> For the complete documentation index, see [llms.txt](https://www.lisppad.app/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://www.lisppad.app/libraries/lispkit/lispkit-math-util.md).
# (lispkit math util)
Library `(lispkit math util)` implements mathematical utility functions.
***
**(sgn *****x*****)** 
Implements the sign/signum function. Returns -1 if *x* is negative, 0 (or a signed zero, when inexact) if *x* is zero, and 1 if *x* is a positive number. `sgn` fails if *x* is not a real number.
**(numbers *****lo hi*****)** \
\&#xNAN;**(numbers *****lo hi f*****)**\
\&#xNAN;**(numbers *****lo hi guard f*****)**
Returns a list of numbers by iterating from integer *lo* to integer *hi* (both inclusive) and applying function *f* to each integer in the range for which *guard* returns true. The default guard always returns true. The default for *f* is `identity`.
**(sum *****xs*****)**
Returns the sum of all numbers of list *xs*. This procedure fails if there is an element in *xs* which is not a number.
**(product *****xs*****)**
Returns the product of all numbers of list *xs*. This procedure fails if there is an element in *xs* which is not a number.
**(minimum *****xs*****)**
Returns the minimum of all numbers of list *xs*. This procedure fails if there is an element in *xs* which is not a number.
**(maximum *****xs*****)**
Returns the maximum of all numbers of list *xs*. This procedure fails if there is an element in *xs* which is not a number.
**(conjugate *****x*****)**
Conjugates number *x*. For real numbers *x*, `conjugate` returns *x*, otherwise *x* is being returned with the opposite sign for the imaginary part.
**(degrees->radians *****x*****)**
Converts degrees into radians.
**(radians->degrees *****x*****)**
Converts radians into degrees.
**(prime? *****n*****)**
Returns `#t` if integer *n* is a prime number, `#f` otherwise.
**(make-nan *****neg quiet payload*****)**
Returns a NaN whose sign bit is equal to *neg* (`#t` for negative, `#f` for positive), whose quiet bit is equal to *quiet* (`#t` for quiet, `#f` for signaling), and whose payload is the positive exact integer *payload*. It is an error if *payload* is larger than a NaN can hold.
**(nan-negative? *****x*****)**
Returns `#t` if the sign bit of *x* is 1 and `#f` otherwise.
**(nan-quiet? *****x*****)**
Returns `#t` if *x* is a quiet NaN.
**(nan-payload *****x*****)**
Returns the payload bits of floating-point number *x* as a positive exact integer.
**(nan=? *****x y*****)**
Returns `#t` if *x* and *y* have the same sign, quiet bit, and payload; and `#f` otherwise.