The RDP uses a priority encoding scheme to compress an eighteen-bit Z value into a fourteen-bit value consisting of a three-bit exponent, followed by an eleven-bit mantissa.
This is a lossy compression scheme that minimises the reconstruction error for larger Z values.

The exponent of the compressed value is first calculated by taking the leading one count of the seven most significant bits of the value.
This operation will provide the three-bit value which is used as the exponent. Using the leading one count, we can reproduce up to seven bits of the original Z value whilst only using three-bits.
This compression comes at the expense of smaller values, whose exponents use more bits than are necessary.

One to seven bits can be represented using the exponent, meaning that the remaining number of bits is from seventeen to eleven.
As the mantissa is eleven bits wide, up to six bits will have to be lost.

Figure 1 shows the format of the eight possible exponent values and the following eleven bits (marked "m") which will be used as the mantissa.
Any remaining blank bits will be lost during compression, and will contribution to the reconstruction error of the decompression operation.

Figure 2 shows the layout of the fourteen-bit compressed Z value, with the three-bit exponent (marked "e"), and the eleven-bit mantissa (marked "m").

17                                                                      0
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
| 0 | m | m | m | m | m | m | m | m | m | m | m |   |   |   |   |   |   |
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
  exponent = 0, discarded = 6 bits

+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
| 1 | 0 | m | m | m | m | m | m | m | m | m | m | m |   |   |   |   |   |
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
  exponent = 1, discarded = 5 bits
  
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
| 1 | 1 | 0 | m | m | m | m | m | m | m | m | m | m | m |   |   |   |   |
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
  exponent = 2, discarded = 4 bits

+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
| 1 | 1 | 1 | 0 | m | m | m | m | m | m | m | m | m | m | m |   |   |   |
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
  exponent = 3, discarded = 3 bits

+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
| 1 | 1 | 1 | 1 | 0 | m | m | m | m | m | m | m | m | m | m | m |   |   |
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
  exponent = 4, discarded = 2 bits

+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
| 1 | 1 | 1 | 1 | 1 | 0 | m | m | m | m | m | m | m | m | m | m | m |   |
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
  exponent = 5, discarded = 1 bit

+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
| 1 | 1 | 1 | 1 | 1 | 1 | 0 | m | m | m | m | m | m | m | m | m | m | m |
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
  exponent = 6, discarded = 0 bits

+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | m | m | m | m | m | m | m | m | m | m | m |
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
  exponent = 7, discarded = 0 bits

Figure 1 - Eighteen-bit Z value

13                                                      0
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
| e | e | e | m | m | m | m | m | m | m | m | m | m | m |
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+

Figure 2 - Fourteen-bit compressed Z value


Written by https://github.com/KieronJ