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Values: -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -
+0.3 -0.2 -0.1 0 0.1 0.111111 0.12 0.13 0.16 0.19 0.2 0.21 0.22 0.3 0.
+4 0.5 0.6 0.7 0.8 0.9 1 1.00001 1.001 1.1 1.2 1.3 1.8 1.9 2.000001 2.
+001 2.1 2.11 2.2 2.3 2.4 3.1 4 5 6 7 8 9 10 1.16873493792849e-006 108
+8.99977561893
Squared: 100 81 64 49 36 25 16 9 4 1 0.81 0.64 0.49 0.36 0.25 0.16 0.0
+9 0.04 0.01 0 0.01 0.012345654321 0.0144 0.0169 0.0256 0.0361 0.04 0.
+0441 0.0484 0.09 0.16 0.25 0.36 0.49 0.64 0.81 1 1.0000200001 1.00200
+1 1.21 1.44 1.69 3.24 3.61 4.000004000001 4.004001 4.41 4.4521 4.84 5
+.29 5.76 9.61 16 25 36 49 64 81 100 1.36594135513471e-012 1185920.511
+29808

sub xform{ 
    my $v = shift; 
...
    $v = $v * $sgn; 
    return $sgn * sqrt( $v ) * 10; 
};;

-31.6227766016838 -30 -28.2842712474619 -26.4575131106459 -24.49489742
+78318 -22.3606797749979 -20 -17.3205080756888 -14.142135623731 -10 -9
+.48683298050514 -8.94427190999916 -8.36660026534076 -7.74596669241483
+ -7.07106781186548 -6.32455532033676 -5.47722557505166 -4.47213595499
+958 -3.16227766016838 0 3.16227766016838 3.33333166666625 3.464101615
+13775 3.60555127546399 4 4.35889894354067 4.47213595499958 4.58257569
+495584 4.69041575982343 5.47722557505166 6.32455532033676 7.071067811
+86548 7.74596669241483 8.36660026534076 8.94427190999916 9.4868329805
+0514 10 10.000049999875 10.0049987506246 10.4880884817015 10.95445115
+01033 11.4017542509914 13.4164078649987 13.7840487520902 14.142139159
+2644 14.1456707158056 14.4913767461894 14.525839046334 14.83239697419
+13 15.1657508881031 15.4919333848297 17.606816861659 20 22.3606797749
+979 24.4948974278318 26.4575131106459 28.2842712474619 30 31.62277660
+16838 0.0108108044933228 329.999966002866

 sub xform2{ 
    my $v = shift; 
...
    my $root3 = exp( log( $v||1e-100 ) / 3 ); 
    return $sgn * $root3 * 100; 
}

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+83214 -170.99759466767 -158.74010519682 -144.224957030741 -125.992104
+989487 -100 -96.548938460563 -92.8317766722556 -88.7904001742601 -84.
+3432665301749 -79.37005259841 -73.6806299728077 -66.943295008217 -58.
+4803547642573 -46.4158883361278 0 46.4158883361278 48.074969651913 49
+.3242414866094 50.6579701910089 54.2883523318981 57.4889707894483 58.
+4803547642573 59.4392195276313 60.3681073679769 66.943295008217 73.68
+06299728077 79.37005259841 84.3432665301749 88.7904001742601 92.83177
+66722556 96.548938460563 100 100.000333332222 100.033322228391 103.22
+8011545637 106.265856918261 109.139288306111 121.644039911468 123.856
+232963017 125.992125988168 126.013100174843 128.057916498749 128.2608
+61238441 130.059144685139 132.000612179591 133.886590016434 145.80997
+3582671 158.74010519682 170.99759466767 181.712059283214 191.29311827
+7239 200 208.00838230519 215.443469003188 1.05334832497567 1028.82757
+714918