[argyllcms] Pre-linearization table for BtoA LUT

When I build profiles with Argyll using the tags:

 -bh -ni,
then the BtoA tables have a pre-linearization table containing 2048 lines and a LUT that is 33 x 33 x 33.
As I understand it, the real purpose of this pre-linearization table is to guarantee that the value for a or b corresponding to the case where the index in the 33x33x33 matrix is 16 actually map to a or b values very close to 0.
I am still a bit confused as to how this pre-linearization matrix works. Below are the values for L,a,b that correspond to the 33x33x33 matrix indices prior to processing with the pre-linearization: 

idx     L       a       b
0       0.00    -128.00 -128.00
1       3.13    -120.03 -120.03
2       6.25    -112.06 -112.06
3       9.38    -104.09 -104.09
4       12.50   -96.13  -96.13
5       15.63   -88.16  -88.16
6       18.75   -80.19  -80.19
7       21.88   -72.22  -72.22
8       25.00   -64.25  -64.25
9       28.13   -56.28  -56.28
10      31.25   -48.31  -48.31
11      34.38   -40.34  -40.34
12      37.50   -32.38  -32.38
13      40.63   -24.41  -24.41
14      43.75   -16.44  -16.44
15      46.88   -8.47   -8.47
16      50.00   -0.50   -0.50
17      53.13   7.47    7.47
18      56.25   15.44   15.44
19      59.38   23.41   23.41
20      62.50   31.38   31.38
21      65.63   39.34   39.34
22      68.75   47.31   47.31
23      71.88   55.28   55.28
24      75.00   63.25   63.25
25      78.13   71.22   71.22
26      81.25   79.19   79.19
27      84.38   87.16   87.16
28      87.50   95.13   95.13
29      90.63   103.09  103.09
30      93.75   111.06  111.06
31      96.88   119.03  119.03
32      100.00  127.00  127.00
I would love if someone would help me understand exactly the formula used to apply the pre-linearization table to these points.
Attached is an excel file containing the 2048 points for the pre-linearization table from my profiles. 

--
John Weissberg
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