Score Underflow

Specifications

Versions: 1.00a
Shottype: Seija
Scenes: All except: 1-1, 3-1, 5-1, 6-1, 8-1
Main items:
Sub items: None

What happens

The game sets your score to a score of 9,999,999,990. This can only happen in scenes in which a spell-card is used, which are almost all scenes.

How it happens

The current score must reach a negative value. The only way to reduce your score is by capturing a spell that has a negative spell bonus. Furthermore, you must make sure that the negative spell bonus is large enough such that your current total score is negative.

Why it happens

In order to understand this we must understand how numbers are stored.
Your current score and your highscore is stored as an unsigned 32-bit integer. This means it can store values ranging from 0 to 4,294,967,295, in total having 2^32 possibilities.
In the case of a replay getting a score of 9,999,999,990, the value the game reads/writes is 999,999,999,NOT 9,999,999,990. The last digit of the displayed score is saved somewhere else.

Underflow

Since score can take values from the range [0; 4,294,967,295] values that go above the limit of 4,294,967,295 is called overflow. Values that go below the limit of 0 is called underflow.

The integer 0 in binary is 0000 0000 0000 0000 0000 0000 0000 0000₂. If 1 is subtracted from 0 we get a number that in binary is 1111 1111 1111 1111 1111 1111 1111 1111₂.

As an analogy, just imagine the number 40,000 in decimal notation. You are only able to read the first 4 digits from the right (0000). If 1 is subtracted from 40,000 we get 39,999. However, since you are only able to read the first 4 digits from the right the digits you can see are 9999. This means subtracting 1 from 0 sets the score to 4,294,967,295.

Method

In order to achieve getting a "negative score", the player must use the camera item.

The way spell bonus is calculated is by subtracting a constant from the current bonus when five seconds have passed. The constant depends on the initial value of the spell bonus.

Usually, the spell-card would be timed out when waiting too long. However, it is possible to extend the duration of the spell-card while letting the spell bonus reduction keep running.

This is done by using the camera, slowing down the timer but not slowing down the spell bonus reduction. Once the absolute value of the negative spell-bonus is approaching is greater than your current score, the spell-card must be captured. If done well, the spell bonus gained should be a negative value. This triggers the underflow.

9,999,999,990

There is a scorecap in the modern games of Touhou, which is set at 9,999,999,990. This is an arbitrary number chosen by ZUN. It is not possible to get a score higher than 9,999,999,990 without the use of modifications.

This is why the score is set to 9,999,999,990 and not anything else.