Language basics - JavaTech: An Introduction to Scientific and Technical Computing with Java - page 47

operands, as in x+i :
If either operand is of type double , the other is converted to double .
Otherwise, if either operand is of type float , the other is converted to float .
Otherwise, if either operand is of type long , the other is converted to long .
Otherwise, both operands are converted to type int .
This last rule can lead to confusion if adding two byte values. For example, the
code
byte a = 3, b = 6, c;
c = a+b;
does not compile because the a and b operands are automatically promoted to
type int before the addition occurs, meaning that the result is also an int . The
code then attempts to place the resulting int back into a byte type, resulting in
a “possible loss of precision” compiler error. The solution is to make an explicit
cast to byte :
c = (byte)(a + b);
2.11 Floating-point
Floating-point representation is obviously an important aspect of numerical com-
putation and how Java handles it while maintaining platform portability should be
understood. We first look at floating-point in general and then in Java. Appendix
3gives further details about Java floating-point representation and operations.
2.11.1 Floating-point basics
A floating-point number is represented in binary as
- b 0 .b 1 b 2 b 3 ...b n-1 *2 exponent
where b i represents the i bit in the n bits of the significand (also called the
mantissa). There is also a bit to indicate the sign. A floating-point value is calcu-
lated as
(-1) s · (b 0 +b 1 ·2 - 1 +b 2 ·2 - 2 +b 3 ·2 - 3 +...+b n - 1 · 2 - (n - 1) )·2 exponent
where s is a bit for the sign. Floating-point numbers involve a number of com-
plications with which the processor designers must deal. These complications
include:
Approximations - The limited number of places in the significand means that only a
finite number of fractional values can be represented exactly. Similarly, the finite width
of the exponents limits the upper and lower size of the numbers.