# Extended Real Number Line

The (affine) extended real number line, where real numbers are enriched with positive and negative infinity, compactifying their order. Positive infinity is represented by IEEE number +inf.0 while negative infinity is represented by IEEE number -inf.0, so that common operations like < <= + *, etc., already work. However, a few operations are provided in a library so that max and min functions work better with infinities. Notably:

• (xmin) will return +inf.0 where (min) throws an error, and similarly (xmax) will return -inf.0 where (max) throws an error.
• (xmax -inf.0 (+ 1 (expt 2 54))) will return the exact integer 18014398509481985, where (max -inf.0 (+ 1 (expt 2 54))) returns the rounded 1.8014398509481984e16. More generally, xmin and xmax preserve the type of the argument they return.

(import :std/misc/number)

# xmin

(xmin <x1> ... <xn>) -> real

xmin returns the lower bound of the set of its extended real arguments. In particular, it returns +inf.0 (the positive infinity) if provided zero arguments, and is the identity function when given a single argument.

# xmin/list

(xmin/list <l>) -> real

xmin/list returns the lower bound of the list of extended real arguments passed as its arguments. In particular, it returns +inf.0 (the positive infinity) if provided an empty list.

# xmin!

(xmin! <var> <x> ...) -> void

xmin! side-effects a variable to change it to the xmin of the previous value and the provided arguments.

# xmin/map

(xmin/map <f> <l> [<base>]) -> real

Given a list <l> or any thing you can iterate on, and a function <f>, xmin/map returns the lower bound of the images by <f> of the items in <l>, and of a <base> real, by default +inf.0 (the positive infinity). The function is short-circuiting and will not evaluate further values and their side-effects after the bottom value -inf.0 is reached.

# xmax

(xmax <x1> ... <xn>) -> real

xmax returns the upper bound of the set of its extended real arguments. In particular, it returns -inf.0 (the negative infinity) if provided zero arguments, and is the identity function when given a single argument.

# xmax/list

(xmax/list <l>) -> real

xmax/list returns the lower bound of the list of extended real arguments passed as its arguments. In particular, it returns -inf.0 (the negative infinity) if provided an empty list.

# xmax!

(xmax! <var> <x> ...) -> void

xmax! side-effects a variable to change it to the xmax of the previous value and the provided arguments.

# xmax/map

(xmax/map <f> <l> [<base>]) -> real

Given a list <l> or any thing you can iterate on, and a function <f>, xmax/map returns the upper bound of the images by <f> of the items in <l>, and of a <base> xreal, by default -inf.0 (the negative infinity). The function is short-circuiting and will not evaluate further values and their side-effects after the top value +inf.0 is reached.

# increment!, pre-increment!, post-increment!, decrement!, pre-decrement!, post-decrement!

(increment! place) -> (void)
(increment! place increment ...) -> (void)
(pre-increment! place) -> number
(pre-increment! place increment ...) -> number
(post-increment! place) -> number
(post-increment! place increment ...) -> number
(decrement! place) -> (void)
(decrement! place decrement ...) -> (void)
(pre-decrement! place) -> number
(pre-decrement! place decrement ...) -> number
(post-decrement! place) -> number
(post-decrement! place decrement ...) -> number

These macro will modify a variable or other place containing a number to increment (respectively, decrement) its value, adding to it (respectively, subtracting from it) one (if no further argument is specified) or the provided arguments (if specified). increment! and decrement! return #!void, pre-increment! and pre-decrement! return the value after addition (respectively, subtraction), and post-increment! and post-decrement! return the value before addition (respectively, subtraction).

# make-counter

(make-counter) -> counter
(make-counter n) -> counter

This function creates a new counter, a function that takes zero or more arguments, adds the sum of these arguments to the counter (or 1, not 0, if no argument was provided), and returns the original value of the counter before the addition.