Q: Are historical stock prices generally weighted for changes in outstanding shares?

This has been on my mind lately. One of the main problems in my mind about looking at historical stock prices is that the number of outstanding shares on the market today for a company may not be the same as it was 5 years ago.

Example:

Today Company A's shares are worth $10 / share. There are 10 million outstanding shares. This makes the company's market cap $100 million.

5 years ago Company A's shares were worth $10 / share. But there were only 1 million outstanding shares. This makes the company's market cap $10 million.

If the price from 5 years ago was weighted for this change in outstanding shares, it would have essentially been worth $1 / share.

When a company splits their stock, the historical prices are updated to reflect the split. But when new shares are issued our bought back, are they updated in the same way?

Thanks!