sqrt, flsqrt - principal square root

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LIBRARY

(import (rnrs))                     ;R6RS
(import (rnrs base))                ;R6RS
(import (scheme r5rs))              ;R7RS
(import (scheme inexact))           ;R7RS

SYNOPSIS

(sqrt z)
(flsqrt fl)                         ;R6RS

DESCRIPTION

Rational arguments

For rational z, the result has either positive real part, or zero real part and non-negative imaginary part.

Non-real arguments

Let the value of log z for non-real z be defined in terms of log on real numbers as

log z = log |z| + (angle z)i

The value of (sqrt z) can then be expressed as e**((log z)/2).

Exact arguments

The sqrt procedure may return an inexact result even when given an exact argument.

Flonum variant

flsqrt returns the principal square root of fl. For -0.0 it should return −0.0; for other negative arguments, the result may be a NaN or some unspecified flonum.

IMPLEMENTATION NOTES

Chez Scheme

For exact arguments where the principal square root is an integer, Chez Scheme returns an exact integer.

RETURN VALUES

EXAMPLES

(sqrt 9)         =>  3
(sqrt -1)        =>  +i
(sqrt -5)        =>  0.0+2.23606797749979i ; approximately
(sqrt +inf.0)    =>  +inf.0
(sqrt -inf.0)    =>  +inf.0i
(flsqrt +inf.0)  =>  +inf.0
(flsqrt -0.0)    =>  -0.0

COMPATIBILITY

ERRORS

&assertion (R6RS)

The wrong number of arguments was passed or an argument was outside its domain.

R7RS

The assertions described above are errors. Implementations may signal an error, extend the procedure's domain of definition to include such arguments, or fail catastrophically.

SEE ALSO

STANDARDS

HISTORY

AUTHORS