1/*
2 * simple arithmetic expression evaluator
3 *
4 * Copyright (c) 2002-2006 Michael Niedermayer <michaelni@gmx.at>
5 * Copyright (c) 2006 Oded Shimon <ods15@ods15.dyndns.org>
6 *
7 * This file is part of FFmpeg.
8 *
9 * FFmpeg is free software; you can redistribute it and/or
10 * modify it under the terms of the GNU Lesser General Public
11 * License as published by the Free Software Foundation; either
12 * version 2.1 of the License, or (at your option) any later version.
13 *
14 * FFmpeg is distributed in the hope that it will be useful,
15 * but WITHOUT ANY WARRANTY; without even the implied warranty of
16 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
17 * Lesser General Public License for more details.
18 *
19 * You should have received a copy of the GNU Lesser General Public
20 * License along with FFmpeg; if not, write to the Free Software
21 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
22 */
23
24/**
25 * @file libavcodec/eval.c
26 * simple arithmetic expression evaluator.
27 *
28 * see http://joe.hotchkiss.com/programming/eval/eval.html
29 */
30
31#include "avcodec.h"
32#include "eval.h"
33
34#include <stdio.h>
35#include <stdlib.h>
36#include <string.h>
37#include <math.h>
38
39#ifndef NAN
40  #define NAN 0.0/0.0
41#endif
42
43#ifndef M_PI
44#define M_PI 3.14159265358979323846
45#endif
46
47typedef struct Parser{
48    int stack_index;
49    char *s;
50    const double *const_value;
51    const char * const *const_name;          // NULL terminated
52    double (**func1)(void *, double a); // NULL terminated
53    const char **func1_name;          // NULL terminated
54    double (**func2)(void *, double a, double b); // NULL terminated
55    const char **func2_name;          // NULL terminated
56    void *opaque;
57    const char **error;
58#define VARS 10
59    double var[VARS];
60} Parser;
61
62static const int8_t si_prefixes['z' - 'E' + 1]={
63    ['y'-'E']= -24,
64    ['z'-'E']= -21,
65    ['a'-'E']= -18,
66    ['f'-'E']= -15,
67    ['p'-'E']= -12,
68    ['n'-'E']= - 9,
69    ['u'-'E']= - 6,
70    ['m'-'E']= - 3,
71    ['c'-'E']= - 2,
72    ['d'-'E']= - 1,
73    ['h'-'E']=   2,
74    ['k'-'E']=   3,
75    ['K'-'E']=   3,
76    ['M'-'E']=   6,
77    ['G'-'E']=   9,
78    ['T'-'E']=  12,
79    ['P'-'E']=  15,
80    ['E'-'E']=  18,
81    ['Z'-'E']=  21,
82    ['Y'-'E']=  24,
83};
84
85/** strtod() function extended with 'k', 'M', 'G', 'ki', 'Mi', 'Gi' and 'B'
86 * postfixes.  This allows using f.e. kB, MiB, G and B as a postfix. This
87 * function assumes that the unit of numbers is bits not bytes.
88 */
89static double av_strtod(const char *name, char **tail) {
90    double d;
91    char *next;
92    d = strtod(name, &next);
93    /* if parsing succeeded, check for and interpret postfixes */
94    if (next!=name) {
95
96        if(*next >= 'E' && *next <= 'z'){
97            int e= si_prefixes[*next - 'E'];
98            if(e){
99                if(next[1] == 'i'){
100                    d*= pow( 2, e/0.3);
101                    next+=2;
102                }else{
103                    d*= pow(10, e);
104                    next++;
105                }
106            }
107        }
108
109        if(*next=='B') {
110            d*=8;
111            next++;
112        }
113    }
114    /* if requested, fill in tail with the position after the last parsed
115       character */
116    if (tail)
117        *tail = next;
118    return d;
119}
120
121static int strmatch(const char *s, const char *prefix){
122    int i;
123    for(i=0; prefix[i]; i++){
124        if(prefix[i] != s[i]) return 0;
125    }
126    return 1;
127}
128
129struct ff_expr_s {
130    enum {
131        e_value, e_const, e_func0, e_func1, e_func2,
132        e_squish, e_gauss, e_ld,
133        e_mod, e_max, e_min, e_eq, e_gt, e_gte,
134        e_pow, e_mul, e_div, e_add,
135        e_last, e_st, e_while,
136    } type;
137    double value; // is sign in other types
138    union {
139        int const_index;
140        double (*func0)(double);
141        double (*func1)(void *, double);
142        double (*func2)(void *, double, double);
143    } a;
144    AVEvalExpr * param[2];
145};
146
147static double eval_expr(Parser * p, AVEvalExpr * e) {
148    switch (e->type) {
149        case e_value:  return e->value;
150        case e_const:  return e->value * p->const_value[e->a.const_index];
151        case e_func0:  return e->value * e->a.func0(eval_expr(p, e->param[0]));
152        case e_func1:  return e->value * e->a.func1(p->opaque, eval_expr(p, e->param[0]));
153        case e_func2:  return e->value * e->a.func2(p->opaque, eval_expr(p, e->param[0]), eval_expr(p, e->param[1]));
154        case e_squish: return 1/(1+exp(4*eval_expr(p, e->param[0])));
155        case e_gauss: { double d = eval_expr(p, e->param[0]); return exp(-d*d/2)/sqrt(2*M_PI); }
156        case e_ld:     return e->value * p->var[av_clip(eval_expr(p, e->param[0]), 0, VARS-1)];
157        case e_while: {
158            double d = NAN;
159            while(eval_expr(p, e->param[0]))
160                d=eval_expr(p, e->param[1]);
161            return d;
162        }
163        default: {
164            double d = eval_expr(p, e->param[0]);
165            double d2 = eval_expr(p, e->param[1]);
166            switch (e->type) {
167                case e_mod: return e->value * (d - floor(d/d2)*d2);
168                case e_max: return e->value * (d >  d2 ?   d : d2);
169                case e_min: return e->value * (d <  d2 ?   d : d2);
170                case e_eq:  return e->value * (d == d2 ? 1.0 : 0.0);
171                case e_gt:  return e->value * (d >  d2 ? 1.0 : 0.0);
172                case e_gte: return e->value * (d >= d2 ? 1.0 : 0.0);
173                case e_pow: return e->value * pow(d, d2);
174                case e_mul: return e->value * (d * d2);
175                case e_div: return e->value * (d / d2);
176                case e_add: return e->value * (d + d2);
177                case e_last:return e->value * d2;
178                case e_st : return e->value * (p->var[av_clip(d, 0, VARS-1)]= d2);
179            }
180        }
181    }
182    return NAN;
183}
184
185static AVEvalExpr * parse_expr(Parser *p);
186
187void ff_eval_free(AVEvalExpr * e) {
188    if (!e) return;
189    ff_eval_free(e->param[0]);
190    ff_eval_free(e->param[1]);
191    av_freep(&e);
192}
193
194static AVEvalExpr * parse_primary(Parser *p) {
195    AVEvalExpr * d = av_mallocz(sizeof(AVEvalExpr));
196    char *next= p->s;
197    int i;
198
199    /* number */
200    d->value = av_strtod(p->s, &next);
201    if(next != p->s){
202        d->type = e_value;
203        p->s= next;
204        return d;
205    }
206    d->value = 1;
207
208    /* named constants */
209    for(i=0; p->const_name && p->const_name[i]; i++){
210        if(strmatch(p->s, p->const_name[i])){
211            p->s+= strlen(p->const_name[i]);
212            d->type = e_const;
213            d->a.const_index = i;
214            return d;
215        }
216    }
217
218    p->s= strchr(p->s, '(');
219    if(p->s==NULL){
220        *p->error = "undefined constant or missing (";
221        p->s= next;
222        ff_eval_free(d);
223        return NULL;
224    }
225    p->s++; // "("
226    if (*next == '(') { // special case do-nothing
227        av_freep(&d);
228        d = parse_expr(p);
229        if(p->s[0] != ')'){
230            *p->error = "missing )";
231            ff_eval_free(d);
232            return NULL;
233        }
234        p->s++; // ")"
235        return d;
236    }
237    d->param[0] = parse_expr(p);
238    if(p->s[0]== ','){
239        p->s++; // ","
240        d->param[1] = parse_expr(p);
241    }
242    if(p->s[0] != ')'){
243        *p->error = "missing )";
244        ff_eval_free(d);
245        return NULL;
246    }
247    p->s++; // ")"
248
249    d->type = e_func0;
250         if( strmatch(next, "sinh"  ) ) d->a.func0 = sinh;
251    else if( strmatch(next, "cosh"  ) ) d->a.func0 = cosh;
252    else if( strmatch(next, "tanh"  ) ) d->a.func0 = tanh;
253    else if( strmatch(next, "sin"   ) ) d->a.func0 = sin;
254    else if( strmatch(next, "cos"   ) ) d->a.func0 = cos;
255    else if( strmatch(next, "tan"   ) ) d->a.func0 = tan;
256    else if( strmatch(next, "atan"  ) ) d->a.func0 = atan;
257    else if( strmatch(next, "asin"  ) ) d->a.func0 = asin;
258    else if( strmatch(next, "acos"  ) ) d->a.func0 = acos;
259    else if( strmatch(next, "exp"   ) ) d->a.func0 = exp;
260    else if( strmatch(next, "log"   ) ) d->a.func0 = log;
261    else if( strmatch(next, "abs"   ) ) d->a.func0 = fabs;
262    else if( strmatch(next, "squish") ) d->type = e_squish;
263    else if( strmatch(next, "gauss" ) ) d->type = e_gauss;
264    else if( strmatch(next, "mod"   ) ) d->type = e_mod;
265    else if( strmatch(next, "max"   ) ) d->type = e_max;
266    else if( strmatch(next, "min"   ) ) d->type = e_min;
267    else if( strmatch(next, "eq"    ) ) d->type = e_eq;
268    else if( strmatch(next, "gte"   ) ) d->type = e_gte;
269    else if( strmatch(next, "gt"    ) ) d->type = e_gt;
270    else if( strmatch(next, "lte"   ) ) { AVEvalExpr * tmp = d->param[1]; d->param[1] = d->param[0]; d->param[0] = tmp; d->type = e_gt; }
271    else if( strmatch(next, "lt"    ) ) { AVEvalExpr * tmp = d->param[1]; d->param[1] = d->param[0]; d->param[0] = tmp; d->type = e_gte; }
272    else if( strmatch(next, "ld"    ) ) d->type = e_ld;
273    else if( strmatch(next, "st"    ) ) d->type = e_st;
274    else if( strmatch(next, "while" ) ) d->type = e_while;
275    else {
276        for(i=0; p->func1_name && p->func1_name[i]; i++){
277            if(strmatch(next, p->func1_name[i])){
278                d->a.func1 = p->func1[i];
279                d->type = e_func1;
280                return d;
281            }
282        }
283
284        for(i=0; p->func2_name && p->func2_name[i]; i++){
285            if(strmatch(next, p->func2_name[i])){
286                d->a.func2 = p->func2[i];
287                d->type = e_func2;
288                return d;
289            }
290        }
291
292        *p->error = "unknown function";
293        ff_eval_free(d);
294        return NULL;
295    }
296
297    return d;
298}
299
300static AVEvalExpr * new_eval_expr(int type, int value, AVEvalExpr *p0, AVEvalExpr *p1){
301    AVEvalExpr * e = av_mallocz(sizeof(AVEvalExpr));
302    e->type     =type   ;
303    e->value    =value  ;
304    e->param[0] =p0     ;
305    e->param[1] =p1     ;
306    return e;
307}
308
309static AVEvalExpr * parse_pow(Parser *p, int *sign){
310    *sign= (*p->s == '+') - (*p->s == '-');
311    p->s += *sign&1;
312    return parse_primary(p);
313}
314
315static AVEvalExpr * parse_factor(Parser *p){
316    int sign, sign2;
317    AVEvalExpr * e = parse_pow(p, &sign);
318    while(p->s[0]=='^'){
319        p->s++;
320        e= new_eval_expr(e_pow, 1, e, parse_pow(p, &sign2));
321        if (e->param[1]) e->param[1]->value *= (sign2|1);
322    }
323    if (e) e->value *= (sign|1);
324    return e;
325}
326
327static AVEvalExpr * parse_term(Parser *p){
328    AVEvalExpr * e = parse_factor(p);
329    while(p->s[0]=='*' || p->s[0]=='/'){
330        int c= *p->s++;
331        e= new_eval_expr(c == '*' ? e_mul : e_div, 1, e, parse_factor(p));
332    }
333    return e;
334}
335
336static AVEvalExpr * parse_subexpr(Parser *p) {
337    AVEvalExpr * e = parse_term(p);
338    while(*p->s == '+' || *p->s == '-') {
339        e= new_eval_expr(e_add, 1, e, parse_term(p));
340    };
341
342    return e;
343}
344
345static AVEvalExpr * parse_expr(Parser *p) {
346    AVEvalExpr * e;
347
348    if(p->stack_index <= 0) //protect against stack overflows
349        return NULL;
350    p->stack_index--;
351
352    e = parse_subexpr(p);
353
354    while(*p->s == ';') {
355        p->s++;
356        e= new_eval_expr(e_last, 1, e, parse_subexpr(p));
357    };
358
359    p->stack_index++;
360
361    return e;
362}
363
364static int verify_expr(AVEvalExpr * e) {
365    if (!e) return 0;
366    switch (e->type) {
367        case e_value:
368        case e_const: return 1;
369        case e_func0:
370        case e_func1:
371        case e_squish:
372        case e_ld:
373        case e_gauss: return verify_expr(e->param[0]);
374        default: return verify_expr(e->param[0]) && verify_expr(e->param[1]);
375    }
376}
377
378AVEvalExpr * ff_parse(const char *s, const char * const *const_name,
379               double (**func1)(void *, double), const char **func1_name,
380               double (**func2)(void *, double, double), const char **func2_name,
381               const char **error){
382    Parser p;
383    AVEvalExpr * e;
384    char w[strlen(s) + 1], * wp = w;
385
386    while (*s)
387        if (!isspace(*s++)) *wp++ = s[-1];
388    *wp++ = 0;
389
390    p.stack_index=100;
391    p.s= w;
392    p.const_name = const_name;
393    p.func1      = func1;
394    p.func1_name = func1_name;
395    p.func2      = func2;
396    p.func2_name = func2_name;
397    p.error= error;
398
399    e = parse_expr(&p);
400    if (!verify_expr(e)) {
401        ff_eval_free(e);
402        return NULL;
403    }
404    return e;
405}
406
407double ff_parse_eval(AVEvalExpr * 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_eval2(const char *s, const double *const_value, const char * const *const_name,
416               double (**func1)(void *, double), const char **func1_name,
417               double (**func2)(void *, double, double), const char **func2_name,
418               void *opaque, const char **error){
419    AVEvalExpr * e = ff_parse(s, const_name, func1, func1_name, func2, func2_name, error);
420    double d;
421    if (!e) return NAN;
422    d = ff_parse_eval(e, const_value, opaque);
423    ff_eval_free(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_eval2("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_eval2("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_eval2("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_eval2")
448    }
449    return 0;
450}
451#endif
452