# Re: numerical conditioning MAGNITUDE and /

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```
On Jun 19, 2006, at 2:47 PM, Aubrey Jaffer wrote:

```
```A correct implementation is:

(define (mag z)
(define c (abs (real-part z)))
(define d (abs (imag-part z)))
(if (< d c)
(* c (sqrt (+ 1 (square (/ d c)))))
(if (zero? d) d (* d (sqrt (+ 1 (square (/ c d))))))))
```
```
This gives the wrong answer on, e.g.,

> (mag +inf.+inf.i)
+nan.

```
And the code's not symmetric in d and c, which it should be, so it's immediately suspect.
```
```
```
(define (div z1 z2)
(define a (real-part z1))
(define b (imag-part z1))
(define c (real-part z2))
(define d (imag-part z2))
(if (< (abs d) (abs c))
(let ((r (/ d c)))
(define den (+ c (* d r)))
(make-rectangular (/ (+ a (* b r)) den)
(/ (- b (* a r)) den)))
(let ((r (/ c d)))
(define den (+ d (* c r)))
(make-rectangular (/ (+ b (* a r)) den)
(/ (- a (* b r)) den)))))
```
```
This code has similar problems with IEEE 754 infinities:

> (div 1.0+0.0i +inf.+inf.i)
+nan.+nan.i

```