{"id":53,"date":"2009-02-18T10:46:28","date_gmt":"2009-02-18T18:46:28","guid":{"rendered":"http:\/\/127.0.0.1:8000\/?p=53"},"modified":"2021-10-28T15:46:08","modified_gmt":"2021-10-28T22:46:08","slug":"fast-fourier-transform-with-booleans","status":"publish","type":"post","link":"https:\/\/dmitriplotnikov.com\/ru\/blog\/fast-fourier-transform-with-booleans\/","title":{"rendered":"\u0411\u044b\u0441\u0442\u0440\u043e\u0435 \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435 \u0424\u0443\u0440\u044c\u0435 \u0432 \u0431\u0443\u043b\u0435\u0432\u043e\u0439 \u0430\u043b\u0433\u0435\u0431\u0440\u0435"},"content":{"rendered":"<h2>Abstract<\/h2>\n<p>\u0412 \u044d\u0442\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u043e\u043f\u0438\u0441\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u0438\u0437\u043e\u0431\u0440\u0435\u0442\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0439 \u043c\u0435\u0442\u043e\u0434 \u043e\u0442\u043b\u0430\u0434\u043a\u0438 \u043a\u043e\u0434\u0430, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u044f \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043b \u0432 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u043b\u043e\u0433\u0438\u043a\u0438. \u0415\u0441\u043b\u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u043b\u043e\u0433\u0438\u043a\u0430 \u0432\u0430\u0441 \u043d\u0435 \u0438\u043d\u0442\u0435\u0440\u0435\u0441\u0443\u0435\u0442, \u0447\u0438\u0442\u0430\u0439\u0442\u0435 \u0442\u043e\u043b\u044c\u043a\u043e \u0434\u0432\u0430 \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0438\u0445 \u043f\u0430\u0440\u0430\u0433\u0440\u0430\u0444\u0430.<\/p>\n<h2>\u041f\u0440\u043e\u0435\u043a\u0442<\/h2>\n<p class=\"translation-block\">\u042d\u0442\u043e \u0431\u044b\u043b\u0430 \u043c\u043e\u044f \u043f\u0435\u0440\u0432\u0430\u044f \u0440\u0430\u0431\u043e\u0442\u0430 \u0432 1985-1986 \u0433\u043e\u0434\u0430\u0445. \u042f \u0440\u0430\u0431\u043e\u0442\u0430\u043b \u043d\u0430 \u0444\u0430\u043a\u0443\u043b\u044c\u0442\u0435\u0442\u0435 \u043f\u0440\u0438\u043a\u043b\u0430\u0434\u043d\u043e\u0439 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0430. \u041b\u043e\u0433\u0438\u043a\u0438 \u043a\u0430\u0444\u0435\u0434\u0440\u044b \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438, \u0420\u043e\u0431\u0435\u0440\u0442 \u0418\u0441\u0430\u0430\u043a\u043e\u0432\u0438\u0447 \u0424\u0440\u0435\u0439\u0434\u0437\u043e\u043d \u0438 \u0434\u0440\u0443\u0433\u0438\u0435, \u0440\u0430\u0431\u043e\u0442\u0430\u043b\u0438 \u043d\u0430\u0434 \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u043e\u0439 <a href=\"https:\/\/ru.wikipedia.org\/wiki\/NP-_\" target=\"_self\">NP-\u043f\u043e\u043b\u043d\u043e\u0442\u044b<\/a>. \u0412 \u0447\u0430\u0441\u0442\u043d\u043e\u0441\u0442\u0438, \u043e\u043d\u0438 \u043f\u044b\u0442\u0430\u043b\u0438\u0441\u044c \u043e\u043f\u0440\u043e\u0432\u0435\u0440\u0433\u043d\u0443\u0442\u044c \u0442\u0435\u0437\u0438\u0441 \u043e \u0442\u043e\u043c, \u0447\u0442\u043e \u043f\u043e\u0438\u0441\u043a \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0441\u0438\u0441\u0442\u0435\u043c\u044b \u0431\u0443\u043b\u0435\u0432\u044b\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f NP-\u043f\u043e\u043b\u043d\u043e\u0439 \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u043e\u0439.<\/p>\n<p class=\"translation-block\">\u0414\u043b\u044f \u043f\u0440\u043e\u0432\u0435\u0440\u043a\u0438 \u0441\u0432\u043e\u0438\u0445 \u0442\u0435\u043e\u0440\u0438\u0438, \u0438\u043c \u043d\u0443\u0436\u043d\u043e \u0431\u044b\u043b\u043e \u043a\u043e\u043d\u0441\u0442\u0440\u0443\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u0441\u0438\u0441\u0442\u0435\u043c\u044b \u0431\u0443\u043b\u0435\u0432\u044b\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439, \u0438\u043c\u0435\u044e\u0449\u0438\u0445 \u0440\u043e\u0432\u043d\u043e \u043e\u0434\u043d\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u0435. \u0420\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0430\u043d\u043d\u044b\u0439 \u0438\u043c\u0438 \u043f\u043e\u0434\u0445\u043e\u0434 \u0431\u044b\u043b \u043e\u0441\u043d\u043e\u0432\u0430\u043d \u043d\u0430 \u043f\u0440\u043e\u0441\u0442\u043e\u043c \u0446\u0435\u043b\u043e\u0447\u0438\u0441\u043b\u0435\u043d\u043d\u043e\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0438: <code class=\"prettyprinted\"><span class=\"pln\">A<\/span><span class=\"pun\"> * <\/span><span class=\"pln\">B <\/span><span class=\"pun\">=<\/span><span class=\"pln\"> C<\/span><\/code>.<\/p>\n<p class=\"translation-block\">\u041a\u0430\u0436\u0434\u043e\u0435 \u0438\u0437 \u0442\u0440\u0435\u0445 \u0447\u0438\u0441\u0435\u043b, <code class=\"prettyprinted\"><span class=\"pln\">A<\/span><\/code>, <code class=\"prettyprinted\"><span class=\"pln\">B<\/span><\/code> \u0438 <code class=\"prettyprinted\"><span class=\"pln\">C<\/span><\/code>, \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u043e \u043a\u0430\u043a \u043d\u0430\u0431\u043e\u0440 \u0431\u0443\u043b\u0435\u0432\u044b\u0445 \u043f\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445 \u0441 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u0435\u043c \u0434\u0432\u043e\u0438\u0447\u043d\u043e\u0433\u043e \u043a\u043e\u0434\u0430: \n<code class=\"prettyprinted\"><span class=\"pun\">(<\/span><span class=\"pln\">A1<\/span><span class=\"pun\">,<\/span><span class=\"pln\"> A2<\/span><span class=\"pun\">,<\/span><span class=\"pln\"> <\/span><span class=\"pun\">...)<\/span><span class=\"pln\"> <\/span><span class=\"pun\">*<\/span><span class=\"pln\"> <\/span><span class=\"pun\">(<\/span><span class=\"pln\">B1<\/span><span class=\"pun\">,<\/span><span class=\"pln\"> B2<\/span><span class=\"pun\">,<\/span><span class=\"pln\"> <\/span><span class=\"pun\">...)<\/span><span class=\"pln\"> <\/span><span class=\"pun\">=<\/span><span class=\"pln\"> <\/span><span class=\"pun\">(<\/span><span class=\"pln\">C1<\/span><span class=\"pun\">,<\/span><span class=\"pln\"> C2<\/span><span class=\"pun\">,<\/span><span class=\"pln\"> <\/span><span class=\"pun\">...)<\/span><\/code><\/p>\n<p class=\"translation-block\">\u0426\u0435\u043b\u043e\u0447\u0438\u0441\u043b\u0435\u043d\u043d\u043e\u0435 \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u0435 \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u043e \u0441\u0438\u0441\u0442\u0435\u043c\u043e\u0439 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439, \u0441\u0432\u044f\u0437\u044b\u0432\u0430\u044e\u0449\u0438\u0445 \u0432\u0441\u0435 \u044d\u0442\u0438 \u0431\u0443\u043b\u0435\u0432\u044b \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0435: <code class=\"prettyprinted\"><span class=\"pln\">C1<\/span><\/code>, <code class=\"prettyprinted\"><span class=\"pln\">A1<\/span><\/code>, <code class=\"prettyprinted\"><span class=\"pln\">B1<\/span><\/code>, <code class=\"prettyprinted\"><span class=\"pln\">C2<\/span><\/code>, <code class=\"prettyprinted\"><span class=\"pln\">A2<\/span><\/code>, <code class=\"prettyprinted\"><span class=\"pln\">B2<\/span><\/code>, \u0438 \u0442.\u0434. \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0434\u043b\u044f 4-\u0431\u0438\u0442\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b \u043e\u0434\u043d\u043e \u0438\u0437 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u0431\u0443\u0434\u0435\u0442 \u043f\u0440\u0438\u043c\u0435\u0440\u043d\u043e \u0442\u0430\u043a\u0438\u043c: <code class=\"prettyprinted\"><span class=\"pun\">\u00ac<\/span><span class=\"pln\">A4 <\/span><span class=\"pun\">\u22c0<\/span><span class=\"pln\"> B4 <\/span><span class=\"pun\">\u22c1<\/span><span class=\"pln\"> A4 <\/span><span class=\"pun\">\u22c0<\/span><span class=\"pln\"> <\/span><span class=\"pun\">\u00ac<\/span><span class=\"pln\">B4 <\/span><span class=\"pun\">=<\/span><span class=\"pln\"> C8<\/span><\/code><\/p>\n<p class=\"translation-block\">\u0412\u043e\u0437\u044c\u043c\u0435\u043c \u0434\u0432\u0430 \u043f\u0440\u043e\u0441\u0442\u044b\u0445 \u0447\u0438\u0441\u043b\u0430, \u043f\u0435\u0440\u0435\u043c\u043d\u043e\u0436\u0438\u043c \u0438\u0445 \u0438 \u043f\u043e\u0434\u0441\u0442\u0430\u0432\u0438\u043c \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0432 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 <code class=\"prettyprinted\"><span class=\"pln\">C<\/span><\/code>. \u0422\u0435\u043f\u0435\u0440\u044c \u0443 \u043d\u0430\u0441 \u0435\u0441\u0442\u044c \u0441\u0438\u0441\u0442\u0435\u043c\u0430 \u0431\u0443\u043b\u0435\u0432\u044b\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u0438\u043c\u0435\u0435\u0442 \u0440\u043e\u0432\u043d\u043e \u043e\u0434\u043d\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u0435: \u0434\u0432\u043e\u0438\u0447\u043d\u044b\u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u044f <code class=\"prettyprinted\"><span class=\"pln\">A<\/span><\/code> \u0438 <code class=\"prettyprinted\"><span class=\"pln\">B<\/span><\/code>. \u0412\u044b\u0431\u043e\u0440 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u043b\u044c\u043d\u043e \u0431\u043e\u043b\u044c\u0448\u0438\u0445 <code class=\"prettyprinted\"><span class=\"pln\">A<\/span><\/code> \u0438 <code class=\"prettyprinted\"><span class=\"pln\">B<\/span><\/code> \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u0435\u0442 \u043d\u0430\u043c \u0441\u043e\u0437\u0434\u0430\u0432\u0430\u0442\u044c \u0441\u043a\u043e\u043b\u044c \u0443\u0433\u043e\u0434\u043d\u043e \u0431\u043e\u043b\u044c\u0448\u0438\u0435 \u0441\u0438\u0441\u0442\u0435\u043c\u044b \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u0441 \u0435\u0434\u0438\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u043c \u0440\u0435\u0448\u0435\u043d\u0438\u0435\u043c.<\/p>\n<h2>\u0417\u0430\u0434\u0430\u0447\u0430<\/h2>\n<p class=\"translation-block\">\u042f \u0434\u043e\u043b\u0436\u0435\u043d \u0431\u044b\u043b \u043d\u0430\u043f\u0438\u0441\u0430\u0442\u044c \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u0443 \u043d\u0430 PL\/I, \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u0434\u0430\u0432\u0430\u043b\u0438\u0441\u044c \u0431\u044b \u0434\u0432\u0430 \u043f\u0440\u043e\u0441\u0442\u044b\u0445 \u0447\u0438\u0441\u043b\u0430, \u0438 \u043e\u043d\u0430 \u0431\u044b \u0433\u0435\u043d\u0435\u0440\u0438\u0440\u043e\u0432\u0430\u043b\u0430 \u0431\u044b \u0432\u0441\u0435 \u044d\u0442\u0438 \u0431\u0443\u043b\u0435\u0432\u044b \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f. \u0414\u043e\u0431\u0430\u0432\u043e\u0447\u043d\u043e\u0439 \u0446\u0435\u043b\u044c\u044e \u0431\u044b\u043b\u043e \u0441\u0434\u0435\u043b\u0430\u0442\u044c \u0441\u0438\u0441\u0442\u0435\u043c\u0443 \u0443\u0440\u043e\u0432\u043d\u0435\u043d\u0438\u0439 \u043a\u0430\u043a \u043c\u043e\u0436\u043d\u043e \u043a\u043e\u043c\u043f\u0430\u043a\u0442\u043d\u0435\u0435. \u042f \u0440\u0435\u0448\u0438\u043b \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u044f, \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u043d\u044b\u0439 \u043d\u0430 <a href=\"http:\/\/en.wikipedia.org\/wiki\/Multiplication_algorithm#Fourier_transform_methods\" target=\"_self\">\u0431\u044b\u0441\u0442\u0440\u043e\u043c \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0438 \u0424\u0443\u0440\u044c\u0435<\/a>. \u0410\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u0438 \u0441\u0430\u043c \u043f\u043e \u0441\u0435\u0431\u0435 \u0441\u043b\u043e\u0436\u043d\u044b\u0439, \u043d\u043e, \u0432\u0434\u043e\u0431\u0430\u0432\u043e\u043a \u043a\u043e \u0432\u0441\u0435\u043c\u0443, \u044f \u0434\u043e\u043b\u0436\u0435\u043d \u0431\u044b\u043b \u0440\u0435\u0430\u043b\u0438\u0437\u043e\u0432\u044b\u0432\u0430\u0442\u044c \u0435\u0433\u043e \u043d\u0435 \u043d\u0430\u043f\u0440\u044f\u043c\u0443\u044e. \u0412\u043c\u0435\u0441\u0442\u043e \u044d\u0442\u043e\u0433\u043e, \u044f \u0434\u043e\u043b\u0436\u0435\u043d \u0431\u044b\u043b \u043d\u0430\u043f\u0438\u0441\u0430\u0442\u044c \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0431\u044b \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u0438\u043b \u043b\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f, \u043a\u043e\u0442\u043e\u0440\u044b\u0435, \u0432 \u0441\u0432\u043e\u044e \u043e\u0447\u0435\u0440\u0435\u0434\u044c, \u0443\u0436\u0435 \u0431\u044b \u0440\u0435\u0430\u043b\u0438\u0437\u043e\u0432\u044b\u0432\u0430\u043b\u0438 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c.<\/p>\n<h2>\u041f\u0440\u043e\u0431\u043b\u0435\u043c\u0430<\/h2>\n<p>\u041f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u0443 \u043d\u0430\u043f\u0438\u0441\u0430\u043b. \u041e\u043d\u0430 \u0447\u0442\u043e-\u0442\u043e \u0433\u0435\u043d\u0435\u0440\u0438\u0440\u043e\u0432\u0430\u043b\u0430, \u043d\u043e \u0434\u0430\u0436\u0435 \u0434\u043b\u044f \u043e\u0447\u0435\u043d\u044c \u043c\u0430\u043b\u0435\u043d\u044c\u043a\u0438\u0445 \u043f\u0440\u043e\u0441\u0442\u044b\u0445 \u0447\u0438\u0441\u0435\u043b \u043e\u043d\u0430 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u0438\u043b\u0430 \u043e\u0447\u0435\u043d\u044c \u0431\u043e\u043b\u044c\u0448\u043e\u0435 \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439, \u0438 \u044d\u0442\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0431\u044b\u043b\u0438 \u043d\u0435\u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u044b\u043c\u0438: \u043f\u043e\u0434\u0441\u0442\u0430\u043d\u043e\u0432\u043a\u0430 \u0438\u0441\u0445\u043e\u0434\u043d\u044b\u0445 \u043f\u0440\u043e\u0441\u0442\u044b\u0445 \u0447\u0438\u0441\u0435\u043b \u043d\u0435 \u0443\u0434\u043e\u0432\u043b\u0435\u0442\u0432\u043e\u0440\u044f\u043b\u0430 \u0441\u0438\u0441\u0442\u0435\u043c\u0443. \u0423 \u043c\u0435\u043d\u044f \u044f\u0432\u043d\u043e \u0431\u044b\u043b\u0438 \u043e\u0448\u0438\u0431\u043a\u0438 \u0432 \u0433\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440\u0435. \u0418 \u044f \u043f\u043e\u043d\u044f\u0442\u0438\u044f \u043d\u0435 \u0438\u043c\u0435\u043b, \u043a\u0430\u043a \u0435\u0433\u043e \u043e\u0442\u043b\u0430\u0436\u0438\u0432\u0430\u0442\u044c: \u043e\u043d \u0432\u044b\u0434\u0430\u0432\u0430\u043b \u0442\u0440\u0435\u0445\u043c\u0435\u0442\u0440\u043e\u0432\u0443\u044e \u0440\u0430\u0441\u043f\u0435\u0447\u0430\u0442\u043a\u0443, \u0441\u043e\u0441\u0442\u043e\u044f\u0449\u0443\u044e \u0438\u0437 \u043d\u0435\u0447\u0438\u0442\u0430\u0435\u043c\u044b\u0445 \u043b\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0439, \u043a\u0430\u043a\u0438\u0435-\u0442\u043e \u0438\u0437 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u0431\u044b\u043b\u0438 \u043d\u0435\u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u044b\u043c\u0438.<\/p>\n<h2>\u0420\u0435\u0448\u0435\u043d\u0438\u0435<\/h2>\n<p class=\"translation-block\">\u042f \u043f\u0435\u0440\u0435\u043f\u0438\u0441\u0430\u043b \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u0443 \u0441 PL\/I \u043d\u0430 <a href=\"https:\/\/en.wikipedia.org\/wiki\/PL\/I_preprocessor\" target=\"_self\">\u044f\u0437\u044b\u043a \u043c\u0430\u043a\u0440\u043e-\u043f\u0440\u0435\u043f\u0440\u043e\u0446\u0435\u0441\u0441\u043e\u0440\u0430 PL\/I<\/a>. \u042d\u0442\u043e\u0442 \u043c\u0430\u043a\u0440\u043e\u044f\u0437\u044b\u043a \u0431\u044b\u043b \u043d\u0435\u043e\u0431\u044b\u0447\u0430\u0439\u043d\u043e \u043c\u043e\u0449\u043d\u044b\u043c: \u043e\u043d \u0441\u0430\u043c \u0431\u044b\u043b \u043f\u043e\u043b\u043d\u043e\u0446\u0435\u043d\u043d\u044b\u043c \u044f\u0437\u044b\u043a\u043e\u043c \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f. \u0412 \u043d\u043e\u0432\u043e\u0439 \u0432\u0435\u0440\u0441\u0438\u0438 \u043c\u043e\u0439 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u044f \u0431\u044b\u043b \u0432\u044b\u0440\u0430\u0436\u0435\u043d \u0432 \u0442\u0435\u0440\u043c\u0438\u043d\u0430\u0445 \u043e\u0441\u043d\u043e\u0432\u043d\u044b\u0445 \u043b\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0439, \u0440\u0435\u0430\u043b\u0438\u0437\u043e\u0432\u0430\u043d\u043d\u044b\u0445 \u043a\u0430\u043a \u043c\u0430\u043a\u0440\u043e-\u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u042f \u0441\u0434\u0435\u043b\u0430\u043b \u0434\u0432\u0430 \u043d\u0430\u0431\u043e\u0440\u0430 \u044d\u0442\u0438\u0445 \u0431\u0430\u0437\u043e\u0432\u044b\u0445 \u043b\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u043c\u0430\u043a\u0440\u043e\u0441\u043e\u0432: \u043e\u0434\u043d\u0430 \u0440\u0435\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u044f <code class=\"prettyprinted\"><span class=\"pln\">OR<\/span><span class=\"pun\">(<\/span><span class=\"pln\">A<\/span><span class=\"pun\">,<\/span><span class=\"pln\">B<\/span><span class=\"pun\">)<\/span><\/code> \u0433\u0435\u043d\u0435\u0440\u0438\u0440\u043e\u0432\u0430\u043b\u0430 \u0444\u0440\u0430\u0433\u043c\u0435\u043d\u0442 \u043b\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f, \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440 <code class=\"prettyprinted\"><span class=\"pln\">\"A <\/span><span class=\"pun\">\u22c1<\/span><span class=\"pln\"> B\"<\/span><\/code>; \u0434\u0440\u0443\u0433\u0430\u044f \u0440\u0435\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u044f \u043d\u0435 \u0441\u043e\u0437\u0434\u0430\u0432\u0430\u043b\u0430 \u0441\u0442\u0440\u043e\u043a\u0443, \u0430 \u043f\u0440\u043e\u0441\u0442\u043e \u0438\u0441\u043f\u043e\u043b\u043d\u044f\u043b\u0430 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u043a\u0430\u043a \u0435\u0441\u0442\u044c. \u041e\u0434\u043d\u0438\u043c \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u043e\u043c \u044f \u043c\u043e\u0433 \u0437\u0430\u0441\u0442\u0430\u0432\u0438\u0442\u044c \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u0443 \u043b\u0438\u0431\u043e \u0433\u0435\u043d\u0435\u0440\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f, \u043b\u0438\u0431\u043e \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0442\u044c \u043b\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438! \u042f \u043e\u0442\u043b\u0430\u0434\u0438\u043b \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u044f \u0432 \u044d\u0442\u043e\u043c \u043f\u0440\u043e\u0441\u0442\u043e\u043c \u0440\u0435\u0436\u0438\u043c\u0435. \u042f \u0443\u0431\u0435\u0434\u0438\u043b\u0441\u044f, \u0447\u0442\u043e \u043e\u043d <em>\u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u043e<\/em> \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442 \u0442\u0430\u043a\u0438\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f, \u043a\u0430\u043a <code class=\"prettyprinted\"><span class=\"lit\">3<\/span><span class=\"pun\"> * <\/span><span class=\"lit\">2<\/span><span class=\"pln\"> <\/span><span class=\"pun\">=<\/span><span class=\"pln\"> <\/span><span class=\"lit\">6<\/span><\/code>. \u041f\u043e\u0441\u043b\u0435 \u044d\u0442\u043e\u0433\u043e \u044f \u0449\u0435\u043b\u043a\u043d\u0443\u043b \u043f\u0435\u0440\u0435\u043a\u043b\u044e\u0447\u0430\u0442\u0435\u043b\u0435\u043c, \u0438 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u0430 \u043d\u0430\u0447\u0430\u043b\u0430 \u0433\u0435\u043d\u0435\u0440\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0431\u0435\u0437 \u0434\u043e\u043f\u043e\u043b\u043d\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u0439 \u043e\u0442\u043b\u0430\u0434\u043a\u0438.<\/p>\n<pre><code>%DECLARE (GenerateExpression) BIT;\n%GenerateExpression = 1;\n\n%DECLARE ExpressionType CHAR;\n%IF GenerateExpression\n  %THEN ExpressionType = &#039;CHAR&#039;;\n  %ELSE ExpressionType = &#039;BIT&#039;;\n\n%AND: PROCEDURE (Left, Right) RETURNS CHAR;\n  DECLARE (Left, Right) CHAR;\n  DECLARE Code CHAR;\n\n  IF GenerateExpression\n    THEN Code = &#039;&#039;&#039;(&#039;&#039;&#039; || Left || &#039;&#039;&#039; || &#039;&#039; \u22c0 &#039;&#039; || &#039;&#039;&#039; || Right || &#039;&#039;&#039;)&#039;&#039;&#039;;\n    ELSE Code = &#039;(&#039; || Left || &#039; &amp; &#039; || Right || &#039;)&#039;;\n\n  RETURN Code;\n%END AND;\n\n%OR: \/\/ Similar to AND\n\n%NOT: \/\/ Similar to AND\n...<\/code><\/pre>\n<p>\u0422\u0435\u043f\u0435\u0440\u044c \u0434\u0430\u0432\u0430\u0439\u0442\u0435 \u0432\u043e\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c\u0441\u044f \u044d\u0442\u0438\u043c\u0438 \u043c\u0430\u043a\u0440\u043e\u0441\u0430\u043c\u0438:<\/p>\n<pre><code>PROCEDURE SOME_LOGIC(A, B,C) RETURNS ExpressionType;\n   DECLARE (A, B, C) ExpressionType;\n   RETURN OR(AND(A, NOT(B)), C);\nEND;<\/code><\/pre>\n<p class=\"translation-block\">\u0415\u0441\u043b\u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 <code class=\"prettyprinted\"><span class=\"typ\">GenerateExpression<\/span><\/code> \u0440\u0430\u0432\u043d\u043e False, \u044d\u0442\u0430 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u0430 \u0441\u0433\u0435\u043d\u0435\u0440\u0438\u0440\u0443\u0435\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u043a\u043e\u0434:<\/p>\n<pre><code>PROCEDURE SOME_LOGIC(A, B, C) RETURNS BIT;\n  DECLARE (A, B, C) BIT;\n  RETURN ((A &amp; ^(B)) | C);\nEND;<\/code><\/pre>\n<p class=\"translation-block\">\u0421\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0435\u043d\u043d\u043e, <code class=\"prettyprinted\"><span class=\"pln\">PUT LIST <\/span><span class=\"str\">'RESULT: '<\/span><span class=\"pun\">,<\/span><span class=\"pln\"> SOME_LOGIC<\/span><span class=\"pun\">(<\/span><span class=\"lit\">1<\/span><span class=\"pun\">,<\/span><span class=\"pln\"> <\/span><span class=\"lit\">1<\/span><span class=\"pun\">,<\/span><span class=\"pln\"> <\/span><span class=\"lit\">0<\/span><span class=\"pun\">);<\/span><\/code> \u043d\u0430\u043f\u0435\u0447\u0430\u0442\u0430\u0435\u0442:<\/p>\n<pre><code>RESULT: 0<\/code><\/pre>\n<p class=\"translation-block\">\u0415\u0441\u043b\u0438 \u0436\u0435 <code class=\"prettyprinted\"><span class=\"typ\">GenerateExpression<\/span><\/code> \u0440\u0430\u0432\u043d\u043e \u0422rue, \u0442\u043e \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u0430 \u0441\u0433\u0435\u043d\u0435\u0440\u0438\u0440\u0443\u0435\u0442:<\/p>\n<pre><code>PROCEDURE SOME_LOGIC(A, B, C) RETURNS CHAR;\n  DECLARE (A, B, C) CHAR;\n  RETURN &#039;(&#039; || &#039;(&#039; || A || &#039; \u22c0 &#039; || &#039;\u00ac(&#039; || B || &#039;)&#039; || &#039;)&#039; || &#039; \u22c1 &#039; || C || &#039;)&#039;;\nEND;<\/code><\/pre>\n<p class=\"translation-block\">\u0438 <code class=\"prettyprinted\"><span class=\"pln\">PUT LIST <\/span><span class=\"str\">'RESULT: '<\/span><span class=\"pun\">,<\/span><span class=\"pln\"> SOME_LOGIC<\/span><span class=\"pun\">(<\/span><span class=\"str\">'X'<\/span><span class=\"pun\">,<\/span><span class=\"pln\"> <\/span><span class=\"str\">'Y'<\/span><span class=\"pun\">,<\/span><span class=\"pln\"> <\/span><span class=\"str\">'Z'<\/span><span class=\"pun\">);<\/span><\/code> \u043d\u0430\u043f\u0435\u0447\u0430\u0442\u0430\u0435\u0442:<\/p>\n<pre><code>RESULT: ((X \u22c0 \u00ac(Y)) \u22c1 Z)<\/code><\/pre>\n<p>\u0422\u0430 \u0436\u0435 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u0430, \u043d\u043e \u0441\u043e\u0432\u0435\u0440\u0448\u0435\u043d\u043d\u043e \u0434\u0440\u0443\u0433\u043e\u0439 \u0442\u0438\u043f \u043f\u043e\u0432\u0435\u0434\u0435\u043d\u0438\u044f.<\/p>\n<h2>\u041d\u0435 \u043f\u043e \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443<\/h2>\n<p>\u0412 1992 \u0433\u043e\u0434\u0443 \u044f \u0431\u044b\u043b \u0432 \u0410\u043c\u0435\u0440\u0438\u043a\u0435 \u0432 \u043a\u043e\u043c\u0430\u043d\u0434\u0438\u0440\u043e\u0432\u043a\u0435. \u0420\u043e\u0431\u0435\u0440\u0442 \u0418\u0441\u0430\u0430\u043a\u043e\u0432\u0438\u0447 \u0424\u0440\u0435\u0439\u0434\u0437\u043e\u043d, \u043c\u043e\u0439 \u0431\u044b\u0432\u0448\u0438\u0439 \u043f\u0440\u043e\u0444\u0435\u0441\u0441\u043e\u0440 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u043b\u043e\u0433\u0438\u043a\u0438, \u0432 \u0442\u043e \u0432\u0440\u0435\u043c\u044f \u0436\u0438\u043b \u0432 \u0411\u043e\u0441\u0442\u043e\u043d\u0435. \u041c\u044b \u0440\u0430\u0437\u0433\u043e\u0432\u0430\u0440\u0438\u0432\u0430\u043b\u0438 \u0441 \u043d\u0438\u043c \u043f\u043e \u0442\u0435\u043b\u0435\u0444\u043e\u043d\u0443, \u0438 \u044f \u0435\u043c\u0443 \u0441\u043a\u0430\u0437\u0430\u043b, \u0447\u0442\u043e \u043c\u043e\u044f \u043f\u043e\u0435\u0437\u0434\u043a\u0430 \u0437\u0430\u043a\u0430\u043d\u0447\u0438\u0432\u0430\u0435\u0442\u0441\u044f \u0438 \u044f \u0435\u0434\u0443 \u0434\u043e\u043c\u043e\u0439. \u0415\u0433\u043e \u0440\u0435\u0430\u043a\u0446\u0438\u044f \u0431\u044b\u043b\u0430: \u00ab\u0422\u044b \u043e\u0445\u0443\u0435\u043b \u0447\u0442\u043e-\u043b\u0438? \u0422\u0435\u0431\u0435 \u0436\u0435 \u0434\u0430\u043d\u0430 \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u044c \u0438\u0437\u043c\u0435\u043d\u0438\u0442\u044c \u0432\u0441\u044e \u0441\u0432\u043e\u044e \u0436\u0438\u0437\u043d\u044c! \u041f\u043e\u0441\u043b\u0443\u0448\u0430\u0439 \u043c\u0435\u043d\u044f: \u043d\u0435 \u0434\u0443\u0440\u0438 \u0438 \u043d\u0430\u0439\u0434\u0438 \u0441\u043f\u043e\u0441\u043e\u0431 \u043e\u0441\u0442\u0430\u0442\u044c\u0441\u044f!\u00bb<\/p>\n<p>Instead of figuring out how to debug my life, I popped on a plane and went home to be with my wife whose grandmother had died while I was in America. About two years later, when another opportunity presented itself, I got smarter and permanently substituted one variable in my professional career: the country of residence.  Same programming languages, but an entirely different type of life.<\/p>","protected":false},"excerpt":{"rendered":"<p class=\"translation-block\">\u0423 \u043c\u0435\u043d\u044f \u0431\u044b\u043b\u0430 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043c\u0430, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u0441\u043e\u0437\u0434\u0430\u0432\u0430\u043b\u0430 \u043b\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f \u0441 \u0442\u044b\u0441\u044f\u0447\u0430\u043c\u0438 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445 \u0438 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0439, \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u044b \u0437\u0430 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0430\u043c\u0438 \u043d\u0435\u0447\u0438\u0442\u0430\u0435\u043c\u043e\u0439 \u0430\u0431\u0440\u0430\u043a\u0430\u0434\u0430\u0431\u0440\u044b \u0442\u0438\u043f\u0430 <br><code class=\"prettyprinted\"> <span class=\"str\">\"\u2026 \u22c1 (\u00acA473 \u22c0 B732) \u22c1 (A232 \u22c0 \u00acC987) \u22c1 \u2026\"<\/span> <\/code><\/p>\n<p>\u0413\u0435\u043d\u0435\u0440\u0430\u0442\u043e\u0440 \u043f\u043e\u043d\u0430\u0447\u0430\u043b\u0443 \u0431\u044b\u043b \u0434\u043e\u0432\u043e\u043b\u044c\u043d\u043e \u0433\u043b\u044e\u0447\u043d\u044b\u043c. \u041a\u0430\u043a \u043c\u043d\u0435 \u0431\u044b\u043b\u043e \u043d\u0430\u0439\u0442\u0438 \u0432 \u043d\u0435\u043c \u043e\u0448\u0438\u0431\u043a\u0438?<\/p>\n<p class=\"translation-block\"><b>\u041d\u0435 \u043f\u043e \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443:<\/b> \u0420\u043e\u0431\u0435\u0440\u0442 \u0418\u0441\u0430\u0430\u043a\u043e\u0432\u0438\u0447 \u0424\u0440\u0435\u0439\u0434\u0437\u043e\u043d \u0441\u043a\u0430\u0437\u0430\u043b \u043c\u043d\u0435, \u0447\u0442\u043e \u044f <em>\u043e\u0445\u0443\u0435\u043b<\/em>.<\/p>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"footnotes":""},"categories":[2],"tags":[],"series":[],"class_list":["post-53","post","type-post","status-publish","format-standard","hentry","category-adv-software"],"_links":{"self":[{"href":"https:\/\/dmitriplotnikov.com\/ru\/wp-json\/wp\/v2\/posts\/53","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/dmitriplotnikov.com\/ru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/dmitriplotnikov.com\/ru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/dmitriplotnikov.com\/ru\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/dmitriplotnikov.com\/ru\/wp-json\/wp\/v2\/comments?post=53"}],"version-history":[{"count":5,"href":"https:\/\/dmitriplotnikov.com\/ru\/wp-json\/wp\/v2\/posts\/53\/revisions"}],"predecessor-version":[{"id":421,"href":"https:\/\/dmitriplotnikov.com\/ru\/wp-json\/wp\/v2\/posts\/53\/revisions\/421"}],"wp:attachment":[{"href":"https:\/\/dmitriplotnikov.com\/ru\/wp-json\/wp\/v2\/media?parent=53"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/dmitriplotnikov.com\/ru\/wp-json\/wp\/v2\/categories?post=53"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/dmitriplotnikov.com\/ru\/wp-json\/wp\/v2\/tags?post=53"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/dmitriplotnikov.com\/ru\/wp-json\/wp\/v2\/series?post=53"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}