\d is less efficient than [0-9]

Question

I made a comment yesterday on an answer where someone had used [0123456789] in a regular expression rather than [0-9] or \d. I said it was probably more efficient to use a range or digit specifier than a character set.

I decided to test that out today and found out to my surprise that (in the C# regex engine at least) \d appears to be less efficient than either of the other two which don't seem to differ much. Here is my test output over 10000 random strings of 1000 random characters with 5077 actually containing a digit:

Regular expression \d           took 00:00:00.2141226 result: 5077/10000
Regular expression [0-9]        took 00:00:00.1357972 result: 5077/10000  63.42 % of first
Regular expression [0123456789] took 00:00:00.1388997 result: 5077/10000  64.87 % of first

It's a surprise to me for two reasons:

1. I would have thought the range would be implemented much more efficiently than the set.
2. I can't understand why \d is worse than [0-9]. Is there more to \d than simply shorthand for [0-9]?

Here is the test code:

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Diagnostics;
using System.Text.RegularExpressions;

namespace SO_RegexPerformance
{
    class Program
    {
        static void Main(string[] args)
        {
            var rand = new Random(1234);
            var strings = new List<string>();
            //10K random strings
            for (var i = 0; i < 10000; i++)
            {
                //Generate random string
                var sb = new StringBuilder();
                for (var c = 0; c < 1000; c++)
                {
                    //Add a-z randomly
                    sb.Append((char)('a' + rand.Next(26)));
                }
                //In roughly 50% of them, put a digit
                if (rand.Next(2) == 0)
                {
                    //Replace one character with a digit, 0-9
                    sb[rand.Next(sb.Length)] = (char)('0' + rand.Next(10));
                }
                strings.Add(sb.ToString());
            }

            var baseTime = testPerfomance(strings, @"\d");
            Console.WriteLine();
            var testTime = testPerfomance(strings, "[0-9]");
            Console.WriteLine("  {0:P2} of first", testTime.TotalMilliseconds / baseTime.TotalMilliseconds);
            testTime = testPerfomance(strings, "[0123456789]");
            Console.WriteLine("  {0:P2} of first", testTime.TotalMilliseconds / baseTime.TotalMilliseconds);
        }

        private static TimeSpan testPerfomance(List<string> strings, string regex)
        {
            var sw = new Stopwatch();

            int successes = 0;

            var rex = new Regex(regex);

            sw.Start();
            foreach (var str in strings)
            {
                if (rex.Match(str).Success)
                {
                    successes++;
                }
            }
            sw.Stop();

            Console.Write("Regex {0,-12} took {1} result: {2}/{3}", regex, sw.Elapsed, successes, strings.Count);

            return sw.Elapsed;
        }
    }
}

Answer 1

\d checks all Unicode digits, while [0-9] is limited to these 10 characters. For example, Persian digits, ۱۲۳۴۵۶۷۸۹, are an example of Unicode digits which are matched with \d, but not [0-9].

You can generate a list of all such characters using the following code:

var sb = new StringBuilder();
for(UInt16 i = 0; i < UInt16.MaxValue; i++)
{
    string str = Convert.ToChar(i).ToString();
    if (Regex.IsMatch(str, @"\d"))
        sb.Append(str);
}
Console.WriteLine(sb.ToString());

Which generates:

0123456789٠١٢٣٤٥٦٧٨٩۰۱۲۳۴۵۶۷۸۹߀߁߂߃߄߅߆߇߈߉०१२३४५६७८९০১২৩৪৫৬৭৮৯੦੧੨੩੪੫੬੭੮੯૦૧૨૩૪૫૬૭૮૯୦୧୨୩୪୫୬୭୮୯௦௧௨௩௪௫௬௭௮௯౦౧౨౩౪౫౬౭౮౯೦೧೨೩೪೫೬೭೮೯൦൧൨൩൪൫൬൭൮൯๐๑๒๓๔๕๖๗๘๙໐໑໒໓໔໕໖໗໘໙༠༡༢༣༤༥༦༧༨༩၀၁၂၃၄၅၆၇၈၉႐႑႒႓႔႕႖႗႘႙០១២៣៤៥៦៧៨៩᠐᠑᠒᠓᠔᠕᠖᠗᠘᠙᥆᥇᥈᥉᥊᥋᥌᥍᥎᥏᧐᧑᧒᧓᧔᧕᧖᧗᧘᧙᭐᭑᭒᭓᭔᭕᭖᭗᭘᭙᮰᮱᮲᮳᮴᮵᮶᮷᮸᮹᱀᱁᱂᱃᱄᱅᱆᱇᱈᱉᱐᱑᱒᱓᱔᱕᱖᱗᱘᱙꘠꘡꘢꘣꘤꘥꘦꘧꘨꘩꣐꣑꣒꣓꣔꣕꣖꣗꣘꣙꤀꤁꤂꤃꤄꤅꤆꤇꤈꤉꩐꩑꩒꩓꩔꩕꩖꩗꩘꩙０１２３４５６７８９