Most complex algorithm: <...!oliveb!cirrusl!paul> Paul E. Black	Paul E. Black	CIRRUS LOGIC, Inc.	1463 Centre Pointe Dr.	Milpitas, CA 	95035 	USAJudges notes:	The original source contained a long line which caused many	mailers to barf.  The original file may be re-constructed by	removeing the trailing "\" on line 12 and joining lines 12 and	13 together without a space.	WHAT FOLLOWS IS A DETAILED PROGRAM EXPLINATION AND SPOILER.	IF YOU WANT A REAL CHALLENGE, DON'T READ ANY FURTHER AND TRY	TO UNDERSTAND THE PROGRAM VIA THE SOURCE.Selected notes from the author:	This programs computes and prints Fibonacci numbers by	simulating a Turing machine with the proper program.	Understanding the C program, i.e., a Turing machine simulator,	is only the first and simplest step.  The Turing machine	program must be understood, too!  (it is trivial, perhaps even	natural to write incredibly obscure Turing programs.)	If the program is invoked with an operand, the operand is used	as the Turing program.  It includes a "trace" facility,	subroutine r (commented out for obscurity), to help write and	debug Turing programs.  Just the thing for some fun in a Theory	of Computation class.	The Turing machine tape is represented as a doubly linked list	of pointers.  The forward and backward links are XOR'd together	and stored in one pointer.  If we always keep one of the links	on hand, we can recover the other link at any time.  The	variable q is the scan head (and a pointer at some tape cell),	and p is a "previous" link.  The state of the tape is stored in	the low order bit of the pointer.  Since we always allocate an	even number of bytes, the low order bit carries no information	(see portability below.) Memory representing a tape cell is	allocated when the cell is first scanned.  Thus the simulation	begins with a tape effectively the size of virtual memory set	to all zeros.  Since a header can be added to any Turing	program to write initial data and position the scan head, this	is little loss of generality.	The simulated Turing machine has a single tape with either an 1	or a 0 in each cell.  The Turing machine language format is a	string of three bytes.  The first byte is the current state.	The second byte is the next state.  (The last bit of states is	ignored, e.g., B and C are the same state, in an attempt to be	able to have interesting words in the program.)  The third byte	is composed of bits.  Bit 1 (2&byte) is the symbol scanned,	i.e. an instruction is selected for state and for a match with	the symbol under the scan head.  Bit 2 (4&byte) is the new	symbol to be written to the cell.  Bit 3 (8&byte) is the	direction to move the scan head: 0 for left and 1 for right.	If bit 4 (16&byte) is true, the next character is sent to	stdout.  (I added this feature so programs could print	results.)	The Turing machine has next state 'j' when it begins.  The	cycle is 1) exit if the state is 'x', 2) find the next	instruction (given the state and the character under the scan	head).  [The program string is searched forward for the next	matching instruction.  If the end of the string is reached, the	search begins again at the first of the string.  Thus states	can be used as local labels in different places.]  3) change to	the next state, 4) print a character if indicated, 5) write the	tape symbol, and 6) move the scan head.  The cycle then repeats	with step 1.  A call to the trace routine is just before step	2, but is commented out.	The following ROT13'ed text is a quick outline of the actual	Turing program:		Urer vf n dhvpx bhgyvar bs gur Ghevat cebtenz: gur		cerivbhf naq pheerag Svobanppv ahzoref ner xrcg va onfr		1 sbez jvgu gur pheerag ba gur evtug.  Gur svefg guerr		fgrcf frg hc gur svefg gjb ahzoref, 1 naq 1.  Gura		[ortvaavat jvgu "@ ("] n znexre bs VVV vf perngrq naq		gur pheerag ahzore vf pbcvrq gb gur evtug bs gur		znexre.  Gura [ortvaavat jvgu "BI "] gur ahzore vf		pbairegrq gb ovanel ol ercrngrq qvivqvat ol 2 yrnivat V		sbe erznvaqre 1, naq VV sbe erznvaqre 0.  Arkg		[ortvaavat jvgu "JI "] gur ovanel ercerfragngvba vf		cevagrq naq vgf flzobyf naq gur znexre ner renfrq.		Svanyyl [ortvaavat jvgu "RRa"] gur gjb ahzoref ner		nqqrq naq gur pheerag ahzore pbcvrq gb gur yrsg gb		orpbzr gur cerivbhf.  Gura gur plpyr ercrngf.	The program requires that the lowest bit of a pointer to be 0.	I could have squeezed the program under 1024 bytes without the	trace subroutine, but I felt it was important for understanding	the program.  Besides it is fun to watch the tape zooming back	and forth as the program runs.  A much better debugger or trace	could easily be added.