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• Why is processing a sorted array faster than an unsorted array?

  - by GManNickG

  Here is a piece of code that shows some very peculiar performance. For some strange reason, sorting the data miraculously speeds up the code by almost 6x: #include <algorithm> #include <ctime> #include <iostream> int main() { // generate data const unsigned arraySize = 32768; int data[arraySize]; for (unsigned c = 0; c < arraySize; ++c) data[c] = std::rand() % 256; // !!! with this, the next loop runs faster std::sort(data, data + arraySize); // test clock_t start = clock(); long long sum = 0; for (unsigned i = 0; i < 100000; ++i) { // primary loop for (unsigned c = 0; c < arraySize; ++c) { if (data[c] >= 128) sum += data[c]; } } double elapsedTime = static_cast<double>(clock() - start) / CLOCKS_PER_SEC; std::cout << elapsedTime << std::endl; std::cout << "sum = " << sum << std::endl; } Without std::sort(data, data + arraySize);, the code runs in 11.54 seconds. With the sorted data, the code runs in 1.93 seconds. Initially I thought this might be just a language or compiler anomaly. So I tried it Java... import java.util.Arrays; import java.util.Random; public class Main { public static void main(String[] args) { // generate data int arraySize = 32768; int data[] = new int[arraySize]; Random rnd = new Random(0); for (int c = 0; c < arraySize; ++c) data[c] = rnd.nextInt() % 256; // !!! with this, the next loop runs faster Arrays.sort(data); // test long start = System.nanoTime(); long sum = 0; for (int i = 0; i < 100000; ++i) { // primary loop for (int c = 0; c < arraySize; ++c) { if (data[c] >= 128) sum += data[c]; } } System.out.println((System.nanoTime() - start) / 1000000000.0); System.out.println("sum = " + sum); } } with a similar but less extreme result. My first thought was that sorting brings the data into cache, but my next thought was how silly that is because the array was just generated. What is going on? Why is a sorted array faster than an unsorted array? The code is summing up some independent terms, the order should not matter.

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• Meassure website

  - by s0mmer

  Hi, I was wondering if it is possible to install or use any online service to measure your website's performance? I've seen many just checking the download speed of images, external files etc. But is it possible to meassure how long asp/php code takes to execute? I have a site running a bit slowly, and it would be very nice with some app/service guiding where to optimize.

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• Postgre database ignoring created index ?!

  - by drasto

  I have an Postgre database and a table called my_table. There are 4 columns in that table (id, column1, column2, column3). The id column is primary key, there are no other constrains or indexes on columns. The table has about 200000 rows. I want to print out all rows which has value of column column2 equal(case insensitive) to 'value12'. I use this: SELECT * FROM my_table WHERE column2 = lower('value12') here is the execution plan for this statement(result of set enable_seqscan=on; EXPLAIN SELECT * FROM my_table WHERE column2 = lower('value12')): Seq Scan on my_table (cost=0.00..4676.00 rows=10000 width=55) Filter: ((column2)::text = 'value12'::text) I consider this to be to slow so I create an index on column column2 for better prerformance of searches: CREATE INDEX my_index ON my_table (lower(column2)) Now I ran the same select: SELECT * FROM my_table WHERE column2 = lower('value12') and I expect it to be much faster because it can use index. However it is not faster, it is as slow as before. So I check the execution plan and it is the same as before(see above). So it still uses sequential scen and it ignores the index! Where is the problem ?

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• Does the <script> tag position in HTML affects performance of the webpage?

  - by Rahul Joshi

  If the script tag is above or below the body in a HTML page, does it matter for the performance of a website? And what if used in between like this: <body> ..blah..blah.. <script language="JavaScript" src="JS_File_100_KiloBytes"> function f1() { .. some logic reqd. for manipulating contents in a webpage } </script> ... some text here too ... </body> Or is this better?: <script language="JavaScript" src="JS_File_100_KiloBytes"> function f1() { .. some logic reqd. for manipulating contents in a webpage } </script> <body> ..blah..blah.. ..call above functions on some events like onclick,onfocus,etc.. </body> Or this one?: <body> ..blah..blah.. ..call above functions on some events like onclick,onfocus,etc.. <script language="JavaScript" src="JS_File_100_KiloBytes"> function f1() { .. some logic reqd. for manipulating contents in a webpage } </script> </body> Need not tell everything is again in the <html> tag!! How does it affect performance of webpage while loading? Does it really? Which one is the best, either out of these 3 or some other which you know? And one more thing, I googled a bit on this, from which I went here: Best Practices for Speeding Up Your Web Site and it suggests put scripts at the bottom, but traditionally many people put it in <head> tag which is above the <body> tag. I know it's NOT a rule but many prefer it that way. If you don't believe it, just view source of this page! And tell me what's the better style for best performance.

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• Coalesce function for PHP?

  - by mikl

  Many programming languages has a coalesce function (example). PHP, sadly, does not. What would be the most efficient way to implement one in PHP?

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• Faster way to split a string and count characters using R?

  - by chrisamiller

  I'm looking for a faster way to calculate GC content for DNA strings read in from a FASTA file. This boils down to taking a string and counting the number of times that the letter 'G' or 'C' appears. I also want to specify the range of characters to consider. I have a working function that is fairly slow, and it's causing a bottleneck in my code. It looks like this: ## ## count the number of GCs in the characters between start and stop ## gcCount <- function(line, st, sp){ chars = strsplit(as.character(line),"")[[1]] numGC = 0 for(j in st:sp){ ##nested ifs faster than an OR (|) construction if(chars[[j]] == "g"){ numGC <- numGC + 1 }else if(chars[[j]] == "G"){ numGC <- numGC + 1 }else if(chars[[j]] == "c"){ numGC <- numGC + 1 }else if(chars[[j]] == "C"){ numGC <- numGC + 1 } } return(numGC) } Running Rprof gives me the following output: > a = "GCCCAAAATTTTCCGGatttaagcagacataaattcgagg" > Rprof(filename="Rprof.out") > for(i in 1:500000){gcCount(a,1,40)}; > Rprof(NULL) > summaryRprof(filename="Rprof.out") self.time self.pct total.time total.pct "gcCount" 77.36 76.8 100.74 100.0 "==" 18.30 18.2 18.30 18.2 "strsplit" 3.58 3.6 3.64 3.6 "+" 1.14 1.1 1.14 1.1 ":" 0.30 0.3 0.30 0.3 "as.logical" 0.04 0.0 0.04 0.0 "as.character" 0.02 0.0 0.02 0.0 $by.total total.time total.pct self.time self.pct "gcCount" 100.74 100.0 77.36 76.8 "==" 18.30 18.2 18.30 18.2 "strsplit" 3.64 3.6 3.58 3.6 "+" 1.14 1.1 1.14 1.1 ":" 0.30 0.3 0.30 0.3 "as.logical" 0.04 0.0 0.04 0.0 "as.character" 0.02 0.0 0.02 0.0 $sampling.time [1] 100.74 Any advice for making this code faster?

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• How can I optimize this subqueried and Joined MySQL Query?

  - by kevzettler

  I'm pretty green on mysql and I need some tips on cleaning up a query. It is used in several variations through out a site. Its got some subquerys derived tables and fun going on. Heres the query: # Query_time: 2 Lock_time: 0 Rows_sent: 0 Rows_examined: 0 SELECT * FROM ( SELECT products . *, categories.category_name AS category, ( SELECT COUNT( * ) FROM distros WHERE distros.product_id = products.product_id) AS distro_count, (SELECT COUNT(*) FROM downloads WHERE downloads.product_id = products.product_id AND WEEK(downloads.date) = WEEK(curdate())) AS true_downloads, (SELECT COUNT(*) FROM views WHERE views.product_id = products.product_id AND WEEK(views.date) = WEEK(curdate())) AS true_views FROM products INNER JOIN categories ON products.category_id = categories.category_id ORDER BY created_date DESC, true_views DESC ) AS count_table WHERE count_table.distro_count > 0 AND count_table.status = 'published' AND count_table.active = 1 LIMIT 0, 8 Heres the explain: +----+--------------------+------------+-------+---------------+-------------+---------+------------------------------------+------+----------------------------------------------+ | id | select_type | table | type | possible_keys | key | key_len | ref | rows | Extra | +----+--------------------+------------+-------+---------------+-------------+---------+------------------------------------+------+----------------------------------------------+ | 1 | PRIMARY | <derived2> | ALL | NULL | NULL | NULL | NULL | 232 | Using where | | 2 | DERIVED | categories | index | PRIMARY | idx_name | 47 | NULL | 13 | Using index; Using temporary; Using filesort | | 2 | DERIVED | products | ref | category_id | category_id | 4 | digizald_db.categories.category_id | 9 | | | 5 | DEPENDENT SUBQUERY | views | ref | product_id | product_id | 4 | digizald_db.products.product_id | 46 | Using where | | 4 | DEPENDENT SUBQUERY | downloads | ref | product_id | product_id | 4 | digizald_db.products.product_id | 14 | Using where | | 3 | DEPENDENT SUBQUERY | distros | ref | product_id | product_id | 4 | digizald_db.products.product_id | 1 | Using index | +----+--------------------+------------+-------+---------------+-------------+---------+------------------------------------+------+----------------------------------------------+ 6 rows in set (0.04 sec) And the Tables: mysql> describe products; +---------------+--------------------------------------------------+------+-----+-------------------+----------------+ | Field | Type | Null | Key | Default | Extra | +---------------+--------------------------------------------------+------+-----+-------------------+----------------+ | product_id | int(10) unsigned | NO | PRI | NULL | auto_increment | | product_key | char(32) | NO | | NULL | | | title | varchar(150) | NO | | NULL | | | company | varchar(150) | NO | | NULL | | | user_id | int(10) unsigned | NO | MUL | NULL | | | description | text | NO | | NULL | | | video_code | text | NO | | NULL | | | category_id | int(10) unsigned | NO | MUL | NULL | | | price | decimal(10,2) | NO | | NULL | | | quantity | int(10) unsigned | NO | | NULL | | | downloads | int(10) unsigned | NO | | NULL | | | views | int(10) unsigned | NO | | NULL | | | status | enum('pending','published','rejected','removed') | NO | | NULL | | | active | tinyint(1) | NO | | NULL | | | deleted | tinyint(1) | NO | | NULL | | | created_date | datetime | NO | | NULL | | | modified_date | timestamp | NO | | CURRENT_TIMESTAMP | | | scrape_source | varchar(215) | YES | | NULL | | +---------------+--------------------------------------------------+------+-----+-------------------+----------------+ 18 rows in set (0.00 sec) mysql> describe categories -> ; +------------------+------------------+------+-----+---------+----------------+ | Field | Type | Null | Key | Default | Extra | +------------------+------------------+------+-----+---------+----------------+ | category_id | int(10) unsigned | NO | PRI | NULL | auto_increment | | category_name | varchar(45) | NO | MUL | NULL | | | parent_id | int(10) unsigned | YES | MUL | NULL | | | category_type_id | int(10) unsigned | NO | | NULL | | +------------------+------------------+------+-----+---------+----------------+ 4 rows in set (0.00 sec) mysql> describe compatibilities -> ; +------------------+------------------+------+-----+---------+----------------+ | Field | Type | Null | Key | Default | Extra | +------------------+------------------+------+-----+---------+----------------+ | compatibility_id | int(10) unsigned | NO | PRI | NULL | auto_increment | | name | varchar(45) | NO | | NULL | | | code_name | varchar(45) | NO | | NULL | | | description | varchar(128) | NO | | NULL | | | position | int(10) unsigned | NO | | NULL | | +------------------+------------------+------+-----+---------+----------------+ 5 rows in set (0.01 sec) mysql> describe distros -> ; +------------------+--------------------------------------------------+------+-----+---------+----------------+ | Field | Type | Null | Key | Default | Extra | +------------------+--------------------------------------------------+------+-----+---------+----------------+ | id | int(10) unsigned | NO | PRI | NULL | auto_increment | | product_id | int(10) unsigned | NO | MUL | NULL | | | compatibility_id | int(10) unsigned | NO | MUL | NULL | | | user_id | int(10) unsigned | NO | | NULL | | | status | enum('pending','published','rejected','removed') | NO | | NULL | | | distro_type | enum('file','url') | NO | | NULL | | | version | varchar(150) | NO | | NULL | | | filename | varchar(50) | YES | | NULL | | | url | varchar(250) | YES | | NULL | | | virus | enum('READY','PASS','FAIL') | YES | | NULL | | | downloads | int(10) unsigned | NO | | 0 | | +------------------+--------------------------------------------------+------+-----+---------+----------------+ 11 rows in set (0.01 sec) mysql> describe downloads; +------------+------------------+------+-----+---------+----------------+ | Field | Type | Null | Key | Default | Extra | +------------+------------------+------+-----+---------+----------------+ | id | int(10) unsigned | NO | PRI | NULL | auto_increment | | product_id | int(10) unsigned | NO | MUL | NULL | | | distro_id | int(10) unsigned | NO | MUL | NULL | | | user_id | int(10) unsigned | NO | MUL | NULL | | | ip_address | varchar(15) | NO | | NULL | | | date | datetime | NO | | NULL | | +------------+------------------+------+-----+---------+----------------+ 6 rows in set (0.01 sec) mysql> describe views -> ; +------------+------------------+------+-----+---------+----------------+ | Field | Type | Null | Key | Default | Extra | +------------+------------------+------+-----+---------+----------------+ | id | int(10) unsigned | NO | PRI | NULL | auto_increment | | product_id | int(10) unsigned | NO | MUL | NULL | | | user_id | int(10) unsigned | NO | MUL | NULL | | | ip_address | varchar(15) | NO | | NULL | | | date | datetime | NO | | NULL | | +------------+------------------+------+-----+---------+----------------+ 5 rows in set (0.00 sec)

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• How to improve performance of map that loads new overlay images

  - by anthonysomerset

  I have inherited a website to maintain that uses a html map overlaying a real map to link specific countries to specific pages. previously it loaded the default map image, then with some javascript it would change the image src to an image with that particular country in a different colour on mouseover and reset the image source back to the original image on mouse out to make maintenance (adding new countries) easier i made the initial map a background image by utilising some CSS for the div tag, and then created new images for each country which only had that countries hightlight so that the images remain fairly small. this works great but theres one issue which is particularly noticeable on slower internet connections when you hover over a country if you dont have the image file in your browser cache or downloaded it wont load the image unless you hover over another country and then back onto the first country - i guess this is due to the image having to manually be downloaded on first hover. My question: is it possible to force the load of these extra images AFTER the page and all the other assets have finished loading so that this behaviour is all but eliminated? the html code for the MAP is as follows: <div class="gtmap"><img id="Image-Maps_6200909211657061" src="<?php echo cdnhttpsCheck(); ?>assets/wmap/a-guided-tours-map-blank.png" usemap="#Image-Maps_6200909211657061" alt="We offer Guided Motorcycle Tours all around the world" width="615" height="296" /> <map id="_Image-Maps_6200909211657061" name="Image-Maps_6200909211657061"> <area shape="poly" coords="511,134,532,107,542,113,520,141" href="/guided-motorcycle-tours-japan/" alt="Guided Japan Motorcycle Tours" title="Japan" onmouseover="if(document.images) document.getElementById('Image-Maps_6200909211657061').src='<?php echo cdnhttpsCheck(); ?>assets/wmap/a-guided-tours-map-japan.png';" onmouseout="if(document.images) document.getElementById('Image-Maps_6200909211657061').src='<?php echo cdnhttpsCheck(); ?>assets/wmap/a-guided-tours-map-blank.png';" /> <area shape="poly" coords="252,61,266,58,275,64,262,68" href="/guided-motorcycle-tour.php?iceland-motorcycle-adventure-39" alt="Guided Iceland Motorcycle Tours" title="Iceland" onmouseover="if(document.images) document.getElementById('Image-Maps_6200909211657061').src='<?php echo cdnhttpsCheck(); ?>assets/wmap/a-guided-tours-map-iceland.png';" onmouseout="if(document.images) document.getElementById('Image-Maps_6200909211657061').src='<?php echo cdnhttpsCheck(); ?>assets/wmap/a-guided-tours-map-blank.png';" /> <area shape="poly" coords="587,246,597,256,577,279,568,270" href="/guided-motorcycle-tour.php?new-zealand-south-island-adventure-10" alt="New Zealand Guided Motorcycle Tours" title="New Zealand" onmouseover="if(document.images) document.getElementById('Image-Maps_6200909211657061').src='<?php echo cdnhttpsCheck(); ?>assets/wmap/a-guided-tours-map-nz.png';" onmouseout="if(document.images) document.getElementById('Image-Maps_6200909211657061').src='<?php echo cdnhttpsCheck(); ?>assets/wmap/a-guided-tours-map-blank.png';" /> <area shape="poly" coords="418,133,412,145,412,154,421,178,430,180,430,166,443,154,443,145,438,144,433,142,430,138,431,130,430,129,425,128" href="/guided-motorcycle-tours-india/" alt="India Guided Motorcycle Tours" title="India" onmouseover="if(document.images) document.getElementById('Image-Maps_6200909211657061').src='<?php echo cdnhttpsCheck(); ?>assets/wmap/a-guided-tours-map-india.png';" onmouseout="if(document.images) document.getElementById('Image-Maps_6200909211657061').src='<?php echo cdnhttpsCheck(); ?>assets/wmap/a-guided-tours-map-blank.png';" /> <area shape="poly" coords="460,152,466,149,474,165,470,171,466,161" href="/guided-motorcycle-tours-laos/" alt="Laos Guided Motorcycle Tours" title="Laos" onmouseover="if(document.images) document.getElementById('Image-Maps_6200909211657061').src='<?php echo cdnhttpsCheck(); ?>assets/wmap/a-guided-tours-map-laos.png';" onmouseout="if(document.images) document.getElementById('Image-Maps_6200909211657061').src='<?php echo cdnhttpsCheck(); ?>assets/wmap/a-guided-tours-map-blank.png';" /> <area shape="poly" coords="468,179,475,166,468,152,475,152,482,169" href="/guided-motorcycle-tour.php?indochina-motorcycle-adventure-tour-32" onClick="javascript: pageTracker._trackPageview('/internal-links/guided-tours/map/vietnam');" alt="Vietnam Guided Motorcycle Tours" title="Vietnam" onmouseover="if(document.images) document.getElementById('Image-Maps_6200909211657061').src='<?php echo cdnhttpsCheck(); ?>assets/wmap/a-guided-tours-map-viet.png';" onmouseout="if(document.images) document.getElementById('Image-Maps_6200909211657061').src='<?php echo cdnhttpsCheck(); ?>assets/wmap/a-guided-tours-map-blank.png';" /> <area shape="poly" coords="330,239,337,235,347,226,352,233,351,243,344,250,335,253,327,255,323,249,322,242,323,241" href="/guided-motorcycle-tours-southafrica/" alt="South Africa Guided Motorcycle Tours" title="South Africa" onmouseover="if(document.images) document.getElementById('Image-Maps_6200909211657061').src='<?php echo cdnhttpsCheck(); ?>assets/wmap/a-guided-tours-map-sa.png';" onmouseout="if(document.images) document.getElementById('Image-Maps_6200909211657061').src='<?php echo cdnhttpsCheck(); ?>assets/wmap/a-guided-tours-map-blank.png';" /> <area shape="poly" coords="290,77,293,86,298,96,286,102,285,97,285,89,282,84,282,79" href="/guided-motorcycle-tour.php?great-britain-isle-of-man-scotland-wales-uk-18" alt="United Kingdom" title="United Kingdom Guided Motorcycle Tours" onmouseover="if(document.images) document.getElementById('Image-Maps_6200909211657061').src='<?php echo cdnhttpsCheck(); ?>assets/wmap/a-guided-tours-map-uk.png';" onmouseout="if(document.images) document.getElementById('Image-Maps_6200909211657061').src='<?php echo cdnhttpsCheck(); ?>assets/wmap/a-guided-tours-map-blank.png';" /> <area shape="poly" coords="357,118,368,118,369,126,345,129,338,125,338,117,342,115,348,116" href="/guided-motorcycle-tour.php?explore-turkey-adventure-45" alt="Turkey" title="Turkey Guided Motorcycle Tours" onmouseover="if(document.images) document.getElementById('Image-Maps_6200909211657061').src='<?php echo cdnhttpsCheck(); ?>assets/wmap/a-guided-tours-map-turkey.png';" onmouseout="if(document.images) document.getElementById('Image-Maps_6200909211657061').src='<?php echo cdnhttpsCheck(); ?>assets/wmap/a-guided-tours-map-blank.png';" /> <area shape="poly" coords="206,95,193,101,185,101,178,106,165,111,157,109,147,105,134,103,121,103,107,103,96,103,86,104,81,99,77,91,70,83,62,79,60,72,61,64,59,57,60,51,71,50,83,49,95,50,107,54,117,53,129,47,137,36,148,37,163,38,177,44,187,54,195,60,184,72,191,80,200,87" href="/guided-motorcycle-tours-canada/" alt="Guided Canada Motorcycle Tours" title="Canada" onmouseover="if(document.images) document.getElementById('Image-Maps_6200909211657061').src='<?php echo cdnhttpsCheck(); ?>assets/wmap/a-guided-tours-map-canada.png';" onmouseout="if(document.images) document.getElementById('Image-Maps_6200909211657061').src='<?php echo cdnhttpsCheck(); ?>assets/wmap/a-guided-tours-map-blank.png';" /> <area shape="poly" coords="61,75,60,62,60,55,59,44,51,44,43,43,36,42,28,43,23,48,17,51,15,62,19,74,27,79,19,83,16,93,35,83,43,77,50,75,55,75" href="/guided-motorcycle-tours-alaska/" alt="Guided Alaska Motorcycle Tours" title="Alaska" onmouseover="if(document.images) document.getElementById('Image-Maps_6200909211657061').src='<?php echo cdnhttpsCheck(); ?>assets/wmap/a-guided-tours-map-alaska.png';" onmouseout="if(document.images) document.getElementById('Image-Maps_6200909211657061').src='<?php echo cdnhttpsCheck(); ?>assets/wmap/a-guided-tours-map-blank.png';" /> <area shape="poly" coords="82,101,99,101,133,101,148,105,161,110,172,106,187,100,180,113,171,122,165,131,159,149,147,141,137,140,129,147,120,141,112,138,103,137,93,132,86,122,86,112,86,106" href="/guided-motorcycle-tours-usa/" alt="USA Guided Motorcycle Tours" title="USA" onmouseover="if(document.images) document.getElementById('Image-Maps_6200909211657061').src='<?php echo cdnhttpsCheck(); ?>assets/wmap/a-guided-tours-map-usa.png';" onmouseout="if(document.images) document.getElementById('Image-Maps_6200909211657061').src='<?php echo cdnhttpsCheck(); ?>assets/wmap/a-guided-tours-map-blank.png';" /> <area shape="poly" coords="178,225,180,214,175,208,174,204,178,198,174,193,167,192,157,199,158,204,164,211,167,218" href="/guided-motorcycle-tour.php?peru-machu-picchu-adventure-25" alt="Peru Guided Motorcycle Tours" title="Peru" onmouseover="if(document.images) document.getElementById('Image-Maps_6200909211657061').src='<?php echo cdnhttpsCheck(); ?>assets/wmap/a-guided-tours-map-peru.png';" onmouseout="if(document.images) document.getElementById('Image-Maps_6200909211657061').src='<?php echo cdnhttpsCheck(); ?>assets/wmap/a-guided-tours-map-blank.png';" /> <area shape="poly" coords="172,226,169,239,166,256,166,267,164,279,171,277,174,262,175,250,179,234,180,225,176,224" href="/guided-motorcycle-tours-chile/" alt="Guided Chile Motorcycle Tours" title="Chile" onmouseover="if(document.images) document.getElementById('Image-Maps_6200909211657061').src='<?php echo cdnhttpsCheck(); ?>assets/wmap/a-guided-tours-map-chile.png';" onmouseout="if(document.images) document.getElementById('Image-Maps_6200909211657061').src='<?php echo cdnhttpsCheck(); ?>assets/wmap/a-guided-tours-map-blank.png';" /> <area shape="poly" coords="199,260,194,261,187,265,184,276,183,296,170,292,168,282,174,270,174,257,177,245,180,230,190,228,205,237,199,245" href="/guided-motorcycle-tours-argentina/" alt="Guided Argentina Motorcycle Tours" title="Argentina" onmouseover="if(document.images) document.getElementById('Image-Maps_6200909211657061').src='<?php echo cdnhttpsCheck(); ?>assets/wmap/a-guided-tours-map-arg.png';" onmouseout="if(document.images) document.getElementById('Image-Maps_6200909211657061').src='<?php echo cdnhttpsCheck(); ?>assets/wmap/a-guided-tours-map-blank.png';" /> </map> </div> The <?php echo cdnhttpsCheck(); ?> is just a site specific function that gets the correct web domain/url from a config file to load resources from CDN where possible (eg all non HTTPS requests) We are loading Jquery at the bottom of the HTML if anybody wonders why it is missing from the code snippet for reference, the page with the map in question is found here: http://www.motoquest.com/guided-motorcycle-tours/

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• Is SQL DATEDIFF(year, ..., ...) an Expensive Computation?

  - by rlb.usa

  I'm trying to optimize up some horrendously complicated SQL queries because it takes too long to finish. In my queries, I have dynamically created SQL statements with lots of the same functions, so I created a temporary table where each function is only called once instead of many, many times - this cut my execution time by 3/4. So my question is, can I expect to see much of a difference if say, 1,000 datediff computations are narrowed to 100?

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• How can I optimize retrieving lowest edit distance from a large table in SQL?

  - by Matt

  Hey, I'm having troubles optimizing this Levenshtein Distance calculation I'm doing. I need to do the following: Get the record with the minimum distance for the source string as well as a trimmed version of the source string Pick the record with the minimum distance If the min distances are equal (original vs trimmed), choose the trimmed one with the lowest distance If there are still multiple records that fall under the above two categories, pick the one with the highest frequency Here's my working version: DECLARE @Results TABLE ( ID int, [Name] nvarchar(200), Distance int, Frequency int, Trimmed bit ) INSERT INTO @Results SELECT ID, [Name], (dbo.Levenshtein(@Source, [Name])) As Distance, Frequency, 'False' As Trimmed FROM MyTable INSERT INTO @Results SELECT ID, [Name], (dbo.Levenshtein(@SourceTrimmed, [Name])) As Distance, Frequency, 'True' As Trimmed FROM MyTable SET @ResultID = (SELECT TOP 1 ID FROM @Results ORDER BY Distance, Trimmed, Frequency) SET @Result = (SELECT TOP 1 [Name] FROM @Results ORDER BY Distance, Trimmed, Frequency) SET @ResultDist = (SELECT TOP 1 Distance FROM @Results ORDER BY Distance, Trimmed, Frequency) SET @ResultTrimmed = (SELECT TOP 1 Trimmed FROM @Results ORDER BY Distance, Trimmed, Frequency) I believe what I need to do here is to.. Not dumb the results to a temporary table Do only 1 select from `MyTable` Setting the results right in the select from the initial select statement. (Since select will set variables and you can set multiple variables in one select statement) I know there has to be a good implementation to this but I can't figure it out... this is as far as I got: SELECT top 1 @ResultID = ID, @Result = [Name], (dbo.Levenshtein(@Source, [Name])) As distOrig, (dbo.Levenshtein(@SourceTrimmed, [Name])) As distTrimmed, Frequency FROM MyTable WHERE /* ... yeah I'm lost */ ORDER BY distOrig, distTrimmed, Frequency Any ideas?

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• SQL Server indexed view matching of views with joins not working

  - by usr

  Does anyone have experience of when SQL Servr 2008 R2 is able to automatically match indexed view (also known as materialized views) that contain joins to a query? for example the view select dbo.Orders.Date, dbo.OrderDetails.ProductID from dbo.OrderDetails join dbo.Orders on dbo.OrderDetails.OrderID = dbo.Orders.ID cannot be automatically matched to the same exact query. When I select directly from this view ith (noexpand) I actually get a much faster query plan that does a scan on the clustered index of the indexed view. Can I get SQL Server to do this matching automatically? I have quite a few queries and views... I am on enterprise edition of SQL Server 2008 R2.

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• Single Large v/s Multiple Small MySQL tables for storing Options

  - by Prasad

  Hi there, I'm aware of several question on this forum relating to this. But I'm not talking about splitting tables for the same entity (like user for example) Suppose I have a huge options table that stores list options like Gender, Marital Status, and many more domain specific groups with same structure. I plan to capture in a OPTIONS table. Another simple option is to have the field set as ENUM, but there are disadvantages of that as well. http://www.brandonsavage.net/why-you-should-replace-enum-with-something-else/ OPTIONS Table: option_id <will be referred instead of the name> name value group Query: select .. from options where group = '15' - Since this table is expected to be multi-tenant, the no of rows could grow drastically. - I believe splitting the tables instead of finding by the group would be easier to write & faster to execute. - or perhaps partitioning by the group or tenant? Pl suggest. Thanks

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• Most Efficient Alternative Method of Storing Settings for iPhone Apps

  - by JPK

  I am not using the Settings bundle to store the settings for my app, as I prefer to allow the user to access the settings within the app (they may be changed fairly often). I do realize that there is the option to do both, but for now, I am trying to find the most optimal place to store the settings within the app. I have a good number of settings (from what I have read, probably too many for NSUserDefaults), and the two main options I am considering are: 1) storing the settings in a dictionary in the plist, loading the settings into a NSDictionary property in the app delegate and accessing them via the sharedDelegate 2) storing the settings in a Core Data entity (1 row on Settings entity), loading the settings into a Settings object in the app delegate and accessing them via the sharedDelegate Of these two, which would be the optimal method, performance wise?

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• Trying to reduce the speed overhead of an almost-but-not-quite-int number class

  - by Fumiyo Eda

  I have implemented a C++ class which behaves very similarly to the standard int type. The difference is that it has an additional concept of "epsilon" which represents some tiny value that is much less than 1, but greater than 0. One way to think of it is as a very wide fixed point number with 32 MSBs (the integer parts), 32 LSBs (the epsilon parts) and a huge sea of zeros in between. The following class works, but introduces a ~2x speed penalty in the overall program. (The program includes code that has nothing to do with this class, so the actual speed penalty of this class is probably much greater than 2x.) I can't paste the code that is using this class, but I can say the following: +, -, +=, <, > and >= are the only heavily used operators. Use of setEpsilon() and getInt() is extremely rare. * is also rare, and does not even need to consider the epsilon values at all. Here is the class: #include <limits> struct int32Uepsilon { typedef int32Uepsilon Self; int32Uepsilon () { _value = 0; _eps = 0; } int32Uepsilon (const int &i) { _value = i; _eps = 0; } void setEpsilon() { _eps = 1; } Self operator+(const Self &rhs) const { Self result = *this; result._value += rhs._value; result._eps += rhs._eps; return result; } Self operator-(const Self &rhs) const { Self result = *this; result._value -= rhs._value; result._eps -= rhs._eps; return result; } Self operator-( ) const { Self result = *this; result._value = -result._value; result._eps = -result._eps; return result; } Self operator*(const Self &rhs) const { return this->getInt() * rhs.getInt(); } // XXX: discards epsilon bool operator<(const Self &rhs) const { return (_value < rhs._value) || (_value == rhs._value && _eps < rhs._eps); } bool operator>(const Self &rhs) const { return (_value > rhs._value) || (_value == rhs._value && _eps > rhs._eps); } bool operator>=(const Self &rhs) const { return (_value >= rhs._value) || (_value == rhs._value && _eps >= rhs._eps); } Self &operator+=(const Self &rhs) { this->_value += rhs._value; this->_eps += rhs._eps; return *this; } Self &operator-=(const Self &rhs) { this->_value -= rhs._value; this->_eps -= rhs._eps; return *this; } int getInt() const { return(_value); } private: int _value; int _eps; }; namespace std { template<> struct numeric_limits<int32Uepsilon> { static const bool is_signed = true; static int max() { return 2147483647; } } }; The code above works, but it is quite slow. Does anyone have any ideas on how to improve performance? There are a few hints/details I can give that might be helpful: 32 bits are definitely insufficient to hold both _value and _eps. In practice, up to 24 ~ 28 bits of _value are used and up to 20 bits of _eps are used. I could not measure a significant performance difference between using int32_t and int64_t, so memory overhead itself is probably not the problem here. Saturating addition/subtraction on _eps would be cool, but isn't really necessary. Note that the signs of _value and _eps are not necessarily the same! This broke my first attempt at speeding this class up. Inline assembly is no problem, so long as it works with GCC on a Core i7 system running Linux!

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• Any difference between lazy loading Javascript files vs. placing just before </body>

  - by mhr

  Looked around, couldn't find this specific question discussed. Pretty sure the difference is negligible, just curious as to your thoughts. Scenario: All Javascript that doesn't need to be loaded before page render has been placed just before the closing </body> tag. Are there any benefits or detriments to lazy loading these instead through some Javascript code in the head that executes when the DOM load/ready event is fired? Let's say that this only concerns downloading one entire .js file full of functions and not lazy loading several individual files as needed upon usage. Hope that's clear, thanks.

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• "Anagram solver" based on statistics rather than a dictionary/table?

  - by James M.

  My problem is conceptually similar to solving anagrams, except I can't just use a dictionary lookup. I am trying to find plausible words rather than real words. I have created an N-gram model (for now, N=2) based on the letters in a bunch of text. Now, given a random sequence of letters, I would like to permute them into the most likely sequence according to the transition probabilities. I thought I would need the Viterbi algorithm when I started this, but as I look deeper, the Viterbi algorithm optimizes a sequence of hidden random variables based on the observed output. I am trying to optimize the output sequence. Is there a well-known algorithm for this that I can read about? Or am I on the right track with Viterbi and I'm just not seeing how to apply it?

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• An image from byte to optimized web page presentation

  - by blgnklc

  I get the data of the stored image on database as byte[] array; then I convert it to System.Drawing.Image like the code shown below; public System.Drawing.Image CreateImage(byte[] bytes) { System.IO.MemoryStream memoryStream = new System.IO.MemoryStream(bytes); System.Drawing.Image image = System.Drawing.Image.FromStream(memoryStream); return image; } (*) On the other hand I am planning to show a list of images on asp.net pages as the client scrolls downs the page. The more user gets down and down on the page he/she does see the more photos. So it means fast page loads and rich user experience. (you may see what I mean on www.mashable.com, just take care the new loads of the photos as you scroll down.) Moreover, the returned imgae object from the method above, how can i show it in a loop dynamically using the (*) conditions above. Regards bk

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• Find point which sum of distances to set of other points is minimal

  - by Pawel Markowski

  I have one set (X) of points (not very big let's say 1-20 points) and the second (Y), much larger set of points. I need to choose some point from Y which sum of distances to all points from X is minimal. I came up with an idea that I would treat X as a vertices of a polygon and find centroid of this polygon, and then I will choose a point from Y nearest to the centroid. But I'm not sure whether centroid minimizes sum of its distances to the vertices of polygon, so I'm not sure whether this is a good way? Is there any algorithm for solving this problem? Points are defined by geographical coordinates.

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• Can anyone recommend a decent tool for optimising images other than photoshop

  - by toomanyairmiles

  Can anyone recommend a decent tool for optimising images other than adobe photoshop, the gimp etc? I'm looking to optimise images for the web preferably online and free. Basically I have a client who can't install additional software on their work PC but needs to optimise photographs and other images for their website and is presently uploading 1 or 2 Mb files. On a personal level I'm interested to see what other people are using...

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• Speeding up inner joins between a large table and a small table

  - by Zaid

  This may be a silly question, but it may shed some light on how joins work internally. Let's say I have a large table L and a small table S (100K rows vs. 100 rows). Would there be any difference in terms of speed between the following two options?: OPTION 1: OPTION 2: --------- --------- SELECT * SELECT * FROM L INNER JOIN S FROM S INNER JOIN L ON L.id = S.id; ON L.id = S.id; Notice that the only difference is the order in which the tables are joined. I realize performance may vary between different SQL languages. If so, how would MySQL compare to Access?

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• Rewriting a for loop in pure NumPy to decrease execution time

  - by Statto

  I recently asked about trying to optimise a Python loop for a scientific application, and received an excellent, smart way of recoding it within NumPy which reduced execution time by a factor of around 100 for me! However, calculation of the B value is actually nested within a few other loops, because it is evaluated at a regular grid of positions. Is there a similarly smart NumPy rewrite to shave time off this procedure? I suspect the performance gain for this part would be less marked, and the disadvantages would presumably be that it would not be possible to report back to the user on the progress of the calculation, that the results could not be written to the output file until the end of the calculation, and possibly that doing this in one enormous step would have memory implications? Is it possible to circumvent any of these? import numpy as np import time def reshape_vector(v): b = np.empty((3,1)) for i in range(3): b[i][0] = v[i] return b def unit_vectors(r): return r / np.sqrt((r*r).sum(0)) def calculate_dipole(mu, r_i, mom_i): relative = mu - r_i r_unit = unit_vectors(relative) A = 1e-7 num = A*(3*np.sum(mom_i*r_unit, 0)*r_unit - mom_i) den = np.sqrt(np.sum(relative*relative, 0))**3 B = np.sum(num/den, 1) return B N = 20000 # number of dipoles r_i = np.random.random((3,N)) # positions of dipoles mom_i = np.random.random((3,N)) # moments of dipoles a = np.random.random((3,3)) # three basis vectors for this crystal n = [10,10,10] # points at which to evaluate sum gamma_mu = 135.5 # a constant t_start = time.clock() for i in range(n[0]): r_frac_x = np.float(i)/np.float(n[0]) r_test_x = r_frac_x * a[0] for j in range(n[1]): r_frac_y = np.float(j)/np.float(n[1]) r_test_y = r_frac_y * a[1] for k in range(n[2]): r_frac_z = np.float(k)/np.float(n[2]) r_test = r_test_x +r_test_y + r_frac_z * a[2] r_test_fast = reshape_vector(r_test) B = calculate_dipole(r_test_fast, r_i, mom_i) omega = gamma_mu*np.sqrt(np.dot(B,B)) # write r_test, B and omega to a file frac_done = np.float(i+1)/(n[0]+1) t_elapsed = (time.clock()-t_start) t_remain = (1-frac_done)*t_elapsed/frac_done print frac_done*100,'% done in',t_elapsed/60.,'minutes...approximately',t_remain/60.,'minutes remaining'

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• Can I use Duff's Device on an array in C?

  - by Ben Fossen

  I have a loop here and I want to make it run faster. I am passing in a large array. I recently heard of Duff's Device can it be applied to this for loop? any ideas? for (i = 0; i < dim; i++) { for (j = 0; j < dim; j++) { dst[RIDX(dim-1-j, i, dim)] = src[RIDX(i, j, dim)]; } }

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• Optimize a MySQL count each duplicate Query

  - by Onema

  I have the following query That gets the city name, city id, the region name, and a count of duplicate names for that record: SELECT Country_CA.City AS currentCity, Country_CA.CityID, globe_region.region_name, ( SELECT count(Country_CA.City) FROM Country_CA WHERE City LIKE currentCity ) as counter FROM Country_CA LEFT JOIN globe_region ON globe_region.region_id = Country_CA.RegionID AND globe_region.country_code = Country_CA.CountryCode ORDER BY City This example is for Canada, and the cities will be displayed on a dropdown list. There are a few towns in Canada, and in other countries, that have the same names. Therefore I want to know if there is more than one town with the same name region name will be appended to the town name. Region names are found in the globe_region table. Country_CA and globe_region look similar to this (I have changed a few things for visualization purposes) CREATE TABLE IF NOT EXISTS `Country_CA` ( `City` varchar(75) NOT NULL DEFAULT '', `RegionID` varchar(10) NOT NULL DEFAULT '', `CountryCode` varchar(10) NOT NULL DEFAULT '', `CityID` int(11) NOT NULL DEFAULT '0', PRIMARY KEY (`City`,`RegionID`), KEY `CityID` (`CityID`) ) ENGINE=MyISAM DEFAULT CHARSET=utf8; AND CREATE TABLE IF NOT EXISTS `globe_region` ( `country_code` char(2) COLLATE utf8_unicode_ci NOT NULL, `region_code` char(2) COLLATE utf8_unicode_ci NOT NULL, `region_name` varchar(50) COLLATE utf8_unicode_ci NOT NULL, PRIMARY KEY (`country_code`,`region_code`) ) ENGINE=MyISAM DEFAULT CHARSET=utf8 COLLATE=utf8_unicode_ci; The query on the top does exactly what I want it to do, but It takes way too long to generate a list for 5000 records. I would like to know if there is a way to optimize the sub-query in order to obtain the same results faster. the results should look like this City CityID region_name counter sheraton 2349269 British Columbia 1 sherbrooke 2349270 Quebec 2 sherbrooke 2349271 Nova Scotia 2 shere 2349273 British Columbia 1 sherridon 2349274 Manitoba 1

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• approximating log10[x^k0 + k1]

  - by Yale Zhang

  Greetings. I'm trying to approximate the function Log10[x^k0 + k1], where .21 < k0 < 21, 0 < k1 < ~2000, and x is integer < 2^14. k0 & k1 are constant. For practical purposes, you can assume k0 = 2.12, k1 = 2660. The desired accuracy is 5*10^-4 relative error. This function is virtually identical to Log[x], except near 0, where it differs a lot. I already have came up with a SIMD implementation that is ~1.15x faster than a simple lookup table, but would like to improve it if possible, which I think is very hard due to lack of efficient instructions. My SIMD implementation uses 16bit fixed point arithmetic to evaluate a 3rd degree polynomial (I use least squares fit). The polynomial uses different coefficients for different input ranges. There are 8 ranges, and range i spans (64)2^i to (64)2^(i + 1). The rational behind this is the derivatives of Log[x] drop rapidly with x, meaning a polynomial will fit it more accurately since polynomials are an exact fit for functions that have a derivative of 0 beyond a certain order. SIMD table lookups are done very efficiently with a single _mm_shuffle_epi8(). I use SSE's float to int conversion to get the exponent and significand used for the fixed point approximation. I also software pipelined the loop to get ~1.25x speedup, so further code optimizations are probably unlikely. What I'm asking is if there's a more efficient approximation at a higher level? For example: Can this function be decomposed into functions with a limited domain like log2((2^x) * significand) = x + log2(significand) hence eliminating the need to deal with different ranges (table lookups). The main problem I think is adding the k1 term kills all those nice log properties that we know and love, making it not possible. Or is it? Iterative method? don't think so because the Newton method for log[x] is already a complicated expression Exploiting locality of neighboring pixels? - if the range of the 8 inputs fall in the same approximation range, then I can look up a single coefficient, instead of looking up separate coefficients for each element. Thus, I can use this as a fast common case, and use a slower, general code path when it isn't. But for my data, the range needs to be ~2000 before this property hold 70% of the time, which doesn't seem to make this method competitive. Please, give me some opinion, especially if you're an applied mathematician, even if you say it can't be done. Thanks.

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• c++ optimize array of ints

  - by a432511

  I have a 2D lookup table of int16_t. int16_t my_array[37][73] = {{**DATA HERE**}} I have a mixture of values that range from just above the range of int8_t to just below the range of int8_t and some of the values repeat themselves. I am trying to reduce the size of this lookup table. What I have done so far is split each int16_t value into two int8_t values to visualize the wasted bytes. int8_t part_1 = original_value >> 4; int8_t part_2 = original_value & 0x0000FFFF; // If the upper 4 bits of the original_value were empty if(part_1 == 0) wasted_bytes_count++; I can easily remove the zero value int8_t that are wasting a byte of space and I can also remove the duplicate values, but my question is how do I do remove those values while retaining the ability to lookup based on the two indices? I contemplated translating this into a 1D array and adding a number following each duplicated value that would represent the number of duplicates that were removed, but I am struggling with how I would then identify what is a lookup value and what is a duplicate count. Also, it is further complicated by stripping out the zero int8_t values that were wasted bytes. EDIT: This array is stored in ROM already. RAM is even more limited than ROM so it is already stored in ROM. EDIT: I am going to post a bounty for this question as soon as I can. I need a complete answer of how to store the information AND retrieve it. It does not need to be a 2D array as long as I can get the same values. EDIT: Adding the actual array below: {150,145,140,135,130,125,120,115,110,105,100,95,90,85,80,75,70,65,60,55,50,45,40,35,30,25,20,15,10,5,0,-4,-9,-14,-19,-24,-29,-34,-39,-44,-49,-54,-59,-64,-69,-74,-79,-84,-89,-94,-99,104,109,114,119,124,129,134,139,144,149,154,159,164,169,174,179,175,170,165,160,155,150}, \ {143,137,131,126,120,115,110,105,100,95,90,85,80,75,71,66,62,57,53,48,44,39,35,31,27,22,18,14,9,5,1,-3,-7,-11,-16,-20,-25,-29,-34,-38,-43,-47,-52,-57,-61,-66,-71,-76,-81,-86,-91,-96,101,107,112,117,123,128,134,140,146,151,157,163,169,175,178,172,166,160,154,148,143}, \ {130,124,118,112,107,101,96,92,87,82,78,74,70,65,61,57,54,50,46,42,38,34,31,27,23,19,16,12,8,4,1,-2,-6,-10,-14,-18,-22,-26,-30,-34,-38,-43,-47,-51,-56,-61,-65,-70,-75,-79,-84,-89,-94,100,105,111,116,122,128,135,141,148,155,162,170,177,174,166,159,151,144,137,130}, \ {111,104,99,94,89,85,81,77,73,70,66,63,60,56,53,50,46,43,40,36,33,30,26,23,20,16,13,10,6,3,0,-3,-6,-9,-13,-16,-20,-24,-28,-32,-36,-40,-44,-48,-52,-57,-61,-65,-70,-74,-79,-84,-88,-93,-98,103,109,115,121,128,135,143,152,162,172,176,165,154,144,134,125,118,111}, \ {85,81,77,74,71,68,65,63,60,58,56,53,51,49,46,43,41,38,35,32,29,26,23,19,16,13,10,7,4,1,-1,-3,-6,-9,-13,-16,-19,-23,-26,-30,-34,-38,-42,-46,-50,-54,-58,-62,-66,-70,-74,-78,-83,-87,-91,-95,100,105,110,117,124,133,144,159,178,160,141,125,112,103,96,90,85}, \ {62,60,58,57,55,54,52,51,50,48,47,46,44,42,41,39,36,34,31,28,25,22,19,16,13,10,7,4,2,0,-3,-5,-8,-10,-13,-16,-19,-22,-26,-29,-33,-37,-41,-45,-49,-53,-56,-60,-64,-67,-70,-74,-77,-80,-83,-86,-89,-91,-94,-97,101,105,111,130,109,84,77,74,71,68,66,64,62}, \ {46,46,45,44,44,43,42,42,41,41,40,39,38,37,36,35,33,31,28,26,23,20,16,13,10,7,4,1,-1,-3,-5,-7,-9,-12,-14,-16,-19,-22,-26,-29,-33,-36,-40,-44,-48,-51,-55,-58,-61,-64,-66,-68,-71,-72,-74,-74,-75,-74,-72,-68,-61,-48,-25,2,22,33,40,43,45,46,47,46,46}, \ {36,36,36,36,36,35,35,35,35,34,34,34,34,33,32,31,30,28,26,23,20,17,14,10,6,3,0,-2,-4,-7,-9,-10,-12,-14,-15,-17,-20,-23,-26,-29,-32,-36,-40,-43,-47,-50,-53,-56,-58,-60,-62,-63,-64,-64,-63,-62,-59,-55,-49,-41,-30,-17,-4,6,15,22,27,31,33,34,35,36,36}, \ {30,30,30,30,30,30,30,29,29,29,29,29,29,29,29,28,27,26,24,21,18,15,11,7,3,0,-3,-6,-9,-11,-12,-14,-15,-16,-17,-19,-21,-23,-26,-29,-32,-35,-39,-42,-45,-48,-51,-53,-55,-56,-57,-57,-56,-55,-53,-49,-44,-38,-31,-23,-14,-6,0,7,13,17,21,24,26,27,29,29,30}, \ {25,25,26,26,26,25,25,25,25,25,25,25,25,26,25,25,24,23,21,19,16,12,8,4,0,-3,-7,-10,-13,-15,-16,-17,-18,-19,-20,-21,-22,-23,-25,-28,-31,-34,-37,-40,-43,-46,-48,-49,-50,-51,-51,-50,-48,-45,-42,-37,-32,-26,-19,-13,-7,-1,3,7,11,14,17,19,21,23,24,25,25}, \ {21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,21,20,18,16,13,9,5,1,-3,-7,-11,-14,-17,-18,-20,-21,-21,-22,-22,-22,-23,-23,-25,-27,-29,-32,-35,-37,-40,-42,-44,-45,-45,-45,-44,-42,-40,-36,-32,-27,-22,-17,-12,-7,-3,0,3,7,9,12,14,16,18,19,20,21,21}, \ {18,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,18,17,16,14,10,7,2,-1,-6,-10,-14,-17,-19,-21,-22,-23,-24,-24,-24,-24,-23,-23,-23,-24,-26,-28,-30,-33,-35,-37,-38,-39,-39,-38,-36,-34,-31,-28,-24,-19,-15,-10,-6,-3,0,1,4,6,8,10,12,14,15,16,17,18,18}, \ {16,16,17,17,17,17,17,17,17,17,17,16,16,16,16,16,16,15,13,11,8,4,0,-4,-9,-13,-16,-19,-21,-23,-24,-25,-25,-25,-25,-24,-23,-21,-20,-20,-21,-22,-24,-26,-28,-30,-31,-32,-31,-30,-29,-27,-24,-21,-17,-13,-9,-6,-3,-1,0,2,4,5,7,9,10,12,13,14,15,16,16}, \ {14,14,14,15,15,15,15,15,15,15,14,14,14,14,14,14,13,12,11,9,5,2,-2,-6,-11,-15,-18,-21,-23,-24,-25,-25,-25,-25,-24,-22,-21,-18,-16,-15,-15,-15,-17,-19,-21,-22,-24,-24,-24,-23,-22,-20,-18,-15,-12,-9,-5,-3,-1,0,1,2,4,5,6,8,9,10,11,12,13,14,14}, \ {12,13,13,13,13,13,13,13,13,13,13,13,12,12,12,12,11,10,9,6,3,0,-4,-8,-12,-16,-19,-21,-23,-24,-24,-24,-24,-23,-22,-20,-17,-15,-12,-10,-9,-9,-10,-12,-13,-15,-17,-17,-18,-17,-16,-15,-13,-11,-8,-5,-3,-1,0,1,1,2,3,4,6,7,8,9,10,11,12,12,12}, \ {11,11,11,11,11,12,12,12,12,12,11,11,11,11,11,10,10,9,7,5,2,-1,-5,-9,-13,-17,-20,-22,-23,-23,-23,-23,-22,-20,-18,-16,-14,-11,-9,-6,-5,-4,-5,-6,-8,-9,-11,-12,-12,-12,-12,-11,-9,-8,-6,-3,-1,0,0,1,1,2,3,4,5,6,7,8,9,10,11,11,11}, \ {10,10,10,10,10,10,10,10,10,10,10,10,10,10,9,9,9,7,6,3,0,-3,-6,-10,-14,-17,-20,-21,-22,-22,-22,-21,-19,-17,-15,-13,-10,-8,-6,-4,-2,-2,-2,-2,-4,-5,-7,-8,-8,-9,-8,-8,-7,-5,-4,-2,0,0,1,1,1,2,2,3,4,5,6,7,8,9,10,10,10}, \ 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