eval: Allow specifying the variable id.

Reviewed-by: Nicolas George <nicolas.george@normalesup.org>
Signed-off-by: Michael Niedermayer <michaelni@gmx.at>

doc/eval.texi

@@ -107,9 +107,10 @@ the evaluation of @var{y}, return 0 otherwise.
 Evaluate @var{x}, and if the result is zero return the result of the
 evaluation of @var{y}, return 0 otherwise.
 
-@item taylor(expr, x)
+@item taylor(expr, x) taylor(expr, x, id)
 Evaluate a taylor series at x.
-expr represents the LD(0)-th derivates of f(x) at 0.
+expr represents the LD(id)-th derivates of f(x) at 0. If id is not specified
+then 0 is assumed.
 note, when you have the derivatives at y instead of 0
 taylor(expr, x-y) can be used
 When the series does not converge the results are undefined.

libavutil/eval.c

@@ -184,18 +184,19 @@ static double eval_expr(Parser *p, AVExpr *e)
         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[0];
+            double var0 = p->var[id];
             for(i=0; i<1000; i++) {
                 double ld = d;
-                p->var[0] = i;
+                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[0] = var0;
+            p->var[id] = var0;
             return d;
         }
         default: {
@@ -523,6 +524,9 @@ static int verify_expr(AVExpr *e)
         case e_not:
         case e_random:
             return verify_expr(e->param[0]) && !e->param[2];
+        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];
     }
 }
@@ -722,7 +726,7 @@ int main(int argc, char **argv)
         "ifnot(0, 23)",
         "ifnot(1, NaN) + if(0, 1)",
         "taylor(1, 1)",
-        "taylor(eq(mod(ld(0),4),1)-eq(mod(ld(0),4),3), PI/2)",
+        "taylor(eq(mod(ld(1),4),1)-eq(mod(ld(1),4),3), PI/2, 1)",
         NULL
     };
 

tests/ref/fate/eval

@@ -172,8 +172,8 @@ Evaluating 'ifnot(1, NaN) + if(0, 1)'
 Evaluating 'taylor(1, 1)'
 'taylor(1, 1)' -> 2.718282
 
-Evaluating 'taylor(eq(mod(ld(0),4),1)-eq(mod(ld(0),4),3), PI/2)'
-'taylor(eq(mod(ld(0),4),1)-eq(mod(ld(0),4),3), PI/2)' -> 1.000000
+Evaluating 'taylor(eq(mod(ld(1),4),1)-eq(mod(ld(1),4),3), PI/2, 1)'
+'taylor(eq(mod(ld(1),4),1)-eq(mod(ld(1),4),3), PI/2, 1)' -> 1.000000
 
 12.700000 == 12.7
 0.931323 == 0.931322575