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Sean Silvad7fb3962012-12-05 00:26:32 +00001============================================================
2Kaleidoscope: Extending the Language: User-defined Operators
3============================================================
4
5.. contents::
6 :local:
7
Sean Silvad7fb3962012-12-05 00:26:32 +00008Chapter 6 Introduction
9======================
10
11Welcome to Chapter 6 of the "`Implementing a language with
12LLVM <index.html>`_" tutorial. At this point in our tutorial, we now
13have a fully functional language that is fairly minimal, but also
14useful. There is still one big problem with it, however. Our language
15doesn't have many useful operators (like division, logical negation, or
16even any comparisons besides less-than).
17
18This chapter of the tutorial takes a wild digression into adding
19user-defined operators to the simple and beautiful Kaleidoscope
20language. This digression now gives us a simple and ugly language in
21some ways, but also a powerful one at the same time. One of the great
22things about creating your own language is that you get to decide what
23is good or bad. In this tutorial we'll assume that it is okay to use
24this as a way to show some interesting parsing techniques.
25
26At the end of this tutorial, we'll run through an example Kaleidoscope
Alex Denisov596e9792015-12-15 20:50:29 +000027application that `renders the Mandelbrot set <#kicking-the-tires>`_. This gives an
Sean Silvad7fb3962012-12-05 00:26:32 +000028example of what you can build with Kaleidoscope and its feature set.
29
30User-defined Operators: the Idea
31================================
32
33The "operator overloading" that we will add to Kaleidoscope is more
Mehdi Aminibb6805d2017-02-11 21:26:52 +000034general than in languages like C++. In C++, you are only allowed to
Sylvestre Ledru843b7512016-08-28 20:29:18 +000035redefine existing operators: you can't programmatically change the
Sean Silvad7fb3962012-12-05 00:26:32 +000036grammar, introduce new operators, change precedence levels, etc. In this
37chapter, we will add this capability to Kaleidoscope, which will let the
38user round out the set of operators that are supported.
39
40The point of going into user-defined operators in a tutorial like this
41is to show the power and flexibility of using a hand-written parser.
42Thus far, the parser we have been implementing uses recursive descent
43for most parts of the grammar and operator precedence parsing for the
Mehdi Aminibb6805d2017-02-11 21:26:52 +000044expressions. See `Chapter 2 <LangImpl2.html>`_ for details. By
45using operator precedence parsing, it is very easy to allow
Sean Silvad7fb3962012-12-05 00:26:32 +000046the programmer to introduce new operators into the grammar: the grammar
47is dynamically extensible as the JIT runs.
48
49The two specific features we'll add are programmable unary operators
50(right now, Kaleidoscope has no unary operators at all) as well as
51binary operators. An example of this is:
52
53::
54
55 # Logical unary not.
56 def unary!(v)
57 if v then
58 0
59 else
60 1;
61
62 # Define > with the same precedence as <.
63 def binary> 10 (LHS RHS)
64 RHS < LHS;
65
66 # Binary "logical or", (note that it does not "short circuit")
67 def binary| 5 (LHS RHS)
68 if LHS then
69 1
70 else if RHS then
71 1
72 else
73 0;
74
75 # Define = with slightly lower precedence than relationals.
76 def binary= 9 (LHS RHS)
77 !(LHS < RHS | LHS > RHS);
78
79Many languages aspire to being able to implement their standard runtime
80library in the language itself. In Kaleidoscope, we can implement
81significant parts of the language in the library!
82
83We will break down implementation of these features into two parts:
84implementing support for user-defined binary operators and adding unary
85operators.
86
87User-defined Binary Operators
88=============================
89
90Adding support for user-defined binary operators is pretty simple with
91our current framework. We'll first add support for the unary/binary
92keywords:
93
94.. code-block:: c++
95
96 enum Token {
97 ...
98 // operators
Lang Hames59b0da82015-08-19 18:15:58 +000099 tok_binary = -11,
100 tok_unary = -12
Sean Silvad7fb3962012-12-05 00:26:32 +0000101 };
102 ...
103 static int gettok() {
104 ...
Lang Hames59b0da82015-08-19 18:15:58 +0000105 if (IdentifierStr == "for")
106 return tok_for;
107 if (IdentifierStr == "in")
108 return tok_in;
109 if (IdentifierStr == "binary")
110 return tok_binary;
111 if (IdentifierStr == "unary")
112 return tok_unary;
Sean Silvad7fb3962012-12-05 00:26:32 +0000113 return tok_identifier;
114
115This just adds lexer support for the unary and binary keywords, like we
Alex Denisov596e9792015-12-15 20:50:29 +0000116did in `previous chapters <LangImpl5.html#lexer-extensions-for-if-then-else>`_. One nice thing
Sean Silvad7fb3962012-12-05 00:26:32 +0000117about our current AST, is that we represent binary operators with full
118generalisation by using their ASCII code as the opcode. For our extended
119operators, we'll use this same representation, so we don't need any new
120AST or parser support.
121
122On the other hand, we have to be able to represent the definitions of
123these new operators, in the "def binary\| 5" part of the function
124definition. In our grammar so far, the "name" for the function
125definition is parsed as the "prototype" production and into the
126``PrototypeAST`` AST node. To represent our new user-defined operators
127as prototypes, we have to extend the ``PrototypeAST`` AST node like
128this:
129
130.. code-block:: c++
131
132 /// PrototypeAST - This class represents the "prototype" for a function,
133 /// which captures its argument names as well as if it is an operator.
134 class PrototypeAST {
135 std::string Name;
136 std::vector<std::string> Args;
Lang Hames09bf4c12015-08-18 18:11:06 +0000137 bool IsOperator;
Sean Silvad7fb3962012-12-05 00:26:32 +0000138 unsigned Precedence; // Precedence if a binary op.
Lang Hames59b0da82015-08-19 18:15:58 +0000139
Sean Silvad7fb3962012-12-05 00:26:32 +0000140 public:
Lang Hames09bf4c12015-08-18 18:11:06 +0000141 PrototypeAST(const std::string &name, std::vector<std::string> Args,
142 bool IsOperator = false, unsigned Prec = 0)
143 : Name(name), Args(std::move(Args)), IsOperator(IsOperator),
144 Precedence(Prec) {}
Sean Silvad7fb3962012-12-05 00:26:32 +0000145
Mehdi Aminibb6805d2017-02-11 21:26:52 +0000146 Function *codegen();
147 const std::string &getName() const { return Name; }
148
Lang Hames09bf4c12015-08-18 18:11:06 +0000149 bool isUnaryOp() const { return IsOperator && Args.size() == 1; }
150 bool isBinaryOp() const { return IsOperator && Args.size() == 2; }
Sean Silvad7fb3962012-12-05 00:26:32 +0000151
152 char getOperatorName() const {
153 assert(isUnaryOp() || isBinaryOp());
Mehdi Aminibb6805d2017-02-11 21:26:52 +0000154 return Name[Name.size() - 1];
Sean Silvad7fb3962012-12-05 00:26:32 +0000155 }
156
157 unsigned getBinaryPrecedence() const { return Precedence; }
Sean Silvad7fb3962012-12-05 00:26:32 +0000158 };
159
160Basically, in addition to knowing a name for the prototype, we now keep
161track of whether it was an operator, and if it was, what precedence
162level the operator is at. The precedence is only used for binary
163operators (as you'll see below, it just doesn't apply for unary
164operators). Now that we have a way to represent the prototype for a
165user-defined operator, we need to parse it:
166
167.. code-block:: c++
168
169 /// prototype
170 /// ::= id '(' id* ')'
171 /// ::= binary LETTER number? (id, id)
Lang Hames09bf4c12015-08-18 18:11:06 +0000172 static std::unique_ptr<PrototypeAST> ParsePrototype() {
Sean Silvad7fb3962012-12-05 00:26:32 +0000173 std::string FnName;
174
175 unsigned Kind = 0; // 0 = identifier, 1 = unary, 2 = binary.
176 unsigned BinaryPrecedence = 30;
177
178 switch (CurTok) {
179 default:
Lang Hamesf9878c52016-03-25 17:33:32 +0000180 return LogErrorP("Expected function name in prototype");
Sean Silvad7fb3962012-12-05 00:26:32 +0000181 case tok_identifier:
182 FnName = IdentifierStr;
183 Kind = 0;
184 getNextToken();
185 break;
186 case tok_binary:
187 getNextToken();
188 if (!isascii(CurTok))
Lang Hamesf9878c52016-03-25 17:33:32 +0000189 return LogErrorP("Expected binary operator");
Sean Silvad7fb3962012-12-05 00:26:32 +0000190 FnName = "binary";
191 FnName += (char)CurTok;
192 Kind = 2;
193 getNextToken();
194
195 // Read the precedence if present.
196 if (CurTok == tok_number) {
197 if (NumVal < 1 || NumVal > 100)
Mehdi Aminibb6805d2017-02-11 21:26:52 +0000198 return LogErrorP("Invalid precedence: must be 1..100");
Sean Silvad7fb3962012-12-05 00:26:32 +0000199 BinaryPrecedence = (unsigned)NumVal;
200 getNextToken();
201 }
202 break;
203 }
204
205 if (CurTok != '(')
Lang Hamesf9878c52016-03-25 17:33:32 +0000206 return LogErrorP("Expected '(' in prototype");
Sean Silvad7fb3962012-12-05 00:26:32 +0000207
208 std::vector<std::string> ArgNames;
209 while (getNextToken() == tok_identifier)
210 ArgNames.push_back(IdentifierStr);
211 if (CurTok != ')')
Lang Hamesf9878c52016-03-25 17:33:32 +0000212 return LogErrorP("Expected ')' in prototype");
Sean Silvad7fb3962012-12-05 00:26:32 +0000213
214 // success.
215 getNextToken(); // eat ')'.
216
217 // Verify right number of names for operator.
218 if (Kind && ArgNames.size() != Kind)
Lang Hamesf9878c52016-03-25 17:33:32 +0000219 return LogErrorP("Invalid number of operands for operator");
Sean Silvad7fb3962012-12-05 00:26:32 +0000220
Lang Hames59b0da82015-08-19 18:15:58 +0000221 return llvm::make_unique<PrototypeAST>(FnName, std::move(ArgNames), Kind != 0,
222 BinaryPrecedence);
Sean Silvad7fb3962012-12-05 00:26:32 +0000223 }
224
225This is all fairly straightforward parsing code, and we have already
226seen a lot of similar code in the past. One interesting part about the
227code above is the couple lines that set up ``FnName`` for binary
228operators. This builds names like "binary@" for a newly defined "@"
Mehdi Aminibb6805d2017-02-11 21:26:52 +0000229operator. It then takes advantage of the fact that symbol names in the
Sean Silvad7fb3962012-12-05 00:26:32 +0000230LLVM symbol table are allowed to have any character in them, including
231embedded nul characters.
232
233The next interesting thing to add, is codegen support for these binary
234operators. Given our current structure, this is a simple addition of a
235default case for our existing binary operator node:
236
237.. code-block:: c++
238
Lang Hames2d789c32015-08-26 03:07:41 +0000239 Value *BinaryExprAST::codegen() {
240 Value *L = LHS->codegen();
241 Value *R = RHS->codegen();
Lang Hames59b0da82015-08-19 18:15:58 +0000242 if (!L || !R)
243 return nullptr;
Sean Silvad7fb3962012-12-05 00:26:32 +0000244
245 switch (Op) {
Lang Hames59b0da82015-08-19 18:15:58 +0000246 case '+':
247 return Builder.CreateFAdd(L, R, "addtmp");
248 case '-':
249 return Builder.CreateFSub(L, R, "subtmp");
250 case '*':
251 return Builder.CreateFMul(L, R, "multmp");
Sean Silvad7fb3962012-12-05 00:26:32 +0000252 case '<':
253 L = Builder.CreateFCmpULT(L, R, "cmptmp");
254 // Convert bool 0/1 to double 0.0 or 1.0
Mehdi Aminibb6805d2017-02-11 21:26:52 +0000255 return Builder.CreateUIToFP(L, Type::getDoubleTy(TheContext),
Sean Silvad7fb3962012-12-05 00:26:32 +0000256 "booltmp");
Lang Hames59b0da82015-08-19 18:15:58 +0000257 default:
258 break;
Sean Silvad7fb3962012-12-05 00:26:32 +0000259 }
260
261 // If it wasn't a builtin binary operator, it must be a user defined one. Emit
262 // a call to it.
Mehdi Aminibb6805d2017-02-11 21:26:52 +0000263 Function *F = getFunction(std::string("binary") + Op);
Sean Silvad7fb3962012-12-05 00:26:32 +0000264 assert(F && "binary operator not found!");
265
266 Value *Ops[2] = { L, R };
267 return Builder.CreateCall(F, Ops, "binop");
268 }
269
270As you can see above, the new code is actually really simple. It just
271does a lookup for the appropriate operator in the symbol table and
272generates a function call to it. Since user-defined operators are just
273built as normal functions (because the "prototype" boils down to a
274function with the right name) everything falls into place.
275
276The final piece of code we are missing, is a bit of top-level magic:
277
278.. code-block:: c++
279
Lang Hames2d789c32015-08-26 03:07:41 +0000280 Function *FunctionAST::codegen() {
Mehdi Aminibb6805d2017-02-11 21:26:52 +0000281 // Transfer ownership of the prototype to the FunctionProtos map, but keep a
282 // reference to it for use below.
283 auto &P = *Proto;
284 FunctionProtos[Proto->getName()] = std::move(Proto);
285 Function *TheFunction = getFunction(P.getName());
Lang Hames59b0da82015-08-19 18:15:58 +0000286 if (!TheFunction)
287 return nullptr;
Sean Silvad7fb3962012-12-05 00:26:32 +0000288
289 // If this is an operator, install it.
Mehdi Aminibb6805d2017-02-11 21:26:52 +0000290 if (P.isBinaryOp())
291 BinopPrecedence[P.getOperatorName()] = P.getBinaryPrecedence();
Sean Silvad7fb3962012-12-05 00:26:32 +0000292
293 // Create a new basic block to start insertion into.
Mehdi Aminibb6805d2017-02-11 21:26:52 +0000294 BasicBlock *BB = BasicBlock::Create(TheContext, "entry", TheFunction);
295 ...
Sean Silvad7fb3962012-12-05 00:26:32 +0000296
297Basically, before codegening a function, if it is a user-defined
298operator, we register it in the precedence table. This allows the binary
299operator parsing logic we already have in place to handle it. Since we
300are working on a fully-general operator precedence parser, this is all
301we need to do to "extend the grammar".
302
303Now we have useful user-defined binary operators. This builds a lot on
304the previous framework we built for other operators. Adding unary
305operators is a bit more challenging, because we don't have any framework
306for it yet - lets see what it takes.
307
308User-defined Unary Operators
309============================
310
311Since we don't currently support unary operators in the Kaleidoscope
312language, we'll need to add everything to support them. Above, we added
313simple support for the 'unary' keyword to the lexer. In addition to
314that, we need an AST node:
315
316.. code-block:: c++
317
318 /// UnaryExprAST - Expression class for a unary operator.
319 class UnaryExprAST : public ExprAST {
320 char Opcode;
Lang Hames09bf4c12015-08-18 18:11:06 +0000321 std::unique_ptr<ExprAST> Operand;
Lang Hames59b0da82015-08-19 18:15:58 +0000322
Sean Silvad7fb3962012-12-05 00:26:32 +0000323 public:
Lang Hames09bf4c12015-08-18 18:11:06 +0000324 UnaryExprAST(char Opcode, std::unique_ptr<ExprAST> Operand)
325 : Opcode(Opcode), Operand(std::move(Operand)) {}
Mehdi Aminibb6805d2017-02-11 21:26:52 +0000326
327 Value *codegen() override;
Sean Silvad7fb3962012-12-05 00:26:32 +0000328 };
329
330This AST node is very simple and obvious by now. It directly mirrors the
331binary operator AST node, except that it only has one child. With this,
332we need to add the parsing logic. Parsing a unary operator is pretty
333simple: we'll add a new function to do it:
334
335.. code-block:: c++
336
337 /// unary
338 /// ::= primary
339 /// ::= '!' unary
Lang Hames09bf4c12015-08-18 18:11:06 +0000340 static std::unique_ptr<ExprAST> ParseUnary() {
Sean Silvad7fb3962012-12-05 00:26:32 +0000341 // If the current token is not an operator, it must be a primary expr.
342 if (!isascii(CurTok) || CurTok == '(' || CurTok == ',')
343 return ParsePrimary();
344
345 // If this is a unary operator, read it.
346 int Opc = CurTok;
347 getNextToken();
Lang Hames09bf4c12015-08-18 18:11:06 +0000348 if (auto Operand = ParseUnary())
Mehdi Aminibb6805d2017-02-11 21:26:52 +0000349 return llvm::make_unique<UnaryExprAST>(Opc, std::move(Operand));
Lang Hames09bf4c12015-08-18 18:11:06 +0000350 return nullptr;
Sean Silvad7fb3962012-12-05 00:26:32 +0000351 }
352
353The grammar we add is pretty straightforward here. If we see a unary
354operator when parsing a primary operator, we eat the operator as a
355prefix and parse the remaining piece as another unary operator. This
356allows us to handle multiple unary operators (e.g. "!!x"). Note that
357unary operators can't have ambiguous parses like binary operators can,
358so there is no need for precedence information.
359
360The problem with this function, is that we need to call ParseUnary from
361somewhere. To do this, we change previous callers of ParsePrimary to
362call ParseUnary instead:
363
364.. code-block:: c++
365
366 /// binoprhs
367 /// ::= ('+' unary)*
Lang Hames09bf4c12015-08-18 18:11:06 +0000368 static std::unique_ptr<ExprAST> ParseBinOpRHS(int ExprPrec,
369 std::unique_ptr<ExprAST> LHS) {
Sean Silvad7fb3962012-12-05 00:26:32 +0000370 ...
371 // Parse the unary expression after the binary operator.
Lang Hames09bf4c12015-08-18 18:11:06 +0000372 auto RHS = ParseUnary();
Lang Hames59b0da82015-08-19 18:15:58 +0000373 if (!RHS)
374 return nullptr;
Sean Silvad7fb3962012-12-05 00:26:32 +0000375 ...
376 }
377 /// expression
378 /// ::= unary binoprhs
379 ///
Lang Hames09bf4c12015-08-18 18:11:06 +0000380 static std::unique_ptr<ExprAST> ParseExpression() {
381 auto LHS = ParseUnary();
Lang Hames59b0da82015-08-19 18:15:58 +0000382 if (!LHS)
383 return nullptr;
Sean Silvad7fb3962012-12-05 00:26:32 +0000384
Lang Hames09bf4c12015-08-18 18:11:06 +0000385 return ParseBinOpRHS(0, std::move(LHS));
Sean Silvad7fb3962012-12-05 00:26:32 +0000386 }
387
388With these two simple changes, we are now able to parse unary operators
389and build the AST for them. Next up, we need to add parser support for
390prototypes, to parse the unary operator prototype. We extend the binary
391operator code above with:
392
393.. code-block:: c++
394
395 /// prototype
396 /// ::= id '(' id* ')'
397 /// ::= binary LETTER number? (id, id)
398 /// ::= unary LETTER (id)
Lang Hames09bf4c12015-08-18 18:11:06 +0000399 static std::unique_ptr<PrototypeAST> ParsePrototype() {
Sean Silvad7fb3962012-12-05 00:26:32 +0000400 std::string FnName;
401
402 unsigned Kind = 0; // 0 = identifier, 1 = unary, 2 = binary.
403 unsigned BinaryPrecedence = 30;
404
405 switch (CurTok) {
406 default:
Lang Hamesf9878c52016-03-25 17:33:32 +0000407 return LogErrorP("Expected function name in prototype");
Sean Silvad7fb3962012-12-05 00:26:32 +0000408 case tok_identifier:
409 FnName = IdentifierStr;
410 Kind = 0;
411 getNextToken();
412 break;
413 case tok_unary:
414 getNextToken();
415 if (!isascii(CurTok))
Lang Hamesf9878c52016-03-25 17:33:32 +0000416 return LogErrorP("Expected unary operator");
Sean Silvad7fb3962012-12-05 00:26:32 +0000417 FnName = "unary";
418 FnName += (char)CurTok;
419 Kind = 1;
420 getNextToken();
421 break;
422 case tok_binary:
423 ...
424
425As with binary operators, we name unary operators with a name that
426includes the operator character. This assists us at code generation
427time. Speaking of, the final piece we need to add is codegen support for
428unary operators. It looks like this:
429
430.. code-block:: c++
431
Lang Hames2d789c32015-08-26 03:07:41 +0000432 Value *UnaryExprAST::codegen() {
433 Value *OperandV = Operand->codegen();
Lang Hames59b0da82015-08-19 18:15:58 +0000434 if (!OperandV)
435 return nullptr;
Sean Silvad7fb3962012-12-05 00:26:32 +0000436
Mehdi Aminibb6805d2017-02-11 21:26:52 +0000437 Function *F = getFunction(std::string("unary") + Opcode);
Lang Hames59b0da82015-08-19 18:15:58 +0000438 if (!F)
Lang Hamesf9878c52016-03-25 17:33:32 +0000439 return LogErrorV("Unknown unary operator");
Sean Silvad7fb3962012-12-05 00:26:32 +0000440
441 return Builder.CreateCall(F, OperandV, "unop");
442 }
443
444This code is similar to, but simpler than, the code for binary
445operators. It is simpler primarily because it doesn't need to handle any
446predefined operators.
447
448Kicking the Tires
449=================
450
451It is somewhat hard to believe, but with a few simple extensions we've
452covered in the last chapters, we have grown a real-ish language. With
453this, we can do a lot of interesting things, including I/O, math, and a
454bunch of other things. For example, we can now add a nice sequencing
455operator (printd is defined to print out the specified value and a
456newline):
457
458::
459
460 ready> extern printd(x);
461 Read extern:
462 declare double @printd(double)
463
464 ready> def binary : 1 (x y) 0; # Low-precedence operator that ignores operands.
Mehdi Aminibb6805d2017-02-11 21:26:52 +0000465 ...
Sean Silvad7fb3962012-12-05 00:26:32 +0000466 ready> printd(123) : printd(456) : printd(789);
467 123.000000
468 456.000000
469 789.000000
470 Evaluated to 0.000000
471
472We can also define a bunch of other "primitive" operations, such as:
473
474::
475
476 # Logical unary not.
477 def unary!(v)
478 if v then
479 0
480 else
481 1;
482
483 # Unary negate.
484 def unary-(v)
485 0-v;
486
487 # Define > with the same precedence as <.
488 def binary> 10 (LHS RHS)
489 RHS < LHS;
490
491 # Binary logical or, which does not short circuit.
492 def binary| 5 (LHS RHS)
493 if LHS then
494 1
495 else if RHS then
496 1
497 else
498 0;
499
500 # Binary logical and, which does not short circuit.
501 def binary& 6 (LHS RHS)
502 if !LHS then
503 0
504 else
505 !!RHS;
506
507 # Define = with slightly lower precedence than relationals.
508 def binary = 9 (LHS RHS)
509 !(LHS < RHS | LHS > RHS);
510
511 # Define ':' for sequencing: as a low-precedence operator that ignores operands
512 # and just returns the RHS.
513 def binary : 1 (x y) y;
514
515Given the previous if/then/else support, we can also define interesting
516functions for I/O. For example, the following prints out a character
517whose "density" reflects the value passed in: the lower the value, the
518denser the character:
519
520::
521
Mehdi Aminibb6805d2017-02-11 21:26:52 +0000522 ready> extern putchard(char);
523 ...
524 ready> def printdensity(d)
Sean Silvad7fb3962012-12-05 00:26:32 +0000525 if d > 8 then
526 putchard(32) # ' '
527 else if d > 4 then
528 putchard(46) # '.'
529 else if d > 2 then
530 putchard(43) # '+'
531 else
532 putchard(42); # '*'
533 ...
534 ready> printdensity(1): printdensity(2): printdensity(3):
535 printdensity(4): printdensity(5): printdensity(9):
536 putchard(10);
537 **++.
538 Evaluated to 0.000000
539
540Based on these simple primitive operations, we can start to define more
Mehdi Aminibb6805d2017-02-11 21:26:52 +0000541interesting things. For example, here's a little function that determines
542the number of iterations it takes for a certain function in the complex
543plane to diverge:
Sean Silvad7fb3962012-12-05 00:26:32 +0000544
545::
546
547 # Determine whether the specific location diverges.
548 # Solve for z = z^2 + c in the complex plane.
Hans Wennborg1d8b31b2016-06-14 16:05:12 +0000549 def mandelconverger(real imag iters creal cimag)
Sean Silvad7fb3962012-12-05 00:26:32 +0000550 if iters > 255 | (real*real + imag*imag > 4) then
551 iters
552 else
Hans Wennborg1d8b31b2016-06-14 16:05:12 +0000553 mandelconverger(real*real - imag*imag + creal,
Sean Silvad7fb3962012-12-05 00:26:32 +0000554 2*real*imag + cimag,
555 iters+1, creal, cimag);
556
557 # Return the number of iterations required for the iteration to escape
Hans Wennborg1d8b31b2016-06-14 16:05:12 +0000558 def mandelconverge(real imag)
559 mandelconverger(real, imag, 0, real, imag);
Sean Silvad7fb3962012-12-05 00:26:32 +0000560
561This "``z = z2 + c``" function is a beautiful little creature that is
562the basis for computation of the `Mandelbrot
563Set <http://en.wikipedia.org/wiki/Mandelbrot_set>`_. Our
564``mandelconverge`` function returns the number of iterations that it
565takes for a complex orbit to escape, saturating to 255. This is not a
566very useful function by itself, but if you plot its value over a
567two-dimensional plane, you can see the Mandelbrot set. Given that we are
568limited to using putchard here, our amazing graphical output is limited,
569but we can whip together something using the density plotter above:
570
571::
572
Hans Wennborg1d8b31b2016-06-14 16:05:12 +0000573 # Compute and plot the mandelbrot set with the specified 2 dimensional range
Sean Silvad7fb3962012-12-05 00:26:32 +0000574 # info.
575 def mandelhelp(xmin xmax xstep ymin ymax ystep)
576 for y = ymin, y < ymax, ystep in (
577 (for x = xmin, x < xmax, xstep in
Hans Wennborg1d8b31b2016-06-14 16:05:12 +0000578 printdensity(mandelconverge(x,y)))
Sean Silvad7fb3962012-12-05 00:26:32 +0000579 : putchard(10)
580 )
581
582 # mandel - This is a convenient helper function for plotting the mandelbrot set
583 # from the specified position with the specified Magnification.
584 def mandel(realstart imagstart realmag imagmag)
585 mandelhelp(realstart, realstart+realmag*78, realmag,
586 imagstart, imagstart+imagmag*40, imagmag);
587
Hans Wennborg1d8b31b2016-06-14 16:05:12 +0000588Given this, we can try plotting out the mandelbrot set! Lets try it out:
Sean Silvad7fb3962012-12-05 00:26:32 +0000589
590::
591
592 ready> mandel(-2.3, -1.3, 0.05, 0.07);
593 *******************************+++++++++++*************************************
594 *************************+++++++++++++++++++++++*******************************
595 **********************+++++++++++++++++++++++++++++****************************
596 *******************+++++++++++++++++++++.. ...++++++++*************************
597 *****************++++++++++++++++++++++.... ...+++++++++***********************
598 ***************+++++++++++++++++++++++..... ...+++++++++*********************
599 **************+++++++++++++++++++++++.... ....+++++++++********************
600 *************++++++++++++++++++++++...... .....++++++++*******************
601 ************+++++++++++++++++++++....... .......+++++++******************
602 ***********+++++++++++++++++++.... ... .+++++++*****************
603 **********+++++++++++++++++....... .+++++++****************
604 *********++++++++++++++........... ...+++++++***************
605 ********++++++++++++............ ...++++++++**************
606 ********++++++++++... .......... .++++++++**************
607 *******+++++++++..... .+++++++++*************
608 *******++++++++...... ..+++++++++*************
609 *******++++++....... ..+++++++++*************
610 *******+++++...... ..+++++++++*************
611 *******.... .... ...+++++++++*************
612 *******.... . ...+++++++++*************
613 *******+++++...... ...+++++++++*************
614 *******++++++....... ..+++++++++*************
615 *******++++++++...... .+++++++++*************
616 *******+++++++++..... ..+++++++++*************
617 ********++++++++++... .......... .++++++++**************
618 ********++++++++++++............ ...++++++++**************
619 *********++++++++++++++.......... ...+++++++***************
620 **********++++++++++++++++........ .+++++++****************
621 **********++++++++++++++++++++.... ... ..+++++++****************
622 ***********++++++++++++++++++++++....... .......++++++++*****************
623 ************+++++++++++++++++++++++...... ......++++++++******************
624 **************+++++++++++++++++++++++.... ....++++++++********************
625 ***************+++++++++++++++++++++++..... ...+++++++++*********************
626 *****************++++++++++++++++++++++.... ...++++++++***********************
627 *******************+++++++++++++++++++++......++++++++*************************
628 *********************++++++++++++++++++++++.++++++++***************************
629 *************************+++++++++++++++++++++++*******************************
630 ******************************+++++++++++++************************************
631 *******************************************************************************
632 *******************************************************************************
633 *******************************************************************************
634 Evaluated to 0.000000
635 ready> mandel(-2, -1, 0.02, 0.04);
636 **************************+++++++++++++++++++++++++++++++++++++++++++++++++++++
637 ***********************++++++++++++++++++++++++++++++++++++++++++++++++++++++++
638 *********************+++++++++++++++++++++++++++++++++++++++++++++++++++++++++.
639 *******************+++++++++++++++++++++++++++++++++++++++++++++++++++++++++...
640 *****************+++++++++++++++++++++++++++++++++++++++++++++++++++++++++.....
641 ***************++++++++++++++++++++++++++++++++++++++++++++++++++++++++........
642 **************++++++++++++++++++++++++++++++++++++++++++++++++++++++...........
643 ************+++++++++++++++++++++++++++++++++++++++++++++++++++++..............
644 ***********++++++++++++++++++++++++++++++++++++++++++++++++++........ .
645 **********++++++++++++++++++++++++++++++++++++++++++++++.............
646 ********+++++++++++++++++++++++++++++++++++++++++++..................
647 *******+++++++++++++++++++++++++++++++++++++++.......................
648 ******+++++++++++++++++++++++++++++++++++...........................
649 *****++++++++++++++++++++++++++++++++............................
650 *****++++++++++++++++++++++++++++...............................
651 ****++++++++++++++++++++++++++...... .........................
652 ***++++++++++++++++++++++++......... ...... ...........
653 ***++++++++++++++++++++++............
654 **+++++++++++++++++++++..............
655 **+++++++++++++++++++................
656 *++++++++++++++++++.................
657 *++++++++++++++++............ ...
658 *++++++++++++++..............
659 *+++....++++................
660 *.......... ...........
661 *
662 *.......... ...........
663 *+++....++++................
664 *++++++++++++++..............
665 *++++++++++++++++............ ...
666 *++++++++++++++++++.................
667 **+++++++++++++++++++................
668 **+++++++++++++++++++++..............
669 ***++++++++++++++++++++++............
670 ***++++++++++++++++++++++++......... ...... ...........
671 ****++++++++++++++++++++++++++...... .........................
672 *****++++++++++++++++++++++++++++...............................
673 *****++++++++++++++++++++++++++++++++............................
674 ******+++++++++++++++++++++++++++++++++++...........................
675 *******+++++++++++++++++++++++++++++++++++++++.......................
676 ********+++++++++++++++++++++++++++++++++++++++++++..................
677 Evaluated to 0.000000
678 ready> mandel(-0.9, -1.4, 0.02, 0.03);
679 *******************************************************************************
680 *******************************************************************************
681 *******************************************************************************
682 **********+++++++++++++++++++++************************************************
683 *+++++++++++++++++++++++++++++++++++++++***************************************
684 +++++++++++++++++++++++++++++++++++++++++++++**********************************
685 ++++++++++++++++++++++++++++++++++++++++++++++++++*****************************
686 ++++++++++++++++++++++++++++++++++++++++++++++++++++++*************************
687 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++**********************
688 +++++++++++++++++++++++++++++++++.........++++++++++++++++++*******************
689 +++++++++++++++++++++++++++++++.... ......+++++++++++++++++++****************
690 +++++++++++++++++++++++++++++....... ........+++++++++++++++++++**************
691 ++++++++++++++++++++++++++++........ ........++++++++++++++++++++************
692 +++++++++++++++++++++++++++......... .. ...+++++++++++++++++++++**********
693 ++++++++++++++++++++++++++........... ....++++++++++++++++++++++********
694 ++++++++++++++++++++++++............. .......++++++++++++++++++++++******
695 +++++++++++++++++++++++............. ........+++++++++++++++++++++++****
696 ++++++++++++++++++++++........... ..........++++++++++++++++++++++***
697 ++++++++++++++++++++........... .........++++++++++++++++++++++*
698 ++++++++++++++++++............ ...........++++++++++++++++++++
699 ++++++++++++++++............... .............++++++++++++++++++
700 ++++++++++++++................. ...............++++++++++++++++
701 ++++++++++++.................. .................++++++++++++++
702 +++++++++.................. .................+++++++++++++
703 ++++++........ . ......... ..++++++++++++
704 ++............ ...... ....++++++++++
705 .............. ...++++++++++
706 .............. ....+++++++++
707 .............. .....++++++++
708 ............. ......++++++++
709 ........... .......++++++++
710 ......... ........+++++++
711 ......... ........+++++++
712 ......... ....+++++++
713 ........ ...+++++++
714 ....... ...+++++++
715 ....+++++++
716 .....+++++++
717 ....+++++++
718 ....+++++++
719 ....+++++++
720 Evaluated to 0.000000
721 ready> ^D
722
723At this point, you may be starting to realize that Kaleidoscope is a
724real and powerful language. It may not be self-similar :), but it can be
725used to plot things that are!
726
727With this, we conclude the "adding user-defined operators" chapter of
728the tutorial. We have successfully augmented our language, adding the
729ability to extend the language in the library, and we have shown how
730this can be used to build a simple but interesting end-user application
731in Kaleidoscope. At this point, Kaleidoscope can build a variety of
732applications that are functional and can call functions with
733side-effects, but it can't actually define and mutate a variable itself.
734
735Strikingly, variable mutation is an important feature of some languages,
736and it is not at all obvious how to `add support for mutable
737variables <LangImpl7.html>`_ without having to add an "SSA construction"
738phase to your front-end. In the next chapter, we will describe how you
739can add variable mutation without building SSA in your front-end.
740
741Full Code Listing
742=================
743
744Here is the complete code listing for our running example, enhanced with
Mehdi Aminibb6805d2017-02-11 21:26:52 +0000745the support for user-defined operators. To build this example, use:
Sean Silvad7fb3962012-12-05 00:26:32 +0000746
747.. code-block:: bash
748
749 # Compile
Eric Christophera8c6a0a2015-01-08 19:07:01 +0000750 clang++ -g toy.cpp `llvm-config --cxxflags --ldflags --system-libs --libs core mcjit native` -O3 -o toy
Sean Silvad7fb3962012-12-05 00:26:32 +0000751 # Run
752 ./toy
753
754On some platforms, you will need to specify -rdynamic or
755-Wl,--export-dynamic when linking. This ensures that symbols defined in
756the main executable are exported to the dynamic linker and so are
757available for symbol resolution at run time. This is not needed if you
758compile your support code into a shared library, although doing that
759will cause problems on Windows.
760
761Here is the code:
762
Logan Chien855b17d2013-06-08 09:03:03 +0000763.. literalinclude:: ../../examples/Kaleidoscope/Chapter6/toy.cpp
764 :language: c++
Sean Silvad7fb3962012-12-05 00:26:32 +0000765
766`Next: Extending the language: mutable variables / SSA
Wilfred Hughes945f43e2016-07-02 17:01:59 +0000767construction <LangImpl07.html>`_
Sean Silvad7fb3962012-12-05 00:26:32 +0000768