/* * simple arithmetic expression evaluator * * Copyright (c) 2002-2006 Michael Niedermayer <michaelni@gmx.at> * Copyright (c) 2006 Oded Shimon <ods15@ods15.dyndns.org> * * This file is part of FFmpeg. * * FFmpeg is free software; you can redistribute it and/or * modify it under the terms of the GNU Lesser General Public * License as published by the Free Software Foundation; either * version 2.1 of the License, or (at your option) any later version. * * FFmpeg is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU * Lesser General Public License for more details. * * You should have received a copy of the GNU Lesser General Public * License along with FFmpeg; if not, write to the Free Software * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA */ /** * @file eval.c * simple arithmetic expression evaluator. * * see http://joe.hotchkiss.com/programming/eval/eval.html */ #include "avcodec.h" #include "eval.h" #include <stdio.h> #include <stdlib.h> #include <string.h> #include <math.h> #ifndef NAN #define NAN 0.0/0.0 #endif #ifndef M_PI #define M_PI 3.14159265358979323846 #endif typedef struct Parser{ int stack_index; char *s; double *const_value; const char **const_name; // NULL terminated double (**func1)(void *, double a); // NULL terminated const char **func1_name; // NULL terminated double (**func2)(void *, double a, double b); // NULL terminated char **func2_name; // NULL terminated void *opaque; const char **error; #define VARS 10 double var[VARS]; } Parser; static int8_t si_prefixes['z' - 'E' + 1]={ ['y'-'E']= -24, ['z'-'E']= -21, ['a'-'E']= -18, ['f'-'E']= -15, ['p'-'E']= -12, ['n'-'E']= - 9, ['u'-'E']= - 6, ['m'-'E']= - 3, ['c'-'E']= - 2, ['d'-'E']= - 1, ['h'-'E']= 2, ['k'-'E']= 3, ['K'-'E']= 3, ['M'-'E']= 6, ['G'-'E']= 9, ['T'-'E']= 12, ['P'-'E']= 15, ['E'-'E']= 18, ['Z'-'E']= 21, ['Y'-'E']= 24, }; /** strtod() function extended with 'k', 'M', 'G', 'ki', 'Mi', 'Gi' and 'B' * postfixes. This allows using f.e. kB, MiB, G and B as a postfix. This * function assumes that the unit of numbers is bits not bytes. */ static double av_strtod(const char *name, char **tail) { double d; char *next; d = strtod(name, &next); /* if parsing succeeded, check for and interpret postfixes */ if (next!=name) { if(*next >= 'E' && *next <= 'z'){ int e= si_prefixes[*next - 'E']; if(e){ if(next[1] == 'i'){ d*= pow( 2, e/0.3); next+=2; }else{ d*= pow(10, e); next++; } } } if(*next=='B') { d*=8; next++; } } /* if requested, fill in tail with the position after the last parsed character */ if (tail) *tail = next; return d; } static int strmatch(const char *s, const char *prefix){ int i; for(i=0; prefix[i]; i++){ if(prefix[i] != s[i]) return 0; } return 1; } struct ff_expr_s { enum { e_value, e_const, e_func0, e_func1, e_func2, e_squish, e_gauss, e_ld, e_mod, e_max, e_min, e_eq, e_gt, e_gte, e_pow, e_mul, e_div, e_add, e_last, e_st, e_while, } type; double value; // is sign in other types union { int const_index; double (*func0)(double); double (*func1)(void *, double); double (*func2)(void *, double, double); } a; AVEvalExpr * param[2]; }; static double eval_expr(Parser * p, AVEvalExpr * e) { switch (e->type) { case e_value: return e->value; case e_const: return e->value * p->const_value[e->a.const_index]; case e_func0: return e->value * e->a.func0(eval_expr(p, e->param[0])); case e_func1: return e->value * e->a.func1(p->opaque, eval_expr(p, e->param[0])); case e_func2: return e->value * e->a.func2(p->opaque, eval_expr(p, e->param[0]), eval_expr(p, e->param[1])); case e_squish: return 1/(1+exp(4*eval_expr(p, e->param[0]))); case e_gauss: { double d = eval_expr(p, e->param[0]); return exp(-d*d/2)/sqrt(2*M_PI); } case e_ld: return e->value * p->var[av_clip(eval_expr(p, e->param[0]), 0, VARS-1)]; case e_while: { double d = NAN; while(eval_expr(p, e->param[0])) d=eval_expr(p, e->param[1]); return d; } default: { double d = eval_expr(p, e->param[0]); double d2 = eval_expr(p, e->param[1]); switch (e->type) { case e_mod: return e->value * (d - floor(d/d2)*d2); case e_max: return e->value * (d > d2 ? d : d2); case e_min: return e->value * (d < d2 ? d : d2); case e_eq: return e->value * (d == d2 ? 1.0 : 0.0); case e_gt: return e->value * (d > d2 ? 1.0 : 0.0); case e_gte: return e->value * (d >= d2 ? 1.0 : 0.0); case e_pow: return e->value * pow(d, d2); case e_mul: return e->value * (d * d2); case e_div: return e->value * (d / d2); case e_add: return e->value * (d + d2); case e_last:return e->value * d2; case e_st : return e->value * (p->var[av_clip(d, 0, VARS-1)]= d2); } } } return NAN; } static AVEvalExpr * parse_expr(Parser *p); void ff_eval_free(AVEvalExpr * e) { if (!e) return; ff_eval_free(e->param[0]); ff_eval_free(e->param[1]); av_freep(&e); } static AVEvalExpr * parse_primary(Parser *p) { AVEvalExpr * d = av_mallocz(sizeof(AVEvalExpr)); char *next= p->s; int i; /* number */ d->value = av_strtod(p->s, &next); if(next != p->s){ d->type = e_value; p->s= next; return d; } d->value = 1; /* named constants */ for(i=0; p->const_name && p->const_name[i]; i++){ if(strmatch(p->s, p->const_name[i])){ p->s+= strlen(p->const_name[i]); d->type = e_const; d->a.const_index = i; return d; } } p->s= strchr(p->s, '('); if(p->s==NULL){ *p->error = "missing ("; p->s= next; ff_eval_free(d); return NULL; } p->s++; // "(" if (*next == '(') { // special case do-nothing av_freep(&d); d = parse_expr(p); if(p->s[0] != ')'){ *p->error = "missing )"; ff_eval_free(d); return NULL; } p->s++; // ")" return d; } d->param[0] = parse_expr(p); if(p->s[0]== ','){ p->s++; // "," d->param[1] = parse_expr(p); } if(p->s[0] != ')'){ *p->error = "missing )"; ff_eval_free(d); return NULL; } p->s++; // ")" d->type = e_func0; if( strmatch(next, "sinh" ) ) d->a.func0 = sinh; else if( strmatch(next, "cosh" ) ) d->a.func0 = cosh; else if( strmatch(next, "tanh" ) ) d->a.func0 = tanh; else if( strmatch(next, "sin" ) ) d->a.func0 = sin; else if( strmatch(next, "cos" ) ) d->a.func0 = cos; else if( strmatch(next, "tan" ) ) d->a.func0 = tan; else if( strmatch(next, "atan" ) ) d->a.func0 = atan; else if( strmatch(next, "asin" ) ) d->a.func0 = asin; else if( strmatch(next, "acos" ) ) d->a.func0 = acos; else if( strmatch(next, "exp" ) ) d->a.func0 = exp; else if( strmatch(next, "log" ) ) d->a.func0 = log; else if( strmatch(next, "abs" ) ) d->a.func0 = fabs; else if( strmatch(next, "squish") ) d->type = e_squish; else if( strmatch(next, "gauss" ) ) d->type = e_gauss; else if( strmatch(next, "mod" ) ) d->type = e_mod; else if( strmatch(next, "max" ) ) d->type = e_max; else if( strmatch(next, "min" ) ) d->type = e_min; else if( strmatch(next, "eq" ) ) d->type = e_eq; else if( strmatch(next, "gte" ) ) d->type = e_gte; else if( strmatch(next, "gt" ) ) d->type = e_gt; else if( strmatch(next, "lte" ) ) { AVEvalExpr * tmp = d->param[1]; d->param[1] = d->param[0]; d->param[0] = tmp; d->type = e_gt; } else if( strmatch(next, "lt" ) ) { AVEvalExpr * tmp = d->param[1]; d->param[1] = d->param[0]; d->param[0] = tmp; d->type = e_gte; } else if( strmatch(next, "ld" ) ) d->type = e_ld; else if( strmatch(next, "st" ) ) d->type = e_st; else if( strmatch(next, "while" ) ) d->type = e_while; else { for(i=0; p->func1_name && p->func1_name[i]; i++){ if(strmatch(next, p->func1_name[i])){ d->a.func1 = p->func1[i]; d->type = e_func1; return d; } } for(i=0; p->func2_name && p->func2_name[i]; i++){ if(strmatch(next, p->func2_name[i])){ d->a.func2 = p->func2[i]; d->type = e_func2; return d; } } *p->error = "unknown function"; ff_eval_free(d); return NULL; } return d; } static AVEvalExpr * new_eval_expr(int type, int value, AVEvalExpr *p0, AVEvalExpr *p1){ AVEvalExpr * e = av_mallocz(sizeof(AVEvalExpr)); e->type =type ; e->value =value ; e->param[0] =p0 ; e->param[1] =p1 ; return e; } static AVEvalExpr * parse_pow(Parser *p, int *sign){ *sign= (*p->s == '+') - (*p->s == '-'); p->s += *sign&1; return parse_primary(p); } static AVEvalExpr * parse_factor(Parser *p){ int sign, sign2; AVEvalExpr * e = parse_pow(p, &sign); while(p->s[0]=='^'){ p->s++; e= new_eval_expr(e_pow, 1, e, parse_pow(p, &sign2)); if (e->param[1]) e->param[1]->value *= (sign2|1); } if (e) e->value *= (sign|1); return e; } static AVEvalExpr * parse_term(Parser *p){ AVEvalExpr * e = parse_factor(p); while(p->s[0]=='*' || p->s[0]=='/'){ int c= *p->s++; e= new_eval_expr(c == '*' ? e_mul : e_div, 1, e, parse_factor(p)); } return e; } static AVEvalExpr * parse_subexpr(Parser *p) { AVEvalExpr * e = parse_term(p); while(*p->s == '+' || *p->s == '-') { e= new_eval_expr(e_add, 1, e, parse_term(p)); }; return e; } static AVEvalExpr * parse_expr(Parser *p) { AVEvalExpr * e; if(p->stack_index <= 0) //protect against stack overflows return NULL; p->stack_index--; e = parse_subexpr(p); while(*p->s == ';') { p->s++; e= new_eval_expr(e_last, 1, e, parse_subexpr(p)); }; p->stack_index++; return e; } static int verify_expr(AVEvalExpr * e) { if (!e) return 0; switch (e->type) { case e_value: case e_const: return 1; case e_func0: case e_func1: case e_squish: case e_ld: case e_gauss: return verify_expr(e->param[0]); default: return verify_expr(e->param[0]) && verify_expr(e->param[1]); } } AVEvalExpr * ff_parse(const char *s, const char **const_name, double (**func1)(void *, double), const char **func1_name, double (**func2)(void *, double, double), char **func2_name, const char **error){ Parser p; AVEvalExpr * e; char w[strlen(s) + 1], * wp = w; while (*s) if (!isspace(*s++)) *wp++ = s[-1]; *wp++ = 0; p.stack_index=100; p.s= w; p.const_name = const_name; p.func1 = func1; p.func1_name = func1_name; p.func2 = func2; p.func2_name = func2_name; p.error= error; e = parse_expr(&p); if (!verify_expr(e)) { ff_eval_free(e); return NULL; } return e; } double ff_parse_eval(AVEvalExpr * e, double *const_value, void *opaque) { Parser p; p.const_value= const_value; p.opaque = opaque; return eval_expr(&p, e); } double ff_eval2(const char *s, double *const_value, const char **const_name, double (**func1)(void *, double), const char **func1_name, double (**func2)(void *, double, double), char **func2_name, void *opaque, const char **error){ AVEvalExpr * e = ff_parse(s, const_name, func1, func1_name, func2, func2_name, error); double d; if (!e) return NAN; d = ff_parse_eval(e, const_value, opaque); ff_eval_free(e); return d; } #if LIBAVCODEC_VERSION_INT < ((52<<16)+(0<<8)+0) attribute_deprecated double ff_eval(char *s, double *const_value, const char **const_name, double (**func1)(void *, double), const char **func1_name, double (**func2)(void *, double, double), char **func2_name, void *opaque){ const char *error=NULL; double ret; ret = ff_eval2(s, const_value, const_name, func1, func1_name, func2, func2_name, opaque, &error); if (error) av_log(NULL, AV_LOG_ERROR, "Error evaluating \"%s\": %s\n", s, error); return ret; } #endif #ifdef TEST #undef printf static double const_values[]={ M_PI, M_E, 0 }; static const char *const_names[]={ "PI", "E", 0 }; int main(void){ int i; printf("%f == 12.7\n", ff_eval("1+(5-2)^(3-1)+1/2+sin(PI)-max(-2.2,-3.1)", const_values, const_names, NULL, NULL, NULL, NULL, NULL)); printf("%f == 0.931322575\n", ff_eval("80G/80Gi", const_values, const_names, NULL, NULL, NULL, NULL, NULL)); for(i=0; i<1050; i++){ START_TIMER ff_eval("1+(5-2)^(3-1)+1/2+sin(PI)-max(-2.2,-3.1)", const_values, const_names, NULL, NULL, NULL, NULL, NULL); STOP_TIMER("ff_eval") } return 0; } #endif