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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 )