the implementation of the Karatsuba algorithm, the method only counts the small numbers true, but the big answer is not correct, what's the problem?

Question

The implementation of the Karatsuba algorithm, the method only counts the small numbers true, but the big answer is not correct, what's the problem?

var x = "1685287499328328297814655639278583667919355849391453456921116729";
var y = "7114192848577754587969744626558571536728983167954552999895348492";

function karatsuba(x, y) {
    if (x.length < 2 && y.length < 2) {
        return BigInt(parseInt(x) * parseInt(y));
    }
    var m = Math.min(x.length, y.length);
    var m2 = m / 2;
    var a = BigInt(x.substring(0, m2));
    var b = BigInt(x.substring(m2));
    var c = BigInt(y.substring(0, m2));
    var d = BigInt(y.substring(m2));
    var ac = a * c;
    var bd = b * d;
    var sum = (a + b) * (c + d) - ac - bd;

    return BigInt(Math.pow(10, m)) * ac + BigInt(Math.pow(10, m2)) * sum + bd;
}

console.log(karatsuba(x, y));

Welcome to StackOverflow! Please add your actual code to the question rather than a screenshot of your code. Thank you! — Nick, Jan 15 '19 at 15:24

score 1 · Accepted Answer · answered Jan 15 '19 at 23:29

1

Invoking Math.pow is very suspicious. According to documentation, it

Returns an implementation-dependent approximation to the result of raising x to the power y.

You don't want any approximations in Karatzuba.

answered Jan 15 '19 at 23:29

user58697

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score 1 · Answer 2 · answered Jan 16 '19 at 00:01

1

return BigInt(parseInt(x) * parseInt(y));

It defeats the point to multiply large things together before constructing a BigInt.

answered Jan 16 '19 at 00:01

djechlin

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(I think I see your point, but the code quoted is used when *both* factors are shorter than two digits (not large by my book). But then, there is scaling using the `*` operator …) – greybeard Jan 16 '19 at 01:29

score 0 · Answer 3 · answered Jan 15 '19 at 23:56

In addition to user58697's word of warning about floating point arithmetic in general and transcendental functions in particular:

You use m2 in splitting the numbers, but m (too) in scaling before/in combination/"(polynomial) evaluation".

You need to use 2*m2.

the implementation of the Karatsuba algorithm, the method only counts the small numbers true, but the big answer is not correct, what's the problem?

3 Answers3