NAME¶
Data::Integer - details of the native integer data type
SYNOPSIS¶
use Data::Integer qw(natint_bits);
$n = natint_bits;
# and other constants; see text
use Data::Integer qw(nint sint uint nint_is_sint nint_is_uint);
$ni = nint($ni);
$si = sint($si);
$ui = uint($ui);
if(nint_is_sint($ni)) { ...
if(nint_is_uint($ni)) { ...
use Data::Integer qw(
nint_sgn sint_sgn uint_sgn
nint_abs sint_abs uint_abs
nint_cmp sint_cmp uint_cmp
nint_min sint_min uint_min
nint_max sint_max uint_max
nint_neg sint_neg uint_neg
nint_add sint_add uint_add
nint_sub sint_sub uint_sub
);
$sn = nint_sgn($ni);
$sn = sint_sgn($si);
$sn = uint_sgn($ui);
$ni = nint_abs($ni);
$si = sint_abs($si);
$ui = uint_abs($ui);
@sorted_nints = sort { nint_cmp($a, $b) } @nints;
@sorted_sints = sort { sint_cmp($a, $b) } @sints;
@sorted_uints = sort { uint_cmp($a, $b) } @uints;
$ni = nint_min($na, $nb);
$si = sint_min($sa, $sb);
$ui = uint_min($ua, $ub);
$ni = nint_max($na, $nb);
$si = sint_max($sa, $sb);
$ui = uint_max($ua, $ub);
$ni = nint_neg($ni);
$si = sint_neg($si);
$ui = uint_neg($ui);
$ni = nint_add($na, $nb);
$si = sint_add($sa, $sb);
$ui = uint_add($ua, $ub);
$ni = nint_sub($na, $nb);
$si = sint_sub($sa, $sb);
$ui = uint_sub($ua, $ub);
use Data::Integer qw(
sint_shl uint_shl
sint_shr uint_shr
sint_rol uint_rol
sint_ror uint_ror
);
$si = sint_shl($si, $dist);
$ui = uint_shl($ui, $dist);
$si = sint_shr($si, $dist);
$ui = uint_shr($ui, $dist);
$si = sint_rol($si, $dist);
$ui = uint_rol($ui, $dist);
$si = sint_ror($si, $dist);
$ui = uint_ror($ui, $dist);
use Data::Integer qw(
nint_bits_as_sint nint_bits_as_uint
sint_bits_as_uint uint_bits_as_sint
);
$si = nint_bits_as_sint($ni);
$ui = nint_bits_as_uint($ni);
$ui = sint_bits_as_uint($si);
$si = uint_bits_as_sint($ui);
use Data::Integer qw(
sint_not uint_not
sint_and uint_and
sint_nand uint_nand
sint_andn uint_andn
sint_or uint_or
sint_nor uint_nor
sint_orn uint_orn
sint_xor uint_xor
sint_nxor uint_nxor
sint_mux uint_mux
);
$si = sint_not($si);
$ui = uint_not($ui);
$si = sint_and($sa, $sb);
$ui = uint_and($ua, $ub);
$si = sint_nand($sa, $sb);
$ui = uint_nand($ua, $ub);
$si = sint_andn($sa, $sb);
$ui = uint_andn($ua, $ub);
$si = sint_or($sa, $sb);
$ui = uint_or($ua, $ub);
$si = sint_nor($sa, $sb);
$ui = uint_nor($ua, $ub);
$si = sint_orn($sa, $sb);
$ui = uint_orn($ua, $ub);
$si = sint_xor($sa, $sb);
$ui = uint_xor($ua, $ub);
$si = sint_nxor($sa, $sb);
$ui = uint_nxor($ua, $ub);
$si = sint_mux($sa, $sb, $sc);
$ui = uint_mux($ua, $ub, $uc);
use Data::Integer qw(
sint_madd uint_madd
sint_msub uint_msub
sint_cadd uint_cadd
sint_csub uint_csub
sint_sadd uint_sadd
sint_ssub uint_ssub
);
$si = sint_madd($sa, $sb);
$ui = uint_madd($ua, $ub);
$si = sint_msub($sa, $sb);
$ui = uint_msub($ua, $ub);
($carry, $si) = sint_cadd($sa, $sb, $carry);
($carry, $ui) = uint_cadd($ua, $ub, $carry);
($carry, $si) = sint_csub($sa, $sb, $carry);
($carry, $ui) = uint_csub($ua, $ub, $carry);
$si = sint_sadd($sa, $sb);
$ui = uint_sadd($ua, $ub);
$si = sint_ssub($sa, $sb);
$ui = uint_ssub($ua, $ub);
use Data::Integer qw(natint_hex hex_natint);
print natint_hex($value);
$value = hex_natint($string);
DESCRIPTION¶
This module is about the native integer numerical data type. A native integer is
one of the types of datum that can appear in the numeric part of a Perl
scalar. This module supplies constants describing the native integer type.
There are actually two native integer representations: signed and unsigned. Both
are handled by this module.
NATIVE INTEGERS¶
Each native integer format represents a value using binary place value, with
some fixed number of bits. The number of bits is the same for both signed and
unsigned representations. In each case the least-significant bit has the value
1, the next 2, the next 4, and so on. In the unsigned representation, this
pattern continues up to and including the most-significant bit, which for a
32-bit machine therefore has the value 2^31 (2147483648). The unsigned format
cannot represent any negative numbers.
In the signed format, the most-significant bit is exceptional, having the
negation of the value that it does in the unsigned format. Thus on a 32-bit
machine this has the value -2^31 (-2147483648). Values with this bit set are
negative, and those with it clear are non-negative; this bit is also known as
the "sign bit".
It is usual in machine arithmetic to use one of these formats at a time, for
example to add two signed numbers yielding a signed result. However, Perl has
a trick: a scalar with a native integer value contains an additional flag bit
which indicates whether the signed or unsigned format is being used. It is
therefore possible to mix signed and unsigned numbers in arithmetic, at some
extra expense.
CONSTANTS¶
Each of the extreme-value constants has two names, a short one and a long one.
The short names are more convenient to use, but the long names are clearer in
a context where other similar constants exist.
Due to the risks of Perl changing the behaviour of a native integer value that
has been involved in floating point arithmetic (see "BUGS"), the
extreme-value constants are actually non-constant functions that always return
a fresh copy of the appropriate value. The returned value is always a pure
native integer value, unsullied by floating point or string operations.
- natint_bits
- The width, in bits, of the native integer data types.
- min_nint
- min_natint
- The minimum representable value in either representation. This is
-2^(natint_bits - 1).
- max_nint
- max_natint
- The maximum representable value in either representation. This is
2^natint_bits - 1.
- min_sint
- min_signed_natint
- The minimum representable value in the signed representation. This is
-2^(natint_bits - 1).
- max_sint
- max_signed_natint
- The maximum representable value in the signed representation. This is
2^(natint_bits - 1) - 1.
- min_uint
- min_unsigned_natint
- The minimum representable value in the unsigned representation. This is
zero.
- max_uint
- max_unsigned_natint
- The maximum representable value in the unsigned representation. This is
2^natint_bits - 1.
FUNCTIONS¶
Each "nint_", "sint_", or "uint_" function
operates on one of the three integer formats. "nint_" functions
operate on Perl's union of signed and unsigned; "sint_" functions
operate on signed integers; and "uint_" functions operate on
unsigned integers. Except where indicated otherwise, the function returns a
value of its primary type.
Parameters
A,
B, and
C, where present, must be numbers of
the appropriate type: specifically, with a numerical value that can be
represented in that type. If there are multiple flavours of zero, due to
floating point funkiness, all zeroes are treated the same. Parameters with
other names have other requirements, explained with each function.
The functions attempt to detect unsuitable arguments, and "die" if an
invalid argument is detected, but they can't notice some kinds of incorrect
argument. Generally, it is the caller's responsibility to provide a sane
numerical argument, and supplying an invalid argument will cause mayhem. Only
the numeric value of plain scalar arguments is used; the string value is
completely ignored, so dualvars are not a problem.
Canonicalisation and classification¶
These are basic glue functions.
- nint(A)
- sint(A)
- uint(A)
- These functions each take an argument in a specific integer format and
return its numerical value. This is the argument canonicalisation that is
performed by all of the functions in this module, presented in
isolation.
- nint_is_sint(A)
- Takes a native integer of either type. Returns a truth value indicating
whether this value can be exactly represented as a signed native
integer.
- nint_is_uint(A)
- Takes a native integer of either type. Returns a truth value indicating
whether this value can be exactly represented as an unsigned native
integer.
Arithmetic¶
These functions operate on numerical values rather than just bit patterns. They
will all "die" if the true numerical result doesn't fit into the
result format, rather than give a wrong answer.
- nint_sgn(A)
- sint_sgn(A)
- uint_sgn(A)
- Returns +1 if the argument is positive, 0 if the argument is zero, or -1
if the argument is negative.
- nint_abs(A)
- sint_abs(A)
- uint_abs(A)
- Absolute value (magnitude, discarding sign).
- nint_cmp(A, B)
- sint_cmp(A, B)
- uint_cmp(A, B)
- Arithmetic comparison. Returns -1, 0, or +1, indicating whether A is less
than, equal to, or greater than B.
- nint_min(A, B)
- sint_min(A, B)
- uint_min(A, B)
- Arithmetic minimum. Returns the arithmetically lesser of the two
arguments.
- nint_max(A, B)
- sint_max(A, B)
- uint_max(A, B)
- Arithmetic maximum. Returns the arithmetically greater of the two
arguments.
- nint_neg(A)
- sint_neg(A)
- uint_neg(A)
- Negation: returns -A.
- nint_add(A, B)
- sint_add(A, B)
- uint_add(A, B)
- Addition: returns A + B.
- nint_sub(A, B)
- sint_sub(A, B)
- uint_sub(A, B)
- Subtraction: returns A - B.
Bit shifting¶
These functions all operate on the bit patterns representing integers, mostly
ignoring the numerical values represented. In most cases the results for
particular numerical arguments are influenced by the word size, because that
determines where a bit being left-shifted will drop off the end of the word
and where a bit will be shifted in during a rightward shift.
With the exception of rightward shifts (see below), each pair of functions
performs exactly the same operations on the bit sequences. There inevitably
can't be any functions here that operate on Perl's union of signed and
unsigned; you must choose, by which function you call, which type the result
is to be tagged as.
- sint_shl(A, DIST)
- uint_shl(A, DIST)
- Bitwise left shift (towards more-significant bits). DIST is the
distance to shift, in bits, and must be an integer in the range [0,
natint_bits). Zeroes are shifted in from the right.
- sint_shr(A, DIST)
- uint_shr(A, DIST)
- Bitwise right shift (towards less-significant bits). DIST is the
distance to shift, in bits, and must be an integer in the range [0,
natint_bits).
When performing an unsigned right shift, zeroes are shifted in from the
left. A signed right shift is different: the sign bit gets duplicated, so
right-shifting a negative number always gives a negative result.
- sint_rol(A, DIST)
- uint_rol(A, DIST)
- Bitwise left rotation (towards more-significant bits, with the
most-significant bit wrapping round to the least-significant bit).
DIST is the distance to rotate, in bits, and must be an integer in
the range [0, natint_bits).
- sint_ror(A, DIST)
- uint_ror(A, DIST)
- Bitwise right rotation (towards less-significant bits, with the
least-significant bit wrapping round to the most-significant bit).
DIST is the distance to rotate, in bits, and must be an integer in
the range [0, natint_bits).
These functions convert between the various native integer formats by
reinterpreting the bit patterns used to represent the integers. The bit
pattern remains unchanged; its meaning changes, and so the numerical value
changes. Perl scalars preserve the numerical value, rather than just the bit
pattern, so from the Perl point of view these are functions that change
numbers into other numbers.
- nint_bits_as_sint(A)
- Converts a native integer of either type to a signed integer, by
reinterpreting the bits. The most-significant bit (whether a sign bit or
not) becomes a sign bit.
- nint_bits_as_uint(A)
- Converts a native integer of either type to an unsigned integer, by
reinterpreting the bits. The most-significant bit (whether a sign bit or
not) becomes an ordinary most-significant bit.
- sint_bits_as_uint(A)
- Converts a signed integer to an unsigned integer, by reinterpreting the
bits. The sign bit becomes an ordinary most-significant bit.
- uint_bits_as_sint(A)
- Converts an unsigned integer to a signed integer, by reinterpreting the
bits. The most-significant bit becomes a sign bit.
Bitwise operations¶
These functions all operate on the bit patterns representing integers,
completely ignoring the numerical values represented. They are mostly not
influenced by the word size, in the sense that they will produce the same
numerical result for the same numerical arguments regardless of word size.
However, a few are affected by the word size: those on unsigned operands that
return a non-zero result if given zero arguments.
Each pair of functions performs exactly the same operations on the bit
sequences. There inevitably can't be any functions here that operate on Perl's
union of signed and unsigned; you must choose, by which function you call,
which type the result is to be tagged as.
- sint_not(A)
- uint_not(A)
- Bitwise complement (NOT).
- sint_and(A, B)
- uint_and(A, B)
- Bitwise conjunction (AND).
- sint_nand(A, B)
- uint_nand(A, B)
- Bitwise inverted conjunction (NAND).
- sint_andn(A, B)
- uint_andn(A, B)
- Bitwise conjunction with inverted argument (A AND (NOT B)).
- sint_or(A, B)
- uint_or(A, B)
- Bitwise disjunction (OR).
- sint_nor(A, B)
- uint_nor(A, B)
- Bitwise inverted disjunction (NOR).
- sint_orn(A, B)
- uint_orn(A, B)
- Bitwise disjunction with inverted argument (A OR (NOT B)).
- sint_xor(A, B)
- uint_xor(A, B)
- Bitwise symmetric difference (XOR).
- sint_nxor(A, B)
- uint_nxor(A, B)
- Bitwise symmetric similarity (NXOR).
- sint_mux(A, B, C)
- uint_mux(A, B, C)
- Bitwise multiplex. The output has a bit from B wherever A has a 1 bit, and
a bit from C wherever A has a 0 bit. That is, the result is (A AND B) OR
((NOT A) AND C).
Machine arithmetic¶
These functions perform arithmetic operations that are inherently influenced by
the word size. They always produce a well-defined output if given valid
inputs. There inevitably can't be any functions here that operate on Perl's
union of signed and unsigned; you must choose, by which function you call,
which type the result is to be tagged as.
- sint_madd(A, B)
- uint_madd(A, B)
- Modular addition. The result for unsigned addition is (A + B) mod
2^natint_bits. The signed version behaves similarly, but with a different
result range.
- sint_msub(A, B)
- uint_msub(A, B)
- Modular subtraction. The result for unsigned subtraction is (A - B) mod
2^natint_bits. The signed version behaves similarly, but with a different
result range.
- sint_cadd(A, B, CARRY_IN)
- uint_cadd(A, B, CARRY_IN)
- Addition with carry. Two word arguments (A and B) and an input carry bit
(CARRY_IN, which must have the value 0 or 1) are all added together.
Returns a list of two items: an output carry and an output word (of the
same signedness as the inputs). Precisely, the output list (CARRY_OUT, R)
is such that CARRY_OUT*2^natint_bits + R = A + B + CARRY_IN.
- sint_csub(A, B, CARRY_IN)
- uint_csub(A, B, CARRY_IN)
- Subtraction with carry (borrow). The second word argument (B) and an input
carry bit (CARRY_IN, which must have the value 0 or 1) are subtracted from
the first word argument (A). Returns a list of two items: an output carry
and an output word (of the same signedness as the inputs). Precisely, the
output list (CARRY_OUT, R) is such that R - CARRY_OUT*2^natint_bits = A -
B - CARRY_IN.
- sint_sadd(A, B)
- uint_sadd(A, B)
- Saturating addition. The result is A + B if that will fit into the result
format, otherwise the minimum or maximum value of the result format is
returned depending on the direction in which the addition overflowed.
- sint_ssub(A, B)
- uint_ssub(A, B)
- Saturating subtraction. The result is A - B if that will fit into the
result format, otherwise the minimum or maximum value of the result format
is returned depending on the direction in which the subtraction
overflowed.
String conversion¶
- natint_hex(VALUE)
- VALUE must be a native integer value. The function encodes VALUE in
hexadecimal, returning that representation as a string. Specifically, the
output is of the form " s0xdddd", where
" s" is the sign and " dddd" is a
sequence of hexadecimal digits.
- hex_natint(STRING)
- Generates and returns a native integer value from a string encoding it in
hexadecimal. Specifically, the input format is "[
s][0x] dddd", where " s" is the
sign and " dddd" is a sequence of one or more hexadecimal
digits. The input is interpreted case insensitively. If the value given in
the string cannot be exactly represented in the native integer type, the
function "die"s.
The core Perl function "hex" (see "hex" in perlfunc)
does a similar job to this function, but differs in several ways.
Principally, "hex" doesn't handle negative values, and it gives
the wrong answer for values that don't fit into the native integer type.
In Perl 5.6 it also gives the wrong answer for values that don't fit into
the native floating point type. It also doesn't enforce strict syntax on
the input string.
BUGS¶
In Perl 5.6, when a native integer scalar is used in any arithmetic other than
specifically integer arithmetic, it gets partially transformed into a floating
point scalar. Even if its numerical value can be represented exactly in
floating point, so that floating point arithmetic uses the correct numerical
value, some operations are affected by the floatness. In particular, the
stringification of the scalar doesn't necessarily represent its exact value if
it is tagged as floating point.
Because of this transforming behaviour, if you need to stringify a native
integer it is best to ensure that it doesn't get used in any non-integer
arithmetic first. If an integer scalar must be used in standard Perl
arithmetic, it may be copied first and the copy operated upon to avoid causing
side effects on the original. If an integer scalar might have already been
transformed, it can be cleaned by passing it through the canonicalisation
function "nint". The functions in this module all avoid modifying
their arguments, and always return pristine integers.
Perl 5.8+ still internally modifies integer scalars in the same circumstances,
but seems to have corrected all the misbehaviour that resulted from it.
Also in Perl 5.6, default Perl arithmetic doesn't necessarily work correctly on
native integers. (This is part of the motivation for the myriad arithmetic
functions in this module.) Default arithmetic here is strictly floating point,
so if there are native integers that cannot be exactly represented in floating
point then the arithmetic will approximate the values before operating on
them. Perl 5.8+ attempts to use native integer operations where possible in
its default arithmetic, but as of Perl 5.8.8 it doesn't always succeed. For
reliable integer arithmetic, integer operations must still be requested
explicitly.
SEE ALSO¶
Data::Float, Scalar::Number,
perlnumber(1)
AUTHOR¶
Andrew Main (Zefram) <zefram@fysh.org>
COPYRIGHT¶
Copyright (C) 2007, 2010 Andrew Main (Zefram) <zefram@fysh.org>
LICENSE¶
This module is free software; you can redistribute it and/or modify it under the
same terms as Perl itself.