modulus : Java Glossary

Happily, Java division has the Euclidean property namely when you multiply the quotient by the divisor and add the remainder you get back to the dividend. When you ask for % 3 in Java, you may be astounded to sometimes get an answer outside the range 0..2. See remainder/modulus sign rules. Be especially careful when corralling random numbers into a smaller range with the % operator.

Negative Operands

For example, when you do a day of week calculation by taking day_number % 7 in Java, you will be astounded to sometimes get a negative answer outside the range 0 .. 6, namely when the dividend is negative. See sign rules. Java division is truncated division.

Mixed Base Calculations

static final long MILLISECONDS_PER_DAY = 24 * 60 * 60 * 1000L;
static final long MILLISECONDS_PER_HOUR = 60 * 60 * 1000L;
static final long MILLISECONDS_PER_MINUTE = 60 * 1000L;
static final long MILLISECONDS_PER_SECOND = 1000L;

long millis = days * MILLISECONDS_PER_DAY + hours * MILLISECONDS_PER_HOUR
              + minutes * MILLISECONDS_PER_MINUTE
              + seconds * MILLISECONDS_PER_SECOND
              + milliseconds;

You can use similar logic to deal with other goofy mixed base systems like latitude and longitude with its degrees, minutes and seconds, yards, feet and inches or tons, pounds and ounces. APL (A Programming Language) has built-in operators to neatly handle these. In Java you have to code the conversions out longhand.

Sign Rules

Honing Your Intuition

Getting the digits of a Number, any Radix

Even or Odd?

boolean even = x % 2 == 0;
boolean odd = x % 2 != 0;

boolean even = x % 2 == 0;
boolean odd = x % 2 == 1; // does not work for negative x

boolean even = ( x & 1 ) == 0;
boolean odd = ( x & 1 ) != 0;

int odd = x & 1;

Every nth

Other Uses

int nextbuf = ( thisbuf + 1 ) % supply;

int recordNumber = fileOffset / blockSize;
int recordOffset = fileOffset % blockSize;

Floating Point %

The result of a floating-point remainder operation as computed by the % operator is not the same as that produced by the remainder operation defined by the IEEE 754 floating point standard. The IEEE (Institute of Electrical & Electronics Engineers) 754 remainder operation computes the remainder from a rounding division, not a truncating division. % on floating-point operations behaves analogously to the integer remainder operator; this may be compared with the C library function fmod. The IEEE 754 remainder operation may be computed by the library routine Math. IEEEremainder. (Note the violation of the naming conventions.)

Learning More