You want to match a floating-point number and specify whether the sign, integer, fraction and exponent parts of the number are required, optional, or disallowed. You don’t want to use the regular expression to restrict the numbers to a specific range, and instead leave that to procedural code, as explained in Recipe 3.12.

Mandatory sign, integer, fraction, and exponent:

^[-+][0-9]+.[0-9]+[eE][-+]?[0-9]+$

Mandatory sign, integer, and fraction, but no exponent:

^[-+][0-9]+.[0-9]+$

Optional sign, mandatory integer and fraction, and no exponent:

^[-+]?[0-9]+.[0-9]+$

Optional sign and integer, mandatory fraction, and no exponent:

^[-+]?[0-9]*.[0-9]+$

Optional sign, integer, and fraction. If the integer part is omitted, the fraction is mandatory. If the fraction is omitted, the decimal dot must be omitted, too. No exponent.

^[-+]?([0-9]+(.[0-9]+)?|.[0-9]+)$

Optional sign, integer, and fraction. If the integer part is omitted, the fraction is mandatory. If the fraction is omitted, the decimal dot is optional. No exponent.

^[-+]?([0-9]+(.[0-9]*)?|.[0-9]+)$

Optional sign, integer, and fraction. If the integer part is omitted, the fraction is mandatory. If the fraction is omitted, the decimal dot must be omitted, too. Optional exponent.

^[-+]?([0-9]+(.[0-9]+)?|.[0-9]+)([eE][-+]?[0-9]+)?$

Optional sign, integer, and fraction. If the integer part is omitted, the fraction is mandatory. If the fraction is omitted, the decimal dot is optional. Optional exponent.

^[-+]?([0-9]+(.[0-9]*)?|.[0-9]+)([eE][-+]?[0-9]+)?$

The preceding regex, edited to find the number in a larger body of text:

[-+]?([0-9]+(.[0-9]*)?|.[0-9]+)([eE][-+]?[0-9]+)?

All regular expressions are wrapped between anchors (Recipe 2.5) to make sure we check whether the whole input is a floating-point number, as opposed to a floating-point number occurring in a larger string. You could use word boundaries or lookaround as explained in Recipe 6.1 if you want to find floating-point numbers in a larger body of text.

The solutions without any optional parts are very straightforward: they simply spell things out from left to right. Character classes (Recipe 2.3) match the sign, digits, and the e. The plus and question mark quantifiers (Recipe 2.12) allow for any number of digits and an optional exponent sign.

Making just the sign and integer parts optional is easy. The question mark after the character class with the sign symbols makes it optional. Using an asterisk instead of a plus to repeat the integer digits allows for zero or more instead of one or more digits.

Complications arise when sign, integer, and fraction are all optional. Although they are optional on their own, they are not all optional at the same time, and the empty string is not a valid floating-point number. The naïve solution, ‹[-+]?[0-9]*.?[0-9]*›, does match all valid floating-point numbers, but it also matches the empty string. And because we omitted the anchors, this regex will match the zero-length string between any two characters in your subject text. If you run a search-and-replace with this regex and the replacement «{$&}» on 123abc456, you’ll get {123}{}a{}b{}c{456}{}. The regex does match 123 and 456 correctly, but it finds a zero-length match at every other match attempt, too.

When creating a regular expression in a situation where everything is optional, it’s very important to consider whether everything else remains optional if one part is actually omitted. Floating-point numbers must have at least one digit.

The solutions for this recipe clearly spell out that when the integer and fractional parts are optional, either of them is still required. They also spell out whether 123. is a floating-point number with a decimal dot, or whether it’s an integer number followed by a dot that’s not part of the number. For example, in a programming language, that trailing dot might be a concatenation operator or the first dot in a range operator specified by two dots.

To implement the requirement that the integer and fractional can’t be omitted at the same time, we use alternation (Recipe 2.8) inside a group (Recipe 2.9) to simply spell out the two situations. ‹[0-9]+(.[0-9]+)?› matches a number with a required integer part and an optional fraction. ‹.[0-9]+› matches just a fractional number.

Combined, ‹[0-9]+(.[0-9]+)?|.[0-9]+› covers all three situations. The first alternative covers numbers with both the integer and fractional parts, as well as numbers without a fraction. The second alternative matches just the fraction. Because the alternation operator has the lowest precedence of all, we have to place these two alternatives in a group before we can add them to a longer regular expression.

‹[0-9]+(.[0-9]+)?|.[0-9]+› requires the decimal dot to be omitted when the fraction is omitted. If the decimal dot can occur even without fractional digits, we use ‹[0-9]+(.[0-9]*)?|.[0-9]+› instead. In the first alternative in this regex, the fractional part is still grouped with the question mark quantifier, which makes it optional. The difference is that the fractional digits themselves are now optional. We changed the plus (one or more) into an asterisk (zero or more). The result is that the first alternative in this regex matches an integer with optional fractional part, where the fraction can either be a decimal dot with digits or just a decimal dot. The second alternative in the regex is unchanged.

This last example is interesting because we have a requirement change about one thing, but change the quantifier in the regex on something else. The requirement change is about the dot being optional on its own, rather than in combination with the fractional digits. We achieve this by changing the quantifier on the character class for the fractional digits. This works because the decimal dot and the character class were already inside a group that made both of them optional at the same time.

All the other recipes in this chapter show more ways of matching different kinds of numbers with a regular expression.

Techniques used in the regular expressions in this recipe are discussed in Chapter 2. Recipe 2.1 explains which special characters need to be escaped. Recipe 2.3 explains character classes. Recipe 2.5 explains anchors. Recipe 2.8 explains alternation. Recipe 2.9 explains grouping. Recipe 2.12 explains repetition.