{"header":{"message":"Rewrite some functions to avoid recomputing log^2.","description":"Add Artin-Schreier root function.\n\nAdd tests.","timestamp":"2024-04-25T14:39:29Z","authors":[{"email":"noiioiu@cocaine.ninja","name":"noiioiu"}]},"hash":"MCBWM3FBZPTBMBJM4QISAX45C2D75QGHWXPLAYMN3EXJJ2CV4ASAC","authors":[],"deps":{"hashes":[["MCBWM3FBZPTBMBJM4QISAX45C2D75QGHWXPLAYMN3EXJJ2CV4ASAC","Rewrite some functions to avoid recomputing log^2."],["AA",null],["L6TQHWB6JUMHD6KZR3RMO23UHQ2E37P2BAFZGDXBL5KWK2WWAIJQC","Use fewer multiplications in multiplication algorithm"],["G25ET6HXYNPM2HJ2L76TGOLVV2LBDA3CIWCAN6SL2WKNTUG56RDQC","Use sqr function in definition of recip"],["TEWWDULPAUYV2VFT3LGUTXGVVDPFFTBRHXQVJAZT63D5Q2NLPS6QC","Add power function"],["VG2W2CCBAB7KY4FSDKB4ZLBRYO763USFRDHUOA3GQOTVNS6XQLSAC","Add test for involutivity"],["6U24OB4HZGUVZZTOEHQKTBOHGV5FKEE4EQDGJF6IP3QQ3HXNNWUQC","Add tests for additive and multiplicative identities"],["O6UAIBEXBNE2XMWQWU6YKGGRLDQFI364JMV6HCYCCI3LBQRD6RPQC","Define square roots of nimbers"],["P63H7XZA5FGJP5RTASK5NOWQDV4BSKFFCN4AIS7RW44KUK3LK2JQC","Add test for square roots"],["WFOLCYCZVNRVCEWSDJR36BGSN6IKJ4CMISYCOWBLENMOP2JUTRIQC","Use faster multiplication algorithm"],["VRPOSMITS7VRSIJU6YNEBELCUBTHPMPJD6F6F5PE35R2KECS42KAC","Initial commit"],["PMF36FUOINXVVNP5XW6ZOFPPWFBRK62O4VCX45NE4Y4GDPL2Z3BQC","Represent nimbers as natural numbers instead of sets of sets"],["2Q7SZHYMAFCYLG5MROYQ4BJ7HDIASPLIZJP7SM7BNX4GESUCZXJQC","Add squaring function"],["V7A5CRSQQY3WTZFNH73E6J4YOKE7YJMEW2XW7YJTM37UNTWRMZJQC","Add Fractional instance and test"],["KARMFRM7OJF6RDDAVRISRV223RS6AWE6BG33QMFJ4GYLQFZYL56QC","Move definitions to test"],["BKOAQCTL55P6HCIDOLA3WKRDJPPZTFDFROKMKRCLXT7ANA3JG4NQC","Increase test cases"],["5CXVNGYMMIBKPFJFJK7T5HLMUAP2IE7UCFZBFZTY5DBJFRQHPP5QC","Move Nimbers.hs to Data.Nimber"]],"deps":["L6TQHWB6JUMHD6KZR3RMO23UHQ2E37P2BAFZGDXBL5KWK2WWAIJQC","G25ET6HXYNPM2HJ2L76TGOLVV2LBDA3CIWCAN6SL2WKNTUG56RDQC","TEWWDULPAUYV2VFT3LGUTXGVVDPFFTBRHXQVJAZT63D5Q2NLPS6QC"],"known":["VRPOSMITS7VRSIJU6YNEBELCUBTHPMPJD6F6F5PE35R2KECS42KAC","V7A5CRSQQY3WTZFNH73E6J4YOKE7YJMEW2XW7YJTM37UNTWRMZJQC","VG2W2CCBAB7KY4FSDKB4ZLBRYO763USFRDHUOA3GQOTVNS6XQLSAC","6U24OB4HZGUVZZTOEHQKTBOHGV5FKEE4EQDGJF6IP3QQ3HXNNWUQC","PMF36FUOINXVVNP5XW6ZOFPPWFBRK62O4VCX45NE4Y4GDPL2Z3BQC","WFOLCYCZVNRVCEWSDJR36BGSN6IKJ4CMISYCOWBLENMOP2JUTRIQC","KARMFRM7OJF6RDDAVRISRV223RS6AWE6BG33QMFJ4GYLQFZYL56QC","BKOAQCTL55P6HCIDOLA3WKRDJPPZTFDFROKMKRCLXT7ANA3JG4NQC","O6UAIBEXBNE2XMWQWU6YKGGRLDQFI364JMV6HCYCCI3LBQRD6RPQC","P63H7XZA5FGJP5RTASK5NOWQDV4BSKFFCN4AIS7RW44KUK3LK2JQC","2Q7SZHYMAFCYLG5MROYQ4BJ7HDIASPLIZJP7SM7BNX4GESUCZXJQC"]},"hunks":[{"Edit":{"inode":{"change":5,"pos":22},"path":"test/Main.hs","line":10,"atom":{"NewVertex":{"up_context":[{"change":5,"pos":34}],"down_context":[{"change":17,"pos":2}],"flag":"BLOCK","start":2,"end":19,"inode":{"change":5,"pos":22}}},"contents":[{"Add":"import Data.Bits"}]}},{"Edit":{"inode":{"change":5,"pos":22},"path":"test/Main.hs","line":18,"atom":{"NewVertex":{"up_context":[{"change":5,"pos":123}],"down_context":[{"change":5,"pos":256}],"flag":"BLOCK","start":20,"end":166,"inode":{"change":5,"pos":22}}},"contents":[{"Add":""},{"Add":"prop_floorLog :: Positive Int -> Bool"},{"Add":"prop_floorLog Positive {getPositive = n} ="},{"Add":" floorLog n == floor @Double @Int (logBase 2 $ fromIntegral n)"}]}},{"Replacement":{"inode":{"change":5,"pos":22},"path":"test/Main.hs","line":27,"ins":{"up_context":[{"change":5,"pos":112}],"down_context":[{"change":5,"pos":306}],"flag":"BLOCK","start":167,"end":208,"inode":{"change":5,"pos":22}},"del":{"edges":[{"previous":"BLOCK","flag":"BLOCK | DELETED","from":{"change":5,"pos":112},"to":{"change":5,"start":112,"end":157},"introduced_by":5}],"inode":{"change":5,"pos":22}},"ins_contents":[{"Add":"prop_add_id a = a + 0 == a && 0 + a == a"}],"del_contents":[{"Del":"prop_add_id a = (a + 0) == a && (0 + a == a)\n"}]}},{"Replacement":{"inode":{"change":5,"pos":22},"path":"test/Main.hs","line":30,"ins":{"up_context":[{"change":5,"pos":189}],"down_context":[{"change":5,"pos":235}],"flag":"BLOCK","start":209,"end":251,"inode":{"change":5,"pos":22}},"del":{"edges":[{"previous":"BLOCK","flag":"BLOCK | DELETED","from":{"change":5,"pos":189},"to":{"change":5,"start":189,"end":235},"introduced_by":5}],"inode":{"change":5,"pos":22}},"ins_contents":[{"Add":"prop_mult_id a = a * 1 == a && 1 * a == a"}],"del_contents":[{"Del":"prop_mult_id a = (a * 1) == a && (1 * a == a)\n"}]}},{"Replacement":{"inode":{"change":5,"pos":22},"path":"test/Main.hs","line":35,"ins":{"up_context":[{"change":5,"pos":403}],"down_context":[{"change":5,"pos":498}],"flag":"BLOCK","start":252,"end":357,"inode":{"change":5,"pos":22}},"del":{"edges":[{"previous":"BLOCK","flag":"BLOCK | DELETED","from":{"change":5,"pos":403},"to":{"change":5,"start":403,"end":456},"introduced_by":5},{"previous":"BLOCK","flag":"BLOCK | DELETED","from":{"change":5,"pos":456},"to":{"change":5,"start":135,"end":185},"introduced_by":5}],"inode":{"change":5,"pos":22}},"ins_contents":[{"Add":"prop_assoc_mult :: Nimber -> Nimber -> Nimber -> Bool"},{"Add":"prop_assoc_mult a b c = a * (b * c) == (a * b) * c"}],"del_contents":[{"Del":"prop_assoc_mul :: Nimber -> Nimber -> Nimber -> Bool\n"},{"Del":"prop_assoc_mul a b c = a * (b * c) == (a * b) * c\n"}]}},{"Replacement":{"inode":{"change":5,"pos":22},"path":"test/Main.hs","line":41,"ins":{"up_context":[{"change":5,"pos":237}],"down_context":[{"change":5,"pos":590}],"flag":"BLOCK","start":358,"end":444,"inode":{"change":5,"pos":22}},"del":{"edges":[{"previous":"BLOCK","flag":"BLOCK | DELETED","from":{"change":5,"pos":237},"to":{"change":5,"start":237,"end":302},"introduced_by":5}],"inode":{"change":5,"pos":22}},"ins_contents":[{"Add":"prop_recip :: NonZero Nimber -> Bool"},{"Add":"prop_recip NonZero {getNonZero = a} = a / a == 1"}],"del_contents":[{"Del":"prop_recip :: Nimber -> Bool\nprop_recip a = a == 0 || a / a == 1\n"}]}},{"Edit":{"inode":{"change":5,"pos":22},"path":"test/Main.hs","line":59,"atom":{"NewVertex":{"up_context":[{"change":5,"pos":68}],"down_context":[{"change":5,"pos":46}],"flag":"BLOCK","start":445,"end":553,"inode":{"change":5,"pos":22}}},"contents":[{"Add":"prop_as :: Nimber -> Bool"},{"Add":"prop_as a = let x = artinSchreierRoot a in sqr x + x == a && not (x `testBit` 0)"},{"Add":""}]}},{"Replacement":{"inode":{"change":5,"pos":22},"path":"test/Main.hs","line":75,"ins":{"up_context":[{"change":5,"pos":617}],"down_context":[{"change":5,"pos":124}],"flag":"BLOCK","start":554,"end":627,"inode":{"change":5,"pos":22}},"del":{"edges":[{"previous":"BLOCK","flag":"BLOCK | DELETED","from":{"change":5,"pos":617},"to":{"change":5,"start":617,"end":688},"introduced_by":5}],"inode":{"change":5,"pos":22}},"ins_contents":[{"Add":"nimberMult :: Int -> Int -> Int"},{"Add":"nimberMult = (!!) . (nimberProdTable !!)"}],"del_contents":[{"Del":"nimberMul :: Int -> Int -> Int\nnimberMul = (!!) . (nimberProdTable !!)\n"}]}},{"Replacement":{"inode":{"change":5,"pos":22},"path":"test/Main.hs","line":79,"ins":{"up_context":[{"change":5,"pos":716}],"down_context":[{"change":5,"pos":779}],"flag":"BLOCK","start":628,"end":680,"inode":{"change":5,"pos":22}},"del":{"edges":[{"previous":"BLOCK","flag":"BLOCK | DELETED","from":{"change":5,"pos":716},"to":{"change":5,"start":716,"end":779},"introduced_by":5}],"inode":{"change":5,"pos":22}},"ins_contents":[{"Add":"nimberProdTable = [mult i <$> [0 ..] | i <- [0 ..]]"}],"del_contents":[{"Del":"nimberProdTable = fmap mul <$> [(i,) <$> [0 ..] | i <- [0 ..]]\n"}]}},{"Replacement":{"inode":{"change":5,"pos":22},"path":"test/Main.hs","line":81,"ins":{"up_context":[{"change":5,"pos":787}],"down_context":[{"change":5,"pos":2}],"flag":"BLOCK","start":681,"end":857,"inode":{"change":5,"pos":22}},"del":{"edges":[{"previous":"BLOCK","flag":"BLOCK | DELETED","from":{"change":5,"pos":787},"to":{"change":5,"start":787,"end":965},"introduced_by":5}],"inode":{"change":5,"pos":22}},"ins_contents":[{"Add":" mult a b = mex $ [(nimberProdTable !! a' !! b) `nimberAdd` (nimberProdTable !! a !! b') `nimberAdd` (nimberProdTable !! a' !! b') | a' <- [0 .. a - 1], b' <- [0 .. b - 1]]"}],"del_contents":[{"Del":" mul (a, b) = mex $ [(nimberProdTable !! a' !! b) `nimberAdd` (nimberProdTable !! a !! b') `nimberAdd` (nimberProdTable !! a' !! b') | a' <- [0 .. a - 1], b' <- [0 .. b - 1]]\n"}]}},{"Replacement":{"inode":{"change":5,"pos":22},"path":"test/Main.hs","line":83,"ins":{"up_context":[{"change":5,"pos":3}],"down_context":[{"change":5,"pos":197}],"flag":"BLOCK","start":858,"end":1023,"inode":{"change":5,"pos":22}},"del":{"edges":[{"previous":"BLOCK","flag":"BLOCK | DELETED","from":{"change":5,"pos":3},"to":{"change":5,"start":224,"end":420},"introduced_by":5}],"inode":{"change":5,"pos":22}},"ins_contents":[{"Add":"prop_def_add :: Bool"},{"Add":"prop_def_add = and $ do"},{"Add":" i <- [0 .. 15]"},{"Add":" j <- [0 .. 15]"},{"Add":" pure $ fromIntegral @Int @Nimber (nimberAdd i j) == fromIntegral i + fromIntegral j"}],"del_contents":[{"Del":"-- prop_def_add :: Small Int -> Small Int -> Bool\n-- prop_def_add Small {getSmall = a} Small {getSmall = b} = abs a `nimberAdd` abs b == fromIntegral (getNimber $ fromIntegral a + fromIntegral b)\n"}]}},{"Replacement":{"inode":{"change":5,"pos":22},"path":"test/Main.hs","line":89,"ins":{"up_context":[{"change":5,"pos":198}],"down_context":[{"change":5,"pos":965}],"flag":"BLOCK","start":1024,"end":1192,"inode":{"change":5,"pos":22}},"del":{"edges":[{"previous":"BLOCK","flag":"BLOCK | DELETED","from":{"change":5,"pos":198},"to":{"change":5,"start":421,"end":617},"introduced_by":5}],"inode":{"change":5,"pos":22}},"ins_contents":[{"Add":"prop_def_mult :: Bool"},{"Add":"prop_def_mult = and $ do"},{"Add":" i <- [0 .. 15]"},{"Add":" j <- [0 .. 15]"},{"Add":" pure $ fromIntegral @Int @Nimber (nimberMult i j) == fromIntegral i * fromIntegral j"}],"del_contents":[{"Del":"-- prop_def_mul :: Small Int -> Small Int -> Bool\n-- prop_def_mul Small {getSmall = a} Small {getSmall = b} = abs a `nimberMul` abs b == fromIntegral (getNimber $ fromIntegral a * fromIntegral b)\n"}]}},{"Replacement":{"inode":{"change":5,"pos":880},"path":"src/Data/Nimber.hs","line":46,"ins":{"up_context":[{"change":5,"pos":211}],"down_context":[{"change":5,"pos":3728}],"flag":"BLOCK","start":1196,"end":1732,"inode":{"change":5,"pos":880}},"del":{"edges":[{"previous":"BLOCK","flag":"BLOCK | DELETED","from":{"change":5,"pos":211},"to":{"change":5,"start":211,"end":430},"introduced_by":5},{"previous":"BLOCK","flag":"BLOCK | DELETED","from":{"change":5,"pos":430},"to":{"change":2,"start":30,"end":125},"introduced_by":2}],"inode":{"change":5,"pos":880}},"ins_contents":[{"Add":" mult' _ 0 _ = 0"},{"Add":" mult' _ _ 0 = 0"},{"Add":" mult' _ 1 t = t"},{"Add":" mult' _ s 1 = s"},{"Add":" mult' k s t ="},{"Add":" let semiD = bit (bit k - 1) -- semimultiple of D"},{"Add":" s1 = s `shiftR` bit k -- a = a1D+a2"},{"Add":" s2 = s .^. (s1 `shiftL` bit k)"},{"Add":" t1 = t `shiftR` bit k -- b = b1D+b2"},{"Add":" t2 = t .^. (t1 `shiftL` bit k)"},{"Add":" c = mult' (k-1) s2 t2"},{"Add":" in ((mult' (k-1) (s1 + s2) (t1 + t2) - c) `shiftL` bit k) + mult' (k-1) (mult' (k-1) s1 t1) semiD + c"},{"Add":" in mult' m a b"}],"del_contents":[{"Del":" semiD = bit (bit m - 1) -- semimultiple of D\n a1 = a `shiftR` bit m -- a = a1D+a2\n a2 = a .^. (a1 `shiftL` bit m)\n b1 = b `shiftR` bit m -- b = b1D+b2\n b2 = b .^. (b1 `shiftL` bit m)\n"},{"Del":" c = a2 * b2\n in (((a1 + a2) * (b1 + b2) - c) `shiftL` bit m) + a1 * b1 * semiD + c\n"}]}},{"Replacement":{"inode":{"change":5,"pos":880},"path":"src/Data/Nimber.hs","line":69,"ins":{"up_context":[{"change":5,"pos":959}],"down_context":[{"change":4,"pos":388}],"flag":"BLOCK","start":1733,"end":2062,"inode":{"change":5,"pos":880}},"del":{"edges":[{"previous":"BLOCK","flag":"BLOCK | DELETED","from":{"change":5,"pos":959},"to":{"change":5,"start":959,"end":1164},"introduced_by":5}],"inode":{"change":5,"pos":880}},"ins_contents":[{"Add":" sqr' _ 0 = 0"},{"Add":" sqr' _ 1 = 1"},{"Add":" sqr' k l ="},{"Add":" let a = l `shiftR` bit k -- n = aD+b"},{"Add":" aD = a `shiftL` bit k"},{"Add":" b = l .^. aD"},{"Add":" semiD = bit (bit k - 1) -- semimultiple of D"},{"Add":" sqra = sqr' (k - 1) a"},{"Add":" in sqra `shiftL` bit k + sqra * semiD + sqr' (k - 1) b"},{"Add":" in sqr' m n"}],"del_contents":[{"Del":" a = n `shiftR` bit m -- n = aD+b\n aD = a `shiftL` bit m\n b = n .^. aD\n semiD = bit (bit m - 1) -- semimultiple of D\n sqra = sqr a\n in sqra `shiftL` bit m + sqra * semiD + sqr b\n"}]}},{"Replacement":{"inode":{"change":5,"pos":880},"path":"src/Data/Nimber.hs","line":81,"ins":{"up_context":[{"change":4,"pos":467}],"down_context":[{"change":5,"pos":5}],"flag":"BLOCK","start":2063,"end":2282,"inode":{"change":5,"pos":880}},"del":{"edges":[{"previous":"BLOCK","flag":"BLOCK | DELETED","from":{"change":4,"pos":467},"to":{"change":4,"start":467,"end":786},"introduced_by":4}],"inode":{"change":5,"pos":880}},"ins_contents":[{"Add":"pow :: (Integral a, Bits a) => Nimber -> a -> Nimber"},{"Add":"x `pow` n"},{"Add":" | n < 0 = recip x `pow` negate n"},{"Add":" | otherwise = product . fmap snd . filter (testBit n . fst) . zip [0 ..] . take (1 + floorLog (n + 1)) $ iterate sqr x"}],"del_contents":[{"Del":"pow :: (Integral a) => Nimber -> a -> Nimber\n_ `pow` 0 = 1\na `pow` n\n | n < 0 = recip a `pow` negate n\n | otherwise = if even n then sqr a `pow` quot n 2 else powAcc (sqr a) (quot n 2) a\n where\n powAcc _ 0 x = x\n powAcc b m x = if even m then powAcc (sqr b) (quot m 2) x else powAcc (sqr b) (quot m 2) (b * x)\n"}]}},{"Replacement":{"inode":{"change":5,"pos":880},"path":"src/Data/Nimber.hs","line":93,"ins":{"up_context":[{"change":3,"pos":458}],"down_context":[{"change":3,"pos":656}],"flag":"BLOCK","start":2283,"end":2589,"inode":{"change":5,"pos":880}},"del":{"edges":[{"previous":"BLOCK","flag":"BLOCK | DELETED","from":{"change":3,"pos":458},"to":{"change":3,"start":458,"end":656},"introduced_by":3}],"inode":{"change":5,"pos":880}},"ins_contents":[{"Add":" recip' _ 1 = 1"},{"Add":" recip' k l ="},{"Add":" let a = l `shiftR` bit k -- n = aD+b"},{"Add":" aD = a `shiftL` bit k"},{"Add":" b = l .^. aD"},{"Add":" semiD = bit (bit k - 1) -- semimultiple of D"},{"Add":" in (aD + a + b) * recip' (k - 1) (semiD * sqr a + b * (a + b))"},{"Add":" in recip' m n"}],"del_contents":[{"Del":" a = n `shiftR` bit m -- n = aD+b\n aD = a `shiftL` bit m\n b = n .^. aD\n semiD = bit (bit m - 1) -- semimultiple of D\n in (aD + a + b) / (semiD * sqr a + b * (a + b))\n"}]}},{"Replacement":{"inode":{"change":5,"pos":880},"path":"src/Data/Nimber.hs","line":108,"ins":{"up_context":[{"change":5,"pos":311}],"down_context":[{"change":5,"pos":517}],"flag":"BLOCK","start":2590,"end":2953,"inode":{"change":5,"pos":880}},"del":{"edges":[{"previous":"BLOCK","flag":"BLOCK | DELETED","from":{"change":5,"pos":311},"to":{"change":5,"start":311,"end":456},"introduced_by":5},{"previous":"BLOCK","flag":"BLOCK | DELETED","from":{"change":5,"pos":456},"to":{"change":5,"start":1165,"end":1247},"introduced_by":5}],"inode":{"change":5,"pos":880}},"ins_contents":[{"Add":" sqrt' _ 0 = 0"},{"Add":" sqrt' _ 1 = 1"},{"Add":" sqrt' k l ="},{"Add":" let a = l `shiftR` bit k -- n = aD+b"},{"Add":" aD = a `shiftL` bit k"},{"Add":" b = l .^. aD"},{"Add":" semiD = bit (bit k - 1) -- semimultiple of D"},{"Add":" sqrta = sqrt' (k - 1) a"},{"Add":" in sqrta `shiftL` bit k + sqrta * sqrt semiD + sqrt' (k - 1) b"},{"Add":" in sqrt' m n"}],"del_contents":[{"Del":" a = n `shiftR` bit m -- n = aD+b\n aD = a `shiftL` bit m\n b = n .^. aD\n semiD = bit (bit m - 1) -- semimultiple of D\n"},{"Del":" sqrta = sqrt a\n in sqrta `shiftL` bit m + sqrta * sqrt semiD + sqrt b\n"}]}},{"Edit":{"inode":{"change":5,"pos":880},"path":"src/Data/Nimber.hs","line":133,"atom":{"NewVertex":{"up_context":[{"change":5,"pos":1401}],"down_context":[],"flag":"BLOCK","start":2954,"end":4538,"inode":{"change":5,"pos":880}}},"contents":[{"Add":""},{"Add":"evens :: [a] -> [a]"},{"Add":"evens (x : _ : xs) = x : evens xs"},{"Add":"evens xs = xs"},{"Add":""},{"Add":"-- | @'artinSchreierRoot' n@ is the smallest solution to the equation \$x^2 - x = n\$."},{"Add":"-- The algorithm is due to Chin-Long Chen: ."},{"Add":"-- In fields of characteristic 2, the standard quadratic formula does not work, but any quadratic equation can be solved using square roots and Artin-Schreier roots."},{"Add":"--"},{"Add":"-- This function is __much__ slower than @'sqrt'@."},{"Add":"artinSchreierRoot :: Nimber -> Nimber"},{"Add":"artinSchreierRoot 0 = 0"},{"Add":"artinSchreierRoot 1 = 2"},{"Add":"artinSchreierRoot 2 = 4"},{"Add":"artinSchreierRoot 3 = 6"},{"Add":"artinSchreierRoot n ="},{"Add":" let m = 1 + floorLog @Int (floorLog n) -- 2^2^m is the order of the smallest field containing n"},{"Add":" m' = if n < bit (bit m - 1) then m else m + 1 -- 2^2^m' is the order of the smallest field containing the Artin-Schreier root of n"},{"Add":" squares = iterate sqr n"},{"Add":" quarts = evens squares"},{"Add":" t4k = sum $ take (bit (m' - 1)) quarts -- trace of the Artin-Screier root of n"},{"Add":" in if t4k == 1"},{"Add":" then"},{"Add":" let s = sum $ do"},{"Add":" j <- [1 .. bit (m' - 2) - 1]"},{"Add":" i <- [j .. bit (m' - 2) - 1]"},{"Add":" pure $ (squares !! (shiftL i 1 - 1 .^. bit (m' - 1))) * (squares !! (shiftL j 1 - 2))"},{"Add":" in flip clearBit 0 $"},{"Add":" s"},{"Add":" + sqr s"},{"Add":" + (squares !! (bit m' - 1))"},{"Add":" * (1 + sum (take (bit (m' - 2)) $ drop (bit (m' - 2)) quarts))"},{"Add":" else"},{"Add":" let y = bit $ bit m' - 1"},{"Add":" z = artinSchreierRoot $ sqr y + y + n"},{"Add":" in y + z"}]}}],"owner":"noiioiu","repo":"nimbers","token":"okhD3bnFLi/r55KpPLX26iLpiKMH091oI7ZvAmiwEoE=","login":null}

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