Modulo Multiplication:

Правка en3, от RNR, 2017-10-05 21:19:11

How does this work?

  • llui mul_mod(llui a, llui b, llui m){
  • llui y = (llui)((float64)a*(float64)b/m+(float64)1/2);
  • y = y * m;
  • llui x = a * b;
  • llui r = x — y;
  • if ( (lli)r < 0 ){
  • r = r + m; y = y — 1;
  • }
  • return r;
  • }

For example if we do c = (a+b)%m;

What if a+b itself causes the overflow that is a+b is larger than the size of typeof a or b.

Doesn’t x in the above code cause overflow that is a*b is larger than a size of llui.

Here llui means long long unsigned int and lli means long long int and float64 stands for long double

Теги modular arithmetic, multiplication, c++

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  Rev. Язык Кто Когда Δ Комментарий
en4 Английский RNR 2017-10-05 21:20:21 20 Tiny change: 'lui r = x &mdash; y;\n- ' -> 'lui r = x - y;\n- '
en3 Английский RNR 2017-10-05 21:19:11 27 Tiny change: 'the above image cause ov' -> 'the above code cause ov'
en2 Английский RNR 2017-10-05 21:14:36 269
en1 Английский RNR 2017-10-05 21:12:58 438 Initial revision (published)