Path: utzoo!utgpu!water!watmath!clyde!rutgers!cmcl2!brl-adm!brl-smoke!gwyn
From: gwyn@brl-smoke.ARPA (Doug Gwyn )
Newsgroups: comp.lang.c
Subject: Re: why just a power operator?
Message-ID: <7024@brl-smoke.ARPA>
Date: 11 Jan 88 07:43:48 GMT
References: <3410@megaron.arizona.edu>
Reply-To: gwyn@brl.arpa (Doug Gwyn (VLD/VMB) <gwyn>)
Organization: Ballistic Research Lab (BRL), APG, MD.
Lines: 72

In article <3410@megaron.arizona.edu> gmt@arizona.edu (Gregg Townsend) writes:
>Why is everyone so interested in a power operator compared to, say, 
>square root or logarithm?

Basically, it's because exponentiation involving one or two integers
can usually be done much faster than through use of the floating-point
pow() function, and in the common case **2 can be highly optimized.
Also, as pointed out previously by someone else, pow() fails for
converted integers for which the operation makes perfect sense.

By the way, here is a generic integer-to-integer function written
in "old C" that I sometimes find myself using (since the language
doesn't take care of it for me); it uses the "binary exponent
representation" trick mentioned in eralier messages:

/*
	LPow -- long exponentiation (no overflow detection)

	last edit:	86/06/29	D A Gwyn

	SCCS ID:	@(#)lpow.c	1.3
*/

long
LPow( base, exponent )			/* returns base^exponent */
	register long	base;
	register long	exponent;
	{
	register long	result;		/* result accumulator */

	/* handle simple special cases separately: */

	if ( exponent == 0 )
		return 1;		/* includes 0^0 */
	else if ( base == 0 )
		return 0;		/* exp. < 0 should be EDOM */
	else if ( base == 1 )
		return 1;
	else if ( base == -1 )
#if 0	/* intended code: */
		return exponent % 2 == 0 ? 1 : -1;
#else	/* faster equivalent (suggested by Dan Levy of Teletype): */
		return (exponent & 1) == 0 ? 1 : -1;
#endif
	else if ( exponent < 0 )
		return 0;

	/* general case with exponent > 0: */

	result = 1;

	for ( ; ; )	/* LOOP INVARIANT: result*base^exponent */
		{
#if 0	/* intended code: */
		if ( exponent % 2 != 0 )
#else	/* faster equivalent (suggested by Dan Levy of Teletype): */
		if ( (exponent & 1) != 0 )
#endif
			result *= base;

#if 0	/* intended code: */
		if ( (exponent /= 2) == 0 )
#else	/* faster equivalent (suggested by Dan Levy of Teletype): */
		if ( (exponent >>= 1) == 0 )
#endif
			break;		/* result now stable */

		base *= base;
		}

	return result;
	}