Number and its Types in Julia

Julia is a high-level, dynamic, general-purpose programming language that can be used to write software applications, and is well-suited for data analysis and computational science. Numbers are important in any programming language. Numbers in Julia is classified into two types: Integer and Floating-Point Numbers. Julia provides a wide range of primitive numeric types. These inbuilt numeric datatypes help Julia to take full advantage of computational resources. Julia also provides software support for Arbitrary Precision Arithmetic, which can handle numeric operations which is difficult to represent in native hardware representations. However, support for Arbitrary Precision Arithmetic comes at the cost of slower performance. Complex and Rational Numbers are defined on top of primitive numeric types.

The following are Julia’s primitive numeric types:

1. Integer
   

   Type	Signed	Number of bits	Range
   Int8	Yes	8	-2^7 to 2^7 – 1
   UInt8	No	8	0 to 2^8-1
   Int16	Yes	16	-2^15 to 2^15-1
   UInt16	No	16	0 to 2^16 – 1
   Int32	Yes	32	-2^31 to 2^31-1
   UInt32	No	32	0 to 2^32-1
   Int64	Yes	64	-2^63 to 2^63-1
   UInt64	No	64	0 to 2^64 – 1
   Int128	Yes	128	-2^127 to 2^127 – 1
   UInt128	No	128	0 to 2^128 – 1
   Bool	N/A	8	false(0) and true(1)

2. Floating point numbers
   

   Type	Precision	Number of bits
   Float16	half	16
   Float32	single	32
   Float64	double	64

Integers

The default type for an integer literal depends on whether the system is 32-bit or 64-bit. The variable Sys.WORD_SIZE indicates whether the system is 32-bit or 64-bit:

println(Sys.WORD_SIZE)
println(typeof(123))

Output:

However, larger integer literals that cannot be represented using 32 bits are represented using 64 bits, regardless of the system type.
Unsigned integers are represented using the 0x prefix and hexadecimal digits 0-9a-f or 0-9A-F. Size of the unsigned integer is determined by the number of hex digits used.

println(typeof(0x12))
println(typeof(0x123))
println(typeof(0x1234567))
println(typeof(0x123456789abcd))
println(typeof(0x1112223333444555566677788))

Output:

Binary and octal literals are also supported in Julia.

println(typeof(0b10))
println(typeof(0o10))
println(0b10)
println(0o10)

Output:

Min-Max Values of Integers

println(typemin(Int8), ' ', typemax(Int8))
println(typemin(Int16), ' ', typemax(Int16))
println(typemin(Int32), ' ', typemax(Int32))
println(typemin(Int64), ' ', typemax(Int64))
println(typemin(Int128), ' ', typemax(Int128))

Output:

Floating Point Numbers

Floating Point Numbers are represented in a standard format. There is no literal format for Float32, but we can convert values to Float32 by writing an ‘f’ or explicit typecasting.

println(typeof(1.0))
println(typeof(.5))
println(typeof(-1.23))
println(typeof(0.5f0))
println(2.5f-4)
println(typeof(2.5f-4))
println(typeof(Float32(-1.5)))

Output:

Floating point zero

Floating point numbers have a positive zero and a negative zero which are equal to each other but have different binary representations.

julia> 0.0 == -0.0
true

julia> bitstring(0.0)
"0000000000000000000000000000000000000000000000000000000000000000"

julia> bitstring(-0.0)
"1000000000000000000000000000000000000000000000000000000000000000"

Special floating-point values

Name	Type	Description
positive infinity	Inf16, Inf32, Inf	a value greater than all finite floating-point values
negative infinity	-Inf16, -Inf32, -Inf	a value less than all finite floating-point values
not a number	NaN16, NaN32, NaN	a value not comparable to any floating point values including itself

Complex Number

Global constant ‘im’ is used to represent complex number i where i is square root of -1.

println(typeof(1+2im))

# performing mathematical operations

println()
println((1 + 2im) + (2 + 3im))
println((5 + 5im) - (3 + 2im))
println((5 + 2im) * (3 + 2im))
println((1 + 2im) / (1 - 2im))
println(3(2 - 5im)^2)

Output:

Rational Number

Julia has rational numbers to represent exact ratios of integers. Rational numbers are constructed using the // operator.

println(typeof(6//9))
println(6//9)
println(-6//9)
println(-6//-9)
println(5//8 + 3//12)
println(6//5 - 10//13)
println(5//8 * 3//12)
println(6//5 / 10//3)

Output: