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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