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This file is integer square root and cube root functions in Haskell language\n-- by W. Gordon Goodsman (GordonBGood), 2025\n\n{-\nThis is based on binomial square explansion where\n(old + inc)^2 -> old^2 + 2*inc*old + inc^2 = new^2, thus\nnew^2 - old^2 or deltasqr = 2*old*inc + inc^2.\nNow this is really easy in binary where multiplying by two is just a left shift by one and\nwhen inc is an even power of two as in 2^j, where the above expression becomes\ndeltasqr = old<<(j + 1) + 1<<(2j). Also, this works relative to inc or 2^j or 1< Integer\nisqrt n =\n if n < 2 then max 0 n else\n if n < 2^(64 :: Int) then pisqrt n else\n let shft o = if o > n then o `shiftR` 2 else shft (o `shiftL` 2)\n go x one rslt =\n if one <= 0 then rslt else\n let nrslt = rslt `shiftR` 1 -- `rslt` is couble the current `nrslt`!\n dltasqr = rslt + one -- is the same as 2*`rslt` + `one` where `one` = `inc` above\n in\n if x < dltasqr then go x (one `shiftR` 2) nrslt\n else go (x - dltasqr) (one `shiftR` 2) (nrslt + one)\n in go n (shft 1) 0\n\npisqrt :: Integer -> Integer\npisqrt n =\n let !(W# n##) = fromIntegral n\n shft# o## = case o## `leWord#` n## of\n 0# -> o## `uncheckedShiftRL#` 2#\n _ -> case o## `ltWord#` 0x4000000000000000## of\n 0# -> o##\n _ -> shft# (o## `uncheckedShiftL#` 2#)\n go# x## one## rslt## =\n case one## `gtWord#` 0## of\n 0# -> rslt##\n _ ->\n let none## = one## `uncheckedShiftRL#` 2#\n nrslt## = rslt## `uncheckedShiftRL#` 1# -- `rslt` is couble the current `nrslt`!\n dltasqr## = rslt## `plusWord#` one## -- is the same as 2*`rslt` + `one` where `one` = `inc` above\n in\n case x## `ltWord#` dltasqr## of\n 0# -> go# (x## `minusWord#` dltasqr##) none## (nrslt## `plusWord#` one##)\n _ -> go# x## none## nrslt##\n in fromIntegral $ W# $ go# n## (shft# 1##) 0##\n\n{-\nThe cube root works the same as the square root except that the expansion is\n(old + inc)^3 = old^3 + 3*old^2*inc + 3*old*inc^2 + inc^3 meaning that\ndeltacube = 3*old^2*inc + 3*old*inc^2 + inc^3\nthat can be simplified by two powers in the same way, with the only complication\nthat the current square of the current `rslt` value must be kept and updated,\nwhich updating is done progressively as per the relationship in the sqrt algorithm.\n-}\n\nicbrt :: Integer -> Integer\nicbrt n =\n let neg = if n < 0 then -1 else 1\n absn = abs n in\n if absn < 2 then n else\n if absn < 2^(64 :: Int) then neg * picbrt absn else\n let shft o = if o > absn then o `shiftR` 3 else shft (o `shiftL` 3)\n go x one sqr rslt =\n if one <= 0 then rslt else\n let none = one `shiftR` 3\n nsqr = sqr `shiftR` 1\n twicerslt = rslt `shiftR` 1 -- `twicerslt` is double the current `nrslt`!\n nrslt = rslt `shiftR` 2\n -- is the same as 3*`nsqr` + 3*`nrslt``+``one`` where`one` =``inc` above\n dltacube = sqr + nsqr + twicerslt + nrslt + one\n in\n if x < dltacube then go x none nsqr nrslt\n else go (x - dltacube) none (nsqr + twicerslt + one) (nrslt + one) \n in (go absn (shft 1) 0 0) * neg\n\npicbrt :: Integer -> Integer\npicbrt n =\n let !(W# n##) = fromIntegral n\n shft# o## = case o## `leWord#` n## of\n 0# -> o## `uncheckedShiftRL#` 3#\n _ -> case o## `ltWord#` 0x8000000000000000## of\n 0# -> o##\n _ -> shft# (o## `uncheckedShiftL#` 3#)\n go# x## one## sqr## rslt## =\n case one## `gtWord#` 0## of\n 0# -> rslt##\n _ ->\n let none## = one## `uncheckedShiftRL#` 3#\n nsqr## = sqr## `uncheckedShiftRL#` 1#\n twicerslt## = rslt## `uncheckedShiftRL#` 1#\n nrslt## = rslt## `uncheckedShiftRL#` 2#\n -- is the same as 3*`rslt##^2 + 3*`rst##` + `one##` where `one##` is ``inc`` above\n dltacube## = sqr## `plusWord#` nsqr## `plusWord#` twicerslt## `plusWord#` nrslt## `plusWord#` one##\n in\n case sqr## `leWord#` dltacube## of\n 0# -> go# x## none## nsqr## nrslt## -- overflow!\n _ ->\n case x## `ltWord#` dltacube## of\n 0# -> go# (x## `minusWord#` dltacube##) none##\n (nsqr## `plusWord#` twicerslt## `plusWord#` one##) (nrslt## `plusWord#` one##)\n _ -> go# x## none## nsqr## nrslt##\n in fromIntegral $ W# $ go# n## (shft# 1##) 0## 0##\n\nxisqrt :: Integer -> Integer\nxisqrt n =\n if n < 2 then max 0 n else\n let absn = fromIntegral n :: Word\n est = floor $ sqrt (fromIntegral n :: Double) :: Word\n chktoohi e = let chk = e * e in\n if chk < e || chk > absn then chktoohi (e - 1) else e + 1\n chktoolo ep1 = let chk = ep1 * ep1 in\n if chk < ep1 || chk > absn then ep1 - 1 else chktoolo (ep1 + 1)\n in fromIntegral (chktoolo $ chktoohi est)\n\nxicbrt :: Integer -> Integer\nxicbrt n =\n let neg = if n < 0 then -1 else 1\n absn = fromIntegral $ abs n :: Word in\n if absn < 2 then n else\n let est = floor $ (fromIntegral absn :: Double)**(1.0/3.0 :: Double) :: Word\n chktoohi e = let chk0 = e * e in let chk = chk0 * e in\n if chk < chk0 || chk > absn then chktoohi (e - 1) else e + 1\n chktoolo ep1 = let chk0 = ep1 * ep1 in let chk = chk0 * ep1 in\n if chk < chk0 || chk > absn then ep1 - 1 else chktoolo (ep1 + 1)\n in fromIntegral (chktoolo $ chktoohi est) * neg\n\nmain :: IO ()\nmain = do\n let arg = 2^(64 :: Int) - 1\n putStrLn $ \"The square root of \" ++ show arg ++ \" is \" ++ show (xisqrt arg) ++ \".\"\n putStrLn $ \"The cube root of \" ++ show arg ++ \" is \" ++ show (xicbrt arg) ++ \".\"\n-- let rng = [ 2^(64 :: Int) - 1 - 10^(8 :: Int) .. 2^(64 :: Int) - 1 ] -- [-1000 .. 100000] ++ [10^(20 :: Int) .. 10^(20 :: Int) + 10^(4 :: Int)]\n let rng = [ -1000 .. 10000000] -- ++ [10^(20 :: Int) .. 10^(20 :: Int) + 10^(4 :: Int)]\n strt <- getPOSIXTime\n if all id [ isqrt v == xisqrt v | v <- rng ] then putStrLn \"SQRT CORRECT\" else putStrLn \"SQRT FAILURE!!!!!\"\n if all id [ icbrt v == xicbrt v | v <- rng ] then putStrLn \"CBRT CORRECT\" else putStrLn \"CBRT FAILURE!!!!!\"\n stop <- getPOSIXTime\n let elpsd = round (1000.0 * (realToFrac $ stop - strt) :: Double) :: Int\n putStrLn $ \"This took \" ++ show elpsd ++ \" milliseconds.\"","codes",[],"stdin","compiler","haskell-warning,haskell-optimize","createdAt",1765083511,"title","description","isPrivate","compilerInfo",{"_11":1146,"_13":1147,"_15":1148,"_17":1149,"_19":3430,"_22":23,"_24":25,"_26":1151,"_28":3431},[1149],[3432,3434],{"_31":32,"_33":3433},{"_11":1155,"_36":23,"_37":1156,"_17":39},{"_31":32,"_33":3435},{"_11":1159,"_36":25,"_37":1160,"_17":44},"results",[3438,3442,3445,3447,3450,3453],{"_31":3439,"_3440":3441},"Control","data","Start",{"_31":3443,"_3440":3444},"CompilerMessageS","[1 of 2] Compiling Main ( prog.hs, prog.o )\n",{"_31":3443,"_3440":3446},"[2 of 2] Linking prog.exe\n",{"_31":3448,"_3440":3449},"StdOut","The square root of 18446744073709551615 is 4294967295.\nThe cube root of 18446744073709551615 is 2642245.\nSQRT CORRECT\nCBRT CORRECT\nThis took 4743 milliseconds.\n",{"_31":3451,"_3440":3452},"ExitCode","0",{"_31":3439,"_3440":3454},"Finish","hpplib",[3457,3474,3485,3494,3503,3512,3521,3530,3540,3549,3560,3571,3582,3593,3604,3615],{"_11":3458,"_3459":3460,"_3426":3461,"_3462":3463,"_3464":3465,"_3470":3471},"CLI11","repository","CLIUtils/CLI11","CLI11 is a command line parser for C++11 and beyond that provides a rich feature set with a simple and intuitive interface.","headerDescription","","wandbox",{"_3466":3467,"_3468":3469},"tagName","v2.6.1","publishedAt","2025-10-27T13:19:41Z","clangd",{"_3466":3472,"_3468":3473},"v2.5.0","2025-02-27T12:29:12Z",{"_11":3475,"_3459":3476,"_3426":3477,"_3462":3478,"_3464":3479,"_3470":3482},"cxxopts","jarro2783/cxxopts","Lightweight C++ command line option parser","",{"_3466":3480,"_3468":3481},"v3.3.1","2025-05-26T08:12:04Z",{"_3466":3483,"_3468":3484},"v3.2.0","2024-02-15T05:32:43Z",{"_11":3486,"_3459":3487,"_3426":3488,"_3462":3489,"_3464":3490,"_3470":3493},"nanobench","martinus/nanobench","Simple, fast, accurate single-header microbenchmarking functionality for C++11/14/17/20","",{"_3466":3491,"_3468":3492},"v4.3.11","2023-02-16T19:06:26Z",{"_3466":3491,"_3468":3492},{"_11":3495,"_3459":3496,"_3426":3497,"_3462":3498,"_3464":3499,"_3470":3502},"toml11","ToruNiina/toml11","TOML for Modern C++","",{"_3466":3500,"_3468":3501},"v4.4.0","2025-02-15T16:20:52Z",{"_3466":3500,"_3468":3501},{"_11":3504,"_3459":3505,"_3426":3506,"_3462":3507,"_3464":3508,"_3470":3511},"toml++","marzer/tomlplusplus","Header-only TOML config file parser and serializer for C++17.","",{"_3466":3509,"_3468":3510},"v3.4.0","2023-10-13T13:45:17Z",{"_3466":3509,"_3468":3510},{"_11":3513,"_3459":3514,"_3426":3515,"_3462":3516,"_3464":3517,"_3470":3520},"rapidjson","Tencent/rapidjson","A fast JSON parser/generator for C++ with both SAX/DOM style API","",{"_3466":3518,"_3468":3519},"v1.1.0","2016-08-25T08:01:22Z",{"_3466":3518,"_3468":3519},{"_11":3522,"_3459":3523,"_3426":3524,"_3462":3525,"_3464":3526,"_3470":3529},"picojson","kazuho/picojson","a header-file-only, JSON parser serializer in C++","",{"_3466":3527,"_3468":3528},"v1.3.0","2015-02-25T04:12:53Z",{"_3466":3527,"_3468":3528},{"_11":3531,"_3459":3531,"_3426":3532,"_3462":3533,"_3464":3534,"_3470":3537},"nlohmann/json","JSON for Modern C++","",{"_3466":3535,"_3468":3536},"v3.12.0","2025-04-11T08:43:39Z",{"_3466":3538,"_3468":3539},"v3.11.3","2023-11-28T21:38:09Z",{"_11":3541,"_3459":3542,"_3426":3543,"_3462":3544,"_3464":3545,"_3470":3548},"csv-parser","vincentlaucsb/csv-parser","A high-performance, fully-featured CSV parser and serializer for modern C++.","",{"_3466":3546,"_3468":3547},"2.3.0","2024-06-15T20:23:18Z",{"_3466":3546,"_3468":3547},{"_11":3550,"_3459":3551,"_3426":3552,"_3462":3553,"_3464":3554,"_3470":3557},"rapidcsv","d99kris/rapidcsv","C++ CSV parser library","",{"_3466":3555,"_3468":3556},"v8.90","2025-11-08T06:11:56Z",{"_3466":3558,"_3468":3559},"v8.84","2024-09-28T05:31:16Z",{"_11":3561,"_3459":3562,"_3426":3563,"_3462":3564,"_3464":3565,"_3470":3568},"fmt","fmtlib/fmt","A modern formatting library","",{"_3466":3566,"_3468":3567},"12.1.0","2025-10-29T14:58:05Z",{"_3466":3569,"_3468":3570},"11.1.4","2025-02-26T18:33:33Z",{"_11":3572,"_3459":3573,"_3426":3574,"_3462":3575,"_3464":3576,"_3470":3579},"NumCpp","dpilger26/NumCpp","C++ implementation of the Python Numpy library","",{"_3466":3577,"_3468":3578},"Version_2.16.0","2025-11-30T20:31:41Z",{"_3466":3580,"_3468":3581},"Version_2.14.0","2025-02-09T04:16:30Z",{"_11":3583,"_3459":3584,"_3426":3585,"_3462":3586,"_3464":3587,"_3470":3590},"spdlog","gabime/spdlog","Fast C++ logging library.","",{"_3466":3588,"_3468":3589},"v1.17.0","2026-01-04T16:51:07Z",{"_3466":3591,"_3468":3592},"v1.15.1","2025-02-01T12:08:58Z",{"_11":3594,"_3459":3595,"_3426":3596,"_3462":3597,"_3464":3598,"_3470":3601},"expected-lite","martinmoene/expected-lite","expected lite - 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