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From: mhx@iae.nl (mhx)
Newsgroups: comp.lang.forth
Subject: Re: Complex square root of -1 : zsqrt(-1)
Date: Wed, 28 Aug 2024 21:42:15 +0000
Organization: novaBBS
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On Wed, 28 Aug 2024 19:49:02 +0000, ahmed wrote:

> Another definition for |z|
>
> : |z| ( z: a+ib -- m) ( f: a b--m)
> fover fabs fover fabs ( f: a b |a| |b|)
> fmax                  ( f: a b mx)
> frot frot             ( f: mx a b)
> fover fabs fover fabs fmax ( f: mx a b mx)
> ftuck                      ( f: mx a mx b mx)
> f/                         ( f: mx a mx b/mx)
> fdup f* frot frot          ( f: mx [b/mx]^2 a mx)
> f/ fdup f* f+ fsqrt f* ;

How about
: xpythag ( F: a b -- c )	\ compute sqrt(a^2+b^2) without overflow
	FABS FSWAP FABS FSWAP
	F2DUP F> IF  FOVER ( F: a b a -- ) F/ FSQR F1+ FSQRT  F*  EXIT  ENDIF
	FDUP F0= IF  0e
	       ELSE  FTUCK ( F: b a b -- ) F/ FSQR F1+ FSQRT  F*
	      ENDIF ;

FORTH> 1e-309 0e xpythag +e.  1.0000000000000000000e-0309 ok
FORTH> 1e-319 0e xpythag +e.  9.9999999999999999992e-0320 ok

-marcel