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Annotation of Examples/AppKit/Graph/Expression.m, revision 1.1

1.1     ! root        1: /*
        !             2:     Expression.m
        !             3: 
        !             4:     The Expression class is implemented using a grammar generated by the Unix
        !             5:     program yacc, and a lexical scanner generated by the Unix program lex.
        !             6:     The only interface between these parsing modules and this class is the
        !             7:     function _EXPParseExpression, which actually performs the parse.  The
        !             8:     results of the parse are returned in two data structures: a parse tree
        !             9:     representing the expression and a hashtable which holds that variables
        !            10:     found in the expression.
        !            11: 
        !            12:     The parse tree's nodes are Term structs (declared in exprDefs.h).  There
        !            13:     is a node for each piece of the expression.  For example, when the
        !            14:     expression "A+5" is parsed, three nodes result.  The top node of the tree
        !            15:     represents the binary operator "+".  This top node has two subnodes.  The
        !            16:     first subnode represents the variable "A".  The second represents the
        !            17:     integer constant "5".  Since variables can appear more than once in an
        !            18:     expression, their nodes may occur more than once in the parse tree.
        !            19:     
        !            20:     A parse tree is evaluated by doing a depth first traversal of the tree,
        !            21:     bubbling up the results of each sub-tree until the final value rises
        !            22:     to the top.
        !            23: 
        !            24:     You may freely copy, distribute, and reuse the code in this example.
        !            25:     NeXT disclaims any warranty of any kind, expressed or implied, as to its
        !            26:     fitness for any particular use.
        !            27: */
        !            28: 
        !            29: #import "Graph.h"
        !            30: 
        !            31: /* declaration of methods static to this class */
        !            32: @interface Expression(ExpressionPrivate)
        !            33: - (int)_updateResults;
        !            34: - (EXPTermPtr)_addVarTerm:(const char *)name;
        !            35: @end
        !            36: 
        !            37: @implementation Expression
        !            38: 
        !            39: /* function which can be applied to parse tree nodes with applyToTerms() */
        !            40: typedef void ParseTreeFunc(void *info, Term *term);
        !            41: 
        !            42: static void freeContents(Expression *self);
        !            43: static void applyToTerms(Term *t, ParseTreeFunc *func, void *data, int mask);
        !            44: static void updateTerm(void *data, Term *t);
        !            45: static float evalTerm(Term *t, int *indices);
        !            46: static Term *termOfVar(Expression *self, const char *varName);
        !            47: static NXHashTable *makeBuiltInFuncTable(NXZone *zone);
        !            48: static NXHashTable *getBuiltInFuncs(void);
        !            49: static Function *addFuncTerm(NXHashTable *table, const char *name, int min, int max, EXPTermEvalFunc *func);
        !            50: static void safeFree(void **data);
        !            51: static EXPTermEvalFunc sinStub, cosStub, tanStub;
        !            52: static EXPTermEvalFunc asinStub, acosStub, atanStub;
        !            53: static EXPTermEvalFunc expStub, lnStub, sqrtStub, sumStub;
        !            54: static char *termName(const Term *t);
        !            55: static void FunctionFree(const void *info, void *data);
        !            56: static unsigned        VarTermHash(const void *info, const void *data);
        !            57: static int VarTermCompare(const void *info, const void *data1, const void *data2);
        !            58: 
        !            59: /*
        !            60:  * Shared table of built in functions.  All Expressions which haven't had
        !            61:  * any application functions added to them shared this table, which contains
        !            62:  * just the built in functions.
        !            63:  */
        !            64: static NXHashTable *BuiltInFuncTable = NULL;
        !            65: 
        !            66: /* data for a built in function */
        !            67: typedef struct _BuiltInFunc {
        !            68:     const char *name;          /* name of the function */
        !            69:     EXPTermEvalFunc *func;     /* proc to call for evaluation */
        !            70:     int minArgs;
        !            71:     int maxArgs;
        !            72: } BuiltInFunc;
        !            73: 
        !            74: /* table of built in functions */
        !            75: static const BuiltInFunc FuncList[] = {
        !            76:        {"sin", &sinStub, 1, 1},
        !            77:        {"cos", &cosStub, 1, 1},
        !            78:        {"tan", &tanStub, 1, 1},
        !            79:        {"asin", &asinStub, 1, 1},
        !            80:        {"acos", &acosStub, 1, 1},
        !            81:        {"atan", &atanStub, 1, 1},
        !            82:        {"exp", &expStub, 1, 1},
        !            83:        {"ln", &lnStub, 1, 1},
        !            84:        {"sqrt", &sqrtStub, 1, 1},
        !            85:        {"sum", &sumStub, 1, -1}
        !            86: };
        !            87: 
        !            88: #define NUM_BUILTIN_FUNCS      (sizeof(FuncList)/sizeof(BuiltInFunc))
        !            89: 
        !            90: /* prototype used to create hashtables of variable terms */
        !            91: static NXHashTablePrototype VarTermProto = {&VarTermHash, &VarTermCompare, (void (*)(const void *info, void *data))&_EXPFreeTerm, 0};
        !            92: 
        !            93: - init {
        !            94:     [super init];
        !            95:     resolution = 1;
        !            96:     dimensions = 1;
        !            97:     varTerms = NXCreateHashTableFromZone(VarTermProto, 0, NULL, [self zone]);
        !            98:     return self;
        !            99: }
        !           100: 
        !           101: - free {
        !           102:     freeContents(self);
        !           103:   /* if we have a function table and its not the shared one */
        !           104:     if (validFuncs && validFuncs != BuiltInFuncTable)
        !           105:        NXFreeHashTable(validFuncs);
        !           106:     return [super free];
        !           107: }
        !           108: 
        !           109: - (BOOL)parse:(const char *)expressionString {
        !           110:     NXZone *zone;
        !           111: 
        !           112:     zone = [self zone];
        !           113:   /* clear away any results from a previous parse */
        !           114:     freeContents(self);
        !           115:     varTerms = NXCreateHashTableFromZone(VarTermProto, 0, NULL, zone);
        !           116:     resultsValid = NO;
        !           117:     text = NXCopyStringBufferFromZone(expressionString, zone);
        !           118:     if (!validFuncs)
        !           119:        validFuncs = getBuiltInFuncs();
        !           120:     return _EXPParseExpression(text, validFuncs, &parseTree, varTerms, zone);
        !           121: }
        !           122: 
        !           123: - (const char *)text {
        !           124:     return text;
        !           125: }
        !           126: 
        !           127: - setResolution:(int)count {
        !           128:     if (resolution != count) {
        !           129:       /*
        !           130:        * Changing the resolution means we have to recalculate next time
        !           131:        * we're asked for results
        !           132:        */
        !           133:        resultsValid = NO;
        !           134:        resolution = count;
        !           135:     }
        !           136:     return self;
        !           137: }
        !           138: 
        !           139: - (int)resolution {
        !           140:     return resolution;
        !           141: }
        !           142: 
        !           143: - setVar:(const char *)varName value:(float)val {
        !           144:     Term *t;
        !           145: 
        !           146:     t = termOfVar(self, varName);
        !           147:     if (!t)
        !           148:        t = [self _addVarTerm:varName];
        !           149:   /*
        !           150:    * If the term was previously a vector term, we change it to a variable
        !           151:    * term (one that has a single value).
        !           152:    */
        !           153:     if (t->tag == vectorTerm) {
        !           154:        t->tag = varTerm;
        !           155:        safeFree((void **)&t->data.vector.vals);
        !           156:        t->data.var.name = t->data.vector.name;
        !           157:        resultsValid = NO;
        !           158:     }
        !           159:     NX_ASSERT(t->tag == varTerm, "Invalid term type in setVar:value:");
        !           160:     if (t->data.var.val != val) {
        !           161:        t->data.var.val = val;
        !           162:        resultsValid = NO;              /* must recalc after a var is set */
        !           163:     }
        !           164:     return self;
        !           165: }
        !           166: 
        !           167: - (float)varValue:(const char *)varName {
        !           168:     Term *t;
        !           169: 
        !           170:     t = termOfVar(self, varName);
        !           171:     if (t) {
        !           172:        if (t->tag == varTerm)
        !           173:            return t->data.var.val;
        !           174:        else
        !           175:            NX_RAISE(expErrInvalidVarType, self, (void *)varName);
        !           176:     } else
        !           177:        NX_RAISE(expErrInvalidVarName, self, (void *)varName);
        !           178: }
        !           179: 
        !           180: - setVar:(const char *)varName vector:(float *)vals numVals:(int)count {
        !           181:     Term *t;
        !           182: 
        !           183:     resultsValid = NO;
        !           184:     t = termOfVar(self, varName);
        !           185:     if (!t)
        !           186:        t = [self _addVarTerm:varName];
        !           187:   /*
        !           188:    * If the term was previously a non-vector variable, we change it to a
        !           189:    * vector variable term.
        !           190:    */
        !           191:     if (t->tag == varTerm) {
        !           192:        t->tag = vectorTerm;
        !           193:        t->data.vector.name = t->data.var.name;
        !           194:        t->data.vector.hasRange = NO;
        !           195:        t->data.vector.vals = NULL;
        !           196:        t->data.vector.resolution = 0;
        !           197:        t->data.vector.dimension = 0;
        !           198:     }
        !           199:     NX_ASSERT(t->tag == vectorTerm, "Invalid term type in setVar:vector:");
        !           200:     safeFree((void **)&t->data.vector.vals);
        !           201:     t->data.vector.resolution = count;
        !           202:     t->data.vector.vals = vals;
        !           203:     t->data.vector.changed = YES;
        !           204:     resolution = count;
        !           205:     return self;
        !           206: }
        !           207: 
        !           208: - varVector:(const char *)varName vector:(float **)vals numVals:(int *)count {
        !           209:     Term *t;
        !           210: 
        !           211:     t = termOfVar(self, varName);
        !           212:     if (t) {
        !           213:        if (t->tag == vectorTerm) {
        !           214:            updateTerm(self, t);
        !           215:            *count = t->data.vector.resolution;
        !           216:            *vals = t->data.vector.vals;
        !           217:        } else
        !           218:            NX_RAISE(expErrInvalidVarType, self, (void *)varName);
        !           219:     } else
        !           220:        NX_RAISE(expErrInvalidVarName, self, (void *)varName);
        !           221:     return self;
        !           222: }
        !           223: 
        !           224: - setVar:(const char *)varName min:(float)minVal max:(float)maxVal {
        !           225:     Term *t;
        !           226: 
        !           227:     if (minVal > maxVal)
        !           228:        NX_RAISE(expErrMinMax, self, NULL);
        !           229:     t = termOfVar(self, varName);
        !           230:     if (!t)
        !           231:        t = [self _addVarTerm:varName];
        !           232:   /*
        !           233:    * If the term was previously a non-vector variable, we change it to a
        !           234:    * vector variable term.
        !           235:    */
        !           236:     if (t->tag == varTerm) {
        !           237:        t->tag = vectorTerm;
        !           238:        t->data.vector.name = t->data.var.name;
        !           239:        t->data.vector.hasRange = YES;
        !           240:        t->data.vector.vals = NULL;
        !           241:        t->data.vector.changed = YES;
        !           242:        t->data.vector.dimension = 0;
        !           243:     }
        !           244:     NX_ASSERT(t->tag == vectorTerm, "Invalid term type in setVar:min:max:");
        !           245: 
        !           246:   /*
        !           247:    * We optimize and do nothing if the passed values are the same as our
        !           248:    * current values.
        !           249:    */
        !           250:     if (t->data.vector.changed || t->data.vector.min != minVal || t->data.vector.max != maxVal) {
        !           251:        safeFree((void **)&t->data.vector.vals);
        !           252:        t->data.vector.resolution = 0;
        !           253:        t->data.vector.min = minVal;
        !           254:        t->data.vector.max = maxVal;
        !           255:        t->data.vector.changed = YES;
        !           256:        resultsValid = NO;
        !           257:     }    
        !           258:     return self;
        !           259: }
        !           260: 
        !           261: - var:(const char *)varName min:(float *)minVal max:(float *)maxVal {
        !           262:     Term *t;
        !           263: 
        !           264:     t = termOfVar(self, varName);
        !           265:     if (t) {
        !           266:        if (t->tag == vectorTerm) {
        !           267:            updateTerm(self, t);
        !           268:            *minVal = t->data.vector.min;
        !           269:            *maxVal = t->data.vector.max;
        !           270:        } else
        !           271:            NX_RAISE(expErrInvalidVarType, self, (void *)varName);
        !           272:     } else
        !           273:        NX_RAISE(expErrInvalidVarName, self, (void *)varName);
        !           274:     return self;
        !           275: }
        !           276: 
        !           277: - setVar:(const char *)varName dimension:(short)dimensionNum {
        !           278:     Term *t;
        !           279: 
        !           280:     if (dimensionNum < 0 || dimensionNum >= dimensions)
        !           281:        NX_RAISE(expInvalidDimension, self, (void *)varName);
        !           282:     resultsValid = NO;
        !           283:     t = termOfVar(self, varName);
        !           284:     if (!t)
        !           285:        t = [self _addVarTerm:varName];
        !           286:   /*
        !           287:    * If the term was previously a non-vector variable, we change it to a
        !           288:    * vector variable term.
        !           289:    */
        !           290:     if (t->tag == varTerm) {
        !           291:        t->tag = vectorTerm;
        !           292:        t->data.vector.name = t->data.var.name;
        !           293:        t->data.vector.hasRange = YES;
        !           294:        t->data.vector.vals = NULL;
        !           295:        t->data.vector.changed = YES;
        !           296:        t->data.vector.dimension = 0;
        !           297:     }
        !           298:     NX_ASSERT(t->tag == vectorTerm, "Invalid term type in setVar:dimension:");
        !           299:     t->data.vector.dimension = dimensionNum;
        !           300:     return self;
        !           301: }
        !           302: 
        !           303: - var:(const char *)varName dimension:(short *)dimensionNum {
        !           304:     Term *t;
        !           305: 
        !           306:     t = termOfVar(self, varName);
        !           307:     if (t) {
        !           308:        if (t->tag == vectorTerm)
        !           309:            *dimensionNum = t->data.vector.dimension;
        !           310:        else
        !           311:            NX_RAISE(expErrInvalidVarType, self, (void *)varName);
        !           312:     } else
        !           313:        NX_RAISE(expErrInvalidVarName, self, (void *)varName);
        !           314:     return self;
        !           315: }
        !           316: 
        !           317: - (float)resultValue {
        !           318:     [self _updateResults];
        !           319:     return *results;
        !           320: }
        !           321: 
        !           322: - resultsVector:(float **)vals numVals:(int *)count {
        !           323:     *count = [self _updateResults];
        !           324:     *vals = results;
        !           325:     return self;
        !           326: }
        !           327: 
        !           328: - resultsMin:(float *)minVal max:(float *)maxVal {
        !           329:     [self _updateResults];
        !           330:     *minVal = resultsMin;
        !           331:     *maxVal = resultsMax;
        !           332:     return self;
        !           333: }
        !           334: 
        !           335: - setDimensions:(short)count {
        !           336:     if (dimensions != count)
        !           337:        resultsValid = NO;
        !           338:     dimensions = count;
        !           339:     return self;
        !           340: }
        !           341: 
        !           342: - (short)dimensions {
        !           343:     return dimensions;
        !           344: }
        !           345: 
        !           346: /*
        !           347:  * Since the varables are all in a NXHashTable, we just use the NXHashTable
        !           348:  * functions to enumerate through the names of the variables.
        !           349:  */
        !           350: 
        !           351: - (EXPEnumState)beginVariableEnumeration {
        !           352:     NXHashState *state;
        !           353: 
        !           354:     state = NXZoneMalloc([self zone], sizeof(NXHashState));
        !           355:     *state = NXInitHashState(varTerms);
        !           356:     return state;
        !           357: }
        !           358: 
        !           359: - (const char *)nextVariable:(EXPEnumState)state {
        !           360:     const Term *t;
        !           361: 
        !           362:     if (NXNextHashState(varTerms, (NXHashState *)state, (void **)&t))
        !           363:        return termName(t);
        !           364:     else
        !           365:        return NULL;
        !           366: }
        !           367: 
        !           368: - (void)endVariableEnumeration:(EXPEnumState)state {
        !           369:     free(state);
        !           370: }
        !           371: 
        !           372: - addFuncTerm:(const char *)name minArgs:(int)min maxArgs:(int)max
        !           373:                                        evalFunc:(EXPTermEvalFunc *)func {
        !           374:     Function *existingType;
        !           375: 
        !           376:   /*
        !           377:    * If we dont have a function table yet, get one.  If we do have one, but
        !           378:    * its the shared built in table, get a new one that we can safely modify.
        !           379:    */
        !           380:     if (!validFuncs || validFuncs == BuiltInFuncTable)
        !           381:        validFuncs = makeBuiltInFuncTable([self zone]);
        !           382:     existingType = addFuncTerm(validFuncs, name, min, max, func);
        !           383:     if (existingType)
        !           384:        NX_RAISE(expFuncTypeInUse, self, existingType);
        !           385:     return self;
        !           386: }
        !           387: 
        !           388: - removeFuncTerm:(const char *)name {
        !           389:     Function *realFunc;
        !           390:     Function key;
        !           391: 
        !           392:     if (validFuncs) {
        !           393:       /* look up the func term by name in our table of functions */
        !           394:        key.name = (char *)name;
        !           395:        if (realFunc = NXHashGet(validFuncs, &key)) {
        !           396:          /*
        !           397:           * If we are using the shared table of built ins, get a new table
        !           398:           * that we can safely modify (this covers the case of someone
        !           399:           * wishing to remove a built in function, possibly to redefine it).
        !           400:           */
        !           401:            if (validFuncs == BuiltInFuncTable) {
        !           402:                validFuncs = makeBuiltInFuncTable([self zone]);
        !           403:                realFunc = NXHashGet(validFuncs, &key);
        !           404:            }
        !           405:            NXHashRemove(validFuncs, realFunc);
        !           406:            free(realFunc);
        !           407:            return self;
        !           408:        }
        !           409:     }
        !           410:     return self;
        !           411: }
        !           412: 
        !           413: /*
        !           414:  * This is a utililty routine that recursively applies a function to all
        !           415:  * terms of a parse tree. data is a blind pointer that is simply passed
        !           416:  * along through the function call.  The function is only called on terms
        !           417:  * whose type match the given mask.
        !           418:  */
        !           419: static void applyToTerms(Term *t, ParseTreeFunc *func, void *data, int mask) {
        !           420:     int i;
        !           421:     Term **tPtr;
        !           422: 
        !           423:     for (i = t->numSubterms, tPtr = t->subterms; i--; tPtr++)
        !           424:        applyToTerms(*tPtr, func, data, mask);
        !           425:     if (t->tag & mask)
        !           426:        (*func)(data, t);
        !           427: }
        !           428: 
        !           429: /*
        !           430:  * Empties the contents of the Expression.  Since the variable terms can
        !           431:  * exist multiple times in the tree, we first run through the tree and
        !           432:  * free all the nodes except that variable nodes.  Then we free the hash
        !           433:  * table of variable terms, including the terms themselves. 
        !           434:  */
        !           435: static void freeContents(Expression *self) {
        !           436:     safeFree((void **)&self->text);
        !           437:   /* free the non-variable terms */
        !           438:     if (self->parseTree)
        !           439:        applyToTerms(self->parseTree, _EXPFreeTerm, NULL, ~(varTerm|vectorTerm));
        !           440:   /* free the shared variable terms */
        !           441:     NXFreeHashTable(self->varTerms);
        !           442:     safeFree((void **)&self->results);
        !           443: }
        !           444: 
        !           445: /*
        !           446:  * Allocates a new term of the given type, with room for subterms.  The
        !           447:  * subterms themselves follow as a variable number of arguments.  The are
        !           448:  * copied into the subterms list of the new term.
        !           449:  */
        !           450: Term *_EXPAllocTerm(NXZone *zone, TermTag tag, int numSubterms, ...) {
        !           451:     Term *t;
        !           452:     int i;
        !           453:     va_list args;
        !           454: 
        !           455:     t = NXZoneCalloc(zone, sizeof(Term) + (numSubterms-1) * sizeof(Term *), 1);
        !           456:     t->tag = tag;
        !           457:     t->numSubterms = numSubterms;
        !           458:     va_start(args, numSubterms);
        !           459:     for (i = 0; i < numSubterms; i++)
        !           460:        t->subterms[i] = va_arg(args, Term *);
        !           461:     va_end(args);
        !           462:     return t;
        !           463: }
        !           464: 
        !           465: /*
        !           466:  * Frees a term and any associated data.  This routine can be used as the
        !           467:  * free function of a NXHashTable prototype, or as a proc passed to
        !           468:  * applyToTerms().
        !           469:  */
        !           470: void _EXPFreeTerm(void *info, Term *data) {
        !           471:     Term *t = (Term *)data;
        !           472: 
        !           473:     if (t->tag == vectorTerm) {
        !           474:        free(t->data.vector.vals);
        !           475:        free(t->data.vector.name);
        !           476:     } else if (t->tag == varTerm)
        !           477:        free(t->data.var.name);
        !           478:     free(t);
        !           479: }
        !           480: 
        !           481: /*
        !           482:  * Makes sure a term is up to date.  Since terms recalculate any internal
        !           483:  * state lazily, this must be called before making use of a term's value.
        !           484:  * We apply this function recursively to all terms before evaluating an
        !           485:  * Expression, and apply to any term if we are asked to return the values
        !           486:  * held within the term (for example, from -varVector:vector:numVals:).
        !           487:  */
        !           488: static void updateTerm(void *data, Term *t) {
        !           489:     Expression *self = data;
        !           490: 
        !           491:     if (t->tag != vectorTerm)
        !           492:        return;         /* only vector terms require work to stay up to date */
        !           493: 
        !           494:   /* Ensure this term has the same resolution as the rest of the Expression. */ 
        !           495:     if (self->resolution != t->data.vector.resolution) {
        !           496:       /*
        !           497:        * We can change its resolution if we interpolate values for this term
        !           498:        * within a range.  Else if we were passed a list of values for this
        !           499:        * term, its an exception if the resolution is no longer in sync.
        !           500:        */
        !           501:        if (t->data.vector.hasRange) {
        !           502:            safeFree((void **)&t->data.vector.vals);
        !           503:            t->data.vector.vals = NXZoneMalloc([self zone],
        !           504:                                        self->resolution * sizeof(float));
        !           505:            t->data.vector.resolution = self->resolution;
        !           506:            t->data.vector.changed = YES;    /* remember to re-interpolate */
        !           507:        } else
        !           508:            NX_RAISE(expErrResolutionMismatch, self,
        !           509:                                        (void *)t->data.vector.name);
        !           510:     }
        !           511: 
        !           512:     if (t->data.vector.changed) {
        !           513:        if (t->data.vector.hasRange) {
        !           514:          /* interpolate a list of values between min and max */
        !           515:            int i;
        !           516:            float delta;
        !           517:            float *val, *prevVal;
        !           518: 
        !           519:            i = self->resolution - 1;
        !           520:            if (i) {
        !           521:                delta = (t->data.vector.max - t->data.vector.min) / i;
        !           522:                prevVal = t->data.vector.vals;
        !           523:                *prevVal = t->data.vector.min;
        !           524:                val = prevVal + 1;
        !           525:                while (i--)
        !           526:                    *val++ = *prevVal++ + delta;
        !           527:                *(val-1) = t->data.vector.max;  /* to be sure we hit max */
        !           528:            } else
        !           529:                *t->data.vector.vals = t->data.vector.min;
        !           530:        } else {
        !           531:          /* scan the list of values passed in to find the min and max */
        !           532:            int i;
        !           533:            float newMin, newMax;
        !           534:            float *val;
        !           535: 
        !           536:            val = t->data.vector.vals;
        !           537:            newMin = newMax = *val++;
        !           538:            for (i = t->data.vector.resolution; i--; val++) {
        !           539:                if (*val > newMax)
        !           540:                    newMax = *val;
        !           541:                else if (*val < newMin)
        !           542:                    newMin = *val;
        !           543:            }
        !           544:            t->data.vector.min = newMin;
        !           545:            t->data.vector.max = newMax;
        !           546:        }
        !           547:        t->data.vector.changed = NO;    /* we're now up to date */
        !           548:     }
        !           549: }
        !           550: 
        !           551: /*
        !           552:  * Ensures that the results calculated for this Expression are up to date.
        !           553:  * We first make sure all the terms in the parse tree are up to date by
        !           554:  * applying updateTerm() to all of them.  We then evaluate the Expression
        !           555:  * for every n times, depending on the resolution, storing all the results
        !           556:  * and calculating their min and max. 
        !           557:  */
        !           558: - (int)_updateResults {
        !           559: #define MAX_INDICES 10
        !           560:     int i, j;
        !           561:     float *f;
        !           562:     int indicesBuffer[MAX_INDICES];
        !           563:     int *indices = indicesBuffer;
        !           564:     int totalVals;
        !           565:     NXZone *zone = [self zone];
        !           566: 
        !           567:     totalVals = resolution;
        !           568:     for (i = 1; i < dimensions; i++)
        !           569:        totalVals *= resolution;
        !           570:     if (!resultsValid) {
        !           571:        if (parseTree) {
        !           572:            applyToTerms(self->parseTree, updateTerm, self, -1);
        !           573:            safeFree((void **)&results);
        !           574:            results = NXZoneMalloc(zone, sizeof(float) * totalVals);
        !           575:            if (dimensions > MAX_INDICES)
        !           576:                indices = NXZoneMalloc(zone, sizeof(int) * dimensions);
        !           577:            bzero(indices, sizeof(int) * dimensions);
        !           578:            *results = evalTerm(parseTree, indices);
        !           579:            resultsMin = *results;
        !           580:            resultsMax = *results;
        !           581:            for (i = 1, f = results + 1; i < totalVals; i++, f++) {
        !           582: 
        !           583:              /*
        !           584:               * Increment the indices.  The first one always changes.  The
        !           585:               * others change only when the previous one wraps around (like
        !           586:               * an odometer with base = resolution).
        !           587:               */
        !           588:                for (j = 0; j < dimensions; j++) {
        !           589:                    indices[j] = (indices[j] + 1) % resolution;
        !           590:                    if (indices[j])
        !           591:                        break;
        !           592:                }
        !           593: 
        !           594:              /*
        !           595:               * We pass the loop indices down through the evaluation recursion
        !           596:               * so vector terms can know which element of their vectors they
        !           597:               * should use for this evaluation.
        !           598:               */
        !           599:                *f = evalTerm(parseTree, indices);
        !           600:                if (*f > resultsMax)
        !           601:                    resultsMax = *f;
        !           602:                else if (*f < resultsMin)
        !           603:                    resultsMin = *f;
        !           604:            }
        !           605:            if (dimensions > MAX_INDICES)
        !           606:                NXZoneFree(zone, indices);
        !           607:        } else
        !           608:            NX_RAISE(expErrNoText, self, NULL);
        !           609:        resultsValid = YES;
        !           610:     }
        !           611:     return totalVals;
        !           612: }
        !           613: 
        !           614: #define MAX_ARGS       50
        !           615: 
        !           616: /*
        !           617:  * Evaluates a particular term.  In order to evaluate itself, any term with
        !           618:  * subterms must recursively evaluate those first.
        !           619:  */
        !           620: static float evalTerm(Term *t, int *indices) {
        !           621:     float result = 0.0;                /* initted to quiet -Wall */
        !           622:     float base;
        !           623:     float argsBuffer[MAX_ARGS];
        !           624:     float *args;
        !           625:     int i;
        !           626: 
        !           627:     switch (t->tag) {
        !           628:        case constantTerm:
        !           629:            NX_ASSERT(t->numSubterms == 0, "Wrong #subterms in evalTerm");
        !           630:            result = t->data.constant.val;
        !           631:            break;
        !           632:        case varTerm:
        !           633:            NX_ASSERT(t->numSubterms == 0, "Wrong #subterms in evalTerm");
        !           634:            result = t->data.var.val;
        !           635:            break;
        !           636:        case vectorTerm:
        !           637:            NX_ASSERT(t->numSubterms == 0, "Wrong #subterms in evalTerm");
        !           638:            result = t->data.vector.vals[indices[t->data.vector.dimension]];
        !           639:            break;
        !           640:        case binOpTerm:
        !           641:            NX_ASSERT(t->numSubterms == 2 ||
        !           642:                        (t->data.binOp.op == '-' && t->numSubterms == 1),
        !           643:                                        "Wrong #subterms in evalTerm");
        !           644:            switch (t->data.binOp.op) {
        !           645:                case '+':
        !           646:                    result = evalTerm(t->subterms[0], indices) +
        !           647:                                evalTerm(t->subterms[1], indices);
        !           648:                    break;
        !           649:                case '-':
        !           650:                    if (t->numSubterms == 2)
        !           651:                        result = evalTerm(t->subterms[0], indices) -
        !           652:                                        evalTerm(t->subterms[1], indices);
        !           653:                    else
        !           654:                        result = - evalTerm(t->subterms[0], indices);
        !           655:                    break;
        !           656:                case '*':
        !           657:                    result = evalTerm(t->subterms[0], indices) *
        !           658:                                evalTerm(t->subterms[1], indices);
        !           659:                    break;
        !           660:                case '/':
        !           661:                    result = evalTerm(t->subterms[0], indices) /
        !           662:                                evalTerm(t->subterms[1], indices);
        !           663:                    break;
        !           664:                case '%':
        !           665:                    result = (int)rint(evalTerm(t->subterms[0], indices)) %
        !           666:                                (int)rint(evalTerm(t->subterms[1], indices));
        !           667:                    break;
        !           668:                case '^':
        !           669:                  /* optimize for raising to an integral power */
        !           670:                    if (t->subterms[1]->tag == constantTerm &&
        !           671:                                t->subterms[1]->data.constant.isInt &&
        !           672:                                t->subterms[1]->data.constant.val >= 1) {
        !           673:                        result = base = evalTerm(t->subterms[0], indices);
        !           674:                        for (i = t->subterms[1]->data.constant.val; --i; )
        !           675:                            result *= base;
        !           676:                    } else
        !           677:                        result = pow(evalTerm(t->subterms[0], indices),
        !           678:                                        evalTerm(t->subterms[1], indices));
        !           679:                    break;
        !           680:                default:
        !           681:                    NX_ASSERT(FALSE, "Unknown binary op type in evalTerm");
        !           682:            }
        !           683:            break;
        !           684:        case funcTerm:
        !           685:          /*
        !           686:           * For functions, we first ensure we have a large enough buffer
        !           687:           * for the values of all the arguments.  If there are few enough
        !           688:           * arguments, we use a buffer on the stack instead of thrashing
        !           689:           * the heap.  We then buffer up all the results of evaluating
        !           690:           * the arguments, and then pass this array of argument values
        !           691:           * to the proc that we use to evaluate this type of function.
        !           692:           */
        !           693:            if (t->numSubterms > MAX_ARGS)
        !           694:                args = NXZoneMalloc(NXDefaultMallocZone(),
        !           695:                                        sizeof(float) * t->numSubterms);
        !           696:            else
        !           697:                args = argsBuffer;
        !           698:            for (i = 0; i < t->numSubterms; i++)
        !           699:                args[i] = evalTerm(t->subterms[i], indices);
        !           700:            result = t->data.func.type->evalFunc(t->numSubterms, args);
        !           701:            if (t->numSubterms > MAX_ARGS)
        !           702:                NXZoneFree(NXDefaultMallocZone(), args);
        !           703:            break;
        !           704:        default:
        !           705:            NX_ASSERT(FALSE, "Invalid term type in evalTerm");
        !           706:     }
        !           707:     return result;
        !           708: }
        !           709: 
        !           710: /* Utility routine to look up a variable by name in the variable hashtable. */
        !           711: static Term *termOfVar(Expression *self, const char *varName) {
        !           712:     Term key;
        !           713: 
        !           714:     if (self->parseTree) {
        !           715:        key.tag = varTerm;
        !           716:        key.data.var.name = (char *)varName;
        !           717:        return NXHashGet(self->varTerms, &key);
        !           718:     } else
        !           719:        NX_RAISE(expErrNoText, self, NULL);
        !           720: }
        !           721: 
        !           722: /* adds a variable term to the Expressions hashtable of them */
        !           723: - (Term *)_addVarTerm:(const char *)name {
        !           724:     Term *newTerm;
        !           725:     Term *existingTerm;
        !           726: 
        !           727:     newTerm = _EXPAllocTerm([self zone], varTerm, 0);
        !           728:     newTerm->data.var.name = NXCopyStringBufferFromZone(name, [self zone]);
        !           729:     existingTerm = NXHashInsertIfAbsent(varTerms, newTerm);
        !           730:     NX_ASSERT(existingTerm == newTerm, "_addVarTerm: called with existing term");
        !           731:     return newTerm;
        !           732: }
        !           733: 
        !           734: /* frees some storage, NULL'ing out the pointer */
        !           735: static void safeFree(void **data) {
        !           736:     free(*data);
        !           737:     *data = NULL;
        !           738: }
        !           739: 
        !           740: /* free function used in the NXHashTable prototype for functions */
        !           741: static void FunctionFree(const void *info, void *data) {
        !           742:     free(((Function *)data)->name);
        !           743:     free(data);
        !           744: }
        !           745: 
        !           746: /*
        !           747:  * Adds a func term to a HashTable of them.  Returns any existing entry
        !           748:  * with the same name, else NULL.
        !           749:  */
        !           750: static Function *addFuncTerm(NXHashTable *table, const char *name, int min, int max, EXPTermEvalFunc *func) {
        !           751:     Function *newFunc;
        !           752:     Function *existingType;
        !           753: 
        !           754:     newFunc = NXZoneMalloc(NXZoneFromPtr(table), sizeof(Function));
        !           755:     newFunc->name = NXCopyStringBufferFromZone(name, NXZoneFromPtr(table));
        !           756:     newFunc->minArgs = min;
        !           757:     newFunc->maxArgs = max;
        !           758:     newFunc->evalFunc = func;
        !           759:     existingType = NXHashInsertIfAbsent(table, newFunc);
        !           760:     if (existingType != newFunc)
        !           761:        return existingType;
        !           762:     else
        !           763:        return NULL;
        !           764: }
        !           765: 
        !           766: /*
        !           767:  * Returns a global table of all built in functions.  This table is shared
        !           768:  * by expressions that dont have application functions added to them.
        !           769:  */
        !           770: static NXHashTable *getBuiltInFuncs(void) {
        !           771:     if (!BuiltInFuncTable)
        !           772:        BuiltInFuncTable = makeBuiltInFuncTable(NXDefaultMallocZone());
        !           773:     return BuiltInFuncTable;
        !           774: }
        !           775: 
        !           776: /* Returns a new hashtable of all built in functions. */
        !           777: static NXHashTable *makeBuiltInFuncTable(NXZone *zone) {
        !           778:     NXHashTable *table;
        !           779:     NXHashTablePrototype FuncTermProto;
        !           780:     const BuiltInFunc *bif;
        !           781:     int i;
        !           782: 
        !           783:     FuncTermProto = NXStrStructKeyPrototype;
        !           784:     FuncTermProto.free = FunctionFree;
        !           785:     table = NXCreateHashTableFromZone(FuncTermProto, NUM_BUILTIN_FUNCS,
        !           786:                                                                NULL, zone);
        !           787:     for (i = NUM_BUILTIN_FUNCS, bif = FuncList; i--; bif++)
        !           788:        (void)addFuncTerm(table, bif->name, bif->minArgs, bif->maxArgs, bif->func);
        !           789:     return table;
        !           790: }
        !           791: 
        !           792: /* Returns the name of a term. */
        !           793: static char *termName(const Term *t) {
        !           794:     switch (t->tag) {
        !           795:        case varTerm:
        !           796:            return t->data.var.name;
        !           797:        case vectorTerm:
        !           798:            return t->data.vector.name;
        !           799:        default:
        !           800:            NX_ASSERT(FALSE, "Bogus term type in VarTermHash");
        !           801:            return NULL;
        !           802:     }
        !           803: }
        !           804: 
        !           805: /* hashing function for variable terms.  Used in hashtable prototypes. */
        !           806: static unsigned        VarTermHash(const void *info, const void *data) {
        !           807:     return NXStrHash(info, termName(data));
        !           808: }
        !           809: 
        !           810: /* comparison function for variable terms.  Used in hashtable prototypes. */
        !           811: static int VarTermCompare(const void *info, const void *data1, const void *data2) {
        !           812:     return NXStrIsEqual(info, termName(data1), termName(data2));
        !           813: }
        !           814: 
        !           815: @end
        !           816: 
        !           817: /* These procs implement the built in functions */
        !           818: 
        !           819: static float sinStub(int numArgs, float *arg)  { return sin(*arg); }
        !           820: static float cosStub(int numArgs, float *arg)  { return cos(*arg); }
        !           821: static float tanStub(int numArgs, float *arg)  { return tan(*arg); }
        !           822: static float asinStub(int numArgs, float *arg) { return asin(*arg); }
        !           823: static float acosStub(int numArgs, float *arg) { return acos(*arg); }
        !           824: static float atanStub(int numArgs, float *arg) { return atan(*arg); }
        !           825: static float expStub(int numArgs, float *arg)  { return exp(*arg); }
        !           826: static float lnStub(int numArgs, float *arg)   { return log(*arg); }
        !           827: static float sqrtStub(int numArgs, float *arg) { return sqrt(*arg); }
        !           828: 
        !           829: static float sumStub(int numArgs, float *arg) {
        !           830:     float sum = 0.0;
        !           831: 
        !           832:     while (numArgs--)
        !           833:        sum += *arg++;
        !           834:     return sum;
        !           835: }

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