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Comment by nick238 | Hacker News Reader

Don't know adding, but multiplication has diagram on the last page of the PDF.

xy = eml(eml(1, eml(eml(eml(eml(1, eml(eml(1, eml(1, x)), 1)), eml(1, eml(eml(1, eml(y, 1)), 1))), 1), 1)), 1)

From Table 4, I think addition is slightly more complicated?

Thanks for posting that. You had a transcribing typo which was corrected in the ECMAScript below. Here's the calculation for 5 x 7:

    const eml = (x,y) => Math.exp(x) - Math.log(y);
    const mul = (x,y) => eml(eml(1,eml(eml(eml(1,eml(eml(1,eml(1,x)),1)),eml(1,eml(eml(1,eml(y,1)),1))),1)),1);
    console.log(mul(5,7));

> 35.00000000000001

For larger or negative inputs you get a NaN because ECMAScript has limited precision and doesn't handle imaginary numbers.

> For larger or negative inputs you get a NaN because ECMAScript has limited precision and doesn't handle imaginary numbers.

This also shows why EML is not practical for computation.

x+y = ln(exp(x) * exp(y))

exp(a) = eml(a, 1) ln(a)=eml(1,eml(eml(1,a),1))

Plugging those in is an excercise to the reader

might need to turn the paper sideways

You use multiplication in the first line, which you have not expressed through eml yet.

Because of how exp and log turn addition into multiplication and vice versa, once you have the one, you get the other easily.

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