Possible issue with the nthRoot() function

[sonnyk22]

After passing the expressions below to the MathJS.eval() function, I get the exception shown below thrown back.

nthRoot(e ^ -2, e ^ -4):

nthRoot(-2, 3)

However, on other calculators such as Microsoft, I do get results back.

Is the expression that I am passing in to the MathJS.eval() function incorrect?

[josdejong]

Thanks for reporting this. I've done a little bit of debugging and found that JavaScripts Math.pow (used in an iteration in nthroot) doesn't always behave like we want. From MDN:

// due to "even" and "odd" roots laying close to each other, 
// and limits in the floating number precision, 
// negative bases with fractional exponents always return NaN
Math.pow(-7, 1/3); // NaN

In this particular case the algorithm evaluates the following, resulting in NaN:

Math.pow(-46.209093934213584, -0.9816843611112658); // NaN

So we have to see if we can improve nthRoot and work around this limitation in Math.pow.

[ericman314]

I will take a look at it tonight as well.

[josdejong]

Ok thanks @ericman314 , I don't have time tonight so that would be great...

[ericman314]

See #496.

[ericman314]

I submitted a pull request #496 which replaces the algorithm with this:

// x = a ^ (1/root)
var x = Math.pow(Math.abs(a), 1/root);
// If a is negative and root is odd, then  (-1) ^ (1/root) = -1
x = a < 0 ? -x : x;

The square root algorithm (and cube root, etc.) is one of my favorite algorithms. The algorithm comes from Newton's method, which converges quickly but occasionally runs into problems. nthRoot(-2, 3) just happens to result in a division by zero, although choosing an alternative starting point could fix that.

I thought that perhaps the algorithm may be faster than my suggestion above when root is an integer, since pow can be optimized for integer exponents, but the timing results below are not looking very good for the algorithm even with the (supposed) optimization:

80000 iterations of nthRoot(x, y), real-valued y
original: 6483ms
proposed: 15ms

80000 iterations of nthRoot(x, y), integer-valued y
original: 1186ms
original-optimized: 1257ms
proposed: 12ms

Even when using my own "optimized" version of pow(real, integer) (which is not actually any faster than the built-in implementation, no surprises there!) the algorithm is slower. It looks like the proposed solution is much faster in every case.

[josdejong]

This is fixed now in v2.4.1

[sonnyk22]

Thank you