{"id":31252,"date":"2023-01-20T08:56:18","date_gmt":"2023-01-20T03:26:18","guid":{"rendered":"https:\/\/jassweb.com\/solved\/solved-bits-set-by-lookup-table-recursive-macro-duplicate\/"},"modified":"2023-01-20T08:56:18","modified_gmt":"2023-01-20T03:26:18","slug":"solved-bits-set-by-lookup-table-recursive-macro-duplicate","status":"publish","type":"post","link":"https:\/\/jassweb.com\/solved\/solved-bits-set-by-lookup-table-recursive-macro-duplicate\/","title":{"rendered":"[Solved] bits set by lookup table – Recursive macro [duplicate]"},"content":{"rendered":"

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The idea is “recursively defining the problem down to 2-bit values”: 00, 01, 10, 11. They’re not recursive macros, but does represent the technique of recursive decomposition<\/em> of the problem. The arrangement of macros as a cascade<\/em> attacks the problem of generating the table of 2^8 values by solving the problem for 2-bits (generating 4 values), then for 4-bits (using the 2-bit solution 4 times), then for 6-bits (using the 4-bit solution 4 times), then for the whole problem (using the 6-bit solution 4 times).<\/p>\n

2 bits gives you four values: 0, 1, 2, 3. 0 has 0 bits set, 1 has 1 bit set,
\n2 also has just 1 bit set, and 3 has 2 bits set.<\/p>\n

The values for 4 bit numbers use the same pattern and use the 2-bit pattern for the extra 2 bits of each value.<\/p>\n

It could be “simplified” down to 1-bit per macro.<\/p>\n

#define B1(n) n,     n+1\n#define B2(n) B1(n), B1(n+1),\n#define B3(n) B2(n), B2(n+1),\n#define B4(n) B3(n), B3(n+1),\n#define B5(n) B4(n), B4(n+1),\n#define B6(n) B5(n), B5(n+1),\n#define B7(n) B6(n), B6(n+1),\n B7(0), B7(1)\n<\/code><\/pre>\n
Remember the purpose of a lookup table is to replace a function call howmanybits(x)<\/code> with a table-lookup howmanybits[x]<\/code>. So each value in the table should represent the f(i) for that index i and the overall function f. <\/p>\n
So to really get a handle on it, trace through the first few values. B6(0)<\/code> starts with B4(0)<\/code>, which starts with B2(0)<\/code>, which goes 0, 1, 1, 2. f(0)=0, f(1)=1, f(2)=1, f(3)=2. B4(0)<\/code> continues with B2(1)<\/code> which goes 1, 2, 2, 3. f(4)=1, f(5)=2, f(6)=2, f(7)=3. If you look at these numbers in a binary representation, it should be clear that it’s correct for these 8 results.<\/p>\n
x  x_2  f(x)\n0 0000  0 bits set\n1 0001  1\n2 0010  1\n3 0011  2\n4 0100  1\n5 0101  2\n6 0110  2\n7 0111  3\n...\n<\/code><\/pre>\n<\/p><\/div>\n
<\/div>\n<\/div>\n
            3<\/span> <\/p><\/div>\n<\/div>\n
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solved bits set by lookup table – Recursive macro [duplicate] <\/p>\n","protected":false},"excerpt":{"rendered":"
[ad_1] The idea is “recursively defining the problem down to 2-bit values”: 00, 01, 10, 11. They’re not recursive macros, but does represent the technique of recursive decomposition of the problem. The arrangement of macros as a cascade attacks the problem of generating the table of 2^8 values by solving the problem for 2-bits (generating … Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[320],"tags":[2005,324,1971,4407,494],"class_list":["post-31252","post","type-post","status-publish","format-standard","hentry","category-solved","tag-bit","tag-c","tag-macros","tag-preprocessor-directive","tag-recursion"],"yoast_head":"\n[Solved] bits set by lookup table - Recursive macro [duplicate] - JassWeb<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/jassweb.com\/solved\/solved-bits-set-by-lookup-table-recursive-macro-duplicate\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"[Solved] bits set by lookup table - Recursive macro [duplicate] - JassWeb\" \/>\n<meta property=\"og:description\" content=\"[ad_1] The idea is “recursively defining the problem down to 2-bit values”: 00, 01, 10, 11. 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