Add decimal math to the EVM by adding the following OPCODEs:
DECADD, DECNEG , DECMUL, DECINV, DECEXP, DECLN, DECSIN
A Decimal defined as c∗10^q with c (coefficiant) and q (exponent) taken from the stack and interpreted as int256.
Why decimal?
Most calculations conducted by humans work with decimal values. E.g. 0.1 is a very commonly used number, but cannot be represented in binary finitely.
Why exp, ln, sin?
exp, ln, sin are universal functions. Combining exp and ln allows one to compute powers (a^b = exp(b*ln(a))), which gives access to all polynomials. From sin, one can derive all of trigonometry. In total, we get all elementary functions
This invites mathematical finance, machine learning, science, digital arts and more to Ethereum.
It allows one to solve integrals, differential equations, optimize and so much more.
eVm
The EVM is a virtual machine and thereby not restricted by hardware. Usually, assembly languages provide OPCODEs that reflect the ability of the hardware. In a virtual machine, we have no such limitations and nothing stops us from adding more complex OPCODEs, as long as fair gas is paid. At the same time, we do not want to clutter the OPCODEs library.
OPCODE definitions
DECADD a+b OpCode = 0xd0 (ac, aq, bc, bq, precision) → (cc, cq)
DECNEG -a OpCode = 0xd1 (ac, aq) → (bc, bq)
DECMUL a*b OpCode = 0xd2 (ac, aq, bc, bq, precision) → (cc, cq)
DECINV 1/a OpCode = 0xd3 (ac, aq, precision) → (bc, bq)
DECEXP exp(a) OpCode = 0xd4 (ac, aq, precision, steps) → (bc, bq)
DECLN ln(a) OpCode = 0xd5 (ac, aq, precision, steps) → (bc, bq)
DECSIN sin(a) OpCode = 0xd6 (ac, aq, precision, steps) → (bc, bq)
precision is the # of digits kept. steps for DECEXP and DECSIN are the # of Taylor expansion steps. steps for DECLN is the depth of the continued fractions expansion.
Implementation
I have implemented these OPCODEs already, as part of the ETHOnline hackathon (2023); pls see the link at the bottom.
My plan for the hackathon was submitting an EIP. I was not aware that a discussion on this forum was required beforehand.
More details can be found in the Readme.md, incl. gas considerations, etc. Not sure whether I should rewrite those things here.
The geth implementation is functional, with precise gas costs, charged double. It is currently named EVM+, to suggest that this is like going from a basic calculator (EVM) to a scientific calculator (EVM+). I will soon run an (open) EVM+ node and welcome anyone to do the same.
Two first examples that work, as Yul smart contracts:
The BlackScholes formula, gas cost ca. 32k.
A single sigmoid Neuron, gas cost ca. 24k.
The actual charged gas is currently doubled.
repo: GitHub - 1m1-github/EVMPlus: add decimal math to EVM
live node: https://github.com/1m1-github/EVMPlus/blob/main/README.md#live
EIP: https://github.com/1m1-github/EthereumEIPs/blob/main/EIPS/eip-7543.md