CODEWITHSUNDEEP
javavariablesdoublecalculus
danielleontiev
danielleontiev

Reputation: 899

double numbers are not too accurate

I've wrote a method for polynomial long division. And it works perfect with "good" polynomials. Under "good" I mean coefficients that divides accurate. Today I've faced with issue when tried to divide 2*x^3-18*x^2+.... / 7.00000(much zeros)0000028*x^2 + 5*x + ... After division 2*x^3 / 7.000...000028*x^2 I got 0.285714....53*x. On next step we need to multiply 0.2857....53*x on 7.00000...0000028*x^2 + 5*x + .. and subtract it from dividend polynomial 2*x^3-18*x^2+... and get new polynomial with degree = 2. But because of problem with double type I actually got polynomial 2.220....E-16*x^3 - 6*x^2 + .... I know that it is in fact zero near the x^3. I do not want to invent smth new and strange, that is why I am asking how to resolve it beautifully and correctly. Thanks.

Upvotes: 0

Views: 64

Answers (1)

Patricia Shanahan
Patricia Shanahan

Reputation: 26185

Many division results such as 1/7 cannot be represented exactly in either double or BigDecimal. If you go with BigDecimal you would have to pick a number of digits to preserve, and deal with rounding error. For double, you get more convenient arithmetic, but a fixed number of significant bits.

You have two options.

One is to handle rounding error. When a result is very close to zero, so close that it is probably due to rounding error, treat it as zero. I don't know whether that will work for your algorithm or not. If you go this way, you can use either double or BigDecimal.

The second option is to use a rational number package. In rational number arithmetic all division results can be represented exactly. 1/7 remains 1/7, without being rounded to a terminating decimal or binary fraction. If you go this way, search for "java rational number" (no quotes) and decide which one you like best.

Upvotes: 2

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