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FFmpeg/libavutil/eval.c
Nicolas George 40963ea9e9 eval: add mathematical constants (PI, E, PHI). 
Signed-off-by: Nicolas George <nicolas.george@normalesup.org>
Signed-off-by: Michael Niedermayer <michaelni@gmx.at>
2011-10-13 16:50:20 +02:00

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/*
* 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
* simple arithmetic expression evaluator.
*
* see http://joe.hotchkiss.com/programming/eval/eval.html
*/
#include "avutil.h"
#include "eval.h"
#include "log.h"
typedef struct Parser {
const AVClass *class;
int stack_index;
char *s;
const double *const_values;
const char * const *const_names; // NULL terminated
double (* const *funcs1)(void *, double a); // NULL terminated
const char * const *func1_names; // NULL terminated
double (* const *funcs2)(void *, double a, double b); // NULL terminated
const char * const *func2_names; // NULL terminated
void *opaque;
int log_offset;
void *log_ctx;
#define VARS 10
double *var;
} Parser;
static const AVClass class = { "Eval", av_default_item_name, NULL, LIBAVUTIL_VERSION_INT, offsetof(Parser,log_offset), offsetof(Parser,log_ctx) };
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,
};
static const struct {
const char *name;
double value;
} constants[] = {
{ "E", M_E },
{ "PI", M_PI },
{ "PHI", M_PHI },
};
double av_strtod(const char *numstr, char **tail)
{
double d;
char *next;
if(numstr[0]=='0' && (numstr[1]|0x20)=='x') {
d = strtoul(numstr, &next, 16);
} else
d = strtod(numstr, &next);
/* if parsing succeeded, check for and interpret postfixes */
if (next!=numstr) {
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;
}
#define IS_IDENTIFIER_CHAR(c) ((c) - '0' <= 9U || (c) - 'a' <= 25U || (c) - 'A' <= 25U || (c) == '_')
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 only if the s identifier is terminated */
return !IS_IDENTIFIER_CHAR(s[i]);
}
struct AVExpr {
enum {
e_value, e_const, e_func0, e_func1, e_func2,
e_squish, e_gauss, e_ld, e_isnan,
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, e_floor, e_ceil, e_trunc,
e_sqrt, e_not, e_random, e_hypot, e_gcd,
} 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;
struct AVExpr *param[2];
double *var;
};
static double eval_expr(Parser *p, AVExpr *e)
{
switch (e->type) {
case e_value: return e->value;
case e_const: return e->value * p->const_values[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_isnan: return e->value * !!isnan(eval_expr(p, e->param[0]));
case e_floor: return e->value * floor(eval_expr(p, e->param[0]));
case e_ceil : return e->value * ceil (eval_expr(p, e->param[0]));
case e_trunc: return e->value * trunc(eval_expr(p, e->param[0]));
case e_sqrt: return e->value * sqrt (eval_expr(p, e->param[0]));
case e_not: return e->value * (eval_expr(p, e->param[0]) == 0);
case e_random:{
int idx= av_clip(eval_expr(p, e->param[0]), 0, VARS-1);
uint64_t r= isnan(p->var[idx]) ? 0 : p->var[idx];
r= r*1664525+1013904223;
p->var[idx]= r;
return e->value * (r * (1.0/UINT64_MAX));
}
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_gcd: return e->value * av_gcd(d,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);
case e_hypot:return e->value * (sqrt(d*d + d2*d2));
}
}
}
return NAN;
}
static int parse_expr(AVExpr **e, Parser *p);
void av_expr_free(AVExpr *e)
{
if (!e) return;
av_expr_free(e->param[0]);
av_expr_free(e->param[1]);
av_freep(&e->var);
av_freep(&e);
}
static int parse_primary(AVExpr **e, Parser *p)
{
AVExpr *d = av_mallocz(sizeof(AVExpr));
char *next = p->s, *s0 = p->s;
int ret, i;
if (!d)
return AVERROR(ENOMEM);
/* number */
d->value = av_strtod(p->s, &next);
if (next != p->s) {
d->type = e_value;
p->s= next;
*e = d;
return 0;
}
d->value = 1;
/* named constants */
for (i=0; p->const_names && p->const_names[i]; i++) {
if (strmatch(p->s, p->const_names[i])) {
p->s+= strlen(p->const_names[i]);
d->type = e_const;
d->a.const_index = i;
*e = d;
return 0;
}
}
for (i = 0; i < FF_ARRAY_ELEMS(constants); i++) {
if (strmatch(p->s, constants[i].name)) {
p->s += strlen(constants[i].name);
d->type = e_value;
d->value = constants[i].value;
*e = d;
return 0;
}
}
p->s= strchr(p->s, '(');
if (p->s==NULL) {
av_log(p, AV_LOG_ERROR, "Undefined constant or missing '(' in '%s'\n", s0);
p->s= next;
av_expr_free(d);
return AVERROR(EINVAL);
}
p->s++; // "("
if (*next == '(') { // special case do-nothing
av_freep(&d);
if ((ret = parse_expr(&d, p)) < 0)
return ret;
if (p->s[0] != ')') {
av_log(p, AV_LOG_ERROR, "Missing ')' in '%s'\n", s0);
av_expr_free(d);
return AVERROR(EINVAL);
}
p->s++; // ")"
*e = d;
return 0;
}
if ((ret = parse_expr(&(d->param[0]), p)) < 0) {
av_expr_free(d);
return ret;
}
if (p->s[0]== ',') {
p->s++; // ","
parse_expr(&d->param[1], p);
}
if (p->s[0] != ')') {
av_log(p, AV_LOG_ERROR, "Missing ')' or too many args in '%s'\n", s0);
av_expr_free(d);
return AVERROR(EINVAL);
}
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" )) { AVExpr *tmp = d->param[1]; d->param[1] = d->param[0]; d->param[0] = tmp; d->type = e_gt; }
else if (strmatch(next, "lt" )) { AVExpr *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, "isnan" )) d->type = e_isnan;
else if (strmatch(next, "st" )) d->type = e_st;
else if (strmatch(next, "while" )) d->type = e_while;
else if (strmatch(next, "floor" )) d->type = e_floor;
else if (strmatch(next, "ceil" )) d->type = e_ceil;
else if (strmatch(next, "trunc" )) d->type = e_trunc;
else if (strmatch(next, "sqrt" )) d->type = e_sqrt;
else if (strmatch(next, "not" )) d->type = e_not;
else if (strmatch(next, "pow" )) d->type = e_pow;
else if (strmatch(next, "random")) d->type = e_random;
else if (strmatch(next, "hypot" )) d->type = e_hypot;
else if (strmatch(next, "gcd" )) d->type = e_gcd;
else {
for (i=0; p->func1_names && p->func1_names[i]; i++) {
if (strmatch(next, p->func1_names[i])) {
d->a.func1 = p->funcs1[i];
d->type = e_func1;
*e = d;
return 0;
}
}
for (i=0; p->func2_names && p->func2_names[i]; i++) {
if (strmatch(next, p->func2_names[i])) {
d->a.func2 = p->funcs2[i];
d->type = e_func2;
*e = d;
return 0;
}
}
av_log(p, AV_LOG_ERROR, "Unknown function in '%s'\n", s0);
av_expr_free(d);
return AVERROR(EINVAL);
}
*e = d;
return 0;
}
static AVExpr *new_eval_expr(int type, int value, AVExpr *p0, AVExpr *p1)
{
AVExpr *e = av_mallocz(sizeof(AVExpr));
if (!e)
return NULL;
e->type =type ;
e->value =value ;
e->param[0] =p0 ;
e->param[1] =p1 ;
return e;
}
static int parse_pow(AVExpr **e, Parser *p, int *sign)
{
*sign= (*p->s == '+') - (*p->s == '-');
p->s += *sign&1;
return parse_primary(e, p);
}
static int parse_factor(AVExpr **e, Parser *p)
{
int sign, sign2, ret;
AVExpr *e0, *e1, *e2;
if ((ret = parse_pow(&e0, p, &sign)) < 0)
return ret;
while(p->s[0]=='^'){
e1 = e0;
p->s++;
if ((ret = parse_pow(&e2, p, &sign2)) < 0) {
av_expr_free(e1);
return ret;
}
e0 = new_eval_expr(e_pow, 1, e1, e2);
if (!e0) {
av_expr_free(e1);
av_expr_free(e2);
return AVERROR(ENOMEM);
}
if (e0->param[1]) e0->param[1]->value *= (sign2|1);
}
if (e0) e0->value *= (sign|1);
*e = e0;
return 0;
}
static int parse_term(AVExpr **e, Parser *p)
{
int ret;
AVExpr *e0, *e1, *e2;
if ((ret = parse_factor(&e0, p)) < 0)
return ret;
while (p->s[0]=='*' || p->s[0]=='/') {
int c= *p->s++;
e1 = e0;
if ((ret = parse_factor(&e2, p)) < 0) {
av_expr_free(e1);
return ret;
}
e0 = new_eval_expr(c == '*' ? e_mul : e_div, 1, e1, e2);
if (!e0) {
av_expr_free(e1);
av_expr_free(e2);
return AVERROR(ENOMEM);
}
}
*e = e0;
return 0;
}
static int parse_subexpr(AVExpr **e, Parser *p)
{
int ret;
AVExpr *e0, *e1, *e2;
if ((ret = parse_term(&e0, p)) < 0)
return ret;
while (*p->s == '+' || *p->s == '-') {
e1 = e0;
if ((ret = parse_term(&e2, p)) < 0) {
av_expr_free(e1);
return ret;
}
e0 = new_eval_expr(e_add, 1, e1, e2);
if (!e0) {
av_expr_free(e1);
av_expr_free(e2);
return AVERROR(ENOMEM);
}
};
*e = e0;
return 0;
}
static int parse_expr(AVExpr **e, Parser *p)
{
int ret;
AVExpr *e0, *e1, *e2;
if (p->stack_index <= 0) //protect against stack overflows
return AVERROR(EINVAL);
p->stack_index--;
if ((ret = parse_subexpr(&e0, p)) < 0)
return ret;
while (*p->s == ';') {
p->s++;
e1 = e0;
if ((ret = parse_subexpr(&e2, p)) < 0) {
av_expr_free(e1);
return ret;
}
e0 = new_eval_expr(e_last, 1, e1, e2);
if (!e0) {
av_expr_free(e1);
av_expr_free(e2);
return AVERROR(ENOMEM);
}
};
p->stack_index++;
*e = e0;
return 0;
}
static int verify_expr(AVExpr *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:
case e_isnan:
case e_floor:
case e_ceil:
case e_trunc:
case e_sqrt:
case e_not:
case e_random:
return verify_expr(e->param[0]);
default: return verify_expr(e->param[0]) && verify_expr(e->param[1]);
}
}
int av_expr_parse(AVExpr **expr, const char *s,
const char * const *const_names,
const char * const *func1_names, double (* const *funcs1)(void *, double),
const char * const *func2_names, double (* const *funcs2)(void *, double, double),
int log_offset, void *log_ctx)
{
Parser p = { 0 };
AVExpr *e = NULL;
char *w = av_malloc(strlen(s) + 1);
char *wp = w;
const char *s0 = s;
int ret = 0;
if (!w)
return AVERROR(ENOMEM);
while (*s)
if (!isspace(*s++)) *wp++ = s[-1];
*wp++ = 0;
p.class = &class;
p.stack_index=100;
p.s= w;
p.const_names = const_names;
p.funcs1 = funcs1;
p.func1_names = func1_names;
p.funcs2 = funcs2;
p.func2_names = func2_names;
p.log_offset = log_offset;
p.log_ctx = log_ctx;
if ((ret = parse_expr(&e, &p)) < 0)
goto end;
if (*p.s) {
av_expr_free(e);
av_log(&p, AV_LOG_ERROR, "Invalid chars '%s' at the end of expression '%s'\n", p.s, s0);
ret = AVERROR(EINVAL);
goto end;
}
if (!verify_expr(e)) {
av_expr_free(e);
ret = AVERROR(EINVAL);
goto end;
}
e->var= av_mallocz(sizeof(double) *VARS);
*expr = e;
end:
av_free(w);
return ret;
}
double av_expr_eval(AVExpr *e, const double *const_values, void *opaque)
{
Parser p = { 0 };
p.var= e->var;
p.const_values = const_values;
p.opaque = opaque;
return eval_expr(&p, e);
}
int av_expr_parse_and_eval(double *d, const char *s,
const char * const *const_names, const double *const_values,
const char * const *func1_names, double (* const *funcs1)(void *, double),
const char * const *func2_names, double (* const *funcs2)(void *, double, double),
void *opaque, int log_offset, void *log_ctx)
{
AVExpr *e = NULL;
int ret = av_expr_parse(&e, s, const_names, func1_names, funcs1, func2_names, funcs2, log_offset, log_ctx);
if (ret < 0) {
*d = NAN;
return ret;
}
*d = av_expr_eval(e, const_values, opaque);
av_expr_free(e);
return isnan(*d) ? AVERROR(EINVAL) : 0;
}
#if FF_API_OLD_EVAL_NAMES
int av_parse_expr(AVExpr **expr, const char *s,
const char * const *const_names,
const char * const *func1_names, double (* const *funcs1)(void *, double),
const char * const *func2_names, double (* const *funcs2)(void *, double, double),
int log_offset, void *log_ctx)
{
return av_expr_parse(expr, s, const_names, func1_names, funcs1, func2_names, funcs2,
log_offset, log_ctx);
}
double av_eval_expr(AVExpr *e, const double *const_values, void *opaque)
{
return av_expr_eval(e, const_values, opaque);
}
int av_parse_and_eval_expr(double *res, const char *s,
const char * const *const_names, const double *const_values,
const char * const *func1_names, double (* const *funcs1)(void *, double),
const char * const *func2_names, double (* const *funcs2)(void *, double, double),
void *opaque, int log_offset, void *log_ctx)
{
return av_expr_parse_and_eval(res, s, const_names, const_values, func1_names, funcs1, func2_names, funcs2,
opaque, log_offset, log_ctx);
}
void av_free_expr(AVExpr *e)
{
av_expr_free(e);
}
#endif /* FF_API_OLD_EVAL_NAMES */
#ifdef TEST
#undef printf
#include <string.h>
static double const_values[] = {
M_PI,
M_E,
0
};
static const char *const_names[] = {
"PI",
"E",
0
};
int main(int argc, char **argv)
{
int i;
double d;
const char **expr, *exprs[] = {
"",
"1;2",
"-20",
"-PI",
"+PI",
"1+(5-2)^(3-1)+1/2+sin(PI)-max(-2.2,-3.1)",
"80G/80Gi",
"1k",
"1Gi",
"1gi",
"1GiFoo",
"1k+1k",
"1Gi*3foo",
"foo",
"foo(",
"foo()",
"foo)",
"sin",
"sin(",
"sin()",
"sin)",
"sin 10",
"sin(1,2,3)",
"sin(1 )",
"1",
"1foo",
"bar + PI + E + 100f*2 + foo",
"13k + 12f - foo(1, 2)",
"1gi",
"1Gi",
"st(0, 123)",
"st(1, 123); ld(1)",
/* compute 1+2+...+N */
"st(0, 1); while(lte(ld(0), 100), st(1, ld(1)+ld(0));st(0, ld(0)+1)); ld(1)",
/* compute Fib(N) */
"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)",
"while(0, 10)",
"st(0, 1); while(lte(ld(0),100), st(1, ld(1)+ld(0)); st(0, ld(0)+1))",
"isnan(1)",
"isnan(NAN)",
"floor(NAN)",
"floor(123.123)",
"floor(-123.123)",
"trunc(123.123)",
"trunc(-123.123)",
"ceil(123.123)",
"ceil(-123.123)",
"sqrt(1764)",
"isnan(sqrt(-1))",
"not(1)",
"not(NAN)",
"not(0)",
"pow(0,1.23)",
"pow(PI,1.23)",
"PI^1.23",
"pow(-1,1.23)",
NULL
};
for (expr = exprs; *expr; expr++) {
printf("Evaluating '%s'\n", *expr);
av_expr_parse_and_eval(&d, *expr,
const_names, const_values,
NULL, NULL, NULL, NULL, NULL, 0, NULL);
if(isnan(d)){
printf("'%s' -> nan\n\n", *expr);
}else{
printf("'%s' -> %f\n\n", *expr, d);
}
}
av_expr_parse_and_eval(&d, "1+(5-2)^(3-1)+1/2+sin(PI)-max(-2.2,-3.1)",
const_names, const_values,
NULL, NULL, NULL, NULL, NULL, 0, NULL);
printf("%f == 12.7\n", d);
av_expr_parse_and_eval(&d, "80G/80Gi",
const_names, const_values,
NULL, NULL, NULL, NULL, NULL, 0, NULL);
printf("%f == 0.931322575\n", d);
if (argc > 1 && !strcmp(argv[1], "-t")) {
for (i = 0; i < 1050; i++) {
START_TIMER;
av_expr_parse_and_eval(&d, "1+(5-2)^(3-1)+1/2+sin(PI)-max(-2.2,-3.1)",
const_names, const_values,
NULL, NULL, NULL, NULL, NULL, 0, NULL);
STOP_TIMER("av_expr_parse_and_eval");
}
}
return 0;
}
#endif
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