Enhancement to %HYPOT

[Robert Smith]

1. Lines 128-134 of `src/code/irrat.lisp` read

#!+win32
(progn
  ;; FIXME: libc hypot "computes the sqrt(x*x+y*y) without undue overflow or underflow"
  ;; ...we just do the stupid simple thing.
  (declaim (inline %hypot))
  (defun %hypot (x y)
    (sqrt (+ (* x x) (* y y)))))

For more accuracy, this can be replaced with

#!+win32
(progn
  ;; This is written in a peculiar way to avoid overflow. Note that in
  ;; sqrt(x^2 + y^2), either square or the sum can overflow.
  ;;
  ;; Without loss of generality, assume |x| >= |y|. Then (y/x)^2 lies
  ;; in the unit interval [0,1], so 1 + (y/x)^2 lies in [1,2]. The
  ;; square root of that lies in [1,1.414] approximately.
  ;;
  ;; Factoring x^2 out of sqrt(x^2 + y^2) gives us the expression
  ;; |x|sqrt(1 + (y/x)^2), which can only overflow if |x| is
  ;; sufficiently large.
  (declaim (inline %hypot))
  (defun %hypot (x y)
    (cond
      ((zerop x) (abs y))
      ((zerop y) (abs x))
      ((= (abs x) (abs y)) (* (abs x) (sqrt 2)))
      (t (progn
           ;; Swap to make quotient in unit interval.
           (when (< (abs x) (abs y))
             (rotatef x y))

           ;; Compute the hypotenuse length.
           (let ((y/x (/ y x)))
             (* (abs x)
                (sqrt (1+ (* y/x y/x))))))))))

2. No real test cases.

3. SBCL 1.0.52

4. Darwin DiapentePomum.local 9.8.0 Darwin Kernel Version 9.8.0: Wed Jul 15 16:57:01 PDT 2009; root:xnu-1228.15.4~1/RELEASE_PPC Power Macintosh

5. (:SWANK :QUICKLISP :SB-BSD-SOCKETS-ADDRINFO :ASDF2 :ASDF :ASDF-UNIX :ANSI-CL
 :COMMON-LISP :SBCL :SB-DOC :SB-TEST :SB-LDB :SB-PACKAGE-LOCKS :SB-UNICODE
 :SB-EVAL :SB-SOURCE-LOCATIONS :IEEE-FLOATING-POINT :PPC :UNIX :MACH-O :BSD
 :DARWIN :GENCGC :STACK-ALLOCATABLE-CLOSURES :STACK-ALLOCATABLE-LISTS
 :LINKAGE-TABLE :RAW-INSTANCE-INIT-VOPS :MEMORY-BARRIER-VOPS
 :COMPARE-AND-SWAP-VOPS :MULTIPLY-HIGH-VOPS :OS-PROVIDES-DLOPEN
 :ALIEN-CALLBACKS :OS-PROVIDES-DLOPEN :OS-PROVIDES-DLADDR :OS-PROVIDES-PUTWC
 :OS-PROVIDES-BLKSIZE-T :OS-PROVIDES-SUSECONDS-T)

[Paul Khuong (pvk)]

Slightly modified and committed in 79c4a7f More numerically stable %hypot (ABS of complex floats) on win32.