# Enhancement to %HYPOT

Bug #888410 reported by Robert Smith on 2011-11-10
This bug affects 1 person
Affects Status Importance Assigned to Milestone
Low
Unassigned

### Bug Description

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
:COMPARE-AND-SWAP-VOPS :MULTIPLY-HIGH-VOPS :OS-PROVIDES-DLOPEN
:OS-PROVIDES-BLKSIZE-T :OS-PROVIDES-SUSECONDS-T)

 description: updated
 description: updated
 description: updated
 description: updated description: updated
Paul Khuong (pvk) on 2011-11-11
 Changed in sbcl: status: New → Triaged importance: Undecided → Low assignee: nobody → Paul Khuong (pvk)
 Paul Khuong (pvk) wrote on 2011-11-13: #1

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

 Changed in sbcl: status: Triaged → Fix Committed assignee: Paul Khuong (pvk) → nobody
 Changed in sbcl: status: Fix Committed → Fix Released