Package org.apfloat
All application code using apfloat generally needs to only call the classes in this package.
A sample apfloat program might look like this:
import org.apfloat.Apfloat; import org.apfloat.ApfloatMath; public class ApfloatTest { public static void main(String[] args) { Apfloat x = new Apfloat(2, 1000); // Value 2, precision 1000 digits Apfloat y = ApfloatMath.sqrt(x); // Square root of 2, to 1000 digits System.out.println(y); } }As apfloats are immutable, they can be easily passed by reference. Also the mantissa data of numbers can be efficiently shared in various situations.
An inherent property of an Apfloat
is the radix
.
The radix is specified at the time an apfloat is created. Due to the way the
default implementation works, there is no real performance difference in using
radix 2 or some other radix in the internal calculations. While it's generally
not possible to use numbers in different radixes in operations, it's possible
to convert a number to a different radix using the Apfloat.toRadix(int)
method.
The rounding mode for apfloat calculations is undefined. Thus, it's not
guaranteed that rounding happens to an optimal direction and more often
than not it doesn't. This should be carefully considered when designing
numerical algorithms. Roundoff errors can accumulate faster than expected,
and loss of precision (as returned by Apfloat.precision()
)
can happen quickly. This bad behaviour is further accelerated by using a radix
bigger than two, e.g. base 10, which is the default. Note that precision is
defined as the number of digits in the number's radix. If numbers need to
be rounded in a specific way then the ApfloatMath.round(Apfloat,long,RoundingMode)
method can be invoked explicitly.
Generally, the result of various mathematical operations is accurate to the second last digit in the resulting number. This means roughly that the last significant digit of the result can be inaccurate. For example, the number 12345, with precision 5, should be considered 12345 ± 10. This only applies to elementary mathematical operations. More complicated functions may have slightly larger errors due to error accumulation. This should generally not be a problem, as you should typically be using apfloats for calculations with a precision of thousands or millions of digits.
There is no concept of an infinity or NotaNumber with apfloats. Whenever
the result of an operation would be infinite or undefined, an exception is
thrown (usually an ArithmeticException
).
All of the apfloatspecific exceptions being thrown by the apfloat library
extend the base class ApfloatRuntimeException
. This
exception, or various subclasses can be thrown in different situations, for
example:
InfiniteExpansionException
 The result of an operation would have infinite size. For example,new Apfloat(2).divide(new Apfloat(3))
, in radix 10.OverflowException
 Overflow. If the exponent is too large to fit in along
, the situation can't be handled. Also, there is no "infinity" apfloat value that could be returned as the result.LossOfPrecisionException
 Total loss of precision. For example,ApfloatMath.sin(new Apfloat(1e100))
. If the magnitude (100) is far greater than the precision (1) then the value of thesin()
function can't be determined to any accuracy.
RuntimeException
, because it should "never happen",
and in general the cases where it is thrown are irrecoverable with the current
implementation. Also any of the situations mentioned above may be relaxed in
the future, so this exception handling strategy should be more futureproof
than others, even if it has its limitations currently.
The Apfloat
class is the basic building block of all the
objects used in the apfloat package. An Apcomplex
simply
consists of two apfloats, the real part and the imaginary part. An
Apint
is implemented with an apfloat and all its operations
just guarantee that the number never gets a fractional part. Last, an
Aprational
is an aggregate of two apints, the numerator
and the denominator. The relations of these classes are shown in a class
diagram format below:

ClassDescriptionArbitrary precision complex number class.Various mathematical functions for arbitrary precision complex numbers.Arbitrary precision floatingpoint number class.Exception indicating an error in the apfloat configuration.This class encapsulates the information needed by the apfloat implementation to perform computations.Exception indicating that the computation was interrupted.Various mathematical functions for arbitrary precision floatingpoint numbers.Exception indicating some unexpected error situation.Arbitrary precision integer class.Various mathematical functions for arbitrary precision integers.Arbitrary precision rational number class.Various mathematical functions for arbitrary precision rational numbers.Fixedprecision mathematical functions for complex numbers.Fixedprecision mathematical functions for floatingpoint numbers.Exception indicating that the result of an operation would have infinite size.Exception indicating a result that would have no significant digits.Exception indicating that something went wrong in a numeric computation.Exception indicating an overflow in a calculation.