Math in Dart - working with numbers other than base 10 - dart

Question

I was trying to do some math in something other than base 10, and wanted to get some input from the Dart community on possible directions I can take.
So, for example, suppose p = 2. Then, looking at 100 in base 2:
100 = (1 · 26
) + (1 · 25
) + (0 · 24
) + (0 · 23
) + (1 · 22
) + (0 · 21
) + (0 · 20
)
so
100 base 2 = 1100100
Add 1 to each digit and multiply the answers together:
(1 + 1)(1 + 1)(0 + 1)(0 + 1)(1 + 1)(0 + 1)(0 + 1) = 8
Try it for 3:
100 = (1 · 34
) + (0 · 33
) + (2 · 32
) + (0 · 31
) + (1 · 30
)
so
100 base 3 = 10201
(1 + 1)(0 + 1)(2 + 1)(0 + 1)(1 + 1) = 12
In Dart, I came up with the following;
https://gist.github.com/anonymous/11345381
int rows = 1000000000;
int total = 0;
for(int i = 0 ; i < rows ; i++ ){
total += i.toRadixString(7)
.split('')
.map((s) => int.parse(s) + 1)
.reduce((prev,next) => prev*next);
}
print('${total} results');
This does work, and seems to be ok for small number of rows. But for larger numbers, it is really quite slow.
As shown, I am converting an int to a string (resulting in a string representation of a number), splitting it, mapping the split characters back to ints, adding 1 to each int, and then multiplying them all together.
Am I missing something when it comes to working with numbers in Dart, other than base 10?

Answer 1

Going through the string seems inefficient. How about doing it directly?
int digitProduct(int n, int base) { // non-negative n and base only
int product = 1;
while (n > 0) {
int digit = n % base;
n = n ~/ base;
product *= (digit + 1);
}
return product;
}
main() {
int rows = 1000000000;
int total = 0;
for (int i = 0; i < rows; i++) {
total += digitProduct(i, 7);
}
print("${total} results");
}
Also 1000000000 is a pretty big number. If it takes a microsecond per row, it will still take ~16 minutes to complete.
Division by arbitrary bases is slow. If you hardcode the base to be 7, it'll probably be significantly faster (I expect ~90% of the time spent in digitProduct to be used on ~/ and %).