Week 14 Update 14.1

This is the first week since the start of the program that I slowed down a bit. I spent the week rereading the yellow paper to make a proposal of the gas cost of a potential Poseidon precompile.

Some precompiles have a fixed gas cost, while others have a dependency on the input size. Te table below summarizes the gas costs for each precompile contract. See the the yellow paper for details.

Precompile	Gas cost
ECREC	3000
SHA256	$60+12\lceil \frac{\parallel I_d\parallel }{32}\rceil$
RIPEMD160	$60+120\lceil \frac{\parallel I_d\parallel }{32}\rceil$
ID	$15+3\lceil \frac{\parallel I_d\parallel }{32}\rceil$
EXMOD	$g_{\mathtt{\text{exmod}}}$
BN_ADD	150
BN_MUL	6000
SNARKV	$34000\frac{\parallel I_d\parallel }{192}+45000$
BLAKE2_F	number of rounds $r$, maximum 4 bytes

In the table above

$\parallel I_d\parallel$ is the input size in bits. The gas costs for the modular exponentiation contract is given by

$$g_{\mathtt{\text{exmod}}}=max(200,\lfloor \frac{f(max({\ell }_M,{\ell }_B))\cdot max({\ell }_E^{\prime },1)}{3}\rfloor ),$$
where

$f(x)=\lceil x/8{\rceil }^2$,

${\ell }_M$ and

${\ell }_B$ are positive integers of 4 bytes denoting the lenght in bits of the modulus and the basis, and

$${\ell }_E^{\prime }=\{\begin{array}{ll}0& \text{if }{\ell }_E\le 32\text{ and }E=0\\ \lfloor {\log }_{2}E\rfloor & \text{if }{\ell }_E\le 32\text{ and }E\ne 0\\ 8({\ell }_E-32)+\lfloor {\log }_2(i[(96+{\ell }_B)\dots (127+{\ell }_B)])\rfloor & \text{if }32<{\ell }_E\text{ and }i[(96+{\ell }_B)\dots (127+{\ell }_B)]\ne 0\\ 8({\ell }_E-32)& \text{otherwise.}\end{array}$$
The subvector

$i[(96+{\ell }_B)\dots (127+{\ell }_B)]$ of the input

$i$ is the exponent whose size is given by

${\ell }_E.$