Malbolge

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This article is about the programming language. For the eighth circle of hell in Dante's Inferno, see Malebolge.

Malbolge is a public domain esoteric programming language invented by Ben Olmstead in 1998, named after the eighth circle of hell in Dante's Inferno, the Malebolge.

Malbolge was specifically designed to be impossible to write useful programs in. However, weaknesses in this design have been found that make it possible (though still very difficult) to write Malbolge programs in an organized fashion.

Programming in Malbolge

Malbolge was so difficult to understand when it arrived that it took two years for the first Malbolge program to appear. That program was not written by a human being: it was generated by a beam search algorithm designed by Andrew Cooke and implemented in Lisp.^[1]

Later, Lou Scheffer posted a cryptanalysis of Malbolge and provided a program to copy its input to its output.^[2]

Olmstead believed Malbolge to be a linear bounded automaton. There is a discussion about whether one can implement sensible loops in Malbolge — it took many years before the first non-terminating one was introduced. A correct 99 Bottles of Beer program, which deals with non-trivial loops and conditions, was not announced for seven years; the first correct one was by Hisashi Iizawa in 2005.^[3]

"Hello World!" in Malbolge

This Malbolge program displays "Hello World!", with both words capitalized and exclamation mark at the end.

('&%:9]!~}|z2Vxwv-,POqponl$Hjig%eB@@>}=<M:9wv6WsU2T|nm-,jcL(I&%$#"
`CB]V?Tx<uVtT`Rpo3NlF.Jh++FdbCBA@?]!~|4XzyTT43Qsqq(Lnmkj"Fhg${z@>

A significantly shorter version:

(=<`#9]~6ZY32Vx/4Rs+0No-&Jk)"Fh}|Bcy?`=*z]Kw%oG4UUS0/@-ejc(:'8dc

Workings

Malbolge is machine language for a ternary virtual machine, the Malbolge interpreter.

Notes

The standard interpreter and the official specification do not match perfectly.
This is a simplified explanation of the interpreter source code: it omits useless encryption and subtraction steps and introduces an assembly language.

Registers

Malbolge has three registers, a, c, and d. When a program starts, the value of all three registers is zero. c is special: it points to the current instruction.

Pointer notation

d can hold a memory address; [d] is the value stored at that address. [c] is similar.

Memory

The virtual machine has 59049 (3¹⁰) memory locations that can each hold a ten-digit ternary number. Each memory location has an address from 0 to 59048 and can hold a value from 0 to 59048. Incrementing past this limit wraps back to zero.

Before a Malbolge program starts, the first part of memory is filled with the program. All whitespace in the program is ignored and, to make programming more difficult, everything else in the program must start out as one of the instructions below.

The rest of memory is filled by using the crazy operation (see below) on the previous two addresses ([m] = crz [m - 2], [m - 1]). Memory filled this way will repeat every twelve addresses (the individual ternary digits will repeat every three or four addresses, so a group of ternary digits is guaranteed to repeat every twelve).

Instructions

Malbolge has eight instructions. Malbolge figures out which instruction to execute by taking the value at [c], adding the value of c to it, and taking the remainder when this is divided by 94. The final result tells the interpreter what to do:

Instructions
Value of ([c] + c) % 94	Instruction represented	Explanation
4	jmp [d] + 1	The value at [d], plus one, is where Malbolge will jump to and start executing instructions.
5	out a	Prints the value of a, as an ASCII character, to the screen.
23	in a	Inputs a character, as an ASCII code, into a. Newlines or line feeds are both code 10. An end-of-file condition is code 59048.
39	rotr [d] mov a, [d]	Rotates the value at [d] by one ternary digit (0002111112 becomes 2000211111). Stores the result both at [d] and in a.
40	mov d, [d]	Copies the value at [d] to d.
62	crz [d], a mov a, [d]	Does the crazy operation (see below) with the value at [d] and the value of a. Stores the result both at [d] and in a.
68	nop	Does nothing.
81	end	Ends the Malbolge program.
Any other value does the same as 68: nothing. These other values are not allowed in a program while it is being loaded, but are allowed afterwards.

After each instruction is executed, the guilty instruction gets encrypted (see below) so that it won't do the same thing next time, unless a jump just happened. Right after a jump, Malbolge will encrypt the innocent instruction just prior to the one it jumped to instead. Then, the values of both c and d are increased by one and the next instruction is executed.

Crazy^{[citation needed]} operation

For each ternary digit of both inputs, use the following table to get a ternary digit of the result. For example, crz 0001112220, 0120120120 gives 100102221.

*Crazy* operation
crz		Input 2
crz		0	1	2
Input 1	0	1	0	0
	1	1	0	2
	2	2	2	1

Encryption

After an instruction is executed, the value at [c] (without anything added to it) will be replaced with itself mod 94. Then, the result is encrypted with one of the following two equivalent methods.

Method 1

Find the result below. Store the ASCII code of the character below it at [c].

0000000000111111111122222222223333333333444444444455555555556666666666777777777788888888889999
0123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123
----------------------------------------------------------------------------------------------
9m<.TVac`uY*MK'X~xDl}REokN:#?G"i@5z]&gqtyfr$(we4{WP)H-Zn,[%\3dL+Q;>U!pJS72FhOA1CB6v^=I_0/8|jsb

Method 2

Find the result below. Store the encrypted version at [c].

Encryption table
Result	Encrypted	Result	Encrypted	Result	Encrypted	Result	Encrypted	Result	Encrypted
0	57	19	108	38	113	57	91	76	79
1	109	20	125	39	116	58	37	77	65
2	60	21	82	40	121	59	92	78	49
3	46	22	69	41	102	60	51	79	67
4	84	23	111	42	114	61	100	80	66
5	86	24	107	43	36	62	76	81	54
6	97	25	78	44	40	63	43	82	118
7	99	26	58	45	119	64	81	83	94
8	96	27	35	46	101	65	59	84	61
9	117	28	63	47	52	66	62	85	73
10	89	29	71	48	123	67	85	86	95
11	42	30	34	49	87	68	33	87	48
12	77	31	105	50	80	69	112	88	47
13	75	32	64	51	41	70	74	89	56
14	39	33	53	52	72	71	83	90	124
15	88	34	122	53	45	72	55	91	106
16	126	35	93	54	90	73	50	92	115
17	120	36	38	55	110	74	70	93	98
18	68	37	103	56	44	75	104

Cycles in the encryption

Lou Scheffer's cryptanalysis of Malbolge mentions six different cycles in the encryption. They are listed here:

33 ⇒ 53 ⇒ 45 ⇒ 119 ⇒ 78 ⇒ 49 ⇒ 87 ⇒ 48 ⇒ 123 ⇒ 71 ⇒ 83 ⇒ 94 ⇒ 57 ⇒ 91 ⇒ 106 ⇒ 77 ⇒ 65 ⇒ 59 ⇒ 92 ⇒ 115 ⇒ 82 ⇒ 118 ⇒ 107 ⇒ 75 ⇒ 104 ⇒ 89 ⇒ 56 ⇒ 44 ⇒ 40 ⇒ 121 ⇒ 35 ⇒ 93 ⇒ 98 ⇒ 84 ⇒ 61 ⇒ 100 ⇒ 97 ⇒ 46 ⇒ 101 ⇒ 99 ⇒ 86 ⇒ 95 ⇒ 109 ⇒ 88 ⇒ 47 ⇒ 52 ⇒ 72 ⇒ 55 ⇒ 110 ⇒ 126 ⇒ 64 ⇒ 81 ⇒ 54 ⇒ 90 ⇒ 124 ⇒ 34 ⇒ 122 ⇒ 63 ⇒ 43 ⇒ 36 ⇒ 38 ⇒ 113 ⇒ 108 ⇒ 39 ⇒ 116 ⇒ 69 ⇒ 112 ⇒ 68 ⇒ 33 ...
37 ⇒ 103 ⇒ 117 ⇒ 111 ⇒ 120 ⇒ 58 ⇒ 37 ...
41 ⇒ 102 ⇒ 96 ⇒ 60 ⇒ 51 ⇒ 41 ...
42 ⇒ 114 ⇒ 125 ⇒ 105 ⇒ 42 ...
50 ⇒ 80 ⇒ 66 ⇒ 62 ⇒ 76 ⇒ 79 ⇒ 67 ⇒ 85 ⇒ 73 ⇒ 50 ...
70 ⇒ 74 ⇒ 70 ...

These cycles can be used to create loops that do different things each time and that eventually become repetitive. Lou Scheffer used this idea to create a Malbolge program (included in his cryptanalysis linked below) that repeats anything the user inputs.

Variants

Malbolge is not Turing-complete, due to its memory limits. Several attempts have been made to create Turing-complete versions of Malbolge.

Malbolge-T is a theoretical version of Malbolge that resets the input/output stream upon reaching the end, allowing for unbounded programs. Malbolge-T would be backward compatible with Malbolge.^[4]
Malbolge Unshackled is a hopefully Turing-complete variation, allowing for programs of any length. However, due to command variations to allow for values above 257, valid Malbolge programs will not necessarily run correctly in Malbolge Unshackled.^[5]

Popular culture

In an episode of the television series Elementary, a clue written on a coffee order is described as having been written in Malbolge.^[6] (The actual code seems to be the above Hello World! program (first version) with a few variations; i.e. the first Y in the first line, replaced by z, the 6 in the first line replaced by a caret, the single left quotes in the second line replaced with carets, extra characters between the fdb and CBA, a ~ (tilde) replaced by a dash, etc.)

References

↑ "andrew cooke: malbolge "hello world"". Acooke.org. Retrieved 2012-11-06.
↑ Programming in Malbolge. Lscheffer.com (2007-12-11). Retrieved on 2011-11-21.
↑ "Language Malbolge". 99 Bottles of Beer. Retrieved 2012-11-06.
↑ "Introduction to Malbolge, Proving formal Turing completeness".
↑ Malbolge Unshackled – Esolang. Esolangs.org (2010-11-24). Retrieved on 2011-11-21.
↑ "Leviathan". Elementary. Season 1. Episode 10. 2012-12-14. CBS.

External links

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Result	Encrypted	Result	Encrypted	Result	Encrypted	Result	Encrypted	Result	Encrypted
0	57	19	108	38	113	57	91	76	79
1	109	20	125	39	116	58	37	77	65
2	60	21	82	40	121	59	92	78	49
3	46	22	69	41	102	60	51	79	67
4	84	23	111	42	114	61	100	80	66
5	86	24	107	43	36	62	76	81	54
6	97	25	78	44	40	63	43	82	118
7	99	26	58	45	119	64	81	83	94
8	96	27	35	46	101	65	59	84	61
9	117	28	63	47	52	66	62	85	73
10	89	29	71	48	123	67	85	86	95
11	42	30	34	49	87	68	33	87	48
12	77	31	105	50	80	69	112	88	47
13	75	32	64	51	41	70	74	89	56
14	39	33	53	52	72	71	83	90	124
15	88	34	122	53	45	72	55	91	106
16	126	35	93	54	90	73	50	92	115
17	120	36	38	55	110	74	70	93	98
18	68	37	103	56	44	75	104

Result	Encrypted	Result	Encrypted	Result	Encrypted	Result	Encrypted	Result	Encrypted
0	57	19	108	38	113	57	91	76	79
1	109	20	125	39	116	58	37	77	65
2	60	21	82	40	121	59	92	78	49
3	46	22	69	41	102	60	51	79	67
4	84	23	111	42	114	61	100	80	66
5	86	24	107	43	36	62	76	81	54
6	97	25	78	44	40	63	43	82	118
7	99	26	58	45	119	64	81	83	94
8	96	27	35	46	101	65	59	84	61
9	117	28	63	47	52	66	62	85	73
10	89	29	71	48	123	67	85	86	95
11	42	30	34	49	87	68	33	87	48
12	77	31	105	50	80	69	112	88	47
13	75	32	64	51	41	70	74	89	56
14	39	33	53	52	72	71	83	90	124
15	88	34	122	53	45	72	55	91	106
16	126	35	93	54	90	73	50	92	115
17	120	36	38	55	110	74	70	93	98
18	68	37	103	56	44	75	104