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Update binary-exp.md#1475

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UtkarshSingh1923
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Distributive law of modulo over multiplication to handle overflow

Distributive law of modulo over multiplication to handle overflow
@mhayter
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Can you give an example of where the previous code fails?

@UtkarshSingh1923
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Can you give an example of where the previous code fails?

a = 3 037 000 500;
b = 2;
m = 3 037 000 501;
a * a = 3 037 000 500 × 3 037 000 500
≈ 9.223 372 037 000 025 000
which is just above LLONG_MAX = 9 223 372 036 854 775 807, so the multiplication overflows.

@mhayter
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The same problem happens with your code:https://www.ideone.com/ZqJd1u

Typically, the assumption is M^2 fits into the data type otherwise you must expand the data type for multiplication.

@mhaytermhayter closed thisJul 1, 2025
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@UtkarshSingh1923@mhayter
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