Digital root calculator

A digital root calculator reads digits as input, calculates the digital root, and finally outputs the digital root digit (preferably with a UNIX newline). The digital root of a number is the reduction of the number to a single digit through repeated summing.

Writing a program to calculate digital root is useful for testing an esoteric programming language's overall performance and speed, as well as its functionality in input/output, memory, looping, and other things.

A digital root calculator is often quite easy to program, as well.

Simple calculation

Here's how the digital root is calculated for base 10:

Take any non-negative integer (can be zero as well). Add all of its digits together. If the result is bigger than 9, add all the digits of the result together to get another result. Continue this until the result has only one digit (0-9).

Efficient calculation

The digital root of $n$ in a base $b$ is equal to $1+((n-1){\bmod {(}}b-1))$. From this we can see that the digit root of a number can be calculated one digit at a time, by maintaining the digital root of the digits read so far. This is especially useful in languages without any built-in mathematical operators, such as Thue and Gravity.

Example

Digital root of 34758 is 9:

Simple         Efficient
------         ---------
34758          1+(3-1)%9   = 3
3+4+7+5+8      1+(3+4-1)%9 = 7
7+7+5+8        1+(7+7-1)%9 = 5
14+5+8         1+(5+5-1)%9 = 1
1+4+5+8        1+(1+8-1)%9 = 9
5+5+8          9
10+8
1+0+8
1+8
9

See Also

• Digital root calculator in Funciton
• Digital root calculator in Gammaplex

External resources

• Digital root calculator in Brainfuck
• Digital root calculator in Thue
• Digital root calculator in Gravity
• Digital root calculator in Revoledu (up to 65,513 digits)
• Digital root calculator in Malbolge