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DEFINITIONS
This source file includes following definitions.
- av_strtod
- strmatch
- eval_expr
- ff_eval_free
- parse_primary
- new_eval_expr
- parse_pow
- parse_factor
- parse_term
- parse_subexpr
- parse_expr
- verify_expr
- ff_parse
- ff_parse_eval
- ff_eval2
- main
/*
* 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 libavcodec/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;
const double *const_value;
const char * const *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
const char **func2_name; // NULL terminated
void *opaque;
const char **error;
#define VARS 10
double var[VARS];
} Parser;
static const 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 = "undefined constant or 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 *const_name,
double (**func1)(void *, double), const char **func1_name,
double (**func2)(void *, double, double), const 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, const 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, const double *const_value, const char * const *const_name,
double (**func1)(void *, double), const char **func1_name,
double (**func2)(void *, double, double), const 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;
}
#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_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));
printf("%f == 0.931322575\n", ff_eval2("80G/80Gi", const_values, const_names, NULL, NULL, NULL, NULL, NULL, NULL));
for(i=0; i<1050; i++){
START_TIMER
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);
STOP_TIMER("ff_eval2")
}
return 0;
}
#endif