{"id":17442,"date":"2023-10-08T08:03:56","date_gmt":"2023-10-08T07:03:56","guid":{"rendered":"https:\/\/www.baeldung.com\/java-find-square-root-biginteger"},"modified":"2023-10-08T08:03:56","modified_gmt":"2023-10-08T07:03:56","slug":"finding-the-square-root-of-a-biginteger-in-java","status":"publish","type":"post","link":"https:\/\/gamefootballmobileanimeiphone.com\/index.php\/2023\/10\/08\/finding-the-square-root-of-a-biginteger-in-java\/","title":{"rendered":"Finding the Square Root of a BigInteger in Java"},"content":{"rendered":"

\"\"<\/p>\n

1. Overview<\/h2>\n
<\/div>\n

Often, while working with big numbers, we are limited by the sizes of int<\/em> and\u00a0long.\u00a0<\/em>Java provides a good way around it with the BigInteger<\/em><\/a> class. However, sometimes, the API doesn’t support all the arithmetic operations we would like to use.<\/p>\n

Finding a square root of a big number is common but often tricky.<\/p>\n

In this tutorial, we’ll learn how to do this and the pros and cons of each approach.<\/p>\n

2. Calculating a Root<\/h2>\n
<\/div>\n

Let’s review a couple of ways to get the desired calculations.<\/p>\n

2.1. Java 9 BigInteger<\/em> API<\/h3>\n
<\/div>\n

We’ll start with the most straightforward approach introduced in Java 9<\/a>. From this version and above, BigInteger<\/em> provides two helpful methods:\u00a0sqrt()\u00a0<\/em>and\u00a0sqrtAndReminder().<\/em> Let’s review the first one:<\/p>\n

BigInteger integer = new BigInteger(bigDecimalNumber);\r\nBigInteger root = integer.sqrt();<\/code><\/pre>\n
The second one is similar but provides additional information about the reminder:<\/p>\n
BigInteger integer = new BigInteger(bigDecimalNumber);\r\nBigInteger[] rootAndReminder = integer.sqrtAndRemainder();<\/code><\/pre>\n
Both methods provide a simple and transparent way to calculate a root. However, it requires a specific Java version, which might be problematic for some applications.<\/p>\n
2.2. Guava’s BigIntegerMath<\/em><\/h3>\n
<\/div>\n
Another way to calculate the root without bumping the Java version is to use the Guava<\/a> library:<\/p>\n
BigInteger integer = new BigInteger(bigDecimalNumber);\r\nBigInteger root = BigIntegerMath.sqrt(integer, RoundingMode.DOWN);<\/code><\/pre>\n
The method takes RoundingMode<\/em> to identify the rounding logic. The library doesn’t provide a simple way to get the reminder, so if we need it, we’ll have to do some additional steps:<\/p>\n
BigInteger integer = new BigInteger(bigDecimalNumber);\r\nBigInteger root = BigIntegerMath.sqrt(integer, RoundingMode.DOWN);\r\nBigInteger reminder = integer.subtract(root.multiply(root));<\/code><\/pre>\n
2.3. NewtonPlus\u00a0method<\/b><\/h3>\n
<\/div>\n
It’s possible, but in most cases, not recommended, to implement a custom solution for finding a square root of a big integer. Often, custom implementations might have higher complexity and lower throughput.\u00a0<\/strong>There are a couple of simple but inefficient algorithms, such as the Binary Search<\/a> and Newton’s Method<\/a>.<\/p>\n
However, there’s one algorithm<\/a> that outperforms both standard Java and Guava’s implementations.\u00a0<\/strong>The NewtonPlus algorithm was introduced by Ryan Scott White<\/a> and based on Newton’s method. The algorithm shows performance improvements starting with the numbers above 5 x 1014<\/sup>.<\/p>\n
3. Performance Comparison<\/h2>\n
<\/div>\n
Let’s run a performance test for the Java, Guava library, NewtonPlus, and Newton’s methods to check for any significant differences between them. We’ll run the test cases on three different values:<\/p>\n
private static final String BIG_NUMBER = "1797693130000000000000000000000..." \/\/ 309 digits\r\nprivate static final String VERY_BIG_NUMBER = "32473927492374927934284792..." \/\/ 1802 digits\r\nprivate static final String INSANELY_BIG_NUMBER = "3247392749237492793428..." \/\/ 3604 digits<\/code><\/pre>\n
After running the JMH benchmarks<\/a>, we got the following results:<\/p>\n
Benchmark                                                  (number)              Mode  Cnt       Score   Error  Units\r\nBigIntegerSquareRootBenchmark.calculateRootWithNewton      BIG_NUMBER           thrpt         2668.642          ops\/s\r\nBigIntegerSquareRootBenchmark.calculateRootWithJava        BIG_NUMBER           thrpt        25417.428          ops\/s\r\nBigIntegerSquareRootBenchmark.calculateRootWithGuava       BIG_NUMBER           thrpt       144117.671          ops\/s\r\nBigIntegerSquareRootBenchmark.calculateRootWithNewtonPlus  BIG_NUMBER           thrpt       308933.077          ops\/s\r\nBigIntegerSquareRootBenchmark.calculateRootWithNewton      VERY_BIG_NUMBER      thrpt           33.627          ops\/s\r\nBigIntegerSquareRootBenchmark.calculateRootWithJava        VERY_BIG_NUMBER      thrpt         1376.668          ops\/s\r\nBigIntegerSquareRootBenchmark.calculateRootWithGuava       VERY_BIG_NUMBER      thrpt         5349.748          ops\/s\r\nBigIntegerSquareRootBenchmark.calculateRootWithNewtonPlus  VERY_BIG_NUMBER      thrpt        12283.677          ops\/s\r\nBigIntegerSquareRootBenchmark.calculateRootWithNewton      INSANELY_BIG_NUMBER  thrpt            9.135          ops\/s\r\nBigIntegerSquareRootBenchmark.calculateRootWithJava        INSANELY_BIG_NUMBER  thrpt          553.475          ops\/s\r\nBigIntegerSquareRootBenchmark.calculateRootWithGuava       INSANELY_BIG_NUMBER  thrpt         1713.520          ops\/s\r\nBigIntegerSquareRootBenchmark.calculateRootWithNewtonPlus  INSANELY_BIG_NUMBER  thrpt         3252.308          ops\/s<\/code><\/pre>\n
The NewtonPlus method shows the best performance, which might be a good option for applications that require a high volume of such computations.<\/strong> At the same time, if adding a custom, highly optimized code to the codebase isn’t a very attractive idea, we can opt for Guava’s BigIntegerMath<\/em>, which has a relatively good performance.<\/p>\n
Also, simple algorithms like Newton’s are inefficient and should be avoided. The Binary Search method, in general, is less performant than Newton’s method as it has a lower rate of convergence.<\/strong><\/p>\n
4. Conclusion<\/h2>\n
<\/div>\n
While working with huge numbers, we need a convenient way to perform standard mathematical operations over them. From a mathematical perspective, the operations are the same regardless of the size of a number, but computer science creates certain constraints. That’s why we need specific libraries and algorithms to work with\u00a0BigIntegers.<\/em><\/strong><\/p>\n
Depending on the specificity of the task at hand, we can opt for a different solution, ranging from standard libraries to custom solutions that are finely tuned to the application requirements. However, premature optimization is never good and often harmful.<\/strong> Thus, we should be reasonable in our choices.<\/p>\n
As usual, all the code is available over on GitHub<\/a>.<\/p>\n
\"\"<\/p>\n
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\"\"<\/p>\n
Learn three approaches to calculating the square root of a big number in Java.<\/p>\n
<\/a>\u00a0<\/a>\u00a0<\/a>\u00a0<\/a>\u00a0<\/a>\u00a0<\/a>\u00a0<\/a>\u00a0<\/div>\n","protected":false},"author":291,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"site-container-style":"default","site-container-layout":"default","site-sidebar-layout":"default","disable-article-header":"default","disable-site-header":"default","disable-site-footer":"default","disable-content-area-spacing":"default","footnotes":""},"categories":[22],"tags":[61,122,127,129,124,128,125,132,131,133,126,130,123,66,94,88,97,56,64,65,60,112,40,75,95,104,33,120,105,101,98,115,30,29,41,86,70,69,68,72,71,26,118,108,87,46,55,48,52,54,51,50,83,62,58,57,109,35,59,63,85,7960,79,82,96,80,27,81,114,44,42,43,45,38,39,110,117,100,111,116,73,89,90,92,91,93,84,78,37,102,34,36,77,67,74,99,113,119,28,121,32,47,49,53,103,31,76],"class_list":["post-17442","post","type-post","status-publish","format-standard","hentry","category-mobile","tag-airpods","tag-anime","tag-anime-characters","tag-anime-cosplay","tag-anime-edits","tag-anime-merchandise","tag-anime-movies","tag-anime-news","tag-anime-recommendations","tag-anime-reviews","tag-anime-series","tag-anime-streaming","tag-animes","tag-app-store","tag-app-store-samsung","tag-appgallery","tag-appgallery-oneplus","tag-apple","tag-apple-music","tag-apple-tv","tag-apple-watch","tag-bbc-sport","tag-best-mobile-games","tag-bixby","tag-bixby-xiaomi","tag-champions-league","tag-cyberpunk","tag-cyberpunk-2077","tag-fantasy-football","tag-fifa","tag-football","tag-formula-1","tag-fortnite","tag-free-fire","tag-free-mobile-games","tag-freebuds-pro","tag-galaxy-a52","tag-galaxy-note-20","tag-galaxy-s21","tag-galaxy-watch-4","tag-galaxy-z-fold-3","tag-game","tag-games","tag-golf","tag-harmonyos","tag-how-to-backup-iphone","tag-how-to-factory-reset-iphone","tag-how-to-reset-iphone","tag-how-to-restore-iphone","tag-how-to-unlock-iphone","tag-how-to-unlock-iphone-5","tag-how-to-unlock-iphone-6","tag-huawei","tag-ios","tag-ipad","tag-iphone","tag-live-soccer","tag-lol","tag-macbook","tag-macos","tag-mate-40-pro","tag-math","tag-mi-11-lite","tag-mi-home-security-camera-basic-1080p","tag-mi-home-security-camera-basic-1080p-huawei","tag-mi-smart-band-6","tag-minecraft","tag-miui","tag-mlb-scores","tag-mobile-game-design","tag-mobile-game-development","tag-mobile-game-marketing","tag-mobile-game-monetization","tag-mobile-games","tag-mobile-gaming","tag-nba-scores","tag-nba-standings","tag-nfl","tag-nfl-scores","tag-nhl-scores","tag-one-ui","tag-oneplus","tag-oneplus-9-pro","tag-oneplus-buds-pro","tag-oneplus-nord-ce-5g","tag-oxygenos","tag-p40-pro-plus","tag-poco-x3-pro","tag-pokemon","tag-premier-league","tag-pubg","tag-pubg-mobile","tag-redmi-note-10-pro","tag-samsung","tag-samsung-pay","tag-soccer","tag-sports","tag-steam","tag-steeam","tag-top-10-anime","tag-valorant","tag-when-do-the-iphone-7-come-out","tag-when-does-the-iphone-7-come-out","tag-when-is-the-iphone-7-coming-out","tag-world-cup","tag-xbox-series-x","tag-xiaomi"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/gamefootballmobileanimeiphone.com\/index.php\/wp-json\/wp\/v2\/posts\/17442","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gamefootballmobileanimeiphone.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gamefootballmobileanimeiphone.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gamefootballmobileanimeiphone.com\/index.php\/wp-json\/wp\/v2\/users\/291"}],"replies":[{"embeddable":true,"href":"https:\/\/gamefootballmobileanimeiphone.com\/index.php\/wp-json\/wp\/v2\/comments?post=17442"}],"version-history":[{"count":1,"href":"https:\/\/gamefootballmobileanimeiphone.com\/index.php\/wp-json\/wp\/v2\/posts\/17442\/revisions"}],"predecessor-version":[{"id":17443,"href":"https:\/\/gamefootballmobileanimeiphone.com\/index.php\/wp-json\/wp\/v2\/posts\/17442\/revisions\/17443"}],"wp:attachment":[{"href":"https:\/\/gamefootballmobileanimeiphone.com\/index.php\/wp-json\/wp\/v2\/media?parent=17442"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gamefootballmobileanimeiphone.com\/index.php\/wp-json\/wp\/v2\/categories?post=17442"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gamefootballmobileanimeiphone.com\/index.php\/wp-json\/wp\/v2\/tags?post=17442"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}