1 files changed, 100 insertions, 4 deletions
diff --git a/doc/eval.texi b/doc/eval.texi
index e1fd7ee484..1ea89d6755 100644
--- a/doc/eval.texi
+++ b/doc/eval.texi
@@ -1,7 +1,7 @@
 @chapter Expression Evaluation
 @c man begin EXPRESSION EVALUATION
 
-When evaluating an arithmetic expression, Libav uses an internal
+When evaluating an arithmetic expression, FFmpeg uses an internal
 formula evaluator, implemented through the @file{libavutil/eval.h}
 interface.
 
@@ -21,37 +21,84 @@ The following unary operators are available: @code{+}, @code{-}.
 The following functions are available:
 @table @option
 @item sinh(x)
+Compute hyperbolic sine of @var{x}.
+
 @item cosh(x)
+Compute hyperbolic cosine of @var{x}.
+
 @item tanh(x)
+Compute hyperbolic tangent of @var{x}.
+
 @item sin(x)
+Compute sine of @var{x}.
+
 @item cos(x)
+Compute cosine of @var{x}.
+
 @item tan(x)
+Compute tangent of @var{x}.
+
 @item atan(x)
+Compute arctangent of @var{x}.
+
 @item asin(x)
+Compute arcsine of @var{x}.
+
 @item acos(x)
+Compute arccosine of @var{x}.
+
 @item exp(x)
+Compute exponential of @var{x} (with base @code{e}, the Euler's number).
+
 @item log(x)
+Compute natural logarithm of @var{x}.
+
 @item abs(x)
+Compute absolute value of @var{x}.
+
 @item squish(x)
+Compute expression @code{1/(1 + exp(4*x))}.
+
 @item gauss(x)
+Compute Gauss function of @var{x}, corresponding to
+@code{exp(-x*x/2) / sqrt(2*PI)}.
+
 @item isinf(x)
 Return 1.0 if @var{x} is +/-INFINITY, 0.0 otherwise.
+
 @item isnan(x)
 Return 1.0 if @var{x} is NAN, 0.0 otherwise.
 
 @item mod(x, y)
+Compute the remainder of division of @var{x} by @var{y}.
+
 @item max(x, y)
+Return the maximum between @var{x} and @var{y}.
+
 @item min(x, y)
+Return the maximum between @var{x} and @var{y}.
+
 @item eq(x, y)
+Return 1 if @var{x} and @var{y} are equivalent, 0 otherwise.
+
 @item gte(x, y)
+Return 1 if @var{x} is greater than or equal to @var{y}, 0 otherwise.
+
 @item gt(x, y)
+Return 1 if @var{x} is greater than @var{y}, 0 otherwise.
+
 @item lte(x, y)
+Return 1 if @var{x} is lesser than or equal to @var{y}, 0 otherwise.
+
 @item lt(x, y)
+Return 1 if @var{x} is lesser than @var{y}, 0 otherwise.
+
 @item st(var, expr)
 Allow to store the value of the expression @var{expr} in an internal
 variable. @var{var} specifies the number of the variable where to
 store the value, and it is a value ranging from 0 to 9. The function
 returns the value stored in the internal variable.
+Note, Variables are currently not shared between expressions.
 
 @item ld(var)
 Allow to load the value of the internal variable with number
@@ -81,21 +128,70 @@ Compute the square root of @var{expr}. This is equivalent to
 
 @item not(expr)
 Return 1.0 if @var{expr} is zero, 0.0 otherwise.
+
+@item pow(x, y)
+Compute the power of @var{x} elevated @var{y}, it is equivalent to
+"(@var{x})^(@var{y})".
+
+@item random(x)
+Return a pseudo random value between 0.0 and 1.0. @var{x} is the index of the
+internal variable which will be used to save the seed/state.
+
+@item hypot(x, y)
+This function is similar to the C function with the same name; it returns
+"sqrt(@var{x}*@var{x} + @var{y}*@var{y})", the length of the hypotenuse of a
+right triangle with sides of length @var{x} and @var{y}, or the distance of the
+point (@var{x}, @var{y}) from the origin.
+
+@item gcd(x, y)
+Return the greatest common divisor of @var{x} and @var{y}. If both @var{x} and
+@var{y} are 0 or either or both are less than zero then behavior is undefined.
+
+@item if(x, y)
+Evaluate @var{x}, and if the result is non-zero return the result of
+the evaluation of @var{y}, return 0 otherwise.
+
+@item ifnot(x, y)
+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) taylor(expr, x, id)
+Evaluate a taylor series at x.
+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.
+
+@item root(expr, max)
+Finds x where f(x)=0 in the interval 0..max.
+f() must be continuous or the result is undefined.
+@end table
+
+The following constants are available:
+@table @option
+@item PI
+area of the unit disc, approximately 3.14
+@item E
+exp(1) (Euler's number), approximately 2.718
+@item PHI
+golden ratio (1+sqrt(5))/2, approximately 1.618
 @end table
 
-Note that:
+Assuming that an expression is considered "true" if it has a non-zero
+value, note that:
 
 @code{*} works like AND
 
 @code{+} works like OR
 
-thus
+and the construct:
 @example
 if A then B else C
 @end example
 is equivalent to
 @example
-A*B + not(A)*C
+if(A,B) + ifnot(A,C)
 @end example
 
 In your C code, you can extend the list of unary and binary functions,