword>
Values:  r – An instance of
<boolean>
 m – An instance of
These functions return a result based on interpreting m
as a signed
integer value.

=
Function¶ Signature: = m1 m2 => r
Signature: = i1 m2 => r
Signature: = m1 i2 => r
Parameters:  m1 – An instance of
<machineword>
 m2 – An instance of
<machineword>
 i1 – An instance of
<abstractinteger>
 i2 – An instance of
<abstractinteger>
Values:  r – An instance of
<boolean>
Discussion: The comparison is performed with the
<machineword>
arguments interpreted as signed integer values. m1 – An instance of

<
Function¶ Signature: < m1 m2 => r
Signature: < i1 m2 => r
Signature: < m1 i2 => r
Parameters:  m1 – An instance of
<machineword>
 m2 – An instance of
<machineword>
 i1 – An instance of
<abstractinteger>
 i2 – An instance of
<abstractinteger>
Values:  r – An instance of
<boolean>
Discussion: The comparison is performed with the
<machineword>
arguments interpreted as signed integer values. m1 – An instance of

as
Function¶ Signature: as t == <integer> m => r
Parameters:  m – An instance of
<machineword>
Values:  r – An instance of
<integer>
Discussion: The result is an
<integer>
with the same value asm
when interpreted as a signed integer value. An error is signaled if the value ofm
cannot be represented as an instance of<integer>
. m – An instance of

as
Function Signature: as t == <abstractinteger> m => r
Parameters:  m – An instance of
<machineword>
Values:  r – An instance of
<abstractinteger>
Discussion: The result is an
<abstractinteger>
with the same value asm
when interpreted as a signed integer value.(The uses for an instance of
<abstractinteger>
that is not also an instance of<integer>
are rather limited without the GenericArithmetic library.) m – An instance of

as
Function Signature: as t == <machineword> i => r
Parameters:  i – An instance of
<abstractinteger>
Values:  r – An instance of
<machineword>
Discussion: If the value of
i
is outside the machine word range, then the result consists of the low$machinewordsize
bits of the twoscomplement representation ofi
. If any of the discarded bits differ from the sign ofi
, then an error is signaled. i – An instance of

limited
Function¶ Signature: limited t == <machineword> #key signed? min max => r
Parameters:  signed? (#key) – An instance of
<boolean>
. Defaults to#t
 min (#key) – An instance of
<machineword>
 max (#key) – An instance of
<machineword>
Values:  r – An instance of
<type>
Discussion: If the
signed?
argument is true (the default) then themin
andmax
arguments are interpreted as signed values. Whensigned?
is false, themin
andmax
arguments are interpreted as unsigned values. The default value for each of min and max depends on the value ofsigned?
. The defaults are taken from the corresponding minimum and maximum machine word values (see$maximumsignedmachineword
and related constants below).For convenience, the values of
min
and/ormax
may also be instances of<abstractinteger>
, in which case they are coerced to instances of<machineword>
as if by using as. signed? (#key) – An instance of
The MACHINEWORDS module¶
This section contains a reference entry for each item exported from the MachineWords module, which is exported by the Common Dylan library.

<machineword>
Sealed Class¶ Summary: The class of objects that can represent a limited range of integral values. Superclasses: <object>
Discussion: The class <machineword>
represents a limited range of integral values. The representation used has the natural size suggested by the implementation architecture. The class<machineword>
is disjoint from all other classes specified by the Dylan language.Operations: The <machineword>
class provides the operations described below and in Useful functions from the Dylan module.
Variables¶
The following variables are exported from the MachineWords module.

$machinewordsize
Constant¶ Type: <integer>
Discussion: The number of bits in the representation of a <machineword>
.

$maximumsignedmachineword
Constant¶ Type: <machineword>
Discussion: The largest machine word, when interpreted as a signed integer value.

$minimumsignedmachineword
Constant¶ Type: <machineword>
Discussion: The smallest machine word, when interpreted as a signed integer value.

$maximumunsignedmachineword
Constant¶ Type: <machineword>
Discussion: The largest machine word, when interpreted as an unsigned integer value.

$minimumunsignedmachineword
Constant¶ Type: <machineword>
Discussion: The smallest machine word, when interpreted as an unsigned integer value.

asunsigned
Function¶ Signature: asunsigned t m => result
Parameters:  t – A type
 m – An instance of
<machineword>
Values:  result – An istance of
t
Discussion: The value of
m
is interpreted as an unsigned value and converted to an instance of<abstractinteger>
, then the result of that conversion is converted to typet
usingas
.
Basic and signed single word operations¶
For all of the following functions, all arguments that are specified as
being specialized to <machineword>
accept an instance of
<abstractinteger>
, which is then coerced to a <machineword>
before performing the operation.

%logior
Function¶ Signature: %logior #rest machinewords => r
Parameters:  machinewords (#rest) – An instance of
<machineword>
Values:  r – An instance of
<machineword>
 machinewords (#rest) – An instance of

%logxor
Function¶ Signature: %logxor #rest machinewords => r
Parameters:  machinewords (#rest) – An instance of
<machineword>
Values:  r – An instance of
<machineword>
 machinewords (#rest) – An instance of

%logand
Function¶ Signature: %logand #rest machinewords => r
Parameters:  machinewords (#rest) – An instance of
<machineword>
Values:  r – An instance of
<machineword>
 machinewords (#rest) – An instance of

%lognot
Function¶ Signature: %lognot m => r
Parameters:  m – An instance of
<machineword>
Values:  r – An instance of
<machineword>
 m – An instance of
These four functions have the same semantics as logior
, logxor
,
logand
, and lognot
in the Dylan library, but they operate on
<machineword>
s instead of <integer>
s.

%logbit?
Function¶ Signature: %logbit? index m => set?
Parameters:  index – An instance of
<integer>
 m – An instance of
<machineword>
Values:  set? – An instance of
<boolean>
Discussion: Returns true iff the indexed bit (zero based, counting from the least significant bit) of
m
is set. An error is signaled unless0 <= index < $machinewordsize
. index – An instance of

%countlowzeros
Function¶ Signature: %countlowzeros m => c
Parameters:  m – An instance of
<machineword>
Values:  c – An instance of
<integer>
Discussion: Returns the number of consecutive zero bits in
m
counting from the least significant bit. m – An instance of
Note
This is the position of the least significant nonzero bit in
m
. So if i
is the result, then %logbit?(i, m)
is true, and for
all values of j
such that 0 <= j < i
, %logbit?(j, m)
is false.

%counthighzeros
Function¶ Signature: %counthighzeros m => c
Parameters:  m – An instance of
<machineword>
 c – An instance of
<integer>
Discussion: Returns the number of consecutive zero bits in
m
counting from the most significant bit. m – An instance of
Note
The position of the most significant nonzero bit in m
can be
computed by subtracting this result from $machinewordsize  1
. So
if i
is the result and p = ($machinewordsize  i  1)
, then
%logbit?(p, m)
is true, and for all values of j
such that p < j <
$machinewordsize*, *%logbit?(j, m)
is false.

%countones
Function¶ Signature: %countones m => c
Parameters:  m – An instance of
<machineword>
.  c – An instance of
<integer>
.
Discussion: Returns the number of bits in m which have been set to 1.
 m – An instance of

%+
Function¶ Signature: %+ m1 m2 => sum overflow?
Parameters:  m1 – An instance of
<machineword>
 m2 – An instance of
<machineword>
Values:  sum – An instance of
<machineword>
 overflow? – An instance of
<boolean>
Discussion: Signed addition.
 m1 – An instance of

%
Function¶ Signature: % m1 m2 => difference overflow?
Parameters:  m1 – An instance of
<machineword>
 m2 – An instance of
<machineword>
Values:  difference – An instance of
<machineword>
 overflow? – An instance of
<boolean>
Discussion: Signed subtraction.
 m1 – An instance of

%*
Function¶ Signature: %* m1 m2 => low high overflow?
Parameters:  m1 – An instance of
<machineword>
 m2 – An instance of
<machineword>
Values:  low – An instance of
<machineword>
 high – An instance of
<machineword>
 overflow? – An instance of
<boolean>
Discussion: Signed multiplication. The value of
overflow?
is false iff thehigh
word result is a sign extension of thelow
word result. m1 – An instance of

%floor/
Function¶ Signature: %floor/ dividend divisor => quotient remainder
Parameters:  dividend – An instance of
<machineword>
 divisor – An instance of
<machineword>
Values:  quotient – An instance of
<machineword>
 remainder – An instance of
<machineword>
 dividend – An instance of

%ceiling/
Function¶ Signature: %ceiling/ dividend divisor => quotient remainder
Parameters:  dividend – An instance of
<machineword>
 divisor – An instance of
<machineword>
Values:  quotient – An instance of
<machineword>
 remainder – An instance of
<machineword>
 dividend – An instance of

%round/
Function¶ Signature: %round/ dividend divisor => quotient remainder
Parameters:  dividend – An instance of
<machineword>
 divisor – An instance of
<machineword>
Values:  quotient – An instance of
<machineword>
 remainder – An instance of
<machineword>
 dividend – An instance of

%truncate/
Function¶ Signature: %truncate/ dividend divisor => quotient remainder
Parameters:  dividend – An instance of
<machineword>
 divisor – An instance of
<machineword>
Values:  quotient – An instance of
<machineword>
 remainder – An instance of
<machineword>
 dividend – An instance of

%divide
Function¶ Signature: %divide/ dividend divisor => quotient remainder
Parameters:  dividend – An instance of
<machineword>
 divisor – An instance of
<machineword>
Values:  quotient – An instance of
<machineword>
 remainder – An instance of
<machineword>
 dividend – An instance of
The functions %divide
, %floor/
, %ceiling/
,
%round/
, and %truncate/
all perform signed division of the
dividend by the divisor, returning a quotient and remainder such that:
(quotient * divisor + remainder = dividend)
When the division is inexact (in other words, when the remainder is not zero), the kind of rounding depends on the operation:
%floor/
The quotient is rounded toward negative infinity.%ceiling/
The quotient is rounded toward positive infinity.%round/
The quotient is rounded toward the nearest integer. If the mathematical quotient is exactly halfway between two integers, then the resulting quotient is rounded to the nearest even integer.%truncate/
The quotient is rounded toward zero.%divide
If both operands are nonnegative, then the quotient is rounded toward zero. If either operand is negative, then the direction of rounding is unspecified, as is the sign of the remainder.
For all of these functions, an error is signaled if the value of the divisor is zero or if the correct value for the quotient exceeds the machine word range.

%negative
Function¶ Signature: %negative m => r overflow?
Parameters:  m – An instance of
<machineword>
Values:  r – An instance of
<machineword>
 overflow? – An instance of
<boolean>
 m – An instance of

%abs
Function¶ Signature: %abs m => r overflow?
Parameters:  m – An instance of
<machineword>
Values:  r – An instance of
<machineword>
 overflow? – An instance of
<boolean>
 m – An instance of

%shiftleft
Function¶ Signature: %shiftleft m count => low high overflow?
Parameters:  m – An instance of
<machineword>
 count – An instance of
<integer>
Values:  low – An instance of
<machineword>
 high – An instance of
<machineword>
 overflow? – An instance of
<boolean>
Discussion: Arithmetic left shift of
m
by count. An error is signaled unless0 <= count < $machinewordsize
. The value ofoverflow?
is false iff the high word result is a sign extension of the low word result. m – An instance of

%shiftright
Function¶ Signature: %shiftright m count => r
Parameters:  m – An instance of
<machineword>
 count – An instance of
<integer>
Values:  r – An instance of
<machineword>
Discussion: Arithmetic right shift of
m
bycount
. An error is signaled unless0 <= count < $machinewordsize
. m – An instance of
Overflow signalling operations¶
For all of the following functions, all arguments that are specified as
being specialized to <machineword>
accept an instance of
<abstractinteger>
, which is then coerced to a <machineword>
before performing the operation.

so%+
Function¶ Signature: so%+ m1 m2 => sum
Parameters:  m1 – An instance of
<machineword>
 m2 – An instance of
<machineword>
Values:  sum – An instance of
<machineword>
Discussion: Signed addition. An error is signaled on overflow.
 m1 – An instance of

so%
Function¶ Signature: so% m1 m2 => difference
Parameters:  m1 – An instance of
<machineword>
 m2 – An instance of
<machineword>
Values:  difference – An instance of
<machineword>
Discussion: Signed subtraction. An error is signaled on overflow.
 m1 – An instance of

so%*
Function¶ Signature: so%* m1 m2 => product
Parameters:  m1 – An instance of
<machineword>
 m2 – An instance of
<machineword>
Values:  product – An instance of
<machineword>
Discussion: Signed multiplication. An error is signaled on overflow.
 m1 – An instance of

so%negative
Function¶ Signature: so%negative m => r
Parameters:  m – An instance of
<machineword>
Values:  r – An instance of
<machineword>
Discussion: Negation. An error is signaled on overflow.
 m – An instance of

so%abs
Function¶ Signature: so%abs m => r
Parameters:  m – An instance of
<machineword>
Values:  r – An instance of
<machineword>
Discussion: Absolute value. An error is signaled on overflow.
 m – An instance of

so%shiftleft
Function¶ Signature: so%shiftleft m count => r
Parameters:  m – An instance of
<machineword>
 count – An instance of
<integer>
Values:  r – An instance of
<machineword>
Discussion: Arithmetic left shift of
m
bycount
. An error is signaled unless0 <= count < $machinewordsize
. An error is signaled on overflow. m – An instance of
Signed double word operations¶
For all of the following functions, all arguments that are specified as
being specialized to <machineword>
accept an instance of
<abstractinteger>
, which is then coerced to a <machineword>
before performing the operation.

d%floor/
Function¶ Signature: d%floor/ dividendlow dividendhigh divisor => quotient remainder
Parameters:  dividendlow – An instance of
<machineword>
 dividendhigh – An instance of
<machineword>
 divisor – An instance of
<machineword>
Values:  quotient – An instance of
<machineword>
 remainder – An instance of
<machineword>
 dividendlow – An instance of

d%ceiling/
Function¶ Signature: d%ceiling/ dividendlow dividendhigh divisor => quotient remainder
Parameters:  dividendlow – An instance of
<machineword>
 dividendhigh – An instance of
<machineword>
 divisor – An instance of
<machineword>
Values:  quotient – An instance of
<machineword>
 remainder – An instance of
<machineword>
 dividendlow – An instance of

d%round/
Function¶ Signature: d%round/ dividendlow dividendhigh divisor => quotient remainder
Parameters:  dividendlow – An instance of
<machineword>
 dividendhigh – An instance of
<machineword>
 divisor – An instance of
<machineword>
Values:  quotient – An instance of
<machineword>
 remainder – An instance of
<machineword>
 dividendlow – An instance of

d%truncate/
Function¶ Signature: d%truncate/ dividendlow dividendhigh divisor => quotient remainder
Parameters:  dividendlow – An instance of
<machineword>
 dividendhigh – An instance of
<machineword>
 divisor – An instance of
<machineword>
Values:  quotient – An instance of
<machineword>
 remainder – An instance of
<machineword>
 dividendlow – An instance of

d%divide
Function¶ Signature: d%divide dividendlow dividendhigh divisor => quotient remainder
Parameters:  dividendlow – An instance of
<machineword>
 dividendhigh – An instance of
<machineword>
 divisor – An instance of
<machineword>
Values:  quotient – An instance of
<machineword>
 remainder – An instance of
<machineword>
 dividendlow – An instance of
The functions d%divide
, d%floor/
, d%ceiling/
,
d%round/
, and d%truncate/
all perform signed division of the
double word dividend by the divisor, returning a quotient and remainder such
that
(quotient * divisor + remainder = dividend)
When the division is inexact (in other words, when the remainder is not zero), the kind of rounding depends on the operation:
d%floor/
The quotient is rounded toward negative infinity.d%ceiling/
The quotient is rounded toward positive infinity.d%round/
The quotient is rounded toward the nearest integer. If the mathematical quotient is exactly halfway between two integers then the resulting quotient is rounded to the nearest even integer.d%truncate/
The quotient is rounded toward zero.d%divide
If both operands are nonnegative, then the quotient is rounded toward zero. If either operand is negative, then the direction of rounding is unspecified, as is the sign of the remainder.
For all of these functions, an error is signaled if the value of the divisor is zero or if the correct value for the quotient exceeds the machine word range.
Unsigned single word operations¶
For all of the following functions, all arguments that are specified as
being specialized to <machineword>
accept an instance of
<abstractinteger>
, which is then coerced to a <machineword>
before performing the operation.

u%+
Function¶ Signature: u%+ m1 m2 => sum carry
Parameters:  m1 – An instance of
<machineword>
 m2 – An instance of
<machineword>
Values:  sum – An instance of
<machineword>
 carry – An instance of
<machineword>
Discussion: Unsigned addition. The value represented by
carry
is either 0 or 1. m1 – An instance of

u%
Function¶ Signature: u% m1 m2 => sum borrow
Parameters:  m1 – An instance of
<machineword>
 m2 – An instance of
<machineword>
Values:  sum – An instance of
<machineword>
 borrow – An instance of
<machineword>
Discussion: Unsigned subtraction. The value represented by
borrow
is either 0 or 1. m1 – An instance of

u%*
Function¶ Signature: u%* m1 m2 => low high
Parameters:  m1 – An instance of
<machineword>
 m2 – An instance of
<machineword>
Values:  low – An instance of
<machineword>
 high – An instance of
<machineword>
Discussion: Unsigned multiplication.
 m1 – An instance of

u%divide
Function¶ Signature: u%divide dividend divisor => quotient remainder
Parameters:  dividend – An instance of
<machineword>
 divisor – An instance of
<machineword>
Values:  quotient – An instance of
<machineword>
 remainder – An instance of
<machineword>
Discussion: Performs unsigned division of the dividend by the divisor, returning a quotient and remainder such that
(quotient * divisor + remainder = dividend)
An error is signaled if the value of the
divisor
is zero. dividend – An instance of

u%rotateleft
Function¶ Signature: u%rotateleft m count => r
Parameters:  m – An instance of
<machineword>
 count – An instance of
<integer>
Values:  r – An instance of
<machineword>
Discussion: Logical left rotation of
m
bycount
. An error is signaled unless0 <= count < $machinewordsize
. m – An instance of

u%rotateright
Function¶ Signature: u%rotateright m count => r
Parameters:  m – An instance of
<machineword>
 count – An instance of
<integer>
Values:  r – An instance of
<machineword>
Discussion: Logical right rotation of
m
bycount
. An error is signaled unless0 <= count < $machinewordsize
. m – An instance of

u%shiftleft
Function¶ Signature: u%shiftleft m count => r
Parameters:  m – An instance of
<machineword>
 count – An instance of
<integer>
Values:  r – An instance of
<machineword>
Discussion: Logical left shift of
m
bycount
. An error is signaled unless0 <= count < $machinewordsize
. m – An instance of

u%shiftright
Function¶ Signature: u%shiftright m count => r
Parameters:  m – An instance of
<machineword>
 count – An instance of
<integer>
Values:  r – An instance of
<machineword>
Discussion: Logical right shift of
m
bycount
. An error is signaled unless0 <= count < $machinewordsize
. m – An instance of

u%<
Function¶ Signature: u%< m1 m2 => smaller?
Parameters:  m1 – An instance of
<machineword>
 m2 – An instance of
<machineword>
Values:  smaller? – An instance of
<boolean>
Discussion: Unsigned comparison.
 m1 – An instance of
Unsigned double word operations¶
For all of the following functions, all arguments that are specified as
being specialized to <machineword>
accept an instance of
<abstractinteger>
, which is then coerced to a <machineword>
before performing the operation.

ud%divide
Function¶ Signature: ud%divide dividendlow dividendhigh divisor => quotient remainder
Parameters:  dividendlow – An instance of
<machineword>
 dividendhigh – An instance of
<machineword>
 divisor – An instance of
<machineword>
Values:  quotient – An instance of
<machineword>
 remainder – An instance of
<machineword>
Discussion: Performs unsigned division of the double word dividend by the
divisor
, returning aquotient
andremainder
such that(quotient * divisor + remainder = dividend)
An error is signaled if the value of the
divisor
is zero or if the correct value for thequotient
exceeds the machine word range. dividendlow – An instance of

ud%shiftleft
Function¶ Signature: ud%shiftleft low high count => low high
Parameters:  low – An instance of
<machineword>
 high – An instance of
<machineword>
 count – An instance of
<integer>
Values:  low – An instance of
<machineword>
 high – An instance of
<machineword>
Discussion: Logical left shift by
count
of the double word value represented bylow
andhigh
. An error is signaled unless0 <= count < $machinewordsize
. low – An instance of

ud%shiftright
Function¶ Signature: ud%shiftright low high count => low high
Parameters:  low – An instance of
<machineword>
 high – An instance of
<machineword>
 count – An instance of
<integer>
Values:  low – An instance of
<machineword>
 high – An instance of
<machineword>
Discussion: Logical right shift by
count
of the double word value represented bylow
andhigh
. An error is signaled unless0 <= count < $machinewordsize
. low – An instance of