Numeric Literals

Among its basic types, Python provides integers (positive and negative whole numbers) and floating-point numbers (numbers with a fractional part, sometimes called “floats” for economy). Python also allows us to write integers using hexadecimal, octal, and binary literals; offers a complex number type; and allows integers to have unlimited precision (they can grow to have as many digits as your memory space allows). Table 5-1 shows what Python’s numeric types look like when written out in a program, as literals.

Table 5-1. Basic numeric literals

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Literal

Interpretation

1234, −24, 0, 99999999999999

Integers (unlimited size)

1.23, 1., 3.14e-10, 4E210, 4.0e+210

Floating-point numbers

0177, 0x9ff, 0b101010

Octal, hex, and binary literals in 2.6

0o177, 0x9ff, 0b101010

Octal, hex, and binary literals in 3.0

3+4j, 3.0+4.0j, 3J

Complex number literals

In general, Python’s numeric type literals are straightforward to write, but a few coding concepts are worth highlighting here:

Integer and floating-point literals

Integers are written as strings of decimal digits. Floating-point numbers have a decimal point and/or an optional signed exponent introduced by an e or E and followed by an optional sign. If you write a number with a decimal point or exponent, Python makes it a floating-point object and uses floating-point (not integer) math when the object is used in an expression. Floating-point numbers are implemented as C “doubles,” and therefore get as much precision as the C compiler used to build the Python interpreter gives to doubles.

Integers in Python 2.6: normal and long

In Python 2.6 there are two integer types, normal (32 bits) and long (unlimited precision), and an integer may end in an l or L to force it to become a long integer. Because integers are automatically converted to long integers when their values overflow 32 bits, you never need to type the letter L yourself—Python automatically converts up to long integer when extra precision is needed.

Integers in Python 3.0: a single type

In Python 3.0, the normal and long integer types have been merged—there is only integer, which automatically supports the unlimited precision of Python 2.6’s separate long integer type. Because of this, integers can no longer be coded with a trailing l or L, and integers never print with this character either. Apart from this, most programs are unaffected by this change, unless they do type testing that checks for 2.6 long integers.

Hexadecimal, octal, and binary literals

Integers may be coded in decimal (base 10), hexadecimal (base 16), octal (base 8), or binary (base 2). Hexadecimals start with a leading 0x or 0X, followed by a string of hexadecimal digits (0–9 and A–F). Hex digits may be coded in lower- or uppercase. Octal literals start with a leading 0o or 0O (zero and lower- or uppercase letter “o”), followed by a string of digits (0–7). In 2.6 and earlier, octal literals can also be coded with just a leading 0, but not in 3.0 (this original octal form is too easily confused with decimal, and is replaced by the new 0o format). Binary literals, new in 2.6 and 3.0, begin with a leading 0b or 0B, followed by binary digits (0–1).
Note that all of these literals produce integer objects in program code; they are just alternative syntaxes for specifying values. The built-in calls hex(I), oct(I), and bin(I) convert an integer to its representation string in these three bases, and int(str, base) converts a runtime string to an integer per a given base.

Complex numbers

Python complex literals are written as realpart+imaginarypart, where the imaginarypart is terminated with a j or J. The realpart is technically optional, so the imaginarypart may appear on its own. Internally, complex numbers are implemented as pairs of floating-point numbers, but all numeric operations perform complex math when applied to complex numbers. Complex numbers may also be created with the complex(real, imag) built-in call.

Coding other numeric types

As we’ll see later in this chapter, there are additional, more advanced number types not included in Table 5-1. Some of these are created by calling functions in imported modules (e.g., decimals and fractions), and others have literal syntax all their own (e.g., sets).