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1
/*
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 * Copyright (c) 2002-2006 Michael Niedermayer <michaelni@gmx.at>
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 * Copyright (c) 2006 Oded Shimon <ods15@ods15.dyndns.org>
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 *
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 * This file is part of FFmpeg.
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 *
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 * FFmpeg is free software; you can redistribute it and/or
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 * modify it under the terms of the GNU Lesser General Public
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 * License as published by the Free Software Foundation; either
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 * version 2.1 of the License, or (at your option) any later version.
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 *
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 * FFmpeg is distributed in the hope that it will be useful,
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 * but WITHOUT ANY WARRANTY; without even the implied warranty of
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 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
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 * Lesser General Public License for more details.
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 *
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 * You should have received a copy of the GNU Lesser General Public
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 * License along with FFmpeg; if not, write to the Free Software
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 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
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 */
21

    
22
/**
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 * @file
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 * simple arithmetic expression evaluator.
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 *
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 * see http://joe.hotchkiss.com/programming/eval/eval.html
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 */
28

    
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#include "libavutil/avutil.h"
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#include "eval.h"
31

    
32
typedef struct Parser {
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    const AVClass *class;
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    int stack_index;
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    char *s;
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    const double *const_values;
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    const char * const *const_names;          // NULL terminated
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    double (* const *funcs1)(void *, double a);           // NULL terminated
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    const char * const *func1_names;          // NULL terminated
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    double (* const *funcs2)(void *, double a, double b); // NULL terminated
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    const char * const *func2_names;          // NULL terminated
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    void *opaque;
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    int log_offset;
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    void *log_ctx;
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#define VARS 10
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    double var[VARS];
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} Parser;
48

    
49
static const AVClass class = { "Eval", av_default_item_name, NULL, LIBAVUTIL_VERSION_INT, offsetof(Parser,log_offset), offsetof(Parser,log_ctx) };
50

    
51
static const int8_t si_prefixes['z' - 'E' + 1] = {
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    ['y'-'E']= -24,
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    ['z'-'E']= -21,
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    ['a'-'E']= -18,
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    ['f'-'E']= -15,
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    ['p'-'E']= -12,
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    ['n'-'E']= - 9,
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    ['u'-'E']= - 6,
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    ['m'-'E']= - 3,
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    ['c'-'E']= - 2,
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    ['d'-'E']= - 1,
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    ['h'-'E']=   2,
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    ['k'-'E']=   3,
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    ['K'-'E']=   3,
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    ['M'-'E']=   6,
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    ['G'-'E']=   9,
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    ['T'-'E']=  12,
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    ['P'-'E']=  15,
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    ['E'-'E']=  18,
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    ['Z'-'E']=  21,
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    ['Y'-'E']=  24,
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};
73

    
74
double av_strtod(const char *numstr, char **tail)
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{
76
    double d;
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    char *next;
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    d = strtod(numstr, &next);
79
    /* if parsing succeeded, check for and interpret postfixes */
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    if (next!=numstr) {
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        if (*next >= 'E' && *next <= 'z') {
82
            int e= si_prefixes[*next - 'E'];
83
            if (e) {
84
                if (next[1] == 'i') {
85
                    d*= pow( 2, e/0.3);
86
                    next+=2;
87
                } else {
88
                    d*= pow(10, e);
89
                    next++;
90
                }
91
            }
92
        }
93

    
94
        if (*next=='B') {
95
            d*=8;
96
            next++;
97
        }
98
    }
99
    /* if requested, fill in tail with the position after the last parsed
100
       character */
101
    if (tail)
102
        *tail = next;
103
    return d;
104
}
105

    
106
#define IS_IDENTIFIER_CHAR(c) ((c) - '0' <= 9U || (c) - 'a' <= 25U || (c) - 'A' <= 25U || (c) == '_')
107

    
108
static int strmatch(const char *s, const char *prefix)
109
{
110
    int i;
111
    for (i=0; prefix[i]; i++) {
112
        if (prefix[i] != s[i]) return 0;
113
    }
114
    /* return 1 only if the s identifier is terminated */
115
    return !IS_IDENTIFIER_CHAR(s[i]);
116
}
117

    
118
struct AVExpr {
119
    enum {
120
        e_value, e_const, e_func0, e_func1, e_func2,
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        e_squish, e_gauss, e_ld, e_isnan,
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        e_mod, e_max, e_min, e_eq, e_gt, e_gte,
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        e_pow, e_mul, e_div, e_add,
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        e_last, e_st, e_while,
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    } type;
126
    double value; // is sign in other types
127
    union {
128
        int const_index;
129
        double (*func0)(double);
130
        double (*func1)(void *, double);
131
        double (*func2)(void *, double, double);
132
    } a;
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    struct AVExpr *param[2];
134
};
135

    
136
static double eval_expr(Parser *p, AVExpr *e)
137
{
138
    switch (e->type) {
139
        case e_value:  return e->value;
140
        case e_const:  return e->value * p->const_values[e->a.const_index];
141
        case e_func0:  return e->value * e->a.func0(eval_expr(p, e->param[0]));
142
        case e_func1:  return e->value * e->a.func1(p->opaque, eval_expr(p, e->param[0]));
143
        case e_func2:  return e->value * e->a.func2(p->opaque, eval_expr(p, e->param[0]), eval_expr(p, e->param[1]));
144
        case e_squish: return 1/(1+exp(4*eval_expr(p, e->param[0])));
145
        case e_gauss: { double d = eval_expr(p, e->param[0]); return exp(-d*d/2)/sqrt(2*M_PI); }
146
        case e_ld:     return e->value * p->var[av_clip(eval_expr(p, e->param[0]), 0, VARS-1)];
147
        case e_isnan:  return e->value * !!isnan(eval_expr(p, e->param[0]));
148
        case e_while: {
149
            double d = NAN;
150
            while (eval_expr(p, e->param[0]))
151
                d=eval_expr(p, e->param[1]);
152
            return d;
153
        }
154
        default: {
155
            double d = eval_expr(p, e->param[0]);
156
            double d2 = eval_expr(p, e->param[1]);
157
            switch (e->type) {
158
                case e_mod: return e->value * (d - floor(d/d2)*d2);
159
                case e_max: return e->value * (d >  d2 ?   d : d2);
160
                case e_min: return e->value * (d <  d2 ?   d : d2);
161
                case e_eq:  return e->value * (d == d2 ? 1.0 : 0.0);
162
                case e_gt:  return e->value * (d >  d2 ? 1.0 : 0.0);
163
                case e_gte: return e->value * (d >= d2 ? 1.0 : 0.0);
164
                case e_pow: return e->value * pow(d, d2);
165
                case e_mul: return e->value * (d * d2);
166
                case e_div: return e->value * (d / d2);
167
                case e_add: return e->value * (d + d2);
168
                case e_last:return e->value * d2;
169
                case e_st : return e->value * (p->var[av_clip(d, 0, VARS-1)]= d2);
170
            }
171
        }
172
    }
173
    return NAN;
174
}
175

    
176
static int parse_expr(AVExpr **e, Parser *p);
177

    
178
void av_expr_free(AVExpr *e)
179
{
180
    if (!e) return;
181
    av_expr_free(e->param[0]);
182
    av_expr_free(e->param[1]);
183
    av_freep(&e);
184
}
185

    
186
static int parse_primary(AVExpr **e, Parser *p)
187
{
188
    AVExpr *d = av_mallocz(sizeof(AVExpr));
189
    char *next = p->s, *s0 = p->s;
190
    int ret, i;
191

    
192
    if (!d)
193
        return AVERROR(ENOMEM);
194

    
195
    /* number */
196
    d->value = av_strtod(p->s, &next);
197
    if (next != p->s) {
198
        d->type = e_value;
199
        p->s= next;
200
        *e = d;
201
        return 0;
202
    }
203
    d->value = 1;
204

    
205
    /* named constants */
206
    for (i=0; p->const_names && p->const_names[i]; i++) {
207
        if (strmatch(p->s, p->const_names[i])) {
208
            p->s+= strlen(p->const_names[i]);
209
            d->type = e_const;
210
            d->a.const_index = i;
211
            *e = d;
212
            return 0;
213
        }
214
    }
215

    
216
    p->s= strchr(p->s, '(');
217
    if (p->s==NULL) {
218
        av_log(p, AV_LOG_ERROR, "Undefined constant or missing '(' in '%s'\n", s0);
219
        p->s= next;
220
        av_expr_free(d);
221
        return AVERROR(EINVAL);
222
    }
223
    p->s++; // "("
224
    if (*next == '(') { // special case do-nothing
225
        av_freep(&d);
226
        if ((ret = parse_expr(&d, p)) < 0)
227
            return ret;
228
        if (p->s[0] != ')') {
229
            av_log(p, AV_LOG_ERROR, "Missing ')' in '%s'\n", s0);
230
            av_expr_free(d);
231
            return AVERROR(EINVAL);
232
        }
233
        p->s++; // ")"
234
        *e = d;
235
        return 0;
236
    }
237
    if ((ret = parse_expr(&(d->param[0]), p)) < 0) {
238
        av_expr_free(d);
239
        return ret;
240
    }
241
    if (p->s[0]== ',') {
242
        p->s++; // ","
243
        parse_expr(&d->param[1], p);
244
    }
245
    if (p->s[0] != ')') {
246
        av_log(p, AV_LOG_ERROR, "Missing ')' or too many args in '%s'\n", s0);
247
        av_expr_free(d);
248
        return AVERROR(EINVAL);
249
    }
250
    p->s++; // ")"
251

    
252
    d->type = e_func0;
253
         if (strmatch(next, "sinh"  )) d->a.func0 = sinh;
254
    else if (strmatch(next, "cosh"  )) d->a.func0 = cosh;
255
    else if (strmatch(next, "tanh"  )) d->a.func0 = tanh;
256
    else if (strmatch(next, "sin"   )) d->a.func0 = sin;
257
    else if (strmatch(next, "cos"   )) d->a.func0 = cos;
258
    else if (strmatch(next, "tan"   )) d->a.func0 = tan;
259
    else if (strmatch(next, "atan"  )) d->a.func0 = atan;
260
    else if (strmatch(next, "asin"  )) d->a.func0 = asin;
261
    else if (strmatch(next, "acos"  )) d->a.func0 = acos;
262
    else if (strmatch(next, "exp"   )) d->a.func0 = exp;
263
    else if (strmatch(next, "log"   )) d->a.func0 = log;
264
    else if (strmatch(next, "abs"   )) d->a.func0 = fabs;
265
    else if (strmatch(next, "squish")) d->type = e_squish;
266
    else if (strmatch(next, "gauss" )) d->type = e_gauss;
267
    else if (strmatch(next, "mod"   )) d->type = e_mod;
268
    else if (strmatch(next, "max"   )) d->type = e_max;
269
    else if (strmatch(next, "min"   )) d->type = e_min;
270
    else if (strmatch(next, "eq"    )) d->type = e_eq;
271
    else if (strmatch(next, "gte"   )) d->type = e_gte;
272
    else if (strmatch(next, "gt"    )) d->type = e_gt;
273
    else if (strmatch(next, "lte"   )) { AVExpr *tmp = d->param[1]; d->param[1] = d->param[0]; d->param[0] = tmp; d->type = e_gt; }
274
    else if (strmatch(next, "lt"    )) { AVExpr *tmp = d->param[1]; d->param[1] = d->param[0]; d->param[0] = tmp; d->type = e_gte; }
275
    else if (strmatch(next, "ld"    )) d->type = e_ld;
276
    else if (strmatch(next, "isnan" )) d->type = e_isnan;
277
    else if (strmatch(next, "st"    )) d->type = e_st;
278
    else if (strmatch(next, "while" )) d->type = e_while;
279
    else {
280
        for (i=0; p->func1_names && p->func1_names[i]; i++) {
281
            if (strmatch(next, p->func1_names[i])) {
282
                d->a.func1 = p->funcs1[i];
283
                d->type = e_func1;
284
                *e = d;
285
                return 0;
286
            }
287
        }
288

    
289
        for (i=0; p->func2_names && p->func2_names[i]; i++) {
290
            if (strmatch(next, p->func2_names[i])) {
291
                d->a.func2 = p->funcs2[i];
292
                d->type = e_func2;
293
                *e = d;
294
                return 0;
295
            }
296
        }
297

    
298
        av_log(p, AV_LOG_ERROR, "Unknown function in '%s'\n", s0);
299
        av_expr_free(d);
300
        return AVERROR(EINVAL);
301
    }
302

    
303
    *e = d;
304
    return 0;
305
}
306

    
307
static AVExpr *new_eval_expr(int type, int value, AVExpr *p0, AVExpr *p1)
308
{
309
    AVExpr *e = av_mallocz(sizeof(AVExpr));
310
    if (!e)
311
        return NULL;
312
    e->type     =type   ;
313
    e->value    =value  ;
314
    e->param[0] =p0     ;
315
    e->param[1] =p1     ;
316
    return e;
317
}
318

    
319
static int parse_pow(AVExpr **e, Parser *p, int *sign)
320
{
321
    *sign= (*p->s == '+') - (*p->s == '-');
322
    p->s += *sign&1;
323
    return parse_primary(e, p);
324
}
325

    
326
static int parse_factor(AVExpr **e, Parser *p)
327
{
328
    int sign, sign2, ret;
329
    AVExpr *e0, *e1, *e2;
330
    if ((ret = parse_pow(&e0, p, &sign)) < 0)
331
        return ret;
332
    while(p->s[0]=='^'){
333
        e1 = e0;
334
        p->s++;
335
        if ((ret = parse_pow(&e2, p, &sign2)) < 0) {
336
            av_expr_free(e1);
337
            return ret;
338
        }
339
        e0 = new_eval_expr(e_pow, 1, e1, e2);
340
        if (!e0) {
341
            av_expr_free(e1);
342
            av_expr_free(e2);
343
            return AVERROR(ENOMEM);
344
        }
345
        if (e0->param[1]) e0->param[1]->value *= (sign2|1);
346
    }
347
    if (e0) e0->value *= (sign|1);
348

    
349
    *e = e0;
350
    return 0;
351
}
352

    
353
static int parse_term(AVExpr **e, Parser *p)
354
{
355
    int ret;
356
    AVExpr *e0, *e1, *e2;
357
    if ((ret = parse_factor(&e0, p)) < 0)
358
        return ret;
359
    while (p->s[0]=='*' || p->s[0]=='/') {
360
        int c= *p->s++;
361
        e1 = e0;
362
        if ((ret = parse_factor(&e2, p)) < 0) {
363
            av_expr_free(e1);
364
            return ret;
365
        }
366
        e0 = new_eval_expr(c == '*' ? e_mul : e_div, 1, e1, e2);
367
        if (!e0) {
368
            av_expr_free(e1);
369
            av_expr_free(e2);
370
            return AVERROR(ENOMEM);
371
        }
372
    }
373
    *e = e0;
374
    return 0;
375
}
376

    
377
static int parse_subexpr(AVExpr **e, Parser *p)
378
{
379
    int ret;
380
    AVExpr *e0, *e1, *e2;
381
    if ((ret = parse_term(&e0, p)) < 0)
382
        return ret;
383
    while (*p->s == '+' || *p->s == '-') {
384
        e1 = e0;
385
        if ((ret = parse_term(&e2, p)) < 0) {
386
            av_expr_free(e1);
387
            return ret;
388
        }
389
        e0 = new_eval_expr(e_add, 1, e1, e2);
390
        if (!e0) {
391
            av_expr_free(e1);
392
            av_expr_free(e2);
393
            return AVERROR(ENOMEM);
394
        }
395
    };
396

    
397
    *e = e0;
398
    return 0;
399
}
400

    
401
static int parse_expr(AVExpr **e, Parser *p)
402
{
403
    int ret;
404
    AVExpr *e0, *e1, *e2;
405
    if (p->stack_index <= 0) //protect against stack overflows
406
        return AVERROR(EINVAL);
407
    p->stack_index--;
408

    
409
    if ((ret = parse_subexpr(&e0, p)) < 0)
410
        return ret;
411
    while (*p->s == ';') {
412
        p->s++;
413
        e1 = e0;
414
        if ((ret = parse_subexpr(&e2, p)) < 0) {
415
            av_expr_free(e1);
416
            return ret;
417
        }
418
        e0 = new_eval_expr(e_last, 1, e1, e2);
419
        if (!e0) {
420
            av_expr_free(e1);
421
            av_expr_free(e2);
422
            return AVERROR(ENOMEM);
423
        }
424
    };
425

    
426
    p->stack_index++;
427
    *e = e0;
428
    return 0;
429
}
430

    
431
static int verify_expr(AVExpr *e)
432
{
433
    if (!e) return 0;
434
    switch (e->type) {
435
        case e_value:
436
        case e_const: return 1;
437
        case e_func0:
438
        case e_func1:
439
        case e_squish:
440
        case e_ld:
441
        case e_gauss:
442
        case e_isnan: return verify_expr(e->param[0]);
443
        default: return verify_expr(e->param[0]) && verify_expr(e->param[1]);
444
    }
445
}
446

    
447
int av_expr_parse(AVExpr **expr, const char *s,
448
                  const char * const *const_names,
449
                  const char * const *func1_names, double (* const *funcs1)(void *, double),
450
                  const char * const *func2_names, double (* const *funcs2)(void *, double, double),
451
                  int log_offset, void *log_ctx)
452
{
453
    Parser p;
454
    AVExpr *e = NULL;
455
    char *w = av_malloc(strlen(s) + 1);
456
    char *wp = w;
457
    const char *s0 = s;
458
    int ret = 0;
459

    
460
    if (!w)
461
        return AVERROR(ENOMEM);
462

    
463
    while (*s)
464
        if (!isspace(*s++)) *wp++ = s[-1];
465
    *wp++ = 0;
466

    
467
    p.class      = &class;
468
    p.stack_index=100;
469
    p.s= w;
470
    p.const_names = const_names;
471
    p.funcs1      = funcs1;
472
    p.func1_names = func1_names;
473
    p.funcs2      = funcs2;
474
    p.func2_names = func2_names;
475
    p.log_offset = log_offset;
476
    p.log_ctx    = log_ctx;
477

    
478
    if ((ret = parse_expr(&e, &p)) < 0)
479
        goto end;
480
    if (*p.s) {
481
        av_log(&p, AV_LOG_ERROR, "Invalid chars '%s' at the end of expression '%s'\n", p.s, s0);
482
        ret = AVERROR(EINVAL);
483
        goto end;
484
    }
485
    if (!verify_expr(e)) {
486
        av_expr_free(e);
487
        ret = AVERROR(EINVAL);
488
        goto end;
489
    }
490
    *expr = e;
491
end:
492
    av_free(w);
493
    return ret;
494
}
495

    
496
double av_expr_eval(AVExpr *e, const double *const_values, void *opaque)
497
{
498
    Parser p;
499

    
500
    p.const_values = const_values;
501
    p.opaque     = opaque;
502
    return eval_expr(&p, e);
503
}
504

    
505
int av_expr_parse_and_eval(double *d, const char *s,
506
                           const char * const *const_names, const double *const_values,
507
                           const char * const *func1_names, double (* const *funcs1)(void *, double),
508
                           const char * const *func2_names, double (* const *funcs2)(void *, double, double),
509
                           void *opaque, int log_offset, void *log_ctx)
510
{
511
    AVExpr *e = NULL;
512
    int ret = av_expr_parse(&e, s, const_names, func1_names, funcs1, func2_names, funcs2, log_offset, log_ctx);
513

    
514
    if (ret < 0) {
515
        *d = NAN;
516
        return ret;
517
    }
518
    *d = av_expr_eval(e, const_values, opaque);
519
    av_expr_free(e);
520
    return isnan(*d) ? AVERROR(EINVAL) : 0;
521
}
522

    
523
#if FF_API_OLD_EVAL_NAMES
524
int av_parse_expr(AVExpr **expr, const char *s,
525
                  const char * const *const_names,
526
                  const char * const *func1_names, double (* const *funcs1)(void *, double),
527
                  const char * const *func2_names, double (* const *funcs2)(void *, double, double),
528
                  int log_offset, void *log_ctx)
529
{
530
    return av_expr_parse(expr, s, const_names, func1_names, funcs1, func2_names, funcs2,
531
                      log_offset, log_ctx);
532
}
533

    
534
double av_eval_expr(AVExpr *e, const double *const_values, void *opaque)
535
{
536
    return av_expr_eval(e, const_values, opaque);
537
}
538

    
539
int av_parse_and_eval_expr(double *res, const char *s,
540
                           const char * const *const_names, const double *const_values,
541
                           const char * const *func1_names, double (* const *funcs1)(void *, double),
542
                           const char * const *func2_names, double (* const *funcs2)(void *, double, double),
543
                           void *opaque, int log_offset, void *log_ctx)
544
{
545
    return av_expr_parse_and_eval(res, s, const_names, const_values, func1_names, funcs1, func2_names, funcs2,
546
                                  opaque, log_offset, log_ctx);
547
}
548

    
549
void av_free_expr(AVExpr *e)
550
{
551
    av_expr_free(e);
552
}
553
#endif /* FF_API_OLD_EVAL_NAMES */
554

    
555
#ifdef TEST
556
#undef printf
557
static double const_values[] = {
558
    M_PI,
559
    M_E,
560
    0
561
};
562

    
563
static const char *const_names[] = {
564
    "PI",
565
    "E",
566
    0
567
};
568

    
569
int main(void)
570
{
571
    int i;
572
    double d;
573
    const char **expr, *exprs[] = {
574
        "",
575
        "1;2",
576
        "-20",
577
        "-PI",
578
        "+PI",
579
        "1+(5-2)^(3-1)+1/2+sin(PI)-max(-2.2,-3.1)",
580
        "80G/80Gi"
581
        "1k",
582
        "1Gi",
583
        "1gi",
584
        "1GiFoo",
585
        "1k+1k",
586
        "1Gi*3foo",
587
        "foo",
588
        "foo(",
589
        "foo()",
590
        "foo)",
591
        "sin",
592
        "sin(",
593
        "sin()",
594
        "sin)",
595
        "sin 10",
596
        "sin(1,2,3)",
597
        "sin(1 )",
598
        "1",
599
        "1foo",
600
        "bar + PI + E + 100f*2 + foo",
601
        "13k + 12f - foo(1, 2)",
602
        "1gi",
603
        "1Gi",
604
        "st(0, 123)",
605
        "st(1, 123); ld(1)",
606
        /* compute 1+2+...+N */
607
        "st(0, 1); while(lte(ld(0), 100), st(1, ld(1)+ld(0));st(0, ld(0)+1)); ld(1)",
608
        /* compute Fib(N) */
609
        "st(1, 1); st(2, 2); st(0, 1); while(lte(ld(0),10), st(3, ld(1)+ld(2)); st(1, ld(2)); st(2, ld(3)); st(0, ld(0)+1)); ld(3)",
610
        "while(0, 10)",
611
        "st(0, 1); while(lte(ld(0),100), st(1, ld(1)+ld(0)); st(0, ld(0)+1))",
612
        "isnan(1)",
613
        "isnan(NAN)",
614
        NULL
615
    };
616

    
617
    for (expr = exprs; *expr; expr++) {
618
        printf("Evaluating '%s'\n", *expr);
619
        av_expr_parse_and_eval(&d, *expr,
620
                               const_names, const_values,
621
                               NULL, NULL, NULL, NULL, NULL, 0, NULL);
622
        printf("'%s' -> %f\n\n", *expr, d);
623
    }
624

    
625
    av_expr_parse_and_eval(&d, "1+(5-2)^(3-1)+1/2+sin(PI)-max(-2.2,-3.1)",
626
                           const_names, const_values,
627
                           NULL, NULL, NULL, NULL, NULL, 0, NULL);
628
    printf("%f == 12.7\n", d);
629
    av_expr_parse_and_eval(&d, "80G/80Gi",
630
                           const_names, const_values,
631
                           NULL, NULL, NULL, NULL, NULL, 0, NULL);
632
    printf("%f == 0.931322575\n", d);
633

    
634
    for (i=0; i<1050; i++) {
635
        START_TIMER
636
            av_expr_parse_and_eval(&d, "1+(5-2)^(3-1)+1/2+sin(PI)-max(-2.2,-3.1)",
637
                                   const_names, const_values,
638
                                   NULL, NULL, NULL, NULL, NULL, 0, NULL);
639
        STOP_TIMER("av_expr_parse_and_eval")
640
    }
641
    return 0;
642
}
643
#endif