/* * 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 "avutil.h" #include "common.h" #include "eval.h" #include "log.h" #include "mathematics.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_isinf, 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_taylor, e_root, e_floor, e_ceil, e_trunc, e_sqrt, e_not, e_random, e_hypot, e_gcd, e_if, e_ifnot, } 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 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_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]) : 0); case e_ifnot: return e->value * (!eval_expr(p, e->param[0]) ? eval_expr(p, e->param[1]) : 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; } 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] = av_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(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 * ((!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 * (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_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==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]== ',') { 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, "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_gte; } else if (strmatch(next, "lt" )) { AVExpr *tmp = d->param[1]; d->param[1] = d->param[0]; d->param[0] = tmp; d->type = e_gt; } 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, "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 if (strmatch(next, "if" )) d->type = e_if; else if (strmatch(next, "ifnot" )) d->type = e_ifnot; 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_isinf: case e_floor: case e_ceil: case e_trunc: case e_sqrt: case e_not: case e_random: return verify_expr(e->param[0]) && !e->param[1]; case e_taylor: return verify_expr(e->param[0]) && verify_expr(e->param[1]) && (!e->param[2] || verify_expr(e->param[2])); default: return verify_expr(e->param[0]) && verify_expr(e->param[1]) && !e->param[2]; } } 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; } #ifdef TEST // LCOV_EXCL_START #undef printf #include <string.h> static const double const_values[] = { M_PI, M_E, 0 }; static const char *const const_names[] = { "PI", "E", 0 }; int main(int argc, char **argv) { int i; double d; const char *const *expr; static const char *const 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)", "lte(0, 1)", "lte(1, 1)", "lte(1, 0)", "lt(0, 1)", "lt(1, 1)", "gt(1, 0)", "gt(2, 7)", "gte(122, 122)", /* 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)", "isnan(INF)", "isinf(1)", "isinf(NAN)", "isinf(INF)", "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)", "if(1, 2)", "ifnot(0, 23)", "ifnot(1, NaN) + if(0, 1)", "taylor(1, 1)", "taylor(eq(mod(ld(1),4),1)-eq(mod(ld(1),4),3), PI/2, 1)", "root(sin(ld(0))-1, 2)", "root(sin(ld(0))+6+sin(ld(0)/12)-log(ld(0)), 100)", "7000000B*random(0)", "squish(2)", "gauss(0.1)", "hypot(4,3)", "gcd(30,55)*min(9,1)", 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; } // LCOV_EXCL_STOP #endif