ToC | DocOverview | CGDoc | RelNotes | Index | PermutedIndex
| Allegro CL

| ANSI Common Lisp 12 Numbers 12.2 Dictionary of Numbers
12.2.38 sqrt, isqrt | Function
  Syntax: sqrt number root isqrt natural natural-root Arguments and Values: number, root - a number. natural, natural-root - a non-negative integer. Description: sqrt and isqrt compute square roots. sqrt returns the principal square root of number. If the number is not a complex but is negative, then the result is a complex. isqrt returns the greatest integer less than or equal to the exact positive square root of natural. If number is a positive rational, it is implementation-dependent whether root is a rational or a float. If number is a negative rational, it is implementation-dependent whether root is a complex rational or a complex float. The mathematical definition of complex square root (whether or not minus zero is supported) follows: `(sqrt x) = (exp (/ (log x) 2))` The branch cut for square root lies along the negative real axis, continuous with quadrant II. The range consists of the right half-plane, including the non-negative imaginary axis and excluding the negative imaginary axis. Examples:
       (sqrt 9.0)  3.0
       (sqrt -9.0)  #C(0.0 3.0)
       (isqrt 9)  3
       (sqrt 12)  3.4641016
       (isqrt 12)  3
       (isqrt 300)  17
       (isqrt 325)  18
       (sqrt 25)
       5
      OR5.0
       (isqrt 25)  5
       (sqrt -1)  #C(0.0 1.0)
       (sqrt #c(0 2))  #C(1.0 1.0)
  Exceptional Situations: The function sqrt should signal type-error if its argument is not a number. The function isqrt should signal type-error if its argument is not a non-negative integer. The functions sqrt and isqrt might signal arithmetic-error. See Also: exp, log, Section 12.1.3.3 Rule of Float Substitutability Notes:
       (isqrt x) ==(values (floor (sqrt x)))
but it is potentially more efficient. Allegro CL Implementation Details: None.

© Franz Inc. All Rights Reserved - File last updated 2022-07-25