Floating Point Numbers

You can now use floating point numbers in Emacs, if you define the macro LISP_FLOAT_TYPE when you compile Emacs.

The printed representation for floating point numbers requires either a decimal point surrounded by digits, or an exponent, or both. For example, `1500.0', `15e2', `15.0e2' and `1.5e3' are four ways of writing a floating point number whose value is 1500.

The existing predicate numberp now returns t if the argument is any kind of number--either integer or floating. The new predicates integerp and floatp check for specific types of numbers.

You can do arithmetic on floating point numbers with the ordinary arithmetic functions, +, -, * and /. If you call one of these functions with both integers and floating point numbers among the arguments, the arithmetic is done in floating point. The same applies to the numeric comparison functions such as = and <. The remainder function % does not accept floating point arguments, and neither do the bitwise boolean operations such as logand or the shift functions such as ash.

There is a new arithmetic function, abs, which returns the absolute value of its argument. It handles both integers and floating point numbers.

To convert an integer to floating point, use the function float. There are four functions to convert floating point numbers to integers; they differ in how they round. truncate rounds toward 0, floor rounds down, ceil rounds up, and round produces the nearest integer.

You can use logb to extract the binary exponent of a floating point number. More precisely, it is the logarithm base 2, rounded down to an integer.

Emacs has several new mathematical functions that accept any kind of number as argument, but always return floating point numbers.

cos

sin

tan

Trigonometric functions.

acos

asin

atan

Inverse trigonometric functions.

exp

The exponential function (power of e).

log

Logarithm base e.

log10

Logarithm base 10

expt

Raise x to power y.

sqrt

The square root function.

The new function string-to-number now parses a string containing either an integer or a floating point number, returning the number.

The format function now handles the specifications `%e', `%f' and `%g' for printing floating point numbers; likewise message.

The new variable float-output-format controls how Lisp prints floating point numbers. Its value should be nil or a string.

If it is a string, it should contain a `%'-spec like those accepted by printf in C, but with some restrictions. It must start with the two characters `%.'. After that comes an integer which is the precision specification, and then a letter which controls the format.

The letters allowed are `e', `f' and `g'. Use `e' for exponential notation (`dig.digitseexpt'). Use `f' for decimal point notation (`digits.digits'). Use `g' to choose the shorter of those two formats for the number at hand.

The precision in any of these cases is the number of digits following the decimal point. With `e', a precision of 0 means to omit the decimal point. 0 is not allowed with `f' or `g'.

A value of nil means to use the format `%.20g'.

No matter what the value of float-output-format, printing ensures that the result fits the syntax rules for a floating point number. If it doesn't fit (for example, if it looks like an integer), it is modified to fit. By contrast, the format function formats floating point numbers without requiring the output to fit the syntax rules for floating point number.