Inaccurate trigonometry table

the vanilla Doom engine uses a pre-built for  trigonometry. The methods used to generate these table can be found in the Doom source code in r_main.c in the functions R_InitTables and R_InitPointToAngle.

The Doom engine represents an angle as a 32-bit value, giving it 2^32 (4294967296) possible angle values. Then cannot be that many values in a table, so the precision is first reduced to 2^13 (8192) possible values (the "fine angles") for the sine and cosine lookup table. Therefore, each entry in corresponds to 2^19 (524288) different angles. (The tangent table is even smaller, with only 2048 unique values.)

For all of these ranges, the precise value that was used to generate the entry in the table is the middle one corresponds to the one in the middle of the range. The result is that there is a 0.02197265625° difference (one half of 360/8192) between the "rounded" angle value and the angle used to compute the result.

One of the outcomes of this inaccuracy is that orthogonal movement is not possible.