Re: Complex square root of -1 : zsqrt(-1)

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