

 
Manual Reference Pages  DATA::INTEGER (3)
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NAME
Data::Integer  details of the native integer data type
CONTENTS
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 leastsignificant 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 mostsignificant bit, which for a 32bit machine
therefore has the value 2^31 (2147483648). The unsigned format cannot
represent any negative numbers.
In the signed format, the mostsignificant bit is exceptional, having
the negation of the value that it does in the unsigned format. Thus on
a 32bit machine this has the value 2^31 (2147483648). Values with
this bit set are negative, and those with it clear are nonnegative;
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 extremevalue 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 extremevalue constants are actually nonconstant 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 leftshifted 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 moresignificant 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 lesssignificant 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 rightshifting a negative number always gives a negative result.

sint_rol(A, DIST)


uint_rol(A, DIST)

Bitwise left rotation (towards moresignificant bits, with the
mostsignificant bit wrapping round to the leastsignificant 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 lesssignificant bits, with the
leastsignificant bit wrapping round to the mostsignificant bit).
DIST is the distance to rotate, in bits, and must be an integer in
the range [0, natint_bits).


Format conversion
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 mostsignificant 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 mostsignificant bit (whether a sign bit
or not) becomes an ordinary mostsignificant bit.

sint_bits_as_uint(A)

Converts a signed integer to an unsigned integer, by reinterpreting
the bits. The sign bit becomes an ordinary mostsignificant bit.

uint_bits_as_sint(A)

Converts an unsigned integer to a signed integer, by reinterpreting
the bits. The mostsignificant 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 nonzero 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 welldefined 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 "s<B>0xB>dddd, 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][<B>0xB>]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 dies.
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 noninteger
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, 2015 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.
perl v5.20.3  DATA::INTEGER (3)  20160317 
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