sqrt, isqrt
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
<i><sup>or</sup>→</i> 5.0
(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.
Expanded Reference: sqrt, isqrt
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(sqrt, isqrt )