Number types

And some problems

How numbers are stored

• In Java, every value is either an object or a primitive type

• An object name is really a reference variable

– Some languages call reference variables pointers

– They are really addresses of bytes in RAM

• A primitive name actually stores the value itself

Numbers in the computer

Primitive types

Four integers type

byte -- 8 bit signed integral value

short -- 16-bit signed

int-- 32 bit signed (most commonly used)

long -- 64 bits

Floats

float – 32 bits (6 to 7 significant decimal digits , exponent to 38)

double – 64 bits (15 significant decimal digits, exponent to 308)

How floats are stored

• As we have said, integers are stored in the binary number system

• Floating point numbers must keep track of the decimal point, so they cannot be stored the same as integers

• The decimal point is moved to the first digit of the number, and the number of places it is moved is the exponent

• The exponent can be either positive or negative

• So for a float, you have to keep track of two things

– The digits in the number (called the mantissa)

– The exponent (the placement of the decimal)

• This makes floating point calculations quite slow

Casting

• Since integers and floats are stored differently in the computer, they are not interchangeable

• If you try to use an integer as a float, the compiler does an automatic cast.

– This means it takes the integer, moves the decimal point to the front, then stores the exponent and mantissa.

• But if you try to use a float as an integer, the compiler complains, since data might be lost.

• If you don’t mind losing the fractional part of the number, you can force the compiler to cast a float into an integer

– It just truncates the fractional part of the number

Syntax for casting

• Anytime you use an integer and a double together in an expression, the compiler will automatically cast the integer to a double

•      Example:
        int num1, num2;
      double dub1, dub2;
      dub2 = num1 + dub1;

num2 = num1 + dub1; // error message

num2 = num1 + (int)dub1; // this will work; it truncates dub1

Formatting floats with printf

• printf(%f) lets you specify two things

– The width of the field

• If you don’t specify the field width, it will just automatically be whatever size needed

– The number of digits after the decimal point (called the precision)

• If you don’t specify the precision, it will print out whatever is needed, max about 14 decimal places

• Syntax
System.out.printf("dub2 is %.2f\n", dub2);

Problems with numbers

• Rounding errors with floats or doubles

– Floating point numbers can often not be expressed exactly

– Example: 1/3 or pi

– The problem is worse in binary than in decimal

– See how the compiler handles 4.35 *100

• Overflow with ints

– If you try to store a number that is larger than the number of bits necessary , the results are wrong

– See how the compiler handles 1000000*1000000

Number types

And some problems

How numbers are stored

• In Java, every value is either an object or a primitive type

• An object name is really a reference variable

– Some languages call reference variables pointers

– They are really addresses of bytes in RAM

• A primitive name actually stores the value itself

Numbers in the computer

Primitive types

Four integers type

byte -- 8 bit signed integral value

short -- 16-bit signed

int-- 32 bit signed (most commonly used)

long -- 64 bits

Floats

float – 32 bits (6 to 7 significant decimal digits , exponent to 38)

double – 64 bits (15 significant decimal digits, exponent to 308)

How floats are stored

• As we have said, integers are stored in the binary number system

• Floating point numbers must keep track of the decimal point, so they cannot be stored the same as integers

• The decimal point is moved to the first digit of the number, and the number of places it is moved is the exponent

• The exponent can be either positive or negative

• So for a float, you have to keep track of two things

– The digits in the number (called the mantissa)

– The exponent (the placement of the decimal)

• This makes floating point calculations quite slow

Casting

• Since integers and floats are stored differently in the computer, they are not interchangeable

• If you try to use an integer as a float, the compiler does an automatic cast.

– This means it takes the integer, moves the decimal point to the front, then stores the exponent and mantissa.

• But if you try to use a float as an integer, the compiler complains, since data might be lost.

• If you don’t mind losing the fractional part of the number, you can force the compiler to cast a float into an integer

– It just truncates the fractional part of the number

Syntax for casting

• Anytime you use an integer and a double together in an expression, the compiler will automatically cast the integer to a double

• Example: int num1, num2; double dub1, dub2; dub2 = num1 + dub1;

num2 = num1 + dub1; // error message

Formatting floats with printf

• printf(%f) lets you specify two things

– The width of the field

• If you don’t specify the field width, it will just automatically be whatever size needed

– The number of digits after the decimal point (called the precision)

• If you don’t specify the precision, it will print out whatever is needed, max about 14 decimal places

• Syntax System.out.printf("dub2 is %.2f\n", dub2);

Problems with numbers

• Rounding errors with floats or doubles

– Floating point numbers can often not be expressed exactly

– Example: 1/3 or pi

– The problem is worse in binary than in decimal

– See how the compiler handles 4.35 *100

• Overflow with ints

– If you try to store a number that is larger than the number of bits necessary , the results are wrong

– See how the compiler handles 1000000*1000000

• Example:
int num1, num2;
double dub1, dub2;
dub2 = num1 + dub1;

• Syntax
System.out.printf("dub2 is %.2f\n", dub2);