perlfaq4 - Data Manipulation ($Revision: 1.73 $, $Date: 2005/12/31 00:54:37 $)
This section of the FAQ answers questions related to manipulating numbers, dates, strings, arrays, hashes, and miscellaneous data issues.
Internally, your computer represents floating-point numbers in binary. Digital (as in powers of two) computers cannot store all numbers exactly. Some real numbers lose precision in the process. This is a problem with how computers store numbers and affects all computer languages, not just Perl.
perlnumber show the gory details of number representations and conversions.
To limit the number of decimal places in your numbers, you can use the printf or sprintf function. See the Floating Point Arithmetic for more details.
Your int() is most probably working just fine. It's the numbers that aren't quite what you think.
First, see the above item "Why am I getting long decimals (eg, 19.9499999999999) instead of the numbers I should be getting (eg, 19.95)?".
For example, this
will in most computers print 0, not 1, because even such simple numbers as 0.6 and 0.2 cannot be presented exactly by floating-point numbers. What you think in the above as 'three' is really more like 2.9999999999999995559.
Perl only understands octal and hex numbers as such when they occur as literals in your program. Octal literals in perl must start with a leading "0" and hexadecimal literals must start with a leading "0x". If they are read in from somewhere and assigned, no automatic conversion takes place. You must explicitly use oct() or hex() if you want the values converted to decimal. oct() interprets hex ("0x350"), octal ("0350" or even without the leading "0", like "377") and binary ("0b1010") numbers, while hex() only converts hexadecimal ones, with or without a leading "0x", like "0x255", "3A", "ff", or "deadbeef". The inverse mapping from decimal to octal can be done with either the "%o" or "%O" sprintf() formats.
This problem shows up most often when people try using chmod(), mkdir(), umask(), or sysopen(), which by widespread tradition typically take permissions in octal.
Note the mistake in the first line was specifying the decimal literal 644, rather than the intended octal literal 0644. The problem can be seen with:
- printf("%#o",644); # prints 01204
Surely you had not intended chmod(01204, $file);
- did you? If you
want to use numeric literals as arguments to chmod() et al. then please
try to express them as octal constants, that is with a leading zero and
with the following digits restricted to the set 0..7.
Remember that int() merely truncates toward 0. For rounding to a certain number of digits, sprintf() or printf() is usually the easiest route.
- printf("%.3f", 3.1415926535); # prints 3.142
The POSIX module (part of the standard Perl distribution) implements ceil(), floor(), and a number of other mathematical and trigonometric functions.
- use POSIX;
- $ceil = ceil(3.5); # 4
- $floor = floor(3.5); # 3
In 5.000 to 5.003 perls, trigonometry was done in the Math::Complex module. With 5.004, the Math::Trig module (part of the standard Perl distribution) implements the trigonometric functions. Internally it uses the Math::Complex module and some functions can break out from the real axis into the complex plane, for example the inverse sine of 2.
Rounding in financial applications can have serious implications, and the rounding method used should be specified precisely. In these cases, it probably pays not to trust whichever system rounding is being used by Perl, but to instead implement the rounding function you need yourself.
To see why, notice how you'll still have an issue on half-way-point alternation:
- for ($i = 0; $i < 1.01; $i += 0.05) { printf "%.1f ",$i}
- 0.0 0.1 0.1 0.2 0.2 0.2 0.3 0.3 0.4 0.4 0.5 0.5 0.6 0.7 0.7
- 0.8 0.8 0.9 0.9 1.0 1.0
Don't blame Perl. It's the same as in C. IEEE says we have to do this. Perl numbers whose absolute values are integers under 2**31 (on 32 bit machines) will work pretty much like mathematical integers. Other numbers are not guaranteed.
As always with Perl there is more than one way to do it. Below are a few examples of approaches to making common conversions between number representations. This is intended to be representational rather than exhaustive.
Some of the examples below use the Bit::Vector module from CPAN. The reason you might choose Bit::Vector over the perl built in functions is that it works with numbers of ANY size, that it is optimized for speed on some operations, and for at least some programmers the notation might be familiar.
Using perl's built in conversion of 0x notation:
- $dec = 0xDEADBEEF;
Using the hex function:
- $dec = hex("DEADBEEF");
Using pack:
Using the CPAN module Bit::Vector:
- use Bit::Vector;
- $vec = Bit::Vector->new_Hex(32, "DEADBEEF");
- $dec = $vec->to_Dec();
Using sprintf:
Using unpack:
Using Bit::Vector:
- use Bit::Vector;
- $vec = Bit::Vector->new_Dec(32, -559038737);
- $hex = $vec->to_Hex();
And Bit::Vector supports odd bit counts:
- use Bit::Vector;
- $vec = Bit::Vector->new_Dec(33, 3735928559);
- $vec->Resize(32); # suppress leading 0 if unwanted
- $hex = $vec->to_Hex();
Using Perl's built in conversion of numbers with leading zeros:
- $dec = 033653337357; # note the leading 0!
Using the oct function:
- $dec = oct("33653337357");
Using Bit::Vector:
Using sprintf:
- $oct = sprintf("%o", 3735928559);
Using Bit::Vector:
Perl 5.6 lets you write binary numbers directly with the 0b notation:
- $number = 0b10110110;
Using oct:
Using pack and ord:
Using pack and unpack for larger strings:
Using Bit::Vector:
- $vec = Bit::Vector->new_Bin(32, "11011110101011011011111011101111");
- $dec = $vec->to_Dec();
Using sprintf (perl 5.6+):
- $bin = sprintf("%b", 3735928559);
Using unpack:
Using Bit::Vector:
- use Bit::Vector;
- $vec = Bit::Vector->new_Dec(32, -559038737);
- $bin = $vec->to_Bin();
The remaining transformations (e.g. hex -> oct, bin -> hex, etc.) are left as an exercise to the inclined reader.
The behavior of binary arithmetic operators depends on whether they're
used on numbers or strings. The operators treat a string as a series
of bits and work with that (the string "3"
is the bit pattern
00110011
). The operators work with the binary form of a number
(the number 3
is treated as the bit pattern 00000011
).
So, saying 11 & 3
performs the "and" operation on numbers (yielding
3
). Saying "11" & "3"
performs the "and" operation on strings
(yielding "1"
).
Most problems with &
and |
arise because the programmer thinks
they have a number but really it's a string. The rest arise because
the programmer says:
- if ("\020\020" & "\101\101") {
- # ...
- }
but a string consisting of two null bytes (the result of "\020\020"
& "\101\101"
) is not a false value in Perl. You need:
- if ( ("\020\020" & "\101\101") !~ /[^\000]/) {
- # ...
- }
Use the Math::Matrix or Math::MatrixReal modules (available from CPAN) or the PDL extension (also available from CPAN).
To call a function on each element in an array, and collect the results, use:
- @results = map { my_func($_) } @array;
For example:
- @triple = map { 3 * $_ } @single;
To call a function on each element of an array, but ignore the results:
- foreach $iterator (@array) {
- some_func($iterator);
- }
To call a function on each integer in a (small) range, you can use:
- @results = map { some_func($_) } (5 .. 25);
but you should be aware that the ..
operator creates an array of
all integers in the range. This can take a lot of memory for large
ranges. Instead use:
- @results = ();
- for ($i=5; $i < 500_005; $i++) {
- push(@results, some_func($i));
- }
This situation has been fixed in Perl5.005. Use of ..
in a for
loop will iterate over the range, without creating the entire range.
will not create a list of 500,000 integers.
Get the http://www.cpan.org/modules/by-module/Roman module.
If you're using a version of Perl before 5.004, you must call srand
once at the start of your program to seed the random number generator.
- BEGIN { srand() if $] < 5.004 }
5.004 and later automatically call srand
at the beginning. Don't
call srand
more than once---you make your numbers less random, rather
than more.
Computers are good at being predictable and bad at being random (despite appearances caused by bugs in your programs :-). see the random article in the "Far More Than You Ever Wanted To Know" collection in http://www.cpan.org/misc/olddoc/FMTEYEWTK.tgz , courtesy of Tom Phoenix, talks more about this. John von Neumann said, "Anyone who attempts to generate random numbers by deterministic means is, of course, living in a state of sin."
If you want numbers that are more random than rand
with srand
provides, you should also check out the Math::TrulyRandom module from
CPAN. It uses the imperfections in your system's timer to generate
random numbers, but this takes quite a while. If you want a better
pseudorandom generator than comes with your operating system, look at
"Numerical Recipes in C" at http://www.nr.com/ .
rand($x)
returns a number such that
0 <= rand($x) < $x
. Thus what you want to have perl
figure out is a random number in the range from 0 to the
difference between your X and Y.
That is, to get a number between 10 and 15, inclusive, you want a random number between 0 and 5 that you can then add to 10.
Hence you derive the following simple function to abstract
that. It selects a random integer between the two given
integers (inclusive), For example: random_int_in(50,120)
.
The localtime function returns the day of the year. Without an argument localtime uses the current time.
- $day_of_year = (localtime)[7];
The POSIX module can also format a date as the day of the year or week of the year.
To get the day of year for any date, use the Time::Local module to get a time in epoch seconds for the argument to localtime.
The Date::Calc module provides two functions to calculate these.
Use the following simple functions:
On some systems, the POSIX module's strftime() function has
been extended in a non-standard way to use a %C
format,
which they sometimes claim is the "century". It isn't,
because on most such systems, this is only the first two
digits of the four-digit year, and thus cannot be used to
reliably determine the current century or millennium.
(contributed by brian d foy)
You could just store all your dates as a number and then subtract. Life isn't always that simple though. If you want to work with formatted dates, the Date::Manip, Date::Calc, or DateTime modules can help you.
If it's a regular enough string that it always has the same format,
you can split it up and pass the parts to timelocal
in the standard
Time::Local module. Otherwise, you should look into the Date::Calc
and Date::Manip modules from CPAN.
(contributed by brian d foy and Dave Cross)
You can use the Time::JulianDay module available on CPAN. Ensure that you really want to find a Julian day, though, as many people have different ideas about Julian days. See http://www.hermetic.ch/cal_stud/jdn.htm for instance.
You can also try the DateTime module, which can convert a date/time to a Julian Day.
- $ perl -MDateTime -le'print DateTime->today->jd'
- 2453401.5
Or the modified Julian Day
- $ perl -MDateTime -le'print DateTime->today->mjd'
- 53401
Or even the day of the year (which is what some people think of as a Julian day)
- $ perl -MDateTime -le'print DateTime->today->doy'
- 31
(contributed by brian d foy)
Use one of the Date modules. The DateTime
module makes it simple, and
give you the same time of day, only the day before.
You can also use the Date::Calc
module using its Today_and_Now
function.
Most people try to use the time rather than the calendar to figure out dates, but that assumes that days are twenty-four hours each. For most people, there are two days a year when they aren't: the switch to and from summer time throws this off. Let the modules do the work.
Short answer: No, Perl does not have a Year 2000 problem. Yes, Perl is Y2K compliant (whatever that means). The programmers you've hired to use it, however, probably are not.
Long answer: The question belies a true understanding of the issue. Perl is just as Y2K compliant as your pencil--no more, and no less. Can you use your pencil to write a non-Y2K-compliant memo? Of course you can. Is that the pencil's fault? Of course it isn't.
The date and time functions supplied with Perl (gmtime and localtime) supply adequate information to determine the year well beyond 2000 (2038 is when trouble strikes for 32-bit machines). The year returned by these functions when used in a list context is the year minus 1900. For years between 1910 and 1999 this happens to be a 2-digit decimal number. To avoid the year 2000 problem simply do not treat the year as a 2-digit number. It isn't.
When gmtime() and localtime() are used in scalar context they return
a timestamp string that contains a fully-expanded year. For example,
$timestamp = gmtime(1005613200)
sets $timestamp to "Tue Nov 13 01:00:00
2001". There's no year 2000 problem here.
That doesn't mean that Perl can't be used to create non-Y2K compliant programs. It can. But so can your pencil. It's the fault of the user, not the language. At the risk of inflaming the NRA: "Perl doesn't break Y2K, people do." See http://www.perl.org/about/y2k.html for a longer exposition.
(contributed by brian d foy)
There are many ways to ensure that values are what you expect or
want to accept. Besides the specific examples that we cover in the
perlfaq, you can also look at the modules with "Assert" and "Validate"
in their names, along with other modules such as Regexp::Common
.
Some modules have validation for particular types of input, such
as Business::ISBN
, Business::CreditCard
, Email::Valid
,
and Data::Validate::IP
.
It depends just what you mean by "escape". URL escapes are dealt
with in perlfaq9. Shell escapes with the backslash (\
)
character are removed with
- s/\\(.)/$1/g;
This won't expand "\n"
or "\t"
or any other special escapes.
(contributed by brian d foy)
You can use the substitution operator to find pairs of characters (or
runs of characters) and replace them with a single instance. In this
substitution, we find a character in (.)
. The memory parentheses
store the matched character in the back-reference \1
and we use
that to require that the same thing immediately follow it. We replace
that part of the string with the character in $1
.
- s/(.)\1/$1/g;
We can also use the transliteration operator, tr///
. In this
example, the search list side of our tr///
contains nothing, but
the c
option complements that so it contains everything. The
replacement list also contains nothing, so the transliteration is
almost a no-op since it won't do any replacements (or more exactly,
replace the character with itself). However, the s
option squashes
duplicated and consecutive characters in the string so a character
does not show up next to itself
- my $str = 'Haarlem'; # in the Netherlands
- $str =~ tr///cs; # Now Harlem, like in New York
(contributed by brian d foy)
This is documented in perlref, and although it's not the easiest thing to read, it does work. In each of these examples, we call the function inside the braces used to dereference a reference. If we have a more than one return value, we can construct and dereference an anonymous array. In this case, we call the function in list context.
- print "The time values are @{ [localtime] }.\n";
If we want to call the function in scalar context, we have to do a bit more work. We can really have any code we like inside the braces, so we simply have to end with the scalar reference, although how you do that is up to you, and you can use code inside the braces.
If your function already returns a reference, you don't need to create the reference yourself.
The Interpolation
module can also do a lot of magic for you. You can
specify a variable name, in this case E
, to set up a tied hash that
does the interpolation for you. It has several other methods to do this
as well.
In most cases, it is probably easier to simply use string concatenation, which also forces scalar context.
This isn't something that can be done in one regular expression, no
matter how complicated. To find something between two single
characters, a pattern like /x([^x]*)x/
will get the intervening
bits in $1. For multiple ones, then something more like
/alpha(.*?)omega/
would be needed. But none of these deals with
nested patterns. For balanced expressions using (
, {
, [
or
<
as delimiters, use the CPAN module Regexp::Common, or see
(??{ code }) in perlre. For other cases, you'll have to write a
parser.
If you are serious about writing a parser, there are a number of modules or oddities that will make your life a lot easier. There are the CPAN modules Parse::RecDescent, Parse::Yapp, and Text::Balanced; and the byacc program. Starting from perl 5.8 the Text::Balanced is part of the standard distribution.
One simple destructive, inside-out approach that you might try is to pull out the smallest nesting parts one at a time:
- while (s/BEGIN((?:(?!BEGIN)(?!END).)*)END//gs) {
- # do something with $1
- }
A more complicated and sneaky approach is to make Perl's regular expression engine do it for you. This is courtesy Dean Inada, and rather has the nature of an Obfuscated Perl Contest entry, but it really does work:
Use reverse() in scalar context, as documented in reverse.
- $reversed = reverse $string;
You can do it yourself:
- 1 while $string =~ s/\t+/' ' x (length($&) * 8 - length($`) % 8)/e;
Or you can just use the Text::Tabs module (part of the standard Perl distribution).
- use Text::Tabs;
- @expanded_lines = expand(@lines_with_tabs);
Use Text::Wrap (part of the standard Perl distribution):
The paragraphs you give to Text::Wrap should not contain embedded newlines. Text::Wrap doesn't justify the lines (flush-right).
Or use the CPAN module Text::Autoformat. Formatting files can be easily done by making a shell alias, like so:
- alias fmt="perl -i -MText::Autoformat -n0777 \
- -e 'print autoformat $_, {all=>1}' $*"
See the documentation for Text::Autoformat to appreciate its many capabilities.
You can access the first characters of a string with substr(). To get the first character, for example, start at position 0 and grab the string of length 1.
- $string = "Just another Perl Hacker";
- $first_char = substr( $string, 0, 1 ); # 'J'
To change part of a string, you can use the optional fourth argument which is the replacement string.
- substr( $string, 13, 4, "Perl 5.8.0" );
You can also use substr() as an lvalue.
- substr( $string, 13, 4 ) = "Perl 5.8.0";
You have to keep track of N yourself. For example, let's say you want
to change the fifth occurrence of "whoever"
or "whomever"
into
"whosoever"
or "whomsoever"
, case insensitively. These
all assume that $_ contains the string to be altered.
- $count = 0;
- s{((whom?)ever)}{
- ++$count == 5 # is it the 5th?
- ? "${2}soever" # yes, swap
- : $1 # renege and leave it there
- }ige;
In the more general case, you can use the /g
modifier in a while
loop, keeping count of matches.
- $WANT = 3;
- $count = 0;
- $_ = "One fish two fish red fish blue fish";
- while (/(\w+)\s+fish\b/gi) {
- if (++$count == $WANT) {
- print "The third fish is a $1 one.\n";
- }
- }
That prints out: "The third fish is a red one."
You can also use a
repetition count and repeated pattern like this:
- /(?:\w+\s+fish\s+){2}(\w+)\s+fish/i;
There are a number of ways, with varying efficiency. If you want a
count of a certain single character (X) within a string, you can use the
tr///
function like so:
- $string = "ThisXlineXhasXsomeXx'sXinXit";
- $count = ($string =~ tr/X//);
- print "There are $count X characters in the string";
This is fine if you are just looking for a single character. However,
if you are trying to count multiple character substrings within a
larger string, tr///
won't work. What you can do is wrap a while()
loop around a global pattern match. For example, let's count negative
integers:
- $string = "-9 55 48 -2 23 -76 4 14 -44";
- while ($string =~ /-\d+/g) { $count++ }
- print "There are $count negative numbers in the string";
Another version uses a global match in list context, then assigns the result to a scalar, producing a count of the number of matches.
- $count = () = $string =~ /-\d+/g;
To make the first letter of each word upper case:
- $line =~ s/\b(\w)/\U$1/g;
This has the strange effect of turning "don't do it
" into "Don'T
Do It
". Sometimes you might want this. Other times you might need a
more thorough solution (Suggested by brian d foy):
- $string =~ s/ (
- (^\w) #at the beginning of the line
- | # or
- (\s\w) #preceded by whitespace
- )
- /\U$1/xg;
- $string =~ /([\w']+)/\u\L$1/g;
To make the whole line upper case:
- $line = uc($line);
To force each word to be lower case, with the first letter upper case:
- $line =~ s/(\w+)/\u\L$1/g;
You can (and probably should) enable locale awareness of those
characters by placing a use locale
pragma in your program.
See perllocale for endless details on locales.
This is sometimes referred to as putting something into "title case", but that's not quite accurate. Consider the proper capitalization of the movie Dr. Strangelove or: How I Learned to Stop Worrying and Love the Bomb, for example.
Damian Conway's Text::Autoformat module provides some smart case transformations:
Several modules can handle this sort of pasing---Text::Balanced, Text::CSV, Text::CSV_XS, and Text::ParseWords, among others.
Take the example case of trying to split a string that is
comma-separated into its different fields. You can't use split(/,/)
because you shouldn't split if the comma is inside quotes. For
example, take a data line like this:
- SAR001,"","Cimetrix, Inc","Bob Smith","CAM",N,8,1,0,7,"Error, Core Dumped"
Due to the restriction of the quotes, this is a fairly complex problem. Thankfully, we have Jeffrey Friedl, author of Mastering Regular Expressions, to handle these for us. He suggests (assuming your string is contained in $text):
If you want to represent quotation marks inside a
quotation-mark-delimited field, escape them with backslashes (eg,
"like \"this\""
.
Alternatively, the Text::ParseWords module (part of the standard Perl distribution) lets you say:
- use Text::ParseWords;
- @new = quotewords(",", 0, $text);
There's also a Text::CSV (Comma-Separated Values) module on CPAN.
(contributed by brian d foy)
A substitution can do this for you. For a single line, you want to replace all the leading or trailing whitespace with nothing. You can do that with a pair of substitutions.
- s/^\s+//;
- s/\s+$//;
You can also write that as a single substitution, although it turns out the combined statement is slower than the separate ones. That might not matter to you, though.
- s/^\s+|\s+$//g;
In this regular expression, the alternation matches either at the
beginning or the end of the string since the anchors have a lower
precedence than the alternation. With the /g
flag, the substitution
makes all possible matches, so it gets both. Remember, the trailing
newline matches the \s+
, and the $
anchor can match to the
physical end of the string, so the newline disappears too. Just add
the newline to the output, which has the added benefit of preserving
"blank" (consisting entirely of whitespace) lines which the ^\s+
would remove all by itself.
- while( <> )
- {
- s/^\s+|\s+$//g;
- print "$_\n";
- }
For a multi-line string, you can apply the regular expression
to each logical line in the string by adding the /m
flag (for
"multi-line"). With the /m
flag, the $
matches before an
embedded newline, so it doesn't remove it. It still removes the
newline at the end of the string.
- $string =~ s/^\s+|\s+$//gm;
Remember that lines consisting entirely of whitespace will disappear, since the first part of the alternation can match the entire string and replace it with nothing. If need to keep embedded blank lines, you have to do a little more work. Instead of matching any whitespace (since that includes a newline), just match the other whitespace.
- $string =~ s/^[\t\f ]+|[\t\f ]+$//mg;
In the following examples, $pad_len
is the length to which you wish
to pad the string, $text
or $num
contains the string to be padded,
and $pad_char
contains the padding character. You can use a single
character string constant instead of the $pad_char
variable if you
know what it is in advance. And in the same way you can use an integer in
place of $pad_len
if you know the pad length in advance.
The simplest method uses the sprintf
function. It can pad on the left
or right with blanks and on the left with zeroes and it will not
truncate the result. The pack
function can only pad strings on the
right with blanks and it will truncate the result to a maximum length of
$pad_len
.
- # Left padding a string with blanks (no truncation):
- $padded = sprintf("%${pad_len}s", $text);
- $padded = sprintf("%*s", $pad_len, $text); # same thing
- # Right padding a string with blanks (no truncation):
- $padded = sprintf("%-${pad_len}s", $text);
- $padded = sprintf("%-*s", $pad_len, $text); # same thing
- # Left padding a number with 0 (no truncation):
- $padded = sprintf("%0${pad_len}d", $num);
- $padded = sprintf("%0*d", $pad_len, $num); # same thing
- # Right padding a string with blanks using pack (will truncate):
- $padded = pack("A$pad_len",$text);
If you need to pad with a character other than blank or zero you can use
one of the following methods. They all generate a pad string with the
x
operator and combine that with $text
. These methods do
not truncate $text
.
Left and right padding with any character, creating a new string:
Left and right padding with any character, modifying $text
directly:
Use substr() or unpack(), both documented in perlfunc. If you prefer thinking in terms of columns instead of widths, you can use this kind of thing:
- # determine the unpack format needed to split Linux ps output
- # arguments are cut columns
- my $fmt = cut2fmt(8, 14, 20, 26, 30, 34, 41, 47, 59, 63, 67, 72);
- sub cut2fmt {
- my(@positions) = @_;
- my $template = '';
- my $lastpos = 1;
- for my $place (@positions) {
- $template .= "A" . ($place - $lastpos) . " ";
- $lastpos = $place;
- }
- $template .= "A*";
- return $template;
- }
(contributed by brian d foy)
You can use the Text::Soundex module. If you want to do fuzzy or close matching, you might also try the String::Approx, and Text::Metaphone, and Text::DoubleMetaphone modules.
Let's assume that you have a string that contains placeholder variables.
- $text = 'this has a $foo in it and a $bar';
You can use a substitution with a double evaluation. The
first /e turns $1
into $foo
, and the second /e turns
$foo
into its value. You may want to wrap this in an
eval
: if you try to get the value of an undeclared variable
while running under use strict
, you get a fatal error.
It's probably better in the general case to treat those variables as entries in some special hash. For example:
- %user_defs = (
- foo => 23,
- bar => 19,
- );
- $text =~ s/\$(\w+)/$user_defs{$1}/g;
The problem is that those double-quotes force stringification-- coercing numbers and references into strings--even when you don't want them to be strings. Think of it this way: double-quote expansion is used to produce new strings. If you already have a string, why do you need more?
If you get used to writing odd things like these:
- print "$var"; # BAD
- $new = "$old"; # BAD
- somefunc("$var"); # BAD
You'll be in trouble. Those should (in 99.8% of the cases) be the simpler and more direct:
- print $var;
- $new = $old;
- somefunc($var);
Otherwise, besides slowing you down, you're going to break code when the thing in the scalar is actually neither a string nor a number, but a reference:
You can also get into subtle problems on those few operations in Perl
that actually do care about the difference between a string and a
number, such as the magical ++
autoincrement operator or the
syscall() function.
Stringification also destroys arrays.
Check for these three things:
If you want to indent the text in the here document, you can do this:
- # all in one
- ($VAR = <<HERE_TARGET) =~ s/^\s+//gm;
- your text
- goes here
- HERE_TARGET
But the HERE_TARGET must still be flush against the margin. If you want that indented also, you'll have to quote in the indentation.
- ($quote = <<' FINIS') =~ s/^\s+//gm;
- ...we will have peace, when you and all your works have
- perished--and the works of your dark master to whom you
- would deliver us. You are a liar, Saruman, and a corrupter
- of men's hearts. --Theoden in /usr/src/perl/taint.c
- FINIS
- $quote =~ s/\s+--/\n--/;
A nice general-purpose fixer-upper function for indented here documents follows. It expects to be called with a here document as its argument. It looks to see whether each line begins with a common substring, and if so, strips that substring off. Otherwise, it takes the amount of leading whitespace found on the first line and removes that much off each subsequent line.
This works with leading special strings, dynamically determined:
- $remember_the_main = fix<<' MAIN_INTERPRETER_LOOP';
- @@@ int
- @@@ runops() {
- @@@ SAVEI32(runlevel);
- @@@ runlevel++;
- @@@ while ( op = (*op->op_ppaddr)() );
- @@@ TAINT_NOT;
- @@@ return 0;
- @@@ }
- MAIN_INTERPRETER_LOOP
Or with a fixed amount of leading whitespace, with remaining indentation correctly preserved:
- $poem = fix<<EVER_ON_AND_ON;
- Now far ahead the Road has gone,
- And I must follow, if I can,
- Pursuing it with eager feet,
- Until it joins some larger way
- Where many paths and errands meet.
- And whither then? I cannot say.
- --Bilbo in /usr/src/perl/pp_ctl.c
- EVER_ON_AND_ON
An array has a changeable length. A list does not. An array is something
you can push or pop, while a list is a set of values. Some people make
the distinction that a list is a value while an array is a variable.
Subroutines are passed and return lists, you put things into list
context, you initialize arrays with lists, and you foreach() across
a list. @
variables are arrays, anonymous arrays are arrays, arrays
in scalar context behave like the number of elements in them, subroutines
access their arguments through the array @_
, and push/pop/shift only work
on arrays.
As a side note, there's no such thing as a list in scalar context. When you say
- $scalar = (2, 5, 7, 9);
you're using the comma operator in scalar context, so it uses the scalar comma operator. There never was a list there at all! This causes the last value to be returned: 9.
The former is a scalar value; the latter an array slice, making it a list with one (scalar) value. You should use $ when you want a scalar value (most of the time) and @ when you want a list with one scalar value in it (very, very rarely; nearly never, in fact).
Sometimes it doesn't make a difference, but sometimes it does. For example, compare:
- $good[0] = `some program that outputs several lines`;
with
- @bad[0] = `same program that outputs several lines`;
The use warnings
pragma and the -w flag will warn you about these
matters.
(contributed by brian d foy)
Use a hash. When you think the words "unique" or "duplicated", think "hash keys".
If you don't care about the order of the elements, you could just
create the hash then extract the keys. It's not important how you
create that hash: just that you use keys
to get the unique
elements.
You can also go through each element and skip the ones you've seen
before. Use a hash to keep track. The first time the loop sees an
element, that element has no key in %Seen
. The next
statement
creates the key and immediately uses its value, which is undef
, so
the loop continues to the push
and increments the value for that
key. The next time the loop sees that same element, its key exists in
the hash and the value for that key is true (since it's not 0 or
undef), so the next skips that iteration and the loop goes to the next
element.
You can write this more briefly using a grep, which does the same thing.
(portions of this answer contributed by Anno Siegel)
Hearing the word "in" is an indication that you probably should have used a hash, not a list or array, to store your data. Hashes are designed to answer this question quickly and efficiently. Arrays aren't.
That being said, there are several ways to approach this. If you are going to make this query many times over arbitrary string values, the fastest way is probably to invert the original array and maintain a hash whose keys are the first array's values.
- @blues = qw/azure cerulean teal turquoise lapis-lazuli/;
- %is_blue = ();
- for (@blues) { $is_blue{$_} = 1 }
Now you can check whether $is_blue{$some_color}. It might have been a good idea to keep the blues all in a hash in the first place.
If the values are all small integers, you could use a simple indexed array. This kind of an array will take up less space:
- @primes = (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31);
- @is_tiny_prime = ();
- for (@primes) { $is_tiny_prime[$_] = 1 }
- # or simply @istiny_prime[@primes] = (1) x @primes;
Now you check whether $is_tiny_prime[$some_number].
If the values in question are integers instead of strings, you can save quite a lot of space by using bit strings instead:
Now check whether vec($read,$n,1)
is true for some $n
.
These methods guarantee fast individual tests but require a re-organization of the original list or array. They only pay off if you have to test multiple values against the same array.
If you are testing only once, the standard module List::Util exports
the function first
for this purpose. It works by stopping once it
finds the element. It's written in C for speed, and its Perl equivalant
looks like this subroutine:
If speed is of little concern, the common idiom uses grep in scalar context (which returns the number of items that passed its condition) to traverse the entire list. This does have the benefit of telling you how many matches it found, though.
If you want to actually extract the matching elements, simply use grep in list context.
Use a hash. Here's code to do both and more. It assumes that each element is unique in a given array:
Note that this is the symmetric difference, that is, all elements in either A or in B but not in both. Think of it as an xor operation.
The following code works for single-level arrays. It uses a stringwise comparison, and does not distinguish defined versus undefined empty strings. Modify if you have other needs.
For multilevel structures, you may wish to use an approach more like this one. It uses the CPAN module FreezeThaw:
This approach also works for comparing hashes. Here we'll demonstrate two different answers:
- use FreezeThaw qw(cmpStr cmpStrHard);
- %a = %b = ( "this" => "that", "extra" => [ "more", "stuff" ] );
- $a{EXTRA} = \%b;
- $b{EXTRA} = \%a;
- printf "a and b contain %s hashes\n",
- cmpStr(\%a, \%b) == 0 ? "the same" : "different";
- printf "a and b contain %s hashes\n",
- cmpStrHard(\%a, \%b) == 0 ? "the same" : "different";
The first reports that both those the hashes contain the same data, while the second reports that they do not. Which you prefer is left as an exercise to the reader.
To find the first array element which satisfies a condition, you can use the first() function in the List::Util module, which comes with Perl 5.8. This example finds the first element that contains "Perl".
If you cannot use List::Util, you can make your own loop to do the same thing. Once you find the element, you stop the loop with last.
If you want the array index, you can iterate through the indices and check the array element at each index until you find one that satisfies the condition.
In general, you usually don't need a linked list in Perl, since with regular arrays, you can push and pop or shift and unshift at either end, or you can use splice to add and/or remove arbitrary number of elements at arbitrary points. Both pop and shift are both O(1) operations on Perl's dynamic arrays. In the absence of shifts and pops, push in general needs to reallocate on the order every log(N) times, and unshift will need to copy pointers each time.
If you really, really wanted, you could use structures as described in perldsc or perltoot and do just what the algorithm book tells you to do. For example, imagine a list node like this:
- $node = {
- VALUE => 42,
- LINK => undef,
- };
You could walk the list this way:
You could add to the list this way:
- my ($head, $tail);
- $tail = append($head, 1); # grow a new head
- for $value ( 2 .. 10 ) {
- $tail = append($tail, $value);
- }
- sub append {
- my($list, $value) = @_;
- my $node = { VALUE => $value };
- if ($list) {
- $node->{LINK} = $list->{LINK};
- $list->{LINK} = $node;
- } else {
- $_[0] = $node; # replace caller's version
- }
- return $node;
- }
But again, Perl's built-in are virtually always good enough.
Circular lists could be handled in the traditional fashion with linked lists, or you could just do something like this with an array:
If you either have Perl 5.8.0 or later installed, or if you have Scalar-List-Utils 1.03 or later installed, you can say:
- use List::Util 'shuffle';
- @shuffled = shuffle(@list);
If not, you can use a Fisher-Yates shuffle.
- sub fisher_yates_shuffle {
- my $deck = shift; # $deck is a reference to an array
- my $i = @$deck;
- while (--$i) {
- my $j = int rand ($i+1);
- @$deck[$i,$j] = @$deck[$j,$i];
- }
- }
- # shuffle my mpeg collection
- #
- my @mpeg = <audio/*/*.mp3>;
- fisher_yates_shuffle( \@mpeg ); # randomize @mpeg in place
- print @mpeg;
Note that the above implementation shuffles an array in place, unlike the List::Util::shuffle() which takes a list and returns a new shuffled list.
You've probably seen shuffling algorithms that work using splice, randomly picking another element to swap the current element with
This is bad because splice is already O(N), and since you do it N times, you just invented a quadratic algorithm; that is, O(N**2). This does not scale, although Perl is so efficient that you probably won't notice this until you have rather largish arrays.
Use for
/foreach
:
- for (@lines) {
- s/foo/bar/; # change that word
- tr/XZ/ZX/; # swap those letters
- }
Here's another; let's compute spherical volumes:
- for (@volumes = @radii) { # @volumes has changed parts
- $_ **= 3;
- $_ *= (4/3) * 3.14159; # this will be constant folded
- }
which can also be done with map() which is made to transform one list into another:
- @volumes = map {$_ ** 3 * (4/3) * 3.14159} @radii;
If you want to do the same thing to modify the values of the
hash, you can use the values
function. As of Perl 5.6
the values are not copied, so if you modify $orbit (in this
case), you modify the value.
- for $orbit ( values %orbits ) {
- ($orbit **= 3) *= (4/3) * 3.14159;
- }
Prior to perl 5.6 values
returned copies of the values,
so older perl code often contains constructions such as
@orbits{keys %orbits}
instead of values %orbits
where
the hash is to be modified.
Use the rand() function (see rand):
- $index = rand @array;
- $element = $array[$index];
Or, simply: my $element = $array[ rand @array ];
Use the List::Permutor module on CPAN. If the list is actually an array, try the Algorithm::Permute module (also on CPAN). It's written in XS code and is very efficient.
For even faster execution, you could do:
Here's a little program that generates all permutations of all the words on each line of input. The algorithm embodied in the permute() function is discussed in Volume 4 (still unpublished) of Knuth's The Art of Computer Programming and will work on any list:
- #!/usr/bin/perl -n
- # Fischer-Kause ordered permutation generator
- sub permute (&@) {
- my $code = shift;
- my @idx = 0..$#_;
- while ( $code->(@_[@idx]) ) {
- my $p = $#idx;
- --$p while $idx[$p-1] > $idx[$p];
- my $q = $p or return;
- push @idx, reverse splice @idx, $p;
- ++$q while $idx[$p-1] > $idx[$q];
- @idx[$p-1,$q]=@idx[$q,$p-1];
- }
- }
- permute {print"@_\n"} split;
Supply a comparison function to sort() (described in sort):
- @list = sort { $a <=> $b } @list;
The default sort function is cmp, string comparison, which would
sort (1, 2, 10)
into (1, 10, 2)
. <=>
, used above, is
the numerical comparison operator.
If you have a complicated function needed to pull out the part you want to sort on, then don't do it inside the sort function. Pull it out first, because the sort BLOCK can be called many times for the same element. Here's an example of how to pull out the first word after the first number on each item, and then sort those words case-insensitively.
which could also be written this way, using a trick that's come to be known as the Schwartzian Transform:
If you need to sort on several fields, the following paradigm is useful.
- @sorted = sort { field1($a) <=> field1($b) ||
- field2($a) cmp field2($b) ||
- field3($a) cmp field3($b)
- } @data;
This can be conveniently combined with precalculation of keys as given above.
See the sort article in the "Far More Than You Ever Wanted To Know" collection in http://www.cpan.org/misc/olddoc/FMTEYEWTK.tgz for more about this approach.
See also the question below on sorting hashes.
Use pack() and unpack(), or else vec() and the bitwise operations.
For example, this sets $vec to have bit N set if $ints[N] was set:
- $vec = '';
- foreach(@ints) { vec($vec,$_,1) = 1 }
Here's how, given a vector in $vec, you can get those bits into your @ints array:
- sub bitvec_to_list {
- my $vec = shift;
- my @ints;
- # Find null-byte density then select best algorithm
- if ($vec =~ tr/\0// / length $vec > 0.95) {
- use integer;
- my $i;
- # This method is faster with mostly null-bytes
- while($vec =~ /[^\0]/g ) {
- $i = -9 + 8 * pos $vec;
- push @ints, $i if vec($vec, ++$i, 1);
- push @ints, $i if vec($vec, ++$i, 1);
- push @ints, $i if vec($vec, ++$i, 1);
- push @ints, $i if vec($vec, ++$i, 1);
- push @ints, $i if vec($vec, ++$i, 1);
- push @ints, $i if vec($vec, ++$i, 1);
- push @ints, $i if vec($vec, ++$i, 1);
- push @ints, $i if vec($vec, ++$i, 1);
- }
- } else {
- # This method is a fast general algorithm
- use integer;
- my $bits = unpack "b*", $vec;
- push @ints, 0 if $bits =~ s/^(\d)// && $1;
- push @ints, pos $bits while($bits =~ /1/g);
- }
- return \@ints;
- }
This method gets faster the more sparse the bit vector is. (Courtesy of Tim Bunce and Winfried Koenig.)
You can make the while loop a lot shorter with this suggestion from Benjamin Goldberg:
Or use the CPAN module Bit::Vector:
- $vector = Bit::Vector->new($num_of_bits);
- $vector->Index_List_Store(@ints);
- @ints = $vector->Index_List_Read();
Bit::Vector provides efficient methods for bit vector, sets of small integers and "big int" math.
Here's a more extensive illustration using vec():
- # vec demo
- $vector = "\xff\x0f\xef\xfe";
- print "Ilya's string \\xff\\x0f\\xef\\xfe represents the number ",
- unpack("N", $vector), "\n";
- $is_set = vec($vector, 23, 1);
- print "Its 23rd bit is ", $is_set ? "set" : "clear", ".\n";
- pvec($vector);
- set_vec(1,1,1);
- set_vec(3,1,1);
- set_vec(23,1,1);
- set_vec(3,1,3);
- set_vec(3,2,3);
- set_vec(3,4,3);
- set_vec(3,4,7);
- set_vec(3,8,3);
- set_vec(3,8,7);
- set_vec(0,32,17);
- set_vec(1,32,17);
- sub set_vec {
- my ($offset, $width, $value) = @_;
- my $vector = '';
- vec($vector, $offset, $width) = $value;
- print "offset=$offset width=$width value=$value\n";
- pvec($vector);
- }
- sub pvec {
- my $vector = shift;
- my $bits = unpack("b*", $vector);
- my $i = 0;
- my $BASE = 8;
- print "vector length in bytes: ", length($vector), "\n";
- @bytes = unpack("A8" x length($vector), $bits);
- print "bits are: @bytes\n\n";
- }
The short story is that you should probably only use defined on scalars or functions, not on aggregates (arrays and hashes). See defined in the 5.004 release or later of Perl for more detail.
Use the each() function (see each) if you don't care whether it's sorted:
If you want it sorted, you'll have to use foreach() on the result of sorting the keys as shown in an earlier question.
(contributed by brian d foy)
The easy answer is "Don't do that!"
If you iterate through the hash with each(), you can delete the key
most recently returned without worrying about it. If you delete or add
other keys, the iterator may skip or double up on them since perl
may rearrange the hash table. See the
entry for each()
in perlfunc.
Create a reverse hash:
- %by_value = reverse %by_key;
- $key = $by_value{$value};
That's not particularly efficient. It would be more space-efficient to use:
- while (($key, $value) = each %by_key) {
- $by_value{$value} = $key;
- }
If your hash could have repeated values, the methods above will only find one of the associated keys. This may or may not worry you. If it does worry you, you can always reverse the hash into a hash of arrays instead:
If you mean how many keys, then all you have to do is use the keys() function in a scalar context:
- $num_keys = keys %hash;
The keys() function also resets the iterator, which means that you may see strange results if you use this between uses of other hash operators such as each().
(contributed by brian d foy)
To sort a hash, start with the keys. In this example, we give the list of keys to the sort function which then compares them ASCIIbetically (which might be affected by your locale settings). The output list has the keys in ASCIIbetical order. Once we have the keys, we can go through them to create a report which lists the keys in ASCIIbetical order.
We could get more fancy in the sort()
block though. Instead of
comparing the keys, we can compute a value with them and use that
value as the comparison.
For instance, to make our report order case-insensitive, we use
the \L
sequence in a double-quoted string to make everything
lowercase. The sort()
block then compares the lowercased
values to determine in which order to put the keys.
Note: if the computation is expensive or the hash has many elements, you may want to look at the Schwartzian Transform to cache the computation results.
If we want to sort by the hash value instead, we use the hash key to look it up. We still get out a list of keys, but this time they are ordered by their value.
From there we can get more complex. If the hash values are the same, we can provide a secondary sort on the hash key.
You can look into using the DB_File module and tie() using the $DB_BTREE hash bindings as documented in In Memory Databases in DB_File. The Tie::IxHash module from CPAN might also be instructive.
Hashes contain pairs of scalars: the first is the key, the
second is the value. The key will be coerced to a string,
although the value can be any kind of scalar: string,
number, or reference. If a key $key is present in
%hash, exists($hash{$key})
will return true. The value
for a given key can be undef
, in which case
$hash{$key}
will be undef
while exists $hash{$key}
will return true. This corresponds to ($key
, undef
)
being in the hash.
Pictures help... here's the %hash table:
- keys values
- +------+------+
- | a | 3 |
- | x | 7 |
- | d | 0 |
- | e | 2 |
- +------+------+
And these conditions hold
- $hash{'a'} is true
- $hash{'d'} is false
- defined $hash{'d'} is true
- defined $hash{'a'} is true
- exists $hash{'a'} is true (Perl5 only)
- grep ($_ eq 'a', keys %hash) is true
If you now say
- undef $hash{'a'}
your table now reads:
- keys values
- +------+------+
- | a | undef|
- | x | 7 |
- | d | 0 |
- | e | 2 |
- +------+------+
and these conditions now hold; changes in caps:
- $hash{'a'} is FALSE
- $hash{'d'} is false
- defined $hash{'d'} is true
- defined $hash{'a'} is FALSE
- exists $hash{'a'} is true (Perl5 only)
- grep ($_ eq 'a', keys %hash) is true
Notice the last two: you have an undef value, but a defined key!
Now, consider this:
- delete $hash{'a'}
your table now reads:
- keys values
- +------+------+
- | x | 7 |
- | d | 0 |
- | e | 2 |
- +------+------+
and these conditions now hold; changes in caps:
- $hash{'a'} is false
- $hash{'d'} is false
- defined $hash{'d'} is true
- defined $hash{'a'} is false
- exists $hash{'a'} is FALSE (Perl5 only)
- grep ($_ eq 'a', keys %hash) is FALSE
See, the whole entry is gone!
This depends on the tied hash's implementation of EXISTS(). For example, there isn't the concept of undef with hashes that are tied to DBM* files. It also means that exists() and defined() do the same thing with a DBM* file, and what they end up doing is not what they do with ordinary hashes.
Using keys %hash
in scalar context returns the number of keys in
the hash and resets the iterator associated with the hash. You may
need to do this if you use last
to exit a loop early so that when you
re-enter it, the hash iterator has been reset.
First you extract the keys from the hashes into lists, then solve the "removing duplicates" problem described above. For example:
Or more succinctly:
- @uniq = keys %{{%foo,%bar}};
Or if you really want to save space:
Either stringify the structure yourself (no fun), or else get the MLDBM (which uses Data::Dumper) module from CPAN and layer it on top of either DB_File or GDBM_File.
Use the Tie::IxHash from CPAN.
If you say something like:
- somefunc($hash{"nonesuch key here"});
Then that element "autovivifies"; that is, it springs into existence
whether you store something there or not. That's because functions
get scalars passed in by reference. If somefunc() modifies $_[0]
,
it has to be ready to write it back into the caller's version.
This has been fixed as of Perl5.004.
Normally, merely accessing a key's value for a nonexistent key does not cause that key to be forever there. This is different than awk's behavior.
Usually a hash ref, perhaps like this:
- $record = {
- NAME => "Jason",
- EMPNO => 132,
- TITLE => "deputy peon",
- AGE => 23,
- SALARY => 37_000,
- PALS => [ "Norbert", "Rhys", "Phineas"],
- };
References are documented in perlref and the upcoming perlreftut. Examples of complex data structures are given in perldsc and perllol. Examples of structures and object-oriented classes are in perltoot.
(contributed by brian d foy)
Hash keys are strings, so you can't really use a reference as the key.
When you try to do that, perl turns the reference into its stringified
form (for instance, HASH(0xDEADBEEF)
). From there you can't get back
the reference from the stringified form, at least without doing some
extra work on your own. Also remember that hash keys must be unique, but
two different variables can store the same reference (and those variables
can change later).
The Tie::RefHash module, which is distributed with perl, might be what you want. It handles that extra work.
Perl is binary clean, so this shouldn't be a problem. For example, this works fine (assuming the files are found):
- if (`cat /vmunix` =~ /gzip/) {
- print "Your kernel is GNU-zip enabled!\n";
- }
On less elegant (read: Byzantine) systems, however, you have to play tedious games with "text" versus "binary" files. See binmode or perlopentut.
If you're concerned about 8-bit ASCII data, then see perllocale.
If you want to deal with multibyte characters, however, there are some gotchas. See the section on Regular Expressions.
Assuming that you don't care about IEEE notations like "NaN" or "Infinity", you probably just want to use a regular expression.
- if (/\D/) { print "has nondigits\n" }
- if (/^\d+$/) { print "is a whole number\n" }
- if (/^-?\d+$/) { print "is an integer\n" }
- if (/^[+-]?\d+$/) { print "is a +/- integer\n" }
- if (/^-?\d+\.?\d*$/) { print "is a real number\n" }
- if (/^-?(?:\d+(?:\.\d*)?|\.\d+)$/) { print "is a decimal number\n" }
- if (/^([+-]?)(?=\d|\.\d)\d*(\.\d*)?([Ee]([+-]?\d+))?$/)
- { print "a C float\n" }
There are also some commonly used modules for the task.
Scalar::Util (distributed with 5.8) provides access to perl's
internal function looks_like_number
for determining
whether a variable looks like a number. Data::Types
exports functions that validate data types using both the
above and other regular expressions. Thirdly, there is
Regexp::Common
which has regular expressions to match
various types of numbers. Those three modules are available
from the CPAN.
If you're on a POSIX system, Perl supports the POSIX::strtod
function. Its semantics are somewhat cumbersome, so here's a getnum
wrapper function for more convenient access. This function takes
a string and returns the number it found, or undef
for input that
isn't a C float. The is_numeric
function is a front end to getnum
if you just want to say, "Is this a float?"
Or you could check out the String::Scanf module on the CPAN
instead. The POSIX module (part of the standard Perl distribution) provides
the strtod
and strtol
for converting strings to double and longs,
respectively.
For some specific applications, you can use one of the DBM modules.
See AnyDBM_File. More generically, you should consult the FreezeThaw
or Storable modules from CPAN. Starting from Perl 5.8 Storable is part
of the standard distribution. Here's one example using Storable's store
and retrieve
functions:
- use Storable;
- store(\%hash, "filename");
- # later on...
- $href = retrieve("filename"); # by ref
- %hash = %{ retrieve("filename") }; # direct to hash
The Data::Dumper module on CPAN (or the 5.005 release of Perl) is great
for printing out data structures. The Storable module on CPAN (or the
5.8 release of Perl), provides a function called dclone
that recursively
copies its argument.
- use Storable qw(dclone);
- $r2 = dclone($r1);
Where $r1 can be a reference to any kind of data structure you'd like.
It will be deeply copied. Because dclone
takes and returns references,
you'd have to add extra punctuation if you had a hash of arrays that
you wanted to copy.
- %newhash = %{ dclone(\%oldhash) };
Use the UNIVERSAL class (see UNIVERSAL).
Get the Business::CreditCard module from CPAN.
The kgbpack.c code in the PGPLOT module on CPAN does just this. If you're doing a lot of float or double processing, consider using the PDL module from CPAN instead--it makes number-crunching easy.
Copyright (c) 1997-2006 Tom Christiansen, Nathan Torkington, and other authors as noted. All rights reserved.
This documentation is free; you can redistribute it and/or modify it under the same terms as Perl itself.
Irrespective of its distribution, all code examples in this file are hereby placed into the public domain. You are permitted and encouraged to use this code in your own programs for fun or for profit as you see fit. A simple comment in the code giving credit would be courteous but is not required.