Error in the org.jorlib.alg.packing.circlePacking.util.sqrt(BigDecimal squarD, MathContext rootMC) method. about jorlib HOT 4 OPEN

Hi Mikhail,
Thanks for reporting this. This Math Utility was originally contributed by Frans Lelieveld, so I'm not very familiar with its implementation. Would you be able (and willing) to look into this issue and see whether this is actually a bug in the code, or for example a rounding issue? Your input is a very long number, and the scaled difference seems very small compared to the very big number you put in, so I wouldn't be surprised if this issue is caused by rounding.

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Joris, I found that the method gives wrong answer for the number 4 * 10^74 + 1 with rounding mode UP. The square root of this number exceeds 2 * 10^37, so correct UP rounding with 1 digit precision should be the number 3 * 10^37. But

BigDecimal number = new BigDecimal(new BigInteger("4"), -74).add(BigDecimal.ONE);
mathContext = new MathContext(1, RoundingMode.UP);
System.out.println(MathUtil.sqrt(number, mathContext).toPlainString());

produces 2E+37.

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Hm I agree with your example. It seems that this error occurs with very
tiny numbers. Given that you were able to study the book which was used to
implement this algorithm, would you be able to spot the implementation
issue? The book refers to an implementation itsqrt.cc, which you can find
on the publisher's website:
http://extras.springer.com/2001/978-3-642-56735-3/hfloat/hfloat/src/hf/itsqrt.cc
The first line states: "#warning 'sqrt_iteration() is experimental (loss
of precision !)'". So I'm not surprised that you encounter precision errors
with such small numbers. Here's another implementation:
https://github.com/rizar/matrix/blob/master/src/com/github/rizar/bigdecimalmath/BigDecimalMath.java
Does this one have similar issues?
I'm happy to help you out wherever I can, but I have very little knowledge
about this specific domain...

Joris

On Fri, Apr 22, 2016 at 9:40 AM, Mikhail Zvagelsky <[email protected]

wrote:

Joris, I found that the method gives wrong answer for the number 4 *
10^74 + 1 with rounding mode UP. The square root of this number exceeds 2

• 10^37, so correct UP rounding with 1 digit precision should be the
  number 3 * 10^37. But

BigDecimal number = new BigDecimal(new BigInteger("4"),
-74).add(BigDecimal.ONE);
mathContext = new MathContext(1, RoundingMode.UP);
System.out.println(MathUtil.sqrt(number, mathContext).toPlainString());

produces 2E+37.

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