{"id":45034,"date":"2015-05-26T07:00:00","date_gmt":"2015-05-26T21:00:00","guid":{"rendered":"https:\/\/blogs.msdn.microsoft.com\/oldnewthing\/2015\/05\/26\/the-tadpole-operators-explained\/"},"modified":"2025-12-23T07:10:44","modified_gmt":"2025-12-23T15:10:44","slug":"20150526-00","status":"publish","type":"post","link":"https:\/\/devblogs.microsoft.com\/oldnewthing\/20150526-00\/?p=45034","title":{"rendered":"The tadpole operators explained"},"content":{"rendered":"

Last time,\u00b9 I introduced the tadpole operators<\/a>. As you have probably figured out by now, it was a joke. There are no new tadpole operators.<\/p>\n

But the sample code works. What’s going on?<\/p>\n

The tadpole operators are pseudo-operators, like the goes to operator<\/a> or the sproing operator<\/a>: They take advantage of existing language features, and come with a creative story.<\/p>\n

The tadpole operators exploit two’s complement arithmetic and overflow.\u00b2 The __ENABLE_EXPERIMENTAL_TADPOLE_OPERATORS<\/code> is just a red herring.<\/p>\n

Start with the identity for two’s complement negation<\/p>\n

-x = ~x + 1\r\n<\/pre>\n
then move the -x<\/code> to the right hand side and the ~x<\/code> to the left hand side:<\/p>\n
-~x = x + 1\r\n<\/pre>\n
If that was too fast for you, we can do it a different way: start with the identity for two’s complement negation<\/p>\n
-x = ~x + 1\r\n<\/pre>\n
subtract 1 from both sides<\/p>\n
-x - 1 = ~x\r\n<\/pre>\n
and finally, negate both sides<\/p>\n
x + 1 = -~x\r\n<\/pre>\n
To get the decrement tadpole operator, start with<\/p>\n
-x = ~x + 1\r\n<\/pre>\n
and substitute x = -y<\/code>:<\/p>\n
-(-y) = ~-y + 1\r\n<\/pre>\n
subtract 1<\/code> from both sides and simplify -(-y)<\/code> to y<\/code>.<\/p>\n
y - 1 = ~-y\r\n<\/pre>\n
Update<\/b>:  Justin Olbrantz (Quantam)<\/a> and  Ben Voigt<\/a> provide a simpler derivation, starting with the identity for two’s complement negation.<\/p>\n\n\n\n\n\n\n\n
-x = ~x + 1<\/code><\/td>\n <\/td>\n <\/td>\n<\/tr>\n
 <\/td>\nRearrange terms<\/td>\n~x = -x - 1<\/code><\/td>\n<\/tr>\n
Let x = ~y<\/code><\/td>\n <\/td>\nLet x = -y<\/code><\/td>\n<\/tr>\n
-~y = ~(~y) + 1<\/code><\/td>\n <\/td>\n~-y = -(-y) - 1<\/code><\/td>\n<\/tr>\n
-~y = y + 1<\/code><\/td>\n <\/td>\n~-y = y - 1<\/code><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\u00b9Why didn’t I post it on April 1st? Well, for one thing, April 1st is overcrowded. Second, it would have interfered with the run-up to the \/\/build conference. And third, yesterday was a holiday in the United States, and I tend to schedule lighter fare on holidays.<\/p>\n
\u00b2This means that they don’t work on a machine that does not use two’s complement, or one which checks overflow. Still, maybe they’ll be useful if you’re entering the  IOCCC<\/a> or some other contest which values minimal code size or obfuscation (or both).<\/p>\n","protected":false},"excerpt":{"rendered":"
Combining two things in an unintuitive way.<\/p>\n","protected":false},"author":1069,"featured_media":111744,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[1],"tags":[25],"class_list":["post-45034","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-oldnewthing","tag-code"],"acf":[],"blog_post_summary":"
Combining two things in an unintuitive way.<\/p>\n","_links":{"self":[{"href":"https:\/\/devblogs.microsoft.com\/oldnewthing\/wp-json\/wp\/v2\/posts\/45034","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/devblogs.microsoft.com\/oldnewthing\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/devblogs.microsoft.com\/oldnewthing\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/devblogs.microsoft.com\/oldnewthing\/wp-json\/wp\/v2\/users\/1069"}],"replies":[{"embeddable":true,"href":"https:\/\/devblogs.microsoft.com\/oldnewthing\/wp-json\/wp\/v2\/comments?post=45034"}],"version-history":[{"count":0,"href":"https:\/\/devblogs.microsoft.com\/oldnewthing\/wp-json\/wp\/v2\/posts\/45034\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/devblogs.microsoft.com\/oldnewthing\/wp-json\/wp\/v2\/media\/111744"}],"wp:attachment":[{"href":"https:\/\/devblogs.microsoft.com\/oldnewthing\/wp-json\/wp\/v2\/media?parent=45034"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/devblogs.microsoft.com\/oldnewthing\/wp-json\/wp\/v2\/categories?post=45034"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/devblogs.microsoft.com\/oldnewthing\/wp-json\/wp\/v2\/tags?post=45034"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}