/* * 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 <float.h>#include "attributes.h"#include "avutil.h"#include "common.h"#include "eval.h"#include "ffmath.h"#include "internal.h"#include "log.h"#include "mathematics.h"#include "time.h"#include "avstring.h"#include "timer.h"#include "reverse.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 eval_class = { "Eval", av_default_item_name, NULL, LIBAVUTIL_VERSION_INT, offsetof(Parser,log_offset), offsetof(Parser,log_ctx) }; static const struct {    double bin_val;    double dec_val;    int8_t exp;} si_prefixes['z' - 'E' + 1] = {    ['y'-'E']= { 8.271806125530276749e-25, 1e-24, -24 },    ['z'-'E']= { 8.4703294725430034e-22, 1e-21, -21 },    ['a'-'E']= { 8.6736173798840355e-19, 1e-18, -18 },    ['f'-'E']= { 8.8817841970012523e-16, 1e-15, -15 },    ['p'-'E']= { 9.0949470177292824e-13, 1e-12, -12 },    ['n'-'E']= { 9.3132257461547852e-10, 1e-9,  -9 },    ['u'-'E']= { 9.5367431640625e-7, 1e-6, -6 },    ['m'-'E']= { 9.765625e-4, 1e-3, -3 },    ['c'-'E']= { 9.8431332023036951e-3, 1e-2, -2 },    ['d'-'E']= { 9.921256574801246e-2, 1e-1, -1 },    ['h'-'E']= { 1.0159366732596479e2, 1e2, 2 },    ['k'-'E']= { 1.024e3, 1e3, 3 },    ['K'-'E']= { 1.024e3, 1e3, 3 },    ['M'-'E']= { 1.048576e6, 1e6, 6 },    ['G'-'E']= { 1.073741824e9, 1e9, 9 },    ['T'-'E']= { 1.099511627776e12, 1e12, 12 },    ['P'-'E']= { 1.125899906842624e15, 1e15, 15 },    ['E'-'E']= { 1.152921504606847e18, 1e18, 18 },    ['Z'-'E']= { 1.1805916207174113e21, 1e21, 21 },    ['Y'-'E']= { 1.2089258196146292e24, 1e24, 24 },}; static const struct {    const char *name;    double value;} constants[] = {    { "E",   M_E   },    { "PI",  M_PI  },    { "PHI", M_PHI },    { "QP2LAMBDA", FF_QP2LAMBDA },}; 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[0] == 'd' && next[1] == 'B') {            /* treat dB as decibels instead of decibytes */            d = ff_exp10(d / 20);            next += 2;        } else if (*next >= 'E' && *next <= 'z') {            int e= si_prefixes[*next - 'E'].exp;            if (e) {                if (next[1] == 'i') {                    d*= si_prefixes[*next - 'E'].bin_val;                    next+=2;                } else {                    d*= si_prefixes[*next - 'E'].dec_val;                    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_isinf,        e_mod, e_max, e_min, e_eq, e_gt, e_gte, e_lte, e_lt,        e_pow, e_mul, e_div, e_add,        e_last, e_st, e_while, e_taylor, e_root, e_floor, e_ceil, e_trunc, e_round,        e_sqrt, e_not, e_random, e_hypot, e_gcd,        e_if, e_ifnot, e_print, e_bitand, e_bitor, e_between, e_clip, e_atan2, e_lerp,    } 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[3];    double *var;}; static double etime(double v){    return av_gettime() * 0.000001;} 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_isinf:  return e->value * !!isinf(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_round:  return e->value * round(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_if:     return e->value * (eval_expr(p, e->param[0]) ? eval_expr(p, e->param[1]) :                                          e->param[2] ? eval_expr(p, e->param[2]) : 0);        case e_ifnot:  return e->value * (!eval_expr(p, e->param[0]) ? eval_expr(p, e->param[1]) :                                          e->param[2] ? eval_expr(p, e->param[2]) : 0);        case e_clip: {            double x = eval_expr(p, e->param[0]);            double min = eval_expr(p, e->param[1]), max = eval_expr(p, e->param[2]);            if (isnan(min) || isnan(max) || isnan(x) || min > max)                return NAN;            return e->value * av_clipd(eval_expr(p, e->param[0]), min, max);        }        case e_between: {            double d = eval_expr(p, e->param[0]);            return e->value * (d >= eval_expr(p, e->param[1]) &&                               d <= eval_expr(p, e->param[2]));        }        case e_lerp: {            double v0 = eval_expr(p, e->param[0]);            double v1 = eval_expr(p, e->param[1]);            double f  = eval_expr(p, e->param[2]);            return v0 + (v1 - v0) * f;        }        case e_print: {            double x = eval_expr(p, e->param[0]);            int level = e->param[1] ? av_clip(eval_expr(p, e->param[1]), INT_MIN, INT_MAX) : AV_LOG_INFO;            av_log(p, level, "%f\n", x);            return x;        }        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;        }        case e_taylor: {            double t = 1, d = 0, v;            double x = eval_expr(p, e->param[1]);            int id = e->param[2] ? av_clip(eval_expr(p, e->param[2]), 0, VARS-1) : 0;            int i;            double var0 = p->var[id];            for(i=0; i<1000; i++) {                double ld = d;                p->var[id] = i;                v = eval_expr(p, e->param[0]);                d += t*v;                if(ld==d && v)                    break;                t *= x / (i+1);            }            p->var[id] = var0;            return d;        }        case e_root: {            int i, j;            double low = -1, high = -1, v, low_v = -DBL_MAX, high_v = DBL_MAX;            double var0 = p->var[0];            double x_max = eval_expr(p, e->param[1]);            for(i=-1; i<1024; i++) {                if(i<255) {                    p->var[0] = ff_reverse[i&255]*x_max/255;                } else {                    p->var[0] = x_max*pow(0.9, i-255);                    if (i&1) p->var[0] *= -1;                    if (i&2) p->var[0] += low;                    else     p->var[0] += high;                }                v = eval_expr(p, e->param[0]);                if (v<=0 && v>low_v) {                    low    = p->var[0];                    low_v  = v;                }                if (v>=0 && v<high_v) {                    high   = p->var[0];                    high_v = v;                }                if (low>=0 && high>=0){                    for (j=0; j<1000; j++) {                        p->var[0] = (low+high)*0.5;                        if (low == p->var[0] || high == p->var[0])                            break;                        v = eval_expr(p, e->param[0]);                        if (v<=0) low = p->var[0];                        if (v>=0) high= p->var[0];                        if (isnan(v)) {                            low = high = v;                            break;                        }                    }                    break;                }            }            p->var[0] = var0;            return -low_v<high_v ? low : high;        }        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((!CONFIG_FTRAPV || d2) ? d / d2 : d * INFINITY) * 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_lt:  return e->value * (d <  d2 ? 1.0 : 0.0);                case e_lte: 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 * ((!CONFIG_FTRAPV || d2 ) ? (d / d2) : d * INFINITY);                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 * hypot(d, d2);                case e_atan2:return e->value * atan2(d, d2);                case e_bitand: return isnan(d) || isnan(d2) ? NAN : e->value * ((long int)d & (long int)d2);                case e_bitor:  return isnan(d) || isnan(d2) ? NAN : e->value * ((long int)d | (long int)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_expr_free(e->param[2]);    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) {        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]== ',') {        p->s++; // ","        parse_expr(&d->param[2], 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, "time"  )) d->a.func0 = etime;    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"   )) d->type = e_lte;    else if (strmatch(next, "lt"    )) d->type = e_lt;    else if (strmatch(next, "ld"    )) d->type = e_ld;    else if (strmatch(next, "isnan" )) d->type = e_isnan;    else if (strmatch(next, "isinf" )) d->type = e_isinf;    else if (strmatch(next, "st"    )) d->type = e_st;    else if (strmatch(next, "while" )) d->type = e_while;    else if (strmatch(next, "taylor")) d->type = e_taylor;    else if (strmatch(next, "root"  )) d->type = e_root;    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, "round" )) d->type = e_round;    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, "print" )) d->type = e_print;    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 if (strmatch(next, "if"    )) d->type = e_if;    else if (strmatch(next, "ifnot" )) d->type = e_ifnot;    else if (strmatch(next, "bitand")) d->type = e_bitand;    else if (strmatch(next, "bitor" )) d->type = e_bitor;    else if (strmatch(next, "between"))d->type = e_between;    else if (strmatch(next, "clip"  )) d->type = e_clip;    else if (strmatch(next, "atan2" )) d->type = e_atan2;    else if (strmatch(next, "lerp"  )) d->type = e_lerp;    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 *make_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  ;

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