In CycleFold we want to compute
$P_{folded} = P_0 + r ⋅ P_1 + r^2 ⋅ P_2 + r^3 ⋅ P_3 + ... + r^{n-2} ⋅ P_{n-2} + r^{n-1} ⋅ P_{n-1}$,
since the scalars follow the pattern r^i Youssef El Housni (@yelhousni)
proposed to update the approach of the CycleFold circuit to reduce the
number of constraints needed, by computing
$P_{folded} = (((P_{n-1} ⋅ r + P_{n-2}) ⋅ r + P_{n-3})... ) ⋅ r + P_0$.

By itself, this update reduces the number of constraints as the number
of points being folded in the CycleFold circuit grows. But it also has
impact at the HyperNova circuit, where it removes the need of using the
bit representations of the powers of the random value, substancially
reducing the amount of constraints used by the HyperNova
AugmentedFCircuit.

The number of constraints difference in the CycleFold circuit and in
the HyperNova's AugmentedFCircuit:

- CycleFold circuit:

| num points* | old       | new       | diff     |
|-------------|-----------|-----------|----------|
| 2           | 1_354     | 1_354     | 0        |
| 3           | 2_683     | 2_554     | -129     |
| 4           | 4_012     | 3_754     | -258     |
| 8           | 9_328     | 8_554     | -744     |
| 16          | 19_960    | 18_154    | -1_806   |
| 32          | 41_224    | 37_354    | -3_870   |
| 64          | 83_752    | 75_754    | -7_998   |
| 128         | 168_808   | 152_554   | -16_254  |
| 1024        | 1_359_592 | 1_227_754 | -131_838 |

*num points: number of points being folded by the CycleFold circuit.

- HyperNova AugmentedFCircuit circuit

| folded instances* | old     | new     | diff     |
|-------------------|---------|---------|----------|
| 5                 | 90_285  | 80_150  | -10_135  |
| 10                | 144_894 | 117_655 | -27_239  |
| 20                | 249_839 | 192_949 | -56_890  |
| 40                | 463_078 | 344_448 | -118_630 |

*folded instances: folded instances per step, half of them being LCCCS
and the other half CCCS.

Co-authored-by: Youssef El Housni <youssef.housni21@gmail.com>