Is it possible to use natural logarithmic in your smartpy code?

Question

If not,is there any alternative way to implement a natural log component into your smart contract code?

FFF · Accepted Answer

As explained by Arvidj, there are no floating point numbers in Michelson (or SmartPy), no exp or log function.
While working with natural numbers, you can implement by hand some examples which may or may not be enough for you. Some examples here:
https://smartpy.io/dev/index.html?template=calculator.py, https://smartpy.io/dev/index.html?template=worldCalculator.py
A complete example for you:
import smartpy as sp

class Calculator(sp.Contract):
    def __init__(self):
        self.init(value = 0)

@sp.entry_point
    def test(self, x):
        self.data.value = self.log2(x)

@sp.global_lambda
    def log2(x):
        result = sp.local('result', 0)
        y = sp.local('y', x)
        sp.while 1 < y.value:
            result.value += 1
            y.value //= 2
        sp.result(result.value)
        
if "templates" not in __name__:
    @sp.add_test(name = "Calculator")
    def test():
        c1 = Calculator()
        scenario = sp.test_scenario()
        scenario += c1
        scenario += c1.test(1000)
        scenario.verify(c1.data.value == 9)

EDIT. Adding a fixed precision implementation in SmartPy.
https://smartpy.io/dev/index.html?template=fixed_precision.py

Sophia Gold · Answer

I have a contract for binary log that uses few multiplications and can be adjusted for any fixed point precision: https://github.com/Sophia-Gold/michelson/blob/master/log2fix.tz. I don't think it can be written in SmartPy because last I checked it lacks shifts. Depending on your needs you could use this with change of base or Arthur's method.

Answered by Sophia Gold on August 20, 2021

Arthur B · Answer

You have to do it manually... Here's one approach for compute log(x) assuming you are representing x as a fraction

find integer m through binary search such that 2^m <= x < 2^(m+1) (m may be negative)
let m' = m + (1 if |x/2^(m+1)-1| < |x/2^m-1| else 0) (the  closests of m or m+1)
let x' = x / 2^m', note that |x'-1| < 1/3 and log(x) = log(2^m' x') = m' log(2) + log(x')
let y = (1-x')/(1+x'), note that -1/7 < y < 1/5
log(x') ~= - 2 y - 2 y^3 / 3

arvidj · Answer

There is no such instruction in Michelson, so probably the same goes for SmartPy. Furthermore, Michelson does not having floating point values. You could implement some version of natural log yourself using repeated divisions, however, precision will suffer. Also, note that this can be costly in gas.
One option is to have the contract take the contract take in parameter the exponent calculated off-chain, and then have the contract verify that the exponent is indeed correct. Instead of (in pseudocode):
   def contract(some_parameter):
       exponent = nl(some_parameter)

have
   def contract(expected_exponent, some_parameter):
       assert e^expected_exponent = some_parameter

but again, you will turn into the issue that exponentiation is not available in Michelson (but which you could implement with repeated multiplications), and nor are floating points values.
We can perhaps help you better if you give more context to the issue you want to resolve?

Is it possible to use natural logarithmic in your smartpy code?

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