diff --git a/vignettes/benchmarks-machine.csv b/vignettes/benchmarks-machine.csv
index a628dec..b66c606 100644
--- a/vignettes/benchmarks-machine.csv
+++ b/vignettes/benchmarks-machine.csv
@@ -4,5 +4,5 @@
 "CPU threads","8"
 "BLAS","libopenblasp-r0.3.34.so"
 "R","R version 4.5.3 (2026-03-11)"
-"gputools","2.0.0.9000 (commit 9e37078)"
-"date","2026-10-15"
+"gputools","2.1.1"
+"date","2026-10-20"
diff --git a/vignettes/benchmarks.Rmd b/vignettes/benchmarks.Rmd
index e810aa7..7615c88 100644
--- a/vignettes/benchmarks.Rmd
+++ b/vignettes/benchmarks.Rmd
@@ -97,8 +97,10 @@ that subtracts two nearly equal sums of squares, use double. `gpuGranger`
 is the clear case: its F statistic is a difference of two residual sums
 of squares, and in single precision it was off by more than 10 percent on
 long random walks, so it now always computes in double, whatever
-`precision` says. (The Granger timings in this vignette were measured
-before that change; `bench/run-benchmarks.R` repeats them.)
+`precision` says; its two columns in the tables are therefore the same
+computation, and it still runs over a hundred times faster than the
+`lm.fit` loop at 50 series, since each effect's own past is projected out
+once and every cause's test against it comes from a few matrix products.
 
 ## When the GPU pays off
 
diff --git a/vignettes/benchmarks.csv b/vignettes/benchmarks.csv
index cbf826a..8bb5e10 100644
--- a/vignettes/benchmarks.csv
+++ b/vignettes/benchmarks.csv
@@ -1,14 +1,14 @@
 "task","size","cpu","single","double"
-"gpuMatMult vs %*%","2000 x 2000",0.032,NA,0.0529999999999999
-"gpuMatMult vs %*%","4000 x 4000",0.22,NA,0.337
-"gpuCor pearson vs cor","2000 obs x 1000 vars",0.909,0.0180000000000007,0.0299999999999994
-"gpuCor kendall vs cor","1000 obs x 100 vars",61.663,0.0229999999999677,0.256000000000029
-"gpuDist vs dist","5000 points x 50 dims",2.43299999999999,0.358000000000004,0.40500000000003
-"gpuHclust vs hclust","5000 points",0.74799999999999,0.735000000000014,1.01499999999999
-"gpuDistClust vs hclust(dist())","5000 points x 50 dims",3.15800000000002,0.546999999999969,0.814000000000021
-"gpuGranger vs lm.fit loop","500 times x 50 series, lag 2",0.41500000000002,0.0989999999999895,0.111999999999966
-"gpuMi (no base-R equivalent)","2000 obs x 200 vars, 10 bins",NA,0.0600000000000023,0.103000000000009
-"gpuLm vs lm","100000 obs x 50 predictors",0.139999999999986,0.125,0.141999999999996
-"gpuQr vs qr","4000 x 1000",1.25600000000003,0.879999999999995,1.02999999999997
-"gpuSolve vs solve","2000 x 2000",0.0959999999999468,0.0400000000000205,0.105999999999995
-"kernel compile, first use of a file","gpuDist kernels",NA,0.361,0.206
+"gpuMatMult vs %*%","2000 x 2000",0.04,NA,0.056
+"gpuMatMult vs %*%","4000 x 4000",0.286,NA,0.345
+"gpuCor pearson vs cor","2000 obs x 1000 vars",0.960999999999999,0.0180000000000007,0.0299999999999994
+"gpuCor kendall vs cor","1000 obs x 100 vars",61.882,0.0240000000000009,0.261000000000024
+"gpuDist vs dist","5000 points x 50 dims",2.45500000000004,0.375,0.423999999999978
+"gpuHclust vs hclust","5000 points",0.764999999999986,0.745999999999981,1.02499999999998
+"gpuDistClust vs hclust(dist())","5000 points x 50 dims",3.19599999999997,0.550999999999988,0.819999999999993
+"gpuGranger vs lm.fit loop","500 times x 50 series, lag 2",0.423000000000002,0.0029999999999859,0.00200000000000955
+"gpuMi (no base-R equivalent)","2000 obs x 200 vars, 10 bins",NA,0.0550000000000068,0.0830000000000268
+"gpuLm vs lm","100000 obs x 50 predictors",0.149999999999977,0.128999999999962,0.145999999999958
+"gpuQr vs qr","4000 x 1000",1.51900000000001,0.893000000000029,1.04300000000001
+"gpuSolve vs solve","2000 x 2000",0.107000000000028,0.0400000000000205,0.108000000000004
+"kernel compile, first use of a file","gpuDist kernels",NA,0.383,0.233
diff --git a/vignettes/call-overhead.csv b/vignettes/call-overhead.csv
index 91a3194..4966c93 100644
--- a/vignettes/call-overhead.csv
+++ b/vignettes/call-overhead.csv
@@ -1,6 +1,6 @@
 "what","seconds"
-"one gpuCor call, 50 x 2",4.97512437810493e-05
+"one gpuCor call, 50 x 2",4.47761194030575e-05
 "one cor call, 50 x 2",1.00000000000477e-05
-"1,000 pairs: a loop of gpuCor calls",0.0647500000000036
-"1,000 pairs: one gpuCor call for all 1,000 x 1,000 (the 1,000 wanted are its diagonal)",0.0145624999999967
-"1,000 pairs: a loop of cor calls",0.0152000000000006
+"1,000 pairs: a loop of gpuCor calls",0.0602499999999964
+"1,000 pairs: one gpuCor call for all 1,000 x 1,000 (the 1,000 wanted are its diagonal)",0.0141764705882378
+"1,000 pairs: a loop of cor calls",0.0144374999999997
diff --git a/vignettes/crossover.csv b/vignettes/crossover.csv
index 4292687..4337487 100644
--- a/vignettes/crossover.csv
+++ b/vignettes/crossover.csv
@@ -1,63 +1,63 @@
 "fn","what","size","cpu","single","double"
-"gpuCor","variables (200 rows)",10,2.48756218905467e-05,6.49999999999995e-05,0.0001285
-"gpuCor","variables (200 rows)",30,0.000114427860696518,9.54999999999999e-05,0.000155000000000003
-"gpuCor","variables (200 rows)",100,0.00099004975124378,0.000282,0.0003815
-"gpuCor","variables (200 rows)",300,0.00853846153846152,0.00156000000000001,0.00177611940298507
-"gpuCor","variables (200 rows)",1000,0.0943333333333332,0.0205833333333333,0.0217272727272728
-"gpuCor","variables (200 rows)",3000,0.870000000000001,0.173499999999999,0.185
-"gpuCor spearman","variables (200 rows)",10,0.000277227722772299,0.000114999999999998,0.000193
-"gpuCor spearman","variables (200 rows)",30,0.000910447761194029,0.000156000000000001,0.000238
-"gpuCor spearman","variables (200 rows)",100,0.00358823529411764,0.000410000000000004,0.000562189054726366
-"gpuCor spearman","variables (200 rows)",300,0.0162142857142857,0.00181188118811881,0.00226865671641787
-"gpuCor spearman","variables (200 rows)",1000,0.1195,0.018166666666667,0.0209000000000003
-"gpuCor spearman","variables (200 rows)",3000,0.951999999999998,0.167999999999999,0.184999999999999
-"gpuCor kendall","variables (200 rows)",5,0.00668000000000006,0.000139303482587058,0.000217500000000001
-"gpuCor kendall","variables (200 rows)",10,0.0253750000000004,0.0001615,0.000334
-"gpuCor kendall","variables (200 rows)",30,0.220000000000006,0.000313432835820907,0.00130693069306929
-"gpuCor kendall","variables (200 rows)",100,2.447,0.00174257425742576,0.0120588235294117
-"gpuCor kendall","variables (200 rows)",300,21.837,0.0132666666666675,0.105000000000004
-"gpuDist","points (20 dimensions)",50,0.000104999999999933,0.000100000000000051,0.000100000000000009
-"gpuDist","points (20 dimensions)",100,0.000379999999999967,0.000171999999999997,0.000192999999999998
-"gpuDist","points (20 dimensions)",300,0.00339215686274513,0.00121499999999997,0.0014100000000002
-"gpuDist","points (20 dimensions)",1000,0.0383333333333364,0.0160833333333343,0.0184545454545431
-"gpuDist","points (20 dimensions)",3000,0.342999999999989,0.168499999999995,0.175500000000014
-"gpuHclust","points",50,5.49999999999784e-05,0.000524752475247498,0.000494999999999948
-"gpuHclust","points",100,0.000211500000000001,0.000919999999999987,0.000969999999999942
-"gpuHclust","points",300,0.00194000000000003,0.0032352941176469,0.00358000000000004
-"gpuHclust","points",1000,0.0204000000000008,0.0203000000000003,0.0240000000000009
-"gpuHclust","points",3000,0.275000000000006,0.233000000000004,0.311000000000007
-"gpuDistClust","points (20 dimensions)",50,0.000168316831683128,0.00046999999999997,0.000485000000000042
-"gpuDistClust","points (20 dimensions)",100,0.000580000000000069,0.000881188118811868,0.000935323383084518
-"gpuDistClust","points (20 dimensions)",300,0.00509756097560983,0.00271641791044758,0.0030298507462687
-"gpuDistClust","points (20 dimensions)",1000,0.0570000000000022,0.0126250000000017,0.0158461538461552
-"gpuDistClust","points (20 dimensions)",3000,0.632000000000005,0.155500000000004,0.224999999999994
-"gpuGranger","series (300 times, lag 2)",5,0.00311764705882393,0.00194117647058803,0.00343137254901983
-"gpuGranger","series (300 times, lag 2)",10,0.0138125000000002,0.00535294117647107,0.00716000000000008
-"gpuGranger","series (300 times, lag 2)",20,0.0587500000000034,0.0181818181818171,0.0207999999999998
-"gpuGranger","series (300 times, lag 2)",50,0.377999999999986,0.0956666666666687,0.103999999999999
-"gpuGranger","series (300 times, lag 2)",100,1.53199999999998,0.377999999999986,0.396000000000015
-"gpuLm","rows (20 predictors)",1000,0.00192537313432822,0.00510344827586194,0.0072413793103451
-"gpuLm","rows (20 predictors)",10000,0.00673529411764745,0.0122352941176486,0.0145333333333326
-"gpuLm","rows (20 predictors)",1e+05,0.0660000000000025,0.11766666666667,0.126500000000007
-"gpuLm","rows (20 predictors)",1e+06,0.576999999999998,1.083,1.04599999999999
-"gpuGlm","rows (20 predictors)",1000,0.00421951219512061,0.0132142857142859,0.0251250000000027
-"gpuGlm","rows (20 predictors)",10000,0.0242222222222242,0.0395000000000039,0.0464000000000055
-"gpuGlm","rows (20 predictors)",1e+05,0.257999999999981,0.267999999999972,0.367999999999995
-"gpuQr","columns (2 x as many rows)",50,8.95522388058321e-05,0.00361999999999966,0.00634482758620779
-"gpuQr","columns (2 x as many rows)",100,0.000500499999999988,0.00755999999999858,0.00999999999999903
-"gpuQr","columns (2 x as many rows)",300,0.0105263157894761,0.0273749999999993,0.0412000000000035
-"gpuQr","columns (2 x as many rows)",1000,0.463999999999999,0.314999999999998,0.534999999999968
-"gpuQr","columns (2 x as many rows)",2000,5.98599999999999,1.971,2.46600000000001
-"gpuSolve","n (n x n system)",50,3.99999999999068e-05,0.000165000000000077,0.000201000000000022
-"gpuSolve","n (n x n system)",100,0.000218999999999994,0.000264999999999986,0.000356999999999999
-"gpuSolve","n (n x n system)",300,0.00125999999999976,0.00106965174129369,0.00198000000000036
-"gpuSolve","n (n x n system)",1000,0.0123125000000002,0.00700000000000108,0.0126470588235313
-"gpuSolve","n (n x n system)",3000,0.120500000000021,0.0442000000000007,0.0985000000000014
-"gpuPrcomp","variables (1,000 rows)",20,0.000849999999999795,0.0013880597014928,0.00205970149253697
-"gpuPrcomp","variables (1,000 rows)",100,0.00900000000000143,0.00796551724137912,0.0108947368421049
-"gpuPrcomp","variables (1,000 rows)",300,0.0335714285714305,0.0255555555555513,0.041166666666669
-"gpuPrcomp","variables (1,000 rows)",1000,0.247000000000014,0.103500000000025,0.212999999999965
-"gpuMatMult","n (n x n by n x n)",100,4.97512437810493e-05,0.000124378109452623,0.000137
-"gpuMatMult","n (n x n by n x n)",300,0.000296999999999997,0.00106467661691542,0.00106499999999983
-"gpuMatMult","n (n x n by n x n)",1000,0.00629411764705878,0.0142631578947376,0.0118095238095234
-"gpuMatMult","n (n x n by n x n)",3000,0.103499999999997,0.144500000000022,0.144999999999982
+"gpuCor","variables (200 rows)",10,2.5e-05,6.50000000000001e-05,0.0001345
+"gpuCor","variables (200 rows)",30,0.000115,9.20000000000001e-05,0.000154228855721394
+"gpuCor","variables (200 rows)",100,0.000985074626865671,0.0002645,0.000398009950248757
+"gpuCor","variables (200 rows)",300,0.00852173913043481,0.00145544554455445,0.00170297029702971
+"gpuCor","variables (200 rows)",1000,0.0933333333333337,0.0170666666666667,0.0173571428571429
+"gpuCor","variables (200 rows)",3000,0.860000000000001,0.151,0.16
+"gpuCor spearman","variables (200 rows)",10,0.000288557213930347,0.000124378109452747,0.000192500000000001
+"gpuCor spearman","variables (200 rows)",30,0.000861386138613859,0.000169154228855734,0.00024
+"gpuCor spearman","variables (200 rows)",100,0.00347999999999999,0.000449999999999999,0.000534999999999997
+"gpuCor spearman","variables (200 rows)",300,0.0159285714285714,0.00185148514851486,0.00208910891089107
+"gpuCor spearman","variables (200 rows)",1000,0.1175,0.0156666666666666,0.0161818181818179
+"gpuCor spearman","variables (200 rows)",3000,0.937999999999999,0.158000000000001,0.166999999999998
+"gpuCor kendall","variables (200 rows)",5,0.00669230769230767,0.000139303482587058,0.000215499999999999
+"gpuCor kendall","variables (200 rows)",10,0.0252500000000007,0.000158999999999999,0.000345000000000013
+"gpuCor kendall","variables (200 rows)",30,0.219999999999999,0.000315000000000012,0.00131
+"gpuCor kendall","variables (200 rows)",100,2.446,0.00177,0.0120588235294117
+"gpuCor kendall","variables (200 rows)",300,21.72,0.0129374999999996,0.105499999999992
+"gpuDist","points (20 dimensions)",50,0.000104477611940232,9.50000000000273e-05,9.64999999999918e-05
+"gpuDist","points (20 dimensions)",100,0.000380000000000109,0.000185000000000031,0.000204999999999984
+"gpuDist","points (20 dimensions)",300,0.00340298507462657,0.00112437810945273,0.00131
+"gpuDist","points (20 dimensions)",1000,0.0381666666666642,0.0159285714285724,0.0157499999999994
+"gpuDist","points (20 dimensions)",3000,0.341000000000008,0.144499999999994,0.152500000000003
+"gpuHclust","points",50,5.49999999999784e-05,0.000519999999999925,0.000515000000000043
+"gpuHclust","points",100,0.000194999999999936,0.000914999999999964,0.000974999999999966
+"gpuHclust","points",300,0.00198019801980187,0.00340298507462699,0.00372000000000014
+"gpuHclust","points",1000,0.0191818181818193,0.0198181818181808,0.0230999999999995
+"gpuHclust","points",3000,0.241000000000014,0.224999999999994,0.299999999999983
+"gpuDistClust","points (20 dimensions)",50,0.000158415841584071,0.000465346534653436,0.000485000000000042
+"gpuDistClust","points (20 dimensions)",100,0.000579999999999927,0.000874999999999915,0.000930000000000035
+"gpuDistClust","points (20 dimensions)",300,0.00507500000000007,0.00271641791044758,0.0030298507462687
+"gpuDistClust","points (20 dimensions)",1000,0.0560000000000045,0.0125625000000014,0.0156923076923083
+"gpuDistClust","points (20 dimensions)",3000,0.593999999999994,0.154499999999999,0.225999999999999
+"gpuGranger","series (300 times, lag 2)",5,0.00294029850746273,0.000739999999999839,0.000739999999999981
+"gpuGranger","series (300 times, lag 2)",10,0.0131875000000008,0.00070999999999998,0.00070999999999998
+"gpuGranger","series (300 times, lag 2)",20,0.0559999999999974,0.000730000000000075,0.000735000000000099
+"gpuGranger","series (300 times, lag 2)",50,0.361000000000018,0.00129999999999995,0.0012970297029703
+"gpuGranger","series (300 times, lag 2)",100,1.465,0.0036274509803922,0.00361999999999966
+"gpuLm","rows (20 predictors)",1000,0.00183582089552225,0.00510344827586194,0.00720000000000027
+"gpuLm","rows (20 predictors)",10000,0.00623529411764674,0.0118749999999999,0.013857142857142
+"gpuLm","rows (20 predictors)",1e+05,0.0597500000000011,0.104666666666664,0.115
+"gpuLm","rows (20 predictors)",1e+06,0.513000000000005,0.984000000000009,0.994
+"gpuGlm","rows (20 predictors)",1000,0.00387804878048761,0.0130714285714281,0.0238888888888893
+"gpuGlm","rows (20 predictors)",10000,0.0227000000000004,0.0376666666666665,0.0447999999999979
+"gpuGlm","rows (20 predictors)",1e+05,0.225999999999999,0.25,0.34099999999998
+"gpuQr","columns (2 x as many rows)",50,9.00000000000034e-05,0.00360975609756088,0.00637931034482766
+"gpuQr","columns (2 x as many rows)",100,0.000489999999999924,0.00744000000000028,0.0099523809523811
+"gpuQr","columns (2 x as many rows)",300,0.0105789473684207,0.0271250000000016,0.0408000000000015
+"gpuQr","columns (2 x as many rows)",1000,0.443999999999988,0.314999999999998,0.533000000000015
+"gpuQr","columns (2 x as many rows)",2000,5.60899999999998,1.97000000000003,2.45100000000002
+"gpuSolve","n (n x n system)",50,3.99999999999068e-05,0.000169154228855681,0.000199999999999818
+"gpuSolve","n (n x n system)",100,0.000219999999999914,0.000260999999999996,0.000348258706467628
+"gpuSolve","n (n x n system)",300,0.00125999999999976,0.00103999999999985,0.00192999999999984
+"gpuSolve","n (n x n system)",1000,0.0115789473684195,0.00648275862068925,0.0117647058823523
+"gpuSolve","n (n x n system)",3000,0.110499999999973,0.0396666666666666,0.0929999999999988
+"gpuPrcomp","variables (1,000 rows)",20,0.000810000000000173,0.00134328358209003,0.00198507462686539
+"gpuPrcomp","variables (1,000 rows)",100,0.0085769230769214,0.00751724137931096,0.0104285714285711
+"gpuPrcomp","variables (1,000 rows)",300,0.031714285714291,0.0246666666666644,0.0403999999999996
+"gpuPrcomp","variables (1,000 rows)",1000,0.23399999999998,0.101500000000016,0.211000000000013
+"gpuMatMult","n (n x n by n x n)",100,4.49999999997885e-05,0.000120000000000005,0.000128999999999991
+"gpuMatMult","n (n x n by n x n)",300,0.000291499999999985,0.000965174129353318,0.000964999999999918
+"gpuMatMult","n (n x n by n x n)",1000,0.00578048780487861,0.0127894736842103,0.0126315789473689
+"gpuMatMult","n (n x n by n x n)",3000,0.101666666666669,0.145499999999998,0.145499999999998