[joubert]

http://gigamonkeys.com/book/numbers-characters-and-strings.h...

One of the reasons Lisp is a nice language for math is its numbers behave more like true mathematical numbers than the approximations of numbers that are easy to implement in finite computer hardware. For instance, integers in Common Lisp can be almost arbitrarily large rather than being limited by the size of a machine word.3 And dividing two integers results in an exact ratio, not a truncated value. And since ratios are represented as pairs of arbitrarily sized integers, ratios can represent arbitrarily precise fractions.4

On the other hand, for high-performance numeric programming, you may be willing to trade the exactitude of rationals for the speed offered by using the hardware's underlying floating-point operations. So, Common Lisp also offers several types of floating-point numbers, which are mapped by the implementation to the appropriate hardware-supported floating-point representations.5 Floats are also used to represent the results of a computation whose true mathematical value would be an irrational number.

Finally, Common Lisp supports complex numbers--the numbers that result from doing things such as taking square roots and logarithms of negative numbers. The Common Lisp standard even goes so far as to specify the principal values and branch cuts for irrational and transcendental functions on the complex domain.

[shiro]

These days quite a few languages already support bignums, rationals and even complex numbers. CL's support for these was unique back then, but I guess it has lost its edge in this domain.

Still, support of strict read/write invariance of floating point numbers (e.g. as described in Burger&Dybvig 1996 and Clinger 1990) doesn't seem to spread widely outside CL/Scheme camp. Concept of exact/inexact numbers as well.