Commands that accept or produce floating point numbers employ the floating point representation of the underlying system, and suffer from rounding error, overflow, and similar floating-point issues. Almost all modern systems use IEEE-754 floating point, and it is typically portable to assume IEEE-754 behavior these days. IEEE-754 has positive and negative infinity, distinguishes positive from negative zero, and uses special values called NaNs to represent invalid computations such as dividing zero by itself. For more information, please see David Goldberg’s paper What Every Computer Scientist Should Know About Floating-Point Arithmetic.
Commands that accept floating point numbers as options, operands or
input use the standard C functions strtod and strtold to
convert from text to floating point numbers. These floating point
numbers therefore can use scientific notation like 1.0e-34 and
-10e100. Commands that parse floating point also understand
case-insensitive inf, infinity, and NaN, although
whether such values are useful depends on the command in question.
Modern C implementations also accept hexadecimal floating point
numbers such as -0x.ep-3, which stands for −14/16 times
2^-3, which equals −0.109375. See Parsing of
Floats in The GNU C Library Reference Manual.
Normally the LC_NUMERIC locale determines the decimal-point
character. However, some commands’ descriptions specify that they
accept numbers in either the current or the C locale; for example,
they treat ‘3.14’ like ‘3,14’ if the current locale uses
comma as a decimal point.