-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1

On 19-May-07, at 11:28 PM, Bradley Lucier wrote:

Marc:

The compiler can expand (sqrt x) as

(define (sqrt x) (cond ((##fixnum? x) (if (and (##fixnum.<= 0 x) (or (##not (##fixnum? 4294967296)) ; 32-bit fixnums (##fixnum.<= x 4503599627370496))) (##flonum->fixnum (##flonum.sqrt (##flonum.<-fixnum x))) (##sqrt x))) ((and (##flonum? x) (##flonum.<= 0. x)) (##flonum.sqrt x)) (else (##sqrt x))))

It's very worthwhile for some programs (and some micro-benchmarks ;-).

This definition is incorrect because:

(sqrt 17)

4

You need something like this:

(define (sqrt x) (cond ((##fixnum? x) (if (and (##not (##fixnum.negative? x)) (or (##not (##fixnum? 4294967296)) ;; 32-bit fixnums (##fixnum.<= x 4503599627370496))) (let* ((f (##flonum.sqrt (##flonum.<-fixnum x))) (i (##flonum->fixnum s))) (if (##fixnum.= x (##fixnum.* i i)) i (##sqrt x))) (##sqrt x))) ((and (##flonum? x) (##not (##flonum.negative? x))) (##flonum.sqrt x)) (else (##sqrt x))))

But that's a lot of code! Can you give good examples of where this pays off?

Marc