1/*
2 * Copyright (c) 2002-2006 Michael Niedermayer <michaelni@gmx.at>
3 * Copyright (c) 2006 Oded Shimon <ods15@ods15.dyndns.org>
4 *
5 * This file is part of FFmpeg.
6 *
7 * FFmpeg is free software; you can redistribute it and/or
8 * modify it under the terms of the GNU Lesser General Public
9 * License as published by the Free Software Foundation; either
10 * version 2.1 of the License, or (at your option) any later version.
11 *
12 * FFmpeg is distributed in the hope that it will be useful,
13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
15 * Lesser General Public License for more details.
16 *
17 * You should have received a copy of the GNU Lesser General Public
18 * License along with FFmpeg; if not, write to the Free Software
19 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
20 */
21
22/**
23 * @file
24 * simple arithmetic expression evaluator.
25 *
26 * see http://joe.hotchkiss.com/programming/eval/eval.html
27 */
28
29#include "libavutil/avutil.h"
30#include "eval.h"
31
32typedef struct Parser{
33    int stack_index;
34    char *s;
35    const double *const_value;
36    const char * const *const_name;          // NULL terminated
37    double (* const *func1)(void *, double a);           // NULL terminated
38    const char * const *func1_name;          // NULL terminated
39    double (* const *func2)(void *, double a, double b); // NULL terminated
40    const char * const *func2_name;          // NULL terminated
41    void *opaque;
42    const char **error;
43#define VARS 10
44    double var[VARS];
45} Parser;
46
47static const int8_t si_prefixes['z' - 'E' + 1]={
48    ['y'-'E']= -24,
49    ['z'-'E']= -21,
50    ['a'-'E']= -18,
51    ['f'-'E']= -15,
52    ['p'-'E']= -12,
53    ['n'-'E']= - 9,
54    ['u'-'E']= - 6,
55    ['m'-'E']= - 3,
56    ['c'-'E']= - 2,
57    ['d'-'E']= - 1,
58    ['h'-'E']=   2,
59    ['k'-'E']=   3,
60    ['K'-'E']=   3,
61    ['M'-'E']=   6,
62    ['G'-'E']=   9,
63    ['T'-'E']=  12,
64    ['P'-'E']=  15,
65    ['E'-'E']=  18,
66    ['Z'-'E']=  21,
67    ['Y'-'E']=  24,
68};
69
70double av_strtod(const char *numstr, char **tail) {
71    double d;
72    char *next;
73    d = strtod(numstr, &next);
74    /* if parsing succeeded, check for and interpret postfixes */
75    if (next!=numstr) {
76
77        if(*next >= 'E' && *next <= 'z'){
78            int e= si_prefixes[*next - 'E'];
79            if(e){
80                if(next[1] == 'i'){
81                    d*= pow( 2, e/0.3);
82                    next+=2;
83                }else{
84                    d*= pow(10, e);
85                    next++;
86                }
87            }
88        }
89
90        if(*next=='B') {
91            d*=8;
92            next++;
93        }
94    }
95    /* if requested, fill in tail with the position after the last parsed
96       character */
97    if (tail)
98        *tail = next;
99    return d;
100}
101
102static int strmatch(const char *s, const char *prefix){
103    int i;
104    for(i=0; prefix[i]; i++){
105        if(prefix[i] != s[i]) return 0;
106    }
107    return 1;
108}
109
110struct AVExpr {
111    enum {
112        e_value, e_const, e_func0, e_func1, e_func2,
113        e_squish, e_gauss, e_ld,
114        e_mod, e_max, e_min, e_eq, e_gt, e_gte,
115        e_pow, e_mul, e_div, e_add,
116        e_last, e_st, e_while,
117    } type;
118    double value; // is sign in other types
119    union {
120        int const_index;
121        double (*func0)(double);
122        double (*func1)(void *, double);
123        double (*func2)(void *, double, double);
124    } a;
125    struct AVExpr *param[2];
126};
127
128static double eval_expr(Parser * p, AVExpr * e) {
129    switch (e->type) {
130        case e_value:  return e->value;
131        case e_const:  return e->value * p->const_value[e->a.const_index];
132        case e_func0:  return e->value * e->a.func0(eval_expr(p, e->param[0]));
133        case e_func1:  return e->value * e->a.func1(p->opaque, eval_expr(p, e->param[0]));
134        case e_func2:  return e->value * e->a.func2(p->opaque, eval_expr(p, e->param[0]), eval_expr(p, e->param[1]));
135        case e_squish: return 1/(1+exp(4*eval_expr(p, e->param[0])));
136        case e_gauss: { double d = eval_expr(p, e->param[0]); return exp(-d*d/2)/sqrt(2*M_PI); }
137        case e_ld:     return e->value * p->var[av_clip(eval_expr(p, e->param[0]), 0, VARS-1)];
138        case e_while: {
139            double d = NAN;
140            while(eval_expr(p, e->param[0]))
141                d=eval_expr(p, e->param[1]);
142            return d;
143        }
144        default: {
145            double d = eval_expr(p, e->param[0]);
146            double d2 = eval_expr(p, e->param[1]);
147            switch (e->type) {
148                case e_mod: return e->value * (d - floor(d/d2)*d2);
149                case e_max: return e->value * (d >  d2 ?   d : d2);
150                case e_min: return e->value * (d <  d2 ?   d : d2);
151                case e_eq:  return e->value * (d == d2 ? 1.0 : 0.0);
152                case e_gt:  return e->value * (d >  d2 ? 1.0 : 0.0);
153                case e_gte: return e->value * (d >= d2 ? 1.0 : 0.0);
154                case e_pow: return e->value * pow(d, d2);
155                case e_mul: return e->value * (d * d2);
156                case e_div: return e->value * (d / d2);
157                case e_add: return e->value * (d + d2);
158                case e_last:return e->value * d2;
159                case e_st : return e->value * (p->var[av_clip(d, 0, VARS-1)]= d2);
160            }
161        }
162    }
163    return NAN;
164}
165
166static AVExpr * parse_expr(Parser *p);
167
168void ff_free_expr(AVExpr * e) {
169    if (!e) return;
170    ff_free_expr(e->param[0]);
171    ff_free_expr(e->param[1]);
172    av_freep(&e);
173}
174
175static AVExpr * parse_primary(Parser *p) {
176    AVExpr * d = av_mallocz(sizeof(AVExpr));
177    char *next= p->s;
178    int i;
179
180    if (!d)
181        return NULL;
182
183    /* number */
184    d->value = av_strtod(p->s, &next);
185    if(next != p->s){
186        d->type = e_value;
187        p->s= next;
188        return d;
189    }
190    d->value = 1;
191
192    /* named constants */
193    for(i=0; p->const_name && p->const_name[i]; i++){
194        if(strmatch(p->s, p->const_name[i])){
195            p->s+= strlen(p->const_name[i]);
196            d->type = e_const;
197            d->a.const_index = i;
198            return d;
199        }
200    }
201
202    p->s= strchr(p->s, '(');
203    if(p->s==NULL){
204        *p->error = "undefined constant or missing (";
205        p->s= next;
206        ff_free_expr(d);
207        return NULL;
208    }
209    p->s++; // "("
210    if (*next == '(') { // special case do-nothing
211        av_freep(&d);
212        d = parse_expr(p);
213        if(p->s[0] != ')'){
214            *p->error = "missing )";
215            ff_free_expr(d);
216            return NULL;
217        }
218        p->s++; // ")"
219        return d;
220    }
221    d->param[0] = parse_expr(p);
222    if(p->s[0]== ','){
223        p->s++; // ","
224        d->param[1] = parse_expr(p);
225    }
226    if(p->s[0] != ')'){
227        *p->error = "missing )";
228        ff_free_expr(d);
229        return NULL;
230    }
231    p->s++; // ")"
232
233    d->type = e_func0;
234         if( strmatch(next, "sinh"  ) ) d->a.func0 = sinh;
235    else if( strmatch(next, "cosh"  ) ) d->a.func0 = cosh;
236    else if( strmatch(next, "tanh"  ) ) d->a.func0 = tanh;
237    else if( strmatch(next, "sin"   ) ) d->a.func0 = sin;
238    else if( strmatch(next, "cos"   ) ) d->a.func0 = cos;
239    else if( strmatch(next, "tan"   ) ) d->a.func0 = tan;
240    else if( strmatch(next, "atan"  ) ) d->a.func0 = atan;
241    else if( strmatch(next, "asin"  ) ) d->a.func0 = asin;
242    else if( strmatch(next, "acos"  ) ) d->a.func0 = acos;
243    else if( strmatch(next, "exp"   ) ) d->a.func0 = exp;
244    else if( strmatch(next, "log"   ) ) d->a.func0 = log;
245    else if( strmatch(next, "abs"   ) ) d->a.func0 = fabs;
246    else if( strmatch(next, "squish") ) d->type = e_squish;
247    else if( strmatch(next, "gauss" ) ) d->type = e_gauss;
248    else if( strmatch(next, "mod"   ) ) d->type = e_mod;
249    else if( strmatch(next, "max"   ) ) d->type = e_max;
250    else if( strmatch(next, "min"   ) ) d->type = e_min;
251    else if( strmatch(next, "eq"    ) ) d->type = e_eq;
252    else if( strmatch(next, "gte"   ) ) d->type = e_gte;
253    else if( strmatch(next, "gt"    ) ) d->type = e_gt;
254    else if( strmatch(next, "lte"   ) ) { AVExpr * tmp = d->param[1]; d->param[1] = d->param[0]; d->param[0] = tmp; d->type = e_gt; }
255    else if( strmatch(next, "lt"    ) ) { AVExpr * tmp = d->param[1]; d->param[1] = d->param[0]; d->param[0] = tmp; d->type = e_gte; }
256    else if( strmatch(next, "ld"    ) ) d->type = e_ld;
257    else if( strmatch(next, "st"    ) ) d->type = e_st;
258    else if( strmatch(next, "while" ) ) d->type = e_while;
259    else {
260        for(i=0; p->func1_name && p->func1_name[i]; i++){
261            if(strmatch(next, p->func1_name[i])){
262                d->a.func1 = p->func1[i];
263                d->type = e_func1;
264                return d;
265            }
266        }
267
268        for(i=0; p->func2_name && p->func2_name[i]; i++){
269            if(strmatch(next, p->func2_name[i])){
270                d->a.func2 = p->func2[i];
271                d->type = e_func2;
272                return d;
273            }
274        }
275
276        *p->error = "unknown function";
277        ff_free_expr(d);
278        return NULL;
279    }
280
281    return d;
282}
283
284static AVExpr * new_eval_expr(int type, int value, AVExpr *p0, AVExpr *p1){
285    AVExpr * e = av_mallocz(sizeof(AVExpr));
286    if (!e)
287        return NULL;
288    e->type     =type   ;
289    e->value    =value  ;
290    e->param[0] =p0     ;
291    e->param[1] =p1     ;
292    return e;
293}
294
295static AVExpr * parse_pow(Parser *p, int *sign){
296    *sign= (*p->s == '+') - (*p->s == '-');
297    p->s += *sign&1;
298    return parse_primary(p);
299}
300
301static AVExpr * parse_factor(Parser *p){
302    int sign, sign2;
303    AVExpr * e = parse_pow(p, &sign);
304    while(p->s[0]=='^'){
305        p->s++;
306        e= new_eval_expr(e_pow, 1, e, parse_pow(p, &sign2));
307        if (!e)
308            return NULL;
309        if (e->param[1]) e->param[1]->value *= (sign2|1);
310    }
311    if (e) e->value *= (sign|1);
312    return e;
313}
314
315static AVExpr * parse_term(Parser *p){
316    AVExpr * e = parse_factor(p);
317    while(p->s[0]=='*' || p->s[0]=='/'){
318        int c= *p->s++;
319        e= new_eval_expr(c == '*' ? e_mul : e_div, 1, e, parse_factor(p));
320        if (!e)
321            return NULL;
322    }
323    return e;
324}
325
326static AVExpr * parse_subexpr(Parser *p) {
327    AVExpr * e = parse_term(p);
328    while(*p->s == '+' || *p->s == '-') {
329        e= new_eval_expr(e_add, 1, e, parse_term(p));
330        if (!e)
331            return NULL;
332    };
333
334    return e;
335}
336
337static AVExpr * parse_expr(Parser *p) {
338    AVExpr * e;
339
340    if(p->stack_index <= 0) //protect against stack overflows
341        return NULL;
342    p->stack_index--;
343
344    e = parse_subexpr(p);
345
346    while(*p->s == ';') {
347        p->s++;
348        e= new_eval_expr(e_last, 1, e, parse_subexpr(p));
349        if (!e)
350            return NULL;
351    };
352
353    p->stack_index++;
354
355    return e;
356}
357
358static int verify_expr(AVExpr * e) {
359    if (!e) return 0;
360    switch (e->type) {
361        case e_value:
362        case e_const: return 1;
363        case e_func0:
364        case e_func1:
365        case e_squish:
366        case e_ld:
367        case e_gauss: return verify_expr(e->param[0]);
368        default: return verify_expr(e->param[0]) && verify_expr(e->param[1]);
369    }
370}
371
372AVExpr *ff_parse_expr(const char *s, const char * const *const_name,
373               double (* const *func1)(void *, double), const char * const *func1_name,
374               double (* const *func2)(void *, double, double), const char * const *func2_name,
375               const char **error){
376    Parser p;
377    AVExpr *e = NULL;
378    char *w = av_malloc(strlen(s) + 1);
379    char *wp = w;
380
381    if (!w)
382        goto end;
383
384    while (*s)
385        if (!isspace(*s++)) *wp++ = s[-1];
386    *wp++ = 0;
387
388    p.stack_index=100;
389    p.s= w;
390    p.const_name = const_name;
391    p.func1      = func1;
392    p.func1_name = func1_name;
393    p.func2      = func2;
394    p.func2_name = func2_name;
395    p.error= error;
396
397    e = parse_expr(&p);
398    if (!verify_expr(e)) {
399        ff_free_expr(e);
400        e = NULL;
401    }
402end:
403    av_free(w);
404    return e;
405}
406
407double ff_eval_expr(AVExpr * e, const double *const_value, void *opaque) {
408    Parser p;
409
410    p.const_value= const_value;
411    p.opaque     = opaque;
412    return eval_expr(&p, e);
413}
414
415double ff_parse_and_eval_expr(const char *s, const double *const_value, const char * const *const_name,
416               double (* const *func1)(void *, double), const char * const *func1_name,
417               double (* const *func2)(void *, double, double), const char * const *func2_name,
418               void *opaque, const char **error){
419    AVExpr * e = ff_parse_expr(s, const_name, func1, func1_name, func2, func2_name, error);
420    double d;
421    if (!e) return NAN;
422    d = ff_eval_expr(e, const_value, opaque);
423    ff_free_expr(e);
424    return d;
425}
426
427#ifdef TEST
428#undef printf
429static double const_values[]={
430    M_PI,
431    M_E,
432    0
433};
434static const char *const_names[]={
435    "PI",
436    "E",
437    0
438};
439int main(void){
440    int i;
441    printf("%f == 12.7\n", ff_parse_and_eval_expr("1+(5-2)^(3-1)+1/2+sin(PI)-max(-2.2,-3.1)", const_values, const_names, NULL, NULL, NULL, NULL, NULL, NULL));
442    printf("%f == 0.931322575\n", ff_parse_and_eval_expr("80G/80Gi", const_values, const_names, NULL, NULL, NULL, NULL, NULL, NULL));
443
444    for(i=0; i<1050; i++){
445        START_TIMER
446            ff_parse_and_eval_expr("1+(5-2)^(3-1)+1/2+sin(PI)-max(-2.2,-3.1)", const_values, const_names, NULL, NULL, NULL, NULL, NULL, NULL);
447        STOP_TIMER("ff_parse_and_eval_expr")
448    }
449    return 0;
450}
451#endif
452