Implement shifts with Take/Drop then Join

2 files changed, 9 insertions, 12 deletions

diff --git a/docs/bqn.js b/docs/bqn.js
index 8a913b06..c54cecf9 100644
--- a/docs/bqn.js
+++ b/docs/bqn.js
@@ -291,9 +291,9 @@ let runtime_0 = [
 ];
 
 let [runtime,setPrims] = run(
-  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  ,[provide[0],provide[1],provide[2],provide[3],provide[4],provide[5],provide[6],provide[7],provide[8],provide[9],provide[10],runtime_0[0],provide[12],provide[13],provide[14],provide[15],provide[16],provide[17],runtime_0[1],runtime_0[2],runtime_0[3],runtime_0[4],runtime_0[5],runtime_0[6],runtime_0[7],runtime_0[8],runtime_0[9],runtime_0[10],runtime_0[11],runtime_0[12],provide[18],provide[19],runtime_0[13],runtime_0[14],runtime_0[15],runtime_0[16],provide[20],provide[21],provide[22],runtime_0[17],runtime_0[18],runtime_0[19],runtime_0[20],runtime_0[21],runtime_0[22],0,1,2,Infinity,-Infinity,-1,3,8,5,4,'∾','+','-','×','÷','⋆','¬','⌊','⌈','∨','∧','≠','=','>','≥','˙','√','<','⊢','⊣','≍','↑','↓','↕','⌽','⍉','/','⊔','˜','¨','⌜','˘','`','∘','○','⌾','⍟','⊘','⊸','⟜',str("+-×÷⋆√⌊⌈|¬∧∨<>≠=≤≥≡≢⊣⊢⥊∾≍↑↓↕«»⌽⍉/⍋⍒⊏⊑⊐⊒∊⍷⊔!˙˜˘¨⌜⁼´˝`∘○⊸⟜⌾⊘◶⎉⚇⍟⎊%"),str("´: Identity not found"),str("´: 𝕩 must be a list"),str("Mapping: Equal-rank argument shapes don\'t agree"),str("Mapping: Argument shape prefixes don\'t agree"),str("⍋𝕩: 𝕩 must have rank at least 1"),str("⍋ or ⍒: Rank of 𝕨 must be at least 1"),str("⍋ or ⍒: Rank of 𝕩 must be at least cell rank of 𝕨"),str("⍋ or ⍒: 𝕨 must be sorted"),str("p⊐𝕩 or 𝕨∊p: p must have rank at least 1"),str("p⊐n or n∊p: Rank of n must be at least cell rank of p"),str("∊𝕩 or ⊐𝕩: 𝕩 must have rank at least 1"),str("⍷𝕩: Rank of 𝕨 cannot exceed rank of 𝕩"),str("/: Replication argument must have rank 1"),str("/: Amounts to replicate must be natural numbers"),str("⌽𝕩: 𝕩 must have rank at least 1"),str("𝕨⌽𝕩: 𝕨 must consist of integers"),str("↑𝕩: 𝕩 must have rank at least 1"),str("↓𝕩: 𝕩 must have rank at least 1"),str("𝕨⊑𝕩: Indices in 𝕨 must consist of integers"),str("𝕨⊑𝕩: Index out of range"),str("𝕨⊏𝕩: Indices in 𝕨 must be integers"),str("𝕨⊏𝕩: Indices out of range"),str("𝕨⊑𝕩: 𝕩 must be a list when 𝕨 is a number"),str("𝕨⊑𝕩: Indices in compound 𝕨 must be lists"),str("𝕨⊑𝕩: Index length in 𝕨 must match rank of 𝕩"),str("⊏𝕩: 𝕩 must have rank at least 1"),str("⊏𝕩: 𝕩 cannot have length 0"),str("𝕨⊏𝕩: 𝕨 must be an array"),str("=≠≡≢"),str("⌾: Incompatible result elements in structural Under"),str(">𝕩: Elements of 𝕩 must have matching shapes"),str("𝕨∾𝕩: Rank of 𝕨 and 𝕩 must differ by at most 1"),str("𝕨∾𝕩: Cell shapes of 𝕨 and 𝕩 must match"),str("∾𝕩: Elements of 𝕩 must all have the same rank"),str("∾𝕩: 𝕩 element rank must be at least argument rank"),str("∾𝕩: 𝕩 element shapes must be compatible"),str("∾𝕩: 𝕩 element trailing shapes must match"),str("∾𝕩: empty 𝕩 fill rank must be at least argument rank"),str("∾𝕩: 𝕩 must be an array"),str("⊢⊣˜∘○⊸⟜⊘◶"),str("=≠≢"),str("<"),str("≍"),str("↕/»«⊔"),str("⥊↑↓⌽⍉⊏⊑"),str("↑"),str("↓"),str("𝕨"),str("𝕩: 𝕨 must "),str("have rank at most 1"),str("consist of integers"),str("« or »: 𝕩 must have rank at least 1"),str("« or »: 𝕨 must not have higher rank than 𝕩"),str("« or »: Rank of 𝕨 must be at least rank of 𝕩 minus 1"),str("« or »: 𝕨 must share 𝕩\'s major cell shape"),str("↕𝕩: 𝕩 must consist of natural numbers"),str("↕𝕩: 𝕩 must be a number or list"),str("𝕨↕𝕩: 𝕨 must have rank at most 1"),str("𝕨↕𝕩: Length of 𝕨 must be at most rank of 𝕩"),str("𝕨↕𝕩: 𝕨 must consist of natural numbers"),str("𝕨↕𝕩: Window length 𝕨 must be at most axis length plus one"),str("˘: Argument lengths don\'t agree"),str("˝: 𝕩 must have rank at least 1"),str("˝: Identity does not exist"),str("First-axis primitive: 𝕩 must have rank at least 1"),str("Multi-axis primitive: 𝕨 must have rank at most 1"),str("Multi-axis primitive: Length of 𝕨 must be at most rank of 𝕩"),str("𝕨/𝕩: Lengths of components of 𝕨 must match 𝕩"),str("∘⌊⌽↑"),str("𝕨⥊𝕩: 𝕨 must have rank at most 1"),str("𝕨⥊𝕩: 𝕨 must consist of natural numbers"),str("𝕨⥊𝕩: Can\'t compute axis length when rest of shape is empty"),str("𝕨⥊𝕩: 𝕨 must consist of natural numbers or ∘ ⌊ ⌽ ↑"),str("𝕨⥊𝕩: Shape must be exact when reshaping with ∘"),str("⊔: Grouping argument must consist of integers"),str("⊔: Grouping argument values cannot be less than ¯1"),str("⊔𝕩: 𝕩 must be a list"),str("𝕨⊔𝕩: Rank of simple 𝕨 must be at most rank of 𝕩"),str("𝕨⊔𝕩: Lengths of 𝕨 must equal to 𝕩, or one more only in a rank-1 component"),str("𝕨⊔𝕩: 𝕩 must be an array"),str("≥: No monadic form"),str("≤: No monadic form"),str("⎉ or ⚇: 𝔽 result must have rank at most 1"),str("⎉ or ⚇: 𝔽 result must have 1 to 3 elements"),str("⎉ or ⚇: 𝔽 result must consist of integers"),str("⍟: Repetition numbers in 𝕨𝔾𝕩 must be integers"),str("𝕨⊔𝕩: Compound 𝕨 must be a list"),str("𝕨⊔𝕩: Total rank of 𝕨 must be at most rank of 𝕩"),str("⊒: Rank of 𝕨 must be at least 1"),str("⊒: Rank of 𝕩 must be at least cell rank of 𝕨"),str("𝕨⍉𝕩: 𝕨 must have rank at most 1"),str("𝕨⍉𝕩: Length of 𝕨 must not exceed rank of 𝕩"),str("𝕨⍉𝕩: 𝕨 must consist of natural numbers"),str("𝕨⍉𝕩: Skipped result axis"),str("Cannot currently invert blocks"),str("Cannot invert modifier"),str("⁼: Inverse failed"),str("⁼: Inverse does not exist"),str("⁼: Inverse not found")]
- ,[[0,1,0,174],[0,0,3654,3],[0,0,3662,3],[0,0,3666,3],[0,0,3679,3],[0,0,3691,3],[0,0,3700,3],[1,1,3706,2],[2,1,3735,3],[1,1,3767,2],[0,0,3784,4],[2,1,3846,5],[0,0,3882,3],[1,0,3889,5],[1,1,3947,4],[1,1,4013,3],[0,0,4086,3],[0,0,4097,4],[1,0,4162,9],[0,0,4231,5],[1,1,4308,3],[1,1,4329,6],[1,1,4423,4],[1,0,4473,8],[0,0,4645,8],[0,0,4802,3],[0,0,4888,6],[0,0,4973,3],[0,0,4997,7],[0,0,5111,4],[0,0,5169,4],[0,0,5277,3],[0,0,5339,4],[0,0,5410,6],[0,0,5480,3],[0,0,5520,5],[0,0,5598,3],[0,0,5615,3],[0,0,5661,3],[0,0,5702,4],[0,0,5769,3],[0,0,5788,3],[2,1,5806,3],[1,0,5844,5],[1,0,5881,5],[0,0,5908,3],[2,0,5912,16],[0,0,6200,3],[0,0,6227,3],[0,0,6252,3],[0,0,6266,3],[2,1,6293,3],[0,0,6352,4],[0,0,6452,7],[0,0,6649,7],[0,0,6695,14],[0,0,6919,5],[0,0,6998,3],[0,0,7006,6],[0,0,7033,5],[0,0,7054,6],[0,1,7081,10],[1,1,7377,9],[0,0,7534,4],[0,0,7598,3],[0,0,7625,5],[0,0,7738,7],[0,0,7873,5],[0,0,7906,4],[0,0,7968,8],[1,0,8080,8],[1,0,8155,7],[2,1,8217,4],[0,0,8255,5],[0,0,8338,3],[0,0,8369,9],[1,0,8527,9],[0,0,8675,4],[0,0,8781,8],[0,0,8997,3],[0,0,9041,3],[0,0,9067,3],[0,0,9088,3],[0,0,9109,3],[1,1,9203,2],[2,0,9265,10],[2,0,9324,8],[2,0,9499,10],[0,0,9572,10],[0,0,9980,4],[0,0,10085,3],[0,0,10159,3],[0,0,10210,4],[0,0,10337,4],[1,1,10453,2],[2,0,10461,6],[1,1,10476,2],[0,0,10579,3],[0,0,10587,3],[0,0,10595,3],[0,0,10615,8],[0,0,10690,3],[0,0,10698,3],[0,0,10706,3],[0,0,10714,3],[0,0,10722,3],[0,0,10730,3],[0,0,10741,3],[2,0,10762,7],[0,0,10803,6],[0,0,11022,4],[0,0,11122,3],[0,0,11165,5],[0,0,11303,3],[0,0,11350,3],[0,0,11376,3],[0,0,11463,3],[0,0,11496,3],[0,0,11540,3],[0,0,11588,3],[0,0,11600,3],[1,1,11673,2],[0,0,11699,4],[0,0,11735,3],[0,0,11750,3],[0,0,11779,3],[0,0,11794,3],[0,0,11812,3],[0,0,11826,3],[0,0,11836,3],[2,0,11888,6],[0,0,11916,3],[0,0,11944,3],[0,0,11952,3],[1,0,11960,6],[1,0,12015,11],[1,0,12222,5],[0,0,12237,3],[0,0,12251,3],[0,0,12265,7],[0,0,12338,6],[0,0,12384,3],[0,0,12402,4],[0,0,12429,3],[2,0,12436,6],[0,0,12471,19],[0,0,12962,4],[0,0,13018,10],[0,0,13213,4],[0,0,13280,3],[1,1,13305,2],[0,0,13320,3],[0,0,13347,3],[0,0,13357,3],[2,0,13374,11],[0,0,13447,5],[0,0,13519,8],[0,0,13597,3],[0,0,13605,3],[1,0,13647,7],[0,0,13673,9],[1,0,13919,5],[0,0,13935,6],[1,0,14057,5],[2,0,14090,6],[0,0,14119,3],[0,0,14129,3],[0,0,14139,4],[0,0,14178,4],[0,0,14201,3],[0,0,14209,3],[1,0,14234,6],[1,1,14330,2],[0,0,14380,8],[0,0,14561,11],[0,0,14766,3],[0,0,14825,3],[0,0,14838,3],[0,0,14860,3],[0,0,14880,3],[0,0,14940,8],[0,0,15201,3],[0,0,15215,3],[1,1,15246,2],[0,0,15280,3],[0,0,15315,3],[0,0,15333,3],[0,0,15351,5],[0,0,15422,3],[0,0,15442,3],[0,0,15470,5],[0,0,15558,3],[0,0,15568,3],[0,0,15587,8],[0,0,15817,3],[0,0,15858,3],[0,0,15888,3],[0,0,15919,3],[0,0,15955,5],[0,0,16023,3],[1,0,16032,6],[0,0,16176,3],[0,0,16186,3],[0,0,16193,9],[0,0,16331,3],[0,0,16357,3],[0,0,16375,3],[0,0,16399,3],[0,0,16420,3],[0,0,16431,3],[1,1,16444,2],[1,0,16448,5],[1,0,16459,5],[0,0,16470,3],[0,0,16506,5],[0,0,16608,3],[0,0,16655,3],[1,0,16675,5],[0,0,16698,3],[0,0,16708,3],[0,0,16724,3],[0,0,16742,13],[0,0,16939,3],[0,0,16963,4],[0,0,17046,3],[0,0,17075,3],[0,0,17086,3],[0,0,17122,7],[0,0,17259,10],[2,0,17420,6],[0,0,17455,3],[0,0,17520,3],[0,0,17548,4],[1,0,17571,5],[0,0,17582,4],[0,0,17593,4],[1,0,17604,5],[0,0,17624,4],[0,0,17699,3],[0,0,17732,3],[1,0,17762,5],[0,0,17787,3],[0,0,17853,3],[0,0,17867,3],[0,0,17878,5],[0,0,17977,3],[0,0,17996,3],[0,0,18015,3],[0,0,18061,3],[0,0,18112,3],[0,0,18145,5],[1,0,18175,5],[0,0,18185,3],[0,0,18228,3],[2,0,18248,6],[1,1,18263,2],[1,1,18271,2],[0,0,18279,5],[0,0,18317,6],[0,0,18396,3],[0,0,18421,6],[0,0,18530,3],[0,0,18570,3],[0,0,18611,5],[0,0,18661,6],[0,0,18795,3],[0,0,18811,3],[0,0,18819,8],[0,0,18876,5],[0,0,18905,3],[0,0,18920,3],[1,1,18970,2],[2,1,18988,3],[0,0,19009,3],[0,0,19027,3],[0,0,19056,3],[1,0,19093,5],[0,0,19108,14],[0,0,19277,3],[0,0,19298,3],[0,0,19314,4],[0,0,19370,3],[0,0,19402,3],[0,0,19485,3],[0,0,19519,3],[0,0,19548,3],[0,0,19565,3],[0,0,19582,3]]
+ ,[[0,1,0,173],[0,0,3642,3],[0,0,3650,3],[0,0,3654,3],[0,0,3667,3],[0,0,3679,3],[0,0,3688,3],[1,1,3694,2],[2,1,3723,3],[1,1,3755,2],[0,0,3772,4],[2,1,3834,5],[0,0,3870,3],[1,0,3877,5],[1,1,3935,4],[1,1,4001,3],[0,0,4074,3],[0,0,4085,4],[1,0,4150,9],[0,0,4219,5],[1,1,4296,3],[1,1,4317,6],[1,1,4411,4],[1,0,4461,8],[0,0,4633,8],[0,0,4790,3],[0,0,4876,6],[0,0,4961,3],[0,0,4985,7],[0,0,5099,4],[0,0,5157,4],[0,0,5265,3],[0,0,5327,4],[0,0,5398,6],[0,0,5468,3],[0,0,5508,5],[0,0,5586,3],[0,0,5603,3],[0,0,5649,3],[0,0,5690,4],[0,0,5757,3],[0,0,5776,3],[2,1,5794,3],[1,0,5832,5],[1,0,5869,5],[0,0,5896,3],[2,0,5900,16],[0,0,6188,3],[0,0,6215,3],[0,0,6240,3],[0,0,6254,3],[2,1,6281,3],[0,0,6340,4],[0,0,6440,7],[0,0,6637,7],[0,0,6683,14],[0,0,6907,5],[0,0,6986,3],[0,0,6994,6],[0,0,7021,5],[0,0,7042,6],[0,1,7069,10],[1,1,7365,9],[0,0,7522,4],[0,0,7598,7],[0,0,7699,6],[0,0,7801,5],[0,0,7834,4],[0,0,7896,8],[1,0,8008,8],[1,0,8083,7],[2,1,8145,4],[0,0,8183,5],[0,0,8266,3],[0,0,8297,9],[1,0,8455,9],[0,0,8603,4],[0,0,8709,8],[0,0,8925,3],[0,0,8969,3],[0,0,8995,3],[0,0,9016,3],[0,0,9037,3],[1,1,9131,2],[2,0,9193,10],[2,0,9252,8],[2,0,9427,10],[0,0,9500,10],[0,0,9908,4],[0,0,10013,3],[0,0,10087,3],[0,0,10138,4],[0,0,10265,4],[1,1,10381,2],[2,0,10389,6],[1,1,10404,2],[0,0,10507,3],[0,0,10515,3],[0,0,10523,3],[0,0,10543,8],[0,0,10618,3],[0,0,10626,3],[0,0,10634,3],[0,0,10642,3],[0,0,10650,3],[0,0,10658,3],[0,0,10669,3],[2,0,10690,7],[0,0,10731,6],[0,0,10950,4],[0,0,11050,3],[0,0,11093,5],[0,0,11231,3],[0,0,11278,3],[0,0,11304,3],[0,0,11391,3],[0,0,11424,3],[0,0,11468,3],[0,0,11516,3],[0,0,11528,3],[1,1,11601,2],[0,0,11627,4],[0,0,11663,3],[0,0,11678,3],[0,0,11707,3],[0,0,11722,3],[0,0,11740,3],[0,0,11754,3],[0,0,11764,3],[2,0,11816,6],[0,0,11844,3],[0,0,11872,3],[0,0,11880,3],[1,0,11888,6],[1,0,11943,11],[1,0,12150,5],[0,0,12165,3],[0,0,12179,3],[0,0,12193,7],[0,0,12266,6],[0,0,12312,3],[0,0,12330,4],[0,0,12357,3],[2,0,12364,6],[0,0,12399,19],[0,0,12890,4],[0,0,12946,10],[0,0,13141,4],[0,0,13208,3],[1,1,13233,2],[0,0,13248,3],[0,0,13275,3],[0,0,13285,3],[2,0,13302,11],[0,0,13375,5],[0,0,13447,8],[0,0,13525,3],[0,0,13533,3],[1,0,13575,7],[0,0,13601,9],[1,0,13847,5],[0,0,13863,6],[1,0,13985,5],[2,0,14018,6],[0,0,14047,3],[0,0,14057,3],[0,0,14067,4],[0,0,14106,4],[0,0,14129,3],[0,0,14137,3],[1,0,14162,6],[1,1,14258,2],[0,0,14308,8],[0,0,14489,11],[0,0,14694,3],[0,0,14753,3],[0,0,14780,3],[0,0,14797,3],[0,0,14814,3],[0,0,14834,3],[0,0,14894,8],[0,0,15155,3],[0,0,15169,3],[1,1,15200,2],[0,0,15234,3],[0,0,15269,3],[0,0,15287,3],[0,0,15305,5],[0,0,15376,3],[0,0,15396,3],[0,0,15424,5],[0,0,15512,3],[0,0,15522,3],[0,0,15541,8],[0,0,15771,3],[0,0,15812,3],[0,0,15842,3],[0,0,15873,3],[0,0,15909,5],[0,0,15977,3],[1,0,15986,6],[0,0,16130,3],[0,0,16140,3],[0,0,16147,9],[0,0,16285,3],[0,0,16311,3],[0,0,16329,3],[0,0,16353,3],[0,0,16374,3],[0,0,16385,3],[1,1,16398,2],[1,0,16402,5],[1,0,16413,5],[0,0,16424,3],[0,0,16460,5],[0,0,16562,3],[0,0,16609,3],[1,0,16629,5],[0,0,16652,3],[0,0,16662,3],[0,0,16678,3],[0,0,16696,13],[0,0,16893,3],[0,0,16917,4],[0,0,17000,3],[0,0,17029,3],[0,0,17040,3],[0,0,17076,7],[0,0,17213,10],[2,0,17374,6],[0,0,17409,3],[0,0,17474,3],[0,0,17502,4],[1,0,17525,5],[0,0,17536,4],[0,0,17547,4],[1,0,17558,5],[0,0,17578,4],[0,0,17653,3],[0,0,17686,3],[1,0,17716,5],[0,0,17741,3],[0,0,17807,3],[0,0,17821,3],[0,0,17832,5],[0,0,17931,3],[0,0,17950,3],[0,0,17969,3],[0,0,18015,3],[0,0,18066,3],[0,0,18099,5],[1,0,18129,5],[0,0,18139,3],[0,0,18182,3],[2,0,18202,6],[1,1,18217,2],[1,1,18225,2],[0,0,18233,5],[0,0,18271,6],[0,0,18350,3],[0,0,18375,6],[0,0,18484,3],[0,0,18524,3],[0,0,18565,5],[0,0,18615,6],[0,0,18749,3],[0,0,18765,3],[0,0,18773,8],[0,0,18830,5],[0,0,18859,3],[0,0,18874,3],[1,1,18924,2],[2,1,18942,3],[0,0,18963,3],[0,0,18981,3],[0,0,19010,3],[1,0,19047,5],[0,0,19062,14],[0,0,19231,3],[0,0,19252,3],[0,0,19268,4],[0,0,19324,3],[0,0,19356,3],[0,0,19439,3],[0,0,19473,3],[0,0,19502,3],[0,0,19519,3],[0,0,19536,3]]
 );
 
 let rtAssert = runtime[42] = assertFn("!");
diff --git a/src/r1.bqn b/src/r1.bqn
index 5cca7041..30c4e410 100644
--- a/src/r1.bqn
+++ b/src/r1.bqn
@@ -489,20 +489,17 @@ ShiftCheck←{
     "« or »: Rank of 𝕨 must be at least rank of 𝕩 minus 1" ! 1≥𝕩
     "« or »: 𝕨 must share 𝕩's major cell shape" ! s MatchS (1-𝕩)↓≢𝕨
   } 𝕩-○=𝕨
-  1×´s
+  (𝕨1⊘{(𝕩≤○=⊢)◶1‿≠𝕨}𝕩) ×´ s
 }
-ShiftLen←1⊘{(𝕩≤○=⊢)◶1‿≠𝕨}
 ShiftBefore←{
-  c←𝕨 ShiftCheck 𝕩
-  n←c×𝕨 ShiftLen 𝕩
-  (≢𝕩)⥊n⊸≤◶⟨𝕨Fill⊘{⊑⟜(Deshape𝕨)}𝕩, -⟜n⊑(⥊𝕩)˙⟩⌜ ↕c×≠𝕩
+  n←𝕨 ShiftCheck 𝕩
+  m←n⌊l←≠d←⥊𝕩
+  (≢𝕩) ⥊ (𝕨{(Fill𝕩)⌜↕𝕨}⟜𝕩⊘(↑⟜Deshape˜)m) ∾ (l-m)↑d
 } _fillBy_ (⊢⊘IF)
 ShiftAfter←{
-  c←𝕨 ShiftCheck 𝕩
-  l←c×≠𝕩
-  n←c×𝕨 ShiftLen 𝕩
-  m←l-n
-  (≢𝕩)⥊m⊸≤◶⟨+⟜n⊑(⥊𝕩)˙, 𝕨Fill⊘{-⟜m⊑(Deshape𝕨)˙}𝕩⟩⌜ ↕l
+  n←𝕨 ShiftCheck 𝕩
+  m←n⌊≠d←⥊𝕩
+  (≢𝕩) ⥊ (m↓d) ∾ 𝕨{(Fill𝕩)⌜↕𝕨}⟜𝕩⊘(n⊸-⊸↓⟜Deshape˜)m
 } _fillBy_ (⊢⊘IF)
 
 Range←{