How to calculate the GDP in the ancient era?

On the internet, there are full of tech YouTubers and journals that introduce the new technologies and other kinds of stuff which is related to productivity.
When they introduce the things sometimes theses graphs are mentioned.

Those two graphs are including almost the same data. Its all about GDP aka. Gross domestic product. Its based on the statistics that one nation recorded. 

Meaning of GDP is simple, in the specific period of time how much that nation turned out the goods and services in terms of market value. Normally its decided with the 1-year term. 

From here my curiosity born. Actually, before 1600years actual nation incomes and market value, related documents are really hard to get. Even though they can get the documents of tax collector and other kinds of government financial statements (or kingdom financial statements) in those days the economic arithmetic and financial statistics are not well defined. So, personally, I cannot believe the documents 100%. I think circumspect economists will think similarly with me I guess.

Then, where those accurate values came from? really?

So, I searched the internet. And this guy came out

                            

His name is Angus Maddison. He is British economists and pioneer of the historical economics.  He literally opened the field that calculates the ancient GDP form year 1. 

Unfortunately, his assumption method is obscure and there is no empirical evidence behind the logic*. His theory is based on 1 crucial assumption that basic subsistence GDP per capita of all societies is $400(1990 international prices). 

$400 for subsistence GDP per capita is his main point. The most recent 2002 paper showed value is slightly different between the continents however, ground logic is still maintained.

Anyway, continue to look at how this subsistence assumption was made. 

"In 1990 USA $ prices, a kilogram of white bread cost $1.55. So Maddison’s $400 is the equivalent of 0.75 kg of wheaten bread per person per day, or 1,500 kcal.[4] That is an extraordinarily low income, rarely observed in practice. Since most societies have inequality, the poorest in such a subsistence economy would have lived on the equivalent of much less than that daily 0.75 kg of bread. So if the poorest people spent nothing on clothing, heat, shelter, light, and consumed only the cheapest form of calories such as bread, they would still be engaging in hard physical labor on a diet well below 1,500 kcal in the Maddison vision of subsistence."*

So, it's based on the 1990 USA the poorest person. And calculate the calories as the indicator of the GDP. 

Hmmmm... is it a reasonable assumption? I don't think so

As Gregory Clark said in the 'A. Maddison: Contours of the World Economy 1-2030 AD' the most primitive person who lived with the mammoth exceeds the assumption of the Angus Maddison. 

So my conclusion is GDP before the industrial revolution is not that accurate. Also, the method of calculating the historical GDP is not well defined. Hope other historical economists reply the better calculation methods or other paper that suggests the methodology.

* A. Maddison: Contours of the World Economy 1-2030 AD)