Java BigDecimal trigonometric methods

Question

I am developing a mathematical parser which is able to evaluate String like '5+b*sqrt(c^2)'. I am using ANTLR for the parsing and make good progress. Now I fell over the Java class BigDecimal and thought: hey, why not thinking about precision here.

My problem is that the Java API does not provide trigonometric methods for BigDecimals like java.lang.Math. Do you know if there are any good math libraries like Apache Commons out there that deal with this problem?

The other questions is how to realize the power method so that I can calculate 4.9 ^ 1.4 with BigDecimals. Is this possible?

A book request about numerical computing is also appreciated.

Solution 1

ApFloat is a library which contains arbitrary-precision approximations of trigometric functions and non-integer powers both; however, it uses its own internal representations, rather than BigDecimal and BigInteger. I haven't used it before, so I can't vouch for its correctness or performance characteristics, but the api seems fairly complete.

Solution 2

BigDecimal does not provide these methods because BigDecimal models a rational number. Trigonometric functions, square roots and powers to non-integers (which I guess includes square roots) all generate irrational numbers.

These can be approximated with an arbitrary-precision number but the exact value can't be stored in a BigDecimal. It's not really what they're for. If you're approximating something anyway, you may as well just use a double.

Solution 3

The big-math library provides all the standard advanced mathematical functions (pow, sqrt, log, sin, ...) for BigDecimal.

https://github.com/eobermuhlner/big-math

Comments

[Pete Kirkham]

Only for some definitions of best. 'broadest' possibly, but always check the algorithms against other sources, and never use the implementations directly - at least if they haven't updated the 1 based indexing in the C version using undefined behaviour.

[Marco]

Just found it myself and have seen that it supports pretty much everything I need. I will keep you posted if everything works

[Admin]

double does also approximate, but with a fixed size of bits. BigDecimals can use more bits.

[Ky -]

BigDecimal is approximate; that's why if you try to do BigDecimal.ONE.divide(BigDecimal.valueOf(3)), you get a java.lang.ArithmeticException: Non-terminating decimal expansion; no exact representable decimal result. Terminating equations work fine, but for non-terminating ones, you must specify an arbitrary precision.

[Al G Johnston]

This library works great for populating accurate double values when I set the accuracy to 1074 decimal places, which is the maximum absolute value of the negative exponent of a Java primitive double value.

[Eric Obermühlner]

I don't think you need 1074 decimal places. The type double as defined in IEEE 754 binary64 is equivalent to MathContext.DECIMAL64 and has 16 digits precision for the mantissa.

[Eric Obermühlner]

To accurately calculate a double value I would use MathContext.DECIMAL128 (34 digits). Remember that precision is not the same thing as digits after the decimal point. Precision in this context refers to the number of significant digits.